in the early stage of this project. ... 1and 2, used an accelerating, rectangular 90 ° elbow as the geometric .... first step in this investigation ..... 800. 1000. 1200. 1400. 1600. 1800. 2000. Iterations. Figure 5._Convergence history. ..... p0 (lbf/in2).
NASA/TMw2001-211219
A Three-Dimensional Secondary Richard Glenn
Flow
CFD Investigation in an Accelerating,
H. Cavicchi Research
National
Center,
Aeronautics
Space
Administration
Glenn
Research
December
Center
2001
Cleveland,
and
Ohio
of
90 ° Elbow
Acknowledgments
The author
gratefully
acknowledges
access
to the wisdom
in consultation
Available NASA Center 7121 Standard Hanover,
for Aerospace Drive
Information
of Dr. John
in the early
stage
W. Slater
of NASA
Glenn
Research
Center
of this project.
from National
Technical
Information
Service
5285 Port Royal Road Springfield, VA 22100
MD 21076
Available
electronically
at http://gltrs.gTc.nasa.gov/GLTRS
A THREE-DIMENSIONAL FLOW
CFD
INVESTIGATION
IN AN ACCELERATING,
Richard
OF
SECONDARY
90 ° ELBOW
H. Cavicchi
National Aeronautics and Space Administration Glenn Research Center Cleveland, Ohio 44135
SUMMARY NASA Glenn Research Center has recently applied the WIND National Code flow solver to an accelerating elbow with a 90 ° bend to reveal aspects of secondary flow. This elbow was designed by NACA in the early 1950's such that flow separation would be avoided. Experimental testing was also done at that time. The current threedimensional CFD investigation shows that separation has indeed been avoided. Using its three-dimensional capability, this investigation provides various viewpoints in several planes that display the inception, development, and final location of a passage vortex. Its shape first becomes discernible as a vortex near the exit of the bend. This rendition of the exit passage vortex compares well with that found in the experiments. The viewpoints show that the passage vortex settles on the suction surface at the exit about one-third of the distance between the plane wall and midspan. Furthermore, it projects into the mainstream to about one-third of the channel width. Of several turbulence models used in this investigation, the Spalart Alimaras, Baldwin Lomax, and SST (Shear Stress Transport) models were by far the most successful
in matching
the experiments.
INTRODUCTION A classic investigation
of secondary
flow, both theoretical
and experimental,
was made at the National
Advi-
sory Committee For Aeronautics (NACA) Lewis Flight Propulsion Laboratory in the early 1950's. This work, reported in references 1 and 2, used an accelerating, rectangular 90 ° elbow as the geometric configuration. The project began with the design of the elbow by the so-called "inverse method." In this mode of design, velocity distributions along the initially unspecified boundaries are prescribed, following which analysis is used to determine the boundary shapes. The more common "direct method" prescribes the shapes of the boundaries, and then uses analysis to determine the velocity distributions. Reference 1 describes the analysis it used in the following way. In the inverse method, the geometry of the channel walls in the X-Y plane is unknown. This fact precludes obtaining a solution in the physical plane, necessitating the use of a new set of coordinates in a transformed plane. The geometric boundaries must be known in the transformed plane. The coordinates in the transformed plane should be orthogonal in the physical plane. Reference ! used the velocity potential phi and stream function psi as coordinates in the transformed plane, and derived a differential equation for the velocity distribution in this plane. Solution of this equation for the velocity distribution yielded the distribution of the flow direction. Finally, the flow direction distribution yielded the distribution of the channel walls in the physical X-Y plane. The differential equation was obtained from continuity and from irrotational fluid motion expressed in terms of _ and _. This equation is nonlinear and was solved by relaxation. Hence, the shape of the elbow was obtained from two-dimensional inviscid flow analysis. For the 90 ° elbow designed in reference 1, a velocity distribution was prescribed such that no deceleration occurred along the boundary walls in order to avoid boundary layer separation. This attempt to avoid separation was intended to provide high quality experimental data of the secondary flow mechanism itself. Although the elbow was designed by two-dimensional analysis, the experimental configuration was made as a three-dimensional model with decreasing rectangular cross sections to yield exit velocity twice the inlet value. The current effort is a three-dimensional computational fluid dynamic investigation using the WIND flow solver applied to the 90 ° elbow designed in reference 1. A complete description of WIND is presented in reference 3. This CFD study investigated the development of secondary flow from several viewpoints made available by threedimensional analysis. These viewpoints are presented in selected planes to show the inception and buildup of
NASA/TMI2001-211219
1
secondary flowthatculminate in the documents a test case, but extends have investigated.
