NASA Technical Reports Server (NTRS) 19910014889: Mixing of multiple jets with a confined subsonic crossflow. Summary of NASA-supported experiments and modeling

50 Pages·2.7 MB·English

by  NASA Technical Reports Server (NTRS)

NASA Technical Memorandum 104412
AIAA-91-2458
Mixing of Multiple Jets With a
Confined Subsonic Crossflow
Summary of NASA-Supported
Experiments and Modeling
James D. Holdeman
Lewis Research Center
Cleveland, Ohio
(NASA-TM-104412) MIXING oF MULTIPLE JETS N91-24202
WITH A CONFINED SUBSONIC CRDSSFLOW. SUMMARY
OF NASA-SUPPORTED EXPERIMENTS AND MODELING
(DiASA) 49 p CSCI 21E Unclas
G3/07 0017/68
Prepared for the
27th Joint Nopulsion Conference .............
cosponsored by AIAA, SAE, ASME, and ASEE
Sacramento, California, June 24-27, i99 i
N/ A

MIXING OF MULTIPLE J_"rsWITH A CONFINED SUBSONIC CROSSFLOW
SummaryofNASA-SupportedExperimentasndModeling
J_nes D. Holdmmm*
National Aeronautics and Space Administration
Lewis Research Center
Cievelmd, Ohio 44135
Abstract
Thispapersummarizesexperimenudandcomputational A/A
re_Itsonthemixingofsingled,oublea,ndopposedrowsof forcm-_e injeceon; (_)/((_Y9 _ m_
jets with an isothermal or variable temperature nminsueam in sideinjection
a confined subsonic crossflow. Xlm studies from which these
mealts came were performed to investigate flow _nd geomeCic C
variations typical of the complex three-dimensional flowfield
in the dilution zone of combustion chambeEs in gas turbine cd orifice discharge coefficimt
engines.
D orifice diameter
The principal observations from the experiments were that
the momentum-flux ratiowas the most significant flow vari-
able, and that temperature disUibutions were similar, indepen-
dent of orifice diameter, when the orifice spacing And the DR jet-to-mainstream density ratio Crm/Tj)
square-mot of the momentum-flux ratio were inversely pro-
lXXtiomL The experiments and empirical model for the mix- dH/dx duct convergence rate
ing of a single row of jets from round holes were extended to
include several variations typical of gas turbine combustors, effective ductheight; H0except foropposed rows of
namely vmdable temperature mainstream, flow area conver- jetswithconterlineisn-lines;eeAppendix
e
gence, noncircular orifices, and double and opposed rows of
jets, both in-line and staggered. All except the last of these duct height at tnje_on plane.
were appropriately modeled with superposition or patches to
the basic empirical model. Combinations of flow and geometry J jet-to-mainstream momentum-flux ratio (DR)(R) z
that gave optimum mixing were identified from the experi-
mental results. M jet-to-mainstream mass-flux ratio (DR)(R)
Based on the results of c,alculations made with a three- n number of holes around can; see Eq. (6)
dimensional numerical model, the empirical model was fur-
ther extended to model the effects of curvature and r radial coordinate
convergence. The principal conclusions from this study were
that the orifr, espacing and momenRun-flux relationships were R jet-to-mainstream velocity ratio (VfU m)
the same as observed previously in astraight duct, but the jet
structure was significantly different for jets injected from the Ra innerradius of curvaturein x-r plane
inner wall of aturnthan for those injected from the outer wall.
Also, curvature in the axial direction caused adrift of the jet inner radius of curvature at inlet in r-z plane
trajectories toward the inner wall, but the mixing in aturning
and converging channel did not seem to be inhibited by the S spacing between orifice centers
convergence, independent of whether the convergence was
or circumferential. The calculated jet penetration and Sx spacingbetween orificreows
mixing in an annulus were similar to those in arectangular
duct when the orifice spacing was specified at the radius T temperature
dividing the annulus into equal areas.
