The present paper will compare temperature field measurements from selected cases in these investigations with distributions calculated with an empirical model based on assumed vertical profile similarity and superposition and with a 3-D elliptic code using a standard K-E turbulence model. The results will show the capability (or lack thereof) of the models to predict the effects of the principle flow and geometric variables

Holdeman, J. D.

Srinivasan, R.

English

NASA Technical Reports Server

• I • _ t
t o.,o,..L AaE N8 4 2 0.54 7 Dz2 ":"
'_ OF POOR QUALITY r.
MOI)ELIN8 OF DILUTION JET FLOI_FIELDS
by J,D. Holo, _an
NASA Lewi_ Research Center
• and
t f_. Srinivasan
B .
_- The Barrett Turbine Engine Company
Considerations of dilution zone mixing in gas turbine
combustion chambers have motivated several studies of the
mixing characteristics of a row of jets injected normally into
a flc_ of a different temperature in a constant area
duct. -- _- I -4 Recently, experiments have been performed
to extend these investigations to include geometric and 41ow
variations characteristic of most gas turbine combustion
chambers, namely a variable temperature mainstream, flow area
: convergence, and opposed rows of jets, either in-line or
staggered; =. '_'see figures 1 & 2.
' The present paper will compare temperature field measurements
from selected cases in these investigations with distributions
calculated with an empirical model based on assumed vertical
prufile similarity and superposition t* and with a 3-I)
elliptic code using a standard K-E turbulence model. 7
The results will show the capability (or lack thereof) of the
models to predict the effects of the principle flow and
geometric variables.-'- '_._.''
Variations w_h Orifice Si_e and_Sl_acinq. At constant i
orifice area, changes In orifice size and spaclng can result in
jets which vary from under-penetration to over-penetration. ,,
, This is shown in figure 3a) and b), for jets from closely : i
. spaced small orifices and widely spaced larger orifices
respectively. The empirlcal ¢a_del reproduces the data very _II
in the small orifice case, since the data are consistent with i
_ the major assumption in the empirical model, that all vertical
, temperature distributions can 3e reduced to similar 8aussian
: profiles. The empirical model does not do as well in the larger , !
_" orifice case however, as the jets have impinged on the opposite , !
' wall and the vertical profiles are not similar.
r The analytical model calculations made with approximately
| 20,000 nodes, although in qualitative agreement with the datat ;,
under-predict the mixing. That is, the temperature gradients, i -
especially in the transverse directionp are too steep. This i
result is typical of the analytlcal model calculations to be
shown in this paper. For the small-orifice ca_e a coarse-grid
calculation using less than bOO0 nodes was also performed. This I
solut:_1 illustrates the dlfeu$ive nature of the calculation
ITS
1984012457-171
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'"' °
, ORIGINAL PAGE II
i OF POOP, QUALITY
and t_ slgnlflcant ll_fiuPncP, of grid seJectlon on the solutlon
obta_ ned.
Coupled Spaclng and Momer_tum Flu-. Ratlo. Examlnat_on o_
the experimental data revealP.d that sJnlilar profile_ can b_
obtained over a range of momentum _lu× ratios, independent of
orifice diameter, _f orifice _paclng and momentum flux ratio
are correctly coupled. -','',_'.'+ [his I__ shown In figure
/, 4a) to c),
¢
In all of the comblnatlons shown here, the emplr_cal model
: r_sults are In very good agreement with the data, a_ the data
are conslste[,t with the Gausslan prof_ie assumptlon. The
analytlcai model cdiculatlons uslng approxlmately 20,000 nodes
for these cases agrL, e qualltlllvely with the data, as in the
previous figure. In the medlum momentum flux ratio case, a
second calculation was performed with the sa_e total number of
grld polpts, but with the nodes sllghtlf more concentrated in
the viclnlty of the let exit. As can be seen In figure 4b),
these two results are not substantially different.
