Mean temperature profiles calculated with an interactive microcomputer code which evaluates dilution-zone design alternatives are presented to show the effects of flow and geometric variables on the mixing of a single row of jets injected through sharp-edged orifices into a uniform flow of a different temperature in a constant area duct. In addition, this program is used to calculate profiles for opposed rows of jets with their centerlines in-line, by assuming that the confining effect of an opposite wall is equivalent to that of a plane of symmetry between opposed jets

Holdeman, J. D.

English

NASA Technical Reports Server

N88- 11154
ON THE MIXING OF A ROW OF JETS WITH A CONFINED CROSSFLOW
J.D. Holdeman
NASA Lewis Research Center
Cleveland, Ohio
INTRODUCTION
Considerations in designing or tailoring temperature patterns at the exit of
gas-turbine combustion chambers, necessary to maximize engine power and life, have
motivated several studies of the thermal mixing characteristics of multiple jets
injected into a confined crossflow (refs. 1 to 11). The objective of these studies
was to identify the dominant physical mechanisms governing the mixing, to develop and
extend empirical models for use as a near-term combustor design tool, and to provide
a data base for the assessment and verification of three-dimensional numerical codes.
These investigations of dilution jet mixing were staged in complexity, beginning
with experiments and analyses (refs. 1 to 5) that investigated the mixing character-
istics of a single row of jets injected into an isothermal main-stream flow in a
constant area duct. Recent experimental and analytical results (refs. 6 to 11)
extended the earlier studies to investigate the role of several flow and geometric
variations typical of gas-turbine combustion chambers, namely, variable temperature
main stream, flow area convergence, opposed in-line and staggered injection, multiple
rows of holes, and noncircular orifices.
From the data of references 1 and 2, an empirical model was developed (eels. 3
and 4) for calculating the temperature field downstream of a row of jets mixing with
a confined crossflow. This model is the basis of an interactive microcomputer code
which evaluates dilution-zone design alternatives (ref. 5). In this paper mean
temperature profiles calculated with this routine are presented to show the effects
of flow and geometric variables on the mixing of a single row of jets injected
through sharp-edged orifices into a uniform flow of a different temperature in a
constant area duct. In addition, this program is used to calculate profiles for
opposed rows of jets with their centerlines in-line, by assuming that the confining
effect of an opposite wall is equivalent to that of a plane of symmetry between
opposed jets.
FLOW FIELD DESCRIPTION
The flow schedule and the principal flow and geometric variables are shown in
figure 1. The independent flow variables are the momentum flux ratio J, the density
ratio DR, and the orifice discharge coefficient CD. The primary independent geo-
metric variables are orifice size and the spacing between adjacent orifices. These
are expressed in dimensionless form as the ratio of the duct height to orifice diam-
eter H/D and as the ratio of the orifice spacing to duct height S/H. Downstream
stations are defined in terms of the ratio of the distance to the duct height X/H.
