A second-order model which predicts the modulation of turbulence in jets laden with uniform size solid particles or liquid droplets is discussed. The approach followed is to start from the separate momentum and continuity equations of each phase and derive two new conservation equations. The first is for the carrier fluid's kinetic energy of turbulence and the second for the dissipation rate of that energy. Closure of the set of transport equations is achieved by modeling the turbulence correlations up to a third order. The coefficients (or constants) appearing in the modeled equations are then evaluated by comparing the predictions with LDA-measurements obtained recently in a turbulent jet laden with 200 microns solid particles. This set of constants is then used to predict the same jet flow but laden with 50 microns solid particles. The agreement with the measurement in this case is very good

Elghobashi, S. E.

Mostafa, A. M.

English

A proposed two equation turbulence model for incompressible dilute two phase flows was validated and extended for steady incompressible two phase flow including phase change. The model was tested for the flow of a turbulent axisymmetric gaseous jet laden with multisize evaporating liquid droplets. Predicted results include distributions of the mean velocity; volume fractions of different phases concentration of the evaporated material in the carrier phase; turbulence intensity and shear stress of the carrier phase; droplet diameter distribution; and the jet spreading rate. Results are analyzed based on a qualitative comparison with the corresponding single phase jet flow

NASA Technical Reports Server

r.... _ 7,°
+
: ,.N84 20533
{
•, EFFECT OF LIQUID DROPLETS ON TURBULENCE
STRUCTURE IN A ROUND GASEOUS JET
Y .A'
A.M. Mostafa and S.E. Elghobashi
Mechanical Engineering Department
: University of California, Irvine
i
Accurate prediction of spray combustion is extremely difficult due to the
complex physical and chemical phenomena encountered in this two-phase process. The
interaction between droplets and the turbulent fluid, turbulence effects on chemical
reaction and heat transfer (and hence on droplet vaporization) are just a few
examples of the complexity. In order to understand the nature of these
interactions, coordinated experimental and theoretical studies need to be performed
in a stepwise manne) thus isolating the phenomenon to be investigated. A turbulent
non-reacting gaseous jet laden with solid particles or evaporating droplets is a
flow which allows the study of the interactions between the two-phases.
The recent experiment of Modarress, et al. (t982, i983), which was performed
in parallel with the present work, provided a much needed data to help understand +
the behavior of two-phase turbulent jets and validate the theoretical models.
Elghobashi and Abou-Arab (1983) reviewed existing turbulence models for two-phase
flows and indicated that these models are based on ad hoc modifications of single-
phase turbulence models. They develoved a two-equation turbulence model for _
incompressible dilute two-phase flows which undergo no phase changes.
In order to validate the proposed model, a turbulent axisymmetrlc gaseous Jet
laden with spherical uniform-size solid particles is studied by Elghobashi, et al.