Uarlable Temperature Mainstream. [he In Èa
non-lsothermal mainstream flow c,_ the profiles for medium
r " momentum flux ratios wlth S/Ho--.3 and Ho/D=4 can be seen by
" comparing figures 5 & b. The sI,=_e of the experlmental profiles
.. In figure b suggests modelllg them os a superposltlon of the
upsLream pro_lle and the corresponding ;ets-ln-an-_sothermal
mainstream dl_trlbutxon.'" This glve_ only a crude
approxlmat_on !-,qwever, as seen in the emplrlcal mod_l results,
because of the cross-stream trapsport of malnstream _/iuid due
to the blockage, which is not accounted for in super_mposlng
the dlstributlon_.
In _he variable temperature mainstream cas_ the analytical
model results aqree w_ll with the experlm_ntal data, espec_ally
on the _et centerplane, but the transv_.rs_ m_xlng is
underpredlcted, as in the corresponding _sothermal ma_natre _m
case _n f_gure 5.
O p___Rows o_ In-l_n_ J_Ls. Fur opposed rows of jets,
with the orlf_ce centerlznes In-line, the optimum ratio o_
orifice spac_i_g to duct height :s one-half c._ the optimum value
fo_ single-s,de In}ectlon a_ the same _o._ent_m flux
ratlo. 'w As as example consider the slngle-s_de case
wlth S/Ho=.5 and Ho/D=4 i_0 flqure 5 and the ,_pposed row of
&n-llne ;ets w_th S/Ho=.25 and Ho/D=8 _n f,c]ure 7.
I
The emp_rical model predicts the oppose_-)et case very _II,
: verifying the prim_ry assumption that the effect of a plane of
symmetry Is _i_lar to _hat of an opposlte _all. _. "_
! Note that the exper_mer, tal profiles on both slde¢, of the plane
i of symmetry support the Gaus_lan profile assumption. Theanalyt,_cal model results sho_ the _teep transverse and lateral
gradients seen ]n almost all qf the previous calculations a|so_
1984012457-172
• but are in otherwise good agreement with the data.
Opposed Rows of Staqqered Jets. For opposed rows of jets,
vJith the orifice centerlines staggered, the optimum ratio of
orifice spacing to duct height is double the optimum value for
single-side injection at the same momentum flux
ratio. _ As an example consider the single-side case
with S/Ho=.5 in figure 5, and the opposed row of staggered-jets
with S/Ho=I in figure 8.
The empirical model does not handle this complex case Nell, as
the fluid dynamic interactions here are not amenable to a
direct extension of the simple Gaussian profile and
superposition type modeling appropriate for most of the
single-side and opposed-jet cases of interest. The analytical
model calculations give slightly better agreement with the data
than does the empirical model, and would be expected to improve
with overall improvements in the capability of the 3-D codes.
f
REFERENCES
1. Walker, R.E. and K_rs, D.L.: Multiple Jet Study Final
Report. NASA CR-121217, 1973.
2. Holdeman, J.D._ Walker, R.E., and Kors_ D.L.: Mixing of j
, _ Multiple Dilution Jets with a Hot Primary Airstream for Gas I
. Turbine Combustors. AIAA Paper 73-1249, 1973. I
3. Walker_ R.E. and Eberhard_ R.G.: Multiple Jet Study Data
Correlations. NASA CR-134796_ 1975.
4. Holdeman, J.D. and Walker_ R.E.: Mixing of a Row of Jets
_ith a Confined Crossflow. AIAA Journal_ vol.15_ no.2p
Feb. l?77, pp243-249.
5. Srinivasan, R., Beren !,”and Mongia_ H.C.: Dilution
Jet Mixing Program - Phase I Report. NASA CR-168031, 1982.
6. Srinivasan_ R._ Coleman, E., Johnson, K._ and Mongia_ H.
C.: Dilution Jet Mixing Program - Phase II Report. NASA
CR-174624_ 1984.
7. Srinivasan_ R._ Reynolds, R., Ball, I., Berry_ R. 9 Johnson_
K._ and Mongia, H.: Aerothermal Modeling Program - Phase I
Final Report. NASA CR-168243_ 1983.
