23 Results - Improvement of turbulence model s for general swi rl i ng reci rcul ati ng ... one NASA contractor report" and one subcontractor reportz3 were pub1 ished ...... W ' w r l . J o. ,uo. V W b 0 2 vsec. 0.2074. O.CO56. G.Cl20. 0.0079. Nil. 0.
NASA Contractor Report 3869
Investigations of Flowfields Found in Typical Combustor Geometries
David G. Lilley OkZaboma State UHiversity StiZZwuter, OkZubomu
Prepared for Lewis Research Center under Grant NAG3-74
National Aeronautics and Space Administration Scientific and Technical Information Branch 1985
ABSTRACT
This is the Final Report on Grant NAG 3-74 and discussion is on those activities undertaken during the entire course of research from July 1, 1980 to June 30, 1984. research on turbulent,
Studies were concerned with experimental and theoretical
2-D
axisymmetric
geometries under
low speed
nonreacting,
swirling flow conditions typical of gas turbine and ramjet
combustion chambers.
They i ncl uded recircul ati on zone characterization, time-
mean and turbulence simulation in swirling recirculating flow, sudden and gradual
expansion
influences.
flowfields,
and
further
complexities
The study included the investigation of:
and
parameter
a complete range of
swirl strengths; swirler performance; downstream contraction nozzle sizes and locations; expansion ratios; and inlet side-wall angles.
Their individual and
combined effects on the test section flowfield were observed, measured and characteri zed. Experimental
methods
included flow
visualization
(with smoke
and
neutrally-buoyant helium-fi lled soap bubbles), five-hole pitot probe time-mean velocity field measurements, and single-, double- and triple-wire hot-wire anemometry measurements of time-mean velocities, normal and shear Reynolds stresses. Computational methods included development o f the STARPIC code from the primitive-variable TEACH computer code, prediction and turbulence model development.
iii
and
its use
in flowfield
CONTENTS
..................................................... INTRODUCTION ................................................. 1.1 The Problem............................................ 1.2 Objectives ............................................. 1.3 The Present Contribution............................... REVIEW OF ACTIVITIES ........................................ 2.1 Progress During First Year (1980-81) ................... 2.2 Progress During Second Year (1981.82) .................. 2.3 Progress During Third Year (1982-83) ................... 2.4 Progress During Fourth Year (1983-84) .................. FACILITIES AND TECHNIQUES ................................... 3.1 Facilities ............................................. 3.2 Flow Visualization ..................................... 3.3 Five-Hole Pitot Probe.................................. 3.4 Hot-wire Anemometer Techniques ......................... 3.5 Computer Code Developments ............................. RESULTS ..................................................... 4.1 Swirler Performance .................................... 4.2 Gross Flowfield Characterization ....................... 4.3 Time-Mean Flowfield Characterization................... 4.4 Turbulence Measurements ................................ 4.5 Turbulence Modeling .................................... 4.6 Computer Predictions ................................... CLOSURE ..................................................... REFERENCES..................................................
ABSTRACT
.
1
2
3
.
.
4.
. 6. 5
V
iii 1 1
2 3 5
5 6 8 9
10 10
11 13 13 15 16 16 17 19 20 23 24 26
27
APPENDIXES A
- On
the Prediction of Swirling Flowfields Found in 31
Axisymmetric Combustor Geometries........,............... B
- Mean
Flowfields in Axisymmetric Combustor Geometries
with Swirl.........................................oe.... C
- Turbulence Measurements in
a Confined Jet Using A
Six-Orientation Hot-Wire Probe Technique..
..... .........
48
D - Five-Hole Pitot Probe Time-Mean Velocity Measurements
in Confined Swirling Flows.,............................. E
-
Confined Swirling Flow Predictions.........................
F - Single-Wire Swirl Flow Turbulence Measurements............. G
-
The Performance of an Annular Vane Swirler.................
61 73 85 98
H - Accuracy and Directional Sensitivity of the SingleWire Technique
...........................................
112
I - Limitations and Empirical Extensions of the k-z Model
as Applied to Turbulent Confined Swirling Flows..........
129
.............................
139
J - Swirl Flow Turbulence Modeling K
-
Swirl, Confinement and Nozzle Effects on Confined Turbulent Flow......................................*....
L
152
- Turbulence Measurements in a Complex Flowfield Using a Crossed Hot-wire......
.................................
162
M - Five-Hole Pitot Probe Measurements of Swirl, Confinement and Nozzle Effects on Confined Turbulent Flow............
vi
173
1,
INTRODUCTION
1.1
The Problem Both experimental
development of relied
heavily
and t h e o r e t i c a l
studies
assist
Up t o now designe *s have
gas t u r b i n e combustion chambers. on
experimental
evidence
to
i n t h e des gn and
produce
empirical
formulas.
However, t r a d i t i o n a l design methods are now being supplemented by a n a l y t i c a l methods (numerical s o l u t i o n o f t h e a p p r o p r i a t e governing p a r t i a l d i f f e r e n t i a l equations).
Computer modeling o f combustion processes i s now an e s t a b l i s h e d
fact,
improvements
but
and
new
developments
t h e o r e t i c a l ) can and should be made,
theoretical
(both
experimental
and
modeling being aided by
c a r e f u l l y chosen experiments. The accuracy o f c u r r e n t l y a v a i l a b l e p r e d i c t i o n codes f o r c i r c u l a t i n g confined
flows
s w i r l i n g re-
i s i n doubt because o f questionable t u r b u l e n c e
models and l a c k o f a s u i t a b l e experimental data base.
A prerequisite t o the
p r e d i c t i o n o f more complex t u r b u l e n t r e a c t i n g f l o w s i s t h e development of s u i t a b l e t u r b u l e n c e models and computer programs f o r f l o w p r e d i c t i o n under nonreacting c o n d i t i o n s , w i t h which t h e present study i s concerned. Progress
needs t o
be made on
computational
methods.
Typically,
a
computer code o f t h e TEACH-T t y p e i s a p p r o p r i a t e l y m o d i f i e d t o i n c l u d e s w i r l and geometric v a r i a t i o n s and t h e two-equations k-E turbulence model simulates t h e mixing characteristics.
One problem i s t h a t a turbulence model whose
b a s i s and parameters a r e adequate f o r simple f l o w s i t u a t i o n s i s n o t adequate f o r t h e more complicated s w i r l i n g r e c i r c u l a t i n g f l o w s i t u a t i o n .
There i s a
need t o develop l o g i c a l extensions o f c u r r e n t l y a v a i l a b l e t u r b u l e n c e models t o s w i r l i n g r e c i r c u l a t i n g flows,
i n t h e form o f modifying t h e i r parameters,
i n c l u s i o n o f n o n i s o t r o p i c e f f e c t s , and/or more complex m o d i f i c a t i o n s .
1
1.2
Objectives The recently-completed research encompassed steady t u r b u l e n t f l o w i n 2-D
axisymmetric
geometries,
under low speed and n o n r e a c t i n g c o n d i t i o n s .
The
p a r t i c u l a r problem addressed was concerned w i t h t u r b u l e n t f l o w i n a round p i p e e n t e r i n g an expansion i n t o another round pipe.
The i n l e t f l o w may possess a
s w i r l component of v e l o c i t y v i a passage through s w i r l vanes a t an angle 4, and t h e s i d e w a l l may slope a t an angle a, t o t h e main f l o w d i r e c t i o n .
The
r e s u l t i n g main f l o w f i e l d domain may possess a c e n t r a l t o r o i d a l r e c i r c u l a t i o n zone i n t h e middle o f t h e r e g i o n on t h e axis, i n a d d i t i o n t o t h e p o s s i b i l i t y of a corner r e c i r c u l a t i o n zone near t h e upper corner provoked by t h e r a t h e r sudden enlargement o f t h e c r o s s - s e c t i o n a l
O f s p e c i a l concern was t h e
area.
c h a r a c t e r i z a t i o n o f f l o w s o f t h i s t y p e i n terms o f t h e e f f e c t s o f s i d e - w a l l a, degree
angle
of
swirl
4, i n l e t expansion
ratio
D/d,
and
downstream
c o n t r a c t i o n area r a t i o A/a on t h e f l o w f i e l d i n terms o f i t s time-mean and turbulence quantities. The
general
goal
of
complementary computations
to
necessary experiments
improve
this
study
with the
calculation
where time-mean
was
to
idea o f
perform
experiments
doing the type o f
capability.
This
involved
and
research performing
and t u r b u l e n c e q u a n t i t i e s were measured,
and
t a k i n g i n p u t c o n d i t i o n s and running a s u i t a b l e computer code f o r a v a r i e t y o f test
cases
validity
so as t o compare p r e d i c t i o n s a g a i n s t experiment.
of
modifications
t u r b u l e n c e model
were a l s o deduced d i r e c t l y
v e l o c i t y gradients. 1.
modifications
c o u l d be assessed.
Hence t h e In fact
from t h e measured stresses
and
The goals o f t h e research included:
Measurements o f mean f l o w p a t t e r n s and s i z e s and shapes o f t h e c o r n e r and c e n t r a l t o r o i d a l r e c i r c u l a t i o n zones.
2
2.
F l o w f i e l d mapping o f time-mean
velocity,
normal and shear Reynolds
stresses, and hence t u r b u l e n t v i s c o s i t i e s i n each (i, j)-orientation. 3.
Development o f a computer program based on t h e I m p e r i a l College TEACH-T program f o r two-dimensional axisymmetric,
swirling, confined
j e t f l o w s w i t h r e c i r c u l a t i o n regions. 4.
Improvement o f t u r b u l e n c e model s f o r general swi r l ing r e c i r c u l a t i ng flows,
1.3
i n c l u d i n g noni s o t r o p i c simul a t i o n .
The Present Contribution The
present
document
is
the
Final
Report
on
Grant
NAG
3-74
with
d i s c u s s i o n on a c t i v i t i e s undertaken d u r i n g t h e e n t i r e course o f t h e research p r o j e c t from J u l y 1, 1980, t o June 30, 1984.
M.S.
these^^-^
papers
'-"
Three Ph.D.
evolved i n connection w i t h t h i s study.
and f i v e
I n a d d i t i o n , conference
were w r i t t e n and presented on v a r i o u s aspects o f t h e work.
one NASA c o n t r a c t o r r e p o r t "
Also,
and one s u b c o n t r a c t o r r e p o r t z 3 were pub1 i s h e d
d u r i n g t h e course o f t h i s i n v e s t i g a t i o n . I n t h e experimental
portion o f
the
research,
a l o g i c a l sequence o f
experiments was undertaken t o e s t a b l i s h t h e e f f e c t s on t h e r e s u l t i n g f l o w f i e l d o f swi r l e r performance and s w i r l s t r e n g t h , downstream nozzle, expansion r a t i o , and
inlet
side-wall
corresponding t o a l l
angle.
Complementary
computations
were
performed
t h e boundary c o n d i t i o n s o f t h e experiments so as t o
p r o v i d e a thorough e v a l u a t i o n o f s t a t e - o f - t h e - a r t
predictive capability, with
standard and m o d i f i e d t u r b u l e n c e models. S e c t i o n 2 contains a general
review o f a c t i v i t i e s undertaken,
S e c t i o n 3 describes f a c i l i t i e s and techniques
used i n t h e i n v e s t i g a t i o n .
S e c t i o n 4 concentrates on r e s u l t s obtained w i t h h i g h l i g h t s o f r e c e n t Ph.D. M.S.
theses being included.
while
and
Discussion a l s o i s on t h e coverage o f r e l e v a n t
conference papers w r i t t e n d u r i n g t h e course o f t h e study; these a r e i n c l u d e d
3
i n t h e present document as Appendixes A through M.
A summary i s given i n
Section 5 and a l i s t i n g o f theses and papers appears i n Section 6.
4
2.
REVIEW OF ACTIVITIES
2.1
Progress During F i r s t Year (1980-81) Items addressed d u r i n g t h e f i r s t year o f t h e study were described i n
d e t a i l by Rhode.'
1.
They included:
Test F a c i l i t y The confined j e t t e s t f a c i l i t y was designed and constructed,
including
t h e .special ly-shaped nozzle t o ensure u n i f o r m f l o w of 1ow t u r b u l e n c e i n t e n s i t y
A variable-angle
on e n t r y t o t h e t e s t section.
scale-up o f NASA plans and constructed. and 45 deg.
s w i r l e r was designed as a
Expansion blocks o f angles
~1
=90, 70
were constructed o f wood f o r t h e large-diameter t e s t s e c t i o n o f
diameter 30 cm, so as t o enable i n l e t e f f e c t s t o be studied. 2.
Expe rimenta 1 Tech niq ues
A flow visualization capability,
w i t h a l i g h t c u r t a i n from a s l i d e
p r o j e c t o r l o c a t e d f a r downstream o f t h e t e s t f a c i l i t y , p a r t i c l e s i n t h e form o f neutrally-buoyant generated by a Sage A c t i o n Inc.
was s e t up.
Marker
h e l i u m - f i l l e d soap bubbles were
bubble generator v i a an i n j e c t o r l o c a t e d
upstream o f t h e t e s t s e c t i o n i n t h e converging s e c t i o n o f t h e wind tunnel. Smoke i n j e c t i o n and t u f t s were a l s o planned f o r and photographic techniques c1a r i f i e d . 3.
Computational Code Development An advanced v e r s i o n o f t h e I m p e r i a l College TEACH-T computer program was
developed.
T h i s code STARPIC"
i n c l u d e d s w i r l flow, a s t a i r s t e p approximation
t o t h e s l o p i n g w a l l boundary,
and several o t h e r f e a t u r e s t o enhance accuracy
and economy o f t h e p r e d i c t i v e technique.
The standard two-equation k-s t u r b u -
lence model was i n c l u d e d a t t h i s stage w i t h o u t refinement.
5
40
Flowfield Characterization Emphasis was on t h e c h a r a c t e r o f t h e f l o w f i e l d i n terms of s t r e a m l i n e
p a t t e r n s and r e c i r c u l a t i o n zones, predictions,
as evidenced by photography and standard
f o r a v a r i e t y of parameter s e t t i n g s of i n l e t s w i r l s t r e n g t h and
s i d e - w a l l expansion angles. 2.2
Progress During Second Year (1981-82) During t h e
finalization
second
of
year,
three
more
student
definitive
results
t h e s e ~ ' , ~ ' ~with
the
emerged
with
following
the
topics
s p e c i f i c a l l y addressed:
1.
Higher S w i r l Strengths Time-mean f l o w f i e l d measurements were performed w i t h a t r a v e r s i n g f i v e -
hole p i t o t
probe
measurements
were
i n the
confined j e t
performed on
a
with
c o n f ined
downstream nonswi r l ing
s w i r l i n g flows, w i t h r e s u l t s given i n Refs. 10 and 12. t h e downstream blockage had an i n c r e a s i n g l y
blockage. f 1ow
These
and v a r i o u s
It was determined t h a t
s i g n i f i c a n t e f f e c t on c o r n e r
r e c i r c u l a t i o n p a t t e r n s as t h e blockage was p o s i t i o n e d c l o s e r and c l o s e r t o t h e inlet.
The data obtained from these experiments was important i n e v a l u a t i n g
t h e p r e d i c t i v e c a p a b i l i t y o f t h e k-E t u r b u l e n c e model and STARPIC computer code
flowfield
calculations.
They
also
assisted
in
turbulence
model
developments. 2.
Swi r l e r Effectiveness
As p a r t o f t h i s a c t i v i t y , c a r e f u l measurements o f t h e f l o w f i e l d o f timemean v e l o c i t i e s u, made l5
v and w immediately downstream o f t h e s w i r l pack were
These measurements were performed and documented f o r v a r i o u s blade
s e t t i n g s , and showed t h a t t h e f l o w f i e l d t y p i c a l l y had a s w i r l f l o w angle which was a few degrees s m a l l e r than t h e blade angle. revealed a l a r g e r a x i a l
flow
i n the outer
6
Also,
t h e measurements
annular p o r t i o n of
t h e duct;
presumably a result of the centrifugal forces associated with the swirl as the flow passed through the swirler. 3.
Flowfield Predictions The STARPIC computer codezz was used to predict confined jet flows
corresponding to those studied experimentally.
The calculation method
included a stairstep boundary representation of the expansion flow and a conventional k-E turbulence model.
The predictions included recirculation
zone characterization and mean streamline patterns, which were compared with concurrent experimental studies, Predictions were made at this stage with the standard k-E turbulence model and no downstream blockage. '913 constraints were removed later in the third year of the program. 17,19
4.
These
Turbulence Measurements A significant effort was made in the application of three hot-wire
methods to the measurement of time-mean and turbulence properties.
The
experiments performed were designed to provide the information necessary for turbulence modeling development in the confined jet facility.
In this phase
of the study, the capability of making measurements in the nonswirling flow and in one swirling flow with swirl vane angle Cp of 38 deg. was established. 11 One-Wire Method. Single normal hot-wire measurements in nonswirling flow have established that the experimental technique was producing reliable results.
Six-orientation hot-wire measurements were made from which a
method was developed to make estimates of all components of the time-mean velocity vector and the Reynolds stress tensor.
A major portion of these
measurements were completed for the nonswirling flowfield,"
and corresponding
measurements in swirling flowfields began, to be completed in the third and fourth years,14 in which the effect of a downstream blockage was also investigated.
7
Two-Wire
A1 though
Method.
the
single
hot-wire
( s ix-orientation)
measurements a r e convenient and p r o v i d e a g r e a t deal o f i n f o r m a t i o n on t h e time-mean
v e l o c i t y and on t h e k i n e t i c energy o f turbulence,
t h e y have a
p o s s i b l e shortcoming i n t h a t measurements o f t h e Reynolds shear stresses a r e l e s s accurate than c o u l d be obtained w i t h a crossed hot-wire.
Because of
t h i s , t h e l a t t e r technique was developed f o r use i n t h e n o n s w i r l i n g f l o w w i t h and w i t h o u t a downstream blockage.20
A p p l i c a t i o n o f t h e crossed-wi r e method
t o s w i r l i n g f l o w f i e l d s would have some d i f f i c u l t y i n t h a t p r i o r knowledge o f time-mean f l o w d i r e c t i o n may be r e q u i r e d p r i o r t o measurement, o r i e n t a t i o n s w i l l a l s o be needed.
and m u l t i p l e
F u r t h e r development o f t h i s technique was
n o t pursued i n t h e research program.
A s e r i e s o f hot-wire measurements u s i n g a three-wire,
Three-Wi r e Method. hot-wire
probe
with
direct
computer
interface
and
data
reduction
were
accomplished on a corresponding n o n s w i r l i n g f l o w and one s w i r l i n g f l o w w i t h s w i r l vane angle 4, equal t o 38 deg. subcontractor Dynamics Technology,
These measurements were performed by
Inc. under t h e d i r e c t i o n o f Dr.
Dennis K.
McLaughlin, a s s i s t e d by S a l i m I.Janjua. 23 5.
Downstream Blockage The e f f e c t s o f weak and s t r o n g downstream c o n t r a c t i o n nozzles o f area
r a t i o A/a o f 2 and 4 l o c a t e d a t x/D values o f 1 and 2 were s t u d i e d v i a f l o w v i s u a l i z a t i o n , f i v e - h o l e p i t o t probe, and corresponding computer p r e d i c t i o n s .
2.3
Progress During Third Year (1982-83) Research continued w i t h a d d i t i o n a l
' p r o d u c t i o n run' a c t i v i t i e s i n both
experimental and p r e d i c t i o n s e c t i o n s o f t h e program. v a r i e t y of
parameter s e t t i n g s f o r a complete range o f s w i r l s t r e n g t h s w i t h
s w i r l vane angle and o f
This i n v o l v e d using a
+
from 0 t o 70 deg.,
l o c a t i o n x/D
o f s i d e - w a l l angle a from 90 t o 45 deg.,
from 1 t o 2 and area r a t i o A/a
8
from 2 t o 4 o f t h e
downstream c o n t r a c t i o n nozzle.
A d d i t i o n a l l y , two f u r t h e r t e s t s e c t i o n s w i t h
s m a l l e r diameters were studied.
2.4
Progress During Fourth Year (1983-84) The f o u r t h year rounded o f f t h e t a s k s i d e n t i f i e d i n t h e t h i r d year, w i t h
f i v e student theses emerging.
1.
S p e c i f i c a l l y , research included:
23396-8
Smaller Expansion R a t i o s E a r l i e r work was done on t h e l a r g e t e s t s e c t i o n o f diameter D o f 30 cm
w i t h D/d o f 2.
Measurements were extended t o i n c l u d e s m a l l e r expansion r a t i o
o f D/d o f 1.5 and 1.'l 2.
Turbulence Measurements Higher s w i r l
blockages, Kinetic
using
energy
s t r e n g t h s were i n v e s t i g a t e d w i t h and w i t h o u t
downstream
the
technique.
of
single-wire
turbulence
six-orientation
k
and
measurement
dissipation
rate
E
were
also
measured. 2,14,16 3.
Turbulence Modeling
A considerable e f f o r t was placed on a n a l y z i n g t h e t u r b u l e n c e measurements o f Reynolds stresses and time-mean
v e l o c i t y gradients.
3917318
This l e d t o
i n f o r m a t i o n about t h e t u r b u l e n t v i s c o s i t y and models f o r i t s s p e c i f i c a t i o n i n confined s w i r l i n g flows.
4.
Flowfield Predictions Corresponding
experimentally,
predictions
using
standard
were and
model s o13,17,19
9
made
for
modified
the
situations
two-equation
studied
k-E t u r b u l e n c e
3,
FACILITIES AlYD TECHNIQUES
3.1
Facilities Oklahoma
State
University
has
the
following
facilities
which
were
purchased and/or c o n s t r u c t e d by students d u r i n g t h e p r o j e c t : 1.
wind tunnel,
2.
one v a r i ab1e-angl e vane swi r ler,
3.
t h r e e p l e x i g l a s s t e x t s e c t i o n s o f diameters 30, 22.5
4.
expansion b l o c k s o f 90 and 45 deg.,
and 15 cm,
f o r each o f t h e t h r e e t e s t
sections , 5.
weak
and s t r o n g downstream c o n t r a c t i o n nozzles,
f o r each o f t h e
t h r e e t e s t sections. The experiments were conducted i n t h e c o n f i n e d j e t t e s t f a c i l i t y which i s described a t l e n g t h i n t h e Appendixes.
The f a c i l i t y has an a x i a l - f l o w f a n
whose speed can be changed by a l t e r i n g a v a r i d r i v e mechanism.
Numerous f i n e
screens and straws produce f l o w i n t h e s e t t l i n g chamber o f r e l a t i v e l y low turbulence intensity.
The c o n t r a c t i o n s e c t i o n l e a d i n g t o t h e t e s t s e c t i o n has
been s p e c i a l l y designed t o produce a minimum adverse pressure g r a d i e n t on t h e boundary
layer
and
s e p a r a t i o n region.
thus
avoid
unsteady
problems
associated w i t h
local
The sudden expansion c o n s i s t s o f a 15 cm diameter c i r c u l a r
j e t nozzle, e x i t i n g a b r u p t l y i n t o a 30 cm diameter t e s t s e c t i o n o f l e n g t h 125 cm, which i s c o n s t r u c t e d o f p l e x i g l a s s t o f a c i l i t a t e f l o w v i s u a l i z a t i o n . s e c t i o n s o f 22.5
and 15 cm diameter have a l s o been i n v e s t i g a t e d .
w a l l angle a and s w i r l vane angle $ a r e v a r i a b l e . by i n s e r t i n g a block w i t h s i d e - w a l l o p e r a t i ng
Reynolds
numbers
(based
diameter) a r e i n t h e range 50,000
angle on
inlet
t o 150,000
aerodynamic blockage o f t h e s w i r l vanes.
10
Test
The s i d e -
The s i d e - w a l l angle i s s e t
a of
90 o r 45 deg.
average
velocity
Typical and
inlet
depending upon f a n speed and
It has been observed t h a t t h i s i s
approximately i n t h e Reynolds number i n s e n s i t i v e range f o r t h i s f a c i l i t y ,
in
terms of nondimensional flow c h a r a c t e r i s t i c f u r t h e r downstream. 1 The annular
vane s w i r l e r used has t e n vanes which a r e i n d i v i d u a l l y
a d j u s t a b l e t o any angle 4, and a hub w i t h a streamlined upstream nose and a
f l a t downstream face.
The h u b - t o - s w i r l e r
diameter r a t i o i s 0.25.
The nose
has a h y p e r b o l i c shape w i t h a very smooth s u r f a c e so as t o o f f e r minimal f l o w interference.
The f l a t blades are wedge-shaped t o g i v e a constant p i t c h - t o -
chord r a t i o o f 0.68 which gives good t u r n i n g e f f i c i e n c y . 1 5
With an expansion
b l o c k attached t o t h e e x i t o f t h e s w i r l pack, t h e expansion plane (x/D = 0 ) i s
3.2 cm downstream o f t h e s w i r l e r e x i t (where x/D = - 0 , l l ) . The e f f e c t s o f a downstream c o n t r a c t i o n nozzle on t h e upstream f l o w i n t h e t e s t s e c t i o n i s important i n combustor aerodynamics. r a t i o 2 and 4 were used. quarter
circle
as
Two nozzles of area
The weaker one has i t s upstream face contoured i n a
found
in
practical
ramjet
combustor,
The
stronger
c o n t r a c t i o n nozzle has i t s upstream face i n a 45 deg. slope, more t y p i c a l o f gas t u r b i n e combustion chamber e x i t s , axial
position
i n the
test
These blocks may be l o c a t e d a t any
section.
Nozzles
c o n s t r u c t e d t o f i t i n each o f t h e 30, 22.5
of
these two types were
and 15 cm diameter t e s t sections,
and used i n t h e experimental program.
3.2
Flow Visualization Flow v i s u a l i z a t i o n techniques included:
soap
bubbles,
smoke-wire,
photography techniques.
easily
investigation. discernable,
r e c i r c u l a t i o n zones.
tufts,
with
appropriate
These p e r m i t a good ' f e e l
t o be obtained q u i c k l y , precise,
and
n e u t r a l ly-buoyant h e l i u m - f i l l e d illumination
for a particular flowfield
and d e f i n e areas i n s p e c i a l need o f f u r t h e r , The c h a r a c t e r i s t i c s o f t h e o v e r a l l
i n c l u d i n g time-mean
and
d i v i d i n g streamline
more
f l o w f i e l d are patterns
and
Results from t h e smoke-wire experiment were u t i 1 i z e d
11
near t h e i n l e t , whereas t u f t and bubble data were b e s t used i n approximating t h e s i z e and shape o f t h e r e c i r c u l a t i o n zones downstream. patterns
reveal
downstream
of
Also,
t h e e x i s t e n c e o f a precessing v o r t e x core, the
central
region,
in
many
of
the
bubble f l o w which occurs
swirl
flow
cases
.
inves t igated 10,21 T u f t v i s u a l i z a t i o n i s very important i n t h a t i t s u p p l i e s an o v e r a l l view of
local
flow
obtained.
direction.
Photographs
at
various
shutter
speeds
Slower speeds show more o f t h e temporal behavior,
were
although t h e
t u f t s a r e sometimes n o t d i s t i n c t l y v i s i b l e i n p o r t i o n s o f t h e f l o w f i e l d . V e l o c i t i e s i n r e c i r c u l a t i o n zones are o f t e n somewhat lower than i n o t h e r portions o f the insufficient
flowfield,
and thus
drag on a t u f t
under such c o n d i t i o n s t h e r e may be
t o a l i g n it accurately with the local flow
d i r e c t i on. Local d e t a i l s i n t h e n o n s w i r l i n g f l o w f i e l d s are c l e a r l y revealed through t h e v i s u a l i z a t i o n o f s t r e a k 1 ines from smoke generated from a kerosine-coated w i r e being suddenly heated v i a an e l e c t r i c current. cases,
I n the swirling flow
s t r o n g m i x i n g d i f f u s e s t h e smoke so t h a t s t r e a k l i n e s are n o t e a s i l y
distinguishable.
However, under such c o n d i t i o n s r e c i r c u l a t i o n zone out1 i n e s
a r e v i s i b l e , e s p e c i a l l y i n t h e r e g i o n near t h e smoke-generation wire. Soap bubbles i n j e c t e d i n t o t h e f l o w upstream o f t h e t e s t s e c t i o n t r a c e p a t h l i n e s c l e a r l y when i l l u m i n a t e d .
I n r e l a t i v e l y lower t u r b u l e n c e i n t e n s i t y
p o r t i o n s o f t h e f l o w f i e l d mean f l o w d i r e c t i o n s can be obtained by ensemble averaging l o c a l tangents t o p a t h l i n e s t r a c e d out by soap bubbles. define the
flowfield
geometry
i n terms
regions.
12
of
the
outline
of
This helps
recirculation
3.3
Five-Hole P i t o t Probe One o f t h e s i m p l e s t i n s t r u m e n t s capable o f simultaneously sensing b o t h
magnitude and d i r e c t i o n o f t h e l o c a l v e l o c i t y v e c t o r i s t h e f i v e - h o l e p i t o t probe,
used e x t e n s i v e l y
i n this
study. 10y12y15y21
The p a r t i c u l a r probe
employed was model DC-125-12-CD from U n i t e d Sensor and C o n t r o l Corp. 3.2 mm diameter sensing t i p and s h a f t c o n t a i n i n g f i v e tubes.
It has a
The sensing head
i s hook-shaped t o a l l o w probe s h a f t r o t a t i o n w i t h o u t a l t e r i n g t h e probe t i p location.
The i n s t r u m e n t a t i o n system,
i n addition t o the five-hole
probe, c o n s i s t s o f a manual t r a v e r s e mechanism, very
sensitive
voltmeter.
pressure transducer,
The
Datametrics, Inc.
differential
power
pressure
two five-way b a l l valves, supply,
transducer
and is
a
an i n t e g r a t i n g
model
590D
from
3 It has a d i f f e r e n t i a l pressure range o f from 0 t o 1.3 x 10
N/m2 ( e q u i v a l e n t l y , 0 t o 10 t o r r ) . 1076.
a
pitot
The i n t e g r a t i n g v o l t m e t e r i s t h e T S I model
As a u x i l i a r y equipment, a model 631-B s t r o b o t a c from General Radio Inc. A P i t o t - s t a t i c probe i s used t o measure t h e
i s used t o check t h e f a n speed.
dynamic pressure i n t h e n o z z l e t h r o a t j u s t upstream o f t h e s w i r l e r ,
and
t h e r e f r o m deduce t h e s w j r l e r i n l e t u n i f o r m a x i a l v e l o c i t y uo which i s used l a t e r f o r v e l o c i t y normalizations.
Also,
a barometer/thermometer u n i t from
Cenco Corp. i s used f o r l o c a l pressure and temperature readings. 3.4
Hot-wire Anemometer Techniques The second measurement technique used e x t e n s i v e l y was t h e s i x - o r i e n t a t i o n
s i n g l e - w i r e h o t - w i r e technique.
11914916
w i t h a predominate f l o w d i r e c t i o n ,
When used on a two-dimensional
flow
a s i n g l e h o t - w i r e normal t o t h e main f l o w
can be used t o measure t h e streamwise components o f t h e time-mean v e l o c i t y and t h e rms v e l o c i t y
fluctuation,
technique p e r m i t s time-mean flowfields.
i n a standard manner. and t u r b u l e n c e data t o
The s i x - o r i e n t a t i o n be taken
i n general
The anemometer used i n t h i s study was DISA t y p e 55M01,
13
CTA
standard b r i d g e with a normal h o t - w i r e probe, D I S A t y p e 55P01. two prongs s e t approximately 3 mm a p a r t which support a 5
T h i s probe has pm
diameter w i r e
which i s g o l d p l a t e d near t h e prongs t o reduce end e f f e c t s and strengthen t h e wire.
The
velocity
six-orientation
components
technique
permits
and t u r b u l e n c e q u a n t i t i e s
measurements
of
time-mean
i n complex three-dimensional
flowfields.
A p p l i e d i n t h i s study t o n o n r e a c t i n g axisymmetric f l o w f i e l d s ,
measurements
of
time-mean
and
root-mean-square
o r i e n t a t i o n s (each separated by a 30 deg.
voltages
at six different
probe support r o t a t i o n ) c o n t a i n
enough i n f o r m a t i o n t o o b t a i n t h e t h r e e time-mean v e l o c i t i e s , t h e t h r e e normal
A t each l o c a t i o n i n t h e flow, t h e r e a r e
and t h r e e shear Reynolds stresses.
s i x d i f f e r e n t values o f each o f t h e above q u a n t i t i e s t h a t can be obtained u s i n g s i x s e t s o f measurements o f t h r e e adjacent o r i e n t a t i o n s .
Ensemble
averages o f t h e output q u a n t i t i e s from t h e s i x combinations o f data appear t o produce estimates w i t h t h e best agreement w i t h independent measurements. mean
voltage
is
measured
with
a
Hickok
Digital
Systems,
Model
The
DP100,
i n t e g r a t i n g v o l t m e t e r and t h e root-mean square v o l t a g e f l u c t u a t i on i s measured u s i n g a Hewlett Packard, Model 400 HR, AC voltmeter. Hot-wire anamometry w i t h m u l t i - w i r e study.
probes have a l s o been used i n t h e
A crossed h o t - w i r e technique was used i n t h e n o n s w i r l i n g flow. 20
Background t o i t s o p e r a t i o n need n o t be i n c l u d e d here.
A t r i p l e - w i r e hot-wire
technique was devel oped under subcontract a c t i v i t y by Dynamics Techno1 ogy, Inc.,
u s i n g a t h r e e - w i r e h o t - w i r e probe w i t h d i r e c t computer i n t e r f a c e and
data reduction.
The raw d a t a from t h e t h r e e sensors were d i g i t i z e d u s i n g A t o
D c o n v e r t e r s and s t o r e d on a T e k t r o n i x 4051 computer.
The data were f u r t h e r
reduced on t h e computer t o o b t a i n t i m e - s e r i e s
f o r t h e t h r e e instantaneous
v e l o c i t y components i n t h e f l o w f i e l d .
t h e time-mean v e l o c i t i e s and
Finally,
t h e t u r b u l e n c e q u a n t i t i e s were deduced.
14
3.5
Computer Code Development
A primitive pressure-velocity variable finite difference computer code was developed to predict swirling recirculating inert turbulent flows in axisymmetric combustors in general , and for application to the present specific idealized combustion chamber with sudden or gradual upstream expansions and weak or strong downstream contraction nozzles.
The technique
involved a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation k-E turbulence model , a stairstep boundary representation of the sloping sidewalls, and realistic accommodation of swirl effects. The development was based on the 1974 Imperial College TEACH-T computer code.
The finally
developed computer program (written in Fortran 4 ) was code-named STARPIC (mnemonic for swirling turbulent axisymmetric yecirculating flows in pactical
isothermal combustor geometries).
The complete report"
included a program
listing and a sample case computation of air flow through a 45 deg. expansion ( a = 45 deg.) from an inlet pipe to a larger pipe (D/d = 2).
The delivered
code and description provide computer runs through a range of seven inlet swirl vane angles
$I
equal to 0, 45, 55, 60, 65, 68 and 70 deg. The extensive
document presents details of the computational solution procedure.
It serves
as a user's manual and deals with the computation problem, showing how the mathematical basis and computational scheme may be translated into a computer program. A flow chart, Fortran 4 listing, notes about various subroutines and a user's guide are included as an aid to prospective users of the code.
15
4,
RESULTS The Ph.D.
theses of Rhode,'
o f J a n j u a Y 4 Yoon,'
Sander,7
with the investigation.
and Scharrer8 evolved i n connection
Conference papers
'-''
were w r i t t e n and presented on
These a r e attached as Appendixes A through
o f these papers have a l s o now been published, form;
Additionally,
theses
M for
and o n l y h i g h l i g h t s o f them a r e c i t e d here i n t h e main t e x t .
completeness,
abridged
and A b u j e l a l a 3 and t h e M.S.
McKillop,6,
v a r i o u s aspects o f t h e work.
Several
Jackson,'
this
is
indicated
i n the
one NASA c o n t r a c t o r r e p o r t "
reference
either i n f u l l or list
in
S e c t i o n 6.
on t h e STARPIC computer code and
one subcontractor r e p o r t z 3 on t h e t r i p l e - w i r e h o t - w i r e measurement method were w r i t t e n d u r i n g t h e course o f t h e study.
4-1 Swi r l e r Performance Throughout t h e e n t i r e research p r o j e c t , t h e s w i r l e r being used i s annular with a hub-to-swirler
diameter
p i t c h - t o - c h o r d r a t i o 0.68.
r a t i o o f 0.25
and t e n a d j u s t a b l e vanes of
Measurements o f time-mean a x i a l , r a d i a l , and s w i r l
v e l o c i t i e s were made i n Refs. 6 and 15 (see Appendix G) a t t h e s w i r l e r e x i t plane u s i n g a f i v e - h o l e p i t o t probe technique w i t h computer data reduction. Nondimensional i z e d v e l o c i t i e s from both r a d i a l and azimuthal t r a v e r s e s were plotted
for
theoretical
a
range
study was
of
swirl
vane
included o f
angles
4 from 0 t o 70 degrees.
idealized exit-plane
velocity
A
profiles
r e l a t i n g t h e s w i r l numbers S and S' t o t h e r a t i o o f maximum s w i r l and a x i a l v e l o c i t i e s f o r each i d e a l i z e d case. Measurements a t t h e s w i r l e r e x i t centrifugal
forces,
velocity profiles.
r e c i r c u l a t i o n zones,
plane show c l e a r l y t h e e f f e c t s o f and blade wakes on t h e e x i t - p l a n e
Assumptions o f f l a t a x i a l and s w i r l p r o f i l e s w i t h r a d i a l
v e l o c i t y equal t o zero were found t o be p r o g r e s s i v e l y l e s s r e a l i s t i c as t h e s w i r l e r blade angle increases.
A t low s w i r l s t r e n g t h s ( 4 = 38 deg.),
16
portions
of
the
u
and w
significant.
profiles
flat
remain
A t moderate s w i r l
+
while the
= 45 deg.,
is
already
l i n e a r l y increasing p r o f i l e s o f u A t s t r o n g e r s w i r l 4 = 60
and w w i t h r a d i u s are a p p r o p r i a t e w i t h v nonzero. deg.,
v-component
even more spiked p r o f i l e s are a p p r o p r i a t e w i t h most o f t h e f l o w l e a v i n g
t h e s w i r l e r near i t s o u t e r edge, strong
swirl
reversal
.
almost
to
4 = 70 deg.,
the
At
and some reverse f l o w near t h e hub.
profiles
are
extremely
spiked
with
flow
The c e n t r a l r e c i r c u l a t i o n zone extends upstream o f t h e e x i t plane, the
recirculation,
swirler
blades
in
high-swirl
cases.
Because
of
this
none o f t h e i d e a l i z a t i o n s considered c o u l d model s t r o n g s w i r l
cases adequately.
The f l o w - t u r n i n g e f f e c t i v e n e s s
g e n e r a l l y adequate f o r a l l vane angles tested.
of the f l a t
blades was
However, t h e l a r g e v a r i a t i o n s
o f f l o w angles and v e l o c i t i e s w i t h r a d i u s made meaningful comparisons w i t h two-dimensional
Monaxisymmetry was found i n a1 1
cascade data impossible.
It i s c l e a r t h a t t h e i n v e s t i g a t i o n o f vane s w i r l e r
s w i r l cases i n v e s t i g a t e d .
performance c h a r a c t e r i s t i c s served i n subsequent p a r t s o f t h e p r o j e c t t o a i d in
computer
modeling
of
gas
turbine
combustor
flowfields,
and
in
the
development and e v a l u a t i o n o f t u r b u l e n c e models f o r s w i r l i n g confined flow. 4.2
Gross Flowfield Characterization R e c i r c u l a t i o n zones are important t o combustor designers and t h e s i z e and
l o c a t i o n o f these regions i n t h e present isothermal f l o w s are r e a d i l y deduced from f l o w v i s u a l i z a t i o n photographs o f t u f t s , smoke, and bubbles responding t o t h e experiment a1 f 1owf ie l d p a t t e r n s
.
R e s u l t ing d i v i d i ng s t ream1ine sketches
as w e l l as s e l e c t e d photographs o f t h e v i s u a l i z a t i o n experiments are presented and discussed i n Refs. the
early
part
of
1, 8, 9, 10, and 21 (see Appendixes A,
the
study ',lo
c h a r a c t e r i z a t i o n o f corner f l o w f i e l d configurations
a major
and c e n t r a l
was
the
In
experimental
r e c i r c u l a t i o n zones i n s i x b a s i c
o f an ax symmet r c
17
outcome
B y and M).
expansion
w i t h side-
w a l l angle a = 90 and 45 and s w i r l vane angle 4 = 0 ( s w i r l e r removed), 45 deg.
38 and
The s i z e and shape o f t h e r e c i r c u l a t i o n bubbles f o r each f l o w f i e l d i s
i l l u s t r a t e d v i a an a r t i s t i c impression deduced from a c o l l e c t i o n o f f l o w v i s u a l i z a t i o n photographs o f t u f t s ,
smoke, and n e u t r a l ly-buoyant soap bubbles
I n c r e a s i n g s w i r l vane angle 4 from 0 t o 38 deg.
responding t o t h e flow.
produces a shortened c o r n e r r e g i o n and t h e appearance o f a c e n t r a l bubble t y p i c a l l y extending downstream t o approximately x/D
= 1.7,
a f t e r which a
precessing v o r t e x core e x i s t s near t h e a x i s reaching t o t h e e x i t o f t h e t e s t
A f u r t h e r i n c r e a s e i n 4 t o 45 deg.
section.
enlarges t h e c e n t r a l zone and
v o r t e x core w i t h n e g l i g i b l e e f f e c t on t h e corner r e g i o n i n those f l o w f i e l d s where i t occurs. negligible.
The e f f e c t o f s i d e - w a l l angle
~1
on t h e n o n s w i r l i n g flows i s
However, a decrease from 90 t o 45 degrees apparently e l i m i n a t e s
t h e corner bubble i n t h e s w i r l i n g f l o w cases i n v e s t i g a t e d .
T h i s decrease i n
a a l s o causes t h e i n l e t f l o w t o impinge more s e v e r e l y on t h e t o p w a l l , where l a r g e r a x i a l v e l o c i t i e s occur. L a t e r work8 continued t h e f l o w v i s u a l i z a t i o n strengths, effects
.
smaller
diameter
Nonswirling
and
tubes,
and
swirling
study f o r h i g h e r s w i r l
downstream
inert
flows
contraction
were
nozzle
investigated
in
axisymmetric t e s t s e c t i o n s w i t h expansion r a t i o 1 and 1.5 and t h e f o l l o w i n g geometric parameters: vane
angle
s i d e - w a l l expansion angle a = 45 and 90 degrees, s w i r l
4 = 0 (swirler
removed),
45
and
70
degrees,
and
downstream
blockages o f area r a t i o s 2 and 4 l o c a t e d 2 and 4 diameters from t h e t e s t section i n l e t .
S i g n i f i c a n t f i n d i n g s from t h e f l o w v i s u a l i z a t i o n and p i t o t
probe measurements a r e discussed i n S e c t i o n 4.3.
18
4.3
Time-Mean Flowfield Characterization
I n i t ia1 work by Rhode',lo
u t i l i z e d t h e f i v e - h o l e p i t o t probe technique t o
measure time-mean v e l o c i t i e s u,
v,
and w i n t h e l a r g e diameter t e s t s e c t i o n
w i t h D/d = 2, low s w i r l s t r e n g t h s 4 = 0 ( s w i r l e r removed), 38 and 45 deg.,
and
L a t e r , Yoon 5,12 (see Appendix D) extended t h e study t o
no downstream nozzles.
h i g h e r s w i r l s t r e n g t h s 4 = 60
and 70 deg. and downstream nozzle e f f e c t s w i t h
b o t h weak and s t r o n g nozzles o f area r a t i o s A/a = 2 and 4 l o c a t e d a t x/D = 1 and 2.
Velocities
were e x t e n s i v e l y p l o t t e d and a r t i s t i c impressions of
r e c i r c u l a t i o n zones were presented.
Findings included t h a t the nonswirling
c o n f i n e d j e t possesses a corner r e c i r c u l a t i o n zone extending t o j u s t beyond x/D
= 2 w i t h no c e n t r a l
r e c i r c u l a t i o n zone.
The presence o f a s w i r l e r
shortens t h e corner r e c i r c u l a t i o n zone and generates a c e n t r a l r e c i r c u l a t i o n zone f o l l o w e d by a precessing v o r t e x core.
The e f f e c t o f a gradual i n l e t
expansion i s t o encourage t h e f l o w t o remain c l o s e t o t h e s i d e w a l l and shorten t h e e x t e n t o f t h e corner r e c i r c u l a t i o n zone i n a l l cases i n v e s t i g a t e d .
A
c o n t r a c t i o n nozzle o f area r a t i o 2 has l i t t l e e f f e c t on weakly s w i r l i n g and s t r o n g l y s w i r l i n g flows,
which are dominated by forward f l o w and c e n t r i f u g a l
forces,
For i n t e r m e d i a t e s w i r l
respectively.
cases,
t h e weak downstream
nozzle encourages forward movement o f otherwise slow-moving a i r and thereby shortens t h e c e n t r a l r e c i r c u l a t i o n zone.
A strorlg c o n t r a c t i o n nozzle of area
r a t i o 4 has a more dramatic e f f e c t on t h e f l o w f i e l d s , b o t h i n t e r m e d i a t e and s t r o n g s w i r l i n g f l o w cases.
particularly affecting
C e n t r a l r e c i r c u l a t i o n zones
a r e shortened considerably, and a x i a l v e l o c i t i e s near t h e f a c i l i t y a x i s become highly positive.
Core regions become narrower w i t h very s t r o n g s w i r l v e l o c i t y
magnitudes and gradients. More r e c e n t l y ,
Scharrer 8921 (see Appendix M) used t h e same measurement
technique w i t h s m a l l e r diameter t e s t s e c t i o n tubes w i t h D/d = 1.5 and 1, again
19
with
downstream nozzles
included t h a t
and a f u l l
t h e corner
expanding flows,
range o f
recirculation
zone
swirl is
strengths.
Findings
prominent i n n o n s w i r l i n g
b u t i t decreases when s w i r l i s introduced.
The presence o f
s w i r l r e s u l t s i n t h e formation o f a Central r e c i r c u l a t i o n zone.
Initially,
increases i n i n l e t s w i r l s t r e n g t h r e s u l t i n an increase i n l e n g t h of t h i s zone.
However,
increasing
to
very
high
shortening and widening o f t h i s zone.
swirl
strengths
results
in
a
P l a c i n g a downstream nozzle i n t h e
f l o w f i e l d creates an adverse pressure g r a d i e n t near t h e w a l l and a f a v o r a b l e pressure g r a d i e n t near t h e c e n t e r l i n e .
This r e s u l t s i n increased a x i a l and
s w i r l v e l o c i t i e s near t h e c e n t e r l i n e and decreased v e l o c i t i e s near t h e w a l l . It a l s o decreases t h e c e n t r a l r e c i r c u l a t i o n zone length.
The degree o f t h e
effect
Reduction of
increases
as t h e degree o f blockage increases.
expansion r a t i o r e s u l t s i n a r e d u c t i o n o f t h e c e n t r a l length. not
the
r e c i r c u l a t i o n zone
The corner r e c i r c u l a t i o n zone l e n g t h (measured i n step h e i g h t s ) does
change appreciably
with
expansion
ratio for
ratios
greater
than
1.
Gradual expansion has a minimal e f f e c t on t h e flow.
4.4
Turbulence Measurements Major a t t e n t i o n was given t o t h e development and a p p l i c a t i o n o f t h e s i x -
o r i e n t a t i o n one-wire confined j e t
hot-wire
facility.
technique
(see S e c t i o n 3.4)
i n t h e present
Applied i n t h i s study t o nonreacting f l o w f i e l d s ,
deductions o f time-mean v e l o c i t i e s , t u r b u l e n c e i n t e n s i t i e s and shear stresses were possible.
The experiments were performed t o p r o v i d e t h e i n f o r m a t i o n
necessary f o r t u r b u l e n c e modeling development i n t h e confined j e t f a c i l i t y . I n i t i a l l y , t h e mathematics and computer r e d u c t i o n code f o r t h e technique were developed f o r t h e n o n s w i r l i n g flow;4
l a t e r t h e v a l i d i t y o f t h e technique was
e s t a b l i s h e d f o r t h e s w i r l i n g f l o w f i e l d w i t h i n l e t s w i r l vane angle of deg."
(see Appendix C).
38
E x c e l l e n t c o s t - e f f e c t i v e r e s u l t s were presented,
20
w i t h comparisons w i t h independent data i l l u s t r a t i n g t h e r e l i a b i l i t y o f t h e technique.
Finally,
a s e n s i t i v i t y a n a l y s i s o f t h e data r e d u c t i o n tec'hnique
was undertaken which formed t h e major i n g r e d i e n t of an u n c e r t a i n t y analysis. 11 Jackson'
further
applied
the
technique
for
a
full
range
of
swirl
s t r e n g t h s i n t h e t e s t s e c t i o n w i t h expansion r a t i o s D/d = 1 and 2, which may be equipped with a s t r o n g c o n t r a c t i o n nozzle o f area r a t i o 4 a t x/D = 2. effect
The
of s w i r l on time-mean v e l o c i t i e s and complete Reynolds s t r e s s t e n s o r
was i n v e s t i g a t e d , and e x t e n s i v e r e s u l t s were given f o r s w i r l vane angles o f 0 (swirler measured.
removed),
38,
60 and 70 deg.
45,
D i s s i p a t i o n r a t e s were a l s o
Major r e s u l t s were r e p o r t e d f o r t h e expansion f l o w f i e l d i n Ref.
(see Appendix F).
14
The e f f e c t o f s w i r l on t h e time-mean v e l o c i t y f i e l d was
found t o shorten t h e c o r n e r r e c i r c u l a t i o n zone l e n g t h and t o generate t h e e x i s t e n c e o f a c e n t r a l r e c i r c u l a t i o n zone, v o r t e x core region.
which i s f o l l o w e d by a precessing
As t h e degree o f s w i r l increases,
the length o f the
c e n t r a l r e c i r c u l a t i o n bubble decreases, whereas i t s width,
and a l s o t h e w i d t h
o f t h e precessing v o r t e x core, section,
directional
s i g n i f i c a n t l y with swirl,
increases.
turbulence
A t the j e t i n l e t t o the t e s t
intensities
are
found
to
increase
Throughout t h e f l o w f i e l d , t h e most dramatic e f f e c t
o f s w i r l i s t o increase values o f t h e t h r e e t u r b u l e n t shear s t r e s s terms. I n t r o d u c t i o n o f a s t r o n g c o n t r a c t i o n n o z z l e a t x/D = 2 w i t h an area r e d u c t i o n r a t i o o f 4 causes a s i g n i f i c a n t flowfield.
e f f e c t on t h e time-mean
swirling
C e n t r a l r e c i r c u l a t i o n zones a r e shortened and a x i a l v e l o c i t i e s
along t h e whole j e t a x i s become p o s i t i v e . s t r o n g s w i r l v e l o c i t i e s and gradients. a l s o increase along t h e j e t
The core regions become narrow w i t h Turbulence l e v e l s and shear s t r e s s e s
c e n t e r l i n e near t h e e x i t o f t h e c o n t r a c t i o n
nozzle.
21
The accuracy and d i r e c t i o n a l assessed,
sensitivity
o f t h e technique were a l s o
w i t h respect t o mean flow v e l o c i t y o r i e n t a t i o n t o t h e probe,
Ref. 16 (Appendix
H).
see
R e s u l t s demonstrate r e l a t i v e i n s e n s i t i v i t y , i n d i c a t i n g
t h a t t h e method i s a u s e f u l c o s t - e f f e c t i v e t o o l f o r t u r b u l e n t f l o w s of unknown dominant f l o w d i r e c t i o n .
The technique adequately measures t h e p r o p e r t i e s of
a f l o w f i e l d independent o f t h e dominant f l o w d i r e c t i o n except when t h e flow i s predominately i n t h e d i r e c t i o n o f t h e probe holder, w i t h t h e s i x - o r i e n t a t i o n s o f t h e probe then c r e a t i n g i n s i g n i f i c a n t changes i n h o t - w i r e response.
A crossed hot-wire technique has been used f o r t h e n o n s w i r l i n g f r e e and confined j e t time-mean
(D/d = 2)
velocities,
(see Appendix L).
A x i a l and r a d i a l
d i r e c t i o n a l turbulence i n t e n s i t i e s ,
and main Reynolds
s t r e s s were measured. throughout.
situation^^'^^
Associated t u r b u l e n t v i s c o s i t y values were deduced
Investigations
were
made
with
and
without
c o n t r a c t i o n nozzle o f area r a t i o 4 l o c a t e d a t x/D = 2.
a
downstream
Measurements i n d i c a t e d
t h a t t h e crossed h o t - w i r e used cannot handle a x i a l f l o w r e v e r s a l
(without
p r i o r knowledge and probe r e o r i e n t a t i o n ) and t h a t t h e experimental technique is
inadequate f o r
t h e measurement
q u a n t i t i e s show a h i g h l e v e l researchers,
time-mean
of
time-mean
o f comparability.
radial
velocity.
Other
I n common w i t h p r e v i o u s
and t u r b u l e n c e c h a r a c t e r i s t i c s
with the contraction
nozzle a t x/D = 2 show l i t t l e change from t h a t o f t h e corresponding f l o w f i e l d w i t h a c o n t r a c t i o n nozzle, f o r t h e n o n s w i r l i n g f l o w case. Subcontractor Dynamics Technology, Dennis
K.
Mclaughlin,
measurements ,23
see
completed
S e c t i o n 3.4.
Inc.,
a
under t h e d i r e c t i o n o f Dr.
series
Experiments
of were
triple-wire
hot-wire
performed and where
p o s s i b l e comparisons were made w i t h t h e r e s u l t s o f independent measurements. For example, five-hole
t h e mean v e l o c i t y components were compared w i t h t h e r e s u l t s of
pitot
probe measurements.
The major q u a l i f i c a t i o n experiments
22
involved
measurements
performed
conventional X-wire measurements. vane angle 4 = 38 deg.,
in
a
nonswirling
flow
compared
with
I n the s w i r l i n g f l o w f i e l d with i n l e t s w i r l
advantages and drawbacks o f t h e t r i p l e - w i r e technique
over t h e s i x - o r i e n t a t i o n s i n g l e hot-wire method were discussed,
4.5
Turbulence Modeling Abujelala3
additionally, Appendix equation
continued
the
prediction
work
of
stressed t u r b u l e n c e modeling p o s s i b i l i t i e s .
