spray combustion modeling with vof and … · spray combustion modeling with vof and finite-rate...
TRANSCRIPT
SPRAY COMBUSTION MODELING WITHVOF AND FINITE-RATE CHEMISTRY
Yen-Sen Chen, Huan-Min Shang and Paul Liaw
Engineering Sciences, Inc., 1900 Golf Road, Suite D, Huntsville, AL 35802and
Ten-See Wang
NASA/Marshall Space Flight Center, ED32, NASA/MSFC, AL 35812
ABSTRACT
A spray atomization and combustion model is developed based on the volume-of-fluid (VOF)
transport equation with finite-rate chemistry model. The gas-liquid interface mass, momentum and
energy conservation laws are modeled by continuum surface force mechanisms. A new solution
method is developed such that the present VOF model can be applied for all-speed range flows.
The objectives of the present study are: (a) to develop and verify the fractional volume-of-fluid
(VOF) cell partitioning approach into a predlctor-corrector algorithm to deal with multiphase (gas-
liquid) free surface flow problems; (b) to implement the developed unified algorithm in a general
purpose computational fluid dynamics (CFD) code, _Finite Difference Navier-Stokes (FDNS), with
droplet dynamics and finite-rate chemistry models; and (c) to demonstrate the effectiveness of the
present approach by simulating benchmark problems of jet breakup/spray atomization and
combustion. Multiphase fluid flows involving free surface fluids can be found in many space
transportation and propulsion systems such as injector atomization in Space Shuttle Main Engine
(SSME) combustors, cavitation in liquid rocket pump operations, handling of cryogenic liquids in
a micro-gravity environment and the operation of cryogenic propellants on board spacecraft.
Modeling these types of flows poses a significant challenge because a required boundary must be
applied to a transient, irregular surface that is discontinuous, and the flow regimes considered can
range from incompressible to high-speed compressible flows. The flow-process modeling is further
complicated by surface tension, interfacial heat and mass transfer, spray formation and turbulence,and their interactions.
The major contribution of the present method is to combine the novel feature of the Volume of
Fluid (VOF) method and the Eulerian/Lagrangian method into a unified algorithm for efficient non-
iterative, time-accurate calculations of multiphase free surface flows valid at all speeds. The
proposed method reformulated the VOF equation to strongly couple two distinct phases (liquid and
gas), and tracks droplets on a Lagrangian frame when spray model is required, using a unified
predlctor-corrector technique to account for the non-linear linkages through the convective
contributions of VOF. The discontinuities within the sharp interface will be modeled as a volume
force to avoid stiffness. Formations of droplets, tracking of droplet dynamics and modeling of the
droplet breakup/evaporation, are handled through the same unified predlctor-corrector procedure.
Thus the new algorithm is non-iterative and is flexible for general geometries with arbitrarily
complex topology in free surfaces. The FDNS finite-difference Navier-Stokes code is employed asthe baseline of the current development.
Benchmark test cases of shear coaxial LOX/H2 liquid jet with atomization/combustion and
impinging jet test cases are investigated in the present work. Preliminary data comparisons show
good qualitative agreement between data and the present analysis. It is indicative from these
results that the present method has great potential to become a general engineering design analysisand diagnostics tool for problems involving spray combustion.
567
https://ntrs.nasa.gov/search.jsp?R=19960029144 2018-07-07T03:02:45+00:00Z
.=.
568
°,,._
U2
re)
0 _ _
_ __zN
m_
o
o
569
Z0B.
0
Z
<
<LT.
E--Z
<
!
E-.1
E-l
©
r_
Z>.
<
r_
r_Z0
<
.l
<Z
r_
Z
Z
Z
Z<
Z
Z<
2
.l<I-
t..)
r_
0
r_;,=1
dZ
0 r.i.1 _-
<
m < Zff - <o N z-- 0< NN N -
< < >_ N .a<
r_
Z
dZ
r_
0
Z©
<
0
0
<
Zr.T.1
ZO
570
0
<
>.
©>Z
Z
©
<
<
©Z©
<
<
ZZ
0
m
"_ Z< _
.1<
<
©r_[-
[-.,Z<
Z<
r..)<
Z, ©
Z-, <
0 :>
Z©
Z ©
o
[-.