8. Holdeman, J.D.: Perspectives on the Mixing of a Row of Jets
with a Confined Crossflow. AIAA-83-1200, 1983.
9. Holdeman, J.D._ Srinivasan_ R. 9 and Berenfeldp A.:
Experiments in Dilution Jet Mixing. AIAA-83-1201, 1983.
/
=w_ 177
1984012457-173
ORIGINAL PAGE IS
OF POOR QUALITY
ORIFICE
_. PROFILE PLATEAIR
GENERATOR SUPPLY
AIRSUPPLY
MAIN IJ[_| RADIAL I_/_1
AIR I/Y_I(YDIRECTION)_/_ fBSUPPLY A-- //t'\1TEMPERATURE ,_i, TRAVERSING
0,25,! <2.0
ORIFICE
PLATEAIR
: i_ .A B SUPPLY
PROFILEGENERATORORIFICEPLATE
(1Of 4 CONFIGURATIONS)
Figure1. - DilutionJetMixingFlowSchematic.
D D
Ho-I0.18¢m "-* )'_7_"_
t_l.0_- ×/Ho [2.O -1.0 X/Ho -1.0 "
SYMMETRIC ASYMMETRIC
CONVERGENCE CONVERGENCE
lESTSECTIONS
j o: 0 0 o o0 o0 ]" o °• j o_ o_,° .O'T 0 o o_
_oO_ o o
-" l/-_ oTo o o-I
0 , 00 0
SID .2 4 2 4 4
Hold • 4 4 8 8 8
ORIFICECONFIGURATIONS
Figure2. - TestSectionsandOrificeConfigurations.
1984012457-174
ORIGINAL PAGE 19
OF POOR QUALITY.
• EXPER I[HENTRL EI_ ! R! CAL ANRLYT ][CAL _'
45x 26x 17 27x 26x 8
, x,H=.= d =_ d _ d
. I I I |
++ _ I.O 1.41 1.41
r, 4 ,I I,I IJl ,,II I
I /flY. t/l I lilT, I/I _ giiT* l/l
_" 1_ Ollt. I/I Z
X/H=1 d _-__ -'+ -d '
| +'-------_ |
1.41 n+41U,O
I.e o.I _ 4 41,1 4,.I
O/It, _I _ gilt, I/1 _ OllT, I/I
roll llllto111
+ CENTERPLA_ PROFILES
.. E_IRICRL 45X26X17 27X26XO
)
+ ,
+5 + '+ '+
x,+.+!'U" +-';. '
f
o DATA
..... |_ ,_ +
o_ _ ,_ oa ,_ ,_ _ _ ,_ _ _ ,4 ,_ _
8 '
+" XIH=I
!!/
+ ..- I_ . ,.... I_ + . . , , .
( T_I_T I/(t_lN-tJ) I T+|N- T |/I T_IN-TJ I I TMi_T )/I T_ I_td I
Fibre 3, E(llct ot Vezlt/_l in _iItCI SiZl and Splcinl on Tap_lture DiltrJbut|onl
.+ 179
+
1984012457-175
_h U&iGiNAL PAGE |g
• . OF POOR QUALrrY
• EXPER IMENTAL EMP IR ICAL ANALYT ICAL40>:,23x 21
_ I "-" = °° -- --
_' 0 .| t,0
i -0.1 0.1 -O.S t_IWI[RS[ 315T, //S _E O_|r, l/8
" TR3V4S_c.q_01$_. L$
d
Q_ °,, , ,, , °_
X II _ "
X/H=1 _ _ t _ -_
| i |
_1 o t.o
"4 -O.il O_
4.1 _ t Tl_¢S'ff,.q_ OII_T./_$ TI_ OllSf.T.,'S
mK._¢[_" OIST LS
, CENTERPLANE PROF ILES
EMPIRICAL 40X23X21
:'_"
ea °
o DATA
|! . ._,---_,,, ." _, ,_, ,_ . ,OalD o a s• sa_ _a_
_I'..\ _.!i_\"• '
.- _ ",\
blS/Ho=I, Ho/D=4.Aj/A.=.o4q. 3=26,7,_/w_=.lq2
Flqure 3, E_{ect of Var;atzonsin Orifice Size andSpaclnoon TemperatureDistributions
180
- ®
1984012457-176
OF _,,r_,;
-..., .... (_ALI'I'Y
E XPER IMENTAL EMP IR ICAL ANALYT ICAL
40x 23x 21
VX/H=. 5 --
! 1 f =
,, I ir _ 1,0
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CENTERPLANE PROF ILES
EMPIRICAL 40X23X21
I
X IH=- 5
; o DATA
i ,'A, ,'_ _,m ,_, Cd,
•'_ t TM_IN-T)/( Tl'lq|N-TJ) (TI'_IN,-T)It TIIRIN-TJ)
,i
: X/H=1
I:
;'= ,:_ _ 7_ om o,, ,,.