Rhode'
I n Ref.
and,
17 (see
I) , shortcomings and recommended c o r r e c t i o n s t o t h e standard twok-E
presented.
turbulence
model
suggested
by
previous
investigators
were
They were assessed regarding t h e i r appl i c a b i 1it y t o t u r b u l e n t
s w i r l i n g r e c i r c u l a t i n g flow. flows,
earlier
Recent experimental data on s w i r l i n g c o n f i n e d
obtained w i t h a f i v e - h o l e
p i t o t probe and a s i x - o r i e n t a t i o n h o t - w i r e
probe, were used t o o b t a i n optimum values of t h e t u r b u l e n c e parameters C and os f o r s w i r l i n g flows.
!J
, C2,
General p r e d i c t i o n s o f moderately and s t r o n g l y
s w i r l i n g flows w i t h these values are more accurate than p r e d i c t i o n s w i t h t h e standard o r previous simple extensions o f t h e k-s t u r b u l e n c e model. The d e t a i l e d data base evolved i n t h e course o f recent studies, Section 3.4,
were analyzed n u m e r i c a l l y as a c o n t r i b u t i o n t o t h e t u r b u l e n c e
modeling e f f o r t 1 8 nozzle were Generally, considerable
see
{see Appendix J ) .
found t o the
most
increase
S w i r l s t r e n g t h and a s t r o n g c o n t r a c t i o n
have s t r o n g e f f e c t s dramatic in
all
effect the
of
on t h e t u r b u l e n c e parameters. the
parameters
increase
of
considered
-
p a r t i c u l a r , increase o f t u r b u l e n t v i s c o s i t y and k i n e t i c energy.
swirl
is
the
that
is,
in
The presence
o f a s t r o n g c o n t r a c t i o n nozzle tends t o increase parameter values i n regions of
a c c e l e r a t i o n where l a r g e r a d i a l v e l o c i t y g r a d i e n t s occur,
them i n t h e d e c e l e r a t i o n r e g i o n near t h e o u t e r boundary. of v i s c o s i t y and l e n g t h s c a l e p r o f i l e s ,
a C
23
!J
-
and t o reduce
Based on s i m i l a r i t y
f o r m u l a t i o n was deduced which
was shown t o improve t h e p r e d i c t i v e c a p a b i l i t y o f t h e standard k-s turbulence model i n s w i r l i n g r e c i r c u l a t i n g flows19 (see Appendix K).
4.6
Computer Predictions A p p l i c a t i o n o f t h e STARPIC computer code22 was made d u r i n g t h e f i r s t year
t o t h e s i m u l a t i o n o f isothermal a i r f l o w i n t h e axisymmetric t e s t f a c i l i t y w i t h diameter expansion r a t i o D/d o f 2, w i t h two w a l l expansion angles 45 deg.
and t h r e e s w i r l vane angles 4 o f 0, 45 and 70 deg.
CX
of 90 and
A l l r e s u l t s were
obtained v i a a nonuniform g r i d system so as t o enhance s o l u t i o n accuracy.
v e l o c i t y w are i d e a l i z e d as
i n l e t p r o f i l e s o f a x i a l v e l o c i t y u and s w i r l " f l a t " ( t h a t i s constant-valued).
The
P r e d i c t e d u and w v e l o c i t y p r o f i l e s f o r t h e
s i x f l o w f i e l d c o n f i g u r a t i o n s are given i n Refs. 1 and 9, t o g e t h e r w i t h deduced parametric e f f e c t s on r e c i r c u l a t i o n zone lengths. s i m i l a r t o t h e experimental f i n d i n g s .
Note t h a t ,
The general
trends are
i n these p r e d i c t i o n s ,
the
i n l e t f l o w angle was taken t o be t h e s w i r l vane angle 4, whereas i n r e a l i t y t h e blades a r e not 100% e f f i c i e n t .
The experimental i n l e t data were not
a v a i l a b l e a t t h e t i m e t h e p r e d i c t i o n s were made, and t h e f l a t i n l e t p r o f i l e assumption
i s now known (see Section 4.1)
s i m u l a t i o n o f t h e present
study,
achieved
swirler
documented
via in
a ten-blade the
experimental
t o be inadequate f o r
precise
i n which t h e i n l e t f l o w c o n d i t i o n s are with
results,
pitch/chord the
actual
ratio inlet
0.68.
As
profiles
are
of
nonuniform w i t h nonzero r a d i a l v e l o c i t y . A b u j e l a l a 3 continued t h e t h e o r e t i c a l study,
and assessed t h e v a l i d i t y of
f l o w f i e l d p r e d i c t i o n s r e s u l t i n g from t h e choice o f i n l e t v e l o c i t y p r o f i l e s . Results, see Ref. 13 (Appendix E),
demonstrated t h a t r e a l i s t i c p r e d i c t i o n s are
forthcoming o n l y from t h e i n c l u s i o n o f r e a l i s t i c a x i a l , v e l o c i t y p r o f i l e s as i n l e t conditions. profiles,
s o l i d body r o t a t i o n o r
r a d i a l and s w i r l
Predictions with e i t h e r f l a t
zero r a d i a l
24
inlet
v e l o c i t y are inappropriate.
P r e d i c t i o n s were given f o r a f u l l i n l e t axial,
s w i r l s t r e n g t h s u s i n g measured
r a d i a l and s w i r l v e l o c i t y p r o f i l e s i n each case,
p r o f i1es , s t ream1ine
vel o c it y
range of
plots
and
a x i a1
v e l o c i ty
and p r e d i c t e d representations
i l l u s t r a t e d t h e l a r g e - s c a l e e f f e c t s o f i n l e t s w i r l on f l o w f i e l d s .
Predictions
were i n c l u d e d f o r t h e e f f e c t of weak and s t r o n g downstream c o n t r a c t i o n nozzles on
the
flow.
I n the
discouragement
of
swirl
central
flow
cases,
a weak
r e c i r c u l a t i o n zones w i t h
on
r e c i r c u l a t i o n zones,
swirl
flow
cases,
leads
to
the
s t r o n g e r v o r t e x cores
A s t r o n g nozzle has more
downstream possessing n e g a t i v e a x i a l v e l o c i t i e s . pronounced e f f e c t s
nozzle
with
discouragement
of
central
and forward f l o w i n h i g h l y s w i r l e d v o r t e x core regions
f u r t h e r downstream. Later
production
predictions o f swirl,
runs
given
i n Ref.
19
K) i n c l u d e d
(see Appendix
confinement and nozzle e f f e c t s on confined t u r b u l e n t
flow which were e x h i b i t e d and compared w i t h f i v e - h o l e p i t o t - p r o b e time-mean v e l o c i t y measurements o f Refs.
12 and 21.
Two s e t s of
computations were
given, one u s i n g t h e standard k-E t u r b u l e n c e model and t h e o t h e r u s i n g a C formulation measurements,
model as
accuracy o f t h e
deduced
discussed
from
six-orientation
i n S e c t i o n 4.5.
l a t t e r model
i s superior.
single-wi r e
R e s u l t s confirmed
-
1.I
hot-wire that
To h i g h l i g h t t h e e f f e c t s
the of
confinement and e x i t n o z z l e area on t h i s flow, t h r e e expansion r a t i o s and two c o n t r a c t i o n r a t i o s were used.
P r e d i c t i o n s were given f o r a f u l l range of
s w i r l s t r e n g t h s u s i n g t h e measured i n l e t c o n d i t i o n s o f Ref. radial
and
sw r l
vel o c ity
i l l u s t r a t e the large-scale
p r o f i1es
.
The
predicted
15 f o r a x i a l ,
vel ocit y
e f f e c t s o f i n l e t s w i r l on t h e f l o w f i e l d s .
appears t h a t a s t r o n g c o n t r a c t i o n nozzle has a pronounced e f f e c t , f l o w cases,
wil
1
p r o f i1 es
discouragement o f c e n t r a l r e c i r c u l a t i o n zones,
f l o w i n h i g h l y s w i r l e d v o r t e x core regions.
on s w i r l
and f o r w a r d
The expansion r a t i o value has
l a r g e - s c a l e e f f e c t s on t h e s i z e and l o c a t i o n o f t h e r e c i r c u l a t i o n zones.
25
It
5,
CLOSURE The main o b j e c t i v e s o f t h e research program were t o determine t h e e f f e c t s
o f s w i r l and combustor geometry on isothermal f l o w f i e l d p a t t e r n s , time-mean v e l o c i t i e s and turbulence q u a n t i t i e s ,
and t o e s t a b l i s h an improved s i m u l a t i o n
i n t h e form o f a computer p r e d i c t i o n code equipped w i t h a s u i t a b l e t u r b u l e n c e model.
The study i n c l u d e d t h e i n v e s t i g a t i o n o f :
strengths;
swirler
performance;
downstream
a complete range o f s w i r l
contraction
l o c a t i o n s ; expansion r a t i o s ; and i n l e t s i d e - w a l l angles.
nozzle
sizes
and
T h e i r i n d i v i d u a l and
combined e f f e c t s on t h e t e s t s e c t i o n f l o w f i e l d were observed,
measured and
characterized. This f i n a l r e p o r t concludes t h e present research on NASA Grant NAG 3-74, summarizing t h e a c t i v i t i e s ,
describing the f a c i l i t i e s
d i s c u s s i n g major r e s u l t s obtained. M.S.
and techniques,
and
F u r t h e r d e t a i l s appear i n t h e Ph.D.
and
theses t h a t have evolved, and i n t h e conference research papers t h a t have
been w r i t t e n and appended t o t h e present document.
26
REFERENCES
6.
The
following
list
of
theses
and
research
papers
covers
research
conducted w i t h t h e support o f t h e grant. 1.
Rhode, D.
L.,
" P r e d i c t i o n s and Measurements o f Isothermal F l o w f i e l d s i n
Axisymmetric Combustor Geometries," Aerospace Engineering,
Ph.D.
Thesis, Dept. o f Mechanical and
Oklahoma S t a t e U n i v e r s i t y ,
Stillwater,
OK, Dec.
1981.
2.
Jackson, Ph.0.
3.
T.
W.,
"Turbulence
Characteristics
of
S w i r l i n g Flowfields",
Thesis, Oklahoma S t a t e U n i v e r s i t y , S t i l l w a t e r , Okla.,
Abujelala,
M.
T.,
Predictions",
"Confined
Ph.D.
Thesis,
Turbulent
Swirling
Dec. 1983.
Recirculating
Oklahoma S t a t e U n i v e r s i t y ,
Stillwater,
Flow OK,
June 1984. 4.
Janjua,
S.
I., "Turbulence Measurements i n a Complex F l o w f i e l d Using a
Six-Orientation
Hot-Wi r e Probe Technique."
M.S.
Thesis,
Oklahoma S t a t e
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M.S. Thesis, Oklahoma S t a t e U n i v e r s i t y , S t i l l w a t e r , OK, Yay 1983. 7.
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"Swirl, M.S.
Expansion R a t i o and Blockage E f f e c t s on Confined
Thesis, Oklahoma S t a t e U n i v e r s i t y , S t i l l w a t e r ,
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Rhode, D. L.,
L i l l e y , D. G.,
and McLaughlin, D. K.,
"On t h e P r e d i c t i o n of
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on F l u i d Mechanics o f Combustion Systems,
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and McLaughlin,
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Janjua,
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I.,
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McLaughlin,
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and L i l l e y ,
D. G.,
"Turbulence Measurements i n a Confined J e t Using A S i x - O r i e n t a t i o n HotW i r e Probe Techni quell,
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1982. 12.
Paper AIAA-82-1262,
Yoon, H. K.
and L i l l e y ,
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Nevada, January 10-13,
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and L i l l e y ,
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Practical
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1982. D.
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"Turbulence Measurements i n a
S w i r l i n g Confined J e t F l o w f i e l d Using a T r i p l e Hot-wire Probe", DT-8178-02,
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Torrance, Calif.,
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1982.
APPENDIX A ON THE PREDICTION OF SWIRLING FLOWFIELDS FOUND IN AXISYMMETRIC COMBUSTOR GEOMETRIES
31
D. L. Rhode GraduateStudent. Assistant Professor, CollegeStation, Texas
D. G. Lilley Professor.
D.
I(. McLaughlin Professor. Group Manager, Torrance, Calif.
Schoolof Mechanical and AerospaceEngineering, Oklahoma State University, Stillwater, Okla. 74078
On the Prediction of Swirling Flowfields Fo nd in Axisymmetric Combustor Geometries Combustor modeling has reached the stage where the most useful research activities are likely to be on specific sub-problems of the general three-dimensionalturbulent reacting flow problem. The present study is concerned with a timely fluid dynamic research task of interest to the combustor modeling community. Numerical computations have been undertakenfor a basic two-dimensionalaxisymmetricfro wfield which is similar to that found in a conventional gas turbine combustor. A swirling nonreacting flow enters a larger chamber via a sudden or gradual expansion. The calculation method includes a stairstep boundary representation of the expansion flow, a conventional k-e turbulence model and realistic accommodation of swirl effects. The results include recirculation zone characterization and predicted mean streamline patterns. In addition, an experimental evaluation using flow visualization of neutrally-buoyant helium-filled soap bubbles is yielding very promising results. Successful outcomes of the work can be incorporated into the more combustion- and hardware-oriented activities of gas turbine engine manufacturers, including incorporating the modeling aspects into already existing comprehensive numerical solutionprocedures.
Introduction The combustor of the gas turbine engine contains high intensity combustion and, as far as possible, must burn fuel completely, cause little pressure drop, produce gases of nearly uniform temperature, occupy small volume, and maintain stable combustion over a wide range of operating conditions [l]. In design situations, the engineer has to seek an optimum path between irreconcilable alternatives of, for example, efficiency and pollution. The general aim of most research investigations is to provide information which is useful to designers by “characterizing” or “modeling” certain features of the phenomenon in question [2]. Up to now designers rely heavily on experimental evidence to produce empirical formulae. However, traditional design methods are now being supplemented by analytical methods (numerical solution of the appropriate governing partial differential equations). Computer modeling of combustion processes is now an established fact, but improvements and new developments (both experimental and theoretical) can and should be made, theoretical modeling being aided by carefully chosen experiments [3]. The present paper addresses research that is restricted to steady turbulent flow in axisymmetric geometries, under low speed and nonreacting conditions - a study area highlighted at a recent workshop [I] as a fundamental research requirement in combustion modeling. The particular problem is concerned with turbulent flow of a given turbulence distribution in a Contributed by the Fluids Engineering Division and presented at the Symposium on the Fluid Mechanics of Combustion Systems, Boulder, Colo., Manuscript received by the Fluids Engineering Division, September2, 1981.
round pipe entering an expansion into another round pipe, as illustrated in Fig. 1. The in-coming flow may possess a swirl component of velocity via passage through swirl vanes at angle 4 [equal approximately to tan-’ (wo/uo)],and the sidewall may slope at an angle a,to the main flow direction. The resulting flowfield domain may possess a central toroidal recirculation zone CTRZ in the middle of the region on the axis, in addition to the possibility of a corner recirculation zone CRZ near the upper corner provoked by the rather sudden enlargement of the cross-sectional area. Of vital concern is the characterization of flows of this type in terms of the effects of side-wall angle a, degree of swirl 4, turbulence intensity ko of the inlet stream and expansion ratio D/d on the resulting flowfield in terms of its time-mean and
(b) EXPECTED REciRcuLAnm ZONES
Fig. 1 The flowfield being investigated
32
MALL
turbulence kinetic energy k,and turbulence dissipation rate E govern this two-dimensional axisymmetric steady flow. They may be expressed in the general form
a
- -( r r ,
INLE
Fig. 2 An example of a coarse grid system being employed to fit the flow domain
turbulence quantities. Such problems have received little attention, yet there is a definite need for work in this area [4-6]. Experimental work in the configuration just described is being complemented by an associated prediction study of the flowfield. Consideration is given to recent work in the finite difference solution, via a primitive variable code, of axisymmetric swirl flow in the combustor geometry of Fig. 1, where the inlet expansion sidewall may slope obliquely to the central axis. Thus a systematic parametric investigation may be contemplated on the effect of sidewall angle a and degree of swirl (b on the resulting flowfield produced. Basic governing equations are presented, together with a brief description of the simulation and solution technique. The equations are elliptic in character and are solved via an advanced version of the Imperial College TEACH-T computer program [7], recently developed at Oklahoma State University [8]. Comparison with available experimental turbulent flow measurements assists in confirming the final predictive capability. One such experiment, underway at Oklahoma State University, is concerned with measuring the effects of swirl and side-wall angle on streamlines, mean flow and turbulence parameters in nonreacting flow. The facility and experimental details are included. For the present paper a preliminary evaluation of the accuracy of the computed flowfields is accomplished by comparison with flow visualization using neutrally-buoyant helium-filled soap bubbles as tracer particles. Photographs of the bubbles can be interpreted to yield time-mean flowfield maps which define approximately the boundaries of recirculation regions and regions of highly turbulent flow. Major features of strongly swirling flow characterization are then presented so as to exemplify the current predictive capability in terms of velocity profiles, streamline patterns and recirculation zone characterization. The final closure summarizes the achievements.
z)]
=s,
ar where 4J represents any of the dependent variables, and the equations differ primarily in their final source terms S, [7-91. Implicit here is the use of the standard two-equation k - e turbulence model, whereby the exchange coefficients rS may be specified in each equation [lo]. All constants appearing in the simulation are given the usual values. The corresponding finite difference equations are solved via an advanced version of the TEACH computer code [7], using a semi-implicit lineby-line method using the tridiagonal matrix algorithm for values at points of a variable size rectangular grid, with variable under-relaxation. A complete description of the finally-developed computer program is now available, with full details in the form of a user’s manual about the solution technique, boundary conditions and their implementation, and the iteration scheme and parameters used [8]. A computer program listing and sample output are included for prospective users. Recent advances include revised cell volumes for the axial and radial velocities, swirl effects on wall functions, and incorporation of sloping boundaries. Figure 2 shows an example of grid specification for the present geometry.
Experimental Approach -Several previous experimenters have investigated nonreacting flows in expansion geometries [11-20]. References [ l l ] and [ 121 also include flowfield predictions, made with versions of the TEACH-T computer program [7]. These experiments include time-mean velocity measurements [with hot-wire and pitot probes and laser Doppler anemometry], turbulence measurements [with hot-wires and laser anemometers] and flow visualization. The majority of the measurements were made in nonswirling flows [14-201, however some noteworthy experiments were made in swirling confined jets [ l l , 131. Direct comparison between the results of the cited experiments and the present experimental results is generally not possible because of differences in geometry. However, in the nonswirling jet comparisons were possible with experiments of Chaturvedi [20], who measured mean and turbulent flow quantities downstream of a sudden expansion of diameter ratio 2.0 and various expansion sidewall angles a. Measurements of mean velocity in regions of high turbulence intensity and where the direction of the velocity vector is unknown were made with a pitot tube. Mean velocity was also Theoretical Model measured with a constant temperature hot-wire anemometer The turbulent Reynolds equations for conservation of using a single wire. In addition, a cross-wire was used to mass, momentum (with x, r, 8 velocity components u, u, w), measure all the Reynolds stresses. Nomenclature u = (u,u, w) = time-mean velocity (in
D = chamber diameter d = nozzlediameter G = axialfluxof momentum k = kinetic energy of turbulence S = swirl number = 2(G,/G,d), source term (with subscript)
x,r,8 direction) x,r,O = axial, radial, azimuthal cylindrical polar coordinates a = side-wallangle r = turbulence exchange coefficient e = turbulence energy dissipation rate
33
p = (b =
time-mean density swirl vane angle [tan( w O / u O ) ] , general dependent variable
Subscripts 0 = value a t flowfield
inlet
to
The present experiments have been conducted in the Oklahoma State University confined jet facility, and from part of an on-going study aimed at the characterization of time-mean and turbulence quantities in swirling confined flows. It has an axial flow fan whose speed can be changed by altering the varidrive mechanism. Numerous fine screens and straws produce flow in the settling chamber of relatively low turbulence intensity. The contraction section leading to the test section has been designed by the method of Morel [21] to produce a minimum adverse pressure gradient on the boundary layer and thus avoid unsteady problems associated with local separation regions. The sudden expansion consists of a 15 cm diameter circular jet nozzle, exiting abruptly into a 30 cm diameter test section as shown in Fig. 1. The substantial size of this test model provides excellent probe resolution for hot-wire measurements which are currently underway and will be reported in a later paper. The test section is constructed of Plexiglas to facilitate flow visualization. The side-wall angle 01 and swirl vane angle 4 are variable. The side-wall angle is set by inserting one of three blocks with a sidewall angle o of 90, 70, or 45 deg. The swirl vane assembly consists of ten vanes which are individually adjustable to any vane angle 4. The pitch/chord ratio at the half radius location is approximately one, and this assures quite high efficiency in generating a swirling motion to the in-coming flow [6]. Typical operating Reynolds numbers [based on inlet average velocity and inlet diameter] are in the range 70,000 to 130,000 depending upon fan speed and aerodynamic blockage of the swirl vanes. It has been observed that this is in the Reynolds number insensitive range for this facility [9], in terms of nondimensional flow characteristics further downstream. The basic technique for the experiment discussed in this paper involves the visualization of individual neutrallybuoyant helium-filled soap bubbles. The bubbles which are approximately 0.5 to 1 mm diameter are produced by a Sage Action, Inc. generator-injector, which can be located at various positions in the flowfield. Because of the substantial size of the injector itself (1.5 cm in diameter and 6 cm long) it
is not inserted directly into regions of flow interest. Instead it is either mounted upstream in the stilling chamber, or flush mounted to the wall of the large diameter pipe of the test section, to inject bubbles directly into the corner recirculation zone. The bubbles are illuminated by a beam of light from a high-power 35 mm slide projector which is located far downstream of the test facility. Photographs of illuminated bubbles are taken with various shutter speeds and camera positions. At relatively long exposure times (such as 1/8 s) a series of streaks are visible in the field of view corresponding to pathlines of individual bubbles. A 35 mm single lens reflex camera with a 45 mm lens was used. Tri-X Pan black and white film with a normal ASA of 400 was used and developed with a special process which pushed the ASA to 5000. In relatively lower turbulence intensity portions of the flowfield, mean-flow directions can be obtained by ensemble averaging local tangents to pathlines traced out by soap bubbles. This helps to define the gross features of the flowfield in terms of the outline of recirculation regions.
Results and Discussion Computer Code Operation. The predictions presented here are computer simulations of the isothermal airflow in axisymmetric combustor geometries. As noted earlier diameter expansion ratio D/dis 2.0, inlet Reynolds number Red = 1.26 x lo5,wall expansion angle o = 90,70, and 45 deg and swirl vane angle 4 varies from 0 to 70 deg. All results are obtained via a nonuniform grid system which enhances solution accuracy. In the r-direction 21 grid lines are employed, and they are clustered near the shear layer region and along the wall and centerline. Cells in the x-direction are gradually expanding, and from 23 to 35 grid lines are employed as required to produce the desired side-wall angle a. Some grid independence tests have been undertaken with refined mesh systems up to 35 x 55; the present values were found to be adequate in terms of accuracy, and no discernable changes to the mean flow patterns to be presented were found.
xI0 = 0.3
x I 0 = 1.0
XI0 = 1.57
"fU0
Fig. 3 (a) (I = 90 dag XI0 = 1 0
XI0 = 0.3
UIUo
Fig. 3 (b) (I = 45 deg Fig. 3 Predicted axial velocity profiles showing the effect of swirl vane angle $, for wall expansion [o- o o Experiment [20]with +=O]
-
34
XI0 = 1.51
0 % 04
0
-
O S
0 p
O h
U
I
r-
*mug
Fig. 4 (b) u = 45 deg . Fig. 4 Predicted swirl velocity profiles showing the effect of swirl vane angle 0 for wall expansion angles a:
Computer runs through a range of seven inlet swirl vane angles Cp equal to 0, 45, 55, 60, 65, 68, and 70 deg are undertaken for each side-wall angle CY. Approximately 200 to 300 iterations [each with 5 field updates for pressure, 4 for axial velocity, and 3 for other primary variables] is needed to converge at each swirl strength, with the solutions for each value of 4 being used as the initial starting values for the next higher value of Cp considered. The inlet profiles of axial velocity u and swirl velocity w are idealized as flat (that is, constant-valued). This is consistent with the assumption of a one hundred percent efficient swirler, which is a little incorrect at the higher swirl angles. The in-coming nonswirling plug flow [u = uo and u= w = 01 is turned through an angle Cp to generate the flat out-going flow [u = uo, w = uo tan4 and u = 01 with the additional assumption that radial velocity remains zero. Axial and swirl velocity profiles are presented for the two CY values and three Cp values, clearly showing details of these parameter influences. Then, streamline plots for each value of 4, calculated and drawn by computer for each a, allow comparison of the shape and size of recirculation zones. Discussion is primarily aimed at guiding designers in judiciously choosing where experimental emphasis should be placed and/or in interpolating results from a limited amount of experimental data. For comparison with other results, it should be noted [6] that swirl number S and Cp are related approximately by S = 2 / 3 tan 4, so that vane angles 45, 60, and 70 deg, for example, correspond to S values of 0.67, 1.15, and 1.83, respectively. Velocity Profiles. Predicted mean axial velocity profiles for the a=90 and 45 deg geometries are shown in Figs. 3(a) and 3(b), respectively. The nonswirling case (Cp=O) exhibits good qualitative agreement with measurements of Chaturvedi [20] in a geometrically similar facility. The influence of Cp is most dramatic near the combustor inIet, where the Cp=O profile in Fig. 3(a) shows a large corner recirculation region, provoked by the sudden increase in flow area. A very large value of m a r occurs near the inlet, which is indicative of high turbulence energy generation in a strong shear layer. Further, the nonswirling centerline velocity exhibits little change in the streamwise direction. With 4 = 45 deg the mean
L .
I
0.00
1.00 2.00 (a) 4 = ' 0
3.00
c I
0.00
1: DO (b)
0.00
1.00
2.00
3'. 00
4 = 45"
2.00
3.00
4 = 70" Axial Position x/D (c)
Fig. 5 Predicted streamline plots with wall expansion angle Q = 90 deg and various swirl vane angles 0: (a) 0 deg, (b)45 deg, and (e) 70 deg
axial velocity profile is dramatically changed. Near the inlet a central toroidal recirculation zone appears and the corner recirculation zone is considerably smaller. Also, a maximum velocity value occurs in an annular fashion near r/D=0.25, although a more flattened shape quickly develops before x / D = 1.O. It should also be noted that the boundary layer on the outer sidewall is too thin to be seen on the figures. The strong swirl case of +=70 deg shows a much wider central recirculation region at x / D = 0.3, which is caused by strong centrifugal effects. This promotes a very high forward velocity near the wall rather than a corner recirculation region. This tendency has been qualitatively observed by combustor designers at high degrees of swirl, but little quantitative data are yet available to precisely substantiate
35
0.00
(a)
0.00
2'. 00
1: 00
1'. 00 (b)
31. DO
0 = 0"
@ =
2 : 00 45"
3: 00
Fig. 7 (a) 9 = 0 deg
0.00
1: 00 (c)
2'. 00 .$ =
3'. 00
70'
Axial Position x/D
Fig. 6 Predicted streamline plots with wall expansion angle (Y = 45 deg and various swirl vane angles 9: (a) 0 deg, (b) 45 deg, and (c) 70 deg
this phenomenon. The radial extent of the central recirculation zone and the velocity near the wall quickly diminish downstream as swirl strength is dissipated. The effect of side-wall angle a is only noticeable on the more strongly swirling flow cases and then only near to the inlet. Figure 3(b) with a = 45 deg shows little effect of a on the nonswirling flow, but dramatic effects on the +=45 and 70 deg flows. In the former case, no corner recirculation zone is present. In the latter case, the reduction of side-wall angle has greatly reduced the velocity near the confining walls and made the central recirculation zone narrower with higher reverse velocities. It should be noted, however, that only a slight effect of a (for the range considered here) remains beyond x/D values of about 1.O. Figures 4(a) and 4(b) show swirl velocity profiles for the corresponding geometries with vane angles of 45,60, and 70 deg. All of these profiles show solid-body-rotation behavior near the centerline, even near the inlet where a flat profile is a specified inlet condition. The radial location of the station maximum for w tends to increase with x/D in Fig. 4(a). Also irregularities of the profiles at x/D = 0.32 disappear with increasing x. Hence, swirl as well as axial velocity profiles appear to approach those corresponding to swirling flow in a pipe [22] as x increases. Comparing Fig. 4(b) with 4(a), it is the weaker swirl cases which show the most appreciable effect of a at x/D=O.32, and again this diminishes with increasing x. Profiles near the inlet are a little flatter in the outer part of the flow, with narrower solid-body-rotation regions near the axis. The profiles at x/D = 1.68 exhibit similarity for each geometry and if normalized with respect to their inlet swirl velocity maximum values, the curves will collapse on to a single characteristic curve. lots. Figure 5 shows results calculated and plotted by computer to show the combustor designer the sequence of predicted streamline patterns he should expect upon increasing the vane angle for the a=90 deg combustor. In particular, the size and shape of recirculation bubbles are emphasized. The nonswirling case shown in Fig. 5(a) exhibits a large corner recirculation region as indicated also in Fig. 3(a). As swirl is introduced, a central recirculation region appears in conjunction with a decrease in size of the corner
Fig. 7 (b) 6 = 45 deg
Fig. 7 (c) 9 = 70 deg Fig. 7 Flow visualization of pathlines produced by helium-filled soap bubbles with wall expansion angle (Y = 90 deg for various vane swirl angles 9:
recirculation region, as seen in the 45 deg swirl angle case. Further increases in swirl vane angle result in continued enlargement of the center zone. Similarly, the corner recirculation zone is gradually reduced in axial extent until it disappears by 4 = 70 deg [see Part (c) of the figure]. The same series of streamline patterns is displayed in Fig. 6 for the 45 deg expansion geometry. The same trend is found as the vane angle is increased, except that in this case the center recirculation zone is generally slightly smaller in both directions. The corner zone is similar in size for nonswirling conditions, but vanishes as swirl strength is increased. Compare, for example, the corresponding Part (b) of Figs. 5 and 6. The combustor designer may obtain further insight by observing a similar series of streamline plots predicted by Novick et al. [23] for an isothermal dump combustor flowfield with the following differences: a 90 deg expansion, an inlet hub, and a constricted exit. Flow isualization. An indication of the validity of the computations can be obtained by comparing predicted mean
36
sudden enlargement. Examination of Fig. 5(a)shows that this is in quite good agreement with the numerical prediction. A photograph with 4=45 deg is shown in Fig. 7(b),where a precessing vortex core, PVC, is clearly seen extending from x / D = 1.25 to the exit, although its upstream starting location fluctuates from about x / D = 1.0 to 1.5. The PVC is a wellknown phenomenon in strongly swirling confined flows, consisting of a central core in the flowfield which exhibits a three-dimensional time-dependent instability. Oscillation is at low frequency [4-61. A corner recirculation zone is faintly visible in Fig. 7(b),.and it seems to extend to about x / D = 0.4. At stronger swirl 4=70 deg, the PVC is even thicker and extends further upstream, merging discretely with the central recirculation zone, see Part (c) of Fig. 7 . There is now little evidence of a corner recirculation region. All these effects are Fig. 8(a) cp = 0 deg in general agreement with the predictions of Figs. 3 and 5. Figure 8 displays a sequence of photographs corresponding to those of Fig. 7 , only now the side-wall angle a = 4 5 deg. Comparing Parts (a) of the two figures reveals no significant changes, as found in earlier experiments [20], and in the present predictions, there being little predicted effect of the side-wall angle in the range a=W to 45 deg on the nonswirling flowfield. The intermediate vane angle case of 4=45 deg is visualized in Fig. 8(b), and careful study of this and other photographs is quite revealing. A large concentration of bubbles is seen centered at about x/D=1.5, probably corresponding to the location of the time-mean rear stagnation point of the central recirculatiofi zone. The PVC extends from here to the exit. Comparison with Part (b) of Fig. 7 reveals that at (b=45 deg the relatively short corner recirculation zone seen with the a =90 deg geometry does not appear with the a = 4 5 deg geometry. This is in conformity Fig. 8(b) cp = 45 deg with the predictions given in Part (b) of Figs. 5 and 6. The 4=70 deg flow shown in Fig. 8(c) illustrates no corner recirculation zone as well, with the vortex core being wider and extending even further upstream, again merging almost imperceptibly with the central recirculation zone, as in Fig. 7w. The flow visualization photographs in general provide an encouraging base of data for comparison with the computations. Further experimental work is in progress at Oklahoma State University including five-hole pitot probe measurements 1241 and single- and multi-wire hot-wire measurements. In all flowfields represented here, the, calculation does a reasonable job of predicting the general flow patterns but it is expected that inaccuracies in detail will occur, as has been encountered by others in predicting Fig. 8(c) = 70 deg recirculation zones with the standard k-e turbulence model, especially under swirl flow conditions [ll, 121. There are a Fig. 8 Flow visualization of pathlines produced by helium-fitfed soap bubbles with wall expansion angle a = 45 deg for various vane swirl number of possible reasons for this, but the most likely one is angles +: (a)0 dag, (b) 45 deg, and (c) 70 deg that a turbulence model whose basis and parameters are adequate for simple flow situations is not adequate to handle the more complicated swirling recirculation flow situation. streamline patterns with the pathlines traced out by the soap bubbles in the flow visualization experiments. Generally, a relatively long exposure time of 1/8 s is used so as to identify Closure pathlines, and infer streamlines therefrom. A sample flow Fundamental theoretical studies are being undertaken on visualization photograph is presented in Fig. 7(a) swirling axisymmetric recircuIating flows, under low speed corresponding to the zero swirl, 90 deg expansion angle and nonreacting conditions. Many factors affect the flowfield. The photograph, with the flow from left to right, existence, size and shape of the corner recirculation zone and clearly shows a great number of individual pathlines. central toroidal recirculation zone. A major outcome of the Photographs of this type can be used to distinguish regions of current work is the ability to characterize and predict more highly turbulent flow from smoother regions (for example realistically than previously the existence, size and shape of near the centerline of the flowfield) which have smoother, the corner and central recirculation zones as a function of the straighter pathlines. In addition, the outline of the corner angle of the sloping wall, the degree of swirl imparted to the recirculation region can be estimated from Fig. 7(a) (and incoming flow, and other swirler and geometric parameters. numerous additional photographs taken at the identical run Computations are made with a suitable computer code which condition). For this geometry the mean stagnation point includes several refinements to improve accuracy and defining the end of the recirculation zone appears to be at economy. A few parameter variations were investigated about 2 chamber diameters (8 step heights) downstream of the computationally in order to make combustor design in(J
37
formation available in a directly usable form. Comparison with flow visualization studies reveals that gross features of the flowfield are predicted quite well. A problem in swirling flows is theaccuracy with which the details may be predicted. This may be partially attributed to the quality of the turbulence model. Further research should emphasize turbulence model development for swirling recirculating flows.
Acknowledgment The authors wish to express their gratitude to NASA Lewis Research Center and Air Force Wright Aeronautical Laboratories for financial support under NASA Grant No. NAG3-74.
References 1 Gerstein, M. (ed.), “Fundamentals of Gas Turbine Combustion,” NASA-CP-2087, 1979, Workshop held at NASA Lewis Research Center, Cleveland, Ohio, Feb. 6-7, 1979. 2 Lefebvre, A. H., (ed.), Gas Turbine Combustion Design Problems, Hemisphere-McGraw-Hill, New York, 1980. 3 Lilley, D. G., “Flowfield Modeling in Practical Combustors: A Review,” Journal ofEnergy, Vol. 3, July-Aug. 1979, pp. 193-210. 4 Syred, N., and Be&, J. M., “Combustion inswirling Flows: A Review,” CombustionandFlame, Vol. 23,1974, pp. 143-201. 5 Lilley, D. G., “Swirl Flows in Combustion: A Review,” AIAA Journal, Vol. 15, NO. 8,Aug. 1977, pp. 1063-1078. 6 Gupta, A, K., Lilley, D. G., and Syred, N., Swirl Flows, Abacus Press, Tunbridge Wells, England, 1982 (in press). 7 Gosman, A. D., and Pun, W. M., “Calculation of Recirculation Flows,” Rept. No. HTS/74/2, 1974, Dept. of Mechanical Engineering, Imperial College, London, England. 8 Lilley, D. G., and Rhode, D. L., “A Computer Code for Swirling Turbulent Axisymmetric Recirculating Flows in Practical Isothermal Combustor Geometries,” NASA CR-3442, Feb. 1982. 9 Rhode, D. L., “Predictions and Measurements of Isothermal Flowfields in Axisymmetric Combustor Geometries,” Ph.D. thesis, School of Mech. and Aero. Engrg., Okla. StateUniv., Stillwater, Okla., 1981.
10 Launder, B. E., and Spalding, D. B., “The Numerical Computation of Turbulent Flows,” Comp. Methods in Appl. Mech. andEngrg., Vol. 3, Mar. 1974, pp. 269-289. 11 Habib, M. A., and Whitelaw, J. H., “Velocity Characteristics of Con-
Flow,” Proc. Symposium on Turbulent Shear Flows, Pennsylvania State University, Apr. 1977, pp. 13.9-13.17. 15 Moon, L. F., and Rudinger, G., “Velocity Distribution in an Abruptly Expanding Circular Duct,” ASME JOURNAL OF FLUIDS ENGINEERING, Mar. 1977, pp. 226-230. 16 Phaneuf, J. T., and Netzer, D. W., “Flow Characteristics in Solid Fuel Ramjets,” Report No. NPS-57Nt-74081, July 1974, Prepared for the Naval Weapons Center by the Naval Postgraduate School. 17 Back, L. H., and Roschke, E. J., “Shear Layer Flow Regimes and Wave Instabilities and Reattachment Lengths Downstream of an Abrupt Circular Channel Expansion,” ASME Journal of Applied Mechanic;, Sept. 1972, pp. 677-781. 18 Roschke, E. J., and Back, L. H.,“The Influence of Upstream Conditions on Flow Reattachment Lengths Downstream of an Abrupt Circular Channel Expansion,”Journal of Biomech., Vol. 9, 1976, pp. 481-483. 19 Krall, K. M., and Sparrow, E. M., “Turbulent Heat Transfer in the Separated, Reattached, and Redevelopment Regions of a Circular Tube,” ASME JournalofHeat Transfer,Feb. 1966,pp. 131-136. 20 Chaturvedi. M. C., “Flow Characteristics of AxisymmetricExpansions,” Proceedings Journal HydraulicsDivision, A X E , Yol. 89, No. HY3, 1963, pp. 61-92. 21 Morel, T., “Comprehensive Design of Axisymmetric Wind Tunnel Contractions,” ASME Paper 75-FE-17, Minneapolis, Minn., May5-7, 1975. 22 Weske, D. R., and Sturov, G. Ye, “Experimental Study of Turbulent Swirled Flows in a Cylindrical Tube,” Fluid Mechanics- Soviet Research, Vol. 3, No. 1, Jan. -Feb. 1974, pp. 77-82. 23 Novick, A. S., Miles, G. A., and Lilley, D. G., “Numerical Solution of Combustor Flowfields: A Primitive Variable Design Capability,” Journal of Energy,Vol. 3, No. 2, Mar.-Apr. 1979, pp. 95-105. 24 Rhode, D. L., Lilley, D. O.,and McLaughlin, D. K., “Mean Flowfields in Axisymmetric Combustor Geometries with Swirl,” Paper AIAA 82-0177, Orlando, Fla., Jan. 11-14, 1982.
38
APPENDIX B MEAN FLOWFIELDS IN AXISYMMETRIC COMBUSTOR GEOMETRIES WITH SWIRL
39
lowfiel~sin symmetric Combustor Geometries with Swirl D.L. m o d e * and D.G. Lilleyt
Oklahoma State University, Stillwater, Oklahoma and D.K. McLaughlinS
Dynamics Technology, Inc., Torrance, California
'
D d k P
R Re u, v, w V x, r, 0 a
P 6 E
P (b
A swirling nonreacting flow enters a larger chamber via a sudden or gradual expansion. Six flowfield configurations are investigated with sidewall angles a=90 and 45 deg and swirl vane angles # = 0,38, and 45 deg. Photography of neutrally buoyant helium-filled soap bubbles, tufts, and injected smoke helps to characterize the time-mean streamlines, recirculation zones, and regions of highly turbulent flow. From the photographic evidence, it is found that central recirculationzones occur for the swirling flow cases investigated, after which a relatively narrow precessing vortex core exists near the axis. Five-hole pitot probe pressure measurements allow the determination of time-mean velocities u, v, and w. At the inlet, the radial velocity profiles exhibit strong nonuniformity. The time-mean velocity measurements presented here constitute a seriously needed data base for the validation of computer prediction codes and the developmentof turbulencemodels for their simulation.
Nomenclature =test section diameter = inlet nozzle diameter = kinetic energy of turbulence = time-mean pressure =radius of test chamber = Reynolds number = time-mean velocity (in x,r,0 direction, respectively) = time-mean vector velocity magnitude =axial, radial, azimuthal cylinGrica1polar coordinates, respectively = side-wall expansion angle =yawangleof flow=tan-' (w/u) =pitch angle of flow=tan-' [ v / ( u 2 wz) = turbulence energy dissipation rate = time-mean density =swirl vane angle = tan-' (w,/u,)
+
modeling. The particular problem discussed in this paper is the flow in a round pipe entering an expansion into another round pipe as illustrated in Fig. 1. The incoming flow may possess a swirl component of velocity via passage through swirl vanes at angle (b from the axial direction, and the side wall may slope at an angle a, also from the axial direction. The resulting flowfield domain may possess a central toroidal recirculation zone in the middle of the region on the axis, in addition to the possibility of a corner recirculation zone near the upper corner provoked by the rather sudden enlargement of the cross-sectional area. Of vital importance is the characterization of flows of this type in terms of the effects of side-wall angle a,degree of swirl (b, turbulence intensity of the inlet stream, and expansion ratio D / d on the resulting flowfield in terms of its time-mean and turbulence quantities. Such problems have received little attention, although they are fundamental to the physical processes occurring in aircraft combustors. A systematic parametric investigation is being undertaken on the effect of side-wall angle a and a swirl vane angle (b on the resulting flowfield produced. The goals of the ongoing study involve comparison of predictions with experimental turbulent flow measurements so as to assist in evaluating turbulence models and improving the final predictive capability. This paper focuses on the experimental study, with identification of recirculation regions from flow visualization and mean velocity measurements using a five-hole pitot probe, thus providing a useful data base for the later turbulence model development aspects of the study.
I
Subscripts
d P
0
=based on inlet nozzle diameter =based on probe tip diameter =value at inlet to flowfield
I.
Introduction
I
N gas turbine and ramjet combustion chamber development, designers are aided by both experimental and theoretical studies. The present research work is concerned with such complementary studies.24 The problem being investigated is concerned with steady turbulent flow in axisymmetric geometries under low speed and nonreacting conditions-a study area which is fundamental to combustor
11.
Experimental Approach
A. Previous Studies
There have been several experiments performed with nonreacting flows in expansion geometries that have been reported in the literature, examples of which are contained in Refs. 5,8. References 5-7 also include flowfield predictions, made with versions of the TEACH-T computer p r ~ g r a m . ~ These experiments include time-mean velocity measurements (with hot-wire and pitot probes and laser Doppler anemometry), turbulence measurements (with hot-wires and laser anemometers) and flow visualization. The majority of the earlier measurements were made in nonswirling flows; however, some noteworthy experiments have been made in swirling confined jets. 5,8 Direct comparison between the results of the cited experiments and the present experimental
Presented as Paper 82-0177 at the AIAA 20th Aerospace Sciences Meeting, Orlando, Fla., Jan. 11-14, 1982; submitted Jan. 22, 1982; revision received June 21, 1982. Copyright 0 American Institute of Aeronautics and Astronautics, Inc., 1982. All rights reserved. *Graduate Student, School of Mechanical and Aerospace Engineering. At present: Assistant Professor, Department of Mechanical Engineering, Texas A&M University, College Station, Texas. ?Professor, School of Mechanical and Aerospace Engineering. Associate Fellow AIAA. $GroupManager. Member AIAA.
40
SWIRL VANE ANGLE
-
9
IG
-k
I
i
I
i i j
b) EXPECTED RECIRCUUTION ZONES
Fig. 1 Schematic of flowfield.
I
K O - M E S H SCREENS
w c' Fig. 3 Five-hole pitot probe.
*9rl E I
SEEION C. Flow Visualization Techniques
HONEYCOMB
A slide projector, located downstream of the test facility, served as the light source. A vertical sheet of light 4 cm thick was produced to illuminate the rx plane of the flow pattern. This was provided by using a slide which is opaque except for a thin slit cut out for light passage to the test section. Tri-X Pan, a very light-sensitive photographic film rated at ASA 400, along with a large camera aperture o f f 2.0, was employed in order to obtain photographs of acceptable contrast. Moreover, the film was substantially overdeveloped to compensate for underexposure; this is equivalent to using an extremely light-sensitive film rated at approximately ASA 6000. Photographs of the bubble streaklines were typically taken at shutter speeds ranging from 1/60 to 114 s. Rhode4 describes at length the flow visualization studies. Three different techniques are used, including neutrally buoyant helium-filled soap bubbles" using a Sage Action, Inc., bubble generator,I2 smoke-wire,'3-I5 and tufts.16J7
Fig. 2 Schematic of overall flow facility.
results is generally not possible because of differences in geometry. However, in the nonswirling jet, comparisons were possible with experiments of Chaturvedi,8 who measured time-mean and turbulent flow quantities downstream of a sudden expansion of diameter ratio D / d = 2 and various expansion side-wallangles a. B. Test Facility
The present experiments have been conducted in the confined jet facility shown schematically in Fig. 2. The facility has an axial flow fan whose speed can be changed by altering the varidrive mechanism. Numerous fine screens and straws produce flow in the settling chamber of relatively low turbulence intensity. The contraction section leading to the test section has been designed by the method of Morello to produce a minimum adverse pressure gradient on the boundary layer and thus avoid unsteady problems associated with local separation regions. The test section consists of a swirl vane assembly and an idealized combustion chamber model. The swirl vane assembly contains ten vanes which are individually adjustable for any vane angle 4. The pitchlchord ratio of 1 provides good turning efficiency. The hub is located at the center of the swirler with a streamlined nose facing upstream. The downstream end is simply a flat face, simulating the geometric shape of a typical fuel spray nozzle. The idealized combustion chamber model is composed of an expansion block and a long plexiglass tube. The expansion block is a 30-cm-diam disk with a 15-cm-diam hole centered on its axis through which the air entering the model flows smoothly. The downstream face of the expansion block has been shaped to provide the desired flow expansion angle a which is shown in Fig. 1. There are currently three interchangeable expansion blocks and the appropriate choice gives a = 90,70,or 45 deg. There are no film-cooling holes or dilution-air holes in the test facility, and the chamber wall consists of a straight pipe. The inside diameter of the pipe is 30 cm and the length is approximately 125 cm. The substantial size of the test model provides excellent resolution for five-hole pitot probe measurements and flow visualization photography.
D.
Mean Velocity Measurement
Many instruments are used for separately measuring the magnitude and direction of fluid velocity. l8 However, there are only a few instruments capable of simultaneously sensing both magnitude and direction. One of the simplest of these is the five-hole pitot probe which has been developed and used by various investigators. 19-22 The particular probe employed in this study is model DC-125-12-CD from United Sensor and Control Corp. It is shown schematically in Fig. 3 and has a 3.2-mm-diam sensing tip and shaft containing five tubes. The sensing head is hook-shaped to allow probe shaft rotation without altering the probe tip location. The instrumentation system, in addition to the five-hole pitot probe, consists of a manual traverse mechanism, two five-way ball valves, a very sensitive pressure transducer, a power supply, and an integrating voltmeter. The differential pressure transducer is model 590D from Datametrics, Inc. The output is read as the dc signal from a TSI model 1076 integrating voltmeter. Prior to production measurements, the five-hole pitot probe is aerodynamically zeroed for yaw, which is in the horizontal plane of Fig. 4, so that x and 0 axes of the measurement coordinate frame coincide with those of the test section. The measurement procedure for each location within a traverse begins with aerodynamically nulling the yaw, and determining the yaw angle p. This is indicated by a zero reading for p w - p E , where the pressures are identified in Fig.
41
3. Then the five-way switching valves are set so that pN -ps is sensed by the transducer. Finally, the reading of pc-pw is similarly obtained. The data reduction employs two calibration curves which were obtained from a single calibration velocity. The underlying principle is that the calibration is independent of probe Reynolds number ReP based on probe tip diameter. Careful calibration experiments reveal that this condition exists for ReP 2 1090 corresponding to a local velocity of 5.4 m/s. Hence measurements of such low velocities suffer from a necessary calibration error. However, this error affects the velocity measurements typically by less than 6% for R e p r 4 0 0 , corresponding to a local velocity greater than 2 m/s. The data at each measurement location are reduced using a computer program by first calculating the pitch coefficient bN-ps)/(pc -p w). From these values an interpolation technique is used to obtain the pitch angle 6 in the vertical plane from the appropriate calibration characteristic. The resulting value of 6 is utilized to determine the velocity coefficient p V2/[2@,- -pw)] using the corresponding calibration characteristic. Values for Vas well as the axial, radial, and swirl velocity ,components u, u, and w,shown in Fig. 4, are calculated from the velocity coefficient, pitch angle 6, and yaw angle 0, which is in the horizontal plane. The magnitude of the velocity vector is given by
i
/'
Fig. 4 Velocity components and flow direction angles associated with five-hole pitot measurements(yaw angle p in the horizontal plane and pitch angle 6 in the vertical piane).
-
-0 5
2a
1.0
0
a)
6
and the velocity components are obtained from this magnitude and the pitch and yaw angles. Elsewhere, Rhode4 describes the five- hole pitot probe calibration procedure, which is extremely critical to the accuracy of the results, and discusses reliability, since turbulence effects on pressure probes are not well known.23 A 5% accuracy is expected for most of the measurements, increasing to 10% in regions of low velocity below approximately 2 m/s because of probe insensitivity to low dynamic pressure. It is further asserted that measurements made at flow Reynolds numbers Re, (based on inlet pipe diameter) equal to 1 . 0 5 ~lo5 and 7 . 8 ~lo4 for the nonswirling and swirling flows, respectively, are in the Reynolds number invariant regime.
3.0
= 0'
-0.5 b)
0 = 38'
,Vortex
Core
-----_-_-___
_ _ _ _ _ -- ---
-0 5
6
J
I
10
20
30
c)
0 = 450
x /D
111. Flow Visualization
Fig. 5 Artistic impressions of dividing streamlines with wall expansion angle a= 90 deg for swirl vane angles.
-05
< / 0
10
a)
05
r/D 0
-05
0
0
1.0
c)
30
0-
/Vortex
A. Artistic Impressions of StreamlinePatterns
Photographs of each of the six flowfields resulting from
Core
+=O, 38, and 45 deg with a=90 and 45 deg have been
_____-
Z : ; = -
10 b)
- 0.5
20
0=
Recirculation zones are important to combustor designers. The size and location of these regions in the present isothermal flows are deduced from flow visualization photographs of tufts, smoke, and bubbles responding to the experimental flowfield patterns. Resulting dividing streamline sketches as well as selected photographs of the visualization experiments are now presented and discussed.
20
examined in detail for each of the three flow visualization methods currently employed. The characteristics of the overall flowfield are illustrated and discussed via the resulting time-mean dividing streamline patterns. These are sketched in Figs. 5 and 6 from information obtained from the entire collection of flow visualization photographs. Results from the smoke-wire experiment are utilized near the inlet, whereas tuft and bubble data are used in approximating the size and shape of the recirculation zones downstream. Also, bubble flow patterns reveal the existence of a precessing vortex core, which occurs downstream of the central region. The resulting streamlines for the three swirl cases of the sudden expansion ar=90-deg geometry are shown in Fig. 5.
30
0 = 38'
20
0 = 450
30
X/D
Fig. 6 Artistic impressions of dividing streamlines with wall expansion angle (Y = 45 deg for swirl vane angles.
42
a) qi= 0 deg.
b) 8 = 38 dee.
c) qi = 45 deg. Fig. 7 Flow visualization photographs of tufts in the rx plane with wall expansion angle a = 90 deg for swirl vane angles.
Fig. 9 Flow visualization photographs of pathlines indicated by illuminated neutrally buoyant soap bubbles for wall expansion angle 01 = 90 deg and swirl vane angles.
u/u, Fig. 10 Measured velocity profiles for wall expansion angle qi = 90 deg and swirl vane angle qi = 0 deg.
The nonswirling flow sketch in Fig. 5a exhibits a large corner recirculation zone which is in excellent agreement with the corresponding streamlines from the measurements of Chaturvedi. * Appropriate prior measurements for the present swirling flows have not been found. For the moderate swirl vane angle case of + = 3 8 deg a central recirculation region appears in conjunction with a decrease in size of the corner zone. A thin precessing vortex core, discussed at length by Syred and Beer,24 is observed near the centerline extending from the end of the central region to the test section exit. The axial location where the vortex core begins fluctuates, ranging approximately from x / D = 1.25 to 1.75. This vortex core is essentially a three-dimensional time-dependent phenomenon, which occurs as a swirling region of negligible axial velocity whose center winds around the test section centerline. A further increase in vane angle to +=45 deg results in slight enlargement of the central zone; however, the corner bubble is essentially unaffected. For this flowfield the vortex core is slightly expanded in the radial direction. The corresponding sequence of dividing streamlines is found in Fig. 6 for the gradual flow expansion case with 01 = 45 deg. As with Fig. 5, the nonswirling flowfield exhibits excellent agreement with corresponding measurements of
c) qi = 45 deg. Fig. 8 Flow visualization photographs of smoke-wire streaklines with wall expansion angle a= 90 deg for swirl vane angles.