0
Z<
-a0>
0
0>
.1
0
.1©>
;..t.1
©Z0
...10r._r-T..l
!I
©
<
Z<
Z0Z0
<
OJ
Z<.a<
Z
©=[-
0>
[-Z<[.-,
©
Z<
<
Z
-.1
0
>.,
[-,
©
<
[-Z
X
©
0[.--
r..T-I..1
<
Z<
Z
kO<
.a
<
Z<
Z<
<,a
dZ,a
©
<
Z
0>
E-
Z©
<N
0E--<>.,<
-1
©
[-
<
I
[-.
Z
Z<
0a:[-
Z0[.-
0
>.,<
<
<.1
Z<
kO©
Z0
©
-a
>
Z<
<
Z0
<
r..T-1
0
>
0
Z<Z
<
Z©[..
0
0
Z
©
<Z<
[-Z
o4
0Z
<
ca
©
¢). ,,,,_
°_,_
571
0
.,e
0
rj
d
O'
[-
0
Z0
<
0 I
Z0
<>
ZQ
Ld
" O _ .1
_. _ o o _..1 _ <
r.v..l _ 0O
< _ _ rOo z
0 r_ <
0 _ 0 r.fi _Z _ _
Z _ _ _ O r_< _ z
_ z _ _
0 r_ ,.
_- <_ Z _ Z_ _ _ _ < <o 0 0
Z0
Z0
<
r.T-I
0
[-r_
<0
<I
<Z0
Z
2:
< _ _- <Z Z
_ Z mZ _ ©
r_ _ 0 <
z _ _
_g
©
e-
572
O
©
[-..,
,.Q
O
©
+
I
-e-
l c'_
Q..
+
O o
O Q
O
©>
573
'!.o=
r._
II
°_
_0
I
-!-
A
A
O
e_
[.-
II
,--t
r_
H
e-,
'El
°,,,_
u_
O9
u_
574
(Di
:
o
©
E
+ -__ <_
<_ <_ <_= > > > _ +
o
f..)
.r-,
575
.o
<
o_
c
_ U
r-
°_
r-
576
Z • • • • •
°_
577
r_
'1::I
I:I._,._
r_
578
I
"0
Z
r_
Z_nq
...... • ,.,.,, n,, i ..i ......
..... ,re.n,. ...ttll ......
.... , ,mltu, , ,_.ml .......
..... nmltn. .111mn ......
• ,,mill, . .1tiffin ......
,,Blh,, ,stm, ......
• ,lllh ..... 11111, .....
• , ilqln ..... *ill, .....
,g_l........ III,
_1, ili
E
II
0m
579
•_ °_° _.....%_k_¢....
u. _ .I
• _,_ .
o o, _ •
• * .m
• °
II
e_
II
.[=
• ,,....I
r_
*m
Z@1,,,,,(
Z
I,i(
@
............. i ..........
, ...... jI_,1.,.i.,_ ,_zz....... , j
• ,d#ll .....J, ], 111_, ...... _ i_ l
• " dll ....... Ib .....A I. ,llz
.... . ,15,
................ i .................
................ i .................
................. i .................
................ i .................
................ i ................
............. i .................
• , • •.. I 111111,
..... . , t flf|_f.,,
:i i'!t:iii
...... ,IIi .....
..._f|Dlltt_., , . .
..-'_|t_, ........
i!li i
580
Jl D*
• ** i* •
", ,,. ;.o ell
.... . ;
_,.-_ '-'_-•
/• •
_e
oe
..''qbq I'',.
_o| _
°* _ "_ °*
* o . •
II
II
.r"
J
Z
kmW
Z
...... _tlllil. .IIINIp,,...
..... , .imlr/, .slflllt,,, ,
...... _ , tmlJi. .slllll_, _ .... . ,
....... *lTfh ,IIIII i .....
...... ' _ l ' ' ) .... ]'111 .........
....... tl,,,t .... _,,|1_.........dll........ IIIIql.,, ]..._. ........
• .d_l, ............
581
• .° _ _111 "D °"'." :" *'. L'"
•._ •- ._.-,, .,_ _ ._""o_ ._.I I_._L %"
..• . _. . _o_ ..
.* ;,s _: *
• -. ,_,.