Tj jet exit temperature
*Senior Research Engineer, Aerothermochemistry Branch.
Member AIAA. Tm mainstreamtemperaRne
Copyright © 1991 by the American Institute of Aeronautics
and Astronautics, Inc. No copyright is asserted in the
United States under Title 17, U.S. Code. The U.S. Govern-
ment has aroyalty-free license to exercise all rights under
the copyright claimed herein for Governmental purposes.
All other riizhtsare reserved by the convrieht owner.
ORIGINAL PAGE IS
OF POOR QUBUTY
U velocity Srinivasan, Berenfeld, & Mongia (1982); Holdeman (1983);
Lipshkz&C-reber(1984); Holdeman, Srinivasan,&Berenfeld
Um mainstreamvelocity (1984); Wiuig, F..lhahar,&Noll (1984); Srinivasan, Coleman,
& Johnson (1984); Holdeman & Srinivasan (1984); Fenell,
vj jet velocity Almjalia, Busmnia, & Lilley (1984); Fenell, Aoki, & Lllky
(1985); Ferrell & Lilley (1985a,b); Srinivasan, Meyers,
Colemaa, & White (1985); Srinivama & White (1986);
•w/wm
Hokrema&n MeMumy&Uney(19s6y,
Ong &Lilley (1986); Lilley (1986); Ong, McMtmay, &Lilley
wj/WT jet-to-mud mass flow ratio; equilibrium e 0986); enay, &Lmey(1987);teym &White
(1987); Soldemn, Reynolds, & White (1987); Srinivasan &
w /wm White(1988); Holdeman, Srinivasan,&White (1988); Vranos
&_ (1988_, Sufit,nm,Breton, Seal,Mzqgm, &Mutthy
I + WjlW m
(1989); N'dtjcx_,Karki,& Mongla (1990); Dwenger (1990);
& Stevens (1990); Stevens & Canotte (1990=,b);
jet half-widthsoninjection(-) oropposite(+) side
Rlchards& Samuelsen(X990=,b,c);Smith(1990);Talpantimr
ofjet centedine;seeFig.5
& Smith (1991); Holdeman, Reynolds, Sdnivasan, & White
(1991), Talpallikar, Smith, Lid, & Holdeman (1991), Vranos
downstream coordinate; 0 atinjection plane
& Liscinsky (1991); Vranos, Liscinsky, True, & Hoideman
0991) andSmith,Tstt mikar&, Holdeman(199D.
cross-stream (radial) coordinate0;atwall;y¢ at
locationof minimum temperaturein a line
One facux making the combustor dilution zone jet-in-
X =constant, Z =constant
cmssflow application unique is that it is a confined mixing
problem, withfrom 10to50percent of the totalflow entering
lateral (circumferential) coordinate; Oateenterplane
throughthe dilution jets. The resdt is that the equilibri=n
temperatme of the exiting flow may differ significantly from
0 frm-T)/('rm-Tj); (1)
thatof the entering mainstream flow. To control or tailorthe
combnstor exit temperatwe patternit isnecessary tobe able
0c temperaturedifferenceradoat Yc
tocharacterize the exit distribution in terms of the upskeam
flow and geometric variables. This requires that the entire
minimumtemperaturedifference rado oninjection
flowfield be either known or modeled.
(-) oropposite(+) sideofjet centerllne;seeFig.5
Description of the Flowfield
Inlroduction
Figure I shows a schematic of the flow in a rectangular
The problem of jets-in-crossflow has been extensively
duct with injection from a row of jets on the top wall. The
treated in the literature, to the point that it can almost be
temperature field results are often presented as plots of the
considered a classical three-dimensional flow problem.
temperature difference ratio, O,where
Although studies to date have all contributed additional
undexstandingof thegeneralproblem, theinformationobtained
O= (Tin "T)
in them was determined by their motivating application, and
(Tm - Tj) (l)
may not satisfy the specific needs of different applications.