43
lower turbulence intensity portions of the flowfield meanflow directions can be obtained by ensemble averaging local tangents to pathlines traced out by soap bubbles. This helps define the flowfield geometry in terms of the outline of recirculation regions. A sample flow visualization photograph is presented in Fig. 9a corresponding to the zero swirl, 90-deg expansion angle flowfield. The photograph, taken with a relatively long time exposure (1/8-s), clearly shows a great number of individual pathlines. Photographs of this type can be used to indicate regions of weakly turbulent flow such as that near the centerline of the flowfield which exhibits relatively straight pathlines. In addition, the outline of the corner recirculation region can be estimated from Fig. 9a (and numerous additional photographs taken at the identical run condition). For this geometry the mean stagnation point defining the end of the recirculation zone appears to be at x / D = 2.0. A photograph with + = 3 8 deg and 118-s shutter speed is shQwn in Fig. 9b, where the precessing vortex core is clearly seen extending from x / D = 1.5 to the exit. Its upstream extent fluctuates randomly from approximately x / D = 1.25 to 1.75. The corner bubble is observed in both the upper and lower portions of the flowfield, extending to approximately x/D=O.4, which agrees almost exactly with the smoke flow pattern for this flowfield in Fig. 8b. A photograph using 1/8-s shutter speed is presented in Fig. 9c for the +=45 deg flowfield where a thicker vortex core is seen. The corner zone is faintly visible here, and its axial length also seems to extend used. For swirl vane angle 38 deg, Fig. 7b is a photograph taken at 1/60 s. The swirl in the counterclockwise direction when viewed from downstream. Tbere is no evidence of a corner zone and the central region apparently extends to x/D=1.5, Finally, the +=a5 deg case shown in Fig. 7c exhibits a central region extending downstream as far as approximately x / D = 1.85 for 1/125-s shutter speed. Local details in the nonswirling flowfields are clearly revealed through the visualization of streaklines indicated from the generation of illuminated smoke. In the swirling flow cases, strong mixing diffuses the smoke so that streaklines are not distinguishable. However, under such conditions recirculation zone outlines are visible, especially in the region near the smoke-generation wire, A selected photograph is exhibited and discussed for each of the three abrupt expansion flowfields. The corner recirculation bubble in the nonswirling wall expansion angle a=90 deg is revealed in Fig. 1130-s shutter speed. Also, the radial location of the zero velocity point within the upper and lower corner bubble is estimated to be approximately 0.15D from the respective walls of the test facility. This agrees with the velocity measurements presented later in Sec. IV. The moderate swirl vane anqle flow with a U3O-s exposure is shown in Fig. 8b. The shortened corner zone is easily identified because the adjacent flow contains no smoke near the inlet. This bubble is seen to extend to approximately x/D=O.45. The tuft photographs for this case indicate a slightly shorter zone knding at approximately x / D = 0.4. The upstream portion of the central zone is also clearly seen, as low velocity fluid carries a dense mass of smo moves upstream of the inlet. Further, the precessing vortex core is seen to contain only slight smgke. Since the core exhibits negligible axial velocity, the smoke is essentially carried around it by the high velocity fluid outside the core. Figure 8c is a photograph at 1/8-s of the +=4S deg case wherein this core is not as distinct. In this case, some smoke has diffused into the core due to a slightly longer delay before activating the camera shutter. Observe that both the corner and central zones near the inlet reveal that the only change from those for #J = 38 deg is a slightly wider central region. Soap bubbles injected into the flow upstream of the test section trace pathlines clearly when illuminated. In relatively #J
terized parametrically for the effects of a! and #J on the corner and central recirculation zone lengths. Several observations should be noted. First, zone lengths are only slightly affected by CY, as found previously for the corner bubble under Reynolds number .%J7 from 90 to 45 deg, and the inlet flow walls. Third, the corner recirculation length decreases upon increasing the swirl vane angle #J from 0 to 38 deg, a parameter change which also provokes the existence of a
ployed an approximation for inlet velocity boundary conditions. It has generally been assumed that u =O and that both u and w exhibit flat velocity profiles. However, the present
44
I
0 0.25
y 0
a1 u/u,
1
y 0
b) w/u,
b l w/u, Fig. 12 Measured velocity profiles for wall expansion angle w = 9 0 deg and swirl vane angle i = 45 deg.
0
u/u, Fig. 13 Measured velocity profiles for wall expansion angle 01=45 deg and swirl vane angle Cp = 0 deg.
x/D
1
QI = 45
proxiniately 4 cm upstream of the flow expansion corner, where x/D=O. This swirler location allows the central recirculation zone to begin upstream of x/D = 0, thereby changing the velocity profiles there. Figure 11 also reveals that a 38-deg swirl vane angle produces a maximum swirl flow angle [tan-' ( w,/u,) 1 of 30 deg at the test chamber inlet. The maximum swirl flow angle for the 45-deg vane angle case shown in Fig. 12 is 34 deg. Thus there is only a slight increase of swirl flow angle, although these two flows are different in that the inlet profiles are considerably more sharply peaked for the latter case. Figures 11 and 12 show zero u and w velocity values near the axis at the inlet, but actually the probe was insensitive to the very low velocities there. This is consistent with earlier flow visualization results that the central bubble extends upstream of the inlet. The measurements shown in Fig. I l a provide no evidence regarding the existence of a corner zone. This is expected because flow visualization reveals that the region only extends to x/D=0.4. However, there is clear evidence of a rather large central zone whose length is similar to that shown in Fig. 5b. Although the axial velocity profiles are beginning to flatten in the downstream direction, they retain a zero velocity value on the axis, which is consistent with soap bubble flow patterns as seen in Fig. 9b. The early erratic behavior shown by the swirl velocity profiles in Fig. l l b quickly transforms, exhibiting a solid-body-rotation core with a rather flat profile outside this region. Figure 12 also reveals the discrepancy regarding inlet velocity profiles, this time for the case Cp =45 deg. The large central recirculation region causes the downstream flow to be accelerated near the top wall. The corresponding swirl velocity component at the x/D = 0.5 axial station typically shows local minima where the mean axial velocity is zero. The accuracy of the velocity measurements at these locations is poor, as discussed in Sec. KD, so that any physical interpretation here is suspect. Again, the early erratic behavior found in the swirl velocity profile at x/D=0.5 quickly develops into a shape similar to that seen in Fig. l l b . The precessing vortex core motion discussed in Sec. I1.B results in poor measurement repeatability which promotes the irregular behavior within this core region.
a1 u/u,
I
I
Fig. 15 Measured velocity profiles for wall expansion angle deg and swirl vane angle Cp = 45 deg.
2
I
05
I
b) w / u o
Fig. 11 Measured velocity profiles for wall expansion angle +=90 deg and swirl vane-angle Cp = 38 deg.
0
*
.a) u / u o P/D 0'50 0.25
0
05
x/D
2
a) u/u,
b) w/u, Fig. 14 Measured velocity profiles for wall expansion angle w=45 deg and swirl vane angle Cp = 38 deg.
B. Gradual Expansion, 01 = 45 deg
Figures 13-15 exhibit velocities for the same sequence of flowfields with side-wall angle a = 4 5 deg. The inlet profiles were not measured in this geometry because the presence of the expansion block interferes with probe positioning. Effects of swirl vane angle Cp on velocities, similar to those found for the sudden expansion cases, are found in the flowfield sequence for this test section geometry. The major difference is that the sloping wall encourages the inlet flow to accelerate near the top wall. Also, it tends to shorten or obliterate the corner recirculation region.
measurements, taken 4 cm downstream of the vane swirler, indicate that this is an unrealistic estimate, with sharply peaked u and w profiles, as shown in Figs. 11 and 12. The difference results from the use of a swirler with ten flat blades with pitch/chord ratio of unity, imperfect blade efficiency, the existence of a hub, and the fact that the downstream edge of swirl vanes of the test facility is actually located ap-
45
’Rhode, D.L., Lilley, D.G., and-McLaughlin, D.K., “On the Prediction of Swirling Flowfields Found in Axisymmetric Combustor Geometries,” Proceedings of ASME Symposium on Fluid Mechanics of Combustion Systems, Boulder, Colo., June 1981, pp. 257-266; see also Journalof Fluids Engineering, Vol. 104, Sept. 1982, pp. 378-384. 3Lilley, D.G., Rhode, D.L., and Samples, J.W., “Prediction of Swirling Reacting Flow in Ramjet Combustors,” AIAA Paper 811485, July 1981. 4Rhode, D.L., Predictions and Measurements of Isothermal Flowfields in Axisymmetric Combustor Geometries, Ph.D. Thesis, Oklahoma State Univ., Stillwater, Okla., Dec. 1981. ’Habib, M.A. and Whitelaw, J.H., “Velocity Characteristics of Confined Coaxial Sets With and Without Swirl,” ASME Paper 79WA/FE-21, Dec. 1979. 6Srinivasan, R. and Mongia, H.C., “Numerical Computations of Swirling Recirculating Flows,” Final Report, NASA-CR-165196, Sept. 1980. 7Sturgess, G.J., Syed, S:A., and Sepulveda, D., “Application of Numerical Modeling to Gas Turbine Combustor Development Problems,” Proceedings of ASME Symposium on Fluid Mechanics of Combustion Systems, Boulder, Colo., June 1981, pp. 241-250. 8Chaturvedi, M.C., “Flow Characteristics of Axisymmetric Expansions,” Proceedings of the Journal of Hydraulics Division, ASCE, VOl. 89, HY3,1963, pp. 61-92. , gGosman, A.D., and Pun, W.M., “Calculation of Reckulating Flows,” Report HTS/74/2, Dept. of Mechanical Engineering, Imperial College, London, England, 1974. ‘OMorel, T., “Comprehensive Design of Axisymmetric Wind Tunnel Contractions,” ASME Paper 75-FE-17, Minneapolis, Minn. May 1975. ”Owen, F.S., Hale, R.W., Johnson, B.V., and Travers, A., “Experimental Investigation of Characteristics of Confined JetDriven Vortex Flows,” United Aircraft Research Laboratories, East Hartford, Conn., Rept. R-2494-2, Nov. 1961. IZHale, R.W., Tan, Pr, Stowell, R.C. and Ordway, D.E., “Development of an Integrated System for Flow Visualization in Air Using Neutrally-Buoyant Bubbles,” Sage Action, Inc., Ithaca, N.Y., for ONR, Rept. SAI-RR7107, Dec. 1971. 13Corke, T., Koga, D., Drubka, R., and Nagib, H., “A New Technique for Introducing Controlled Sheets of Smoke Streaklines in Wind Tunnels,” Proceedings of International Congress on Znstrumentation in Aerospace Simulation Fa , IEEE Publ. 77 CH 1251-8 AES, 1974, p. 74. I4Nagib, H.M., “Visualization of Turbulent and Complex Flows Using Controlled Sheets of Smoke Streaklines,” Proceedings crf International Symposium on Flow Visualization,Tokyo, Oct. 1977, pp. 181-186; see also Supplement, pp. 29-1 to 29-7. Is Cornell, D., “Smoke Generation for Flow Visualization,” Aerophysics Research Report 54, Mississippi State Univ., University, Miss., Nov. 1964. l6Bird, J.D., “Visualization of Flowfields by Use of a Tuft Grid Technique,” Journal of the Aeronautical Sciences, Vol. 19, 1952, pp. 481-485. I7McMahon, H.M., Hester, D.D., and Palfery, J.G., “Vortex Shedding From a Turbulent Jet in a Cross-Wind,” Journal of Fluid Mechanics, Vol. 48, 1971, pp. 73-80. I8Breyer, D.W. and Pankhurst, R.C., “Pressure-Probe Methods for Determining Wind Speed and Flow Direction,” Her Majesty’s Stationery Office, London, England, 1971. lgHiett, G.F. and Powell, G.E., “Three-Dimensional Probe for Investigation of Flow Patterns,” The Engineer, Vol. 213, Jan. 1962, pp. 165-170. 2oPien, P.C., “The Five-Hole Spherical Pitot Tube,” David Taylor Model Basin Report 1229, May 1958. 21 Lee, J.C. and Ash, J.B., “A Three-Dimensional Spherical Pitot Probe,” Transactions of ASME, Journal of Applied Mechanics, Vol. 23, April 1956, pp. 603-608. 22Hale, M.R. and Norrie, D.H., “The Analysis and Calibration of the Five-Hole Spherical Pitot,” ASME Paper 67-WA/FE-24, Nov. 1967. 23Gupta, A.K. and Lfley, D.G., Flowfield Modeling and Diagnostics, Abacus Press, Tunbridge Wells, Kent, England, 1983 (in press). 24Syred, N. and Beer, J.M., “Combustion in Swirling Flows: A Review,” Combustion andFlame, Vol. 23, 1974, pp. 143-201. 25 Lipstein, N.J., “Low Velocity Sudden Expansion Pipe Flow,” Paper presented at ASHRAE 69th Annual Meeting, Miami Beach, Fla., June 1962.
C. Comparison of Measurements and Predictions
Flowfield computations have been made” for a variety of side-wall and swirl vane angles, using the standard k-E turbulence model and the technique discussed at length elsewhere.30 These and other earlier predictions have generally idealized the inlet flow as a plug-flow axial velocity profile with a flat or solid body rotation swirl velocity profile. Though this may be adequate for those applications, it is clearly inadequate for the present study, in which the inlet flow conditions are highly nonuniform. Current work is proceeding with inlet profile effects and turbulence model developments. In this connection, it may be noted that a turbulence model whose basis and parameters are adequate for simple flow situations is not adequate to handle the more complicated swirling recirculating flow situation. Nevertheless, good predictions are available4 for the case of a less difficult test problem (coswirl and counterswirl flow in a pipe using the data of Ref. 31). This turbulence simulation problem in complex flowfields is clearly an area of current research interest.
V. Summary A major outcome of the current study is the experimental characterization of corner and central recirculation zones in six basic flowfield configurations of an axisymmetric expansion with side-wall angle CY = 90 and 45 deg and swirl vane angle 4=0, 38, and 45 deg. The size and shape of the recirculation bubbles for each flowfield is illustrated via an artistic impression deduced from a collection of flow visualization photographs of tufts, smoke, and neutrally buoyant soap bubbles responding to the flow. Increasing swirl vane angle 4 from 0 to 38 deg produces a shortened corner region and the appearance of a central bubble typically extending downstream to approximately x/D= 1.7, after which a precessing vortex core exists near the axis reaching to the exit of the test section. A further increase in 4 to 45 deg enlarges the central zone and vortex core with negligible effect on the corner region in those flowfields where it occurs. The effect of sidewall angle CY on the nonswirling flows is negligible. However, a decrease from 90 to 45 deg apparently eliminates the corner bubble in the swirling flow cases investigated. This decrease in CY also causes the inlet flow to impinge more severely on the top wall, where larger axial velocities occur. A more detailed experiment consists of the measurement of time-meaq velocity components in the axial, radial, and azimuthal directions using a five-hole pitot probe. These measurements generally agree with the flow visualization results and provide a more complete understanding of each flowfield. At the inlet, the axial and swirl velocity profiles exhibit maximum values at approximately r / D = 0.2 in a sharply peaked annular fashion. This nonuniformity arises for several reasons: the use of a ten-blade swirler with pitch/chord ratio of 1, blade inefficiency, the presence of a hub, and the fact that the swirl vane exit station is typically located upstream of the expansion station. This allows the central recirculation zone to begin upstream of the expansion wherexlD=O. Clearly, the time-mean velocity measurements presented here contribute to a seriously needed data base for the validation of computer prediction codes and the development of turbulence models for the simulation of complex turbulent swirling flows. Acknowledgments The authors wish to express their sincere gratitude to NASA Lewis Research Center and Air Force Wright Aeronautkal Laboratories for support under Grant NAG 3-74. References Lefebvre, A.H., ed., Gas Turbine Combustor Design Problems, Hemisphere-McGraw-Hill, New York, 1980.
46
26Pratte, B.D. and Keffer, J.R., :‘The Swirling Turbulent Jet,” Transactions of ASME, Journal of Basic Engineering, Vol. 94, Dec. 1972, pp. 739-748. 27Syred, N. and Dahman, K.R., “Effect of High Levels of Confinement Upon the Aerodynamics of Swirl Burners,” Journal of Energy, Vol. 2, Jan.-Feb. 1978, pp. 8-15. 28Novick, A.S., Miles, G.A., and Lilley, D.G., “Numerical Simulation of Combustor Flowfields,” Journal of Energy, Vol. 3, March-April 1979, pp. 95-105.
From the
29Serag-Eldin, M.A. and Spalding, D.B., “Computations of Three-Dimensional Gas Turbine Combustion Chamber Flows,” Transactionsof ASME, Journal of Engineering f o r Power, Vol. 101, July 1979, pp. 326-336. 30Lilley, D.G. and Rhode, D.L.,“A Computer Code for Swirling Turbulent Axisymmetric Recirculating Flows in Practical Isothermal Combustor Geometries,” NASA CR-3442, Feb. 1982. 3’Vu, B.T. and Gouldin, F.C., “Flow Measurements in a Model Swirl Combustor,” AIAA JournaI, Vol. 20, May 1982, pp. 642-651.
Progress in Astronautics and Aeronautics series
8
8
GASDYNAMICS OF DETONATIONS AND EXPLOSIONS-Ve 75 and CQMBUSTION IN REACTIVE SYSTEMS-Ve 76 Edited by J. Ray Bowen, Universityof Wisconsin, N. Manson, Universitt!de Poitiers, A . K . Oppenheim, Universityof California, and R. I. Soloukhin, BSSR Academy of Sciences The papers in Volumes 75 and 76 of this Series comprise, on a selective basis, the revised and edited manuscripts of the presentations made at the 7th International Colloquium on Gasdynamics of Explosions and Reactive Systems, held in Gottingen, Germany, in August 1979. In the general field of combustion and flames, the phenomena of explosions and detonations involve some of the most complex processes ever to challenge the combustion scientist or gasdynamicist, simply for the reason that both gasdynamics and chemical reaction kinetics occur in an interactive manner in a very short time. It has been only in the past two decades or so that research in tpe field of explosion phenomena has made substantial progress, largely due to advances in fast-response solid-state instrumentation for diagnostic experimentation and highcapacity electronic digital computers for carrying out complex theoretical studies. As the pace of such explosion research quickened, it became evident to research scientists on a broad international scale that it would be desirable to hold a regular series of international conferences devoted specifically to this aspect of combustion science (which might equally be called a special aspect of fluid-mechanical science). As the series continued to develop over the years, the topics included such special phenomena as liquid- and solid-phase explosions, initiation and ignition, nonequilibrium processes, turbulence effects, propagation of explosive waves, the detailed gasdynamic structure of detonation waves, and so on. These topics, as well as others, are included in the present two volumes. Volume 7 5 , Gasdynamics of Detonations and Explosions, covers wall and confinement effects, liquid- and solid-phase phenomena, and cellular structure of detonations; Volume 76, Combustion in Reactive Systems, covers nonequilibrium processes, ignition, turbulence, propagation phenomena, and detailed kinetic modeling. The two volumes are recommended to the attention not only of combustion scientists in general but also to those concerned with the evolving interdisciplinary field of reactive gasdynamics. Volume 75-468pp., 6x 9, illus., $30.00 Mem., $45.OOList Volume 76-688pp., 6 x 9, illus., $30.00Mem., $45.00 List Set- $60.00 Mem ., $75.00 List TO ORDER WRITE: Publications Dept., AIAA, 1290 Avenue of the Americas, New York, N. Y. 10104
APPENDIX C TURBULENCE MEASUREMENTS IN A CONFINED JET USING A
SIX-ORIENTATION HOT-WIRE PROBE TECHNIQUE
( A I AA- 82- 1262 )
48
TURBULENCE MEASUREMENTS IN A CONFINED JET USING A SIX-ORIENTATION HOT-WIRE PROBE TECHNIQUE
*
S . I . Janjua
and D. K. McLaughlin** Dynamics Technology, Inc. , Torrance, California and T. Jacksont and D. G . Lilleytt Oklahoma S t a t e University, S t i l l w a t e r , OK; Abstract
a
The si x-orientation single hot-wire technique has been applied t o t h e complex flowfield of a This flowfield, which swirling, confined jet. contai ns a rapid expansion w i t h r e s u l t i n g reci rcul a t i o n regions, i s typical of those found i n gas t u r b i n e engines and ramjet combustors. The pres e n t study focusses on turbulence measurements i n such a flowfield i n t h e absence of chemical reaction. A modification t o t h e six-orientation hot-wire technique developed by King has been made, which i ncorporates t h e deterrni nati on of t u r b u l e n t shear s t r e s s e s ( i n addition t o normal s t r e s s e s ) and ensenbl e averaging of redundant turbulence output quantities. With t h i s technique,flowfield surveys have been performed in both s w i r l i n g and nonswi r l ing axisymmetric confined j e t s . Where independent data e x i s t , comparisons have been made which demonstrate t h e re1 i abi 1i ty of t h e technique. Finally, a s e n s i t i v i t y a n a l y s i s of t h e data reduction technique has been completed which forms t h e major i ngredi e n t i n an uncertainty analysis.
Nomenclature Calibration constants i n Equation 1 Cooling velocity functions i n Table 1 Test section diameter In1 e t nozzl e diameter Hot-wire voltage Velocity function f o r axial velocity Velocity function f o r azimuthal velocity Vel oci ty function f o r radi a1 velocity Pitch f a c t o r Yaw f a c t o r Covari ance f o r cool i ng vel oci t i e s Zp, and ZQ Selected hot-wire probe p o s i t i o n s In1 e t Reynolds number in Axial velocity coordinates Radi a1 velocity Azimuthal ( s w i r l ) velocity on f a c i l i t y Three components of velocity i n probe coordinates defined by F i g u r e 5 Axial, r a d i a l , azimuthal cylindrical polar coordi nates Effective cooling velocity a c t i n g on a wire
YZiZj a2 (B
e3
Si de-wall expansion angl e Correl a t i on c o e f f t c i e n t (estimated) between cooling v e l o c i t i e s of adjacent wire o r i e n t a t i o n s Variance o f a given quantity Inverse function of c a l i b r a t i o n equation Swirl vane angle
Subscripts
1,2,3,4,5,6 i ,j
P,Q,R
rms
Refers t o the six probe measuring positions Dummy i n d i c i e s which take t h e values 1 to 3 Refers t o t h e t h r e e selected measuri ng posi ti ons Root-mean-squared quantity
Superscripts
I
Ti me-mean average F1 uctuati ng quantity
1. 1.1
Introduction
The Gas Turbine Combustor Flowfield
Recent emphasis on fuel economy and p o l l u t a n t suppression has sparked a renewed i n t e r e s t i n gas A typical axisymturbine combustor analysis metric gas t u r b i n e engine combustor i s shown i n Figure 1. Flowfields w i t h i n such combustors t y p i c a l l y have a rapid expansion and strong swirl imparted t o t h e incoming a i r , which r e s u l t i n corner and central reci rcul a t i on regions. The swi rl i ng, reci rcul a t i ng, turbulent f l ows w i t h i n combustors present one of t h e more d i f f i c u l t f l u i d dynamic problems t o analyze. Thi s compl exi t y i s i ncreased many f o l d by t h e processes of combustion and heat t r a n s f e r w i t h i n t h e flowfield. Despite the comp l e x i t y of combustor flows, si n i f i c a n t progress i s being made i n thei r analysis.
.
9
t
** t tt
Research Engineer, Member A I A A Senior Research S c i e n t i s t , Member AIAA Graduate Student, S t u d e n t Member AIAA Professor, Associate Fellow AIAA
Figure 1.
49
Axisymmetric Combustor o f a Gas Turbine Engine
have been ~ u g g e s t e d . l l - ' ~ One o f t h e most w i d e l y used i n s t r u m e n t s t o o b t a i n t u r b u l e n c e q u a n t i t i e s i s t h e h o t - w i r e anemometer, t h e most common o f which i s a s i n g l e h o t - w i r e . When used a t a s i n g l e o r i e n t a t i o n and i n a two-dimensional f l o w w i t h a predominant f l o w d i r e c t i o n , a s i n g l e hot-Wire can measure t h e streamwi se components o f t h e time-mean v e l o c i ty and t h e root-mean-square v e l o c i ty flUCtuation a t a particular location i n the flowfield. A t w o - w i r e probe can be used t o determi ne t h e time-mean v e l o c i t i e s , s t r e a n w i s e and c r o s s stream t u r b u l e n c e i n t e n s i t i e s , and t h e c r o s s c o r r e l a t i o n between t h e two components o f t h e v e l o c i t y fluCt u a t i ons 1 4 - 1 5
The p r e s e n t paper r e p o r t s on research which i s p a r t of an e x t e n s i v e experimental and computat i o n a l study o f gas t u r b i n e f l o w f i e l d s i n t h e absence o f combustion. F i g u r e 2 shows t h e charact e r i s t i c s o f t h e s i m p l i f i e d f l o w f i e l d being investigated. Flow e n t e r s through a j e t o f diameter d i n t o a tube o f diameter D, a f t e r b e i n g expanded through an a n g l e a. Before e n t e r i n g t h e tube, t h e f l o w may be s w i r l e d b y a s w i r l e r l o c a t e d upstream of t h e i n l e t plane. Shown s c h e m a t i c a l l y a r e t h e c o r n e r r e c i r c u l a t i o n zone (CRZ) and t h e c e n t r a l t o r o i d a l r e c i r c u l a t i o n zone (CTRZ) which a r e t y p i c a l l y p r e s e n t i n these flows.
WlRL VANE ANGLE Y L E T TKE kin
Hot-wire measurements i n complex three-dimens i o n a l f l o w f i e l d s a r e c o n s i d e r a b l y more d i f f i c u l t t h a n i n one- o r two-dimensional f l o w f i e l d s i n which t h e mean f l o w i s predominantly i n one d i r e c tion. To measure t h e t h r e e v e l o c i t i e s and t h e i r corresponding f l u c t u a t i n g components i n a t h r e e dimensional f l o w f i e l d such as encountered in COW b u s t o r s i m u l a t o r s , t h e r e a r e two methods t h a t can b e employed a t a p o i n t i n t h e f l o w f i e l d :
9
1) A t h r e e - w i r e probe used w i t h a single orientation.
2)
F i g u r e 2.
The three-wi r e probe technique p e r m i t s t h e necessary simultaneous measurements from which t h r e e instantaneous v e l o c i t y components can be determined. The a p p r o p r i a t e s i g n a l p r o c e s s i n g can produce e s t i m a t e s o f mean v e l o c i t y components and rlormal and shear t u r b u l e n t s t r e s s e s (such as - -_ u ' and u ' v ' ) .
I d e a l i z e d Combustor F l o w f i e l d
*
The s w i r l i n g c o n f i n e d j e t f l o w f i e l d shown i s 1 F i g u r e 1 i s b e i n g i n v e s t i g a t e d a t Oklahoma S t a t e U n i v e r s i t y and a t Dynamics Technology, w i t h v a r i ous methods of approach. A n a l y t i c a l l y , a computer program (STARPIC) has been assembled which i s designed s p e c i f i c a l l y t o c a l c u l a t e t h e s w i r l i n g confined j e t flowfields.* Experimentally, a series o f f l o w v i sua1 iz a t i on experiments coup1 ed w i t h 5h o l e p i t o t probe measurements have been used t o c h a r a c t e r i z e t h e time-mean f l o w f i e l d . 3 Hot-wire measurements o f t h e t u r b u l e n c e p r o p e r t i e s a r e a1 so b e i n g conducted. T h i s paper r e p o r t s on t h e i n i t i a l r e s u l t s o f t h e h o t - w i r e measurements i n t h e c o n f i n e d j e t f l o w f i e l d.
The three-hot-wi r e probe technique i s s i g n i f i c a n t l y more complex than t h e s i n g l e w i r e m u l t i o r i e n t a t i o n techniques. A mu1t i - d i m e n s i o n a l probe d r i v e i s r e q u i r e d t o o r i e n t t h e probe i n a p p r o x i m a t e l y t h e mean f l o w d i r e c t i o n . Also, s o p h i s t i c a t e d s i g n a l processing e l e c t r o n i c s i s r e q u i r e d t o handle t h e t h r e e instantaneous h o t - w i r e voltages. F i n a l l y , t h e t h r e e - w i r e probe t y p i c a l l y has l e s s s p a t i a l r e s o l u t i o n i n comparison w i t h a s i n g l e w i r e probe.
Several s t u d i e s on time-mean f l o w f i e l d s o f t h e t y p e j u s t described have been c a r r i e d o u t u s i n various turbulence measuring te~hniques.~-l% U n f o r t u n a t e l y , most o f t h e techniques used do n o t g i v e complete and d e t a i l e d i n f o r m a t i o n about t h e f l o w i n terms o f a l l i t s time-mean and t u r b u l e n c e quantities. I n a d d i t i o n , no experiments have been performed on t h e s p e c i f i c geometry o f t h e p r e s e n t s t u d y i n t h e presence o f i n l e t s w i r l . To develop f u r t h e r t h e f l o w f i e l d computational techniques, in c l u d i ng t h e t u r b u l e n c e model ing, t h e r e is a s t r o n g need t o o b t a i n experimental e s t i m a t e s o f t h e t u r b u l e n c e and mean f l o w q u a n t i t i e s i n such flows.
1.2
A sing1 e- o r doubl e-wi r e probe used w i t h mu1 t i - o r i e n t a t i o n .
The Turbulence Measurement Problem
Turbulence measurement i n a complex f l o w f i e l d has always been a c o m p l i c a t e d problem encountered by engineers. I n t h e p a s t , t u r b u l e n c e phenomena have been discussed by v a r i o u s a u t h o r s i n d e t a i 1 and v a r i o u s methods o f t u r b u l e n c e measurements
50
Multi-orientation o f a single hot-wire i s a novel way t o measure t h e t h r e e components o f a v e l o c i t y v e c t o r and t h e i r f l u c t u a t i n g components. A method devised by Dvorak and Syred16 uses a s i n g l e normal h o t - w i r e o r i e n t e d a t t h r e e d i f f e r e n t P o s i t i o n s such t h a t t h e c e n t e r one i s separated b y 45 degrees from t h e o t h e r two. The v e l o c i t y vector a t a l o c a t i o n i s related t o the three orthogonal components u s i n g p i t c h and yaw f a c t o r s as defined by J 0 r g e n ~ e n . l ~ The data a r e o b t a i n e d i n t h e form o f mean and root-mean-square v o l t a g e s a t each o r i e n t a t i o n . However, t h e measurements done w i t h a s i n g l e w i r e do n o t supply a l l t h e i n f o r m a t i on needed t o o b t a i n t h e t u r b u l e n c e quantities. Therefore, i n a d d i t i o n t o a s i n g l e w i r e , Dvorak and Syred used a c r o s s - w i r e probe t o o b t a i n t h e covariances between t h e v o l t a g e s o b t a i n e d a t adjacent hot-wire orientations.
K i ng18 m o d i f i e d t h e technique developed by Dvorak and Syred. H i s method c a l l s f o r a normal h o t - w i r e t o be o r i e n t e d through s i x d i f f e r e n t pos i t i o n s , each o r i e n t a t i o n separated by 30 degrees from t h e a d j a c e n t one. Mean and root-mean-square
v o l t a g e s a r e measured a t each o r i e n t a t i o n . The d a t a r e d u c t i o n i s performed u s i n g some assumptions regarding the s t a t i s t i c a l nature o f turbulence, making i t p o s s i b l e t o s o l v e f o r t h e t h r e e t i m e mean v e l o c i t i e s , t h e t h r e e normal t u r b u l e n t s t r e s s e s , and t h e t h r e e t u r b u l e n t shear s t r e s s e s . 1.3
The axisymmetric n o z z l e was designed t o p r o duce a mlnimum adverse p r e s s u r e g r a d i e n t on t h e boundary 1ayer t o avoi d f l o w unsteadiness assoc i a t e d w i t h l o c a l s e p a r a t i o n regions. The a r e a r a t i o o f the cross sections o f t h e turbulence management s e c t i o n t o t h a t o f t h e n o z z l e t h r o a t i s approximately 22.5. The diameter, d, o f t h e n o z z l e t h r o a t i s approximately 15 cm.
The Scope o f t h e Present Study
I n t h e p r e s e n t study, t h e s l x - o r i e n t a t i o n s i n g l e normal h o t - w i r e technique i s b e i n g employed t o o b t a i n t h e t u r b u l e n c e q u a n t i t i e s in t h e combust o r simulator confined j e t flowfield. Measurements have been c a r r i e d o u t f o r b o t h s w i r l i n g and n o n s w i r l i n g flow w i t h expansion angles o f 90 degrees (sudden expansion) and 45 degrees ( g r a d u a l Only t h e 90 degree a n g l e data a r e expansion). presented here and t h e Reynolds number o f t h e i n l e t f l o w i S = 5 x LO4 which i s comparable w i t h a i r c r a f t combustor f l o w s (a1 though o u r experiments a r e performed i n n o n r e a c t i n g f l o w s ) . The d a t a r e d u c t i o n procedure extends K i n g ' s technique t o o b t a i n t u r b u l e n t shear and normal s t r e s s e s u s i n g s i x b a s i c response equations r e p r e s e n t i n g t h e s i x o r i e n t a t i o n s o f a normal hot-wi r e p o s i t i o n e d in the flowfield. C e r t a i n m o d i f i c a t i o n s a r e made i n t h e procedure t o c a l c u l a t e covariances which a r e an i n t e g r a l p a r t o f t h e d a t a r e d u c t i o n procedure. An u n c e r t a i n t y a n a l y s i s is performed on t h e technique which r e v e a l s t h e s e n s i t i v i t y o f t h i s techn i q u e t o v a r i o u s i n p u t parameters discussed i n t h e l a t e r p a r t s o f t h i s paper. Some o f t h e t u r b u l e n c e q u a n t i t i e s o b t a i n e d a r e compared w i t h measurements performed by Chaturvedi u s i n g a crossed-wi r e probe i n a corresponding f l o w s i t u a t i o n .
2. 2.1
The t e s t s e c t i o n i s composed o f a s w i r l e r ( o p t i o n a l ) , an expansion b l o c k , and a l o n g p l e x i g l a s s tube. The expansion block, a t t a c h e d a f t e r t h e s w i r l e r , i s a 30 cm diameter a n n u l a r d i s k of wood. A t present, t h e r e a r e t h r e e expansion blocks, and t h e a p p r o p r i a t e c h o i c e g i v e s a = 90, 70, o r 45 degrees. The f l o w i s expanded i n t o a p l e x i g l a s s t u b e o f diameter, D, o f 30 cm, t h u s g i v i n g a diameter expansion r a t i o (D/d) o f 2. The t e s t chamber has no f i l m c o o l i n g h o l e s o r d i l u t i o n a i r holes, and t h e chamber w a l l o f t h e t e s t sect i o n i s a c o n s t a n t diameter p i p e .
2.2
p e anemometer used f o r t h e p r e s e n t study i s D I S A t y p e 55M01, CTA standard b r i d g e . A normal h o t - w i r e probe, D I S A t y p e 55P01, i s used i n t h e experiments. T h i s probe has two prongs s e t approximately 3 mm a p a r t which s u p p o r t a 5 pIn diameter w i r e which i s g o l d p l a t e d n e a r t h e prongs t o reduce end e f f e c t s and s t r e n g t h e n t h e w i r e . The mean v o l t a g e i s measured w i t h a Hickok D i g i t a l Systems, Model DP100, i n t e g r a t i n g v o l tmeter and t h e root-mean-square v o l t a g e f l u c t u a t i o n i s measured u s i n g a H e w l e t t Packard, Model 400 HR, AC v o l tmeter. The h o t - w i r e i s supported i n t h e f a c i l i t y by a t r a v e r s i ng mechani sm shown schemati c a l l y in F i g u r e 4. It c o n s i s t s o f a base t h a t i s m o d i f i e d t o mount on t h e p l e x i g l a s s t u b e o f t h e t e s t s e c t i o n a t v a r i o u s a x i a l l o c a t i o n s . The h o t - w i r e probe i s i n s e r t e d i n t o t h e t u b e through a r o t a r y v e r n i e r and t h e base. The r o t a r y v e r n i e r i s a t t a c h e d t o a s l i d e which can t r a v e r s e across t h e f l o w chamber. Thus, i t i s p o s s i b l e f o r t h e probe t o be t r a v e r s e d t o any r a d i a l l o c a t i o n a t s e l e c t e d downstream l o c a t i o n s i n t h e f l o w f i e l d and t o be r o t a t e d through 180 degrees.
Experimental F a c i l i t y and I n s t r u m e n t a t i o n
Idealized Flowfield
The f a c i l i t y , designed and b u i l t a t Oklahoma State U n i v e r s i t y , i s a s i m u l a t i o n o f a t y p i c a l axisyrnmetric combustion chamber o f a gas t u r b i n e engine shown i n F i g u r e 1. The schematic o f t h e t e s t f a c i l i t y with the idealized f l o w f i e l d i s Anbient a i r e n t e r s t h e lowshorrn i n F i g u r e 3. speed wind t u n n e l through a foam a i r f i l t e r . The a i r t h e n f l o w s through an a x i a l f l o w f a n d r i v e n b y a 5 h.p. v a r i d r i v e motor. Thus, t h e f l o w r a t e can be v a r i e d f o r d i f f e r e n t t e s t c o n d i t i o n s . The f l o w passes through a t u r b u l e n c e management s e c t i o n which has two fine-mesh screens, a 12.7 cm l e n g t h o f packed straws, and f i v e more fine-mesh screens.
fiX)-MESH
Hot-Wi r e I n s t r u m e n t a t i o n
Traverse U n i t With Prcbs
SCREENS
HONEYCOMBJ
F i g u r e 3.
Schematic o f t h e Experimenta'l F a c i 1ity
Figure 4.
* 51
Hot-wire Probe Mounted on the Test k t ion
Provided f o r i n f o r m a t i o n and n o t n e c e s s a r i l y a p r o d u c t endorsement.
2.3
C a l i b r a t i o n Nozzle
The h o t - w i r e i s c a l i b r a t e d i n a small a i r j e t . The f a c i l i t y c o n s i s t s o f a compressed a i r l i n e , which d e l i v e r s t h e d e s i r e d f l o w r a t e through a small pressure r e g u l a t o r and a F i s h e r and P o r t e r Model 10A1735A rotameter. The j e t housing cons i s t s of an e f f e c t i v e f l o w management s e c t i o n f o l lowed by a contoured n o z z l e w i t h a 3.5 cm d i a m e t e r throat. A r o t a r y t a b l e i s used t o h o l d t h e probe w h i l e i t i s being c a l i b r a t e d i n t h r e e d i f f e r e n t orientations.
3. 3.1
where G and K a r e t h e p i t c h and Yaw defined by J ~ r g e n s e n ' ~ t o be: N
G =
N
,
v ( u and wZ0) and
factors
and
GO) (3)
H o t - w i r e Data A n a l y s i b which a r e e v a l u a t e d from t h e t h r e e c a l i b r a t i o n curves ( F i g u r e 5) f o r a c o n s t a n t v a l u e o f E2. E q u a t i o n (3) shows t h a t J h e p i t c h and yaw f a c t o r s a r e c a l c u l a t e d with t h e v component i = 2 i n equat i o n (1) o f t h e e f f e c t i v e c o o l i n g v e l o c i t y as t h e reference. Therefore, t h e c a l i b r a t i o n c o n s t a n t s used-in e q u a t i o n ( 1 ) a r e t h e c o e f f i c i e n t s i n t h e E vs. v c a l i b r a t i o n o f F i g u r e 5., i.e., i n a general f 1o w f i e l d:
Hot-Wire Response Equations
The six-orientation hot-wire technique r e q u i r e s a s i n g l e , s t r a i g h t , h o t - w i r e t o be c a l i brated. f o r t h r e e d i f f e r e n t f l o w d i r e c t i o n s i n o r d e r t o determi ne t h e d i r e c t i onal s e n s i t i v i t y o f such a probe. The t h r e e d i r e c t i o n s and t h r e e t y p i c a l c a l i b r a t i o n curves a r e shown i n F i g u r e 5. I n these r e 1a t i o n s , t i l d e s s i g n i f y components o f t h e instantaneous v e l o c i t y v e c t o r i n c o o r d i n a t e s on t h e probe. Each of t h e t h r e e c a l i b r a t i o n curves i s o b t a i n e d w i t h z e r o v e l o c i t y i n t h e o t h e r two d i r e c t i o n s . . The c a l i b r a t i o n c u r v e s demons t r a t e t h a t t h e h o t - w i r e i s most e f f i c i e n t u c o o l e d when t h e f l o w i s i n t h e d i r e c t i o n o f t h e u component, whereas, t h e w i r e i s most i n e f f i c i e n t l y c o o l e d when t h e f l o w i s i n t h e d i r e c t i o n o f t h e w component. Each of t h e c a l i b r a t i o n c u r v e s f o l l o w s a second order, l e a s t square f i t o f t h e form:
+ B2 Z lI2 + c2
E2 =
z
w i t h Z as g i v e n i n Equation (2) above. F i g u r e 6 shows t h e p i t c h and yaw f a c t o r s as a f u n c t i o n o f h o t - w i r e v o l tage determined from t h e Both f a c t o r s v a r y c a l i b r a t i o n c u r v e o f F i g u r e 5. w i t h h o t - w i r e voltage, b u t t h e yaw f a c t o r i s f a r more s e n s i t i v e . The sensi t i v i t y a n a l y s i s d i scussed i n t h e n e x t s e c t i o n demonstrates t h a t u n c e r t a i n t i e s associated w i t h t h e varying p i t c h and yaw f a c t o r s do n o t s e r i o u s l y a f f e c t t h e accuracy o f t h e e s t i m a t e d f l o w q u a n t i t i e s .
(1) which i s an e x t e n s i o n of t h e commonly used K i n g ' s law. I n t h i s equation, -$, B-, and Ci are calLbra_tion c g n s t a n t s and ui can l a k e on a v a l u e o f u, v, and w f o r t h e t h r e e c a l i b r a t i o n curves, respectively
.
5 0
-
N
u
E* =
4.0
- - L E 2
8.0096 + 3.9493
= 7.6016
i?I2- 0.0821
i 3.5880
?lf20.0842
E
lvolrsl EZ = 8.4111 + 1.3554 i?I2 0.0990 - - . . -
30
Z 30
31
32
HOT-WIRE
20
20
F i g u r e 5.
6 0
60
80 100 VELOCITY
120
140
160
3 3 VOLTAGE
I&
3s
EIVMISI
180
F i g u r e 6.
P i t c h and Yaw F a c t o r s P1 o t t e d Against H o t 4 r e Mean E f f e c t i v e Vol t a g e
The Three-Di r e c t i o n a l H o t - w i r e
Cali b r a t i on
To c a r r y o u t measurements i n t h e c o n f i n e d j e t f l o w f i e l d , t h e w i r e i s a l i g n e d i n t h e f l o w i n such a way t h a t i n t h e f i r s t o r i e n t a t i o n , t h e w i r e i s normal t o t h e f l o w i n t h e a x i a l d i r e c t i o n and t h e probe c o o r d i n a t e s c o i n c i de w i t h t h e c o o r d i n a t e s o f
When t h e w i r e i s p l a c e d i n a t h r e e dimensional flowfield, the e f f e c t i v e cooling v e l o c i t y experienced by t h e h o t - w i r e is:
52
t h e experimental f a c i l i t y . Thus, t h e s i x equat i o n s f o r t h e instantaneous c o o l i n g v e l o c i t i e s a t t h e s i x o r i e n t a t i o n s , as g i v e n by K i n g L 0 are:
Zf
+
= v2
G2u2
probe. Therefore, Equations ( 5 ) must be expressed i n terms o f mean and root-mean-square values. Equation (1) can be w r i t t e n as:
+ K2w2
3 = v2 + G2(u cos 30°+
w s i n 3Ool2
+ K2(w cos 30'-
u sin
The above e q u a t i o n i s i n terms of i n s t a n t a n e o u s v e l o c i t y Zi and instantaneous v o l t a g e Ei. In o r d e r t o o b t a i n an expression f o r time-mean v e l o c i t y as a f u n c t i o n o f time-mean voltage, a T a y l o r s e r i e s expansion of Equation (6) can be c a r r i e d o u t as follows:
3Ool2
25 = v 2 + G2(u cos 60°+ w s i n 6Ool2 + K2(w cos 6 0 ' -
u s i n 6Ool2
-
where 4 = Zi(Ei).
The T a y l o r s e r i e s i s t r u n c a t e d a f t e r second o r d e r terms assuming t h e h i g h e r o r d e r terms t o be r e l a t i v e l y small. Time a v e r a g i n g b o t h s i d e s Clf t h e above e q u a t i o n and employing t h e f a c t t h a t E'=O, yields:
262 = v 2 + G2(w s i n 150°+ u cos 15Ool2
+ K2(u s i n 150'-
w cos 15Ool2
S o l v i n g simultaneously any t h r e e a d j a c e n t equati ons p r o v i d e expressions f o r t h e instantaneous values of t h e t h r e e v e l o c i t y components, u, w, and v i n terms o f t h e e q u i v a l e n t c o o l i n g v e l o c i t i e s (Zls Z2 and Z3 f o r example, when t h e f i r s t t h r e e equations a r e chosen). Thus, t h e general form o f t h e instantaneous v e l o c i t y components i s g i v e n as:
To o b t a i n
2;2 = a*
Hinzelg i s :
, the
r e l a t i o n s h i p as g i v e n by
'i
-
Z i 2 = uz
= Expec E Z i l
i Using
W =
802
[ { -A0 + (A02 + 3-)
1 ''
}
-
(5)
I
Equation Set
BO
A0
-zy
(z;
2. 3 , 4
0; - "1
3, 4.
5
4. 5 . 6
(2;
- 22:
+
+ 32;
- 2;)
(-Zz + 3Z2
- 2 Z4z )
(-222
2
3
(2;
2;)
(-ZZ + 2 2 )
b a s i s , Expec [ Z i l
I n a 3-dimensional f l o w , i t i s u s u a l l y d e s i r a b l e t o o b t a i n t h e mean and v a r i a n c e f o r t h e i n d i v i dual v e l o c i t y components i n a x i a l , azimuthal and r a d i a l d i r e c t i o n s , and a l s o t h e i r c r o s s c o r relations. The procedure t o o b t a i n t h e mean and v a r i a n c e of t h e i n d i v i d u a l v e l o c i t y components i s t h e same as f o r t h e e f f e c t i v e c o o l i n g v e l o c i t i e s except t h a t u, w and v a r e f u n c t i o n s o f t h r e e random v a r i a b l e s and t h e r e a r e e x t r a terms i n t h e T a y l o r expansion t o account f o r t h e covariances o f the cooling velocities. Thus, t h e a x i a l mean v e l o c i t y component as g i v e n by Dvorak and Syred,16 and K i n g l a i s :
BO, and CO i n Various Equation *Sets
1. 2, 3
the
(9)
Thus, Equations (8) and (10) g i v e t h e mean and v a r i a n c e of e f f e c t i v e c o o l i n g v e l o c i t i e s i n terms of t h e mean and v a r i a n c e of t h e a p p r o p r i a t e v o l tages.
TABLE 1
ChOICe
as
.
( ExpecCZi 1) can be e v a l u a t e d and s u b s t i t u t e d i n t o Equation (8) t o g e t :
The v a l u e s o f AO, BO and CO depend on t h e s e t o f t h e t h r e e equations chosen and a r e g i v e n i n Table 1 f o r a p p r o p r i a t e e q u a t i o n s e t s .
P.0.R
(8)
CZi1)2
and
,- .. ,
Values o f AO.
Equation
- (Expec
(-22'
(2;
- z;
+
z;)
- 2;)
+ 32:
- 2;)
Yowever, these equations cannot be d i r e c t l y used because i t i s i m p o s s i b l e t o o b t a f n Z1, Z2 and Z3 a t a s i n g l e i n s t a n t i n t i m e w i t h a s i n g l e w i r e
where KZ.Z 1 j
i s t h e covariance o f t h e c o o l i n g velo-
c i t i e s Zi and Z j and i s d e f i n e d as:
53
(Zi-Ti)(Z.-7.) J J
dt
(12)
w
I d e n t i c a l expressions f o r and can a l s o be o b t a i n e d i n terms o f W and V, r e s p e c t i v e l y . D e r i v a t i v e s of t h e form a2U/aZiaZ. a r e determined J a n a l y t i c a l l y from e q u a t i o n s ( 5 ) and Table 1.
t i o n s would b e such t h a t t h e i r c o n t r i b u t i o n t o t h e c o o l i n g o f t h e w i r e would be r e l a t e d by t h e c o s i n e o f t h e a n g l e between t h e wires. T h i s assumption l e a d s t o t h e f o l l o w i n g t h r e e values o f t h e c o r r e l a t i o n coefficients.
=
COS
30 = 0.9
QPZQ
Also, t h e normal s t r e s s e s a r e g i v e n as:
(16)
=
COS
30 = 0.9
'$ZR
To r e l a t e y z
w i t h yZPmZQandyZQZR, K i n g i n t r o P R duced t h e f o l l owing r e 1a t 1 onshi p :
-
w i t h s i m i l a r expressions f o r W ' 2 a n d v S 2
where q i s g i v e n a v a l u e o f 0.8. becomes :
.
= (0.8)(0.9)(0.9)
u'vl =
au av
1 q3.q
i=l
+
1
ii#jJ
1 j
The p r e s e n t study, however, uses Equations (16) and (18) d u r i n g t h e e n t i r e data r e d u c t i o n . The reason f o r t h i s i s c o n t a i n e d in t h e r e s u l t s o f t h e s e n s i t i v i t y a n a l y s i s presented i n t h e n e x t Thi s a n a l y s i s demonstrated t h a t t h e r e is section. n o t s i g n i f i c a n t e r r o r m a g n i f i c a t i o n i n t h e data r e d u c t i o n due t o t h e c o r r e l a t i on terms.
-
Expressions f o r u'w' and v'w' can a l s o be o b t a i n e d i n a s i m i l a r manner and a r e g i v e n i n Reference 22.
3.2
Cal c u l a t i on o f Covariances
Dvorak and Syred16 used a D I S A t i m e c o r r e l a t o r (55A06) t o f i n d t h e c o r r e l a t i o n c o e f f i c i e n t s between t h e v e l o c i t y f l u c t u a t i o n s i n t h e t h r e e directions. K i n g ' s approach i s t o u s e t h e i n f o r m a t i o n o b t a i n e d by a l l s i x o r i e n t a t i o n s and d e v i s e a mathematical procedure t o c a l c u l a t e t h e c o v a r i ances. Covariances a r e c a l c u l a t e d u s i n g t h e r e l a t i o n ship: KZiZj
= YZiZj
.;.I J
1/2
(15)
where y z e Z i s t h e c o r r e l a t i o n c o e f f i c i e n t between 1
j
t h e two c o o l i n g v e l o c i t i e s Zi
(18)
The t h r e e c o v a r i a n c e s a r e t h e n o b t a i n e d b y s u b s t i t u t i ng t h e corresponding Val ues o f t h e c o r r e l a t i on c o e f f i c i e n t s i n t o Equation (15).
i. qq au av z.z
4.
-
= 0.65
P R
%ZR
F i n a l l y , t h e expressions f o r shear s t r e s s e s as g i v e n by Dvorak and Syred16 a r e o f t h e form:
-
Hence y z
and Zj.
By d e f i n i -
t i o n , t h e a b s o l u t e v a l u e o f t h e c o r r e l a t i o n coefi s always l e s s t h a n 1. f i c i e n t yz i j
K i ng18 made c e r t a i n assumptions t o c a l c u l a t e t h e covariances. However, he observed t h a t a t times the calculated value o f t h e c o r r e l a t i o n c o e f f i c i e n t i s g r e a t e r t h a n one a t which i n s t a n c e h e assigned p r e v i o u s l y f i x e d v a l u e s t o t h e c o r r e l a t i o n coefficients. He argued t h a t i f two Wires a r e separated by an a n g l e o f 30 degrees, t h e f l u c :..dating s i g n a l s from t h e w i r e s a t t h e two lOCa-
R e s u l t s o f Hot-Wi r e Measurements
The s i x - o r i e n t a t i o n h o t - w i r e t e c h n i q u e was employed t o measure t h e t u r b u l e n c e q u a n t i t i e s f o r s w i r l i n g and n o n - s w i r l i n g f l o w c o n d i t i o n s i n t h e confined j e t f a c i l i t y described e a r l i e r . Also, an e x t e n s i v e s e n s i t i v i t y a n a l y s i s o f t h e d a t a reduct i o n was conducted t o a s s i s t t h e e s t i m a t i o n o f t h e uncertainties i n the output quantities. 4.1
U n c e r t a i n t y Analysis
The u n c e r t a i n t y a n a l y s i s in c l udes a determination o f the s e n s i t i v i t y o f t h e s i x - o r i e n t a t i o n h o t - w i r e d a t a r e d u c t i o n t o v a r i o u s i n p u t parame t e r s which have m a j o r c o n t r i b u t i o n s i n t h e response equations. P i t c h and yaw f a c t o r s ( G and K) a r e used i n t h e response equations d e s c r i b e d i n S e c t i o n 3 i n o r d e r t o account f o r t h e d i r e c t i o n a l s e n s i t i v i t y o f t h e s i n g l e h o t - w i r e probe. Figure 6 shows t h e p i t c h and t h e yaw f a c t o r s p l o t t e d a g a i n s t t h e h o t - w i r e mean e f f e c t i v e voltage. Both t h e p i t c h and yaw f a c t o r s a r e f u n c t i o n s o f t h e h o t - w i r e mean e f f e c t i v e voltage, b u t t h e yaw f a c t o r i s f a r more s e n s i t i v e . A one p e r c e n t increase i n t h e h o t - w i r e v o l t a g e reduces t h e p i t c h f a c t o r by 1.3 p e r c e n t and t h e yaw f a c t o r b y 56 percent. F o r t h e p r e s e n t study, t h e v a l u e s o f these f a c t o r s a r e chosen a t an average hotwir e vol tage experienced in t h e f l o w f i e l d. T h i s was a p p r o p r i a t e s i n c e t h e o u t p u t q u a n t i t i e s ( u , u h s , u ' v ' , e t c ) a r e o n l y weakly dependent on
-
t h e v a l u e o f K. T h i s can be seen i n t h e d a t a o f Table 2 which s u m a r i z e s a s e n s i t i v i t y a n a l y s i s performed on t h e data r e d u c t i o n program a t a
54
t i o n s Of d a t a from adjacent w i r e o r i e n t a t i o n s . One measure o f t h e u n c e r t a i n t y i n t h e o u t p u t quant i t i e s can be obtained by examining t h e Variance i n these q u a n t i t i e s c a l c u l a t e d from t h e s i x d i f f e r e n t p o s i t i o n combinations. Table 3 shows these comparison data,for a representative p o s i t i o n i n t h e flowfield. F o r each o f t h e o u t p u t q u a n t i -
r e p r e s e n t a t i v e posi ti on in t h e f l owfi e l d. Table 2 demonstrates t h e percen: change i n t h e o u t p u t q u a n t i t i e s f o r a 1 p e r c e n t change i n most o f t h e important i n p u t quantities. F o r t h e data presented in t h i s tab1 e on1 y quanti t i e s c a l cul ated from -
Z
1
a r e used,
flow
f o r simplicity.