The calculated temperature fields are shown in three-dimensional oblique views
where the local temperature is given by the dimensionless temperature difference
ratio, e = (Tm - T)/(T m - Tj. (Note that e is bounded by 0 and 1, with
133
https://ntrs.nasa.gov/search.jsp?R=19880001772 2020-03-20T08:35:33+00:00Z
the foz_ner representing unmixed mainstream fluid and the latter unmixed jet fluid.)
Local values of this parameter are given on the abscissa in the three-dimensional
plots. The ordinate Y and oblique coordinate Z are, respectively, normal to and
along the orifice row, in a constant-X plane. The Z-distance shown in the oblique
plots is twice the orifice spacing for each configuration. The flow and geometric
variables specified as input to the empirical model were DR, J, CD, S/H, H/D, and
X/H. All of the calculated profiles shown are for conditions that are within the
range of the experiments against which the empirical model has been compared.
SUMMARY OF FLOW AND GEOMETRY EFFECTS
The calculated mean temperature profiles shown herein illustrate the effects of
flow and geometric variables on the mixing. These confirm the conclusions reached
previously (refs. 2 and 4) from examination of the experimental data that
(1) Mixing improves with downstream distance (fig.2)
(2) The momentum flux ratio is the most significant flow variable (fig. 3)
(3) Variations in orifice diameter and spacing can have a significant effect on
the profiles (fig. 4)
(4) Similar distributions are obtained over a range of momentum flux ratios,
independent of orifice diameter, if spacing and momentum flux ratio are
coupled such that (S/H)(J) = constant (fig. 5)
(5) Increasing the orifice diameter at constant spacing increases the magnitude
of the temperature difference, but jet penetration and profile shape remain
similar (fig. 6)
(7) For opposed rows of jets with centerlines in-line, the optimum orifice
spacing in one half of the appropriate value for one side injection (fig. 7).
REFERENCES
1. Walker, R.E.; and Kors, D.L.: Multiple Jet Study. NASA CR-121217, 1973.
2. Holdeman, J.D.; Walker, R.E.; and Kors, D.L.: Mixing of Multiple Dilution Jets
with a Hot Primary Airstream for Gas Turbine Combustors. AIAAPaper 73-1249,
Nov. 1973.
3. Walker, R.E.; and Eberhardt, R.G.: Multiple Jet Study Data Correlations. NASA
CR-134795, 1975.
4. Holdeman, J.D.; and Walker, R.E.: Mixing of a Row of Jets with a Confined Cross-
flow. AIAA J., vol. 15, no. 2, Feb. 1977, pp. 243-249.
5. Holdeman, J.D.: Perspectives on the Mixing of a Row of Jets with a Confined
Crossflow. AIAA Paper 83-1200, June 1983.
6. Srinivasan, R.; Berenfeld, A.; and Mongia, H.C.: Dilution Jet Mixing Program -
Phase I. (Garrett 21-4302, Garrett Turbine Engine Co.; NASA Contract NAS3-22110)
NASA CR-168031, 1982.
134
7. Srinivasan, R.; Coleman, E.; and Johnson, K.: Dilution Jet Nixing Program.
(Garrett 21-4804, Garrett Turbine Engine Co.; NASA Contract NAS3-22110) NASA
CR-174624, 1984.
8. Holdeman, J.D.; Scinivasan, R.; and Berenfeld, A.: Experiments in Dilution Jet
Nixing. AIAA J., vol. 22, no. 10, Oct. 1984, pp. 1436-1443.
9. Holdeman, J.D.; and Srinivasan, R.: On Nodellng Dilution Jet Flowfields. AIAA
Paper 84-1379, June 1984.
10. Holdeman, J.D., et al.: Experiments in Dilution Jet Nixing - Effects of Multiple
Rows and Non-circular Orifices. AIAA Paper 85-1104, July 1985.
11. Srinivasan, R.; Neyers, G.D.; and White, C.D.: Dilution Jet Nixing Program.