[ ?_IN-T 1/( TPtRIN-TJ) ( TI'II_iN- T)It TI_CiIPTJ)
Figure 4. TNpwratureO_otr_but:onsw_thCo_pledSpacingandBoeontumFlux Rat:o.
18]
v
1984012457-177
CENTERPL_NE PROFILES
EMP IR ICAL 35X33X 17 32X29X21
2
,. . . * * J
X/H=.5 _ "'" i)
_' o DATA
•.,,,.,.,..,.,._ ;.,.,..,. i+_ ,.,,. 7. l;° .....i• __ eii i,m i,m iai o,ii ill i,m
{TPIAIN-T }/! TPIRIN-TJ ! i TMIIIN-T)/! T_I_IN-TJ I (TPIRIN-T )/(TIIIIN-TJ)
........I
_il _ .-I' : . - ,;.,
x _° "-.
I1 i / "" I1 i"li ll_i o_l i'm l_ ii i • =' I i i i wi i i il I i,,lll i,m 11 i,,ll i,ill li
( TPIRIN-l )11TPIR[N-TJ ) lTMR IN-T )/i TP'RIN-TJ ) l TPIRIN- l IllTMRIN- lJ ) _,F
b) S/Ho'.S,HolD'5,66AilIiI.=,(i49,J=25.5, w_/II_:.205
+
Figure 4. TemperatureDistributions with CoupledSpacingand_olentunFlux Ratio.
_e
" 182
l.,_............ ®,
1984012457-178
._11"I,. , (_),
* E XPER I MENTAL EMP [ R I CAL ANALYT [ CAL
45x 26x [ 7
-" |8 J|,O
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I.ID .ll 4.1 I.I 14
T . e.i TP_ 0liT. /JII fl_ OliTo /41
i ,, i _ .,.
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i .
o,_¢_ _ _o.* I'° _.l la
H OilY, gilT,
. CENTERPLP_IE PROFILES
EMPIRICAL 45X26X17
. !!,_ X/H=. 5 o I[3_TI_• " *',B *'8 _ *m *_ *_ ,'_ -'- ,'_
, { Tf'IAiN- T II1 TRRIN-TJ ) { TRA [N-T )/( TRA [N-TJ )
,-:-
i •
, ], I
i x,,H=1 •
! , , _ , , , -,. _
o._ ,'_ o'_ *_ _'_ ,.m *_ o_ *_ ,,_ ,
[ TI'tCiIN- T )/! THA IN- TJ I ( TMlqIN- T Ill TrlAIN-TJ I
C) SI1_,.25, HoiD=6,A_IIL,,".049_J"92.7, IIjIW'r:._02
Figure 4. TNparatureDistributions with CnupiH6pacingandHommtuoFlux Ratio,
183
• ®
1984012457-179
.,jr,r , o ..
" oR|GINAL pAGE |g
OF pOOR QUALITY
• E XPER IMENTAL EMP IR ICAL ANALYT ICAL
45x 23x 19
• ; • .,., ... i
X,H= L 1,0
TIIINII_mN[ "_ll,T. !, S _RlIMl,lJIK gIST. !/5
..J
N ,2. ....