-
Z6
combination Z5,
t h e probe o r i e n t a t i o n
and
t i e s , an ensemble mean 2 i s c a l c u l a t e d t o g e t h e r w i t h a r l ensemble standard d e v i a t i o n u* The r a t i o ofx i s a measure o f t h e u n c e r t a i n t y i n t h e In t h i s t a b l e , NR stands f o r output quantity. ' n o t resolved', a problem t h a t occurs when t h e d a t a r e d u c t i o n program attempts t o t a k e t h e square r o o t of a n e g a t i v e q u a n t i t y . I n a d d i t i o n , quant i t i e s which a r e more than t h r e e standard deviat i o n s o u t s i d e t h e mean a r e r e j e c t e d as s p u r i o u s calculations.
In this swirling
Z6 was t h e minimum o f t h e 6 mean e f f e c t i v e
cooling velocities. King1* has argued t h a t t h e probe o r i e n t a t i o n combination approximately cent e r e d around t h e lninimum e f f e c t i v e c o o l i n g Vel+ c i t y produces more accurate estimates of c a l c u 1a t e d t u r b u l ence q u a n t i ti es, than do t h e o t h e r o r i e n t a t i o n combinations
.
2 TIBLE
3 TABLE
Elfect of Input Paratneterr on Turbulence (hrsntitier % CHlWGE
C W l G E IN PARAKTER
L
_ "
V
-
W
---%In* 'ran --2.06 t2.75
L a t t e r hang the Turbulence (hrantlties when slved by S i x O I fferent Combinatlonr
IN TII(E-MElW WO TURBULEHCE (1UUITITlES
_
- U'"'
V,"'
+6.0
51.43
+11.94
USV'
Vhr
NROULENCE
oumrm
1.2.3 'UROUL
r y so - -
116.10
+0.66
t4.98
*I
42.19
-2.21
+11.49
-6.50
r2.42
12.88
+4.0
14.29
r7.86
0.21
+l
-10.59
-0.36
-8.50
-1.88
r7.07
-9.54
-6.0
54.29
-11.91,
0.10
+1
+0.27
-0.06
+0.14
+1.63
'0.13
t0.39
+2.0
+2.86
*1.1¶
0.40
+1
t0.05
0.0
+0.14
0.0
-0.13
+1.57
0.0
0.0
+1.49
tl
-0.16
rO.18
-0.14
-0.63
+LO3
-1.08
-2.0
-5.11
0.0
+I
-1.02
0.0
-1.01
-1.0
0.0
-0.98
-2.0
-2.06
-1.49
+I
+0.01
-0.04
+0.01
+om
0.0
t0.01
0.0
0.0
0.0
NR'
NR*
+1
t0.05
0.0
+0.14
-0.13
-0.13
-1.71
0.0
-2.86
r1.49
0.002
o.oia
+I
tO.21
+0.01
+0.05
-1.6:
+0.13
-0.i9
0.0
-5.71
+1.49
*I
-0.16
+0.18
-0.08
+&I?
0.0
4.0.69
L2.0
t2.86
0.0
---
4.5.6
5.6.1
6.1.2
-
--
K-AN
VlATlON
X
- =--- -
s
=
01; 1 3
0.21
0.21
0.19
0.18
0.20
0.01
0.06
0.11
0.17
0.17
0.17
0.14
0.04
0.26
0.39
0.39
0.38
0.37
0.40
0.39
0.01
0.03
0.14
0.14
0.14
0.07
0.08
0.08
0.11
0.03
0.31
0.06
0.11
0.11
0.08
(1.08
0.09
0.09
0.02
0.23
0.13
0.16
0.10
0.11
0.10
0.12
0.12
0.02
0.20
NU*
0.005
0.1104
0.00
0.004
0.62
0.004
0.004
0.0ot
0.00
0.003
0.72
0.002
0.20
WrnD
NU*
0.012 0.002
NR*
--
---- - - 0.003
0.003
0.007
0.001
0.00
0.002
0.58
Hot Resolved
The d a t a i n Tables 2 and 3 can be used t o proiuce estimates i n t h e u n c e r t a i n t i e s o f t h e c a l c u lated turbulence quantities. The data suggest t h a t u n c e r t a i n t i e s on t h e o r d e r o f 5 p e r c e n t a r e t o be expected i n t h e mean v e l o c i t y component estimates. Normal t u r b u l e n t s t r e s s estimates (ulrms, etc.) have u n c e r t a i n t i e s on t h e o r d e r o f 20 t o 30 p e r c e n t and t u r b u l e n t shear s t r e s s e s t i mates a r e s i g n i f i c a n t l y higher, a1 though most of t h i s i s a consequence o f t a k i n g a p r o d u c t o f terms such as u' and v '
It i s n o t unusual i n h o t - w i r e anemometry t o have t h e mean v e l o c i t y components and t u r b u l e n c e q u a n t i t i e s t h a t a r e measured, be q u i t e s e n s i t i v e t o changes i n mean h o t - w i r e voltage. For i n t e r p r e t i v e purposes, t h e mean h o t - w i r e v o l t a g e v a r i a t i o n s can be t h o u g h t o f as b e i n g e i t h e r e r r o r s i n measuring t h e mean voltage, o r s h i f t s i n t h e i n d i v i d u a l w i r e c a l i b r a t i o n s due t o contamination o r s t r a i n 'aging' o f t h e wire. The data of Table 2 demonstrate t h a t t h e most s e r i o u s i n a c c u r a c i e s i n t h e measurement and d a t a r e d u c t i o n technique w i l l be i n t h e estimates o f t u r b u l e n t shear stresses,
.
These u n c e r t a i n t y estimates a r e considered t o be somewhat conservatlve. More a c c u r a t e estimates a r e q u i t e d i f f i c u l t t o o b t a i n because, t o our knowledge, s i m i l a r measurements have n o t been p e r formed with any o t h e r i n s t r u m e n t a t i o n system i n t h i s geometry f l o w f i e l d . Also, comparisons of several r e p r e s e n t a t i v e p o i n t s w i t h independent measurements suggest t h a t t h e ensemble averages estimates a r e t y p i c a l l y i n c l o s e r agreement than are s e l e c t e d s e t s o f t h r e e o r i e n t a t i o n s . Theref o r e , a l l t u r b u l e n c e estimates presented i n t h i s paper a r e c a l c u l a t e d from ensemble averages o f s i x groups of t h r e e a d j a c e n t w i r e o r i e n t a t i o n s . Any data n o t r e s o l v e d a r e n o t i n c l u d e d i n t h i s averaging. T h i s approach represents a departure from t h e technique developed by King1* who t y p i c a l l y
-
t h e most i n a c c u r a t e o u t p u t term b e i n g u'w'
3.4.5
2.34
+I
15.75
E
.E QUUF
.
As a l r e a d y discussed i n Section 3, an ad hoe assumption i s made r e g a r d i n g t h e numerical values o f t h e c o r r e l a t i o n c o e f f i c i e n t s used i n t h e deduct i o n o f time-mean and t u r b u l e n c e q u a n t i t i e s . The r e s u l t s of t h e s e n s i t i v i t y a n a l y s i s (Table 2) show t h e timf+mean and t u r b u l e n c e q u a n t i t i e s t o be r e l a t i v e l y i n s e n s i t i v e t o v a r i a t i o n s i n the corr e l a t i o n coefficients. Therefore, t h e major ad hoc assumption made i n t h e technique does n o t seem t o have a g r e a t e f f e c t on t h e o u t p u t q u a n t i t i e s compared t o t h e e f f e c t o f o t h e r i n p u t q u a n t i t i e s . As mentioned e a r l i e r , t u r b u l e n c e q u a n t i t i e s ! t h e o u t p u t ) can be c a l c u l a t e d from s i x combina-
55
s e l e c t e d one group o f t h r e e o r i e n t a t i o n s from which t o c a l c u l a t e h i s t u r b u l e n c e estimates. 4.2
R e s u l t s o f F l o w f i e l d Surveys
R a d i a l d i s t r i b u t i o n s o f time-mean v e l o c i t i e s , t u r b u l e n t normal s t r e s s e s and shear s t r e s s e s a r e o b t a i n e d f o r b o t h nonswi r ling and s w i r l i n g conditions, a t various a x i a l locations i n the flowfield. N o n s w i r l i n g Flow. In t h e c o n f i n e d j e t , t h e experiments have been conducted w i t h expansion a n g l e s of 90 degrees (sudden expansion) and 45 degrees ( g r a d u a l expansion) and t h e r e s u l t s f o r In t h e b o t h cases a r e presented i n Reference 22. i n t e r e s t o f b r e v i t y , o n l y t h e d a t a f o r a 90 degree expansion a r e p r e s e n t e d here. F i g u r e 7 shows t h e r a d i a l d i s t r i b u t i o n o f time-mean a x i a l and r a d i a l v e l o c i t y components a t various a x i a l locations. The a x i a l v e l o c i t y d i s t r i b u t i o n s a r e compared w i t h a s i m i l a r study performed by Chaturvedi5 w i t h a crossed h o t - w i r e probe. Because of t h e i n a b i l i t y o f t h e s i x - o r i e n t a t i o n h o t - w i r e technique t o determine t h e sense o f t h e flow d i r e c t i o n i n a n o n s w i r l i n g flow, t h e presence o f t h e c o r n e r r e c i r c u l a t i o n zone was sbserved by 3 sudden i n c r e a s e i n t h e a x i a l v e l o c i t y closer ta the wall. Figur,- 8 shows t h e r a d i a l d i s t r i b u t i o n o f a x i a l and r a d i a l components o f t h e t u r b u l e n c e i n t e n s i t y a t v a r i o u s a x i a l l o c a t i o n s i n t h e confined j e t flowfield. These t u r b u l e n c e i n t e n s i t y components a r e compared w i t h C h a t u r v e d i ' s measurem e n t ~ and ~ reasonable agreement i s found. In f a c t , t h e agreement i n most cases i s b e t t e r t h a n t h e u n c e r t a i n t y e s t i m a t e s d e r i v e d from t h e data reduction s e n s i t i v i t y analysis.
The h o t - w i r e r e s u l t s i n t h e case o f time-mean a x i a l and azimuthal ( s w i r l ) v e l o c i t i e s shown i n F i g u r e s 9 and 10, a r e compared w i t h f i v e - h o l e p i t o t probe measurements performed by Rhode3 i n t h e same experimental f a c i l i t y . Agreement among t h e two s t u d i e s i s f a i r l y good. King1* suggested a method t o determine t h e sense o f t h e a x i a l velocity. He advised comparing t h e magnitudes of Z3 and Z5 g i v e n by Equations 4. I n t h e p r e s e n t flowf i e l d , t h e s w i r l v e l o c i t y i s always p o s i t i v e and t h e two e q u a t i o n s g i v i n g Z3 and Z5 d i f f e r o n l y i n the sign o f axial velocity. Therefore, when Z5 i s greater than Z t h e a x i a l v e l o c i t y i s negai s p o s i t i v e . With t h e p r o p e r t i v e , otherwise sense b e i n g assigned t o t h e x v e l o c i t y mean corn ponent, t h e presence o f c e n t r a l t o r i odal r e c i rc u l a t i o n zone i s e v i d e n t i n t h e r e s u l t s Q f b o t h measurement techniques.
is'
F i g u r e 11 shows t h e r a d i a l d i s t r i b u t i o n o f t h e time-mean r a d i a1 v e l o c i t y a t v a r i o u s a x i a1 l o c a t i o n s f o r a s w i r l vane a n g l e o f 38 degrees and w a l l expansion a n g l e o f 90 degrees. Flow v i s u a l i z a t i o n and f i v e h o l e p i t o t probe measurements performed i n Rhode's s t u d y 3 show t h e time-mean r a d i a l v e l o c i t y t o be n e g a t i v e a t a x i a l l o c a t i o n s g r e a t e r I n spite o f the i n a b i l i t y o f the t h a n x/D = 0.5. s i x - o r i e n t a t i o n h o t - w i r e technique t o determine t h e sense o f t h e r a d i a l v e l o c i t y , t h e data a r e presented w i t h t h e a p p r o p r i a t e s i g n change. There is a reasonable agreement among t h e two s t u d i e s in measurements o f t i m e mean r a d i a1 v e l o c i t i e s except a t t h e i n i t i a l measurement s t a t i o n . F i g u r e 12 shows t h e r a d i a l d i s t r i b u t i o n of a x i a1 , r a d i a1 and azimuthal t u r b u l e n t in t e n s i t i e s a t t h r e e a x i a l l o c a t i o n s presented. A t axial l o c a t i o n s c l o s e r t o t h e i n l e t of t h e c o n f i n e d j e t , t h e a x i a l t u r b u l e n c e i n t e n s i t y i s f a i r l y high, up t o 32 p e r c e n t f o r x/D = 0.5 which i s due t o t h e l a r g e a x i a l v e l o c i t y gradients closer t o t h e wall. However, i n t h e case o f r a d i a l t u r b u l e n c e i n t e n s i t y , t h e p r o f i l e s a r e r a t h e r f l a t . The mean a z i muthal v e l o c i t y a1 so experiences sudden changes i n g r a d i e n t s and, hence, t h e outcome i s a l a r g e a z i muthal t u r b u l e n c e i n t e n s i t y c l o s e r t o t h e w a l l a t x/D = 0.5.
Included on F i g u r e 8 a r e measured t u r b u l e n t
--
shear s t r e s s component ( u ' v ' / U 2 ) p r o f i l e s f o r t h e 0
nonswirling confined j e t . For t h e most p a r t , t h e s e measurements a r e i n reasonable agreement with those made by Chaturvedis with a crossed w i r e probe. The two s i g n i f i c a n t e x c e p t i o n s t o t h e good agreement occur a t t h e f u r t h e s t upstream and f u r t h e s t downstream l o c a t i o n s . Upstream, a t x/D = 0.5 t h e shear l a y e r i s v e r y t h i n and, t h e r e f o r e , lnatching d a t a from s e v e r a l w i r e o r i e n t a t i o n s o b t a i n e d a t somewhat d i f f e r e n t t i m e s may be p r a c tically difficult. We b e l i e v e t h e o v e r l y l a r g e measured t u r b u l e n t shear s t r e s s on t h e c e n t e r 1i n e a t t h e f u r t h e s t downstream s t a t i o n (x/D = 3.0) t o be a consequence o f t h e t r a n s i e n t n a t u r e o f t h e flow. The r e c i r c u l a t i o n r e g i o n s i n t h e c o n f i n e d j e t o s c i l l a t e somewhat a t a l o w frequency, l i k e l y c h a r a c t e r i s t i c o f t h e main a c o u s t i c modes i n t h e tube. These l a r g e s c a l e o s c i l l a t i o n s can have s i g n i f i c a n t c o r r e l a t e d v e l o c i t y f l u c t u a t i o n s (such as
-42
F i g u r e 13
-2 u'w'/Uo,
shows
--2
t h e shear
s t r e s s e s u'v'/Uo,
and v'w'/Uo as a f u n c t i o n o f r a d i a l and
a x i a1 d i stance. The s e n s i t i v i t y a n a l y s i s showed t h a t we s h o u l d expect l a r g e u n c e r t a i n t i e s assoc i a t e d w i t h e v a l u a t i o n o f t u r b u l e n t shear s t r e s s e s u s i ng t h e s i x - o r i e n t a t i on technique. Therefore , t h e r e l i a b i l i t y o f t h e p r o f i l e s o f these shear stresses shown i n F i g u r e 13 i s uncertain a t -2
t h i s time. -2
Nevertheless, s t r e s s e s
u'v'/Uo
and
u'w'/Uo a r e found t o have l a r g e v a l u e s c l o s e r t o
t h e w a l l t h a t one would e x p e c t due t o steep a x i a l and azimuthal v e l o c i t y g r a d i e n t s . The f a c t t h a t we have found no o t h e r measurements o f t h i s t y p e i n a swirling, recirculating flow attests t o the f a c t t h a t a c c u r a t e measurements i n such a f l o w a r e qui t e d i ff icul t C1 osure
u'v').
.
S w i r l i n g F1 ow The measurements performed in t h e s w i r l i n g f l o w a r e w i t h a = 90°, IP. = 38", and x/D = 0.5, 1.0, and 1.5. The o b j e c t o f these 1 i m i t e d number of experiments was t o e v a l u a t e t h e r e l i a b i l i t y and accuracy o f t h e s i x - o r i e n t a t i o n h o t - w i r e technique b e f o r e making e x t e n s i v e use o f t h e technique.
The s i x - o r i e n t a t i o n h o t - w i r e technique i s a r e l a t i v e l y new method t o measure time-mean v e l oc i t y components and t u r b u l e n c e q u a n t i t i e s i n corn Pppl i e d in p l ex three-dimensional f l o w f i e l ds.
56
-
-v/uo
Present Study
Figure 7.
Radial D i s t r i b u t i o n s o f Time-Mean Axial and Radial Velocity Components i n t h e Non-Swi rling Conf ined Jet; (Mote t h e Difference i n Velocity Scales)
xlD
2
3
1
XI0
2
3
1
xlD
2
3
1
0
(,
90'
0
04
---- Chaturvedf
.on
.n
- .I.m
Ujr"S/"O
0
0
I
9oo
0
.01
Y.
..-..-
v rms ' /u o
-
0,50 r/D
0
0,25
0
(I
-
-
J"
I/-
-
om .w -2
0 .OOIOOI O O I
u' v' /u
Figure 8.
.-.- . I
ICC
0
Present Study
Radial D i s t r i b u t i o n s o f Turbulent I n t e n s i t i e s u'
-9s
and shear stress u ' v ' / u
57
0
;/
0
, vkrnS/;b
- - - - Chaturvedf
e Present Study a Rhode e t a13
c.
F i g u r e 9.
i
(5-hole p i t o t probe) X'D
= l**
4
Radial D i s t r i b u t i o n o f Time-ban Axial V e l o c i t y i n S w i r l i n g Confined J e t f o r a = 90" and = 38"
e A
Present Study Rhode e t a13
x/D =. 1.5
t.
* b *
D
A A A
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\
L
--
who
F i g u r e 10.
Radial D i s t r i b u t i o n o f Time-Mean Azimuthal V e l o c i t y in Swi rl ing Confined J e t f o r a = 90" and Q, = 38"
t h i s study t o n o n r e a c t i n g a x i symmetric f l o w f i e l ds, measurements o f time-mean and root-mean-square voltages a t s i x d i f f e r e n t o r i e n t a t i o n s contain enough i n f o r m a t i o n t o o b t a i n t h e time-mean v e l o c i t i e s , t u r b u l e n c e i n t e n s i t i e s and shear stresses. A t each l o c a t i o n i n t h e flow, t h e r e a r e s i x d i f f e r e n t values o f each o f t h e above q u a n t i t i e s t h a t can be o b t a i n e d u s i n g s i x s e t s o f measurements o f three adjacent orientations. Ensemble averages o f t h e o u t p u t q u a n t i t i e s from t h e s i x combinations o f data appear t o produce estimates w i t h t h e b e s t dgreement w i t h independent measurements a
F l o w f i e l d surveys o f b o t h s w i r l i n g and nons w i r l i n g c o n f i n e d j e t s have been made w i t h t h e s i x - o r i e n t a t i o n s i n g l e h o t - w i r e technique. These measurements have been used t o c a l c u l a t e estimates o f t h e mean v e l o c i t y components and t h e normal and shear t u r b u l e n t stresses. Where independent data e x i s t , comparisons have been made which demons t r a t e t h e r e l i a b i l i t y o f t h e technique. I n addition, a s e n s i t i v i t y analysis o f the data r e d u c t i o n technique has been conducted which
58
s u r d technique a p p l i e d t o s w i r l f l o w s i s s t i l l an open question.
forms t h e m a j o r i n g r e d i e n t i n t h e u n c e r t a i n t y analysis. It i s demonstrated t h a t t h e l a r g e s t u n c e r t a i n t i e s a r e t o be expected i n t h e t u r b u l e n t shear s t r e s s estimates. Nevertheless, i n nons w i r l i n g flows t h e measured shear s t r e s s e s a r e i n reasonabl e agreement w i t h p r e v i o u s measurements made w i t h a crossed-wire probe. I n s w i r l i n g f l o w , P r e v i o u s s i m i l a r measurements have n o t been found. Consequently, t h e u n i versa1 accuracy o f t h e mea-
x f D = 0.5
k k n o w l edgernent The a u t h o r s wish t o extend t h e i r s i n c e r e grat i t u d e t o NASA Lewis Research Center and t h e A i r Force W r i g h t Aeronautical L a b o r a t o r i e s f o r s u p p o r t under Grant No. NAG3-74.
e
Present Study
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60
v/uo F I g u r e 11.
Radi a1 D i s t r i b u t i o n o f Time-Mean Radi a1 Vel o c i t y in S w i rl ing Confined J e t f o r a = 90" and CP = 38'
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References I
l1
" F l o w f i e l d Modeling i n P r a c t i c a l L i l l e y , D.G., Combustors: A Review," Journal o f Energy, No. 4, 1979.
2,
2
3
Combustion AeroBeer, J.M. and Chigier, N.A. dynamics, Halsted Press D i v i s i o n , John Wiley Sons, Inc., New York, 1972.
L i l l e y , D.G. and Rhode, D.L., " A Computer Code f o r S w i r l i n g Turbulent Axisymnetric Recirculat i n g Flows i n P r a c t i c a l Isothermal Combustor Ceometries ,I' NASA Contractor Report 3442, February 1982.
l3
and McLaughlin, Rhode, D.L., L i l l e y , D.G. D.Y., "Mean F l o w f i e l d s i n Axisynnnetric Corn-' h u s t o r Geometries w i t h S w i r l ,*I A I A A Paper No. 82-0177, 198?, A I A A Journal ( i n press).
I,and F i e d l e r , H., "Some Measurements i n t h e S e l f Preserving Jet," Journal O f F l u i d Mechanics, 38, p . 577, 1969.
-
Chaturvedi , M.C., "F1 ow C h a r a c t e r i s t i c s o f Pxi symnetri c Expansions ,'I Proceedings, Journal o f t h e H y d r a u l i c D i v i s i o n , ASCE, 89, No. HY3, PP. 61-92, 1963.
l5
P r a t t e , B.D. and Keffer, J.R., "The S w i r l i n g T u r b u l e n t Jet," Journal o f Basic Engineering, 94, pp. 739-748,December 1912.
l6
Dvorak, K. and Syred, N., "The S t a t i s t i c a l Analysis o f Hot Wire Anemometer Signals i n Complex Flow Fields," D I S A Conference, Univers i t y o f L e i c e s t e r , 1972.
l7
Jorgensen, F.E., " D i r e c t i o n a l S e n s i t i v i t y of Wire and F i b e r Fi'lm Probes," O I S A I n f o r m a t i o n No. 11, F r a n k l i n Lakes, N.J., pp. 31-37, May 1971.
-
Phaneuf, J.T. and Netzer, D.W., Flow Charact e r i s t i c s i n S o l i d Fuel Ramjets, Report No. NPS-57Nt7408 1 Prepared f o r t h e Naval Weapons Center by t h e Naval Postgraduate School, Monterey , Cal if o r n i a , J u l y 1974.
.
7
and Back, L.H., "The I n f l u e n c e Roschke, E.J. o f Upstream Conditions on F1 ow Reattachment Lenqths Downstream o f an W r u p t C i r c u l a r Channel Expansion," Journal o f Biomechanics, 9, pp. 481-483, 1976.
9
Ha Minh, H. and Chassaing, P., ' P e r t u r b a t i o n s o f Turbulent Pipe F1ow ,I' Proceedings, Symposium on T u r b u l e n t Shear %lows. Pennsylvania April 1977. S t a t e U n i v e r s i t y , pp. 13.9-13 .li,
10
-
King, C.F., "Some Studies o f Vortex Devices Vortex h p l i f i e r Performance Behavior," Ph.D. Thesis, U n i v e r s i t y College o f Wales, C a r d i f f , Wales, 1978.
Back, L.H. and Roschke, E.J., "Shear Layer Flow Regimes and Wave I n s t a b i l i t i e s and Reattachment Lengths Downstream o f an Abrupt Journal of Circular Channel Expansion ,It Applied Mechanics pp. 677-681, September 1972.
0
Syred, N., Beer, J.M. and Chigier, N.A., "Turb u l ence Measurements in S w i r l ing - R e c i r c u l a t i ng f l o w s ,I1 Proceedings, Sal f o r d SymposI um O n I n t e r n a l I-lows, London, England: Znst. of PIechanfcal t n g i n e e r i n g , pp. 827-836, 1971.
l 4 Wygnanski,
K r a l l , K.M. and Sparrow, E.M., "Turbulent Heat Transfer i n t h e Separated, Reattached, and Redevelopment Reqions o f a C i r c u l a r Tube." Journal . o f Heat Transfer, pp. 131-136, February 1966.
b
Bradshaw, P., An I n t r o d u c t i o n t o Turbulence and I t s Measurement, Pegamon Press, New York, 971.
l9
Hinze,
J.O.
Turbulence,
2nd E d i t i o n ,
McGraw-
H i l l , New York, 1915.
Moon, L.F. and Rudinger, G., " V e l o c i t y D i s t r i b u t i o n i n an Pbruptly Expanding C i r c u l a r Duct," Journa'l o f F l u i d s Engineering, pp. 226-
60
*O
Habib, M.A. and Whitelaw, J.H., "Velocity C h a r a c t e r i s t i c s o f Confined Coaxi a1 J e t s W1th and W i t h o u t S w i r l ,I' ASME Paper 797-W WFE-21, New York, N.Y., December 2-7, 1979.
21
Gupta, A.K. and L i l l e y , D.G., F l o w f i e l d Modeli n g and Diagnostics, Abacus Press, Tunbridge ( i n press).
22
Janjua, S . I . , "Turbulence Measurements i n a Complex F l o w f i e l d Using a SIX-Orientation HotW i r e Probe Technique," M.S. Thesis, Oklahoma State University , S t i 11water, Okl ahoma , December 1981.
APPENDIX D FIVE-HOLE PITOT PROBE TIME-MEAN VELOCITY MEASUREMENTS IN CONFINED SWIRLING FLOWS ( A I AA- 83- 031 5)
61
FIVE-HOLE PITOT PROBE TIME-MEAN VELOCITY MEASUREMENTS IN CONFINED SWIRLING FLOWS H. I(. Yoon* and D. G. Lilley** Oklahoma State University, Stillwater, Okla.
Abstract Nonswirling and swirling nonreacting flows are investigated i n an axisymnetric t e s t section w i t h expansion r a t i o D/d = 2, which may be equipped with contraction nozzles of area r a t i o s 2 and 4. The effects of several geometric parameters on the flowf i e l d a r e investigated including: side-wall expansion angle 01 = 90 and 45 deg., swirl vane angle @ = 0 , 38, 45, 60, and 70 deg., and contraction nozzle location L/D = 1 and 2 ( i f present). Data acquisit i o n i s via a five-hole p i t o t probe enabling three time-mean velocity components i n the axial , radial , and azimuthal directions t o be measured. Velocities are extensively plotted and a r t i s t i c impressions of recirculation zones are presented. Nomenclature C D d L P Re
9
v = (u,v,w) V
x,r,e a B 6
velocity coefficient = pv2/[2(pC - p W ) I t e s t section diameter i n l e t nozzle diameter contraction block downstream distance time-mean pressure Reynolds number volume flow r a t e time-mean velocity ( i n x-. r-, edirections) time-mean vector velocity magnitude axial , radial, azimuthal cylindrical polar coordinates side-wall expansion angle yaw angle of probe = tan '-(w/u) pitch n g l e of probe = t a n [v/(E2 dens i ty swirl vane angle w i t h respect to f a c i l i t y axis
0
C d N,S,E,W
Recent studies on this t e s t f a c i l i t y include: 1.
Flow visualization has been achieved via s t i l l 2 and movie3 photography of neutral ly-buoyant helium-filled soap bubbles and smoke produced by an i n j e c t o r and a smoke wire.
2.
Time-mean velocities have been measured w i t h a five-hole p i t o t probe a t low swirl strengths.2
3.
Turbulence measurements have recently been completed on swirling ( u p t o @ = 45 degrees) as well as nonswirling flows using a six-orientation single-wire hot-wire technique,' enabling a l l Reynolds s t r e s s components t o be deduced.
4.
An advanced computer code has been developed t o predict corresponding confined swirling flows t o those studied e ~ p e r i m e n t a l l y . ~
5.
Tentative predictions6 have now been supplemented by predictions made from r e a l i s t i c i n l e t conditions' f o r a complete range of swirl strengths w i t h downstream nozzle e f f e c t s
Previous experimenters have described timemean velocity measurement techniques applicable t o both swirling and nonswirling flows. They are extensively surveyed and categorized i n a recent Ph.D. Thesis The most relevant confined flow experiments are discussed i n Refs. 10-21. These experiments i n cl ude time-mean velocity measurements [with hotwire and p i t o t probes and l a s e r Doppler anemometry], turbulence measurements [ w i t h hot-wires and laser anemometers] and flow visualization. The majority of the measurements were made i n nonswirling flows' 3-19 , however some noteworth experiments were Direct commade i n swirling confined parison between the r e s u l t s of the cited experiments and the present experimental results i s generally not possible because of differences i n geometry. However, i n the nonswirling jet, comparisons are who meapossible w i t h experiments of Chaturvedi sured mean and turbulent flow quantities downstream of a sudden expansion of diameter r a t i o 2.0 and various expansion sidewall angles a. Measurements of mean velocity i n regions of high turbulence i n tensity and where the direction of the velocity vector i s unknown were made w i t h a p i t o t tube. Mean velocity was a l s o measured with a constant temperature hot-wire anemometer using a single wire. In addition, a cross-wire was used t o measure a l l the
central p i t o t pressure port relating to i n l e t nozzle diameter north, south, e a s t , west p i t o t pressure ports value a t i n l e t to flowfield 1.
Previous Studies
.'
Subscripts
.'
Introduction
1.1 The Problem
As part of an on-going project a t Oklahoma State University, studies a r e i n progress concerned w i t h experimental and theoretical research i n 2-D axisymnetric geometries under low speed, nonreacting, turbulent, swirling flow conditions. The flow enters the test section and proceeds into a larger chamber (the expansion r a t i o D/d = 2) via a sudden or gradual expansion (side-wall angle a = 90 and 45 degrees). I n l e t swirl vanes a r e adjustable to a variety of vane angles w i t h @ = 0, 38, 45, 60
* **
1.2
+ w 2 ) ,721
P
0
and 70 degrees being emphasized. A downstream flow contraction nozzle of area r a t i o 2 o r 4 may be located a t L/D = 1 o r 2 and its e f f e c t s t u d i e d . The general aim i s t o characterize the time-mean and turbulence flowfield, recomnend appropriate turbulence model advances, and implement and exhibit r e s u l t s of flowfield predictions. The present contribution concentrates on the time-mean flow characterization via the five-hole p i t o t probe technique. The paper i s based on a recently-completed M.S. Thesis' and extends e a r l i e r work t o higher swirl strengths and downstream nozzle e f f e c t s .
''
Graduate Student, School of Mechanical and AeroSpace Engineering , Student Member AIAA Professor, School of Mechanical and Aerospace Engineering, Assbciate Fellow AIAA
62
Reynolds stresses. Recent swirl flow data a r e now becoming avai lab1 e. 2 o '2
'
1.3 The Present Contribution The objective of the present paper i s to characterize the e f f e c t s of several parameters on t h e time-mean flowfield including: side-wall expansion angle 01 = 90 and 45 deg., swirl vane angle @ = 0, 38, 45, 60, and 70 deg., contraction nozzle area r a t i o AR = 2 and 4 and location L/D = 1 and 2. Section 2 describes the f a c i l i t i e s and instrument a t i o n employed, along with the procedure f o r fivehole p i t o t probe measurements and data reduction. Results a r e presented and discussed i n Section 3, while Section 4 draws conclusions from the study. 2.
Experimental Approach Fmnf "1.-
2.1
Sld. "1."
The Confined J e t Test Facility
The confined j e t f a c i l i t y i s described a t length e l s e ~ h e r e . ' ' ~ I t has an axial flow fan whose speed can be changed by altering a varidrive mechanism. Numerous fine screens and straws produce flow in the s e t t l i n g chamber of relatively low turbulence intensity. The contraction section leading t o the t e s t section has been designed by t o produce a minimum adverse the method of pressure gradient on the boundary layer and t h u s avoid unsteady problems associated with local separation regions. The sudden expansion consists of a 15 cm diameter c i r c u l a r j e t nozzle, exiting abruptly into a 30 cm diameter t e s t section of length 125 cm, which i s constructed of plexiglass t o f a c i l i t a t e flow visualization. The side-wall angle 01 and swirl vane angle @ are variable. The sidewall angle i s s e t by inserting a block with sidewall angle 01 of 90 or 45 deg. Typical operating Reynolds numbers [based on in1 e t average velocity and i n l e t diameter] are in the range 53,000 t o 150,000 depending upon fan speed and aerodynamic blockage of the swirl vanes. I t has been observed t h a t this is approximately i n the Re nolds number insensitive range f o r t h i s facility,' i n terms of nondimensional flow characteristics further downstream.
Fig. 1 Annular vane swirler
I
F i g . 2 The weak contraction nozzle with area ratio 2
A schematic of the swirler i s shown i n Fig. 1. I t has ten vanes which are individually adjustable t o any angle $, and a hub with a streamlined upstream nose and a f l a t downstream face. The nose has a hyperbolic shape with a very smooth surface so as to offer minimal flow interfcrence. The f l a t blades a r e wedge-shaped to give a constant p i tch-to-chord r a t i o of approximately one which should give good t u r n i n g e f f i ~ i e n c y . ' ~ W i t h an expansion block attached t o the e x i t of the swirl pack, the expansion plane [x/D = 01 i s 3.2 cm downstream of the swirl e x i t [where x/D = -O.ll].
I
The e f f e c t s of a downstream contraction nozzle on the upstream flow in the t e s t section i s important in combustor aerodynamics. TWO nozzles of area r a t i o 2 and 4 are being used. The weaker one i s shown diagramatically in Fig. 2. I t s upstream face i s contoured in a quarter c i r c l e as found i n pract i c a l ranljet combustors. The stronger contraction nozzle i s shown in Fiq. 3. I t s upstream face iS 45 degree slope, more typical of gas turbine comb u s t i o n chamber exits. These blocks may be located a t any axial position i n the t e s t section.
SlDl Y I I Y
Fig. 3 The strong contraction nozzle with area ratio 4
63
2.2
2.3
Five-Hole P i t o t Probe Instrumentation
The five-hole pi t o t probe i s one of the few instruments capable of measuring both the magnitude and the direction of .fluid velocity simultaneously. The five-hole p i t o t probe used i n this study i s a model OC-125-12-CD manufactured by United Sensor and Control Corp. The sensing head i s hook-shaped t o allow f o r probe s h a f t rotation without altering the probe t i p location. L i t t l e infomation is available concerning the effects o f turbulence on a pressure probe i n a swirling flow. However, i t i s asserted t h a t the five-hole p i t o t probe i s accurate within approximately 5 percent f o r most of the measurements.2 This value may increase t o 10 percent as the velocity magnitude f a l l s below approximately 2.0 m/s because of the i n s e n s i t i v i t y of the probe to low dynamic pressure and the dependence o f probe calibration on the probe Reynolds number.
Measurement Procedure and Data Reduction
The measurement procedure involves a five-hole p i t o t probe. I t i s aligned w i t h the flow yaw angle B = tan-'(w/u) i n the plane perpendicular to the radi s while the pitch angle 6 = tan [v/(u2 + w2)'y2j and t o t a l velocity magnitude V can t h e n be found from previous corresponding f r e e j e t calibrations. The technique, associated computer code and user instructions a r e documented a t length elsewhere.
'"
Two kinds of calibration are employed t o reduce the raw data from the d i r e c t measurements. One i s the calibration of the voltmeter, which determines a relationship between the voltmeter output and the velocity magnitude. The other is the calibration of the five-hole p i t o t probe, which consists of two calibration characteristics: pitch angle 6 versus differential pressure r a t i o ( P N - Ps)/(Pc - P"), and velocity coefficient
The instrumentation assembly, i n addition t o the five-hole p i t o t probe, is composed of a manual traverse mechanism, two five-way ball valves, a d i f f e r e n t i a l pressure transducer, a power supply, and an integratiq d i g i t a l voltmeter. The differenversus pitch angle 6. t i a l pressure transducer i s model 590D from DataIn the measurement of the flow i n the t e s t metrics, Inc. I t has a differential pressure range of from 0 t o 1.3 x l o 3 N/m2. The integrating voltsection, a s e r i e s of radial traverses i s taken i n a vertical l i n e with probe t i p pointing horizontally. meter i s the TSI model 1076. As auxiliary equipment, a model 631-8 strobotac from General Radio, With obvious compass notation given t o the f i v e Inc. i s used t o check the fan speed A micro-manoholes, the f i r s t measurement for each location i s meter, along with a P i t o t - s t a t i c probe, i s used to the yaw angle 6 f o r a zero reading of (Pw - P,) measure the dynamic pressure i n the nozzle throat This means t h a t the probe t i p i s aligned w i t h the j u s t upstream of the swirler, and therefrom deduce local flow direction i n a horizontal plane. Then the swirler i n l e t uniform axial velocity u which i s the five-way switching valves are s e t so that used l a t e r for velocity normalizations. APSO, a ( P N Ps) i s sensed by the pressure transducer. barometer/thermometer unit from Cenco Corporation i s used f o r local pressure and temperature readings. Measurement apparatus i s shown diagramatically i n Fig. 4.
.
-
Notat ion
1.
Pitot static probe
2.
Swirler
3.
Expansion block
4.
Five-hole pitot probe
5.
Switching valve
6.
Pressure transformer
7. Contraction block 8. 9.
LO.
Voltmeter Integrating Voltmeter Hicro-manometer
Fig. 4 Apparatus for Mean Velocity Measurements
64
Finally, the reading of (Pc measured.
- Pw)
i s similarly
The velocity profiles f o r swirling flows shown i n Fig. 5 parts b through e reveal t h a t the flow entering through the swirl vanes is not uniform and has steep velocity gradients i n the radial direction especially a t h i g h swirl numbers. Furthermore, a considerable back flow around the hub i s observed f o r Q = 70 degrees, as shown i n Fig. 12(e). For a l l values of swirl vane angle used i n t h i s study, the corner recirculation zone does not extend beyond x/D = 0.5, the closest axial location t o the expansion block; instead, the maximum axial velocity is observed close t o the top wall a t x/D = 0.5. The effects result from the strong centrifugal forces present i n the incoming swirling flow.
The data reduction employs the two calibration curves, w i t h turbulence e f f e c t s neglected -- t h e i r precise e f f e c t on pressure probes i n swirl flows is unknown. With the measurement data of the d i f f e r ential pressure r a t i o (PN - P ) / ( P c - Pw), the corresponding pitch angle 6 i s obained w i t h a cubic spline interpolation technique from the appropriate calibration characteristics. The velocity coefficient C is determined from this value by u s i n g the corresponding calibration characteristics. The magnitude of the velocity vector is then calculated from v = ;[2 (Pc - Pw) C) 1/2 and the three time-mean velocity components a r e obtained from this value and the yaw and pitch angles. 3.
Results and Discussion
Nonswirling and swirling nonreacting flows a r e investigated i n an axisymnetric t e s t section w i t h expansion r a t i o D/d = 2, which may be equipped w i t h a contraction nozzle of area r a t i o 2 and 4. Veloci t y measurements are made with the five-hole p i t o t probe as described i n Section 2.3. An analysis is made o f the effects of various geometric parameters on t h e extent of the recirculation zones i n the flowfield. These parameters include side-wall expansion angle 01 = 90 and 45 degrees, swirl vane angle @I = 0, 38, 45, 60, and 70 degrees, and contraction nozzle location LID = 1 and 2 ( i f present). The nozzle i n l e t velocities and Reynolds numbers employed i n this study a r e h i g h enough t o ensure t h a t the flowfields are investigated under conditions independent of Reynolds number variation. All nozzle i nl e t veloci t i es and Reynol ds numbers employed are l i s t e d i n Table 1 . Flow characteristics a r e extensively tabulated i n terms of normalized u, v, and w velocity components, yaw angle B and pitch angle 6 i n Ref. 1. 3.1
Effects of Swirl on Sudden Expansion Flows Swirling flows r e s u l t from the application of
a spiraling motion, w i t h a swirl velocity canponent being imparted t o the flow via the use o f swirl vanes. The swirl vane angles employed in this study a r e 0 (swirler removed), 38, 45, 60, and 70 degrees. Figure 5 parts a through e show the axial and swirl velocity profiles f o r @I = 0, 38, 45, 60, and 70 degrees, respectively, w i t h side-wall expansion angle 01 = 90 degrees.
The central recirculation zone and precessing vortex core a r e now discussed. The precessing vortex core i s defined as the region of h i g h swirl, low axial velocity flow along the a x i s , which has a relatively constant small diameter. In flow visualization studies,2’3 i t i s seen to precess around the axis of the t e s t section. The central recirculation zone i s defined as the wide reverse flow region encountered near the i n l e t . Articulate impressions are given l a t e r i n which lines have been drawn connecting the radial positions of zero axial velocity. In case o f the vortex core, t h a t region i s drawn along the zero axial velocity boundary i n the downstream direction a f t e r the central recirculation region. The s i z e of the central recirculation zone increases with the increasing swirl vane angle u n t i l a certain value of swirl vane angle i s reached (around 40 degrees). Then its length begins t o decrease under stronger swirl conditions, b u t i t s w i d t h continues to increase. The core vortex was present a t a l l values of swirl vane angle used i n this investigation. In contrast t o the central recirculation zone, the vortex core gets continuously wider as the swirl vane angle increases. The swirl velocity peaks sharply around the edge of the expansion block before becoming more uniform further downstream as shown i n F i g . 15 parts b through e. A considerably nonuniform swirl velocity p r o f i l e i s observed a t x/D = 0.5. Therea f t e r , relatively steady and uniform velocity prof i l e s are seen, except f o r the region around the axis. The radial location where the maximum swirl velocity occurs goes up as the swirl vane angle i n creases. T h i s trend is caused by the increase of centrifugal effects. The swirl velocity along the axis i s found t o be zero as expected because of symmetry. 3.2
The nonswirling flow investigated i s obtained w i t h the swirler removed. Figure 5(a) shows an uniform axial velocity entering the t e s t section. The corner recirculation zone extends t o just beyond x/D = 2.0. Measurements f o r a corresponding flow were taken w i t h a stagnation tube and p i t o t tube by Chaturvedi .19 He found the reattachment point t o be a t x/D = 2.3 which i s i n good atreement w i t h the present study. Moon and Rudinger’ located the reattachment point w i t h both theoretical and experimental methods i n a similar c i r c u l a r t e s t section w i t h an expansion r a t i o D/d = 1.43, which i s different from the present study [with D/d = 21. The r e s u l t yielded a value of x/D = 1.25 a s a reattachment point, which corresponds t o an attachment point approximately eight s tep-hei ghts downstream, which is i n good agreement with the present study.
65
Effects of Gradual Expansion
Gradual expansion flows w i t h 01 = 45 degrees were measured a t two axial stations o f x/D = 0.5 and 1.0 f o r swirl vane angles of 0, 38, 45, 60, and 70 degrees. Only the upstream flowfield needed t o be thoroughly investigated in these cases , since i n l e t expansion effects occur i n t h i s region the most, and t h e i r influence rapidly diminishes in the downstream direction.2 Measurements were n o t taken a t the i n l e t i n this geometry because the presence of the expansion block interferes w i t h probe posit i oni ng. The corresponding sequence of axial and swirl velocity profiles t o a sudden expansion are given i n Ref. 1. Velocity profiles f o r a gradual expansion follow a similar trend t o those for a sudden expansion. The major e f f e c t of a gradual i n l e t expansion i s t o encourage the a i r t o flow along the
x /D
0
I
I
2
u/u, (a) Swirl vane angle
x/D
I
0
+ = 0" 2
( a ) u/u,
( b )w/ u, (b) Swirl vane angle
+ = 38"
(c) Swirl vane angle
+ = 45"
0
( b )w/u,
Fig. 5 Velocity profiles for side-wall expansion angle c1 = 90" without contraction nozzle
66
( b l w/u,
( b l w / u,
(d)
S w i r l vane angle I$ = 60"
(e)
S w i r l vane angle I$ = 70' Figure 5
continued present these v e l o c i t y p r o f i l e s w i t h L/D = 2 only; corresponding f i g u r e s w i t h L/D = 1 appear i n Ref. 1.
s i d e sloping w a l l , shorten t h e corner r e c i r c u l a t i o n zone and accelerate a x i a l v e l o c i t i e s c l o s e t o the t o p w a l l . Influence on t h e c e n t r a l r e c i r c u l a t i o n zone f o r the s w i r l f l o w cases i s minimal.
3.3
E f f e c t s o f a Weak Contraction Nozzle
It i s b e s t t o i n t e r p r e t the data obtained when a c o n t r a c t i o n nozzle i s i n s e r t e d a t d i f f e r e n t a x i a l s t a t i o n s on the f l o w f i e l d s by comparing them t o t h e data obtained w i t h o u t i t s presence. The measurements were taken a t a x i a l l o c a t i o n s ranging from t h e i n l e t plane t o t h e a x i a l s t a t i o n j u s t upstream o f the s t a t i o n where the c o n t r a c t i o n block was located. The e f f e c t of a weak c o n t r a c t i o n nozzle w i t h area r a t i o 2 was i n v e s t i g a t e d w i t h t h e c o n t r a c t i o n block located a t L/D = 1 and 2 f o r a range o f s w i r l strengths r$ = 0, 45 and 70 deg. w i t h sudden expansion a = 90 deg. only. Figure 6, parts a, b and c
67
Figure 6(a) shows t h a t the weak c o n t r a c t i o n nozzle generally affects the f l o w f i e l d very l i t t l e under nonswirl i n g conditions. Furthermore, as t h e block i s moved f a r t h e r i n t h e downstream d i r e c t i o n , i t s e f f e c t on the f l o w f i e l d decreases. The o n l y e f f e c t t h a t can be n o t i c e d from the v e l o c i t y prof i l e s i s decreased i n length o f the corner r e c i r c u l a t i o n region due t o t h e nozzle e f f e c t . P a r t b o f Fig. 6 shows t h e a x i a l and s w i r l v e l o c i t y p r o f i l e s f o r t h e intermediate s w i r l i n g f l o w o f Q = 45 degrees with c o n t r a c t i o n nozzle a t L/D = 2. S i g n i f i c a n t p o s i t i v e a x i a l v e l o c i t i e s are observed along t h e centerline, as t h e nozzle i s approached. This s i t u a t i o n i s i n s t r i k i n g cont r a s t t o t h a t o f t h e intermediate s w i r l i n g f l o w w i t h o u t t h e c o n t r a c t i o n block, i n which case t h e
0
x/D
1
2
u/u, (a) Swirl vane angle cp = 0"
I b ) w/u, (b)
Swirl vane angle cp = 45"
0
(c) Swirl vane angle cp = 70" Fig. 6
Velocity profiles with weak contraction nozzle o f area ratio 2 located a t L/D = 2
68
u/u, (a) Swirl vane angle $I = oo
0
( a ) U/u,
( b )w / u o
(b)
Swirl vane angle $I = 4 5 O
0
( b,
''
"0
(c) Swirl vane angle
I$
= 70"
Fig. 7 Velocity profiles with strong contraction nozzle o f area ratio 4 located a t L/D = 2
69
central recirculation zone spreads extensively along the centerline to x/D = 1.5 w i t h vortex core following it i n the t e s t section. Slightly larger swirl velocities are seen i n F i g . 6(b) than i n Fig. 5(c) without contraction block. T h i s is t o be expected as the flow cross-sectional area reduces.23 The axial velocities have q u i t e d i f f e r e n t profiles a t the two axial s t a t i o n s of x/D = 1.0 and 1.5, this region being affected by the proximity of the contraction nozzle. A t the axial s t a t i o n of x/D = 1.0, reverse flow i s not observed a t a l l , and considerable positive axial velocities a r e measured near the axis. A rather uniform velocity p r o f i l e is obtained a t x/D = 1.5. For strong swirling flows of cp = 70 deg., the axi a1 and swirl velocity profiles a r e shown i n Fig. 6(c). The contraction block does not a f f e c t the flowf'ield much except a t the axial s t a t i o n imnediately upstream of the block. Slightly higher swirl velocities and a s l i g h t l y narrower core region occur as the blockage i s approached as compared w i t h the case without dawnstream blockage. In sumnary, a weak contraction nozzle has most e f f e c t on the intermediate swirl case of Q = 45 deg. I t s contraction e f f e c t i n this case i s strong enough t o overwhelm the swirling recirculation region. However, a contraction has l i t t l e e f f e c t on weakly swirling and strongly swirling flows, which a r e dominated by forward flow and centrifugal forces, wspect i ve 1y
.
3.4
Effects of a Strong Contraction Nozzle
The e f f e c t of a stronger contraction nozzle
w a s investigated f o r a range of swirl strengths cp = 0, 45, and 70 deg. w i t h side-wall expansion angle a = 90 degwes. The contraction nozzle, of area r a t i o 4 w i t h 45 degree sloping upstream face, was located a t L/D = 1 and 2. Figure 7 parts a , b, and c show these velocity profiles w i t h L/D = 2 only, while results w i t h L/D = 1 appear i n Ref. 1. Figure 7(a) shows t h a t the flowfield w i t h a strong contraction nozzle changes very l i t t l e as compared t o the corresponding flowfield w i t h a weak contraction nozzle shown i n Fig. 6 ( a ) , o r the corresponding flowfield without a contraction nozzle shown i n Fig. 5(a).
sharp contrast t o t h a t of a weak contraction nozzle, i n which case the contraction block a f f e c t s the flowfield very l i t t l e under strong swirling conditions, w i t h centrifugal effects dominating. Swirl velocity profiles given i n F i g . 7(c) show the even narrower core than a t Q = 45 deg. with very strong swirl velocity magnitudes and gradients. Summarizing, whereas the e f f e c t of a weak contraction nozzle of area r a t i o 2 is confined to intermediate swirl cases, a strong contraction nozzle of area r a t i o 4 a f f e c t s both intermediate and strongly s w i r l i n g flow cases. Visual impact is enhanced by a r t i s t i c impressions of the overall flowfield chara c t e r i s t i c s , which a r e presented i n F i g s . 8, 9 and 10 f o r the cases of no blockage, weak blockage a t L/D = 2 and strong blockage a t L/D = 2. In each case a range of swirl strengths is considered, f o r i n l e t side-wall angle cc = 90 deg. only. 4.
Conclusions
The nonswi r l ing confined j e t possesses a corner recirculation zone extending t o just beyond x/D = 2 w i t h no central recirculation zone. The presence of a swirl er shortens the corner reci rculation zone and generates a central recirculation zone followed by a precessing vortex core. The e f f e c t of a gradual i n l e t expansion is to encourage the flow t o remain close t o the sidewall and shorten the extent of the corner recirculation zone i n a l l cases investigated. A contraction nozzle of area r a t i o 2 has l i t t l e e f f e c t on weakly swirling and strongly swirling flows, which are dominated by forward flow and centrifugal forces , respectively. For intermediate swirl cases, i t encourages forward movement of otherwise slow-moving a i r and thereby shortens the central recirculation zone. A strong contraction nozzle of area r a t i o 4 has a more drama t i c e f f e c t on the flowfields, particularly affecting both intermediate and strong swirling flow cases. Central recircuJation zones a r e shortened considerably, and axial velocities near the f a c i l i t y axis become highly positive. Core regions become narrower w i t h very strong swirl velocity magnitudes and gradients. Acknowledgments
Figure 7(b) shows the axial and swirl velocity profiles f o r a swirl vane angle Q = 45 deg. The presence of a strong contraction nozzle generates a h i g h positive axial velocity near the axis a t a l l axial locations. However, i t decelerates the axial velocity close t o the top wall. The central recirculation zone is much smaller than previous corresponding cases, and i t i s located i n an annular region. The swirl velocity profiles show narrower core regions w i t h stronger swirl velocity magnitudes and gradients than previously. For swirl vane angle 4 = 70 degrees, the axial and swirl velocity profiles a r e given i n F i g . 7(c) w i t h the strong contraction blockage located a t L/D = 2. The axial velocity near the axis i s highly positive and the central recirculation region is very small, extending i n an annular region t o less than x/D = 1.0, much l e s s than its corresponding case w i t h the weak contraction block and considerably l e s s than the no-blockage case of F i g . 5 ( e ) . A t the axial s t a t i o n x/D = 1.0, forward flow occurs across the whole t e s t section. T h i s s i t u a t i o n is i n
70
Special thanks a r e extended t o NASA Lewis Research Center and Air Force Wright Aeronautical Laboratories f o r financial support via NASA Grant No. NAG 3-74, technical monitor Dr. J . D. Holdeman. References 1.
Yoon, H. K., Five-Hole P i t o t Probe Time-Mean Velocity Measurements i n Confined Swirling Flows. MS Thesis, Oklahoma S t a t e University, July 1982.
2.
Rhode, D. L., Lilley, D. G., and McLaughlin, D. K. , Mean Flowfields i n Axisymmetric Combustor Geometries w i t h Swirl, Paper AIAA 820177, Orlando, Florida, Jan. 11-14, 1982. A I A A Journal , 1983 ( i n press).
3.
Lilley, D. G., Turbulent Combustor Flowfield Investigation. Paper i n Combustion Fundament a l s Research Conference, held a t NASA Lewis Research Center, Cleveland, Ohio, Oct. 21-22, 1982, pp. 152-168.
4.
Janjua, S. I., McLaughlin, Jackson, T. W., and Lilley, D. G., Turbulence Measurements i n
a Confined J e t Using a Six-Orientation HotWire Probe Technique. Paper AIAA 82-1262, Cleveland, Ohio, June 21-23, 1982. 5.
6.
7.
8.
9.
18.
Lilley, D. G., and Rhode, D. L., A Computer Code f o r Swirling Turbulent Axisymnetric Recirculation Flows i n Practical Isothermal Combustor Geometries, NASA CR-3442, Feb. 1982.
Krall, K. M., and Sparrow, E. M., Turbulent Heat Transfer i n the Separated, Reattached, and Redevelopment Regions of a Circular Tube, ASME Journal of Heat Transfer, February 1966, pp. 131-136.
19.
Rhode, D. L., Lilley, D. G., and McLaughlin, D. K., On the Prediction of Swirling Flowf i e l d s Found i n Axisymnetric Combustor Geometries. ASME Journal of Fluids Engng., Vol. 104, 1982, pp. 378-384.
Chaturvedi, M. C., Flow Characteristics o f Axisymmetric Expansions, Proc. Journal Hydraulics Division, ASCE, Vol. 89, No. HY3, 1963, pp. 61 -92.
20.
Johnson, B. V.,
Sander, G. F., and Lilley, D. G., The Performance of an Annular Vane Swirler. Report on Work i n Progress, School of Mech. and Aero. Engng., Oklahoma S t a t e University, Stillwater, Okla., Oct. 1982.