formation of a passage vortex. In this way, the current CFD study not only the insight of the secondary flow problem that the experiments of reference 2
Thus, this report provides a further validation of the WIND code. Validation using other configurations has been achieved, and is presented on the World Wide Web. The site in reference 4 presents several CFD cases in complete detail that are compared with experimental data. Calculations were made herein for subsonic flow entering the elbow, and using the Spalart Allmaras one-equation turbulence model. For comparison, WIND was also run for this elbow using several other turbulence models in its capability. This investigation used the following post processing tools: CFPOST (described in ref. 3), PLOTC (described in ref. 5), and PLOT3D (described in ref. 6).
CONFIGURATION Although the original design elbow shape and then computes the current CFD study.
of the elbow used the indirect method, the current CFD application starts with the the flow field. The profile shape of example III of reference 1 was chosen for use in
Figure 1, taken from reference 2, presents a line drawing of the test setup and depicts the elbow shape. The XYZ coordinate system is shown in this figure. These coordinates are defined in appendix A. Because of symmetry about the midspan, only one-half of the elbow was modeled and run for this CFD investigation. The external profile side showing the 90 ° bend is referred to herein as the plane wall. The entire set of X-Y coordinates for example III is presented as table II in reference 1. All 1170 of these coordinates were plotted and are shown in the current report in figure 2(a). Table II includes an 18-in. long constant cross section shape downstream extension that also appears in figure 2(a) herein. In addition to prescribing the suction and pressure surface velocity distributions, reference 1 also sets the exit velocity to be twice the inlet value. The prescribed walls is given by equation (35) of reference 1 as Q=0.5
velocity
Q as a function
of arc length
s along the channel
s" 22 21 20 (b) 19
13.00 12.80 12.60 12.40 12.20
0
1
2
3
4
5
6
7
8
9
12.0o
Z (in.) Figure 8.mTotal pressure contours at exit. (a) Unshielded total-pressure after 500 iterations•
NASA/TM--2001-
211219
24
probe from ref. 2. (b) Wind calculations
Pressure
surface
-_.
Vortex roll up Pressure
surface
Cross-channel boundary
layer flow
Calculated potential flow streamlines Suction
(a)
(b)
L inlet
Figure 9.--Smoke experiments from ref. 7. (a) Vortex roll-up at exit of accelerating and passage vortex roll-up in 90°-turning accelerating duct.
NASA/TM--2001-211219
25
surface
duct. (b) Cross-channel
flow
//_
._!ii!_!i_: __--__ ....
'/'i i' I ] / '
I1' '
Index k=35 (plane wall)
'\
'(a) ;
(c) :
(b)
"-_
/
(_f
Contour!evels
|
59000
I
81500
/
63000
_1_88
68B00
_8_88 _a_BB 70500 _t_88 (d)
(e) Figure lO.--Spanwise
NASA/TM--2001-211219
(_ variation of total pressure contours.
26
72000
! __, / i''/ !
[7 _j r
(Midspa_, ConCur
levels
_8_B8
I
59000
vl I
GISflfl 63flflfl
i 60000
70500
_I_BU (h)
(g)
72000
(i) Figure lO._Concluded.
1.0
"E 0
........
0.9
. .
o.
.
.
____
/
0
Q. 0.8
J
j=l j=2
_O
.=
j=5
O.
0.7
-
J = 10 j=15
......
j = 20 j=30 0.6 0
L 1
1 2
I 3
J 4
Spanwise Figure 11 .--Spanwise
NASA/TM--2001-211219
coordinate,
variation
27
; 5
i 6
J 7
I 8
] 9
Z, in.
of total pressure
at exit.
Velocity
0.8
'
potential,
Static pressure
Static pressure ratio at plane wall _-_._ _ _ _ _ -.
_
ratio at midspan
0.8
X
o.z
_.o.z
_: o._
',
_.o._
=_o.s
-- _
_.\_
_,o.s Q.