(Garrett 21-5418, Garrett Turbine Engine Co.; NASA Contract NAS3-22110) NASA
CR-174884, 1985.
135
Flow ,_chematlc
Um Z I S
Tm
ID
Top
View
. ,,0.Tm View
Independent Variables
DR : Tm./Ti ., density ratio
J DR <O.i/Um)_ momentum flux ratio
CO discharge coefficient
S/H orifice spacing
H/D orifice diameter
X/H downstre._m distance
Dependent Variables
THETA : (Tm-T)/(Tm-Tj> temperature
fIR=mj/m M mass flow split
TB: mi/(ram + m j) equilibrium THETQ
PF:MB (I-THETAmi n/'TB> pattern factor
SIO
X/D
Dilution Jet Mixing Flow and Geometric Va,iables
Figure I
VARIATIONIN TEMPERAIUREDISIRIBUIIONS WITH INCREASINGORIFICEDIAMETER
CONSTANTSPACINGS/H =0.5$ J = 26.4
__.-C_ ZI5
',Tt',bC,'.',,'>.'., ", 1,',
I
1 I t q
B .5 1
THETQ=,:ITn,-T>,( Tm-T i>
S.'H=5 IRi_. .1=264 DR:272
¥
H
I I
B .5 1
THETQ:,iTrf,-T>/ (Trn-Tj ::,
C:C)=.64 S."H=5 I O=Z6'40R=2.2="" '="" CO:,64 S/H: 5
X,'H:. 5 _ X,'H=.5
(a)X/H - O.5.
¥
H
1 I I
B ,5 1
THETQ:<Tm-T)/'(Tm-T i)
C:D=.64
S/H:5
X/H=2
B
¥
H
;'/5
/
1 I " I I
,5 l
THETQ:(Tm-T)/(Tm-T])
CO:.64 S/H=.5X/ 2
B ,5 1
THETQ:(Tm-T).,'(Tm-Tj)
CD:.64 S/H:.5×./H=2
(b)X/H• 2.
," ....L.,-
/..5,.'"
m
¥
I
B .5 1
THETQ=(Tm=T)/(Tm-Tj )
CD:. 64
Figure 2
136
ORIGINAL PAGE IS
OF POOR QUAI3TY
VARIATIONIN TEMPERATUREDISTRIBUTIONSWITH INCREASINGMOMENTUMFLUXRATIO
XIH O.5; SIH = O.5; HID - 5.66
i. 'ii';
TH_TA=(Tm-T).,"(Tm-Ti) THETA--.(Tm-T)/(Tm-T i) THETA=(Tm-T)/(Tm-T,.])
S/H=.5 '= =''" CD--.64 S/H=.5 '= = " CD=.64 S/H=.5 ' = = " CD=.64
Figure 3
VARIATIONIN TEMPERATUREDISTRIBUTIONSWITH INCREASINGDOWNSTREAMDISTANCE
OPPOSEDJETINJECTION; J = 26.4; S/H * O.2.5; HID - 11.3
i_ ,5 I B ,_; 1
TH_TA=<TIn-T),"( Tm-Ti ) THETA:<Trr,-T>.,'(Tm-Ti>
S/H=.25 H,"D:II.31 J:26.4 DR=2.2 CD:.64 S/H:.25 H/D=II.31 J=26.4 DR:2.2 CD:.64
_._m ,c_> ,5'
z/5_,,'l i1
,-l,O,iil,ii[ii,,,9k
,5 I
THETA=(Tm-T>/(Tm-Tj)
S/H=.;'5 H/D=II.31 J=26.4 DR=2.2 CD=.64
FiKu_e 4
VARIATIONIN TEMPERATUREDISTRIBUTIONSWITH INCREASINGDOWNSTREAMDISTANCE
J - 26.4; SIH = 0.5; HID • 5.66
THETA=(Tm-T)/(Tm-Tj) THETA=(Tm-T)/(Tm-Tj) THETA=(Tm-T)/(Tm-Tj)
S,"H=.5 H,"O=5._6 .3=264 DR=2.2 C:D=.64 S/H=.5 H/D=5.66 J=26.4 DR=2.2 CO=.64 S/H=.5 H/D=5.66 J=26.4 DR=2.2
MR=.24 TB=.19 I I MR=,24 TB=.19 I I MR=.24 TB=.[9
CD=.64
ORIC,1NAK PA-OE lr_
OF POOR QUALITy
137
VARIATIONIN TEMPERATUREDISTRIBUTIONSWITH COUPLEDSPACINGAND MOMENTUMFLUXRATIO
B ,5
THETCI: ':Trr,-T 1:,/ (T,,-T.i)
X.'H: 5 MR=. 24 TB= i_ ILF'F=.22
(a) X/H "O. 5.
i I I
B .5 1
THETA=(Tm-T)./(Tm-T i>
CO-- _.4 _I/IISlI_l_/ nR=2"2 CI3=. 64
:%..'H=5 I'1R= 24. TB= 13 I
I _'_, ,/h;_'" I ,',_zt,u/,'I/I,'_
I i I I
,5 ] _ ,5 1
THETA=<Tm-T)/'(Tm-Tj> THETA=(Tm-T),"(Tm-Tj>
X/H=2 MR=24 TS=. 13 I X,'H=2 ME:=. 24 TB= 19
(b)X/H - 2.
,5E*" Z /
.5 1
THETA=(Tm-T)/(Tm-Tj )
CD= 64 _:_:I_II_ DR=2.
X,'H=2 MR=. 24. TB= t9 III
CO=. 64
FiEure 6
VARIATIONIN TEMPERATUREDISTRIBUTIONSWITH ORIFICESPACINGAND DIAMETER
CONSTANTORIFICEAREA_X/H - 0.5_ J = 26.4
_J=26. 4 DR:2. 2
X/H=. 5 r'lR=. 24 TB=. 19 I
_/_.. ,',,",'4.'_,,_ ./;, ',_&\.'h,_'<:_".
I"_:_',.::,:i!,"/1/ ......:, .,_+,'."I.._/
..........,,,. .... _ .......,_, :,_'.>;..:, _,I "_IV i",'%' ,'/' "':'::':'" _'_";;
15 l .5 l
THETA= (Tm-T)/(T_-Tj ) THETA= <Tm-T )/(Tm-Tj )
CO:. 64 _ J=2E 4 DR:2. 2
X/H=. 5 MR=. 24 TB= i__ I
FiEure 7
/ ":"'" _._E". 32 z/5 .,
'b:_,>',
B .5 1
THET_=(Tm-T)./(Tm-T.i)
CD=. g4 _ J:26. 4 OR=;', 2.
X/H=. 5 MR=. Z4 TB=. 19 I
CB=.64
138
ORIGINAIJ PAGE _S
OF POOR QUALITY


On the mixing of a row of jets with a confined crossflow

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