21.
Gouldin, F. C., Depskey, J. S., and Lee, S.-L., Velocity Field Characteristics of a Swirling Flow Combustor. Paper AIAA 83-0314, Reno, Nevada, Jan. 10-13, 1983.
Abujelala, M. T., and Lilley, D. G., Confined S w i r l i n q Flow Predictions, Paper AIAA-83-0316. Reno, Nevada, Jan. 10-13, 1983.
22.
Morel, T., Comprehensive Design of Axisymnetric Wind Tunnel Contractions, ASME Paper 75-FE-17, Minneapolis, MN, May 5-7, 1975.
23.
Gupta, A. K., Lilley, D. G., and Syred, N . , Swirl Flows, Abacus Press, Tunbridge Wells, England, 1983 ( i n press).
Rhode, D. L . , Predictions and Measurements o f Isothermal Flowfields i n Axisymmetric Combust o r Geometries, Ph.D. Thesis, School of Mech. and Aero. Engng. , Oklahoma S t a t e University, Stillwater, Okla. , Dec. 1981.
191-198.
10. Habib, M. A., and Whitelaw, J . H., Velocity Characteristics of Confined Coaxial J e t s With and Without Swirl, ASME Paper No. 79-WA/FE-21, New York, Dec. 2-7, 1979.
Table 1 I n l e t Velocities and Reynolds numbers
11.
Srinivasan, R., and Mongia, H . C., Numerical Compu ta t i ons of Swi r l i ng Reci rcul a t i ng F1ows , Final Report NASA-CR-165196, Sept. 1980.
12.
Vu, B. T., and Gouldin, F. C. , Flow Measuremeant i n a Model Swirl Combustor, AIAA Journal, Vol. 20, No. 5, May 1982, pp. 642-651.
13.
Mass and Momentum Transport Experiments. Paper i n Combustion Fundamentals Research Conference, held a t NASA Lewis Research Center, Cleveland, Ohio, Oct. 21-22, 1982, pp.
Ha M i n h , H . , and Chassaing, P., Perturbations of Turbulent Pipe Flow, Proc. Symposium on Turbulent Shear Flows, Pennsylvania S t a t e University, April 1977, pp. 13.9-13.17.
14.
Moon, L. F., and Rudinger, G., Velocity Distribution i n an Abruptly Expanding Circular Duct, ASME Journal of Fluids Engng., March 1977, pp. 226-230.
15.
Phaneuf, J . T., and Netzer, D. W., Flow Characteristics i n Solid Fuel Ramjets, Report No. NPS-57Nt-74081, July 1974, Prepared f o r the Naval Weapons Center by the Naval Postgraduate School.
16.
Back, L. H., and Roschke, E. J . , Shear Layer Flow Regimes and Wave I n s t a b i l i t i e s and Reattachment Lengths Downstream of an Abrupt Circular Channel Expansion, ASME Journal of Appl ied Mechanics, Septenber 1972, pp. 677-681.
17.
Roschke, E. J., and Back, L. H., The Influence of Upstream Conditions on Flow Reattachment Lengths Downstream of an Abrupt Circular Channel Expansion, J . of Bimech., Vol. 9 , 1976, pp. 481-483.
71
9
a = 90" Red
Uin b / s )
a = 45' Uin (m/s) Red
0"
15.7
150,000
15.5
154,000
38"
10.5
100,000
10.6
105,000
45"
12.6
120,000
14.9
148,000
60
8.84
84,000
9.58
95,000
70"
5.57
53,000
6.25
62,000
-0
. 0
I .o
5 2.0
1 0 I .o 280 3.0
- 0.5
1
3.0
(a1
(a)
0.5
0.5
-------_
0
I
1 .o
2.0
I
I
0
3.0
I .o
2.0
3.0
2 .o
3.0
(b)
(b)
A -
- 0.5
0
I.o
I
(C)
x/D Fig. 8 A r t i s t i c impression o f d i v i d i n g streamlines w i t h o u t c o n t r a c t i o n nozzle f o r various s w i r l vane angles: (a) 4 = O o , ( b ) 4 = 45" and (c) 4 = 70".
-0.51 0
ka
I .o
Fig. 10
A r t i s t i c impression o f d i v i d i n g streamlines w i t h strong c o n t r a c t i o n nozzle f o r various s w i r l vane angles: (a) I$ = O", ( b ) 4 = 45' and (c) 4 = 70".
I
2.0
3.0
2 .o
3 .O
(4
0
1.0 (b)
o;-0
-*:-----I .o
2 .o
3 -0
(C)
x/ D Fig. 9 A r t i s t i c impression o f d i v i d i n g streamlines w i t h weak c o n t r a c t i o n nozzle f o r various s w i r l vane angles: ( a ) 4 = O", ( b ) 4 = 45" and ( c ) 4 = 70".
72
APPENDIX E CONFINED SWIRLING FLOW PREDICTIONS ( AI AA- 83-0316 )
73
CONFINED SWIRLING FLOW PREDICTIONS bY
M. T. Abujelala* and D. G. Lilley** Oklahoma S t a t e University, Stillwater, Okla.
niques will significantly increase understanding and reduce the time and cost of development.'-' The present contribution forms part of a project on the investigation of flowfields found i n typical conbustor geometries ; studies are i n progress concerned with experimental and theoretical research i n 2-0 axisynnnetric conditions. The general aim i s to characterize the time-mean and turbulence flowf i e l d , recomnend appropriate turbulence model advances, and implement and exhibit results of flowfield predictions.
Abstract The validity of flowfield predictions resulting from the choice of i n l e t velocity profiles is assessed. Results demonstrate t h a t r e a l i s t i c predictions are forthcoming only from the inclusion of r e a l i s t i c a x i a l , radial and swirl velocity prof i l e s as i n l e t conditions. Predictions a r e then exhibited f o r a range of swirl strengths Cp = 0 , 38, 45, 60 and 70 degrees using measured i n l e t axial, radial and swirl velocity profiles i n each case. Downstream nozzle effects (two blockage sizes a t two axial locations) are included. The ensuing flowfields a r e characterized via velocity profiles and streamline patterns, and i l l u s t r a t e the largescale effects of i n l e t swirl and o u t l e t nozzles on flowfi el ds.
In the Oklahoma State University confined j e t f a c i l i t y , described a t length elsewhereySy7the a i r flow enters the t e s t section and proceeds into a larger chamber ( t h e expansion r a t i o D/d = 2) via a sudden o r gradual expansion (side-wall angle a = 90 and 45 degrees). I n l e t swirl vanes are adjustable t o a variety of vane angles with values of Cp = 0 , 38, 45, 60 and 70 degrees being emphasized. A downstream flow contraction nozzle of area r a t i o 2 or 4 may be located a t L/D = 1 or 2 and i t s e f f e c t studied. The present paper exhibits predictions t h a t i l l u s t r a t e the need t o specify r e a l i s t i c a l l y the i n l e t conditions , and presents and discusses predictions f o r a range of swirl strengths and downstream nozzles using measured i n l e t conditions i n each case.
Nomenclature D d G k L R S
v = (u,v,w) x,r,e CL
E
Cp
t e s t section diameter i nl e t nozzle diameter = wm/u0 (without subscript), axial flux of mmentum (with subscript) kinetic energy of turbulence contraction nozz 1e downstream distance i n l e t nozzle radius = d/2 swirl number = G /(Gx R) time-mean velocity ( i n x-, r-, 8directions) axial , radial , azimuthal cylindrical polar coordinates side-wall expansion angle turbulent energy dissipation rate swirl vane angle with respect t o f a c i l i t y axis
-
1.2 Previous Studies The current status of the research program i s described with appropriate reference citations i n a companion paper. Preliminary e f f o r t s a t numeri cal rediction of t h i s flowfield have been document e d Y g y gthese u s i n g an advanced version" (called STARPIC) of the Imperial College TEACH-T computer program." Codes of t h i s type have been applied t o other 2-D1'-'' and 3-DZ1-" problems of i n t e r e s t to the combustor designer. Progress in a l l these areas are extensively reviewed in recent textbooks y 2 5 y 2 6 Most application-oriented prediction studies use the familiar two-equation k-E turbulence model , 2 7 r 2 8 which has been found to be inadequate for correct simulation of complicated swirling recirculating flows.'' Success a t the turbulence modeling problem i s a prerequisite t o the prediction of practical turbulent reacting flows, a f a c t which prompted the present research program on nonreacti ng flows.
Subscripts
.'
relating to swirler hub s t a t i o n maximum value value a t i n l e t t o flowfield relating t o axial direction relating t o swirl direction
h
m 0 X
6
Superscripts (
1-
value calculated excluding pressure contribution 1.
1.1
1.3 The Present Contribution The governing differential equations o f swirli n g recirculating flows a r e e l l i p t i c , and solutions depend strongly on the boundary conditions applied around the flow domain. I t i s important t o define adequately the boundary conditions , especially the i n l e t velocity r o f i l e s , y e t most of the studies cited earl iere-" make gross s imp1 i f i c a t i ons regarding i n l e t conditions, and especially with regard t o the i n l e t radial velocity which i s often taken t o be zero. Axial and swirl velocity profiles, i f not measured, are often assumed to be simple f l a t profiles, or sometimes a f l a t axial profile with a solid body rotation swirl profile.
Introduction
The Problem
Designers of gas turbine and ramjet combustion chambers a r e aided n o t only by experiments b u t a l s o by predictions of t h e i r flowfields. Recently, these are being obtained directly via mathematical models incorporating numerical f i n i t e difference computer codes. Improvement and use of these tech-
* Graduate Student, School of Mechanical and Aerospace Engi neeri ng , Student Member AIM ** Professor, School of Mechanical and Aerospace Engi neeri ng , Associate Fellow
74
Numerical predictions of turbulent swirling recirculating confined flows a r e presented u s i n g various i n l e t velocity s t a r t i n g conditions f o r the case of swirl vane angles equal t o 45 and 70 degrees. The validity of flowfield predictions resulting from the choice of i n l e t profiles i s assessed by cmparing the predicted velocity profiles with correspondi n g experimental velocity profiles Results demons t r a t e t h a t real i s t i c predictions are forthcoming only from the inclusion of r e a l i s t i c axial , radial and swirl velocity profiles as i n l e t conditions, and t h a t considerable errors occur i f unrealistic idealized i n l e t conditions are used.
.’
Predictions are then exhibited f o r a range of swirl strengths ( + = 0 , 38, 45, 60 and 70 degrees) using measured i n l e t axial radial and swirl veloci t y profiles i n each case.*g The ensuing flowfields a r e characterized via velocity profiles and streaml i n e patterns, and i l l u s t r a t e the large-scale effects of i n l e t swirl on flowfields. Downstream nozzle effects (two blockage sizes a t two axial locations) are included. Results a r e assessed via comparison w i t h detailed time-mean velocity measurements obtained w i t h a five-hole p i t o t probe,’ and appropriate conclusions are deduced.
2. 2.1
Theoretical Approach
The Swirl Number
T h e degree of swirl usually i s characterized by the swirl number S, which i s a nondimensional number representing axial flux of swirl momentum divided by axial flux of axial momentum times equivalent nozzle radius. That i s
where G = wmo/uo represents the r a t i o of maximum velocities measured a t the e x i t plane. Thus the swirl strength can be inferred from (4) i f pressure i s included in the Gx definition, and S’ = G/2
(5)
i f pressure is omitted i n 6,. Both S and S’ a r e called swirl numbers, b u t a given velocity d i s t r i b u t i o n gives different S and S’ values. The theoretical S vs. G seems t o be valid only f o r low swirl strengths with S 5 0.2, see Refs. 30 and 31. For higher degrees of swirl , however, the axial velocity d i s t r i b u t i o n deviates from plug flow considerably the major portion of the flow leaves the o r i f i c e near the outer edge.29-3z Then measured S values (including pressure contribution) are hi her3’ t h a n measured G values would suggest via Eq. 74). I n many practical experiments , S’ values a r e calculated and quoted based on experimental swirler e x i t veloc i t y profiles only, with the pressure contribution omitted, see for example, Ref. 33. Pressure variations s t i l l e x i s t , although quoted S’ values do n o t make use of these values. Under these circumstances, f o r a vane swirler with swirl vane angle I#, i t can be shownz6 approximately t h a t
where
with plug flow solid body rotation e x i t velocity prof i l e s . Table 1 reveals how +, s’ and G are related under such conditions f o r the swirl vane angles of special i n t e r e s t .
i s the axial flux of swirl mmentum, including the x-6 direction turbulent shear s t r e s s term
Gx =
(3)
is the axial flux of axial momentum including the
x direction turbulent normal s t r e s s term and a pres-
Table 1
sure term.
One useful deduction i s possible when s o l i d body rotation plug flow i s assuned a t the nozzle, with u and w given by the equations of Case 2 i n Section 2.2. That i s , axial velocity u is a cons t a n t f l a t p r o f i l e and swirl velocity w increases ( a t r = d/2, the outer wall from 0 ( a t r = 0) t o w of the nozzle). Then Tocal s t a t i c pressure p and and local swirl velocity w a r e related via P
- ,P
=
- Z1 P W2.
+, S’ and G correspondence f o r plug flow s o l i d body rotation swirlers w i t h dh/d = 0.25
4J
e
5’
0
0
0
38
0.547
1.094
45
0.700
1.400
60
1.212
2.425
70
1.923
3.846
where p,
= s t a t i c absolute pressure a t r = d/2 a t the i n l e t s t a t i o n , x/D = 0.
I f the pressure contribution t o Gx is retained i n the form of a w2/2 term, b u t the turbulent s t r e s s terms a r e omitted, the analysis leads immediately to:
75
Case 2 discussed i n Section 2 . 2 w i t h associated computations given i n Section 3 have axial and swirl S’ GI, with velocities deduced i n t h i s manner [I# appropriate radial pressure gradients being automat i c a l l y s e t up i n the computer program. Notice t h a t
-
,.
a gross error would be made i f Eq. ( 4 ) were t o be used t o s e t up the i n l e t velocities [$I S GI, since Eq. (6) i s valid f o r S’ values, not S values. In f a c t , corresponding G values would be much lower than those of Table 1 , with G asymptotically approaching 2 as + and 5 tend t o 90 deg. and w , respecti vely
Further, previous curved boundaries] is available.” swirling flow measurements are incorporated as wall functions to avoid t h e expense of computing w i t h i n the boundary layer. Zero velocities on a l l walls a r e assumed, w i t h s y m t r y conditions for most variables along the centerline, except swirl velocity which i s given a d e f i n i t e zero value.
2.2
The code i s operated i n the manner described in Ref. 10, w i t h sequential swirl vane angles of 0 , 38, 45, 60 and 70 deg. being computed t o convergence (approximately 400 i t e r a t i o n s , each w i t h 5 f i e l d updates f o r pressure, 4 f o r axial velocity and 3 f o r other primary variables) w i t h a 23 x 21 nonuniform g r i d covering a flow domain of length 40. A typical computer run covering a1 1 these swirl strengths requires about 15 min. of IBM 370/168 CPU time for a basic cost of $200 which i s discounted t o $20 a f t e r the 90 percent category 4 discount i s applied.
- -
.
Types of I n l e t Boundary Conditions Considered
In a l l cases considered, the k i n e t i c energy of turbulence k and i t s dissipation rate E are specif i e d as i n general accepted ways. l o y 2 0 The t o t a l local time-mean velocity magnitude has been used i n specifying k a t any radial position. Four possible specifications of the i n l e t velocities a r e considered: Case 1. Flat i n l e t axial and swirl velocities with velocity zero are assumed. T h a t i s , both u and w are constant valued:
uo = constant wo = uo tan 4 where 4 i s the swirl vane angle. Case 2. As Case 1, except that the i n l e t swirl velocity p r o f i l e i s assumed t o be t h a t of s o l i d body rota t i on :
uo
=
constant
wo = wmo r/R where w i s the maximum o r i f i c e value of w which occurs ?! the outer edge r = R of the i n l e t . The value of wmo i s so chosen as t o maintain the swirl nun-ber S’ the same as i n Case 1 , as described i n Section 2.1. Case 3. Measured i n l e t axial and swirl veloc? t i e s are used2’ with radial velocity assumed to be zero. Case 4. Measured i n l e t a x i a l , radial and swirl velocity values are used, taking data from recent five-hole pitot-probe d a t a i n close vicinity of the swirler exit.29 2.3
I t i s conceded that the k-E turbulence model i s in need of improvement f o r adequate simulation of turbulence swirling recirculating flow. Developments a r e t a k i n g place on differential and algebraic s t r e s s models f o r swirling flows, as exemplified for strongly swirling flow in vortex tube^.^' However, these models, and others f o r three-dimensional trans i e n t precessing vortex cores and coherent structure development, are n o t yet ready f o r use in applicationoriented studies. In addition, such approaches will appreciably increase the computer code complexity and time requirements.
The Solution Procedure
The prediction procedure s t a r t s from partial differential equations of conservation of mass, momentum ( i n x, r and e directions), turbulent k i n e t i c energy and i t s dissipation r a t e , which govern two-dimensional axisymnetric steady flow. The standard two-equation k-E turbulence model i s employed, which h a s been used i n a wide variety of turbulent flow ~ i t u a t i o n s ~ a ngood d predictive capaT h e equations d i f f e r b i l i t y has been achieved. primarily i n t h e i r final source terms. The corresponding f i n i t e difference equations a r e solved via an advanced version called STARPIC” of the TEACH computer code,” using a semi-implicit line-by-line method f o r values a t points of a variable s i z e rectangular g r i d , with variable under-relaxation.
3.
Flowfield Computations
Predictions a r e discussed f i r s t which deal with the flow through the i n l e t swirler with vane angles s e t t o 4 = 45 and 70 deg. Various types of i n l e t profile assunptions, Cases 1 through 4 of Section 2.2, are considered and the similarity and differences in the ensuing flowfield predictions are noted. Predictions are then presented for flowfields with a range of swirl strengths using measured i n l e t flaw velocity profiles f o r a x i a l , radial and swirl veloci t y in each case.*’ These and the effects of s i z e and location of a downstream nozzle are predicted and compared with available experimental evidence.7 With the computer code operated in the manner stated i n Section 2.3, to aid convergence, the solution for each value of 4 (0, 38, 45, 60 and 70 ideg.) i s used f o r the i n i t i a l s t a r t i n g values f o r the next higher value of 4. This includes the predictions for the s p e c i f i c cases of 4 = 45 and 70 deg. discussed a t length i n Section 3.1. The convergence criterion is t h a t a l l normalized residual source sums have t o be less than 0.004 and a l l results discussed have been obtained i n t h i s manner. 3.1
Effects of I n l e t Velocity Profiles
Swirl Vane Angle (p = 45 Ue . Consider f i r s t the flowfield resulting when t h z i n l e t swirl vane anqle is 45 dea. Fiaures 1 throuah 4 show Dredicted veiocity profiies at-various dowktream axial s t a tions, obtained when the i n l e t velocity profiles are spec i f ied by : Case 1: Case 2:
A complete description of the f i n a l l y developed computer program [with a f u l l description of the equation, source terms, revised c e l l volumes f o r axial and radial velocities, constants occurring and techniques f o r handling turbulent swirling flow near
Case 3: Case 4:
Flat u and w profiles, w i t h v zero. Flat u, profile, with solid body rotation w, and v zero. Measured u and w profiles, w i t h v zero. Measured u , v and w profiles.
as discussed i n Section 2.2.
76
The florrfield structure
-0.25
-0.50 0.50
.DO
Case 1
(a)
1.00
i.50
2.00
2.50
3.00
2.50
3.00
A X I R L POSJTION Y / O
Fig. 1 Predicted v e l o c i t y p r o f i l e s f o r I$ = 45 deg. f l o w f i e l d using i n l e t c o n d i t i o n s o f Case 1
0
I
x /D
'
-0.25 2
-0.50
Case 2
(b)
0.00
Fig. 2
Predicted v e l o c i t y p r o f i l e s f o r I$ = 45 deg. f l o w f i e l d using i n l e t c o n d i t i o n s o f Case 2
(c)
RXlFlL P O S I T I O N X I 0
K
\
Case 3
A X J R L P O S I T J O N X/O
-0.25 -0.50
(d)
0.05
case
Fig. 5 Fig. 3
Predicted v e l o c i t y p r o f i l e s f o r I$ = 45 deg. f l o w f i e l d using i n l e t c o n d i t i o n s o f Case 3
Fig. 4
Predicted v e l o c i t y p r o f i l e s f o r I$ = 45 deg. f l o w f i e l d using i n l e t c o n d i t i o n s o f Case 4
0.50
4
1.uo
1.50
R X I R L PCISJTION
2.00
X/O
P r e d i c t e d streamlines f o r I$ = 45 deg. f l o w f i e l d using various i n l e t c o n d i t i o n s
f o r these f o u r cases i s f u r t h e r i l l u s t r a t e d v i a s t r e a m l i n e p l o t s , which a r e computer c a l c u l a t e d and drawn, i n Fig. 5. I n s p e c t i o n o f these f i g u r e s i s q u i t e r e v e a l i n g and may be assessed i n t h e l i g h t o f p i t o t probe experimental data.' Note t h a t i n Cases 3 and 4 t h e a p p r o p r i a t e i n l e t values a r e p l o t t e d a t t h e x/D = 0 l o c a t i o n ; i n f a c t these a r e a c t u a l l y t h e values measured i m n e d i a t e l y downstream o f t h e I t i s con~ w i r l e r , * ~m o c a t i o n x/D = -0.11. v e n i e n t t o r e t a i n these values on t h e p r o f i l e p l o t s i n t h e p r e d i c t i o n study, although c l e a r l y r e s u l t s a t t h e x/D = 0 l o c a t i o n are then not d i r e c t l y comparable w i t h t h e i n l e t s t a t i o n data o f Ref. 7, which are taken p r e c i s e l y a t x/D = 0. These comments apply a l s o t o o t h e r p l o t s given i n t h e present paper.
A l l cases covered i n Figs. 1 through 5 g i v e c e n t r a l r e c i r c u l a t i o n zones t e r m i n a t i n g a t about x/D = 1.5, w i t h Case 4 having a s l i g h t l y s h o r t e r and w i d e r zone. I n i t i a l spreading r a t e s vary cons i d e r a b l y : o n l y i n Cases 3 and 4 does t h e c e n t r a l
77
/o
I
I
0
'-
2
0.M 0.25
1
0.50
Fig. 6 Predicted v e l o c i t y p r o f i l e s f o r Q = 70 deg. f l o w f i e l d using i n l e t c o n d i t i o n s o f Case 1
0.25
--__--
_____I_--
Fig. 7 Predicted v e l o c i t y p r o f i l e s f o r 4 = 70 deg. f l o w f i e l d using i n l e t c o n d i t i o n s o f Case 2 x /D
.OO
(c)
0.50
Case 3
i.00
1.50
2.00
2.50
3.00
AXIflL P O S I T I O N XI0
0.50 0.25
1 la) u/ue
(d)
Fig. 10
Iblw/u,
Fig. 8 Predicted v e l o c i t y p r o f i l e s f o r Q = 70 deg. f l o w f i e l d using i n l e t c o n d i t i o n s o f Case 3 x /D
(a] u/u,
0.25
u,
76lblw/u,
Fig. 9
case
P r e d i c t e d v e l o c i t y p r o f i l e s f o r Q = 70 deg. f l o w f i e l d using i n l e t c o n d i t i o n s o f Case 4
4
A X I A L POS!TION
X/O
.00
P r e d i c t e d streamlines f o r Q = 70 deg. f l o w f i e l d using various i n l e t c o n d i t i o n s
r e c i r c u l a t i o n zone begin imnediately on e n t r y t o t h e l a r g e chamber, w i t h Case 4 spreading most rapidl y i n t h e i n i t i a l region. Cases'l and 2 do n o t possess enough c e n t r i f u g a l e f f e c t because o f t h e i r u n r e a l i s t i c i n l e t s w i r l v e l o c i t y p r o f i l e s . Also, Cases 1 through 3 do n o t have a r a d i a l component o f v e l o c i t y t o encourage i n l e t r a d i a l spreading o f t h e streamlines. These i n l e t f l o w ideas may be conf i n n e d by observing t h e s i z e o f the corner r e c i r c u l a t i o n zone. Cases 2 and 4 e x h i b i t s h o r t e r corner zones, w i t h o n l y Case 4 a l s o possessing t h e c o r r e c t r a p i d spreading c e n t r a l a c t i v i t y near t h e i n l e t w i t h a c e n t r a l r e c i r c u l a t i o n f l o w beginning imnedia t e l y . None of t h e p r e d i c t i o n s match t h e precessing vortex core d e t a i l s found i n f l o w v i s u a l i z a t i o n o r t h e negative a x i a l v e l o c i t i e s measured by p i t o t probe experimentation' near t h e f a c i l i t y a x i s r / D < 0.1 extending a l l t h e way t o the t e s t s e c t i o n e x i t . Nevertheless, comparison o f t h e p r e d i c t i o n s w i t h t h e gross features o f t h e corresponding experimental data7 c l e a r l y i n d i c a t e s t h a t the i n l e t c o n d i t i o n s of Case 4 a r e s u p e r i o r i n a11owi ng r e a l i s t i c f l o w f i e l d p r e d i c t i o n .
--
78
Swirl Vane Angle 4 = 70 Deg. Figures 6 through 10 correspond t o Figs. 1 through 5 b u t w i t h the swirl vane angle increased t o 70 deg. Now the strong centrifugal forces present i n the incoming flow play their part. I n i t i a l spreading rates are very h i g h w i t h very small corner recirculation zones i n a l l cases, except t h a t of Case 3 seen i n Fig. 8 . A l l central recirculation zones begin imnediately a t the i n l e t and are much wider and longer than those w i t h Q = 45 deg. Those of Cases 1 and 2 a r e i n i t i a l l y very wide: much wider than the measurements7 i n d i cate. T h i s results from unrealistically large centrifugal forces attributable t o u n r e a l i s t i c a l l y large swirl velocity magnitudes. Case 3 does not spread rapidly enough a t the inlet and a long central recirculation zone extending to x/D = 2.5 is predicted. With the inclusion o f the correct i n l e t radial veloci t y , a recirculation zone much more l i k e t h a t found experimentally results i n Case 4. None of the cases predict swirl velocity profiles very accurately, w i t h w-profiles more l i k e s o l i d body rotation soon developing i n the downstream direction, in contrast t o the more free-forced vortex profiles found i n the experiments.' Fortuitously, Cases I and 2 seem t o do a b e t t e r job of predicting the long vortex core w i t h negative a x i a l velocity extending a long way downstream, a l b e i t w i t h very poor prediction of i n i t i a l i n l e t flow and very wide central recirculation region.
(b) Q = 38"
I~ U/u, I
Iblw/u,
(c)
Q
=
45" x
/o
A general deduction may be made from Figs. 1 through 10 when compared w i t h the experimental data. Results demonstrate t h a t r e a l i s t i c predictions a r e forthcoming only from the inclusion of the most accurate axial, radial and swirl velocity profiles as i n l e t conditions. Clearly the profiles of Case 4 must be used i n future turbulence modeling development studies for improved simulation of t h i s flowfield. 3.2
la) u / u ,
i b I w-1u, (d)
4 = 60" x /D
(a1 u/u,
(bl w/u.
( e ) Q = 70" Fig. 11 Predicted velocity profiles using measured i n l e t u , v and w profiles
Effects of Swirl
The velocity f i e l d predictions f o r swirl vane angles of 0 (swirler removed), 38, 45, 60 and 70 deg., using measured swirler e x i t u, v and w velocity p r o m each case,29 are displayed i n Fig. 11 parts a through e , respectively. Corresponding streamline patterns a r e plotted as shown in Fig. 12. Three-dimensional axi a1 Leloci ty representations a r e given i n Fig. 13. Here the ordinate of normalized axial velocity i s shown impressively as a function of normalized flowfield position. The flow i s from r i g h t t o l e f t , w i t h the sizes and shapes of corner and central recirculation zones being clearly evident, along w i t h axial velocity magnitudes.
The predicted e f f e c t s of swirl shown i n these figures confirm i n general the well-known ideas about swirl e f f e c t s on axisymnetric turbulent confined j e t flows.26 Under nonswirling conditions a large corner recirculation zone e x i s t s Whicii extends approxinla.tely to x/D = 2.3 f o r the expansion geometry D/d = 2 and to x/D = 1.25 f o r D/d = 1.43, see Pefs. 36 and 37. Both these r e s u l t s a r e consistent with an attachment point about 8 step hei hts downstream, as found by other researchers.6y7sQ4y16The centerline axial velocity changes gradually from its inlet value as downstream development occurs. However, as the degree of i n l e t swirl is increased t o 38 and 45 deg., axial velocity profiles change dramatically. Near the i n l e t a central toroidal recirculation zone appears and the corner recirculation zone shortens considerably. Under strong swirl conditions of Q equal t o 60 and 70 deg., a much wider central r e c i r -
79
u/u
0.25
-= A / .00
(a) 4 = 0"
UIU, I
.e
a.0
8.8. S.2
-0.25 . . I
-G.SO
4 :
0
(c) Q = 45"
e:.
P
XI0
.00
F l X l F I L POSITION X / D
- d . a I -0.0
s:*
(c) Q = 45"
s.0
1.0 0.50
m.2
O'.OO
(d)
0:SO
Q = 60'
(e) Q = 70"
l'.OO
1'.50
2'.00
2:SO
3'.00
F I X I R L POSITION X / U
(d)
A X I F I L POSITION X I 0
$I = 60"
"I
(e) Q
Fig. 12 Predicted streamlines using measured inlet u, v and w profiles
"
= 70'
Fig. 13 Axial velocity representation
80
culation region i s established. I t promotes a very large forward velocity near the confining walls rather than a corner recirculation region. These predicted effects generally agree w i t h the experimental d a t a Y 7except t h a t precessing vortex core regions of s o l i d body rotation backflow, which occur downstream of central recirculation regions i n the swirl flow cases investigated,26 are not well predicted. Only the 70 deg. case predicts almost zero axial velocity on the centerline extendi n g to x/D = 4 . The central recirculation zone is predicted to be longer than found i n practice. Also, swirl velocity profiles do not match well the experimental data -- the radial location of swirl velocity maximum value occurs too close t o the confining chamber walls rather than occurring abruptly a t the edge of a vortex core region. The observed discrepancies may be because of poor probe sensitivi t y i n turbulent low velocity regions, and/or poor turbulence model performance i n these regions. Only further detailed hot-wire and/or l a s e r doppler anemometer measurements and turbulence model development will resolve the inconsistencies.
,.
o m
,
.00 0. 50 0.25
-0.25 -0.50 .oo
0.50
2.50
3.00
= 45"
(b)
3 . 3 Effects of a Weak Contraction Nozzle Sections 3 . 3 and 3 . 4 discuss the prediction of flowfields w i t h downstream contraction nozzles located a t L/D = l and 2 f o r a range of swirl strengths I$ = 0, 45 and 70 deg., using swirler e x i t measured u, v and w velocity profiles i n each case.ls Two
O*
.oo
F i g . 15 Predicted streamlines with weak contraction nozzle a t LID = 2
.. U
I
la1 u/u,
( a ) cp
e .
= 0" X/D
0.2
4.2
(a)
l a ) u/u,
( c ) cp = 70"
I$
=
0"
Figure 16 Axial velocity representation with weak contraction nozzle a t LID = 2
F i g . 14 Predicted velocity profiles w i t h weak contraction nozzle a t L I D = 2
81
u
v
\
0.25
Lv//
0.25 .u
\1
0.25 "0
is found t h a t the weak contraction nozzle has most effect on the intermediate swirl case of $I = 45 deg.
7
.u
\
e f f e c t on weakly swirling and strongly swirling flows, which are dominated by forward flow and centrifugal forces , respectively. The predictions showed a more
\
Predictions a r e now discussed f o r the case of the strong contraction nozzle of area r a t i o 4 being
I -a
82
U 1.1
0.50 0.7
0.0
n nn! V.""
4.2
-
-0*50!U0
0'.50
( a ) 4 = 0"
l'.OO
1'.W
2:OO
A X I A L PDSITION X / D
2'.50
4.00
(a)
4
=
Oo
U
1 .e
I .0 0.W 0.4
4 . 2
X
(b)
4
=
45"
-0.0
9X!AL P O S I T I ~ l u X / D
-0.25
-0.50
7uo
0 50
(c) 4 = 70"
1.uo
2:oo
11.5U
R X I R L POSITI'N
2.50
3.00
X/D
F i g . 18 Predicted streamlines w i t h strong contraction nozzle a t L/D = 1
Fig. 19 Axial velocity representation with strong contraction nozzle a t L / D = 2
predicted velocity profiles, streamline plots and axial velocity representations i l l ustrate t h e largescale effects of i n l e t swirl on flowfields.
4.
Lefebvre, A. H . (ed.), Gas Turbine Combustor Design Problems , Hemisphere-McGraw-Hill , New York, 1980.
Predictions a r e included f o r t h e e f f e c t of weak and strong downstream contraction nozzles on the flow. I t appears t h a t a weak nozzle has only a minor e f f e c t on the flow. In t h e swirl flow cases, a weak nozzle leads t o the discouragement of central recirculation zones w i t h stronger vertex cores downstream possessing negative axial velocities. A strong nozzle has more pronounced e f f e c t s on swirl flow cases, with discouragement of central recirculation zones, and forward flow i n highly swirled vortex core regions further downstream.
5.
Gupta, A. K., and Lilley, D. G . , Flowfield Modeling and Diagnostics. Abacus Press, Tunbridge Wells, England, 1983 ( i n press).
6.
Rhode, D. L . , Lilley, D. G., and bkLaughlin, D. K . , Mean Flowfields i n Axisymnetric Combust o r Geometries w i t h Swirl, Paper AIAA 82-0177, Orlando, Florida, Jan. 11-16, 1982. AIAA Journal, 1983 ( i n press).
7.
Yoon, H. K., and Lilley, D. G . , Five-Hole P i t o t Probe Time-Mean Velocity Measurements i n Confined Swirling Flows, Paper AIAA 83-0315, Reno, Nevada, Jan. 10-13, 1983.
8.
Rhode, D. L., Predictions and Measurements of Isothermal Flowfields in Axisymmetric Combustor Geometries, Ph.D. Thesis, School of Mech. and Aero. Engng. , Oklahoma S t a t e University, S t i l l water, Okla., Dec. 1981.
9.
Rhode, D. L., Lilley, D. G . , and McLaughlin, D. K . , On the Prediction of Swirling Flowfields Found i n Axisymnetric Combustor Geometries, ASME Journal of Fluids Engng., Vol 104, 1982, Pp. 378-384.
Acknowledgments The authors sincerely express their gratitude to NASA Lewis Research Center and Air Force Wright Aeronautical Laboratories f o r financial support via NASA Grant No. NAG 3-74, technical monitor Dr. J . D. Holdeman. References 1.
Lilley, D. G., Swirl Flows i n Combustion: A Review, AIAA Journal, Vol. 15, No. 8, August 1977, pp. 1063-1078.
.
2.
Lilley, D. G . , Flowfield Modeling i n Practical Combustors: A Review, Journal of Energy, Vol. 3, JUly-AUg. 1979, pp. 193-210.
3.
Lilley, D. G . , Prospects f o r Computer Modeling i n Ramjet Combustors, Paper AIAA 80-1189, Hartford, CT, June 30-July 2 , 1980.
83
10.
Lilley, D. G., and Rhode, D. L . , A Computer Code f o r Swirling Turbulent Axisymnetric Recirculating Flows i n Practical Isothermal Combust o r Geometries, NASA CR-3442, Feb. 1982.
11.
Gosman, A. D., and P u n , W. M . , Calculation of Recirculating Flows, Rept. No. HTS/74/12, Dept. of Mech Engng ., Imperial College, London , England, 1974.
25.
Khalil, E. E., Modeling of Furnaces and Combustors, Abacus Press, Tunbridge Wells, England, 1982.
26.
Gupta, A. K., Lilley, D. G., and Syred, N., Swirl F1ows , Abacus Press , Tunbri dge We11s , England, 1983 ( i n press).
27.
Launder, B. E., and Spalding, D. B., Mathematical Models of Turbulence, Academic Press, London, England, 1972.
28.
Launder, B. E., and Spalding, D. B., The Numerical Computation of Turbulent Flows, Comp. Methods i n Appl. Mech. and Engng., Vol. 3, March 1974, pp. 269-289.
.
12.
13.
14.
Khalil, E. E . , Spalding, D. B., and Whitelaw, J. H . , The Calculation of Local Flow Properties i n Two-Dimensional Furnaces, Int. J . Heat Mass Trans. , Vole 18, 1975, pp. 775-791. Kubo, I . , and Gouldin, F. C., Numerical Calculations of Turbulent Swirling Flow, Journal of Fluids Engineering, Vol. 47, Sept. 1975, pp. 310-31 5. Lilley, D. G. , Primitive Pressure-Velocity Code f o r the Computation of Strongly Swirling Flows, AIM Journal, Vol. 14, June 1976, pp. 749-756.
15.
Wuerer, J . E., and Samuelsen, G. S., Predictive Modeling of Backmixed Combustor Flows: Mass and Momentum Transport, AIAA Paper 79-0215, New Orleans, Louisiana, Jan. 15-17, 1979.
16.
Novick, A. S., Miles, G. A . , and Lilley, D. G., Numerical Simulation of Combustor Flowfiel ds: A Primitive Variable Design Capability, J ; of Energy, Vol. 3, No. 2, March-April, 1979, pp. 95-105.
17. Habib, M. A . , and Whitelaw, J . H . , Velocity Characteristics of Confined Coaxial Jets W i t h and Without Swirl , Journal of Fluids Engng. , Vol 102, March 1980, pp. 47-53.
.
18.
19.
20.
21.
22.
23.
24.
Srinivasan, R., and Mongia, H . C., Numerical Computations of Swirling Recirculating Flows, Final Report, NASA-CR-165196, S e p t . 1980.
'
29.
Sander, G. F., and Lilley, D. G., The Performance of an Annular Vane Swirler. Report on Work i n Progress, School of Mech. and Aero. Engng., Oklahoma S t a t e University, Stillwater, Okla., Oct. 1982.
30.
Chigier, N. A., and Chervinsky, A., Experimental Investigation of Swirling Vortex Motion in J e t s , ASME Journal of Applied Mechanics, Vol. 89, June 1967, pp. 443-451.
31.
Beer, J . M . , and Chigier, N. A , , Combustion Aerodynamics , Appl ied Science, London and Wiley, New York, 1972.
32.
Chigier, N. A., and Beer, J. M., Velocity and S t a t i c Pressure Distributions i n Swirling Air Jets Issuing from Annular and Divergent Nozzles, J . of Basic Engng., Dec. 1964, pp. 788-798.
33.
Kerr, N. M., and Fraser, D., Swirl, Part I: Effect on Axisymmetrical Turbulent Jets, J. Inst. Fuel, Vol. 38, Dec. 1965, pp. 519-526.
El-Banhawy, Y . , and Whitelaw, J . H . , Calculation of the Flow Properties of a Confined KeroseneSpray Flame, AIAA J . , Vol. 18, No. 2, Dec. 1980, 34. pp. 1503-1510. Sturgess, G. J., and Syed, S . A., Widely-Spread Coaxial J e t , Diffusion Flame Combustor: Isothermal Flow Calculation Using the Two-Equation 35. Turbulence Model , Paper No. AIAA 82-0113, Orlando, Florida, January 11-14, 1982. Serag-Eldin, M. A., and Spalding, D. B., Computations of Three-Dimensional Gas-Turbine Combustion Chamber Flows, Trans. ASME J. of Eng. 36. f o r Power, Vol. 101 , July 1979, pp. 326-336. Mongia, H. C., and Reynolds, R. S., Combustor Design Criteria Validation Vol. I11 - User's Manual, Report USARTL-TR-78-55CY U.S. Army Res. and Tech. Lab., F t . Eustis, VA, Feb. 1979. [See a l s o Vols. I and 111. Swithenbank, J., Turan, A., and Felton, P. G., Three-Dimensional Two-Phase Mathematical Modeling of Gas Turbine Combustors, i n Gas Turbine Combustor Design Probl ems (Lefebvre , A. H. , ed.) , Hemisphere-McGraw-Hi11 , New York, 1980, pp. 249-314.
Boysan, F., Ayers, W. H . , and Swithenbank, J., A Fundamental Modeling Approach t o Cyclone Design, Trans. J . Chem. E., Vol. 16, No. 4, July 1982, pp. 222-230. Lilley, D. G., Turbulent Combustor Flowfield Investigation, Paper i n Combustion Fundamentals Research Conference, held a t NASA Lewis Research Center, Cleveland, Ohio, Oct. 21-22, 1982, pp. 152-168. Chaturvedi , M. C.
, Flow Characteristics of
Axi-
symnetric Expansions, Proc. Journal Hydraulics Division, ASCE, Vol. 89, No. HYE, 1963, pp. 61-92.
37.
Moon, L. F., and Rudinger, G., Velocity Distri-
38.
Abujelala, M. T . , and Lilley, D. G., Confined Swirling Flow Predictions: Effect of Contraction Nozzles on Flowfields. Report on Work i n Progress , School of Mech. and Aero. Engng. Y Oklahoma S t a t e University, Stillwater, Okla., Jan. 1983.
Srivatsa, S. K . , Computations o f Soot and NOx Emissions from Gas Turbine Combustors, NASA CR-167930, May 1982.
84
bution i n an Abruptly Expanding Circular Duct, ASME Journal of Fluids Engng., March 1977, pp. 226-230.
APPENDIX F SINGLE-WIRE SWIRL FLOW TURBULENCE MEASUREMENTS ( A I AA- 83- 120 2 )
85
SINGLE-WIRE SWIRL FLOW TURBULENCE MEASUREMENTS T. W. Jackson* and D. G. Lilley** Oklahoma State University, Stillwater, Okla.
Abstract A six-orientation single-wire hot-wire technique i s used to investigate nonswirling and swirling nonreacting flow i n an axisymnetric t e s t section with expansion r a t i o D/d = 2, which may be equipped with a strong contraction nozzle of area r a t i o 4 a*t L/D = 2. The flowfield contains corner and central recirculation zones typical of gas turbine and ramjet combustion chambers. Swirl may be imparted to t h e in-coming flow by means of a variable-angle vane swirler. The e f f e c t of swirl on time-mean velocities and complete Reynolds s t r e s s tensor i s investigated, and extensive results are given for swirl vane angles of 0 ( s w i r l e r removed), 38, 45, 60 and 70 deg. The data a r e being used t o aid in the evolution of turbulence models f o r these complex flow situations. A directional s e n s i t i v i t y analysis i s included, which determines the r e l a t i v e accuracy of the measurement technique t o approach velocity orientation.
Nomenclature
P Re V =
(U,V,W)
x,r,e Z
9
calibration constants t e s t sect i on di ameter i n l e t nozzle diameter hot-wire voltage pitch factor yaw factor contraction nozzle downstream distance time-mean pressure Reynolds number time-mean velocity ( i n x-, r-, edirections) in f a c i l i t y coordinates a x i a l , radial, azimuthal cylindrical polar coordinates effective cooling velocity acting on a wire swirl vane angle with respect t o f a c i l i t y axis
Subscripts value a t i n l e t to flowfield root-mean-squared quantity
0 rlllS
Superscripts t i me-mean average fluctuating quantity r e l a t i v e t o probe coordinates 1. 1.1
Some recent researchers6-' measured time-mean and turbulence properties in the vicinity of these recirculation zones w i t h the presence of chemical reaction. However, more fundamental knowledge about the fluctuating velocities and t h e i r cross-correlations f o r a variety of swirl strengths under isothermal conditions i s needed before the complex interactions of chemical reaction and turbulent mixing are f u l l y understood. Chaturvedig measured the time-mean and turbulent properties of a confined j e t in the absence of swirl and found high turbulent mixing on the shear layer produced by the sudden expansion. He also found t h a t the CRZ extended t o 2 chamber diameters downstream of the expansion s t a tion, with a n expansion r a t i o D/d of 2. Some researchers extended t h e i r i n t e r e s t t o swirling confined flows, with emphasis on time-mean velocity distributions (see, f o r example, Refs. 10-13) and turbulence quantities (see, for example, Refs. 1417). However, only low swirl strengths have been cons idered in the 1a t t e r cases. 1.2
Objectives
The focus of the present paper i s the measurement of time-mean and turbulence d a t a for a full range of swirl strengths. This extends the data base given e a r l i e r 1 6 t o higher i n l e t vane swirl angles and more axial measurement stations. Effects of a strong contraction nozzle of area r a t i o 4 10cated a t L/D = 2 are included. Results of an accuracy check on s e n s i t i v i t y of results t o velocity orientation are also given and assessed. 1.3 Outline of the Present Study The experimental f a c i l i t y being used consists of a sudden expansion (3.2 cm downstream of the downstream face of a variable-angle vane swirler) into a larger chamber of diameter 30 un and length 150 cm. The expansion r a t i o D/d i s 2. Figure 1 shows schematically the t e s t section w i t h the associated coordinate system and traversing mechanism. Previous papers describe a t length the t e s t f a c i l i t y and general time-mean flow patterns, the sixorientation single-wire hot-wire measurement technique,16 and the performance of the annular vane swirler being used.
Introduction
The Problem and i t s Significance
The present research forms part of a project on the investigation of flowfields found in typical combustor geometries; studies are in progress concerned with experimental and theoretical re-
* Graduate Student, School of Mechanical and
**
search in 2-0 axisymnetric conditions. The general aim i s t o characterize the time-mean and turbulence flowfield, recomnend appropriate turbulence model advances, and implement and exhibit results of flowf i e l d predictions.' Nonreacting flowfields of t h i s type are important, since swirling j e t s have been found t o play a significant role in j e t growth, entrainment ana decay i n nonreacting flows,' and in the length, s t a b i l i t y and combustion efficiency of flames in combustor chambers. 3-5 Generally, two recirculation zones a r e observed in confined flows: the corner recirculation zone (CRZ) and the central toroidal recirculation zone (CTRZ). Both of these contain large turbulent eddies which promote mixing between the h o t combustion products and the incomina fuel and a i r flows.
Aerospace Engineering, Student Member AIAA Professor, School of Mechanical and Aerospace Engineering, Associate Fellow AIAA
86
s u f f i c i e n t i n f o r m a t i o n . King l 9 developed a technique based on t h a t o f Dvorak and Syred" u s i n g a s i n g l e hot-wi r e t h a t can measure the time-mean and turbulence p r o p e r t i e s i n a complex f l o w f i e l d . The method c a l l s f o r a normal h o t - w i r e t o be o r i e n t a t e d through s i x d i f f e r e n t p o s i t i o n s , each o r i e n t a t i o n separated by 30 degrees f o r t h e adjacent one. O r i e n t a t i o n 1 i s normal t o t h e f a c i l i t y c e n t e r l i n e , o r i e n t a t i o n 2 i s r o t a t e d 30" from t h i s , e t c . Mean and root-meansquare voltages a r e measured a t each o r i e n t a t i o n . The data r e d u c t i o n i s performed using assumptions t h a t turbulence f o l l o w s a normal p r o b a b i l i t y d i s t r i b u t i o n having mean v o l t a g e as t h e mean and t h e squared value o f t h e rms v o l t a g e as t h e variance. I t i s then p o s s i b l e t o o b t a i n t h e t h r e e time-mean v e l o c i t y components, t h e t h r e e normal Reynolds stresses and t h e t h r e e shear Reynolds stresses, i n the manner now described.
Traverse unit V i f h Probe
F i g . 1 Hot-wire probe mounted on the t e s t s e c t i o n The present paper extends t h e a v a i l a b l e timemean and turbulence data base t o f l o w s w i t h s t r o n g Time-mean p r o p e r t i e s and t h e complete swirl Reynolds s t r e s s tensor a r e presented f o r a v a r i e t y o f s w i r l strengths ( w i t h s w i r l vane angle 4 o f 0 ( s w i r l e r removed), 38, 45, 60 and 70 deg.) Sect i o n 2 r e c a l l s b r i e f l y t h e measurement technique, and introduces t h e d i r e c t i o n a l s e n s i t i v i t y study. Results a r e presented and discussed i n S e c t i o n 3, w h i l e Section 4 draws conclusions from t h e study.
.
.
2. 2.1
Measurement Technique
Confined F l o w f i e l d Measurements
One o f the most w i d e l y used instruments t o o b t a i n turbulence q u a n t i t i e s i s t h e h o t - w i r e anemometer, t h e most common o f which i s t h e s i n g l e h o t - w i r e . When used on a two-dimensional f l o w w i t h a predominate f l o w d i r e c t i o n , a s i n g l e h o t w i r e used normal t o t h e main f l o w can be used t o measure t h e streanwise components o f t h e time-mean v e l o c i t y and t h e rms v e l o c i t y f l u c t u a t i o n , i n a standard manner. The anemometer used f o r t h e p r e s e n t study i s DISA t y p e 55M01, CTA standard b r i d g e . A normal h o t - w i r e probe, DISA t y p e 55P01 , i s used i n t h e experiments. T h i s probe has two prongs s e t approximately 3 mm a p a r t which support a 5 urn diame t e r w i r e which i s g o l d p l a t e d near t h e prongs t o reduce end e f f e c t s and strengthen t h e w i r e . The mean v o l t a g e i s measured w i t h a Hickok D i g i t a l Systems, Model DP100, i n t e g r a t i n g v o l t m e t e r and t h e root-mean-square v o l t a g e f l u c t u a t i o n i s measured u s i n g a H e w l e t t Packard, Model 400 HR, AC v o l tmeter. The h o t - w i r e i s supported i n t h e f a c i l i t y by a t r a v e r s i n g mechanism, shown s c h e m a t i c a l l y i n F i g u r e 1. I t c o n s i s t s o f a base t h a t i s m o d i f i e d t o mount on the p l e x i g l a s s tube o f t h e t e s t sect i o n a t various a x i a l l o c a t i o n s . The h o t - w i r e probe i s i n s e r t e d i n t o t h e tube through a r o t a r y v e r n i e r and t h e base. The r o t a r y v e r n i e r i s attached t o a s l i d e which can t r a v e r s e across t h e f l o w chamber. Thus, i t i s p o s s i b l e f o r t h e probe t o be t r a v e r s e d t o any r a d i a l l o c a t i o n a t s e l e c t e d downstream l o c a t i o n s i n t h e f l o w f i e l d and t o be r o t a t e d through 180 degrees.
I n a complex s w i r l i n g f l o w f i e l d t h e dominant flow d i r e c t i o n i s unknown and t h e standard s i n g l e o r i e n t a t i o n s i n g l e h o t - w i r e method f a i 1s t o supply
The s i x - o r i e n t a t i o n h o t - w i r e technique r e q u i r e s a s i n g l e , s t r a i g h t , h o t - w i r e t o be c a l i b r a t e d f o r t h r e e d i f f e r e n t f l o w d i r e c t i o n s i n order t o determine t h e d i r e c t i o n a l s e n s i t i v i t y o f t h e probe. I n the f o l l o w i n g r e l a t i o n s h i p s , t i l d e s s i g n i f y components o f t h e instantaneous v e l o c i t y v e c t o r i n coordinates on t h e probe. Each o f t h e t h r e e c a l i b r a t i o n curves i s obtained w i t h zero v e l o c i t y i n t h e o t h e r two d i r e c t i o n s . The c a l i b r a t i o n curves demonstrate t h a t t h e h o t - w i r e i s most e f f i c i e n t l y cooled when the f l o w i s i n t h e d i r e c t i o n o f t h e ii component (which i s normal t o b o t h t h e w i r e and t h e supports). The w i r e i s most i n e f f i c i e n t l y cooled when t h e f l o w i s i n t h e d i r e c t i o n o f t h e i? component (which i s p a r a l l e l t o t h e w i r e ) . Each o f t h e c a l i b r a t i o n curves f o l l o w s a second order, least-square f i t o f t h e form: E?1 = Ai
+
Biiiiill2
+
CiGi
which i s an extension o f the f a m i l i a r K i n g ' s law. I n t h i s equation, Ai, Bi, and Ci a r e c a l i b r a t i o n constants and ii. can take on a value o f ti, Q, and G f o r t h e t h r e e c a l i b r a t i o n curves, r e s p e c t i v e l y . When t h e w i r e i s placed i n a three-dimensional f l o w f i e l d , the e f f e c t i v e cooling v e l o c i t y experienced by the h o t - w i r e i s :
where G and K a r e t h e p i t c h and yaw f a c t o r s , d e f i n e d by JorgensenZ1 and deduced from t h e c a l i b r a t i o n curves. Hence, equations f o r t h e e f f e c t i v e c o o l i n g v e l o c i t y can now be obtained f o r each o f t h e s i x w i r e o r i e n t a t i o n s . S o l v i n g simultaneously any t h r e e adjacent equations provides expressions f o r t h e instantaneous values o f t h e t h r e e v e l o c i t y components (u, v, and w i n f a c i l i t y x, r, and e c o o r d i nates, r e s p e c t i v e l y ) i n terms o f t h e e q u i v a l e n t c o o l i n g v e l o c i t i e s . I t i s then p o s s i b l e t o o b t a i n t h e t h r e e time-mean v e l o c i t y components and t h e s i x d i f f e r e n t components o f t h e Reynolds s t r e s s tensor, i n t h e manner described i n Ref. 16. Because o f l a c k of d i r e c t i o n a l knowledge, data presented i n Section 3 were o b t a i n e d from an average o f t h e values found i n each o f t h e s i x p o s s i b l e combinat i o n s o f t h r e e adjacent w i r e - o r i e n t a t i o n s .
2.2
D i r e c t i o n a l S e n s i t i v i t y Analysis
The d i r e c t i o n a l s e n s i t i v i t y a n a l y s i s o f t h e technique i s performed i n a f r e e j e t o f known f l o w p r o p e r t i e s . Measurements were taken on t h e centerl i n e i n t h e p o t e n t i a l core o f t h e j e t , correspond-
87
ing t o a laminar flow, and on the shear layer a t three nozzle diameters downstream of the j e t e x i t , i n a turbulent region. The two regions were chosen to check the directional s e n s i t i v i t y of the technique in laminar and turbulent flows. The analysis is performed by i n i t i a l l y placi n g the probe i n t h e j e t such t h a t the coordinate system of the probe coincides w i t h the coordinate system of the j e t . Measurements a r e then taken by rotating the probe i n the manner of the technique described. To simulate the e f f e c t of the flow shifting i t s dominant flow direction, the probe i s rotated by 5 deg. about i t s z-axis, a s shown in F i g . 2. This rotation causes a misalignment between the probe coordinate system and t h e f a c i l i t y coordinates. This discrepancy can be accounted f o r by use of the rotation matrices22 described in Appendix A. In this configuration, the measured time-mean values, normal and shear s t r e s s e s a r e i n a coordinate system oblique t o the j e t coordinate system. However, they can b e transformed back t o the f a c i l i t y coordinate system.23 Results shown l a t e r in Section 3.3 have been obtained i n t h i s manner.