?" _" 0.4
I
_' 0.4
o._ I
_ o._
0.2
I _
o
Suction
surface
Pressure
0.1 0.0 0
I 15
\
surface
J 30
I 45
Suction ._ 0.1 I 75
NAS A,rI'M--2001-211219
variation
along elbow
¢n 0.0 0
15
profile. (a) Experimental
28
surface
Pressure I
Index I Figure 12._Static pressure calculated results.
"t
0.2
_ "_
i 60
\\ _._
surface
I
_t I
30 45 Index I results from
t
_'%] 60
ref. 2. (b) WIND
75
0.8
0.7
0.6
IL 6
0.5
in 0.4 in
0.3 if)
0.2
0.2:
0.1
0.0 0.4
0.5
0.1
0.0
0.2
0.3
0.4
0.5
Z/W Pressure surface S _anwise static pressure on pressure surface
S )anwise static pressure on suction surface 0.8
0.8
........
x
X
c_ 0.7 J,
-
?. 0.7 ==
-
0.6
D
..........
0.5 °- 0.4 5
-
i = 10
"_ 0.5
-
....
i=40 i = 50 i=60 i=70 i=75
.-.c_0.4 .6= 0.3
-
in 0.2 in
-
0.1 .-_ ¢n 0.0
-
'._
0.3 _El -, _02 in
_ =
-.... ...... °
._, 0.1 oo
_
° , • • .
....................
Figure 13.--_Spanwise static pressure variation. (a) Experimental results from ref. 2. (b) WIND calculated
results.
0.2
I
I
I
0.4
0.5
......
-
0.5
0.1
0.3
--
0.0
I 0.2
I 0.3 Z/W
Z/W
NASA/TM--2001-211219
I 0.1
i=10 i=20 i=40 i= 50 i=60 i=70 i=75
I 0.4
o o
I -"_1
, ..................
29
26
X = 24.500 S
P
in.
po (tbf/in2)
25
15.40 15,20 15,00
24
14.80 14.60
•_. 23
14.40
°-
14.20
>.
14.00
22
13.80 13,60 13.40
211 ......
....... ;:_?-=_U_:-" ..........' ,'il ;' 1,il ,:_@.';__:_ ._:t_\-: "-_ "......../,.,_
1 3.20 1 3.00 12.80
19
............ 0 1
................. !a)i 2
3
4
5
6
7
8
12,60 12.40
9
12.20
Z (in.) 26 .............................................................. _......................................... _................................. P
X = 24.500
in.
pO (Ibl/in2)
iS
15.40
25
15.20 15,00
24
14.80 14.60 14.40
..-. 23
14.20
t'-
14.00 1 3.80
>" 22
13.60 1 3.40
21
13.20 13.00 12.80 12.60
(b) l
12.40 12.20
190
i
2
3
4
5
6
7
8
9
Z (in.) 26 r............ - .........*.....
- ................
_
...... _ ........_ ......
X = 24.500
_"
p0 (lbf/in2) '.Z.ZZALZA..... _I ..:........ .
.. ..............................................................
•
15.40
25!
15.20 15.00
24
14.80 14.60 14.40
A
23
14.20
,r-
14.00
>" 22
1 3.80
/i
1 3.60 13.40 13.20 13.00 12o80 12.60
(c)
i [
190
;
1
i
3
4
5
,
•
6
7
8
12.40 12.20
9
Z (in.) Figure 14.--Rendition (a) Spalart
Alimaras.
of exit passage (b) Baldwin
(d) PDT (RD. Thomas).
NASA/TM--2001-211219
vortex
Lomax.
(e) Laminar.
by several
(c) SST (Shear
(t) Inviscid.
30
turbulence Stress
models.
Transport)
in.
26
.....
'
X = 24.500
in.
S 25
po (Ibf/in2) 15,50 15.30
24
15.10 14.90 14.70 14.50
23
14.30 14,10 13.90 13,70
.c_ >. 22
21 1
13.50 13,30
i 19
IIIIIIIIIlrl
I 0
,II.r................
_-,'- ,-,, (d)
...... 1
2
3
4
5
6
7
8
9
13,10 12.90 12.70 12,50 12.30
Z (in.)