A sequence of three-dimensional oblique views of this
Considerations ofmixing ingas turbinecumbustion cham- parameter at several locations downstream of the injection
bers have, during the past two decades, motivated several plane is shown in Fig. 2. In these plots the temperature
studies on themixing characteristics ofjets injected normally distribution isshown (on the abscissa) in y-z planes normal
intoaconfinedcrosdlow. These arereportedin,e.g., Walker& tothe main flow direction, x. Theooordinates y andz are,
Kors (1973); Walker,Kors, & Holdeman (1973); Holdeman, respectively, parallel to the orifice centerlines and therow of
Walker, & Kors (1973); Kamotani & Greber (1973, 1974); orifices. Note thatthejet fluid isidentified by larger values of
Walker& Eberhardt(1975); Holdeman, Walker,&Eberhardt 0 (i.e.,0 =1 if T-Tj, and0-0if T-TIn). The equilib-
(1975); Cox(1975, 1976); Holdeman&Walker(1977); Bruce, rium 0 forany configuration is equal to the fraction of the
Mongia, &Reynolds (1979); Novick, Arvin, &Quinn(1980); total flow entering throughthe dilutionjets, w._/W.TBecause
Novick & Troth (1981); Lipshitz & Greber (1981), the objective inthisapplication was to identify dilution zone
Riddlebaugh, Lipshitz, & Greber(1982); Khan, McGuixk, & configurations to provide a desired mixing patternwithin a
Whitelaw (1982); Atkinson, Khan, & Whitelaw (1982); given com_ length, the downslream stations of interest
- 2
weredefmedinintervals of the duct height at the injection (1983) to illustrate theeffects of separately varying the inde-
location, Ho, ratherthanthe orifice diameter, D. pendent flow and geome_c variables and to identify the
relationships among them which characterized the mixing.
The orifice configurations discussed herein are shown in (Although it isrecognized thatauniform temperature distri-
Fig. 3. Theprimaryindependent geometric variables foreach butionmay not always bedesired, optimum isusedherein (as
of these are the spacing between adjacent orifices, S, the ine.g.,Holdeman &Walker, 1977; andHokieman,Sdnlvaum,
ogifice diameter, D (for noncircular orifices, llds is takenas &Bew.afeld,1984)midentifyflowand_ conditio._
the diameter of a circle of equal area),and, fog double rows, _dch leadt_ aunlfmmtemperaturedlstdlmt_ inamini-
theaxialspacingbetweenrows,Sx. Theseareexpressed in mumdownstwaundistance.)
dimemdomless form as theratio of the orifice q_acingtoduct
height, SM0, the ratio of the duct height to orifice diameter, Theresultsof theseinvestigations of the mixing orasingle
H0/D, and the ratio of the axial spacing to the ductheight, row of circularjets in a smdght ductmay be smnmarized as
S,/H_ fonows: (1) mixing imp_ovodwid__
distance; (2) the momentum-flux ratio was fonnd to be the
Thebasicgeometry fogthe turningandconverging ducts in most significant flow variable; (3) the effect of density ratio
the numerical and empirical studies reported by Holdeman, appeared to be small at constant momentum-flux ratio;
Srtnivasan, Reynolds, & White (1991) is shown in Fig. 4(a). (4)decreasingorificespacingatagivenmomentum-fluxratio
The duct convergence was identified by the ratio of the exit reduced penetration but increased lateral uniformity;
eross-sectional area to thatatthe jet injection location. The (5) increasing orifice diame_ ataconstanrtatio of splicing-
curvedsections inthe x-r planewere generated using circu- to-diameter (S/D) increased_ pene_tion O/N)), butago
lar arcs, and the curvature parameter was specified as the decreased lateraluniformity; (6) increasing orifice diameter at