4 located a t L / D = 2. This nozzle has a 451feg. slope facing upstream as described e a r l i e r . Measurements are made w i t h the single-wire technique described i n Section 2.1 and Ref. 16. The nozzle i n l e t velocities and Reynolds numbers employed i n this study are h i g h enough to ensure t h a t the flowf i e l d s are investigated under conditions independent of Reynolds number variation. They correspond approximately to conditions reported i n associated studies.12 F i r s t l y , time-mean and turbulence chara c t e r i s t i c s f o r f i v e different swirl strengths are presented and discussed. In each case, radial prof i l e s of interesting properties a t s i x axial locations are presented. Secondly, the effects of the strong contraction nozzle on the time-mean and turbulence properties in the flowfield are c l a r i f i e d f o r the cases of no swirl, moderate swirl and strong swirl. All properties shown are normalized w i t h respect t o the swirler i n l e t uniform axial velocity uo deduced independently from a measurement upstream of the swirler. Finally, a directional s e n s i t i v i t y analysis involving t h e time-mean and turbulent properties of a round free j e t has been performed. Three probe-jet axis orientations have been used t o simulate the s h i f t i n g of the dominant flow direction and consequently the effectiveness of the hot-wire technique t o measure the properties of a strongly swirling flow, whose -local flow direction i s unknown a p r i o r i . 3.1
Effects o f Swirl
Nonswirling Flows ( 4 = 0 deg. swirler removed.) Figure 3 shows time-mean and turbulence data f o r the nonswirlina flow. A nearlv-flat axial velocity profile i s see; i n the entrance region of the testsection. As expected, there i s no measurable swirl velocity and only a small radial velocity. Although a corner recirculation zone (CRZ) i s present, there i s no evidence of a central toroidal recirculation zone (CTRZ). Indeed, there i s no swirl-induced centrifugal force t o encourage i t s formation. The hot-wire anemometer cannot sense flow direction; however, directional properties of t h e flow can by2 inferred from e a r l i e r five-hole p i t o t probe data, and flow visual i zation photography. Nevertheless, the authors have retained the positive values on all figures wherever possible uncertainties might e x i s t . The time-mean data shows good agreement w i t h t h a t found by Chaturvedig i n a similar t e s t section, and w i t h that found by Yoon and Lilley’* u s i n g a fivehole pi t o t probe i n the same t e s t faci l i t y with identical flow conditions. Fig. 2
Cases 1 , 2, and 3 of the directional s e n s i t i v i t y study
To examine the directional sensi ti vi ty of the wire further, the probe was subsequently rotated about its new ^x-axis , thereby forming a compound angle between probe and the dominant flow velocity, as a l s o shown i n Fig. 2. Again the time-mean velocities and Reynolds s t r e s s tensor can be deduced i n terms of t h e j e t coordinate system by the method shown i n Appendix A, and the r e s u l t s and t h e i r accuracy a r e also discussed i n Section 3.3. 3.
Results and Discussion
Nonswirling and swirling nonreacting flows a r e investigated i n an axisymnetric test section w i t h expansion r a t i o Dld = 2, which may be equipped w i t h a strong contraction nozzle of area r a t i o
The maximum values of normal s t r e s s e s appear on the shear layer w i t h the axial fluctuation component dominating. Earlier resultsg indicated t h a t the axial turbulence intensity was larger than the other two components and t h a t the radial turbulence intensity was approximately equal t o the tangential turbulence intensity. This i s confirmed in the presen t s tudy
.
The six-orientation technique produces positive values of shear s t r e s s . However, i n certain locations i n the vicinity of recirculation zones, the radial gradient of the axial velocity i s predominately positive which is associated w i t h negative values o f ’LTrlTr. Nevertheless, a l l shear s t r e s s values in t h i s document a r e plotted as positive. Because,of the absence of velocity gradients i n the x- and &directions, only one shear s t r e s s (the xr-component) is s i g n i f i c a n t i n the nonswirling case. T h i s shear s t r e s s , plotted i n Fig. 3, tends
t o be lower than the e a r l i e r study.g I t should be noted, however, t h a t the shear stresses a r e the most d i f f i c u l t turbulent quantities t o measure accurately in a complex flowfield. Uncertainties in measurements of time-mean velocities and turbulence i n t e n s i t i e s a r e increased in the determination of shear stresses. Moderate Swirl (I$ = 38 and 45 deg.). In confined swirling j e t flows the axial and tangential time-mean velocities dominate, a s can be seen from Figs. 4 and 5. The corner recirculation zone can be seen clearly a t the expansion plane of the t e s t section. The CRZ is not seen a t any other axial location, indicating that the swirling flow greatly reduces the length of the CRZ. Swirling flow produces a central toroidal recirculation zone which can also be seen i n t h e figures. The CTRZ appears to have a length of approximately 1.5 D. Downstream of t h i s p o i n t on the j e t a x i s , indication i s given of a precessing vortex core (PVC) extending t o the e x i t plane of the t e s t section. The PVC i s defined as a region of low axial velocity and h i g h almost solid body rotation swirl along the axis and i s found t o be present in the swirling flows considered. Yoon and Lilley” also measured the time-mean swirling flowfield, using a five-hole p i t o t probe and the present data i s found t o be in good agreement. The PVC i s most clearly observed i n flow visualization studies, using s t i l l photography’”2“ and videotape recordings.‘ The three normal turbulent s t r e s s e s appear t o be f a i r l y isotropic a t a l l locations i n the t e s t chamber w i t h maximum values occurring i n regions of recirculation and regions of h i g h shear. I t was found t h a t large-scale turbulence with big eddies occurs in recirculation regions and t h a t small-scale turbulence w i t h small eddies occurs i n regions of peak velocities. In the downstream regions of the t e s t chamber, the turbulence levels are low, with a more uniform radial profile, indicating a more developed nature of the flow.
I t can also be seen t h a t a l l three shear s t r e s s components are s i g n i f i c a n t i n swirling flows, as expected. The maximum values of shear s t r e s s occur in the thin shear layer regions b u t quickly dissipate in the downstream direction a the shear layer broadens. The stresses W / u 0 and u ’ / u are found t o have large values close to the wal?, because of the steep axial and swirl velocity gradients.
3
Strong Swirl (I$ = 60 and 70 deg.) Time-mean velocity profiles f o r the strongest swirl cases considered a r e shown i n Figs. 6 and 7. Almost a l l of the flow leaves the swirler near the outer edge, producing steep velocity gradients i n t h i s vicinity. High velocity gradients can a l s o be seen near the wall, especially a t x/D = 0.5. The strong centrifugal forces present i n the incoming flow produce rapid outflow t o the confining boundary. Both central and corner recirculation zones can be seen clearly from the time-mean plots. However, i t appears t h a t the CTRZ is shorter f o r t h i s strong degree of swirl as compared t o the moderate swirl case. In contrast, the PVC gets wider as the swirl strength increases, as also found i n fivehole p i t o t probe data.” The normal turbulent stresses have increased in magnitude, consistent w i t h the increase i n swirl strength, and s t i l l a good degree of isotropy
i s observed throughout the e n t i r e flowfield. The highest turbclence levels again occur i n regions of recirculation and on the shear layers. I t can also be seen that h i g h turbulence levels are found i n the PVC. The most dramatic e f f e c t of the increase of swirl swirl i s the large increase i n a l l three shear s t r e s s values. I t can be seen t h a t very high values of shear s t r e s s occur i n the shear layers and near the walls. T h e PVC also contains high values of shear stresses and turbulence levels Overall, the values of shear stresses are higher than i n other swirl strengths considered.
.
3.2
Effects of Strong Contraction Nozzle
Nonswi rl i ng F1 ows . Time-mean and turbul ence characteristics f o r the nonswirling flow with a strong contraction nozzle a t L/D = 2 are presented i n F i g . 8. The plots show that results vary very l i t t l e from t h a t of the corresponding flowfield without a contraction nozzle, see Fig. 3 . The major difference appears t o be a s l i g h t reduction i n the length of the CRZ. The measured time-mean flowfield compares favorably w i t h previous d a t a . l 2 Moderate Swirl. The effects of the contraction nozzle on the moderately swirling flow with $I = 45 deg. are shown i n Fig. 9 . The presence of the contraction nozzle accelerates the flow and produces a strong favorable pressure gradient over the enti re flowfield of i n t e r e s t . This pressure gradient conf l i c t s with the adverse pressure gradient inherent i n swirling flows (associated with recirculation zones) . Regions of positive axi a1 velocity occur near the centerline a t a l l axial locations. T h e central recirculation zone i s now located i n annul a r region around the j e t axis and i s much smaller than in the corresponding open flowfield of Fig. 5 . A narrow central core region i s observed t o extend throughout the length of the t e s t section with strong solid body rotation. Positive axial veloci t i e s now occur i n this region, as opposed t o negative ones i n the corresponding open-ended flow case; t h i s and other time-mean data bein in excellent agreement w i t h e a r l i e r experimental” and predi c t i on2 a studi es
.
The directional turbulence intensities do n o t show any s i g n i f i c a n t increase i n magnitude compared to the open-ended swirling flow. However, the turbulent shear s t r e s s e s are found to increase near the j e t axis as the contraction nozzle e x i t i s approached. This i s because of the f a i r l y high turbulence levels i n t h i s region and the e r f e c t of strong velocity gradients with which these s t r e s s e s are associated. Strong Swirl. For swirl vane angle I$ = 70 deg., measurements a r e given in Fig. 10 with the strong contraction blockage located a t L/D = 2 . The axial velocity near the axis i s positive, though l e s s SO than i n the 45 deg. case of Fig. 9, since the favorable pressure gradient has now to overcome an even stronger unfavorable pressure gradient. The central recirculation region i s now very small, extending i n an annular region t o less t h a n x/D = 1.0, considerably less than the no-blockage case of Fig. 7. A t the axial s t a t i o n x/D = 1.0, forward flow occurs across the whole test ‘section. Very strong swirl velocity magnitudes and gradients are seen, which contrasts sharply w i t h the corresponding open-ended flow situation. A wide core region i s again noticed
89
I
0
0
u/u,
i
x/D
u/u,
lu,
x2
u;,,1u,
x 2
Fig. 4 Time-mean and turbulent flowfield Cp = 38 deg
Fig. 3 Time-mean and turbulent flowfield Cp = 0 deg. (no swirler)
.
90
0
"0
vlu,
1
0.5
1
x/D
f
vlu,
I I I \ X
u;,,1u,
r/Do.50
0.25
\
u.-
I
OO3&
/D
x2
I Y
/D
1
Fig. 5 Time-mean and turbulent f l o w f i e l d @ = 45 deg
.
Fig. 6 Time-mean and turbulent f l o w f i e l d $I = 60 deg
.
91
u/u,
w/u,
vlu,
u;,,/u,
VIU,
x 2
u;,,lu,
x 2
Fig. 8 Time-mean and turbulence flowfield 4 = 0 deg. (no swirler) with strong contraction nozzle a t L/D = 2
Fig. 7 Time-mean and turbulent flowfield @ = 70 deg
.
92
w/ u,
w/u,
I
0
0.50
x/D
VIU,
vjrnsluo
VIU,
X
2
Fig. 9 Time-mean and turbulence flowfield $ = 45 deg. w i t h strong contraction nozzle a t L/D = 2
Fig. 10 Time-mean and turbulence flowfield 4 = 70 deg. w i t h strong contraction nozzle a t L/D = 2
93
along the j e t axis containing strong solid body r o t a t i on; movie photography' reveals the precessing nature of t h i s phenomenon. Again, time-mean data compare very well with previous work."
followed by -45 deg. about its new ^x-axis) s o a s to conform t o Case 3 of Fig. 2. Again the laboratorycoordinate deduced values and deviations from expected values are r e l a t i v e l y low though not quite as good as i n the previous case, however, s t i l l well w i t h i n generally accepted 1imi t s . The advantages of ensemble averaging a r e shown on Table 3 , where the under- and/or over-estimation o f the velocities f o r the individual positions are "smoothed" out a f t e r averaging .
The normal components of the Reynolds s t r e s s tensor show an increase in turbulence along the j e t axis as the contraction i s approached -- more so than in the 45 deg. swirl case o f Fig. 9 , b u t similar t o those found in the open-ended case of Fig. 7. NOW, larger values are found near the axis, associated w i t h the strong vortex core region. Turbul ent F1 ow. To examine the directional Shear s t r e s s levels a t the entrance t o the t e s t s e n s i t i v i t y of the technique in a turbulent flowfield, section tend to be s l i g h t l y lower f o r the blockage the probe was placed i n the shear layer of the f r e e case. B u t the levels a r e an order of magnitude j e t a t x/d = 3 and r / d = 0.5. Table 4 shows the rehigher in the core region near the contraction s u l t s of the t e s t with the probe in the position of nozzle. Again, t h i s i s because of the strong Case 1 of Fig. 2. I t i s seen t h a t the time-mean time-mean velocity gradients i n t h i s area. properties of t h e f r e e j e t are very similar t o those of Sami e t a1,26 who reported experimental work on a similar turbulent free j e t exiting from a con3 . 3 Directional Sensitivity Analysis toured nozzle. They also included measurement s t a tions relatively close t o the j e t e x i t . The results The directional s e n s i t i v i t y of the measurecompare favorably except f o r , again the radial velment technique i s now assessed via i t s application ocity. This may i n f e r t h a t the technique may have t o a free j e t exiting from a contoured nozzle. shortcomings i n measuring very low radial velocities The laboratory calibration j e t was used f o r t h i s ( i n the direction of the hot-wire supports). purpose. Results, with the probe in the configuration of Cases 1 , 2 and 3 of Fig. 2, are compared Re-alignment of the probe t o t h a t of Case 2 of with expected values in the laminar potential core Fig. 2 generates data in which the error i n the region and in the turbulent shear layer region radial velocity i s greatly reduced. Table 5 exhibfurther downstreamYz6see Tables 1 through 3 and its the r e s u l t s . The probe i s now more greatly in4 t h r o u g h 6, respectively. The a b i l i t y of the fluenced by the radial component ( i n f a c i l i t y coprobe t o measure time-mean velocities i n f a c i l i t y ordinates) of the flow. However, a reduction in the coordinates , usi ng coordinate transformations accuracy of the other two components can be seen. given in Appendix A, i s now assessed.
Laminar Flow. Table 1 gives the results of placing the single hot-wire in the potential core of the free j e t a t x/d = 0 and r / d = 0 , with the probe coordinates aligned with the f a c i l i t y coordinate systems, as Case 1 i n F i g . 2 i l l u s t r a t e s . The time-mean v e l o c i t i e s , nondimensionalized with the j e t e x i t velocity deduced from an independent measured, are shown w i t h t h e i r percentage errors ( t h a t i s , deviations from expected values). Res u l t s using each of the s i x possible combinations o f three adjacent wire-orientations a r e presented, together w i t h the ensemble average (mean) of these values. As can be seen, the percentage e r r o r f o r the axial and swirl velocities a r e very low f o r each combination. The radial velocity e r r o r tends t o be larger, possibly because of s l i g h t probe misalignment with the normal to the j e t axis. Ensemble averaging t o find the mean of these quant i t i e s brings the data t o well within acceptable 1imi t s . Results of the probe being rotated by 45 deg. about the z a x i s ( a s i n Case 2 of F i g . 2 w i t h 9 = -45 deg.) are shown i n Table 2. The probe coordinate system i s now d i f f e r e n t from the j e t coordinate system b u t the measured velocities can be related t o the f a c i l i t y coordinate by use of the rotational matrices given i n Appendix A. The values and percentage errors i n Table 2 are given in terms of the f a c i l i t y coordinate system. The r e s u l t s show t h a t t h i s misalignment of the probe with the dominant flow direction s t i l l gives exc e l l e n t values of velocities i n the laboratory coordinate system with the use of any of the s i x possible wire combinations. Consequently, ensemble averaging of the data also gives good r e s u l t s .
Table 6 shows the r e s u l t s in the turbulent region a f t e r two rotations of the probe t o the configuration of Case 3 of Fig. 2. The accuracy of the technique f o r time-mean properties can be seen clearly in these resul t s , The measuring technique does not appear to have any dependence on dominant flow direction f o r determination of the time-mean characteristics of t h e flow.
4.
Conclusions
The s ix-ori enta t i on single hot-wire technique i s a novel cost-effective tool f o r use in complex turbulent flow s i t u a t i o n s . The data are being used to aid in the evolution of turbulence models f o r swirling recirculating flows in combustor geometries. Flowfield surveys of confined j e t s w i t h increasing amounts of swirl have been performed using the sixorientation s i n g l e hot-wire technique. These measurements have been used to calculate of the timemean velocity components and the normal and shear turbulent s t r e s s e s . The e f f e c t of swirl on the time-mean velocity f i e l d i s found to shorten the corner recirculation zone length and t o generate the existence of a central recirculation zone, which i s followed by a precessing vortex core region. As the degree of swirl increases, the length of the central recirculation bubble decreases, whereas i t s width, and also the w i d t h of the precessing vortex core, increases. A t the j e t i n l e t t o the t e s t section, directional turbulence i n t e n s i t i e s are found t o increase significantly.with swirl. Throughout the flowfield, the most dramatic e f f e c t of swirl i s to increase values of the three turbulent shear s t r e s s terms .
Table 3 gives corresponding results with the probe rotated twice (-45 deg. about i ts z-axis ,
Introduction of a strong contraction nozzle a t L/D =
94
Table 1.
Laminar f r e e j e t measurements a t x/d = 0 and r / d = 0 using Case 1 probe configurati on
Combination Used
% Deviation
Measured u/u, v/uo
w/uo
u/uo
v/uo
w/uo
612
0.963
0.137
0.020
-3.7
13.7
2.0
123
0.987
0.134
0.030
-1.3 13.4
234
0.988
0.198
0.060 -1.2 19.8
345
Table 4. Turbulent free j e t measurements a t x/d = 3 and r / d = 0.5 using Case 1 probe configuration
% Deviation
Measured u/uo v/uo
w/uo
612
0.578
0.190
0.014 -7.18
3.0
123
0.592
0.184 0.020 -4.53
6.0
234
0.604
NR
0.002
-2.55
NR
0.2
NR
345
0.570
0.143
0.008
-8.03
14.3
0.8
456
NR
456
0.596
0.084
0.015
-3.92
8.4
1.5
561
1.010 0.137
0.010
-5.69
0.986
0.040
Mean
Table 2.
0.152
1.0
1.0
561
0.585 0.187
NR
-1.4 15.2
4.0
Mean
0.587 0.158
0.012 -5.30
% Deviation
Measured u/uo v/uo
w/u,
612
0.978
0.031
123
0.972
234
u/u,
13.7
Laminar f r e e j e t measurements a t x/d = 0 and r / d = 0 using Case 2 probe configurati on
Combination Used
combination Used
w/uo
19.0
1.4
18.4 2.0
18.7 NR 15.8
1.2
Turbulent f r e e j e t measurements a t x/d = 3 and r / d = 0.5 using Case 2 probe configuration
Combination Used
Measured u/u, v/u,
w/uo
% Deviation u/u, v/uo w/uo
v/uo
w/uo
0.035 -2.2
3.1
3.5
612
0.552
0.039 0.043
-10.9
3.9
4.3
0.036
0.040 -2.8
3.6
4.0
123
0.554
0.066 0.033
-10.7
6.6
3.3
0.990
0.056
0.015 -1.0
5.6
1.5
234
0.520
-0.055 0.162
-16.2 -5.5
16.2
345
0.982
0.043
0.022
1.8
4.3
2.2
345
NR
NR
NR
NR
12.4
456
0.988
0.024 0.049 -1.2
2.4
4.9
456
0.527
-0.033 0.081
-14.9
-3.3
8.1
561
0.986 0.022
0.041
-1.4
2.2
4.1
561
0.576
0.033
0.112
-7.1
3.3
11.2
Mean
0.983 0.021
0.033
-1.7
2.1
3.3
Mean
0.555
0.019
0.092
-10.5
1.9
9.2
Table 3.
u/u,
Table 5.
v/uo
Laminar f r e e j e t measurements a t x/d = 0 and r / d = 0 using Case 3 probe configurati on
Combination Used
Measured u/uo v/uo
% Deviation w/uo
u/uo
v/uo
w/uo
0.124
Table 6. Turbulent f r e e j e t measurements a t x/d = 3 and r / d = 0.5 using Case 3 probe configu r a t i on Combination Used
Measured u/uo v/uo
w/uo
% Deviation u/u, v/u, w/uo
612
0.954
-0.030 -0.008 -4.6
-3.00 -0.8
612
0.548
0.103
-0.035 -11.6
123
0.954
-0.031 -0.008 -4.6
-3.10 -0.8
123
0.575
0.076
-0.006
3.4
234
0.967
-0.039 -0.051 -3.3
-3.90 -5.1
234
0.559
0.022
-0.024
-9.9
2.2
-2.4
345
0.948 -0.103
0.080 -5.2
-10.30 8.0
345
0.552
0.037
0.000 -10.9
3.7
0.0
456
0.971
0.001 -0.003 -2.9
0.10 -0.3
456
0.547
0.025
-0.019 -11.7
2.5
-1.9
561
0.951
-0.030
0.006 -4.3
-0.03 -0.6
561
0.547
0.063
-0.034 -11.7
6.3
3.4
Mean
0.958
-0.039
0.001 -4.2
-3.90 0.1
Mean
0.555
0.046
-0.019 -10.5
4.6
-1.9
95
10.3
-3.5
7.6 -0.6
2 w i t h an area reduction r a t i o of 4 causes a significant e f f e c t on the time-mean swirling flowfield. Central recirculation zones a r e shortened and axial velocities along the whole j e t axis become positive. The core regions become narrow w i t h strona swirl velocities and gradients. Turbulence levels and shear stresses a r e found to increase along the j e t centerline near the exit of the contraction nozzle A directional s e n s i t i v i t y analysis of the single-wire measurement technique was performed i n a f r e e j e t of known properties. The analysis reveals that the technique adequately measures the three components o f the time-mean flow velocity independent of the dominant flow direction with respect t o the probe.
Part 2: Enclosed Jets", Journal of the Inst. of Fuel, Vol. 40, June 1967, pp. 238-245. 11.
Rhode, D. L . , Lilley, D. G., and McLaughlin, D. K., "Mean Flowfields i n Axisymetric Combustor Geometries w i t h Swirl", Paper AIM 820177, 1982, AIAA Journal ( i n press).
12.
Yoon, H . K . , and Lilley, 0. G., "Five-Hole P i t o t Probe Time-Mean Velocity Measurements i n Confined Swirl i ng F1 ows" , Paper AIAA-83-0315, Reno, Nev., Jan. 10-13, 1983.
13. Gouldin, F. C., Depsky, J. S., and Lee, S . L., "Velocity Field Characteristics of a Swirling Flow Combustor", Paper AIAA-83-0314, Reno, Nev., Jan. 10-13, 1983.
Acknowledgments The authors a r e indebted t o NASA Lewis Research Center and Air Force Wright Aeronautical Laboratori e s for support under Grant No. NAG 3-74, technical monitor Dr. 3. D. Holdeman.
14. Habib, M. A., and Whitelaw, J . H . , "Velocity Characteristics of Confined Coaxial J e t s W i t h and Wi thout Swirl 'I , Paper ASME 79-WA/FE-21 , New York, N Y , Dec. 2-7, 1979. 15.
Vu, B . T., and Gouldin, F. C . , "Flow Measurements i n a Model Swirl Combustor", AIAA Journal, Vol. 20, No. 5, May 1982, pp. 642-651.
16.
Chigier, N . A . , and Beer, J . M . , "Veloci ty and Static-Pressure Distributions i n Swirling Air J e t s Issuing from Annular and Divergent Nozzles", ASME Journal o f Basic Engineering, Vol. 82, Dec. 1964, pp. 788-796.
Janjua, S. I . , McLaughlin, D. K., Jackson, T. W . , and Lilley, D. G . , "Turbulence Measurements i n a Confined J e t Using a Six-Orientation Hot-wire Probe Technique", Paper AIAA-82-1262, Cleveland, Ohio, June 21-23, 1982. AIAA Journal, 1983 ( i n press).
17.
Somner, H . T., "Swirling Flow i n a Research Combustor", Paper AIAA-83-0313, Reno, Nev., Jan. 10-13, 1983.
3.
Beer, J . M . , and Chigier, N. A . , Combustion Aerodynami cs , Appl i ed Science, London and Wiley, N e w York, 1972. Reprinted by Krieger, Melbourne, Florida, 1983.
18. Sander, G. F., and Lilley, D. G., The Performance of an Annular Vane Swi r l er", Paper AIAA-83-1326 , S e a t t l e , Wash., June 27-29, 1983.
4.
Gupta, A. K. , Lilley, D. G., and Syred, N . , Swi r l F1 ows, Abacus Press Tunbri dge We1 Is, England, 1983 ( i n press).
5.
Lefebvre, A. t i . , Gas Turbine Combustion, McGraw-Hill, New York, 1983.
6.
Owen , F. K. , "Laser Velocimeter Measurements of a Confined Turbulent Diffusion Flame Burner", Paper AIAA-76-33, Washington, D.C., Jan. 26-28, 1976.
References 1.
2.
7.
8.
9.
10 *
Lilley, D. G. , "Turbulent Combustor Flowfield Investigation", Combustion Fundamentals Research Conference, held a t NASA Lewis Research Center, Cleveland, Ohio, Oct. 21-22, 1982, pp. 152-168.
Hutchinson, P . , Khalil, E. E., and Whitelaw, J . H . , "Measurement and Calculation of FurnaceFlow Properties", Paper AIAA-77-50, Los Angeles, Calif., Jan. 24-26, 1977. Baker, R. J. , Hutchinson, P. , and Whitelaw, J . H . , "Velocity Measurements i n the Reci rcul ation Region of an Industrial Flame by Laser Anemometry w i t h L i g h t Frequency Shifting", Combustion and Flame, Vol. 23, 1974, pp. 5772. Chaturvedi , M. C . , "characteristics o f Axis y m e t r i c Expans ions", Proceedings, Journal of the Hydraulics Division, A X E , Vol. 89, NO. HY3, 1963, pp. 61-92. Mathur, M. L . , and MacCallum, N. R. L . , "Swirling Air J e t s Issuing from Vane Swi rl ers,
96
19.
King, C. F., "Some Studies of Vortex Devices Vortex Amplifier Performance Behaviour", Ph .D. Thesis, University College of Wales, Cardiff, Wales, 1978.
20.
Dvorak, K., and Syred, N . , "The S t a t i s t i c a l Analysis of Hot Wire Anemometer Signals in Complex Flowfields", DISA Conference, University of Leicester, 1972.
21.
Jorgensen, F. E., "Directional Sensitivity of Wire and Fiber Film Probes", DISA Information No. 11, Franklin Lakes, NJ, pp. 31-37, May 1971.
22.
Paul, R. P . , Robot Manipulators, MIT Press, Cambridge, Mass. , 1982.
23.
Wang, C-T., Applied E l a s t i c i t y , McGraw-Hill, New York, 1953.
24.
Rhode, D. L., Lilley, D. G., and McLaughlin, D. K., "On the Prediction of Swirling Flowf i e l d s i n Axisymnetri c Combustor Geometries ", ASME Journal of Fluids Engineering, Vol. 104, Sept. 1982, pp. 378-384.
25.
Abujelala, M. T., and-Lilley, D. G., "Confined S w i r l i n g Flow Predictions" , Paper AIAA-83-0316, Reno, Nev., Jan. 10-13, 1983.
26.
Sami, S., Carmody, T., and Rouse, H . , " J e t Diffusion i n the Region of Flow Establishment", A.2 Journal of Fluids Mechanics, Vol. 27, Part 2, 1967, pp. 231-252.
In, the probe directional s e n s i t i v i t y analysis of Sections 2.2 and 3.3, coordinate rotation relationships a r e required i n order t o r e l a t e probesensed data i n Cases 1 , 2 o r 3 of Fig. 2 back t o f a c i l i t y coordinate data. Any ( x , y , z)-Cartesian coordinate axes may be rotated about the x, y , or z a x i s , respectively, by an angle 8, w i t h correspondi ng coordinate transformation matrices
Rxe
[
=
1
0
o
cose
0
sine
cose
-sine
r
A.3
=
Rze [ X Y
wIT
=
Rze [U V
e
O 1
ZIT
WIT
f a c i l i t y coordinates
ii, g, W i n x, y , z probe Case 1 coordinates A
u,
7, G
t, $,
9, ^z
probe Case 2 coordinates
g, $, ^z
probe Case 3 coordinates
i n 2,
in
the following relationships prevail: A.1
Case 2
Case 3
Clearly, the Case 3 velocity components a r e simply related t o the f a c i l i t y velocity components. Further information on coordinate transformations and t h e i r application t o velocities, and normal and shear stress terms , is avai lable.22'23
In the notation o f Fig 2 w i t h velocity components
u, v, w i n x, r,
[G ? GIT
To go from Case 2 to Case 3, a rotation of is applied about the ^x-axis, resulting
Similarly, velocity components ( u , v, w) are related t o (U, v, W) via
[u v
=
$I = -45 deg.
For example, a rotation about the z-axis by angle 8 results i n old (x, y , z) coordinates o f a point being related t o i t s new (X, Y , Z) coordinates via:
[x y zlT
WIT
In this case, a rotation of 0 = -45 deg. is applied about the z , axis, resulting i n
Coordinate Transformation
Appendix A:
[u v
Case 1
The f a c i l i t y and probe Case 1 coordinates a r e coi nci den t and
97
APPENDIX G THE PERFORMANCE OF AN ANNULAR VANE SWIRLER ( A I AA- 83-1 326)
98
THE PERFORMANCE OF AN ANNULAR VANE SWIRLER G. F. Sander* and D. G. Lilley** Oklahoma S t a t e University, Stillwater, Okla.
Abstract
Subscripts
Axial vane swirl e r performance characteristics a r e investigated so as t o aid i n computer modeling of gas turbine combustor flowfields, and i n the development and evaluation of turbulence models f o r swirling confined flow. The s w i r l e r studied i s annular w i t h a hub-to-swirler diameter r a t i o of 0.25 and ten adjustable vanes of pitch-to-chord r a t i o 0.68. Measurements of time-mean a x i a l , r a d i a l , and swirl velocities a r e made a t the swirler e x i t plane using a five-hole p i t o t probe technique w i t h computer data reduction. Nondimensionalized veloci t i e s from both radial and azimuthal traverses are plotted f o r a range of swirl vane angles @ from 0 t o 70 degrees. A theoretical study i s included of idealized exit-plane velocity profiles relating the swirl numbers S and S’ t o the r a t i o of maximum swirl and axial velocities f o r each idealized case.
atm C , N S ,E,W h in
m 0 X
e
W
Supers c r i p ts a l t e r n a t e form, neglecting pressure variation; f 1uctua t i ng quanti t y time-mean quantity 1.
Measurements of time-mean velocity components a t the swirler e x i t plane show clearly the e f f e c t s of centrifugal forces, recirculation zones, and blade wakes on the exi t-plane velocity profiles. Assumptions of f l a t axial and swirl profiles are found t o be progressively l e s s r e a l i s t i c as the swirl vane angle increases, with axial and swirl velocities peaking strongly a t the outer edges of the swirler e x i t and s i g n i f i c a n t non-zero radial velocities present. A l i n e a r idealization of the axial and swirl p r o f i l e s i s appropriate f o r moderate swirl @ = 45 deg. b u t simple idealizations a r e n o t applicable t o s t r o n g swirl cases because of the central recirculation zone extending upstream of t h e e x i t plane. Nonaxisymnetry i s present in a l l swirl cases investigated.
1.1
blade chord width swirl e r e x i t diameter t e s t section diameter velocity r a t i o wo/u f o r case I axial flux of momen?um; velocity r a t i o wmo/uOfor case I1 w?lo/umo f o r cases I11 - V time-mean pressure blade spacing o r pitch swirl number = G /(Gx d / 2 ) axial , radial an8 swirl components of velocity a x i a l , r a d i a l , azimuthal cylindrical polar coordinates hub-to-swirler diameter q t i o d / d yaw angle of probe = tan (w/u8 pitct) angle of probe = tan-’[v/(u2 + P 3
@
* **
w2)‘
Introduction
Combustor Flowfield Investigations
The problem of optimizing gas turbine cornbustion chamber design i s complex, because of the many conflicting design requirements. The need f o r a more compl e t e understanding of the f 1u i d dynamics of the flow in such combustion chambers has been recognized by designers in recent years, and research i s continuing on several fronts t o a l l e v i a t e the problem, As part of an on-going project a t Oklahoma S t a t e University, studies a r e in progress concerned with experimental and theoretical research i n 2-D axisymmetric geometries under low speed, nonreacting, turbulent, swirling flow conditions. The flow enters the t e s t section and proceeds into a larger chamber ( t h e expansion r a t i o D/d = 2) via a sudden or gradyal expansion (side-wall angle 01 = 90 and 45 degrees). I n l e t swirl vanes a r e adjustable t o a variety of vane angles with 4 = 0, 38, 45, 60 and 70 degrees being emphasized. The general aim of the e n t i r e study i s t o characterize the time-mean and turbulence flowfield, recommend appropriate turbulence model advances , and imp1 ement and exhi b i t r e s u l t s of flowfield predictions. The present contribution concentrates on the time-mean flow charact e r i s t i c s being generated by the upstream annular swirler, using a five-hole p i t o t probe technique.
Nomenclature
e
ambient atmospheric conditions center, n o r t h , s o u t h , e a s t , west p i t o t pressure ports hub i n l e t conditions, upstream of swirler maximum p r o f i l e value value a t swirler o u t l e t axial direction tangential direction reference value a t edge of swirler exit
1.2
Previous Studies
Research i s progressing i n several areas r e l a t ed t o the flow f a c i l i t y investigation just described. Computer simulation techniques a r e being used t o study the e f f e c t of geometry and other parameter changes on the flowfield. An advanced computer code has been developed t o predict confined swirli n g flows corresponding t o those studied experiment a l l y . Tentative predictions’ have now been s u p p l e mented by predictions made from r e a l i s t i c i n l e t conditions3 f o r a complete range of swirl strengths with downstream nozzle e f f e c t s .4 Accuracy of predictions from a computer model i s strongly dependent on the i n l e t boundary conditions used, which a r e primarily determined by the swirler and its performance a t d i f f e r e n t vane angle s e t t i n g s . In the e a r l i e r predictions, the velocity boundary conditions a t the i n l e t t o the model combustor were approxi-
21
izimuti; angle density pitch-to-chord r a t i o = s / c swirl vane angle
Graduate Student, School of Mechanical and Aerospace Engineering, Student Member AIAA Professor, School of Mechanical and Aerospace Engineering, Associate Fellow AIM
99
r e s u l t s of a check on s e n s i t i v i t y of the measurements t o calibration e r r o r s . Finally, Section 5 presents conclusions drawn from the above r e s u l t s .
mated by idealized f l a t p r o f i l e s f o r axial and swirl velocity, with radial velocity assumed t o b e zero. However, recent measurements taken closer t o the swirler e x i t show t h a t the p r o f i l e s produced are quite nonuniform, with nonzero radial velocity and nonaxisymmetry.
2.1
1.3 Scope and Objectives A key element i n swirling flow studies i s the swirl generator used. Since i t l i e s a t the i n l e t to the combustor model, the s w i r l e r can have a strong influence on measurements and/or predictions made further downstream. Better d e f i n i t i o n of the performance characteristics of the swirler i s needed. I n the present study, the main objective i s t o make time-mean velocity measurements as close as possible to the swirler e x i t , s o as t o define more accurately the performance characteristics of the s w i r l e r . A range of swirl-blade angles $I from 0 t o 70 deg. i s considered. Specific objectives a r e to:
1.
Investigate the flow turning effectiveness of f l a t blades in annular vane swirlers a t various blade angles, 4.
2.
Investigate the degree of nonaxisymmetry introduced by vane- type swi r l ers
3.
Establish correlations between the blade angle 4 and the velocity p r o f i l e s and degree of swirl actually produced.
4.
.
Idealized Velocity Profiles
A1 1 theoretical analyses of swirl e r performance and most numerical simulations of combustor flowf i e l d s have used simple idealized swirler exit veloci t y p r o f i l e s . Comnon assumptions made include f l a t axial and swirl velocity profiles downstream of the swirler f o r swirlers w i t h vanes of constant ang l e 2 y 5 y 1 1 y 1and 2 a f l a t axial p r o f i l e w i t h a l i n e a r swirl p r o f i l e (solid-body rotation) f o r swirlers with helicoidal vanes and f o r tangential-entry swirl l4 These, however, have been shown generators. t o be q u i t e unreal is ti^^"^"^ and t o lead t o considerable errors in computer predictions of the f l ~ w f i e l d . ~A1 though the best remedy f o r numerical simulations i s t o use experimentally measured swirler e x i t profiles i f they a r e available, idealized prof i l e s a r e very useful i n theoretical work. If more r e a l i s t i c p r o f i l e assumptions can be developed which are s t i l l mathematically t r a c t a b l e , more useful anal y t i c a l results may be derived. Better idealized profiles would a l s o be useful as i n l e t boundary conditions f o r computer modeling when measured data a r e n o t avai lab1 e . Measurements have shown3 t h a t l i n e a r and parabolic p r o f i l e s o f axial velocity a r e more appropriate f o r moderate and high swirl cases, and t h a t the swirl velocity a l s o approaches a parabolic p r o f i l e a t high swirl strengths, with most of the flow leaving near the outer boundary of the swirler. Several combinations of l i n e a r and parabolic idealized profiles a r e shown in F i g . 1 , along with the f l a t , l i n e a r and parabolic p r o f i l e assumptions s t a t e d in the form of profile expressions. Parameters associated with these profiles are investigated in Section 2.3. 2.2
Definition of Swirl Parameters
The swirl number i s a nondimensional parameter used t o characterize the degree of swirl generated by a swirler. I t i s defined as
Evaluate the a p p l i c a b i l i t y of idealized velocity profiles used recently i n flowf i e l d prediction codes, and specify more r e a l i s t i c idealized p r o f i l e s f o r future use.
(1) where the axial flux of angular momentum Go i s given by 2a d/2 2 G@ = r de r [puw + pu'w'] r d r (2)
5. Provide swirler e x i t data usable as i n l e t conditions in prediction codes being used t o establish , evaluate, and improve turbulence models.
-
0
1.4
Theoretical Analysis
2,
The flowfield in the test section i s being characterized experimentally in a variety of ways. Flow visualization has been achieved via s t i l l 5 and movie6 photography of neutrally buoyant heliumf i l l e d soap bubbles and smoke produced by an i n j e c t o r and a smoke w i r e . Time-mean v e l o c i t i e s have been measured with a five-hole p i t o t probe a t low5 and high' swirl strengths. To help i n turbulence model ing, complete turbulence measurements have been made on weakly' and strongly' swirling flows, using a six-orientation single-wire hot-wire technique. An alternative three-wire technique has also been shown t o be useful i n these complex flow s i t u ations."
Outline o f the Paper
0
and the axial f l u x of axial momentum Gx i s given by
Section 2 describes theoretical analysis of idealized swirler e x i t velocity profiles, r e l a t i n g the swirl number t o the r a t i o of maximum swirl and axial velocities f o r several typical cases. Experi mental equipment and procedures used f o r measurement o f the swirler e x i t flowfield a r e covered i n Section 3. I t includes descriptions of the swirler, measurement technique, and data reduction procedure. T h e f i r s t two parts of Section 4 discuss experimental r e s u l t s from radial and azimuthal traverses , respectively, noting the presence of nonaxisymnetry, recirculation, and strong velocity gradients a t the swirler e x i t plane, The t h i r d part describes the
2s d/2 Gx = I d0 [pu 0
+
pd2
+ (p
-
pm)r d r (3)
and d/2 i s the swirler e x i t radius. These equations are obtained from appropriate manipulation of the axial and azimuthal momentum equations , respectively. In f r e e j e t flows these two expressions a r e invariant with respect t o downstream location. In the axial momentum expression, the pressure term ( p - p,) i s given from radial integration of the radial momentum equation l 6 by
100
dj---!mo
( l 2 u=uo r I 0 0
0
uO
- Flat Axial and Swirl Profiles
fa) Case I
I f turbulent s t r e s s terms a r e neglected, i t is apparent t h a t a knowledge o f the distribution of the time-mean u and w velocity components across the swirler i s s u f f i c i e n t t o calculate e i t h e ber. The idealized e x i t velocity profiles provide just such knowledge, and expressions relating swirl number t o the r a t i o of maximum e x i t swirl velocity to maximum o r constant axial velocity can now be derived f o r each of the p r o f i l e types. As the procedure is similar f o r each of the f i v e cases, a det a i l e d derivation i s shown for the f i r s t case only, with r e s u l t s merely s t a t e d for the other four cases. 2.3
By assuming axisymnetric flow and neglecting turbulent s t r e s s e s as s t a t e d previously, the defini t i o n s i n Eqs. ( 2 ) through (4) reduce t o
- Flat Axial and Linear Swirl Profiles
(b) Case I1
Swirl Numbers f o r Idealized Profiles
d/2
Gx = 2a J Case I11
(c)
- Linear Axial
+ (p
[pu*
0
p,)]r
dr
(8)
and Swirl Profiles
(P
-
P),
= J
r
[PW
d/2
21 $dr
(9)
When the expressions f o r axial and swirl velocity for case I (See Fig. 1) a r e substituted into Eq. (7), one obtains
- Parabolic Axial and Linear Swirl Profiles
(d) Case IV
-
Substitution of w(r) = wo i n t o Eq. (9) and integrati n g produces
- Parabolic Axial
[e) Case V
Fig. 1 .
(P and Swirl Profiles
Idealized axial and swirl velocity p r o f i l e cases
(p
-
= Jr
p),
[pw2
d/2
i]d r -
-2 PV'
i
Gx =
2~
2/d
I dB 1 0
0
[PU
+ pu' 3r d r
=
w:
(4)
2
and leads t o an a l t e r n a t e definition of swirl number":
(11)
2
[I
- -1 (-1w o 21 "0
Finally, p u t t i n g Eqs. (10) and (12) into Eq. (1) and defining the velocity r a t i o F = wo/uo, the swirl number S can be expressed t h u s : S =
(5)
-
EW~) ~d/2)1
After substituting Eq. (11) into Eq. (8) and integrating, the expression becomes
6, = rpu0 (d/2)
I f the pressure term i s omitted from the axial momentum, the dynamic axial momentum flux G, i s obt a i ned :
2
- P),
2F/3 1 - F2/2
The a l t e r n a t e swirl number S i follows from finding the dynamic axial flux o f axial momentum: G i = apu,
101
2
(d/2)
2
(14)
Using t h i s i n Eq. (6) leads t o the simple expression 1.5 .
S' = 2F/3 Equations (13) and (15) provide the t o p row i n Table 1 , where equations relating S and S ' t o F, G, H , I , and J [deduced i n a similar manner] a r e given f o r the f i v e cases of F i g . 1 . Note t h a t the p r o f i l e equations a r e given in Fig. 1 and other parameters are defined by: F = wo /uo G = wmo/uo H = wmo/umo 1 = wmo/umo J =
S
wmo/umo
I t is interesting t o see how these parameters vary with S and S ' , and Fig. 2 portrays the relationships of the equations in Table 1 visually, f o r a range of comnonly encountered swirl numbers. Table 1. Case I I1 I11 IV
v
Idealized Swirler E x i t Velocity Profiles S S' S =
2F/3 1 - F2/2
612 1 - G2/4 4H/5 S = 1 - H2/2 I s= 1 - 312/4 s = 4517 1 - 2J2/3 S =
S' = 2F/3
S' = GI2 S =
4H/5
S' = I
Fig. 2.
S ' = 4517
I t i s evident from the equations alone t h a t the S' expressions a r e a l l simple l i n e a r r e l a t i o n s . The parameters F through J will increase without bound as S ' i s increased i n each case. In contrast, the parameter change w i t h S shows asymptotic behavior; the e x i t velocity r a t i o s a l l approach d e f i n i t e values as swirl number increases, o r , conversely, the swirl number goes t o i n f i n i t y f o r a c e r t a i n value of the velocity r a t i o in each case. Although t h e curves a r e generally s i m i l a r i n shape, some observations can b e made. The curves f o r cases I1 and IV a r e the upper and lower extremes f o r both the S and S' relations, w i t h the curves f o r cases I , 111, and V f a l l i n g i n between. T h i s may be anticipated since the w-profile is of higher order than the u-profile f o r case I1 ( t h a t i s , l i n e a r versus constant) and the opposite i s true f o r case IV ( l i n e a r versus parabolic). In the other three cases the u and w p r o f i l e s a r e of the same order.
In appraising the usefulness of the idealized profiles, comparison may be made w i t h the measured profiles given l a t e r i n Section 4. As the swirl strength increases from 0 t o 70 deg., corresponding
1.0
0
S'
20
Variation of velocity r a t i o s F through J [Cases I through V , respectively] w i t h S and S ' .
profiles of cases I t o V are roughly appropriate. However, the presence of the hub and central r e c i r culation zone prevent adequate representation v i a the idealized p r o f i l e s , except f o r moderate swirl ( + = 45 deg.) and i t s corresponding Case 111. 3. 3.1
Experimental Equipment and Procedure
The Facility
The i n s t a l l a t i o n on which a l l t e s t s were performed i s a low-speed wind tunnel designed and b u i l t a t Oklahoma S t a t e University. I t produces uniform flow of r e l a t i v e l y low turbulence i n t e n s i t y , with continuously adjustable flow r a t e . T h e f a c i l i t y consists of a f i l t e r e d intake, an axial blower, a s t i l l i n g chamber, a turbulence management section, and a contoured o u t l e t nozzle. I t is described a t length in several recent d o ~ u m e n t s . ~ ' ~ ' The ' contoured nozzle i s made of molded fiberglass w i t h a steel flange a t the o u t l e t f o r the attachment of the swirler and/or expansion block en route t o the t e s t section i n associated studies. A 1 cm diameter hole a short distance upstream of the o u t l e t allows for insertion of a standard P i t o t - s t a t i c probe t o masure the dynamic pressure upstream of the swirler. This measurement, with a small correction f o r dif-
102
ference i n flow area, i s used t o calculate the swirler i n l e t reference velocity, uin. 3.2
The Swirler
The s w i r l e r used i n t h i s study i s annular with hub and housing diameters of 3.75 and 15.0 cm, respectively, giving a hub-to-swirler diameter r a t i o z of 0.25. The hub has a streamlined parabolic nose facing upstream and a blunt base (corner radius approximately 2 mm) facing downstream. I t i s supported by four thin rectangular-sectioned struts o r spider arms from t h e housing wall. The base of the hub protrudes approximately 3 mm downstream of the swirl e r exi t plane. Photographs and schematics of t h e swirler are shown i n Figs. 3 through 5.
The ten vanes o r blades a r e attached to s h a f t s which pass t h r o u g h the housing wall and allow individual adjustment of each blade’s angle. The standard vanes a r e wedge-shaped t o give a constant pitch-tochord r a t i o (J of 0.68, which according t o two-dimensional cascade data, should give reasonably good flow-turning effectiveness. Sets of vane planforms are shown in F i g . 6.
trailing edge 0.75 width bla
Fig. 6. 3.3
Fig. 3 .
Photograph of s w i r l e r
-
Swirl vanes
Measurement Procedure
The time-mean velocity components are measured with a five-hole p i t o t probe which allows determination of the magnitude and direction of the mean velocity vector s i m u l t a n e ~ u s l y . ~ The ’ ~ probe is mounted in a traversing mechanism which allows i t t o be translated v e r t i c a l l y (on a radial l i n e outward from the t e s t section axis) and rotated about the probe‘s yaw a x i s . In addition t o the motion permitted by the traverse mechanism, the t e s t section tube on which the traverse mechanism i s mounted may be rotated about i t s axis with respect t o the swirler, thereby allowing azimuthal ’traverses t o be performed. Tubing from the probe’s f i v e pressure taps i s routed through selector valves t o a d i f f e r e n t i a l pressure transducer, and the resulting pressure difference values are read d i r e c t l y from an integrating d i g i t a l voltmeter. The pressure data a r e reduced by a computer program t o y i e l d nondimensionalized u, v, and w velocity components, which a r e then plotted in the form of p r o f i l e s . Details appear in Refs. 3, 17, 18.
upstream end
4. Fig. 4.
Photograph of s w i r l e r
-
downstream end
Experimental Results
Velocity profiles from both radial and azimuthal traverses f o r each of the flowfields investigated are now presented and discussed. Table 2 gives a summary of the operating conditions used during the studies. With nonswirling conditions, the low fan speed delivers r e l a t i v e l y high axial velocity and corresponding Reynolds number. A t progressively higher swirl strength conditions, progressively higher fan speeds a r e used, b u t even so e x i t veloci t i e s and Reynolds numbers reduce because of increasi n g flow r e s t r i c t i o n o f the swirler. However, based on a limited study e l ~ e w h e r e , ’i~t i s expected t h a t a l l flowfields a r e i n the Reynolds number independent regime
r
.
Fig. 5.
Diagram of swirler view
-
section and downstream
The radial traverses consist of ten points from the centerline t o the swirler e x i t radius, spaced 7.6 mm apart. Of these ten, only seven stations
103
tice5-10 with one of the expansion blocks. Table 2.
5 Red x 10-
4 (degrees)
FS (rpm)
0
1950
23.00
2.22
38
2265
13.30
1.30
45
2600
13.00
1.26
60
2800
9.20
0.90
70
2800
5.52
0.53
*
uin(m/s)
4
Swirl vane angle
FS
Fan speed
uin
Spatial-mean swirler e x i t axial velocity, deduced from independent upstream measurement, excluding presence of the hub and swirler Swirler-exit Reynolds number based on uin and swirler diameter
were actually measured since the hub blocked t h e inner three positions. The azimuthal traverses contain nine points spaced 6 degrees apart a t a constant radial distance from the centerline. Azim u t h angles 4 were taken from -24 t o +24 degrees, with the e = 0 position i n l i n e with the s h a f t of one of the swirl vanes. A diagram showing the traverse patterns on the face of the s w i r l e r i s given in Fig. 7 .
block affixed t o the downstream face of the swirler and measurements then taken a t x/D = 0.0.
4.1
Velocity Profiles from Radial Traverses
Radial traverses of axial , radial and swirl velocity component data a r e presented f o r f i v e values of swirl blade angle: zero (no s w i r l e r ) , zero (with s w i r l e r ) , 38, 45, 60, and 70 deg., in Figs. 8 through 13, respectively, with the profiles extendi n g from the centerline t o twice the e x i t radius (r/D = 0.5 where D i s the t e s t section diameter used in associated s t u d i e s ) . All velocities shown a r e normalized with respect t o the swirler i n l e t uniform axial velocity U i n , deduced independently from the p i t o t - s t a t i c measurement upstream of the swi r l e r . The outer ten data points a r e zero i n each profile because the presence of the solid boundary of the swirler flange precluded measurements a t these locations.
Abbreviations used are:
Red
In Ref.
3 , some data are also presented w i t h the expansion
Summary of Operating Conditions*
The nonswirling case shown i n Fig. 8 has a nearly-flat axial velocity p r o f i l e , as expected f o r the plain nozzle opening without the swirler ins t a l l e d . There i s no measurable swirl velocity, and the radial velocity 'is zero except f o r p o i n t s very near the edge of the e x i t , where the flow begins to anticipate the abrupt expansion to twice the e x i t diameter. The second nonswirling case, see Fig. 9, has the swirler i n s t a l l e d with the blades s e t t o 4 = 0 deg. The traverse was made midway between two blades and away from any of the h u b supporting s t r u t s . Here again the axial p r o f i l e i s quite f l a t , w i t h just a s l i g h t increase toward the h u b , However, the vel o c i t y has increased by nearly 25 percent, because o f the decrease in flow area with swirler hub and vanes i n place. In addition, the hub induces a negative radial velocity across the e n t i r e annulus , overriding the tendency t o anticipate the expansion corner. The swirl velocity i s , as expected, negligible. The 38-deg. blade-angle case in F i g . 10 shows remnants of the f l a t i n l e t profile over a small portion of the radius near the outside edge in both the axial and swirl p r o f i l e s . The presence of the hub now constrains the three innermost points t o zero, and the region between the hub and the f l a t portion in the axial and swirl profiles is approximately linear. The maximum axial velocity i s 1.5 times the i n l e t axial velocity because the flow area i s decreased by the hub and a l s o because centrifugal e f f e c t s have s h i f t e d the profile outward. The radial velocity has an irregular profile w i t h a maximum value of one-half the i n l e t axial velocity.
Fig. 7.
Measurement locations azimuthal traverses
-
In the @ = 45 deg. case of Fiq. 11, the f l a t segments a r e no longer present and both axial and swirl p r o f i l e s vary from zero a t the hub t o a maximum a t o r near the rim of the swirler i n an almost l i n e a r fashion. The similar shape and magnitude of the profiles indicates t h a t the t u r n i n g angle i s f a i r l y uniform and only s l i g h t l y l e s s than 45 degrees. The radial velocity i s again irregular, b u t shows a s t e p a t r/D = 0.1 similar t o t h a t in the axial and swirl profiles; this i s probably due t o the central recirculation zone downstream beginning t o slow down the flow upstream of i t .
radial and
A l l traverses a r e taken imnediately a f t e r the swirler e x i t downstream face with no expansion
blocks present. Nominally, t h i s location i s x/D = -0.109, where the position x/D = 0.0 is the expansion s t a t i o n , separated from the swirler i n prac-
Profiles ensuing from the case of 4 = 60 deg., see Fig. 12, a l l have a sharply peaked shape, w i t h most of the flow leaving near the outer boundary.
104
085
0,s
r/D
r/D
0
0
0,s
0,s
r/D
r/ D
0
0
0 Fig. 8 .
1
2
0
3
Normalized velocity profiles from radial traverse, 41 = 0 deq. (No swirler)
2
3
Fig. 10. Normalized velocity profiles from radial traverse, 4 = 38 deg.
0,s
0,s
r/D
r/D 0
0
0 Fig. 9 .
1
1
2
3
0
Normalized velocity profiles from radial traverse, 4 = 0 deg. (Swirler installed)
Fig. 1 1 .
105
1
2
3
Normalized velocity profiles from radial traverse, 4 = 45 deg.
0 8 5
u/uin21
r/D
~
0
0
2
085
v/uin 1
r/ D
0
0
0,s r/ 0
0
1
0
2
3 8
Fig. 12.
Normalized velocity profiles from radial = 60 deg. traverse,
+
F i g . 14.