8
II
II e-,
=
e-.,=,_
=
ga.
r.¢3
Z
i
i ...............
.... i_ ZZ
Z
olmU
0m
582
I
//
\\
• °
°_o b °
_.:.• . ' _ S ° . -
..-....__._.
s.4. i_
0
Im
Z
|
Z
° ,,,,,,i
°,,,_
e..,
583
Q;
I
e_
Z
_Q
Z
I
Z
C,Jr,Jc_lm rr_ m cr)rr)_ cr__QQ
C, _ LFJ_ _ _ C[,-., n n-icd U-j
©
_, _n u-o (oq- Enr - -__
/ / l ',\
# I ",\
/
i
!I
\\
L_WWWWWWWWWW_ m h ,-_LO O] rd _ m CO m
_ _ O] rn CO c,J_ O] r_ UD _t#-,_ C0 LO U-_m c_ _ cxJ_ I£)CO
I _ ._ o_ brlr_ 0")_ "-__ _-__
c'_ _).o _J-_ r_%- Cn_Cz- -,_Y
/
584
I%
\
i
0o
=
0o,=.=
u_
Z©r_
©
<
Z©
E-r_ r_
m Z
o rj
t,,,,,,,q
° ,,,-,n
585
o
II
¢D
ro.¢
iIi ¸
:j__: :i¸. _,, x i11_RMlffr/l t _ ,
• /', x II! t t t ¢.\,
i ,/', ,. t_lllQrttlt r .,\,
• f , x X_l_tlttt r r \ .• [, , ", ItlIVIWI1111 ! z ,\,
,Ix , ,, t_lIVImtllll F • z_.
• "I" " " ",t_tWllttttr / _ "I"
. . -..., ..... ,.',1_: ,, r ..... ._ .
: ::: :_i ::"::::':" .... ;55:.. : : :
: :
e",.r_
.=_.,o,D
ii.,l
586
0
II
Z
rOr._
Z
r,,rar_
r._
co
gl o
xLd
0 'q
O'q
O
0 'q
0 <1
<_$$°<123
L_
r
0
0
q
©,q
0 <1
,q
.q
587
r--4
03
r"4
tD
o,
t'_
al
"D
m
II
co
..121
L._.to
m
c5I/1m
c
u
&
tr
_J
°,,,_u
"r_
0
II
Jl iI
. . *.'* x x x ," . ', _ X ", .
/, /, I .... \ \ \
"1:9
II
I0
k..
__I
,P..t
c_
"Izl6
P2
P2
588
ott_,q.
II
Z4-,
i,i
(D,_1@11
0 <1
I
I_I-
C_O <_
O
O ,_
O <J
0 <_
O <]
0 <1
I I
589
r-4
r-4
m
0
13
II
_34-,_3
v
c-O
4o
23
t4.,,bq
bq_q
r-
t_
4__3
13
e_
°_._
8
r_
o
II
590
II
tO4-'
v
®
L
a)
o_1Q
0"
.J
*_mq
0
II
Z
r_
Z
×I,I
0<]
Q
0 q
Q <]
C_
<%
qO,(1 _ i
0 <q
C' <q
C_
r'Y
L1'-
591
I
-+
m
G
A
CD
"E2
$II
_3+..,
£v
Inc-O
D..£2
k_4..-'
_q
C3
bq_q
r-
(.2
£
_D
e.,
e..,
e-
N
#,1
<
!
Z©[-<
Z ,.a
Z<
Z-- ra.13: =
Z<
uaZo_S
o - _L) r_
_ o za. N _rm _
z N _
< rj _
!
.1
..1<
[..
Z
0
[-
[-Z
[-
0
r._r-T-1Z
0 _
Z
E--
©>..1<C_r/)
<
[.-
O
E-
<r._
>
=:[.-r/)
Z<
;<
k)
3:>.,[-.,,.a
<
<k)
r.j<0
<
592
[...,
Z
r...3Z
,dL)Z
0[-
0
,a.<
r_
©
Z©
<N
0
©.1
>
[-
<>
<
Z
0>
Z<
O
ZOg<N
0
<
0r,,pr._Z
ra.1
[...,Z
e-.
° ,,.,.t
e-.
t.r.li.,.,11.1