inner radius of curvature of the duct normalized by the inlet aconstantorificeSl_Cing(S/Ho)increasedthemagnitude (_
ductheight, .Rcl/H0. Theradius of curvaaue ofthe innerduct the temperature difference, but jet penetration and profile
wall inthe r-z planeisgiven nondimensionally by itsratioto shape remained _ (7) lavfiles for conditions with the
the inletductheight, RtfrI0. momentum-flux ratio (J)and orifice spacing (S/Ho) inversely
coupled showed similar distributions over a range of
Curved and converging ducts aredefined byvalues of Rci momentum-flux ratios;(8) smal]e_momentum-flux ratios(and/
and Rt between zero and infmity (see Ha. 4(a)). Some orlargerorifice spicing)requiredaipeater downmeam dis-
limiting cases of interest areas follows: arectangularchannel tancefogequivalent mixing. Note fromthe lasttwo items that
isdefined if Rt and Rci areinfinite; acanresults if Rei is optimum mixing wasobtained fogany given orifice areawhen
infudteand Rt- 0;and anannularductresultsif Rc/ isinfinite the orifice spacing and momentum-flux were coupled, but
and 0 < Rt < infinity. A grid typical of those used in the thatagreater downstream distance was required fog equiva-
numerical turningductcalculations isshown in Fig. 4(b). lent mixing when either the momentum-flux ratio was small
ortheorificespacingwaslarge.
The primary independent flow variables were the jet-to-
mainstream density and momentum-flux ratios. Note thatthe The studies by Srinivasan, Berenfeld, & Mongia (1982),
latter isequal tothe ratio ofjet-to-maiusueam dynamic pres- Srinivasan, Coleman, & Johnson (1984), and Srinivasan,
sures, and the formerisequal tothe ratioofmal_-to-jet Meyers, Coleman, &White (1985) were performed toextend
temperatur_ if the jet static pressure is equal to thatof the the available experimental dataand emplrical correlations eQ
mainslream. Table 1gives the ranges investigated for both the thermal mixing of multiple jets in crossflow to include
the flow and geometric variables. Not all combinations ofthe geometricand flow variations characteristic of gas turbine
independent variables in the table were tested or analyzed; combustion chambers, namely variable temperature main-
only those combinations within the rangegiven forthe derived stream, flow area convergence, noncircular orifices, double
variables representconditions thatarewithin the rangeof the rows of holes, and opposed rows of jets, both in-line and
experiments and calculations performed. staggered. These experiments were anextension of those by
Walker & Kors (1973).
Chronology of Previous Studies of Confined Mixing
in aRectansular Duct The principal conclusions from the second tier of experi-
ments reported in Holdeman, Srinivasan, & Berenfeld (1984)
Fromthe dataof Walker&Kors (1973) formixing ofarow and Holdeman, Sdnivasan, Coleman, Meyers, &White (1987)
of multiple jets in a slraight duct, an empirical model was were: (1) the inverse relationship between the momenUun-
developed (Walker &Eberhardt, 1974; Holdeman &Walker, flux ratio and the orifice spacing was confirmed and quanti-
1977) tocalculate the temperature field downsCeam of arow fied;(2) atconstant momentum-flux ratio,variations indensity
ofjets injected into aconfmed crossflow. A microcomputer ratio hadonly asecond-order effect on the profdes; (3) flow
programbasedonthisempiricalmodel wasused byHoldeman area convergence, especially injection wall convergence,
3
significantly improved the mixing; (4) for odfr.es thatwc_e theyrarelyprovideenough information tocompletely describe
symmetric withrespect tothemain flow direction, the effects the flowfield.