Normalized velocity profiles from azimuthal traverse, = 0 deg. a t r/D = 0.179 (Swirler I n s t a l l e d ) .
+
-1
r/
I
I
I
2 v/u in 1
0,s
r/ D 0
0
w h i n 21
r/ D
Q 0 Fig. 13.
1
2
0
3
Normalized velocity p r o f i l e s from radial traverse, (p = 70 deg.
~i u - 30
30 Fig. 15.
106
0
8
Normalized velocity profiles from azimutha l traverse, 4 = 38 deg. a t r/O = 0.179
2 v/uin 1
0
wluin: 0 30
0
~
F i g . 16.
0
- 30
Normalized velocity profiles from azimuth= 45 deg. a t r/D = 0.179 al traverse,
+
30 Fig. 18.
0
- 30
Normalized velocity profiles from azimuthal traverse, @ = 70 deg. a t r/D = 0.179
0
-0
0
L
2 v/u in 1 0
W
30 F i g . 17.
0
8
- 30
Normalized velocity profiles from azimutha l traverse, @ = 60 deg. a t r/D = 0.179
30 Fig. 19.
107
0
0
-30
Normalized velocity p r o f i l e s from azimutha l traverse, @ = 70 deg. a t r/D = 0.204
The radial component i s considerably stronger, w i t h a peak value nearly twice t h a t of the reference vel o c i t y upstream of the swirler. The s t e p seen previously in t h e 45 deg. axial p r o f i l e , has now developed i n t o reverse flow, indicating t h a t the central recirculation zone now extends upstream past the e x i t plane. The reverse flow i s accompanied by reduced swirl velocity and very low values of radial velocity. The positive axial velocity adjacent t o the hub may be the r e s u l t of a s l i g h t clearance between the blades and the h u b , allowing a i r w i t h greater axial momentum t o pass through. Exit velocity p r o f i l e s obtained f o r the stronge s t swirl case considered ( @= 70 deg.) are shown i n Fig. 13. Almost a l l of the flow leaves the s w i r l e r a t the outside edge. The maximum axial and swirl velocities a r e approximately 3 and 2.5 times the upstream reference values , respectively , and the velocity gradients across the p r o f i l e s a r e quite large. The reverse flow i n t h e center of the axial profile i s stronger than i n the 60-deg. case and i s now accompanied by negative o r inward radial velocity. T h i s suggests the p o s s i b i l i t y of a vortex r i n g s t r u c t u r e occurring a t t h e e x i t of the s w i r l e r under high-swirl conditions. The swirl velocity p r o f i l e remains positive b u t shows a s t e p correspond i n g t o the outer boundary of the recirculation zone.
4.2
Velocity Profiles from Azimuthal Traverses
An indication of the azimuthal o r &variation of a x i a l , r a d i a l , and swirl velocities i s now g i v e n f o r the same vane angle s e t t i n g s used i n the radial traverses. The measurements were taken a t a constant radial position of r/D = 0.179, which i n most cases i l l u s t r a t e s adequately the azimuthal flow variation. However, measurements a t r/D = 0.204 were necessary i n the = 70 degree case t o g e t data more representative of t h e main region of the flow.
+
In a d d i t i o n , azimuthal traverse measurements were taken 0.109 D downstream ( a t x/D = 0.0, the expansion corner with the 90-degree block i n s t a l l e d ) f o r @ = 70 deg. so as t o investigate f u r t h e r the upstream extent of the central recirculation zone. These data a r e reported i n Ref. 3, whereas radial p r o f i l e s a t t h i s locatlon, f o r a l l degrees of s w i r l , a r e already available. Measurements in each case span an angle of 48 degrees , somewhat more than the 36 degrees between successive blades. Velocity p r o f i l e s a r e given i n Figs. 14 through 19. The variations i n a l l normalized velocity components, u , v, and w occur i n approximately 36-deg. cycles, coinciding w i t h the blade spacing. The profiles a l l show s i g n i f i c a n t variation with azimuthal position, except f o r those i n or near recirculation zones where the w-velocity component is dominant. These variations can b e a t t r i b u t e d t o several causes, among them being blade s t a l l from using f l a t blades a t high angles o f attack and wakes from b l u n t t r a i l i n g edges. Figure 14 s h m the azimuthal p r o f i l e w i t h the s w i r l e r i n s t a l l e d , b u t w i t h the vanes set t o zero angle. The $I = 0 deg. position is d i r e c t l y downstream of one of the swirl vanes, approximately 3 mn from the t r a i l i n g edge a t the r/D = 0.179 position. The velocity defect i n t h e wake of the blade is c l e a r l y seen i n the axial velocity profile, a l though the precise accuracy of these measurements i s uncertain because of the velocity gradients
The decreased uvelocity a t the l e f t s i d e o f the p r o f i l e i s caused by the presence of an upstream strut supporting the h u b , located a t 0 = +24 deg. The radial velocity i s uniformly negative indicating inflow over most of the range, which agrees well w i t h the r e s u l t s of the radial traverse shown e a r l i e r i n F i g . 9. The radial velocity i s positive only i n the blade wake region. The swirl velocity, as expected, is effect i v e l y zero.
across the w i d t h of the probe.
Figure 15 presents the r e s u l t s of an azimuthal traverse f o r the 4 = 38 deg. low-swirl case. The measurement position a t r/D = 0.179 is in the middle of the f l a t portion of the radial p r o f i l e , as may be deduced from observation of F i g . 3. The 36 deg. c y c l i c variation from one blade t o the n e x t is apparent i n each of the p r o f i l e s . T h e u and w p r o f i l e s have a f l a t portion, apparently between blade wakes, w i t h an average yaw angle of about 39 deg. T h i s confirms the assumption t h a t the blade pi tch/chord r a t i o of one i s s u f f i c i e n t t o adequately t u r n the flow. In f a c t , over the r e s t of the p r o f i l e , the turning angle i s even higher than the blade angle The radial velocity shows no f l a t region and varies the most of the three components. I t i s a l s o q u i t e large even a t t h i s low degree of swirl.
+.
In the case of @ = 45 deg., Fig. 16 i l l u s t r a t e s t h a t the 36-deg. cycle i s n o t as c l e a r , b u t nevertheless s i g n i f i c a n t variation e x i s t s i n a l l profiles. The radial component i s nearly as large as the axial and swirl components i n some places, and again exh i b i t s the g r e a t e s t variation w i t h azimuthal position.
For the 60-deg. swirl case of Fig. 17, variations with azimuthal position a r e again evident i n a l l p r o f i l e s . The variation i s l e s s t h a n in the cases seen heretofore, possibly because the main flow has s h i f t e d f u r t h e r outward under centrifugal effects and the measurement position i s i n a region of reduced velocity. This e f f e c t i s even more notable i n the + = 70 deg. p r o f i l e s portrayed i n Fig. 18. The measurement position i s now no longer in the main exiting flow, b u t on the edge of the central recirculation zone. The axial velocity here i s effectively zero, although considerable swirl and radial velocities a r e present. The radial velocity, i t should be noted, is negative o r inward towards the centerline. Azimuthal variations a r e f a i r l y small here, which i s t o be expected since the flow is mainly i n the azimuthal direction. To get a more representative sample of the exiting flow from the swirler w i t h blades a t 70 deg., a traverse was made a t the next outward radial s t a t i o n a t r/D = 0.204. When the velocity profiles shown i n Fig. 19 a r e compared w i t h those i n the previous figure, the e f f e c t s of extreme velocity gradients i n the radial direction may be perceived. The accuracy of the radial velocity and pitch angle measurements may be suspect in the presence of high radial velocity gradients, b u t the major features of the flow can s t i l l be assessed. I n a radial distance of only 7.6 mm, the axial velocity jumps from zero t o over 12 m/s. In addition, the swirl velocity increases over 50 percent and t h e radial velocity changes sign. The 36-deg. cyclic variation w i t h blade spacing i s again present in a l l profiles. Azimuthal traverses f o r the flow with swirl vane angle $I = 70 deg., taken 3.25 cm downstream of the location of measurements j u s t discussed, are reported e l ~ e w h e r e . ~The r e s u l t s may be compared
108
with those given i n F i g s . 18 and 19 of the present paper. I t appears from both s e t s of p r o f i l e s t h a t the recirculation zone has narrowed somewhat with the additional length before the expansion corner. A t the inner radial position (r/D = 0.1791, t h e axial velocity i s no longer zero. I t i s now posit i v e , indicating t h a t the main exit flow has moved s l i g h t l y f u r t h e r inward. The azimuthal variation i s s t i l l quite small, however, suggesting t h a t the damping influence of t h e recirculation zone is s t i l l i n e f f e c t . A t the outer radial position (r/D = 0.204), t h e axial and radial velocities are larger than a t the upstream p o s i t i o n , also implying t h a t the outer high-velocity zone has moved f u r t h e r inward. The azimuthal variation i s similar t o t h a t of the exit-plane position a t the same radius. 4.3
Table 3.
Percent Difference
K
Calibration Sensitivity
An indication o f s e n s i t i v i t y of the data reduction procedure t o variations i n probe calibration parameters used was also investigated. The case of swirl vane angle $I = 70 deg. was used, a t x/D = -0.109 and r/D = 0.179. The most recent calibration provided the baselinF8values of the pitch and velocity c o e f f i c i e n t s , which were then varied by increasing the magnitude of each value by ten percent. Three cases were t r i e d : increased pitch coefficient w i t h baseline velocity c o e f f i c i e n t , increased velocity c o e f f i c i e n t w i t h baseline pitch coefficient, and increased values of both coefficients. The percent difference in the output values of the velocity components i s shown i n Tables 3 through 5 f o r each of these three cases respectively
Table 4.
9 (deg.)
U/Uin
V/uin
W/Ui
n
-24.0
1.91
-8.22
1.91
-18.0
0.80
-10.23
0.80
-12.0
0.27
-11.43
0.27
-6.0
0.92
-10.01
0.92
0.0
2.15
-7.89
2.15
6.0
1.87
-7.27
2.87
12.0
2.55
-7.51
2.55
18.0
2.29
-7.73
2.29
24.0
1.93
-8.17
1.93
Calibration S e n s i t i v i t y Comparison Actual vs. 10%Higher Velocity Coefficient Only Percent Difference
K
.
Referring t o Table 3, changing the pitch coefficient value i s seen t o a f f e c t the radial component the most, as expected. The change in output stays below ten percent f o r a l l b u t three of the output values. For t h e case of increased velocity coefficient only, Table 4 shows a q u i t e uniform increase of l e s s than f i v e percent over a l l the values. This indicates a r e l a t i v e l y predictable, low sensit i v i t y response t o changes i n the calibration velocity c o e f f i c i e n t . T h e f i n a l case, shown i n Table 5, indicates t h a t increases i n both c o e f f i c i ents tend to cancel each other f o r the radial veloc i t y measurement, which was the most s e n s i t i v e t o pitch coefficient variation. The axial and swirl components increase somewhat, b u t a l l variations remain well below ten percent. T h i s r e l a t i v e i n s e n s i t i v i t y t o calibration e r r o r s is encouraging b u t i t should be noted t h a t i f the c o e f f i c i e n t changes a r e o f opposite s i g n i n the combined case, e r r o r s of greater than ten percent i n the radial velocity measurements m i g h t ensue.
4.4
Calibration S e n s i t i v i t y Comparison Actual
vs. 10%Higher Pitch Coefficient Only
u/uin
v/uin
W/Ui"
1
-24.0
4.86
4.86
4.86
2
-18.0
4.88
4.88
4.88
3
-12.0
4.88
4.
4
-6.0
4.88
4.88
4. 88
5
0.0
4.86
4.86
4.86
6
6.0
4.88
4.88
4.88
&a
4.88
7
12.0
4.87
4.87
4.87
8
18.0
4.87
4.87
4.87
9
24.0
4.86
4.86
4.86
Table 5.
Calibration S e n s i t i v i t y Comparison Actual
vs. 10%Higher, Both Pitch and Velocity Coeff i cien t s
Swirl Strengths
Swirl numbers S and S ' were calculated from Eqs. ( 1 ) and (6), w i t h the turbulent s t r e s s terms omitted. Measured v e l o c i t i e s and pressure (with reference pressure p, being a t the outer edge of the s w i r l e r a t r/D = 0.25) from t h e radial traverses of Section 4.1 were used w i t h appropriate numerical integration. Results a r e shown i n Table 6 where the f l a t blade swirler exhibits asymptotic behavior in its a b i l i t y t o pFoduce strong swirl. Also shown i s the measured r a t i o wm/umo f o r each swirl vane angle. 9
109
9 (deg.)
-24.0
6.87
-3.75
6.87
-18.0
5.72
-5.85
5.72
-12.0
5.15
-7.12
5.15
-6.0
5.84
-5.62
5.84
0.0
7.12
-3.41
7.12
6.0
7.88
-2.75
7.88
12.0
7.54
-3.01
7.54
18.0
7.27
-3.25
7.27
24.0
6.90
-3.70
6.90
Someone unaware of the actual swirler e x i t velocity and pressure d i s t r i b u t i o n s m i g h t proceed in t h e following way. An ' i d e a l ' f l a t blade swirle r operating on a p l u g flow would produce e x i t profiles like Case I of F i g . 1 w i t h F = wo/uo = tan $I where $I i s the swirl vane angle. Corresponding S and s' values a r e then found from the equations of Table l which a r e plotted i n Fig. 2. These 'idealized theoretical ' values a r e given in Table 7, where negative values occur when the theoretical pressure contribution dominates i n the denominator w i t h negative consequences. I t may be noticed immediately t h a t the actual s w i r l e r performance i s considerably i n f e r i o r t o the idealization, and t h u s observant t h e o r i s t s 4 must continue t o use actual t e s t section i n l e t data i n preference t o the most simple idealization of Case I . Even the other l e s s idealized 'theoretical ' cases a r e a l s o inappropriate. The l a t t e r part of Table 7 gives the calculated swirl strengths on the basis of the most appropriate p r o f i l e s (Cases I through V of Section 2.3) with associated F through J values taken from t h e measurements (values a r e given i n Table 6). These d i s p a r i t i e s a r e a t t r i b u t e d t o the presence of the central hub, the upstream extent of the central recirculation zone, and f l a t swirl-v-ne ineffectiveness a t high angles of attack, with associated wakes and nonaxisymetries. Table 6.
70 deg. using a five-hole p i t o t probe technique. These data form a useful part of a data base f o r t h e evaluation of flowfield prediction codes and t u r b ul ence model s
.
Assumptions of f l a t axial and swirl piwfiles w i t h radial velocity equal t o zero were found t o be progressively less r e a l i s t i c a s the s w i r l e r blade angle increases. A t low swirl strengths ($I = 38 deg.), portions of the u and w p r o f i l e s remain f l a t while t h e v-component i s already s i g n i f i c a n t . A t moderate swirl $I = 45 deg., l i n e a r l y increasing profiles of u and w w i t h radius a r e appropriate w i t h v nonzero. A t stronger swirl $I = 60 deg., even more spiked p r o f i l e s a r e appropriate w i t h most of the flow leavi ng the swirl e r near i t s outer edge, and some reverse flow near the hub. A t strong swirl $I = 70 deg., the p r o f i l e s a r e extremely spiked w i t h flow reversal. The central recirculation zone extends upstream of the e x i t plane, almost to the swirler blades in high-swirl cases. Because of t h i s recirculation, none of the idealizations considered could model strong swirl cases adequately. The flow-turning effectiveness of the f l a t blades was generally adequate f o r a1 1 vane angles tested. However, the large variations of flow angles and vel oci t i es w i t h radi us made meani ngf u l comparisons w i t h two-dimensional cascade data impossible. Nonaxisymmetry was found i n a l l swirl cases investigated. Acknowledgments
Measured Swirl Numbers _ ~ ~ _ _
~~
0
S
S'
~mo/umo
38
0.567
0.559
0.801
45
0.765
0.718
0.876
60
0.850
0.759
0.937
70
0.883
0.750
0.887
Appreciation i s expressed t o NASA Lewis Research Center and Air Force Wright Aeronautical Laboratories f o r financial s u p p o r t via NASA Grant No. NAG 3-74, technical monitor Dr. J. D. Holdeman. References 1.
2.
Table 7.
0
Most Appropriate Case
S
S'
Case
S
S'
38
0.750
0.521
I
0.786
0.534
45
1.333
0.667
I11
1.137
0.584
60
-2.309
1.155
V
1.291
0.625
70
-0.660
1.832
V
1.066
0.591
5,
Rhode, D. L . , Lilley, D. G., and McLaughlin, On the Prediction of S w i r l i n g Flowfields Found i n Axi symmetri c Combus t o r Geometri es , ASME Journal o f Fluids Engng., Vol. 104, 1982 pp. 378-384. D. K.,
Theoretical Swirl Numbew
Ideal Case I
Lilley, D. G., and Rhode, D. L . , A Computer Code f o r Swirling Turbulent Axisymetric Recirculation Flows in Practical Isothermal Combustor Geometries, NASA CR-3442, Feb. 1982.
3.
Sander, G. F., Axial Vane-Type Swirler Performance Characteristics. M.S. Thesis, School of Mechanical and Aerospace Engineering, Oklahoma S t a t e University, S t i l l w a t e r , Okla., May 1983.
4.
Abujelala, M. T., and LilTey, D. G., Confined Swirling Flow Predictions, Paper AIM-83-0316, Reno, Nevada, Jan. 10-13, 1983.
5.
Rhode, 0. L., Lilley, D. G., and McLaughlin, D. K., Mean Flowfields i n Axisymetric Combustor Geometries w i t h Swirl, AIAA Journal, Vol. 21, No. 4, April 1983, pp. 593-600.
Conclusions
Performance c h a r a c t e r i s t i c s of an axial-flow annular vane s w i r l e r have been investigated. A theoretical analysis o f swirl numbers associated w i t h several idealized e x i t velocity p r o f i l e s was included, and values of the r a t i o of maximum swirl velocity t o maximum axial velocity a t d i f f e r e n t swirl strengths a r e given f o r each case. Measurements of actual s w i r l e r e x i t velocity profiles were made f o r swirl vane angles 4 = 0, 38, 45, 60, and
6. Lilley, D. G., Turbulent Combustor Flowfield Investigation. Paper i n Combustion Fundament a l s Research Conference, held a t NASA Lewis Research Center, Cleveland, Ohio, Oct. 21-22, 1982, pp. 152-168. 7.
110
Yoon, Probe fined Reno,
H. K., and Lilley, D. G . , Five-Hole P i t o t Time-Mean Velocity Measurements i n ConSwirling Flows. Paper AIAA-83-0315, Nevada, January 10-13, 1983.
8.
Janjua, S. I . , McLaughlin, D. K., Jackson, T. W., and Lilley, D. G., Turbulence Measurements i n a Confined J e t Using a S i x Orientation Hot-wire Probe Technique, Paper AIM-82-1262, Cleveland, Ohio, June 21-23, 1982.
9.
Jackson, T. W., and Lilley, D. G., Swirl Flow Turbulence Measurements Using a Si ngle-Wi r e Technique. Paper AIM-83-1202, S e a t t l e , Wash., June 27-29, 1983.
10.
Janjua, S. I . , and McLaughlin, D. K., Turbulence Measurements i n a Swirling Confined J e t Flowfield Using a Triple Hot-wire Probe, Report DT-8178-02 , Dynamics Techno1 ogy , Inc. , Torrance, CA, Nov. 1982.
11.
Kerr, N . M., and Fraser, D. , Swirl. Part I: Effect on Axisymmetrical Turbulent J e t s . Journal of the I n s t . of Fuel, Vol. 38, Dec. 1965, pp. 519-526.
12.
Mathur, M. L . , and MacCallum, N. R. L . , Swirling Air J e t s Issuing from Vane Swirlers. Part I : Free J e t s ; Part 11: Enclosed J e t s . Journal of the I n s t . of Fuel, Vol. 40, May 1967, pp. 2T4-245.
13.
Chigier, N. A., and Chervinsky, A., Experiment a l Investigation of Swirling Vortex Motion in J e t s . Journal of Appl ied Mechanics , Vol 34, June 1967, pp. 443-451.
.
14.
Beer, J . M., and Chigier, N. A., Combustion Aerodynamics. Appl ied Science Pub1 ishers, London, 1972.
15.
Bel tagui , S. A. , and MacCallum, N. R. L., Aerodynami cs of Vane-Swi r l ed F1 ames i n Furnaces. Journal of the I n s t . of Fuel, Vol. 49, Dec. 1976, pp. 183-193.
16.
Gupta, A. K., and Lilley, D. G . , Flowfield Modeling and Diagnostics, Abacus Press, Tunbridge Wells, England, 1983 ( i n press).
17.
Rhode, D. L., Predictions and Measurements o f Isothermal F1 owfi el ds i n Axi symnetri c Combus t o r Geometries. Ph.D. Thesis , Oklahoma S t a t e University, S t i l l w a t e r , Okla., Dec. 1981.
18.
Yoon, H. K., Five-Hole P i t o t Probe Time-Mean Velocity Measurements i n Confined Swirling Flows, M.S. Thesis, Oklahoma S t a t e Univ., S t i 11water, Okl a. , July 1982.
111
APPENDIX H ACCURACY AND DIRECTIONAL SENSITIVITY OF THE SINGLE-WIRE TECHNIQUE
( AIAA- 84-0367 )
112
ACCURACY AND DIRECTIONAL S E N S I T I V I T Y
OF THE SINGLE-WIRE TECHNIQUE T. W. Jackson* and D. G. L i l l e y * * Oklahoma State U n i v e r s i t y S t i l l w a t e r , OK 74078 Abstract
1.
Multi-orientation o f a single-hot-wire i s a novel way t o ineasure the t h r e e time-mean v e l o c i t i e s , the t h r e e t u r b u l e n t normal stresses, and the t h r e e t u r b u l e n t shear stresses. The present study focuses on the accuracy and d i r e c t i o n a l s e n s i t i v i t y o f the technique w i t h respect t o mean f l o w v e l o c i t y o r i e n t a t i o n t o the probe. Results demonstrate r e l a t i v e i n s e n s i t i v i t y , i n d i c a t i n g t h a t the method i s a u s e f u l c o s t - e f f e c t i v e t o o l f o r t u r b u l e n t flows o f unknown dominant f l o w d i r e c t i o n . Nomenclature -
E G K L P,(l,R
v =
(u,v,w)
P
c a l i b r a t i o n constants t e s t s e c t i o n diameter i n l e t nozzle diameter h o t - w i r e voltage pitch factor yaw f a c t o r c o n t r a c t i o n nozzle downstream distance selected h o t - w i r e probe posi t i ons time-mean v e l o c i t y ( i n x-, re-directions) i n f a c i l i t y coordinates a x i a l , r a d i a l , azimuthal cy1 i n d r i c a l p o l a r coordinates effective cooling velocity acting on a w i r e correlation coefficient (estimated) between c o o l i n g v e l o c i t i e s o f adjacent w i r e o r i en a t i o n s s w i r l vane angle w i t h respect t o f a c i 1 ty axis
value a t i n l e t t o f l o w f i e l d root-mean-squared q u a n t i t y
rms
The Single-Wire Technf-
As p a r t o f a research program aimed a t the understanding and modeling o f mixing processes i n combustion chambers , the s i x - o r i e n t a t i o n single normal hot-wire technique i s being used i n axisymmetric geometries under low speed, nonreacting, s w i r l i n g flow conditions. The method c a l l s f o r a normal h o t - w i r e t o be o r i e n t e d through s i x d i f f e r e n t p o s i t i o n s , each o r i e n t a t i o n separated by 30 degrees from the adjacent one. Orientation 1 i s normal t o the f a c i l i t y c e n t e r l i n e , o r i e n t a t i o n 2 i s r o t a t e d 30 deg. from t h i s , etc. Mean and r o o t mean-square voltages are measured at each orientation. The data r e d u c t i o n i s performed using assumptions that turbulence f o l l o w s a normal p r o b a b i l i t y d i s t r i b u t i o n having mean voltage as t h e mean and the squared value o f the rms voltage as t h e I t i s then p o s s i b l e t o o b t a i n the t h r e e variance. time-mean v e l o c i t y components, the t h r e e normal Reynolds stresses and the t h r e e shear Reynolds stresses. A t Oklahoma S t a t e U n i v e r s i t y , J a n j u a l s t u d i e d t h e technique, developed a s u i t a b l e data r e d u c t i o n computer code, and presented r e s u l t s o f its a p p l i c a t i o n i n no s w i r l i n g f r e e and confined j e t flows. Jackson' extended the technique to i n v e s t i g a t e nonswi r l i n g and s w i r l i n g nonreacting t u r b u l e n t confined flows i n an axisymmetric t e s t s e c t i o n w i t h expansion r a t i o D/d = 2, which may be equipped w i t h a s t r o n g c o n t r a c t i o n nozzle of area r a t i o 4 a t L/O = 2. The f l o w f i e l d contains corner and c e n t r a l r e c i r c u l a t i o n zones t y p i c a l o f gas t u r b i n e and ramjet combustion chambers. S w i r l may be imparted t o t h e in-coming f l o w by means o f a variable-angle vane s w i r l e r . The technique and i t s appl i c a t i o n t o nonswi r l i n g and weakly-swi r l i n g confined flows i s fescribed a t l e n g t h i n Refs. 3 and 4. A recent paper presents measurements f o r a f u l l range o f s w i r l s t r e n g t h s i n the confined j e t facility. This extended t h e data base giver! e a r l i e r t o h i g h e r i n l e t vane s w i r l angles, more a x i a l measurement s t a t i o n s , and downstream nozzle effects. The data a r e being used t o a i d i n t h e e v o l u t i o n o f turbulence models f o r these complex flow situations.
Subscripts 0
1.1
Introduction
Superscripts time-mean average fluctuating quantity r e l a t i v e t o probe coordinates
*
Graduate Student, School o f Mechanical and Aerospace Engineering, Student Member A I A A
**
Professor, School o f Mechanical and Aerospace Engineering, Associate Fellow A I A A
The method i s based upon e a r l i e r s t u d i e s on mu1t i - 0 r i e n t a t i o % o f a s i n g l e normal hot-wire. Dvorak and Syred presented time-mean and turbulence p r o p e r t y measurements i n a complex f l o w f i e l d w i t h 45 deg. between t h r e e successive o r i e n t a t i o n s o f the A crossed-wire probe was a d d i t i o n a l l y used t o wire. measure c o r r e l a t i o n c o e f f i c i e n t s . Measurements i n s w i r l i n g r e c i r c u l a t i n g flows a t t h e e x i t from a swirl generator were obtained with similar techniques, using up t o six separate poinb Later, King measurements , by Syred e t a1 developed t h e s i x - o r i e n t a t i o n s i n g l e normal h o t - w i r e technique and a p p l i e d i t t o vortex flows.
113
.
1.2
Objectives
The aim o f t h e present paper i s t o address questions about accuracy and d i r e c t i o n a l s e n s i t i v i t y o f the six-orientation s i n g l e normal hot-wire technique. An u n c e r t a i n t y a n a l y s i s i s performed on the data reduction procedure by changing i n d i v i d u a l l y s t r a t e g i c i n p u t parameters, and n o t i n g t h e i r e f f e c t on deduced p r o p e r t i e s o f t h e flow. A d i r e c t i o n a l s e n s i t i v i t y a n a l y s i s i s presented which assesses t h e r e l a t i v e values o f deduced f l o w p r o p e r t i e s ( i n f a c i l i t y coordinates) t o l o c a l timemean v e l o c i t y o r i e n t a t i o n r e l a t i v e t o t h e probe. 1.3
s i g n i f y components o f t h e instantaneous v e l o c i t y vector i n coordinates on t h e probe. Each o f t h e t h r e e c a l i b r a t i o n curves i s obtained w i t h zero v e l o c i t y i n t h e o t h e r two d i r e c t i o n s . The c a l i b r a t i o n curves demonstrate t h a t the hot-wire i s most e f f i c i e n t l y cooled when t h e f l o w i s i n t h e d i r e c t i o n o f t h e u component (which i s normal t o both t h e w i r e and t h e supports). The w i r e i s most i n e f f i c i e n t l y cooled when t h e f l o w i s i n t h e d i r e c t i o n o f t h e w component (which i s p a r a l l e l t o t h e wire). Each o f the c a l i b r a t i o n curves f o l l o w s a second order, least-square f i t o f t h e form: E? = A.
O u t l i n e o f t h e Paper
1
Essential features o f the six-orientation single-wire hot-wire measurement technique are described b r i e f l y i n Section 2. The d i r e c t i o n a l s e n s i t i v i t y study i s discussed i n Section 3, w h i l e Section 4 presents t h e mathematical coordinate t r a n s f o r m a t i o n s f o r v e l o c i t y vectors, normal and shear stresses. Results are presented and discussed i n Section 5, w h i l e Section 6 draws conclusions from t h e study. 2.
1
'" +
+ Bo% i i
Ciii
which i s an extension o f the f a m i l i a r King's law. I n t h i s equation, A B i , and C i are- c a l i b r a t i o n * constants and ii can l i k e on a value o f u, v, and w f o r the t h r e e c a l i b r a t i o n curves, r e s p e c t i v e l y . When t h e w i r e i s placed i n a three-dimensional the effective cooling velocity experienced by t h e hot-wire i s : f lowfield,
Measurement Technique
One o f t h e most widely used instruments t o obtain turbulence quantities i s t h e hot-wire %anemometer, the most common o f which i s the s i n g l e hot-wire. When used on a two-dimensional f l o w w i t h a predominate f l o w d i r e c t i o n , a s i n g l e h o t - w i r e used normal t o the main f l o w can be used t o measure t h e streamwise components o f the time-mean v e l o c i t y a d t h e rms v e l o c i t y f l u c t u a t i o n , i n a standard manner.
a
The anemometer used f o r the present study i s C I S A type 55M01, CTA standard bridge. A normal h o t w i r e probe, D I S A t y p e 55P01, i s used i n the experiments. This probe has two prongs set approximately 3 mm apart which support a 5 pm diameter w i r e which i s gold p l a t e d near t h e prongs t o reduce end e f f e c t s and strengthen t h e wire. The mean voltage i s measured w i t h a Hickok D i g i t a l Systems, Model DP100, i n t e g r a t i n g voltmeter and the root-mean-square voltage f l u c t u a t i o n i s measured u s i n g a Hewlett Packard, Model 400 HR, AC voltmeter. I n a complex s w i r l i n g f l o w f i e l d t h e dominant f l o w d i r e c t i o n i s unknown and t h e standard s i n g l e o r i e n t a t i o n s i n g l e h o t - w i r e method f a i l s t o supply s u f f i c i e n t information. The s i x - o r i e n t a t i on method c a l l s f o r a normal h o t - w i r e t o be o r i e n t e d through s i x d i f f e r e n t p o s i t i o n s , each o r i e n t a t i o n separated by 30 deg. f o r the adjacent one. Orientation 1 i s normal t o t h e f a c i l i t y c e n t e r l i n e , o r i e n t a t i o n 2 i s r o t a t e d 30 deg. from t h i s , etc. Mean and root-meansquare voltages are measured a t each o r i e n t a t i o n . The data r e d u c t i o n i s performed u s i n g assumptions that turbulence follows a normal p r o b a b i l i t y d i s t r i b u t i o n having mean voltage as t h e mean and t h e squared value o f t h e rms v o l t a g e as the variance. It i s then p o s s i b l e t o o b t a i n t h e t h r e e time-mean v e l o c i t y components, t h e t h r e e normal Reynolds stresses and t h e t h r e e shear Reynolds stresses, i n t h e manner now described. The s i x - o r i e n t a t i o n hot-wire technique r e q u i r e s a s i n g l e , s t r a i g h t , h o t - w i r e t o be c a l i b r a t e d f o r t h r e e d i f f e r e n t f l o w d i r e c t i o n s i n order t o determine t h e directional sensitivity of the probe. I n the following relationships, t i l d e s
where G and K r e t h e p i t c h and yaw f a c t o r s , defined by Jorgensen" and deduced from t h e c a l i b r a t i o n curves. Hence, equations f o r the e f f e c t i v e c o o l i n g v e l o c i t y can now be obtained f o r each o f the s i x wire orientations. S o l v i n g simultaneously any t h r e e adjacent equations provides expressions f o r t h e instantaneous values of the three velocity components (u, v, and w i n f a c i l i t y x , r and 9 coordinates, respectively) in terms of the I t i s then p o s s i b l e equivalent c o o l i n g v e l o c i t i e s . t o o b t a i n t h e t h r e e time-mean v e l o c i t y components and the s i x d i f f e r e n t components o f t h e Reynolds s t r e s s tensor, i n t h e manner described i n Refs. 1 and 3. Dvorak and Syred' used a D I S A time c o r r e l a t o r (55A06) t o f i n d t h e c o r r e l a t i o n c o e f f i c i e n t s between the velocity fluctuations i n the three directions. One approach i s t o use t h e i n f o r m a t i o n obtained by a l l s i x o r i e n t a t i o n s and devise a mathematical procedure t o c a l c u l a t e t h e covariances. These are c a l c u l a t e d using t h e r e l a t i o n s h i p : 2 K Z 1. Z
j = YZiZj[0Zi
2 ,1/2
where Y Z . ~ . i s t h e c o r r e l a t i o n t h e two' k o o l i n g v e l o c i t i e s d e f i n i t i o n , t h e absolute value coefficient y i s always l e s s
z;z< ' J
(3)
O Zj
c o e f f i c i e n t between Z i and Z - . By o f the c o i b e l a t i o n than 1.
C e r t a i n assumptions a r e made i n order t o c a l c u l a t e t h e covariances. However, King8 observed t h a t a t times t h e c a l c u l a t e d value of the c o r r e l a t i o n c o e f f i c i e n t i s g r e a t e r than one a t which instance he assigned p r e v i o u s l y f i x e d values t o t h e I t may be deduced t h a t i f correlation coefficients. two wires are separated by an angle of 30 degrees, t h e f l u c t u a t i n g s i g n a l s from t h e wires a t t h e two l o c a t i o n s would be such t h a t t h e i r c o n t r i b u t i o n t o t h e c o o l i n g o f t h e w i r e would be r e l a t e d by t h e cosine o f t h e angle between t h e wires. This assumption leads t o the f o l l o w i n g t h r e e values o f
114
the correlation coefficients = cos 30 = 0.866
yZPZO (4) YZYZR = cos 30 = 0.866
(5)
=
(0.8)(0.866)(0.866)
Hence: =
0.6
YZPZK The three covariances a r e then obtained by s u b s t i t u t i n g the corresponding values o f the c o r r e l a t i o n c o e f f i c i e n t s i n t o Eq. (3). King8 used the above technique. The present study, however, uses Eqs. ( 4 ) and (6) d u r i n g t h e e n t i r e data reduction. This s i m p l i f i c a t i o n i s j u s t i f i e d a p o s t e r i o r i i n Section 5.1, where i t i s demonstrated t h a t deduced r e s u l t s a r e r e l a t i v e l y i n s e n s i t i v e t o c o r re1a t ive t erin inaccuracy. 3.
3 =
00
3 =
00
=
00
Case 2
0 = -450
Case 3
a
Case 4
4 = -900
il =
Case 5
a
p
= -450
)
= -900
= -450
00
= -900
The above f i v e probe/flow c o n f i g u r a t i o n s are used a t each o f f i v e r e p r e s e n t a t i v e s i t u a t i o n s i n a f r e e axisymmetric n o n s w i r l i n g j e t a t x/d = 0 (laminar i n p o t e n t i a l core region), 3 and 10 ( t u r b u l e n t i n shear l a y e r region); and i n a f r e e axisymmetric s w i r l i n g j e t a t a l o c a t i o n i n a r e g i o n o f strong shear j u s t downstream o f the e x i t from a variable-angle vane s w i r l e r w i t h s w i r l vane angles o f 45 and 70 deg., representing moderate and strong I n these s w i r l i n g j e t cases, t h e probe s w i r l cases. was l o c a t e d j u s t downstream o f t h e s w i r l e r e x i t , o u t s i d e o f any regions o f r e c i r c u l a t i o n : This p a r t o f the f l o w was chosen as i t i s i n an area o f r a p i d a c c e l e r a t i o n and i s u n l i k e l y t o c o n t a i n any instantaneous f l o w r e v e r s a l s which might cause erroneous readings. Specifically, the following f i v e s i t u a t i o n s are used:
The c o r r e l a t i o n c o e f f i c i e n t s may be r e l a t e d via:8
where n i s given a value o f 0.8.
Case 1
Situation A Situation B
x/d = 0 x/d = 3
Situation C
x/d = 10
Situation D
x/d = 0
Situation E
x/d = 0
D i r e c t i o n a l S e n s i t i v i t y Analysis
The a n a l y s i s i s performed a t any s p e c i f i c f l o w f i e l d l o c a t i o n by i n i t i a l l y p l a c i n g t h e probe i n a f r e e j e t such t h a t t h e coordinate system o f t h e probe coincides w i t h t h e coordinate system o f t h e j e t , as shown i n P a r t (a) o f Fig. 1. Measurements a r e then taken by r o t a t i n g the probe i n the manner o f t h e technique j u s t described. To simulate t h e e f f e c t of the f l o w s h i f t i n g i t s dominant f l o w d i r e c t i o n , the probe i s r o t a t e d by 9 deg. about i t s This z-axis, as shown i n P a r t ( b ) o f the f i g u r e . r o t a t i o n causes a misalignment between the probe coordinate system and t h e f a c i l i t y coordinates. This discrepancy can be accounted f o r by use o f t h e In this E u l e r i a n matrices described i n Section 4. con f igu r a t ion, t h e measured t ime-mean va 1ues , normal and shear stresses a r e i n a coordinate system o b l i q u e t o the j e t coordinate system. However, they can be l\ransformed back t o t h e f a c i 1it y coordinate system. Notice t h a t the c o r r e c t d i r e c t i o n a l sense o f t h e r o t a t i o n must be f o l l o w e d so t h a t standard coordinate transformations may be used on t h e probe data so as t o o b t a i n f a c i l i t y c o o r d i n a t e data. Results shown l a t e r i n Section 5 have been obtained i n t h i s manner. (b)1
To examine t h e d i r e c t i o n a l s e n s i t i v i t y o f t h e w i r e f u r t h e r , t h e probe was subsequently r o t a t e d about i t s new x-axis, thereby forming a compound angle between probe and t h e dominant f l o w v e l o c i t y , Again t h e as a l s o shown i n Fig. 1, see P a r t (c). time-mean v e l o c i t i e s and Reynolds s t r e s s t e n s o r can be deduced i n terms o f the j e t coordinate system by t h e method shown i n Section 4, and t h e r e s u l t s and t h e i r accuracy are a l s o discussed i n Section 5. Specifically, the directional s e n s i t i v i t y o f t h e technique i s assessed a t f i v e f l o w f i e l d s i t u a t i o n s f o r self-consistency u s i n g t h e f o l l o w i n g f i ve conf igura t ions :
115
Fig. 1.
n o n s w i r l i n g laminar region nonswirling turbulent region nonswirling turbulent region s w i r l i n g turbulent region w i t h s w i r l vane angle 45 deg. s w i r l i n g t u r b u l e n t region w i t h s w i r l vane angle 70 deg.
CASES 2 A N D 4
-
C o n f i g u r a t i o n s Used i n t h e D i r e c t i o n a l Se?si t i v i t y St udy
These l o c a t i o n s are i l l u s t r a t e d i n Figs. 2 and 3. I t w i l l be seen l a t e r t h a t t h e s e n s i t i v i t y a n a l y s i s assures users t h a t knowledge o f l o c a l c o n f i g u r a t i o n o f probe vs f l o w d i r e c t i o n i s not r e q u i r e d a priori, and useful r e s u l t s a r e forthcoming and r e l a t i v e l y i n s e n s i t i v e t o s p e c i f i c configurations.
I
cos0
-sin3
sin0
COSG
sin3
1
O
l
O1 ! Fig. 2.
Free N o n s w i r l i n g J e t Measurement Locations f o r S i t u a t i o n s A, B y and C
For example, a r o t a t i o n about the z-axis by angle 3 r e s u l t s i n o l d (x, y, z ) coordinates o f a p o i n t being r e l a t e d t o i t s new (X, Y, 2 ) coordinates v i e : [x y z l T
= R Z 3 [X Y Z I T
S i m i l a r l y , v e l o c i t y components (u, v, w) are r e l a t e d t o (U, V, W ) v i a
[u v w l T = R Z e [U V W I T I n the n o t a t i o n of Fig. 1 w i t h v e l o c i t y components u, v, w i n x, r, 3 f a c i l i t y coordinates -
A
-
u, v, w i n x , y, z probe Case I coordinates
F i g . 3.
Free S w i r l i n g J e t Measurement Locations f o r S i t u a t i o n s 0 and E 4.
4.1
Coordinate Transformation
,
-
.
To i n v e s t i g a t e t h e s h i f t i n g o f t h e dominant f l o w d i r e c t i o n , t h e probe holder vs l o c a l time-mean f l o w vector c o n f i g u r a t i o n i s v a r i e d through five d i f f e r e n t cases o f i n t e r e s t . To r e l a t e probe coordinate data back t o t h e f a c i l i t y coordinate system, use i s made o f Eulerian rotational matrices. These make i t p o s s i b l e t o r e l a t e a l l time-mean v e l o c i t i e s and t h e f u l l Reynolds s t r e s s t e n s o r back t o t h e f a c i 1it y coordinate system a f t e r any a x i s r o t a t i o n . Any (x,y,z)-Cartesian coordinate axes may be r o t a t e d about t h e x, y, o r z a x i s , r e s p e c t i v e l y , by 9 , with corresponding coordinate an angle t r a n s f o r m a t i on matrices
,
,
,
-
.
,
.
A
u, v, w i n x, y, z probe Case 2 and 4 coordinates ?
-
I
$
2 0 , :
u, v, w i n x, y, z probe Case 3 and 5 coordinates the f o l l o w i n g r e l a t i o n s h i p s p r e v a i l : 4.2
Rotational Matrices
A
Case 1
The f a c i l i t y and probe Case 1 coordinates are c o i n c i d e n t and cu v
4.3
WIT
=
[ii
v GIT
Cases 2 and 4
I n t h i s case, a r o t a t i o n o f 9 about t h e z-axis, r e s u l t i n g i n [u v w l T = RZe
degrees i s a p p l i e d
6 -v -W ]T
which leads t o
Rxe
=
1
0
0
0
cos0
-sine
0
sin0
cos0
=
116
u' [i
cos G sin e
-
j sin
;i
cos
.]
0
Froin t h i s the d i r e c t i o n a l time-mean v e l o c i t i e s i n f a c i l i t y coordinates can e a s i l y be i n f e r r e d . The angle terms i n t h e r l a t i o n s h i p are, i n f a c t , the directional cosines,'' which can be used t o determine the s t r e s s transformations i n terms o f f a c i l i t y coordinates. The d i r e c t i o n a l co_sines betwcen any new coordinate axes, f o r example, x, y, and z, and the o r i g i n a l coordinate axes x, y and z can be conveniently t a b u l a t e d as f o l l o w s :
Again , t h i s re1a t ionshi p permits time-mean v e l o c i t y components t o be converted back i n t o f a c i l i t y coordinates. The c o e f f i c i e n t m a t r i x defines the d i r e c t i o n a l cosines r e l a t i n g t h e two c o o r d i n a t e systems; these can be used f o r normal and shear s t r e s s transformations i n the manner described i n Section 4.3. 5.
5.1
~
Y
e2
Z
23
m3
n3
These d i r e c t i o n a l cosines (zi, m., n i f o r i = 1, 2 and 3) can be used i n the generaj three-dimensional s t r e s s equationjl governing the t r a n s f o r m a t i o n of coordinates v i a T
xx
= 2 2 T,.,
1 xx
+
m2 r e ^ 1 yy
+ n21c Azz-
+
2~l"lri?
+ 2m1n1T yz A - + 2n1z1c;~ I
r c
YY
as above w i t h s u b s c r i p t 1 replaced by 2
=
zz = as above w i t h s u b s c r i p t 1 replaced by 3 xy
r
=
+ m1m2T-O + n1n2r *zz' yy
+ (mln2
+ in2 n1 )TA+ (nlz2 yz
( v 2
+
+
22ml)Txjl
+ n2z1)~;x
U n c e r t a i n t y Analysis
The uncertainty analysis includes a determination o f t h e s e n s i t i v i t y o f t h e s i x o r i e n t a t i o n h o t - w i r e data r e d u c t i o n t o various i n p u t parameters which have major c o n t r i b u t i o n s i n t h e response equations. P i t c h and yaw f a c t o r s (G and K ) are used i n t h e response equations described i n Section 2 i n order t o account f o r the d i r e c t i o n a l s e n s i t i v i t y o f the s i n g l e h o t - w i r e probe. Figure 4 shows t h e p i t c h and the yaw f a c t o r s p l o t t e d against the h o t - w i r e mean e f f e c t i v e voltage. Both the p i t c h and y a w f a c t o r s are f u n c t i o n s o f the h o t - w i r e mean e f f e c t i v e voltage, b u t the yaw f a c t o r i s f a r more sensitive. A one percent increase i n t h e h o t - w i r e v o l t a g e reduces t h e p i t c h f a c t o r by 1.3 percent and F o r the present t h e yaw f a c t o r by 56 percent. study, the values of these f a c t o r s are chosen a t an average hot-wire voltage experienced in the flowfield. This was z o p r i a t e since the output q u a n t i t i e s (u, ulrm , u l v a , , e t c ) a r e only weakly This can be seen i n dependent on t h e vaque o f K. the data o f Table 1 which summarizes an a n a l y s i s performed on t h e data r e d u c t i o n program a t a representative p o s i t i o n i n the flowfield. A Y A W FACTGC
as above with s u b s c r i p t s (1, 2 ) replaced by (2, 3)
=
yz c
z12 2T AxxA
Results
above w i t h s u b s c r i p t s ( 1 , 2 ) zx = as replaced by (3, 1)
v)
cc
0 t-
o
These r e l a t i o n s h i p s lead t o e v a l u a t i o n o f a l l the s t r e s s components i n f a c i l i t y coordinates, from corresponding data o r i g i n a l l y reduced i n probe coordinates. 4.4
4
U
5> io t:
Cases 3 and 5
a
To go from Cases 2 and 4, t o Cases 3 and 5, a r o t a t i o n o f ) degrees i s a p p l i e d about t h e new xaxis, r e s u l t i n g i n
[u j
WIT =
R
x.p
{u v
WIT
HOT-WIRE VOLTAGE C(VOLTS)
and Fig. 4.
which i s COS 9
-
sin 9
+ cos 9 cos sin b
[E] [ =
0
s i n 9 cos j
+
.] [ ]
+ sin 9 sin 3
-
cos 4 s i n cos
)
P i t c h and Yaw Factors G and
Table 1 demonstrates the percent change i n t h e output q u a n t i t i e s f o r a 1 percent change i n most o f F o r t h e data t h e important i n p u t q u a n t i t i e s . presented i n t h i s t a b l e only q u a n t i t i e s c a l c u l a t e d from t h e probe o r i e n t a t i o n combination 5, 6 and 1 are used, f o r s i m p l i c i t y . The s i t u a t i o n i s t h a t o f a moderately s w i r l i n g confined f l o w f i e l d from a In s w i r l generator w i t h vane angle o f 38 degrees. t h i s s w i r l i n g flow o r i e n t a t i o n 6 was t h e minim in o f t h e 6 mean e f f e c t i v e c o o l i n g v e l o c i t i e s . King' has
117
argued t h a t t h e probe o r i e n t a t i o n combination approximately centered around the minimum e f f e c t i v e c o o l i n g v e l o c i t y produces more accurate estimates o f c a l c u l a t e d turbulence q u a n t i t i e s , than do the other o r i e n t a t i o n combinations. However, a l l p r e v i o u s l y r e p o r t e d data has been obtained by averaging a l l t h e s i x p o s s i b l e combinations. It i s not unusual i n h o t - w i r e anemometry t o have the mean v e l o c i t y components and turbulence q u a n t i t i e s t h a t are measured, be q u i t e s e n s i t i v e t o changes i n mean h o t - w i r e voltage. For i n t e r p r e t i v e purposes, the mean h o t - w i r e voltage v a r i a t i o n s can be thought o f as being e i t h e r e r r o r s i n measuring t h e mean voltage, o r s h i f t s i n t h e i n d i v i d u a l w i r e c a l i b r a t i o n s due t o contamination o r s t r a i n 'aging' o f the wire. The data o f Table 1 demonstrate t h a t t h e most serious inaccuracies i n the measurement and data r e d u c t i o n technique w i l l be i n t h e estimates o f t u r b u l e n t shear stresses, t h e most i n a c c u r a t e output term being u'w'.
Table 1-
Effect of Input Parameters on Turbulence Q u a n t i t i e s i n a Confined S w i r l i n g F l o w w i t h S w i r l Angle o f 38 deg. at a Representative F l o w f i e l d P o s i t i o n (x/D = 1, r / O = 0.25).
%
L
,
-
I
I
. _ %,-$Iwr-.
- _. - I L "
- 1
r2.66
0.0 -5.11
\ I "
I j -1.L9
I !
.:.49
3.0
I
I
I
I
As already discussed i n Section 2, an ad hoc assumption i s made regarding t h e numerical values o f t h e c o r r e l a t i o n c o e f f i c i e n t s used i n t h e deduction o f time-mean and turbulence q u a n t i t i e s . The r e s u l t s o f t h e u n c e r t a i n t y a n a l y s i s (Table 1) show the timemean and turbulence q u a n t i t i e s t o be r e l a t i v e l y insensitive t o variations i n the correlation coefficients. Therefore, t h e major ad hoc assumption made i n t h e technique does not seem t o have a g r e a t e f f e c t on t h e output q u a n t i t i e s compared t o t h e e f f e c t o f o t h e r i n p u t q u a n t i t i e s .
5.2
Laminar J e t
The d i r e c t i o n a l s e n s i t i v i t y o f t h e technique i s assessed a t t h e f i v e l o c a t i o n s A through E , see Figs. 2 and 3, corresponding t o f i v e d i f f e r e n t flow situations. The f i r s t o f these i s i n the laminar p o t e n t i a l core region, a t x/d = 0 and r / d = 0. Table 2 gives t h e r e s u l t s w i t h the probe coordinates a l i g n e d w i t h f a c i l i t y coordinates, as Case 1 o f Fig. 1 illustrates. This i s r e f e r r e d t o as S i t u a t i o n A Case 1 w i t h analogous statements l a t e r . The timemean v e l o c i t i e s , nondimensionalized w i t h t h e j e t exit velocity deduced from an independent measurement, are shown. I n t h i s one-dimensional
f l o w f i e l d t h e a x i a l v e l o c i t y i s expected t o be u n i t y w i t h t h e o t h e r two components o f t h e v e l o c i t y v e c t o r t o be equal t o zero. Results using each o f the s i x p o s s i b l e combinations o f t h r e e adjacent w i r e o r i e n t a t i o n s a r e presented, together w i t h the mean o f t h e values. The standard d e v i a t i o n and i t s r a t i o w i t h t h e mean a r e a l s o presented t o show t h e amount of s c a t t e r i n t h e readings. As can be seen, t h e e r r o r f o r t h e a x i a l and s w i r l v e l o c i t i e s are very low f o r each combination. The r a d i a l v e l o c i t y e r r o r tends t o be l a r g e r , p o s s i b l y because o f s l i g h t probe misalignment w i t h t h e normal t o t h e j e t axis. The mean o f these q u a n t i t i e s b r i n g s t h e data t o w e l l w i t h i n acceptable l i m i t s . Results o f the probe being r o t a t e d by 45 deg. about t h e z - a x i s (as i n Case 2 w i t h e = -45 deg.) This i s S i t u a t i o n A Case 2. a r e shown i n Table 3. The probe c o o r d i n a t e system i s now d i f f e r e n t from the j e t c o o r d i n a t e system b u t t h e measured velocities can be related to the facility coordinates by use o f t h e r o t a t i o n a l matrices given i n Section 4. The values given i n Table 3 and indeed a l l t h e Tables are presented i n terms of t h e The r e s u l t s show t h a t f a c i 1it y coordinate system. t h i s misalignment o f t h e probe w i t h t h e dominant f l o w d i r e c t i o n s t i l l gives e x c e l l e n t values o f v e l o c i t i e s i n t h e l a b o r a t o r y coordinate system w i t h the use o f any o f the s i x possible wire combinations. Consequently, averaging o f the data a l s o gives good r e s u l t s . R o t a t i o n about the z-axis by -90 deg. t o o b t a i n Case 4 r e s u l t s i n no data being generated by t h e technique. This i s because i n a steady onedimensional f l o w f i e l d a1 1 the instantaneous cool ing v e l o c i t i e s a c t i n g on t h e hot-wire are equal for a l l o f the 6 r o t a t i o n s . As t h e data a n a l y s i s r e q u i r e s t h a t t h e i r c o o l i n g v e l o c i t i e s be subtracted from each o t h e r (see Ref. 3) a l l t h e output terms are deduced as zero. To f u r t h e r i n v e s t i g a t e t h e s h i f t i n g of t h e dominant f l o w d i r e c t i o n , the probe was r o t a t e d t w i c e (-45 deg. about i t s z-axis, followed by -45 deg. about i t s new x-axis) so as t o conform t o Case 3. The r e s u l t s of these a x i s r o t a t i o n s can be seen i n Table 4. Again the l a b o r a t o r y coordinate deduced values and d e v i a t i o n s from expected values are r e l a t i v e l y low, although n o t q u i t e as good as i n t h e previous case. The advantages o f averaging can be seen i n Table 4, where t h e under- and/or overestimation o f the velocities f o r the individual p o s i t i o n s are smoothed o u t a f t e r averaging. R o t a t i o n s o f e = -90 deg. and + = -90 deg. were a l s o c a r r i e d out a t t h e same f l o w d o c a t i o n , so o b t a i n i n g Case 5. Table 5 shows t h e r e s u l t s o f these r o t a t i o n s . Good a x i a l and t a n g e n t i a l v e l o c i t y values can be seen b u t w i t h a decrease i n t h e accuracy o f the r a d i a l v e l o c i t y . 5.3
Turbulent Nonswirling J e t
S i m i l a r r o t a t i o n s o f t h e probe about i t s axes have been performed on t h e shear l a y e r o f a f r e e n o n s w i r l i n g axisymmetric j e t a t two a x i a l l o c a t i o n s , x/d = 3 and 10, r e f e r r e d t o as S i t u a t i o n s B and C. A t these p o i n t s i n t h e f l o w t h e a x i a l v e l o c i t y dominates w i t h a small c o n t r i b u t i o n from t h e r a d i a l velocity. I n axisymmetric j e t s i t i s well-known t h a t t h e a x i a l d i r e c t i o n a l turbulence l j p e n s i t y i s l a r g e r than i t s other two components. The o n l y s i g n i f i c a n t shear s t r e s s i n t h i s f l o w f i e l d i s t h e
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rx-shear. Tables 6 and 7, obtained w i t h Case 1 probe c o n f i g u r a t i o n i n S i t u a t i o n s B and C y c o n f i r m this. I n c i d e n t l y , a l l t h e data presented i n t h i s paper are a consequence o f a t y p i c a l set o f readings If a large obtained f r o m the h o t - w i r e technique. amount o f s c a t t e r i s found i n deduced r e s u l t s a t a particular location, the problem is further i n v e s t i g a t e d and/or remeasured b e f o r e e i n g accepted as v a l i d . Data r e p o r t e d elsewhereh3.4 has been thoroughly analyzed and checked f o r r e p e a t a b i l i t y . Tables 6 and 7 a r e used as a standard f o r n o n s w i r l i n g f l o w f i e l d values a t l o c a t i o n s B and C y so as t o be able t o compare t h e r e s u l t s obtained from o t h e r probe c o n f i g u r a t i o n cases. However, t h e r a d i a l time-mean v e l o c i t y appears t o be very l a r g e f o r t h i s p a r t i c u l a r f l o w f i e l d and c o u l d p o s s i b l e be i n error. The c o e f f i c i e n t o f v a r i a t i o n ( a / x ) i s seen t o be acceptable f o r most o f t h e f l o w p r o p e r t i e s except f o r t h e shear stresses. These l a r g e v a r i a t i o n s are caused by t h e shear stresses being two orders o f magnitudes lower than the time-mean velocities. Sometimes the data r e d u c t i o n w i l l n o t resolve a p a r t i c u l a r parameter. This i s u s u a l l y t h e consequence of subtracting two almost equal e f f e c t i v e c o o l i n g v e l o c i t i e s as described e a r l i e r . If a l a r g e p r o p o r t i o n o f the data i s n o t resolved from the different combinations of cooling v e l o c i t i e s used, t h e parameter deduced i s taken t o be zero. Results f o r probe c o n f i g u r a t i o n s o f Cases 2 and 4 f o r l o c a t i o n B are given i n Tables 8 and 9, corresponding data f o r l o c a t i o n C are given i n Tables 10 and 11. It can be seen, from Tables 9 and 11, t h a t the Case 4 r e s u l t s g i v e poor estimates o f t h e time-mean r a d i a l and s w i r l v e l o c i t i e s and underestimates o f t h e a x i a l components o f t h e v e l o c i t y vector. This i s expected because t h e timemean v e l o c i t y vector i s almost p a r a l l e l t o t h e h o t w i r e support axis, and r o t a t i n g t h e probe through i t s s i x o r i e n t a t i o n s y i e l d s l i t t l e e f f e c t on t h e sensed data. This a l s o decreases values o f t h e axial turbulence intensity but significantly increases t h e other two normal s t r e s s components. Acceptable values o f the a x i a l normal s t r e s s are 0 = -45 deg. (Case 2 probe obtained via c o n f i g u r a t i o n ) but again t h e t a n g e n t i a l and r a d i a l turbulence i n t e n s i t i e s a r e increased; however, n o t Shear as s i g n i f i c a n t l y as i n t h e previous Case 4. s t r e s s values f o r both Case 2 and 4 are found t o be very poor w i t h l a r g e c o e f f i c i e n t s o f v a r i a t i o n . Also, many o f t h e turbulence q u a n t i t i e s are n o t resolved. I t would appear from these r e s u l t s t h a t t h e s i x - o r i e n t a t i o n hot-wire technique i s a poor t o o l t o use i f the flow i s d o m i n a n t l y i n t h e d i r e c t i o n o f the If this probe support, f o r reasons j u s t described. occurs, simply r e c o n f i g u r i n g t h e probe h o l d e r vs f l o w d i r e c t i o n can overcome t h e problem.