(1984). The predictions of the mean flow properties of the two-phases and the
turbulence kinetic energy and shear stress of the carrier phase show good agreement
with the experimental data.
67 +
i
1984012457-069
https://ntrs.nasa.gov/search.jsp?R=19840012465 2020-03-22T08:35:53+00:00Z
i-
: Mostafa and Etghobashi (1983) extended the proposed model for steady
incompressible two-phase flow including phase change. This model is tested for the
ftow of a turbulent axisymmetric gaseous jet laden with multisize evaporating liquid
droplets by Mostafa and Elghobashi (1983). To avoid the problem of density
fluctuations oE the carrier phase at this stage, only isothermal flow is considered
and vaporization is assumed to be due to the vapor concentration gradient. The
droplets are classified into finite size-groups. Each group is considered as a
continuous phase interpenetrating and interacting with the carrier phase. Predicted
results include distributions of the mean velocity, volume fractions of the
different phases concentration of the evaporated material in the carrier phase,
turbulence intensiZy and shear stress of the carrier phase, droplet diameter
distribution and the jet spreading rate. The results are analyzed based on a
qualitative comparison with the corresponding single phase jet flow.
Move validation testing of the model is needed via well-defined experiments.
REFERENCES
I- Modarress, D., Wuerer, ,I.,and Elghobashi, S., Ig82, "/u_Experimental Study of
a Turbulent Round 1_ao-Phase Jet," AIAA 2|st Aerospace Sciences Meeting, Reno,
New,de.
2- Modarre._s, D., Tan, H., and Elghobashl, S,, |g83, "Two-Component LDA
Measurement in a Two-Phase Turbulent .let," AIAA 21st Aerospace Sciences
Meeting, Reno, New_da.
3- Elghoba,qhl, S., and Ahou-Arah, T., 1983, "A Two-Equation Turbulence Model for
Two-Phase Flows," Phys. Fluids, 26, g31-93g.
4- El_hobashl, S., Abou-Arah, T., Rizk, M., and Mostafa, A., [984, "Prediction of
the Particle-Laden Jet with a Two-Equation Turbulence Model", Int. J.
Multiphase Flow, in press.
5- Mostafa, A., and Elghobashi, S., 1983, "A Study of the Motion of Vaporizing
Droplets in a Turbulent Flow," Ninth International Colloquim on Dynamics of
Explosions and Reactive Systems. Poitiers, France.
6- Mostafa, A., and ElghobaahI, S., 1983, "Prediction of a Turbulent Round Gaseous
Jet Laden with Vaporizing Droplets " Fail MeetlnR of the Western States
Sect ion/The Combustion Institute.
68
1984012457-070
OUJECT[V(S ORIGINAL PAGE ig
, OF POOR QUALITY
• To predict the flow of a turbulent gaseous jet
laden with iultisize liquid droplets undergoing
vaporization,
• To compare the effects, on the flow field, of
vaporizing droplets vtth those of single phase
jet.
ASSUMPTIONS
1. Droplets in a given stze-rahge constitute •
dispersed phase - thus for k sizes there viii be
(k phases in the flow.
2. Each phase behaves as a continuum
(aacroscopical ly).
3. NO collisiOnS between droplets (dilute spray).
4. Droplets remain spherical as they decrease tn
size.
_. Velocity of vapor leaving droplet surface is
"_ equal to that of the droplet,
6. Concentration gradient tS the on1) driving force
for e_tporat ion,
7. Drag relations of a solid sphere apply tu liquid
: droplets (Internal circulation effects on
friction drag are counterbalanced by evaporation