X = 24.500
26 P 25
15.30 15.10 14.90 14.70
24
14.5O 14,30 14.10 13.90
23 c >. 22
_-
13,70 13.50 13,30
21_
20 i 19 _ 0
(e) 1
2
3
4
5
6
7
8
13.10 12.90 12.70 12,50 12.30
9
Z (in,)
.C_ >-
---
__
Jr_.,HI,.,IIU
.................
,
(f)
Z (in.) Figure
NASA/TM--2001-211219
in.
po (Ibf/in2) 15.50
14.mConcluded.
(d)
PDT
(RD.
31
Thomas).
(e) Laminar.
(f) Inviscid.
REPORT Public
reporting
gathering collection Davis
burden
for
and maintaining of information,
Highway,
Suite
this
DOCUMENTATION
collection
of
information
the data needed, including suggestions 1204,
Arlington,
and for
VA
is estimated
completing reducing
22202-4302,
to average
and reviewing this burden, and
1. AGENCY USE ONLY (Leave blank)
to
PAGE
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per
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1 hour
FormApproved
OMB No. 0704-0188
response,
including
of information. Headquarters
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and
Send Services,
Budget, 3.
12. REPORT DATE December 2001
the
time
for
comments Directorate
rewewing
regarding this for information
Paperwork
Reduction
REPORT
TYPE
Project AND
I
CFD
in an Accelerating,
Investigation
(0704-0188),
of Secondary
Washington,
DC
20503
NUMBERS
Flow
90 ° Elbow !4-04-50--4)0
H. Cavicchi 8. PERFORMING ORGANIZATION REPORT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) National John
Aeronautics
H. Glenn
Cleveland,
and Space
Research
Ohio
National
DC
SUPPLEMENTARY
and Space
Administration NASA
Richard
TM--2001-211219
H. Cavicchi,
Available
code
5850,
216---433-5873.
12b. DISTRIBUTION CODE
STATEMENT
02 and
electronically
This publication ABSTRACT
Glenn
to reveal
separation
would
investigation
various
well
that
gov/GLTRS
has recently
of secondary
with
to about
Information,
Baldwin
Lomax,
planes
301-621-0390.
(Shear
also
width. Stress
near
The
done
time.
solver
The
current
show
the plane
that
wall
turbulence models
were
rendition
the passage
and midspan. used
elbow
such
that
three-dimensional
and final
This
models
1950's
capability,
development,
the exit of the bend.
to an accelerating
in the early
its three-dimensional
the inception,
Of several Transport)
flow
by NACA
at that
Using
viewpoints
between
Code
designed
avoided.
that display
of the distance
National
was
was
been
as a vortex
of the channel and SST
elbow
testing
in the experiments.
one-third
one-third
the WIND
This
indeed
discernible
found
about
has
in several
becomes that
applied
flow.
Experimental
separation
viewpoints first
at the exit
Alimaras,
Center
aspects
be avoided.
Its shape
Nonstandard
words)
shows
mainstream
Distribution:
at hno://_ltrs.grc.nasa,
Research
90 ° bend
compares
34
is available from the NASA Center for AeroSpace
(Maximum200
provides
organization
- Unlimited
Categories:
surface
10. SPONSORING/MONITORING AGENCY REPORT NUMBER
20546-0001
person,
Unclassified
vortex.
E-13071
AGENCY NAME(S) AND ADDRESS(ES)
12a. DISTRIBUTION/AVAILABILITY
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Field
NOTES
Responsible
Subject
at Lewis
44135-3191
Aeronautics
Washington,
Administration
Center
9. SPONSORING/MONITORING
13.
sources,
AUTHOR(S)
Richard
11.
data
Memorandum
FUNDING
WU-7 6.
existing
COVERED
Technical
4. TITLE AND SUBTITLE
searching
burden estimate or any other aspect of this Operations and Reports. 1215 Jefferson
DATES
5.
A Three-Dimensional
instructions,
this
location
settles
Furthermore,
CFD of a passage
it projects
successful
vortex
on the suction
in this investigation,
by far the most
a
investigation
of the exit passage
vortex
with
flow
into
the
the Spalart
in matching
the
experiments.
14. SUBJECT TERMS Secondary
17.
SECURITY OF
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CLASSIFICATION
Unclassified NSN 7540-01-280-5500
OF
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REPORT
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