Tables 12 throuqh 15 correspond t o t h e l a s t f o u r tables, b u t now probe c o n f i g u r a t i o n s o f Cases 3 and 5 are used a t l o c a t i o n s B (Tables 12 and 1 3 ) and C (Tables 14 and 15). Now the time-mean v e l o c i t y components are seen t o be i n excel l e n t agreement w i t h t h e values determined from t h e standard The a x i a l normal s t r e s s c o n f i g u r a t i o n o f Case 1. tends t o be underestimated a t x/d = 3 and overestimated a t x/d = 10, r e l a t i v e t o t h e Case 1 calculations. The r a d i a l turbulence i n t e n s i t y i s consistently overestimated for both compound c o n f i g u r a t i o n s and both a x i a l l o c a t i o n s . This c o u l d
i n f e r a f a i l i n g o f the h o t - w i r e technique. The t a n g e n t i a l t u r b u l e n c e i n t e n s i t y measurements are found t o p r o v i d e acceptable r e s u l t s . The dominant shear s t r e s s ( t h e rx-component) i n t h i s f l o w i s found measured very w e l l i n t h e c o n f i g u r a t i o n s o f Cases 3 and 5, r e l a t i v e t o Case 1 values. The coefficient of variation is not too large considering t h e magnitude o f the numbers involved. The f i n a l components o f the Reynolds s t r e s s tensor, although appearing t o be measurable, e x h i b i t a great deal o f s c a t t e r , perhaps i n d i c a t i n g t h a t these values are c l o s e t o zero. 5.4
Turbulent S w i r l i n g J e t
Two f r e e s w i r l i n g j e t s were considered f o r f u r t h e r assessment o f the h o t - w i r e technique. The a i r f l o w e x i t i n g from an axisymmetric nozzle o f a wind tunnel passes through a vane s w i r l e r w i t h 10 a d j u s t a b l e f l a t blades. The t e s t f a c i l i t y and timemean performance t h e s w i r l e r are described a t l e n g t h elsewhere. For t h e present study, t h e subsequent 1arge chamber confinement was removed and t h e f r e e j e t f l o w alone was studied, w i t h s w i r l vane angles o f 45 and 70 deg. being used. Figure 3 gives the s p e c i f i c measurement l o c a t i o n s D and E used f o r measuring t h e 45 and 70 deg. s w i r l s i t u a t i o n s , r e s p e c t i v e l y . These l o c a t i o n s are i n t h e high shear region o f t h e f l o w close t o t h e s w i r l e r e x i t . They were chosen since i t was expected t h a t a l l s i x components of the stress tensor would be s i g n i f i c a n t , thereby p r o v i d i n g a good t e s t o f the technique f o r t h e i r measurement. The hot-wire was a l s o placed w e l l away from the edge o f t h e r e c i r c u l a t i o n zone, so as t o avoid any instantaneous f l o w reversal on t h e wire. Rotations o f the probe axes have been performed conforming t o Cases 4 and 5 only, f o r both o f the s w i r l strengths.
ly
The standard s i x - o r i e n t a t i o n technique i n t h e c o n f i g u r a t i o n o f Case 1 produces the p r o p e r t i e s o f both s w i r l i n g j e t s as given i n Tables 16 and 17. As can be seen a l l components o f the time-mean f l o w and the Reynolds s t r e s s tensor are evaluated. The two sets o f r e s u l t s are n o t q u i t e a t the same f l o w f i e l d l o c a t i o n because o f t h e change i n s i z e and shape o f the recirculation zone as swirl strength increases. However, t h e increase i n the t u r b u l e n t p r o p e r t i e s o f the f l o w are c l e a r l y evident. Rotation about t h e z-axis by -90 deg. t o Case 4 probe c o n f i g u r a t i o n causes a d e t e r i o r a t i o n i n t h e accuracy o f t h e r e s u l t s obtained from t h e technique, as i n s p e c t i o n o f Tables 18 and 19 f o r 45 and 70 deg., r e s p e c t i v e l y , shows. The a x i a l and s w i r l time-mean v e l o c i t i e s are s t i l l f a i r l y accurate f o r both flows b u t t h e r a d i a l v e l o c i t y has suffered a l a r g e increase ( o r decrease), relative t o i t s The normal stresses measurement w i t h Case 1. deduced a f t e r t h e r o t a t i o n appear t o be reasonable except f o r t h e r a d i a l and s w i r l components i n t h e These two s t r o n g s w i r l f l o w o f S i t u a t i o n E. components a r e g r e a t l y overestimated w i t h a g r e a t It i s again f e l t deal o f s c a t t e r i n t h e r e s u l t s . t h a t these poor r e s u l t s a r e because o f t h e technique's i n a b i l i t y t o measure a c c u r a t e l y f l o w p r o p e r t i e s when t h e dominant f l o w d i r e c t i o n i s i n t h e d i r e c t i o n o f t h e probe holder. That i s , when a l a r g e v e l o c i t y i s approximately normal t o t h e w i r e i n each o f the s i x measuring o r i e n t a t i o n s , insensitivity results as already discussed earlier. Correspondingly, t h e shear stresses a l s o show a r e d u c t i o n i n accuracy, w i t h a l l t h r e e components e i t h e r over- o r u n d e r - p r e d i c t i n g t h e Case
119
very w e l l w i t h those o f Ref. 7 and hence o f Refs. 3 through 5; t h e i r measurements o f the t h r e e normal
1 values. The r e s u l t s o f the compound angle o f Case 5 are presented i n Tables 20 and 21, r e s p e c t i v e l y , f o r t h e 45 and 70 deg. s w i r l cases. The a x i a l time-mean v e l o c i t y i s seen t o be good when compared t o t h e standard case, b u t t h e o t h e r two components show a r e d u c t i o n i n accuracy i n these h i g h l y t u r b u l e n t flowfields. The inaccuracy o f t h e r a d i a l v e l o c i t y has been discussed e a r l i e r . The t h r e e components o f t h e turbulence i n t e n s i t y appear t o be f a i r l y good w i t h reasonable values deduced compared t o t h e Again however, t h e r a d i a l standard Case 1 values. and t a n g e n t i a l component are l e s s than d e s i r a b l e f o r t h e s t r o n g l y s w i r l i n g f l o w f i e l d . The shear stresses f o r the 45 deg. s w i r h i t u a t i o n D a r e considered gocd except f o r t h e u'w' term. T h i s component i s s u b j e c t t o great inaccuracies f o r o n l y s l i g h t e r r o r s i n t h i s i n p u t data, as described e a r l i e r i n Section 5.1. For t h e s t r o n g l y s w i r l i n g f l o w ( S i t u a t i o n E ) t h e measured stresses are n o t so good when compared As these w i t h t h e standard Case 1 measurements. t a b l e s i n d i c a t e , t h e time-mean v e l o c i t i e s and normal stresses are subject t o e r r o r which i s magnified i n t h e determination o f t h e shear stresses. 5.5
Assessment o f the Technique
General r e s u l t s o f t h e present and previous s t u d i e s are now assessed i n connection w i t h t h e appl i c a b i 1it y , accuracy and d i r e c t i o n a l s e n s i t i v i t y o f the six-orientation s i n g l e normal h o t - w i r e technique. Previously, i n h i s m asurements o f s t r o n g l y s w i r l i n g vortex flows, King' compared h i s time-mean velocity and normal s t r e s s measurements w i t h corresponding measurements obtained using a Laser Doppler Velocimeter. He found e x c e l l e n t agreement i n d i c a t i n g the v a l i d i t y o f t h e method. He was not a b l e t o compare shear s t r e s s measurements i n h i s s w i r l flow, however, because he was unable t o use h i s LDV f o r t h i s purpose. I n f a c t , d e s p i t e the existence o f advanced m u l t i c o l o r LDV systems, and t h e i r use f o r shear s t r e s s measurement, no one has yet r e p o r t e d them in highly swirling flow situations: c e r t a i n l y not over a range o f s w i r l s t r e n g t h s as r e p o r t e d i n Ref. 5. The present aothors have a1 ready compared t h e i r six-orientation measurements with previouslyavailable data whenever possible. I n the n o n s w i r l i n g confined j e t case, r e s u l t s f o r time-mean v e l o c i t i e s u and v,&rmal stresses ulrms and vlrmS and shear s t r e s s u'v'compare very f a v o r a b l e ( s Ref. 3, Figs. 7 and 8) w i t h those o f Chaturvedi. He used a crossed-wire probe f o r t h e shear s t r e s s measurements. So also d i d McKillop15 f o r n o n s w i r l i n g confined f l o w i n t h e same f a c i l i t y as t h e present author^.^ Results, w i t h and w i t h o u t e x i t nozzles, a r e i n good agreement f o r t h e above q u a n t i t i e s , also, see Ref. 15, Figs. 21 through 28.
Pfi
I n t h e s w i r l i n g c o n f i l t d j e t case, comparison w i t h Janjua and McLaughlin f o r a moderate s w i r l strength i n an identical facility has been possible. They made triple-wi re hot-wire measurements i n a f l o w with an i n l e t s w i r l vane using a n a l o g - t o - d i g i t a l s i g n a l angle 9 = 38 deg., conversion and computer data reduction. For t h i s purpose, i t was necessary t o know i n advance t h e l o c a l time-mean vel0 ' t y v e c t o r d i r e c t i o n ; t h e data of Yoon and L i l l e y y was used f o r t h i s purpose. T h e i r measurements of time-mean v e l o c i t y compare
120
Fig. 5.
Measurement f o r S i t u a t i o n A w i t h D i f f e r e n t Probe C o n f i g u r a t i o n Cases
Reynolds stresses and t h e t h r e e shear Reynolds stresses a r e compared a t x/D = 0.5, 1.0 and 1.5 w i t h t h e s i x - o r i e n t a t i o n s i n g l e - w i r e measurements o f Ref. 5. There i s e x c e l l e n t agreement (see Ref. 16, Figs. 10 through 18), i n d i c a t i n g again t h e v a l i d i t y o f t h e present measurement technique. I t appears t o be an extremely v i a b l e , cost-effective technique f o r t u r b u l e n t f l o w s o f unknown dominant d i r e c t i o n . Probe i n t e r f e r e n c e appears n o t t o be a major prediction problem. Results are u s e f u l i n s t u d i e s f o r confined s w i r l i n g flows.
rfpyh
For t h e present study, Figs. 5 through 9 summarize measured values f o r the f i v e s i t u a t i o n s A through E, respectively. Each f i g u r e presents f a c i l i t y c o o r d i n a t e time-mean v e l o c i t y , norrial and shear s t r e s s values obtained w i t h each o f the f i v e probe h o l d e r vs f a c i l i t y c o n f i g u r a t i o n p o s s i b i l i t i e s A remarkable observation i s o f Cases 1 througn 5. t h a t , i n general, the c o n f i g u r a t i o n i s o f l i t t l e importance, r e s u l t s appearing q u i t e constant across the f i v e cases. On t h e o t h e r hand, production run In have used t h e Case 1 c o n f i g u r a t i o n e x c l u s i v e l y . those r e s u l t s , generally, ensemble average of deduced r e s u l t s from each o f t h e s i x p o s s i b l e combinations o f t h r e e adjacent w i r e o r i e n t a t i o n s has been used. T h i s was because o f lack o f l o c a l flow i f t h i s knowledge i s d i r e c t i o n a l knowledge a v a i l a b l e i t i s expected8 t h a t t h e combination w i t h minimum c o o l i n g v e l o c i t y i n the c e n t r a l of the t h r e e w i r e o r i e n t a t i o n s used w i l l produce more accurate estimates o f deduced f l o w q u a n t i t i e s . From r e s u l t s o f t h e present study f o r S i t u a t i o n s A through E, Table 22 confirms t h i s , e s p e c i a l l y f o r time-mean values. I n any case, t h e a p p r o p r i a t e choice o f w i r e o r i e n t a t i o n f o r minimum c o o l i n g v e l o c i t y i s n o t known a p r i o r i . The values given i n the t a b l e could o n l y be determined a f t e r t h e measurement. However, for turbulence q u a n t i t i e s and i n the 45 and 70 deg. s i t u a t i o n s , more confidence may be placed i n t h e average o f a l l p o s s i b l e w i r e combinations. This smoothinf-5 has been used e x c l u s i v e l y i n recent studies.
-
6.
Conclusions
The accuracy and d i r e c t i o n a l s e n s i t i v i t y o f t h e six-orientation hot-wire technique has been performed i n axisymmetric and s w i r l i n g free j e t s . V a r i a t i o n o f i n p u t parameters and t h e r e e f f e c t on t h e output data has shown t h a t t h e l e a s t accurate output q u a n t i t i e s a r e t h e shear stresses, in p a r t i c u l a r t h e x0 -component.
O
F
Q
f 0.0
CASE1
Fig. 6.
2
c
8
'
$2
5: 81
3
Measurements f o r S i t u a t i o n 6 with D i f f e r e n t Probe Configuration Cases
Fig. 7. Measurements f o r S i t u a t i o n C w i t h D i f f e r e n t Probe Configuration Cases
The d i r e c t i o n a l s e n s i t i v i t y analysis has shown that the technique adequately measures the p r o p e r t i e s o f a f l o w f i e l d independent of t h e dominant flow d i r e c t i o n except when t h e flow i s predominately i n the d i r e c t i o n of the probe holder, w i t h t h e s i x - o r i e n t a t i o n s o f t h e probe c r e a t i n g i n s i g n i f i c a n t changes i n hot-wire response. The analysis shows t h a t t h i s component o f time-mean velocity i s inadequately deduced. Only r e c o n f i g u r a t i n g o f the probe can overcome t h i s problem a posteriori
.
5.
and L i l l e y , D. G., "Single-Wire Jackson, T. W., S w i r l F1 ow Turbulence Measurements , I ' Paper AIAA-83-1202 , Seattle, Washington , June 27-29, 1983.
6.
Dvorak, K., and Syred, N. , "The S t a t i s t i c a l Analysis of Hot Wire Anemometer Signals i n DISA Conference, Complex F l o w f i e l ds", U n i v e r s i t y o f Leicester, 1972.
7.
Syred, N., Beer, J. M. and Chigier, N. A., "Turbulence Measurements in Swirling R e c i r c u l a t i n g Flows." Proc. Salford Symp. on I n t e r n a l Flows, Inst. o f Mech. Engineers, London, 1971, pp. 627-636.
8.
King, C. F., "Some Studies o f Vortex Devices Vortex A m p l i f i e r Performance 6ehaviour", Ph.D. Thesis, U n i v e r s i t y College o f Wales, C a r d i f f , Wales, 1978.
9.
Perry, A. E. , "Hot-wire Anemometry", Oxford, England, 1982.
Acknowledgments The authors wish t o extend there g r a t i t u d e t o NASA Lewis Research Center and the A i r Force Wright Aeronautical Laboratories f o r t h e i r support under Grant No. NAG 3-74, t e c h n i c a l monitor O r . J. D. Holdeman. Thanks are a l s o given t o Lawrence H. Ong f o r assistance w i t h the experiments. References
1.
Janjua, S. I., "Turbulence Measurements i n a Complex F l o w f i e l d Using a Six-Orientation HotWire Probe Technique." M.S. Thesis, Oklahoma S t a t e U n i v e r s i t y , S t i l l w a t e r , OK., Dec. 1981.
2.
Jackson, T. W. , "Turbulence C h a r a c t e r i s t i c s o f S w i r l i n g Flowf i e l ds. " Ph.D. Thesis, Oklahoma S t a t e University, S t i l l w a t e r , OK., Dec. 1983.
3.
4.
Janjua, S. I., McLaughlin, D. K., Jackson, T. W., and L i l l e y , D. G., "Turbulence Measurements i n a Confined J e t Using a Six-Orientation HotWire Probe Technique", Paper AIAA-82-1262, Cleveland, Ohio, June 21-23, 1982. Janjua, S. I.,McLaughlin, D. K., Jackson, T. W. and L i l l e y , 0. G. , "Turbulence Measurements i n Confined Jets Using a R o t a t i n g Single-Wire A I A A Journal, 1984 ( i n Probe Technique." press).
-
Clarendon,
10.
Jorgensen, F. E. , " D i r e c t i o n a l S e n s i t i v i t y o f Wire and F i b e r F i l m Probes", D I S A Information No. 11, F r a n k l i n Lakes, NJ, May 1971, pp. 31-37.
11.
Yuan, S. W., "Foundations o f F l u i d Mechanics", Prentice-Hall , Englewood C l i f f s , NJ, 1967.
12.
Corrsin, S. and Uberoi, M. S., "Spectrums and Diffusion i n a Round Turbulent Jet", NACA Report No. 1040, 1949.
13.
Sander, G. F., and L i l l e y , D. G., "The Performance o f an Annular Vane Swirler", Paper AIAA-83-1326, Seattle, Wash. , June 27-29, 1983.
14.
Chaturvedi , M. C. , "Characteristics of Axi symmetri c Expansions", Proceedings , Journal o f the Hydraulics Division, ASCE, Vol. 89, No. HY3, 1963, pp. 61-92.
121
0.0
-
~1 0.0301-
Fig. 9. Measurements f o r S i t u a t i o n E w i t h D i f f e r e n t Probe Configuration Cas-:>
Fig. 8. Measurements f o r S i t u a t i o n D w i t h D i f f e r e n t Probe Configuration Cases 15.
McKillop, B. E., "Turbulence Measurements i n CI Complex F l o w f i e l d Using a Crossed Hot-wire", M.S. Thesis, Oklahoma State University, S t i l l w a t e r , OK., J u l y 1983.
16.
Janjua, S. I., and McLaughlin, D. K., "Turbulence Measurements i n a S w i r l i n g Confined J e t F l o w f i e l d Using a T r i p l e Hot-wire Probe", Report DT-8178-02 from Dynamics Technoloqy t o NASA Lewis Research Center, Nov. 1982.
17.
Yoon, H. K., and L i l l e y , D. G., "Five-Hole P i t o t Probe Time-Mean V e l o c i t y Measurements i n Confined S w i r l ing F1ows", Paper AIAA-83-0315, Reno, Nev., Jan. 10-13, 1983.
Table 2.
A I
Q
19.
lbujelala, M. T., and L i l l e y , D. G., " C o n f i i a f S w i r l i n g Flow Predictions,18 Paper AIAA-83-0316, Reno, Nevada, Jan. 10-13, 1983.
19.
M. T., and Lilley, D. G., Abujelala, " L i m i t a t i o n s and Empirical Extensions o f t h e k Model as Applied t o Turbulent S w i r l i n g Flows." Paper AIAA-84-0441, Reno, Nevada, Jan. 9-12, 1984.
20.
and L i l l e y , Abujelala, PI. T., Jackson, T. W., 0. G., "Turbulence Parameter V a r i a t i o n i n Confined S w i r l i n g F1ows,Ii Paper f o r 29th I n t . Gas Turbine Conference, Amsterdam, June 4-7, !954.
Measurements f o r S i t u a t i o n A Case 1
Measurements f o r S i t u a t i o n A Case 2
Table 3.
Ccnibination Used
Eeasured uluo
vluo
Corbinatim
wluo
Used
U l uo
lkdsured VI11
____ 612
0.978
0.203
0.009
61 2
W I 1l0 -.
__
0.97~
0.051
0.035
123
0.961
0.i99
123
0.972
0.036
0.046
234
0.970
0.126
0.020
234
0.990
0.056
0.015
345
0.968
MR"
0.013
345
0.982
0.043
0
456
0.976
0.011
0,008
456
0.989
0.024
0.049
561
0.967
0.193
0.017
561
0.986
0.022
0.041
0.970
0.147
0.013
Mean
X
0.983
3.021
0.c33
S.D. G
0.006
0.012
0.017
G fi
0.006
0.55'3
0.353
Mean i;
NR
S.D. a
0.006
0.074
0.005
0 6
0.006
0.503
0.353
* Not
Resolved
122
.an
Table 4.
Conibifiation Urd
Measured viuo
u/uo
Coeibi n3 t ion Used
W/Uo
_._____612
0.554
-0.030
-0.008
123
0.954
-0.031
-0.008
234
0.967
-0.039
-C.Ojl
345
0.948
-0.103
0.080
4 56
0.971
n.ooi
-0.003
561
0.951
-0.030
0.006
X
0.958
-0.039
0.001
S.O. 0
0.008
0.031
0.039
Man
0.805
0.009
a/:
Measurements for Situation A Case 5
Table 5.
Measurements for Situation A Case 3
liParuV.c.6
u/uo
\'/ 11
W/Y
612
0.97~5
0.203
0.010
123
0.960
0.700
NE
2 34
0.971
0.126
0.019
365
0.96U
112
0.013
456
0.976
0.0:0
0.OUC
561
0.968
0.1s:.
0.017
Mean
X
0.960
0.147
0.013
S.O.
0
0.005
0.014
0.004
G.006
0.503
0.311
38.986 O/Y
Table 6.
Cowbi n a t i o n
Measurements f o r S i t u a t i o n
B
Neasured v;ms/uo
Case 1
u'v'lu;
m/u:
w/u;
Used
U/G0
v/uo
w/uo
6i2
0.593
0.211
0.036
0.171
0.062
0.066
0.0101
0.0019
NR
123
0.577
0.195
0.056
0.142
0.035
0.099
0.0020
0.0010
0.0037
2 34
0.582
0.220
0.012
0.142
0.091
0.136
0.0001
0.0029
NR
345
0.587
0.110
0.019
0.125
0.209
0.126
0.0001
0.0000
NR
556
0.616
NR
0.014
0.156
0.027
0.148
NR
NR
0.0221
561
0.602
0.207
0.042
0.157
0.079
0.056
0.0031
0.0000
NR
u;;ns/uo
WL&/UO
Mean
iT
0.593
0.189
0.030
0.149
0.084
0.105
0.0031
0.0012
0.0129
S.O.
a
0.013
0.040
0.016
0.014
0.060
0.035
0.0037
0.0011
0.0092
0.022
0.212
0.537
0.098
0.718
0.330
1.1910
0.9350
0.7130
oJ;
Table 7.
Measurencnts for S i t u a t i o n C
Case 1
612
0.433
0.158
0.009
0.147
0.052
0.059
0.0077
0.0011
Nn
123
0.464
0.153
0.026
0.128
0.067
0.051
0.0022
NR
NR
23:
0.477
0.093
0.026
0.127
0.066
0.119
NR
NR
0.0057
345
NR
456
0.460
0.167
0.034
0.123
0.070
0.118
0.0032
NR
0.001 5
561
0.449
0.151
NR
0.124
0.056
0.070
0.0016
NR
NR
0.0011
yean;
S.D. 01:
P
0.456
0.145
0.023
0.13
0.062
0.083
0.0038
0.015
0.C26
0.009
0.009
0.007
0.029
0.0024
0
0.0021
0.032
0.182
0.396
0.068
0.112
0.353
0.6468
0
0.5833
123
0.0037
Table 8.
Combination Used
Eledured w'ms/uo
ul"o
vluo
WIUo
61 2
0.552
0.039
0.043
0.133
0.133
123
0.554
0.066
0.033
0.168
0.168
234
0.520
-0.055
0.162
0.147
0.149
345
:iR
KR
0.124
0.21i
0.217
456
0.527
-3.033
0.081
0.137
0.142
5bl
0.576
0.033
0.112
0.155
Hem?
0.545
0.010
0.032
5.3.
0.023
G.046
O.OS5
I:
0.037
4.600
0.493
0
Tabl? 9.
u',.&o
uluo
612
0.537
123
0.607
234
0.501
345
__
u"lu,2
0.174
-0.0215
-0.0339
0.0039
0.125
0.0126
0.0011
-0.0011
0.156
-0.0053
KR
NR
0.300
0.0972
Nil
Ha
0.164
0.0205
RR
liR
0.155
0.103
-0.0001
KR
hR
0.159
0.161
C.170
C.0163
-0.0014
0.0014
0.028
0.027
0.C63
0.0365
O.C0?5
0.0C25
0.177
0.170
0.369
2.2371
1.7875
7.7375
Measurements for Situation
B
Measured v&uo w;m;/uo
u;msluo
0.342
0.197
0.G97
0.179
0.289
0.157
0.236
0.140
0.270
0.123
0.379
0.023
0.071
0.245
0.190
0.594
0.119
0.326
0.129
456
0.484
0.065
0.408
561
0.568
NR
NR
T I U ,
Case 4
w/uo
VlU0
2
U'V'IU:
V'rms/Uo
CorSlnatlon Used
Case 2
ledwresents for Situation 8
m/u;
m/u;
0.0032
0.0003
1:R
NR
0.0031
0.0234
N2
0.0031
hR
0.0053
0.0008
0.314
0.079
NR
N4
0.422
0.126
tiR
0.0428
0.117
0.281
0.289
NR
Nil
I
NR 0.0:07
tieac
?
0.549
0.212
0.238
0.111
0.285
0.184
0.0332
0.0109
O.cIO83
S.U.
a
0.045
0.125
0.130
0.024
0.074
0.082
0
0.0160
0.C107
0.083
0.589
0.546
0.221
0.259
0.446
0
1.4700
1.2864
a/?
__________
__
-__.
Table 10. Measurements f o r Situation f
___
Case 2
6: 2
0.46
0.052
0.007
0.049
0.099
0.:53
0.2350
3.5312
r~.icos
123
3.447
0.076
0.050
0.123
0.123
C.CS6
!I9
c.0030
'+a
235
O.fi50
5.084
0.016
3.124
0.124
0,:l;
3.1?1;5
345
3.458
-0.W4
0.004
C.iO5
0.105
0.132
C.C??C
456
0.443
0.095
O.Oi7
0.13
0.150
0.132
0.0?.10
561
0.428
0.100
iiR
0.136
0.135
C.CBS
C.J::0
Fean
6.445
0.C66
0.0!0
O.li9
0.!15
C.iZ1
S.2. G
O.OC3
J.057
O.Gl6
0.013
3.013
G.G23
:x
0.G2C
0.561
0.%2
0.111
0.111
0.163
3.2861
-_
-
--
124
:;a 0.C32j KR
Ra N;I
A?
O.OC16
O.OC?5
5.3160
3.G313
C.0212
5.CO6?
0.0008
0.5512
0.6421
!.SCC3
Case 4
Table 11. Weasurements for Situation C
u/uo
612
0.300
0.471
0.085
NR
NR
0.347
0.0262
hR
123
0.260
0.073
0.191
0.049
0.285
0.210
IR
h'R
NR
234
0.382
0.124
RR
0.109
0.237
0.225
NR
NR
0.0236
345
0.354
0.244
0.135
0.080
0.185
0.214
0.0036
0.0053
NR
0.181
NR
0.0161
NR
0.248
NR
NR
NR
G.380
456
v/uo
u;ms/uo
w/uo
0.105
0.191
0.227
ou/,v
Measured
u'v'lug
ConSi nation Used
0.216
w&/u,
W / U f
m u g 0.0779
56 1
0.289
NR
0.279
NR
0.337
nean 5(
0.343
0.228
0.176
0.098
0.252
0.237
0.0149
O.C!07
0.0507
0.053
0.0113
0.0054
0.0271
0.223
0.7584
0.53.27
0.5355
S.O.
a
a/;
0.037
0.137
0.065
0.011
0.053
O.lG7
0.602
0.368
0.113
0.210
Table 12. Heasurenents for Situation 8 Comoi "ation
LkeG
LlU0
--
vluo
Noaswed U~r*s/Uo v~m5130 W'rms/uo
w:u
Case 3
u'v-luo2
;T;;'/" 2
-
612
0.548
0.053
-0.022
0.069
C.112
0.:18
-0.C015
-0.0261
123
0.575
0.0?6
-0.006
0.120
0.089
C.038
-0.0564
0.0342
234
0.559
0.022
-0.024
0.099
0.116
0.lgl
-0.OC24
-0.OiES
-0.0058
-0.0272 -0.0073
345
0.559
0.937
0.000
9.142
0.139
0.1C6
-0.0533
-0.0060
-0,0033
45s
0.547
0.025
-0.319
0.118
0.159
0.162
3.0181
4.0428
0.0181
561
0.547
0.063
-0.034
0.135
0.125
0.136
0.0112
0.OOr-4
C.0112
xe!ean si
0.556
0.056
-0.013
3.117
0.123
0.128
0.0031
5.3.
C.010
0.020
0.011
0.0186
0.023
0.023
0.0100
G.G?43
0.0145
o.o:a
0.429
0.665
0.159
0.188
0.183
2.9016
2.7612
6.030
C
ZIT
Table 13. Neasurenents for Situation 8 ComSi 6a tion Used
uluo
v/uo
WlU,
u;ms/uo
Mea:ured v;msluo
Case ou/,w
-0.0~1
-0.oc2s
j
m1u:
w1u;
m/";
612
0.656
0.211
0.015
0.170
0.069
0.060
NR
0.0103
NR
123
0.579
0.188
0.043
0.161
0.114
0.031'
0.0017
0.0021
0.0051
234
0.587
0.141
0.221
0.163
0.157
0.101
0.0080
NR
NR
345
0.504
0.354
0.012
0.164
0.154
0.133
RR
NR
WR
456
0.590
0.130
0.053
0.148
0.137
0.120
0.0008
NI:
NR
56 1
0.583
0.205
0.065
0.147
0.066
0.047
NR
0.0040
0.0019
0.082
0.0035
0.0054
0.0035
Mean; s.0.
01:
(f
0.583
0.205
0.035
0.159
0.116
0.044
0.073
0.020
0.008
0.037
0.038
0.0032
0.0035
0.0016
0.076
0.357
0.573
0.053
0.320
0.465
0.9143
3.6490
0.4571
125
Table 14. Measu;ecie?ts
f o r Sitbation C
Conbi na ti on J/U0
v/uo
61 2
0.467
0.043
-0.057
Jsed
w/uo
Neasured w'rms/uo
u'rm/uo
V*r!ps/Uo
0.073
0.090
0.C92
Case 3
_uwu;
U"/u;
v.r./uo2
-0.0130
-0.0146
-0.0008
123
0.45:
0.066
-0.063
0.100
0,074
0.075
0.0010
0.0256
-0.0002
234
0.456
0.055
-0.063
0.065
0.106
0.108
-0.0011
0.0199
-0.0029
345
0.446
-0.017
0.002
0.111
0.380
0.114
0.009$
-3.0523
0.0068
456
0.434
0.046
-0.141
0.118
0.115
c . 1 ~
o.ma
0.0013
0.021 1
561
o.4ia
0.097
-0.141
0.100
0.101
0.105
0.0143
-0.0032
0.0120
Wean
0.445
0.948
-0.060
0.09s
0.094
0.102
0.0049
0.0044
C.0063
S.2. G
0.158
5.034
0.042
0.015
0.014
0.015
0.0106
0.0139
C .LO25
0.C35
0.713
0.707
0.154
0.153
0.i45
2.1632
3.:641
1.3516
SIX
Table 15. Neasurements for Situation C
?leasured
Comb1 r,a t 1on u/uo
L'seC
Case 5
v/uo
w/uo
NR
612
0.417
0.162
0.142
0.062
0.047
0.0044
c.036a
123
0.454
0.013
0.152
0.156
0.069
0.061
NR
0.0025
o.ooii
NR
2 34
0.473
0.024
0.075
0.154
0.147
0.032
NR
NR
0.0083
345
NR
456
0.453
0.064
0.176
0.141
0.131
0.041
0.00;l
0.0038
0.0039
56:
0.431
0.014
0.168
0.141
0.038
0.054
0.0023
0.0324
N9
x
0.446
0.029
0.147
0.147
0.089
0.047
0.0036
0.0038
0.0644
S.D. a
0.019
0.021
0.037
0.037
0.042
0.010
0.0009
O.GO18
0.003
a/;
0.344
0.717
0.249
0.046
0.473
0.214
0.2608
0.4676
0.6735
Mean
Table 15. Xea,urfnents
0.136
0 Zi73
0.2074
O.CO56
0.03E
O.CC65
G.Cl20
0.0079
0 138
0.142
Nil
0.G018
0.0127
0.136
0.1;s
hi7
O.CC53
:,;
0.1-S
3.CS75
0.??5
:iR
0.1C3
:-G:3
C CC45
0.C366
0.149
0.123
0.0053
0.0057
o.ooaz
C.JPC
C.CO4
0.019
0.0313
0.3035
0.0927
0.213
0.225
0.1553
0.1983
0.6131
0.721
V,hG
612
1.66;
0.633
1.6:6
0.C77
0.142
i23
3.753
5.217
1.72-
3.i27
0.14E
2 3$
'.e08
0.355
1.550
0.129
3:s
1.773
0.457
1.597
0.170
455
1.726
0.223
1.552
3.142
3.18;
56 i
'.E?
0.565
1.659
0.1:3
3
Nsan JI
1.i;g
o 565
1.613
O.;i4
5.3.
0.0'15
0.022
0.055
0.029
0.035
3.335
-
01s;
J
1
uI*.. ,uo 2
nea su red
"'n;,s/uo
u/uu
w!?io
Cqse
-.U'"'!.; 2
Coxbination
vsec
for Situation D
--
V*rms/"o
3 1
126
W'wrl.Jo
VWb02
Table 17. Measurenents for Situation E
Combination
Case 1
-
Measured
2
USEd
-
612
0.708
0.522
0.424
0.218
0.303
0.341
0.0623
0.0057
123
0.562
0.590
0.419
0.420
0.322
0.252
0.0298
0.0108
0.0691
234
0.752
0.269
0.338
0.4S7
0.129
0.433
NR
o.oozo
c.3m
345
0.563
0.482
0.373
0.591
0.121
0.649
0.3900
NR
0.0475
456
0.628
0.323
0.478
0.463
0.135
0.525
0.0384
0.0411
NR
561
0.533
0.563
0.383
0.443
0.304
0.332
NR
0.0881
0.0462
x
0.62$
0.458
0.403
0.437
0.219
0.422
0.0424
0.0295
0.0362
5.0. u
0.081
0.120
0.044
0.112
0.091
0.133
0.01207
0.0324
0.0141
ci/Y
0.130
0.263
0.110
0.256
0.451
0.315
0.2846
1.0975
0.3903
Mean
Table 1R. Neasurenents for Situation D
0.0422
---
cHse 4
_- ___
Combination
Measured v*rmsluo W'm,sluo
Used
u/uo
v/uo
w/uo
61 2
1.640
0.336
1.556
C.126
0.112
0.lGO
L~'n,s/Uo
m/uo2
U.k'iL02
m j u2
0.0053
O.XE.7
NR
123
1.641
0.747
1.523
0.122
0.098
0.1!4
?IR
0.0002
0.0033
2 34
1.680
0.806
1.439
0.141
0.171
0.096
0.0024
0.0028
0.0043
345
1.774
0.209
1.394
0.107
G.179
0.183
0.0045
It7
0.0323
456
1.Si2
i.C26
1.532
0.097
0.167
6.155
O.GUl8
NR
0.0315
561
1.639
0.856
1.654
0.130
0.114
0.132
0.0044
NH
0.0109
man j ;
1.641
0.833
1.525
0.121
0.140
0.133
0.0037
0.0032
O.OC44
S.O.
0.089
0.051
0.078
0.015
0.033
0.03
OS014
0.0027
0.0033
0.059
0.107
0.051
0.120
0.234
0.226
0.3E90
0.8348
0.7578
a
Olh
I _
--
Table 19. F!easurements for Situation E
Combi na :ion
61 2
0.320
0,347
123
0.698
0.556
C.157
234
0.442
0.156
315
F~R
456
0.43
561
0.723
S.D. a/?
G
Case 4
Heasured
Used
&an
-
rm 0.476 Nil
NR
EIR
0.856
0.370
0.196
0.647
!Ut
0.642
NR
NU
0.435
NR
NR
NR
0 .ow2
NR
0.563
0.008i)
0.0192
0.0060 NR
0.637
0.0421
0.0309
0.914
NR
NR
NR
0.694
O.E.94
0.0313
#H
0.0458 C.03:6
NR
0.289
0.375
0.41M
0.613
NR
NR
3.521
0.394
0.362
0.373
0.561
0.704
0.0271
0.0440
0.157
0.163
0.182
0.002
0.230
0.108
0.0142
0.0273
0.0167
0.322
0.414
0.476
0.007
0.410
0.1%
0.5251
0.6197
0.0582
--
127
0.02e8
Table 20. Measurements for Situation 0
Case 5
612
1.777
0.452
1.445
0.128
0.155
0.158
0.0133
NS
123
1.744
0.491
1.428
c.186
0.183
0.174
0.0004
NR
0.0186
234
1.703
0.310
1.603
0.196
0.202
0.178
3.0031
hR
0.0179 0.0215
0.c133
3 45
!.a52
0.362
1.388
0 . i ~
0.183
0.184
NR
0.COOS
436
1.853
0.350
1.387
0.124
0.113
0.184
0.0103
0.0009
0.0314
561
1.886
0.491
1.433
0.090
0.110
0.198
Nil
NR
0.0124
rean x
1.802
0.409
1.417
0.142
0.158
0.186
o.me
0.0907
0.0142
S.S. J
0.066
0.072
0.073
0.037
0.035
0.033
0.0052
0.0003
0.0365
01;
0.336
0.175
0.050
0.026
0.224
0.492
0.7682
3.3571
0.4571
Table 21. Neasurements f o r Situation E
Case 5
-
Combination Used
2
Measured
-
2
61 2
0.757
NR
0.547
0.318
0.447
0.316
0.0195
0.0103
0.0275
123
0.552
Na
0.613
0.624
0.338
0.356
0.0342
KR
0.0831
234
0.740
0.103
0.245
0.645
0.610
NR
0.0143
0.0386
NR
345
0.734
0.251
0.336
0.573
G.564
0.165
0.0460
NR
0.0170
456
0.435
0.225
0.695
0.546
0.363
0.319
0.0147
0.3300
NR
561
0.424
0.31
0.613
0.496
3.177
0.346
0.0175
hR
0.0284
! 1) a blockage shortens the CTRZ. 5.
Conclusions
The corner recirculation zone is prominent i n nonswi rl i ng expanding fl ows, b u t i t decreases when
181
0
x/D
I
2
u/u,
w/u, (b)
0
I
I$
= 45'
x/D
2
u/u,
w/u, (c) Fig. 5.
(I =
70"
Velocity Profi 1 es for Flows with Expansion Ratio D/d = 1.5, Expansion Angle a = 90" and Small B1 ockage
182
0 r/ry50 0.25 UO
x/D
I I
3 L
I
1
\
~ 0
0.5
1
0
x/D
1
2
u/uo
w/u, (b)
0
4
=
45"
2
I
u/uo
w/u, ( c ) 4 = 70"
Fig. 6 .
Velocity P r o f i l e s f o r Flow with Expansion Ratio D/d = 1.0 and Small Blockage
183
0
x/D
I
2
u/u, (a) 4 = 0"
0
x/D
I
2
u/u,
( b ) 4 = 45'
0
x/D
I
2
u/u,
w/u, (c)
4 = 70"
Fig. 7. Velocity Profiles for Flow with Expansion Ratio D/d CL = 9 0' and Large Blockage
184
=
1.5, Expansion Angle
W/U, ( b ) I$ = 45”
0
I
2
u/u,
w/u, ( c ) $.= 70”
Fig. 8.
Velocity P r o f i l e s for Flow w i t h Expansion Ratio D/d = 1.0 and Blockage
185
6. Nozaki , T. , and Hatta, Keiji , "Reattachment
swirl is introduced and disappears when centrifugal forces predominate. The presence of swirl results in the formation of a central recirculation zone. Initially, increases in d result in an increase in is length, but increasing d to very high swirl strengths results in a shortening and widening o f this zone.
Flow Issuing From a Finite Width Nozzle (Report 3: Effects of Inclinations of Reattachment Wall ) , Bu 1 1etin of the JSEM, Volume 25, No. 200, February 1982. 'I
7. Rhode, D. L., "Predictions and Measurements o f
Isothermal Flowfields in Axisymmetric Combustor Geometries, Ph. D. Thesis, Oklahoma State University, Stillwater, Okla., Dec. 1981.
Placing a blockage in the flowfield creates an adverse pressure gradient near the wall and a favorable pressure gradient near the center1ine. This results in increased axial and swirl velocities near the centerline and decreased velocities near the wall. The Blockage also decreases the central recirculation zone length, except for strong swirl flows with no expansion (that is, D/d = 1). The degree of the effect increases as the degree of blockage increases.
'I
8. Rhode, D. L.,
Lilley, D. G., and McLaughlin, D. K., "On the Prediction of Swirling Flowfields Found in Axisymmetric Combustor Geometries," ASME Journal of Fluids Engng., Vol. 104, 1982, pp. 378-384.
9. Rhode, D. L., Lilley, D. G., and McLaughlin,
Reduction of the expansion ratio results in a reduction of the size of the central recirculation zone, as is apparent when the present data are compared previous studies. This central zone vanishes for moderate swirl in a nonexpanding flow. Also, placing a blockage in a nonexpanding, strongly swirling flow increases the narrow central recirculation zone length; an opposite effect is observed for expanding (that is, D/d > 1) flows. The corner recirculation zone length (measured in step heights) does not change with expansion ratio for D/d > 1.
D. K., "Mean Flowfields in Axisymmetric Combustor Geometries with Swirl Paper AIAA-82-0177, Orlando, Florida, Jan. 11-14, ,'I
1982.
H. K., "Five-Hole Pitot Probe Time-Mean Velocity Measurements in Confined Swirling Flows," M.S. Thesis Oklahoma State University, Stillwater, Okla., July 1982.
10.
Yoon,
11.
Yoon, H. K., and Lilley, D. G., 'Five-Hole Pitot Probe Time-Mean Velocity Measurements in Confined Swirling Flows," Paper AIAA-830315, Reno, Nevada, January 10-13, 1983.
Changing the inlet from sudden to gradual expansion has a minimal effect on the flow.
12. Moon,
L. F., and Rudinger, "Velocity Distribution in an Abruptly Expanding Circular Duct," Journal of Fluids Engineering, March 1977, pp. 226-230.
Acknowledgments
The authors wish to gratefully acknowledge NASA Lewis Research Center and Air Force Wright Aeronautical Laboratories for financial support under Grant No. NAG 3-74, technical monitor Dr. J. D. Holdeman. Special thanks are offered to Dr. M. T. Abujelala for assistance with the data reduction and graphics. References
13. Janjua, S. I., "Turbulence Measurements in a
Complex Flowfield Using a Six-Orientation Hot-wire Technique," M.S. Thesis Oklahoma State University, Stillwater, Okla., Dec. 1981. 14.
1. Abujelala, M. T. and Lilley, D. G., "Confined Swirling Flow Predictions," Paper AIAA-830316, Reno, Nevada, January 10-13, 1983. 2. Ha Minh, H. and Chassaing, P., "Perturbations
Chaturvedi, M. C. "Flow Characteristics of Axisymmetric Expansions," Proceeding, Journal of Hydraulics Division, ASCE, Vol. 89, NO. HY3, 1963, pp. 61-92.
15. Mathur, M.
L., and MacCallum, N. R. L., "Swirling Air Jets Issuing from Vane Swirlers. Part 1: Free Jets; Part 2:. Enclosed Jets," Journal o f the Institute of Fuel, Vol. 40, May, 1967, pp. 238-245.
of Turbulent Pipe Flow," Proceedings, Symposium on Turbulent Shear Flows, Pennsylvania State University, April 1977, pp. 13.9-13.17.
16. Syred, N., and Dahman, K. R., "Effect of High 3.
Bradshaw, P. and Wong, F. Y. F., "Reattachment of a Confined Turbulent Diffusion Flame Burner," Journal of Fluid Mechanics, Volume 52, Pt. 1, 1972, pp. 113-135.
4.
Hutchinson, P., Khalil, E. E., and Whitelaw, J. H., "Measurement and Calculation o f Furnace-Flow Properties," Journal of Energy, Volume 1, July-August 1977, pp.
Levels of Confinement Upon the Aerodynamics of Swirl Burners," Journal of Energy, Vol. 2, No. 1, Jan. - Feb. 1978, pp. 8-15. 17. Afrosimova, V. N., "Study of the Aerodynamics
of a Furnace Space," Thermal Engineering, Vol. 14, Part 1, 1967, pp. 10-15. 18. Yang, B. T., and Yu, M. H., "The Flowfield in
211-219.
E. D., and Hung, Tin-Kan, 'Computational and Experimental Study of a Captive Annular Eddy," Journal of Fluid Mechanics, Vol. 28, Pt. 1, 1967, pp. 43-64.
a Suddenly Enlarged Combustion Chamber," AIAA Journal, Vol. 21, No. 1, Jan. 1983,
5. Macagno,
pp. 92-97. 19. Owen, F. K. , "Laser Velocimeter Measurements
186
of a Confined Turbulent Diffusion Flame Burner," Paper AIAA-76-33,, Washington, 0. C., Jan. 26-28, 1976.
20.
Sander, 6. F., "Axial Vane-Type Swirler Performance Characteristics," M.S. Thesis, Oklahoma State University, Stillwater, Okla., July 1983.
21.
Abbott, D. E., and Kline, S. J., "Experimental Investigation of Subsonic Turbulent Flow Over Single and Double Backward Facing Steps," Journal of Basic Engineering, Sept. 1962, pp. 317-325.
22.
Bird, J. D., "Visualization of a, Flowfield by Tuft Grid Technique," /Journal of Aeronautical Science, Vol. /19, 1952, pp. 481-485.
23.
Back, L. H. and Roschke, E. J., "Shear Layer Flow Regimes and Wave Instabilities and Reattachment Lengths Downstream of an Abrupt Circular Channel Expansion," Journal of Applied Mechanics, Transactions ASME, Vol. 94E, Sept. 1972, pp. 677-81.
24.
Runchal, A. K., "Mass Transfer Investigation in Turbulent Flow Downstream of Sudden Enlargement of a Circular Pipe for Very High Schmidt Numbers," Journal of Heat Transfer, Transactions of ASME, Vol, 88C, Feb. 1966, pp. 131-136.
25.
Scharrer, G. L., "Swirl, Expansion Ratio and BlocNage Effects on Confined Turbulent Flow, M.S. Thesis, Oklahoma State University, Stillwater, Okla., May 1984.
1
T., "Comprehensive Design of 26. Morel, Axisymmetric Wind Tunnel Contractions," Paper ASME 75-FE-17, Minneapolis, Minn., May 5-7, 1975. Gudta, A. K., Lilley, D. 6. and Syred, N., "Swirl Abacus Press, Tunbridge Wells, England, 1984. "A kKillop, 8. E., and Lilley, D. G., Variable Vane Angle Swirler," Report, Oklahoma State University, Stillwater, Okla., July, 1982.
29.
Sander, G. F., and Lilley, D. G., "The Performance of an Annular Vane Swirler," Paper AIAA 83-1326, Seattle, Wash., June 27-29, 1983.
30.
Sinder, M. M., and Harsha, P. T., "Assessment of Turbulence Models for Scramjet Flowfields", NASA CR 3643, 1982.
187
1. Report No.
3. Recipient's Catalog No.
2. Government Accession No.
NASA CR-3864 5. Report Date
February 1985 6. Performing Organization Code
8. Performing Organization Report No.
None 0. Work Unit No.
1. Contract or Grant No.
NAG3-74 3. Type of Report and Period Covered
Contractor Report'
112. Sponsoring Agency Name and Address
National Aeronautics and Space Administration Washington, D.C. 20546
4. Sponsoring Agency Code
533-04-1A
( E- 2374)
15. Supplementary Notes
Final re ort. Project Mana er, J.D. Holdeman Internal Fluid Mechanics Division, NASA Lewis Research Center Eleveland, Ohio 441!!5. (Work partially funded by Ramjet Technology Branch, AFWAL.) Append;x A - On the Prediction of Swirlin Flowfields Found in Axisymmetric Combustor Geometries by D.L. Rhode, D.G. Lilley, and D.K. McLaughYin; Appendix B - Mean Flowfields in Axisymmetric Combustor Geometries With Swirl by D.L. Rhode, D.G. Lilley, and D.K. McLaughlin; Appendix C - Turbulence Measurements in a Confined Jet Using a Six-Orientation Hot-wire Probe Technique by S.I. Janjua, D.K. McLaughlin, T.W. Jackson, and D.G. Lilley; Appendix D Five-Hole Pitot Probe Time-Mean Velocity Measurements in Confined Swirling Flows by H.K. Yoon and D.G. Lilley; Appendix E - Confined Swirling Flow Predictions by M.T. Abujelala and D.G. Lilley; Appendix F Single-Wire Swirl Flow Turbulence Measurements by T.W. Jackson and D.G. Lilley; Appendix G - The Performance of an Annular Vane Swirler by G.F. Sander and D.G. Lilley; Appendix H Accuracy and Directional Sensitivity of the Single-Wire Technique by T.W. Jackson and D.G. Lilley; Appendix I - Limitations and Empirical Extensions of the k-E Model as Applied to Turbulent Confined Swirling Flows by M.T. Abujelala and D.G. Lilley; Appendix J - Swirl Flow Turbulence Modeling by M.T. Abujelala, T.W. Jackson, and D.G. Lilley; Appendix K Swirl, Confinement and Nozzle Effects on Confined Turbulent Flow by M.T. Abujelala and D.G. Lilley; Appendix L - Turbulence Measurements in a Complex Flowfield Using a Crossed Hot-wire by B.E. McKillop and 0.6. Lilley; Appendix M ,Five-Hole Pitot Probe Measurements of Swirl, Confinement and Nozzle Effects on Confined Turbulent Flow by G.L. Scharrer and D.G. Lilley.
-
-
-
-
-
16. Abstract
This is-the Final Report on Grant NAG3-74 and discussion is on those activities undertaken during the entire course of research from July 1, 1980 to June 30, 1984. Studies were concerned wlth experimental and theortetical research on 2-D axisymmetric geometries under low speed nonreacting, turbulent, swirling flow conditions typical of gas turbine and ramjet combustion chambers. They included recirculation zone characterization, time-mean and turbulence simulation in swirling recirculating flow, sudden and gradual expansion flowfields, and further complexities and parameter influences. The study included the investigation of: a complete range o f swirl strengths; swirler performance; downstream contraction nozzle sizes and locations; expansion ratios; and inlet side-wall angles. Their individual and combined effects on the test section flowfield were observed, measured and characterized. Experimental methods included flow visualization (with smoke and neutrallybuoyant helium-filled soap bubbles), five-hole pitot probe time-mean velocity field measurements, and single-, double-, and triple-wire hot-wire anemometry measurements of time-mean velocities, normal and shear Reynolds stresses. Computational methods included development of the STARPIC code from the primitive-variable TEACH computer code, and its use in flowfield prediction and turbulence model development. 17. Key Words (Suggested by Author(s))
18. Distribution Statement
Combustor; Swirl; Turbulent flow; Hot wire measurements; Axisymmetric; Pitot probe measurements 19. Security Classif. (of this report)
Uncl ass ified
Unclassified - Unlimited STAR Category 07
20. Security Classif. (of this page)
Uncl assi fied
21. No. of pages
191
For sale by the National Technical Information Service, Springfield, Virginia 221 61
22. Price
A09 NASA-Langley, 1985