ofshapeweresignificant only withinthefirstfewjet diameters
downstream from the injection plane; (5) penetration of slots Althoughtheexperimen_ results reportedby Lipshitz&
slanted with respect to the main flow direction was less than Greber (1981), Riddlebangh, Lipshie,, & Greb_ (1982),
for circular holes or slots aligned with, orperpendicular to, Lipshitz &_ (1984) andZizehnan (1985) haveprovided
themain flow; (6) temperaturedistributions downstream from considerable insight into the flowfield in the annular 180°
slantesdlotwsesem_ted andshiftehdterpllwyithrespectto cm_d duct_ mmm_ theaxltof6e omnlms¢_iodm inlet
the injection centerplane; (7)jet penetration from two- of thefirst stage tud>inein gas turbineengines ruing revegse-
dimensional (mntin_) slotswas _ tothatdownstream now,_stor metkumtiem, e_-ywm mt _e
from closely-spaced circular holes, except that temperatures enoughto define the flow inall threecoordinate directions as
in the wake behind thejet was signifieandy higher for con- would be needed toexu_l the empirical model.
tinuous slots; (8) afirst-orderapproximation tothe mixing of
jets with a variable temperature mainstream was achieved by Holdeman, Reynolds, &White (1987) stmmm'ized re0.flts
superimposing the upstream and jets-in-an-isothermal- the computations by iteynotds & White (1987) who
mainstream Wofiles; (9) at the same momentmn-flux ratio, used a _rce-dimenslmal, mdmlmt, viscom-flow computer
andwiththesame orificespacing(S/He), doublerowsof in-line code to investigate the effects of curvature and ccnverlpmce
jets had temperature distributions similar to those from a on the mixing of single and opposed rows of dilution jets.
single row of circularholes ofequal _ atthe same spacing; Basedon theseresults (Reynolds & White, 1987), the empiri-
(10) jets from double rows of orifices of different size Jnd modelrepemd by tto]deman,sztaivw_ cokman, &
spacing, orfrom double rows with orifices staggered, maybe White (1987) forthe temperature field downstream of single
approximated by superimposing independent calculations of and multiple rows of jets injected into a straight duct was
the two rows, but caution should be exercised using this extended tomodel theeffects of both axialandcigumfeeential
modelforvery smalloffsetsbetween therows;(11) forcppesed curvaturewith and without conveage.n_ (Srinivasan &White,
rows of.jets, withthe orifice centerlines in-line, the optimum 1988).
ratio of orifice spacing to ductheight isme-half of the opti-
mum value for single-side injection atthe same momentum- This extension of the empirical model addedthe capability
ratio; (12) for opposed rows of jets, with the orifice to investigate the effects of curvature while retaining all the _
centerlines staggered, the optimum ratioof orifice spacing to capabilities and limitations of the eat-fief versions. Also,
ductheightisdouble the optimum value forsingle-side injec- because the empirical model calculations (for dilulion jet
tion at the same momentum-flux ratio. mixing in straight ducts) shown by Holdoman & Srinivasan
(1986a) were ingenerally better quantitative agreement with
Inthe studies by Srinivasan, Berenfeld, & Mongia (1982), thedatathanthree-dimensioual numerical model calculations,
Srinivasan, Coleman, & Johnson (1984), and Srinivasan, theempirical model wnsextended tomodel thetnmds,butnot
Meyers, Coleman, & White (1985) the empirical model the quantitative results, from the numerical calculations.