X/H=I _ ; _
Io
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CENTERPLANE PROFILES
" EMPIRICAL 45X23X19
,,.. ..... ,_ ..... .• • __4
" ._.
m_
:- _. :...5
_1 ._, _ ". --.
" X/H=.5 g _ _" " -"
/
• _ _._-.-.
_ o DATAi'e 11 •
"' _
B_
IIM_IN-TI, IIMRIN-TjI (TMRIN-?)IITM_IN-Tj)
ill ell _.I
_I :._ ,,- ',- _-- i .-
• _ _i. :i _",1 '. _ _ .
X/H= I " "-'",
!t "_' |I •
_ I_ L.,;.___ , ,-----",,.,,,lm i'm i_ lib Oil ,11 _ll _
iT_RIN-; t : T_RIN-fjI ,"_ll_,_-T] r 'rf"_IN-}'j_
F_gure5. TeiperatureO,str=butlonsfor S_ngle-s=de_top)Injection=ntoan IsothermalMainstream
: (S/Ho=,5, Ho=4, AitA.=.O_8, J:18.6, "_/",:..lt)
_" 184
• ®
1984012457-180
_ .L j
L
"" (_f_;_.f._L P/._ _._ EXPERIMENTAL EMPIRICAL ANALYTICAL
•• :_ OF POOR QUALji"y 45x 23x 19
". _ _
I I .0
4.| _JlE lilT. I[/| _ _I|T. _J| a.i
_" Twm1[_ Olllf. IL41
b,
i i i '
|
Ol|r, /18 _ OlIT. L/i 414 o.I0111I. L/I
• CENTERPLANE PROFILES
f EMPIRICAL 45X23X19
X/H=.5 ; _ ._
":,
l!i .
• _ • . av
•
0 DATA ,_._._I.
mm o ,o 14e e,dg _4g 9 • ,'m e_e o,Q e'm ="e
r_X- r 1/( TPRX- TJ ) I TP_X- T _/ I TI_X - T_ ',
, :]
• .* .
/7 • ell •e
•|, •
,.,, o,, ,,, ,.. ,,, ?,, l;,,, ,=1 ,,, , • '
i ( TffRX-Y I,'1 Tt'I_X- TJ ) I TI'I_IX-T _/1 TRRX*TJ !
F_Qure6. Te|peratureOIstr|bution_ for Variable leaperature (TopCohl) nainutream
($/Ho=.5,Hol_=4,AjI_.:,098, ,1_=_|,,_)
185
J_
1984012457-181
1984012457-182
._ ORIGINALPAGE|g
OF POOR QUALITY
E XPER IMENTAL EMP IR ICAL ANAL YT ICAL
22x 27x 33
'e ]
: .i" _"
J
'_ X/H =. 5 : I ,
. • , |
% ,.I.I o.O 4.1IIIqGAImE Ol|f. IV// _ Bill, 14 4,11 B lilT. I/I M
" _ eJI _1 a t mini ,04 I
X/H=1
I
_,l / i.e -- -- la
O$ 4.1 44 IIJI
4.1 _ OIll*, UI _ OIIf. Ib'l _ lilT.
CENTERPLANE PROFILES aw
EMP IR ICAL 22 X27 X33 i
• i
a_
" I
X/H=. 5 i' :
o DATA •
e4l e_ eaiJ OIll ,,I e,II _ [ _ _ "ee _ |,l i,i
! TNqIN- r )/! T_IIN- TJ! ! TMAIN,, f 1/( TPIR|N-,TJ I
v ,_' '
•'"' iil :
! flSltll_- T )/! TWIIN-TJ I I TRIIIN- f )1¢ TRIII_TJ )
Fi0ure 8. leeperature Distributions (or Two-side (staggered) In)Ktnon
(S/He,t, Hel0,4. ij/_l.,.096. J,27.1, ._/.,=.3271
187
I
1984012457-183


Modeling of dilution jet flowfields

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