effects on pressure drag).
69
1984012457-071
ORI_NAL PAGE Ig
OF POOR QUALITY
' _ _
A= Y LLI II V'l
,;. ! 8 d ..
o° --.
-I-
)=-
-, ¢
1984012457-072
ORIGINAL PAGE lY
OF POOR QUALITY _
_ '- ,,,
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- ,_ ,
_" -- '_ _," I
II
1984012457-073
p,
I
ii=F
ORIGINALPAGE IS
i ,,,.-,Lowco...o-,o OF POOR QUALITY [ ......
FLUID * DAOPLIETS I (' _ chsNrud PflOZe
" _. / ,,,,,o,_,,,o [ |
. _-- 0o*'.o0o¢,ys,eJm X I.Gr" VelOcity ( ..... ¢o, lor I_se
] j _.:!._. u_.,,,14L'"_\ ,,o,,,,_.f,°:to_....
, *z _=- _ F--'-" nz,_ \\\\%
_:-_., u.I ,_.d,.,o_,,, u= I \\\" %
_.: %_1.' .-_ 4-/ _ I %% •
2 ..-,ff_!::'_ _ . ur.,=_ I --w_,_\
" " z_• DIIIOPL(T _
•...is,:..:- - ,, ,...,,
' "t- " I"",, ?_ "",':',,,
•-lulrJ : Rir" 0.4L \ \'_,, " "
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r,,*v_ 00_ $" -- _ "_ _ ' "'"'_.:.N,,,,'z'_.:, ,_1[0: _,_,=,l,,,..._14_,% 002 0'04 006 008 Oi 0'12 014
:.._, .'_,.,,_i_ : II/o r._/._ r/z
,-,'nl_ _¢,,_,[_y * =, I Jr_/_l£il Ft| I _z'_a_.Lzed =ean ve].octr. Let and voLzmze fr,tctLom
proll],es at lID - _,0 ;nd a¢ X - 0.5
03 • •
• _ _ I00 ,
U'.a 0 I0 U_'= I 0
%.
" oo o---_ ,/, o_,--- ooo'7- .... dot, ,/, 0'.
Fll ,_ The _ll_uJ_nCe tnten_lly dizltr;._,lxon _ndelr IrL| ) "_'ht _he_r _lr('_l dlzitr_.bulf.o_ _nder di[[_lenl maSl
dtfferent _a.s L_,,_d_nli rar._,os 4t z/D * _0 Lo_dt_| r._zto-, ,_¢ z/O • 20
1984012457-074
,.| OF PC,O;_QJALI__' P
- )
' o
' _.,: _ ,/o • IO uz,o U:,ol .... =i,w_¢'m.e
" C_'_-s ..... z/O • 30 I-0_ *..... cm'rklrPhase
F-_ _,_ _ di.psrsedphOS.
0.8
0.8
0.6
0.7
0.2
0 0 0.0' 0'02 0.04 -do60.OB O.l 0._2 0._4 0.16 0.,:,
Fl_ ;, Nor_'.al_:¢d v_or cnn_vntr4r, ton _r, diffvrrnt
02L ---
O.t[
-I-'_--- _Eo _o ,_o
Ft| 5 The a,,,Lal dttcrt)u¢ton of the =w..tnveloctl:les
,z¢ X -0.5
0
dW
.T
do
tO _%--..-.__.
O" o, ",,., ",. Ic--.,_ C..e,_oc:0 ,-
_° ,o o_ --_/ "oo.__.
_ 60 S '. 0 (6 /
I// "--
04 0_. I / _. -- -- O.S_._' 2
,,, #"
o oo oo :o "" z'o _n
II F t K I _he _t_l ,i_[r_butlon of the drop[ell vo|u=4=
Ftltb The .tu_,a| dL_tftbut_on of _he volume _r_'_on=
,=nd che 4ver=Ke diJ,-v_cers ,it X • 0.5
o %.
13 -_
1984012457-075
i:
,: [_uqz_.l
u,,c ..>>°°°'__ ":_oo ORIGINAl. PAGE IS
O.ZO /_-_ o z_ _-"----
/ 1.0
;' / J//
• ,'7/1/"
°°oo ,b .... :_d _o ,_o--
°°oo ,b :_o _o ,/o 4o
Fig 8 The axial dtsttibution of the m_ximum turbulence
inrensl_y Jnder different mass loadirg ratios rlg 9 The axial distribution of the maximum shear stress
under different mass loading ratios
Ioo
:2
2O
_""------I"IO0
§O - _- - - - z/O. 15
; 40
-30-2_-10 0 IO 20 30"
r (,,'_m_
Fi R I0 Radial distributions of the local droplets diameters at different
,xlul loc_tlos_A Ind at X - 0.5
o
74
1984012457-076
C
YI/2
D
•+ 3o ORIGIN,CLPAG_ |_1
-- /
,; OF PC_OR QUALITY /
'!
..,.++ ,o
i ,, i _00 0 0 t0 20 40
z/D
Fig 11 The spreading rate under different nass loading ratios
SUNN_RY
• The proposed turbulence model (validated
experimentally for solid particles) Is applied to
predict the turbulent round jet laden with
iu|tlslze vaporizing droplets.
• Predicted changes in the flow field (mean and
turbulent quantities) are significant and should
be considered tn liquid spray combustion
calculations.
e _xpertient to validate the proposed model ulll be
•, perforIeo when funds become a_atlable,
75
1984012457-077


