for all Mach numbers. Eigenvalue. Stiffness. Problem. ⢠Pressure rescaled so that all eigenvalues have tile same order of mag- nitude. Physical acoustic waves.
N94-1 549 (b
A COUPLED TURBULENT
IMPLICIT
SPRAY
SOLUTION
COMBUSTION
K.-H. The
METHOD
IN
FOR
PROPULSION
SYSTEMS
CHEN
University
of Toledo,
Ohio
and J.-S. Sverdrup
SHUEN
Technology,
Aerothermochemistry Internal NASA
Lewis
Fluid Research
Inc.,
Ohio
Branch
Mechanics
Division
Center,
Cleveland,
Ohio
OBJECTIVES
• Develop chemically low
Mach
• Calculate bine
an efficient reacting number turbulent
combustor.
and flows
robust at all
algorithm speeds,
for multi-phase with
emphasis
flow
in
on
flows. spray
combustion
a gas
tur-
MOTIVATION
Many
reacting
modern
flows
in propulsion
compressible rocket
motor
velocity gas
--
at closed
turbine
variation
wide end
cannot
algorithms,
range
--
of Mach
numbers, at nozzle
low subsonic
incompressible
be efficiently
from
velocity,
compressible to low-speed
desirable.
OUTLINES
EQUATIONS
Gas-Phase
-
Liquid-Phase
Equations Equations
• NUMERICAL
ALGORITHM
• NUMERICAL
TEST
RESULTS
• CONCLUSION • FUTURE
PLAN
FOR
near
zero
but
large
density
approach.
progress made in high-speed Extending application range
-
by
exit.
reacting flow codes based on TEACH-type lack of robustness for complex flows.
• GOVERNING
calculated
e.g.,
to supersonic
combustor precludes
Most low-speed inefficient and
Tremendous two decades.
flow CFD
devices
ALLSPD
CODE
technologies
flow CFD in past flow regime highly
-
GOVERNING
• Gas-Phase
Equations
o_
o_
o(_,- _.)
o(P- P_) = i_° + R,,
(1)
u
1/_ .//3 _/_
o p o
o o p
000 000 000
.... .... ....
h
h/fl-1
pu
pv
p
....
_/_ _/_ Y_/_ Y2/_
o o o o
o o o o
pg ?2
K y6 C
q=7
EQUATIONS
r
._
Y_
00 p
0
0 p
YN-I/fl
o
o
•
"
"
p
0 3
rI¢'-
tt),
if
Time
(ti)
u_I
L_ < r]_'-
u_l
where Lc - C3.14tz312/ e
t,=LU(2_/3) '/_. tt = --rln[1 • Spray
Time
step
- AT.p_
At.p.
=
a mln
-
LU(,Id'-
a_l)]
(t_, tl, Is, tg, ti)
(ts)
INTERACTION
1. Initialize 2.
Solve
3.
Evaluate
4.
Solve
gas
BETWEEN
and
liquid
liquid-phase
TWO
phase
PHASES
variables.
equations.
spray
source
gas-phase
term,
equations
Hr. and
update
gas-phase
variables. 5. Update
spray
No,
to step
Yes,
go go
source
to step
2.
TEST
Backward-Facing
• Evaporating
Turbulent
• Gas
Spray
Turbine
HI ?
4.
NUMERICAL
• Turbulent
term,
RESULTS
Step Spray
Combustion
Flow
Flow. Flow.
- non-reacting.
PARTICI.E
TRACES
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