Effect of liquid droplets on turbulence structure in a round gaseous jet

EFFECT OF L I Q U I D  DROPLETS ON TURBULENCE 
STRUCTURE I N  A ROUND GASEOUS JET 
S.E. Elghobashi and A.M. Mostafa 
Mechanical Eng ineer ing  Department 
U n i v e r s i t y  o f  C a l i f o r n i a  
I r v i n e  , C a l i f o r n i a  9271 7 
A b s t r a c t  
Experiments 11-51 show t h a t  t h e  a d d i t i o n  of s o l i d  p a r t i c . 2 ~  o r  l i q u i d  d r o p l e t s  
t o  f r e e  t u r b u l e n t  j e t s  modi f i e s  t h e i r  tu rbu lence  s t r u c t u r e .  For example t h e  
t u r b u l e n c e  i n t e n s i t y  and s h e a r  s t r e s s  a r e  reduced due t o  t h e  presence of  t h e  
d i s p e r s e d  phase. Although t h e  n a t u r e  of i n t e r a c t i o n  between t h e  d i s p e r s e d  
phase  and t h e  c a r r i e r  f l u i d  is r a t h e r  complex and no t  we l l  understood a t  p r e s e n t  
161, t h e r e  have been s e v e r a l  a t t e m p t s  t o  p r e d i c t  t h e  behavior  of p a r t i c l e - l a d e n  
t u r b u l e n t  f lows E1,7,81. 
The o b j e c t i v e  of  t h e  p r e s e n t  work is t o  deve lop  and v a l i d a t e  a  second-order 
model which p r e d i c t s  t h e  modulation of  t u r b u l e n c e  i n  j e t s  l aden  wi th  uniform 
s i z e  s o l i d  p a r t i c l e s  o r  l i q u i d  d r o p l e t s .  
The approach followed he re  is t o  s t a r t  from t h e  s e p a r a t e  momentum and c o n t i n u i t y  
e q u a t i o n s  o f  each phase and d e r i v e  two new conse rva t ion  equa t ions .  The f i r s t  
i s  f o r  t h e  c a r r i e r  f l u i d ' s  k i n e t i c  energy of tu rbu lence  and t h e  second f o r  t h e  
d i s s i p a t i o n  r a t e  of  t h a t  energy.  Closure  of t h e  s e t  of  t r a n s p o r t  e q u a t i o n s  is 
ach ieved  by modeling t h e  t u r b u l e n c e  c o r r e l a t i o n s  up t o  a  t h i r d  o r d e r .  
The c o e f f i c i e n t s  ( o r  c o n s t a n t s )  appear ing  i n  t h e  modeled e q u a t i o n s  a r e  then 
e v a l u a t e d  by comparing t h e  p r e d i c t i o n s  wi th  LDA-measurements ob ta ined  r e c e n t l y  
i n  a  t u r b u l e n t  j e t  l aden  wi th  20011 s o l i d  p a r t i c l e s .  Th i s  s e t  of  c o n s t a n t s  is 
t h e n  used t o  p r e d i c t  t h e  same j e t  f low bu t  l aden  wi th  50U s o l i d  p a r t i c l e s .  The 
agreement wi th  t h e  measurement i n  t h i s  c a s e  is very good. 
https://ntrs.nasa.gov/search.jsp?R=19830020944 2020-03-22T00:51:24+00:00Z
References  
G. He t s ron i  and M. Sokolov, " D i s t r i b u t i o n  o f  Mass. V e l o c i t y  and I n t e n s i t y  
o f  Turbulence i n  a TWO-phase Turbu len t  J e t , "  J. A ~ P I .  ~ e c h , ,  Vol. 93, 
pp. 315-327, 1971. 
J .  Popper,  N.  Abuaf and G. H e t s r o n i ,  "Ve loc i ty  Measurements i n  a Two-Phase 
Jet," Int. J. Int. J. Mult iphase  Flow, Vol. 1, pp. 715-726, 1974. 
M.K. L a a t s ,  "Exper imenta l  S tudy of t h e  Dynamics of  an Air-Dust J e t , "  
Inzh.  Fiz .  Zh., Vol. 10, pp. 1-7, 1966. 
T.A. Gi r shov ich ,  A . I .  K a r t u s h i n s k i i ,  M.K. L a a t s ,  V.A. Leonov and A.S. 
Mulgi ,  "Exper imenta l  I n v e s t i g a t i o n  of a Turbu len t  J e t  Carryng Heavy 
P a r t i c l e s  of  a Dispe r se  Phase,"  Izv .  Akad. Nauk SSSR, Mekh. Zh. i Gaza, 
No. 5,  pp. 26-31, Sept.-Oct. 1981. 
D. Modarress,  J .  Wuerer and S. Elghobashi ,  "An Exper imenta l  S tudy of a 
Turbu len t  Round Two-Phase J e t , "  AIAA/ASME 3rd J q i n t  Thermophysics,  
F l u i d s ,  Plasma and Heat T r a n s f e r  Conference,  AIAA-82-0964, S t .  L o u i s , '  
M i s s o u r i ,  June  1982. 
J.L. Lumley , "Two-Phase and non-Newtonian Flows ," Topics  i n  Applied 
P h y s i c s ,  Vol. 12, pp. 289-324, 1976. 
H. Danon, M. Wolfshte in  and G. H e t s r o n i ,  "Numerical C a l c u l a t i o n s  o f  Two- 
Phase Turbu len t  Round J e t , "  I n t .  J .  Mul t iphase  Flow, Vol. 3, pp. 223-237, 
1977. 
A.M. A l  Taweel and J. Landau, "Turbulence Modulation i n  Two-Phase J e t s , "  
I n t .  J .  Mul t iphase  Flow, Vol. 3, pp.341-351, 1977. 
ASSUMPTIONS 
@ BOTH PHASES BEHAVE MACROSCOPICALLY 
AS A CONTINUUM, BUT ONLY THE CARRIER 
FLUID BEHAVES MICRORCOPICALLY AS A 
CONTINUUM 
@ THE DISPERSED PHASE CONSISTS OF 
SPHERICAL PARTICLES OF UNIFORM SIZE* 
@ NO COLLISIONS-OCCUR BETWEEN 
THE PARTICLES 
@ NO PHASE CHANGE TAKES PLACE 
G W R N I N G  EQUATIONS 
MOMENTUM OF CARRIER FLUID 
MOMENTUM 
OF DISPERSED PHASE 
CONTINUITY 
The mean continuity equation of the dispersed phase is 
the Dean g l o b a l  continuity is 
TURWLENCE KINETIC ENERGY 
DISSIPATION RATE OF 
TURBULENCE ENERGY 
A SAMPLE CALCULATION 
JHE F I  O!,l: o A TUREULENT ROUND JET ISSUES FP\O?l P, PIPE, 
o THE JET F L U I D  CONSISTS OF A COMTIII'UOYS 
LIGHT PHASE (AIR)  A!ID A PARTICULATE PHASE 
OF UNIFORM S I Z E  AND SPHERICAL, 
o . NO PIIASE CHANGE TAKES PLACE 
EQII RED : CALCULATE THE VELOCITY CO3POf ENTS 
(u,; uz), (vl, v2), AND T l lE  VOLU/iE 
FRACTIONS 4,s 42, TURRULEtiCE PROPERTIES 
(EKERGY AND LENGTH SCALE) AS FUNCTIOPlS 
OF (x,  r), 
NOZZLE CONDITIONS: 
- .  . - . .  
v I E A N  GAS VELOCITY AT CENTERLINE 12,6 M/S . . . .  . 
r REYNOLDS NUIIBER 16503. 
o PARTICLE S I Z E  2 0 0 ,  p 
r PARTICLE DENSITY 2 9 9 0 ,  K G / M ~  
r MASS RATIO 0 , 6 4  
r VOLUYETRIC RATIO 2 . 6  x 
MEAN VELOCITY 
OF CARRIER FLUID 
0 . 0 0  0 . 0 5  0 . 1 0  0.15 
r / x  
Experiment Predict ions 
Single Phase  o ----- 
Two Phase A - 
TWO PHASE now EXPERIMENT 
la 
k 945  { K - f ( z p k )  - 
K-L  ( I P ~ . )  --- 
0.5 -- 
0. I I 
0, 0.05 4.6.1 % 
I 
I 
I ? 
Flow t 5pp solid paf;c/e, 
L
Mc75j Rate .Gf,b & = 0 -2 9 
E$P 7 4  Fred2 f?hs 
-.,= 
pk4K 
\ 7m ph~r54 
- 
0 . 0 0  0 . 0 5  0 .10  0.15 
r / x  
Exper iment  Predict ions 
Single Phase o ----- 
Two Phase A - 
TURBULENTSHEAR STRESS 
Experiment Predictions 
Single Phase 0 (present )  
----- (Wygnanski)  
Two Phase A - 
SPREAD!NG RATE 
Experiment Predict  ions 
Single Phose o - 
Two Phose A - - - -  
CONCLUDING REMPPKS 
r I T  HAS BEEN SHOVII THAT THE NEWLY- DEVELOPED K-€TURBULENCE 
MODEL PREDICTS THE BEHAVIOR OF THE TWO- PHASE J E T  
r A NUMBER OF UNCERTAINTIES REMAIN AND ONE SHOULDJFOR THE 
PRESENT EXERCISE DUE CAUTION IN APPLYING THE MODEL TO 
F L O E  THAT ARE SUBST.INTIALLY DIFFERENT FROY THE ONE 
CQSIDERED HERE, 
r EXPERIMENT I S  URGENTLY NEE9ED TO r!EASURE !IEAN AND TURBIJLENT 
OUAMTITIES I N  P. GASEOUS J E T  IN WHICH UPIIFORM S I Z E  DROPLETS 
A9E IIIJECTED, 


Effect of Liquid Droplets on Turbulence Structure in a Round Gaseous Jet

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