reported by Holdeman & Walker (1977) was extended
Ololdeman & Srinivasan, 19861); Holdeman, Srinivasan, Flowfield Models
Coleman, Meyers, & White, 1987) tomodel the effects of a
variable temperature mainstream, fow area convergence, Empificol
noucircular orifices, and double rows of jets, both axially
staged and cpposecL Theempirical model for the temperaturefield downstream
of jets mixing with a confined _w is based on the
Empirical correlation of experimental datawere shown observation that,formost cases of interest, vertical tempera-
(e.g., Holdeman & Sfinivasan, 1986a) toprovide a good pre- ture profdes everywhere in the flowfield could beexpressed
dictive capability within the parameterrange of the generat- inthefollowing self-similar form(Holdeman &Walker,1977):
ing experiments, but empirical models must be used with
:
caution, ornot atall, outside thatrange. Physical modeling,
in various levels of sophistication and complexity, may be (oo-
used toobviate thisweakness. Inthisregard, several oneand
two dimensional integral and differential jet-in-crossflow
models have beendeveloped (e.g., NASA, 1969; Karagozian,
1986) and shown to give, forexample, trajectorypredictions (2)
thatare ingood agreement with experiments. These models
may provide insightintothedominantphysical mechanism(s),
and predict some of the characteristic parameters well, but
where 0 is the temperature difference ratioat vertical loca- calculations, inthe context of the effects of the primaryinde-
a± W± scaling parameters as pendent variables. The flow andgeometry conditkms corre-
tion y, and vmin, _, 0¢,and Yc are
sponding tothefigures shown aregiven inTable 1. Complete
shown in Fig. 5.
flow and gemztry conditions for the cases discussed are
Note thatFig. 5 shows injection from the.top (y/Ho=O) given inTables 2 and3 fortheexperimentaalndnumerical
studiesrespectively.Thecasenumbersshowncomspondto
towardan opposite wall (YMo= l) at the bottom. 0¢ isthe
maximum temperature diff_ ratiointhe vertical p_file, those inIxeviom mpom u noted.
and y¢ Isitslocation. Theline defined by thelocns of y¢ as
Singe Row of Orifices
a functioa ofdownsueam distance, x, for z =Oisthe d_mal
trajectory(contedine). Because the flow isconfined, andthe
Variations with orifice size andspacing.--At constant ori-
vertical profiles are not symmetric about the centerline, the
rice area, Changesin orifr_ size and spacing can have a
minimumtemperaturedifference (eL) m not zero,
significantinflueace onthe 6 dimilmeons. This isdxnvuby
aud they and the hslf-widths (W_) are different for the
the experimental profiles in Fig. 6 where jets from closely
injection (-) side (y<Yc)and theopposite (+) side(y >yJ of
thejet. Note also that Fig. 5andEq.(2) arethe samewhether spaced small odfr.es undet-peaeuate and remain near the
injection wall (lxrt a), and jets from widely spaced larger
the jets are hotter or cool_ than the mainslzemn, but that
orifices over-penetrate and impinge ou the opposite wall
T_iin > Tc &T when thejets are cooler.
(pan b). In this figure, a ductcross-section isshown to the
Coaelations have been developed foreach of these in temis left of the data. Note thatboth of these configurations have
the same ratio of orifice area to mainstream cross-sectional
of the independent variables J, S/D, H0/D, z/S, and x/H0,
plus RciH0 and Rt/H0 for curved ducts andaspect ratio for area
noncircular orifices. These aregiven inthe Appendix.
The dataforthese conditions at zfrI0" 0.5 arecompared
Numerical with calculated distributions in Fig. 7. The empirical model
reproduces the datavery well in the small orifice case, since
Thenumerical code used byReynolds &White (1987) was the data are consisumt with the major assumption in the
based on the USARTL three-dimensional model (Bruce, empiricalmodel thatallvertical temperature distributions can
Mongia, &Reynolds, 1979), andused pressure andvelocities bereduced tosimilarOanssian profiles. Theempirical model
as the main hydrodynamic variables. This code, or others does not doas well inthe largerorifice case however, as the
with similar capabilities, have been used inprevious valida- impingement of thejets onthe opposite wall resultsinvertical
tionand assessment studies reported bySrinivasan, Reynolds, profiles which arenot similar.
Berry, Ball, Johnson, & Mongia (1983), Kenworthy, Correa,
& Burrus (1983), Sturgess (1983), Mongia, Reynolds, & Thenuaua'icalmodel calculations made withapproximately
Srinivasan (1986), andHoldeman, Mongia, &Mularz (1988). 20 000 nodes, althoughinqualitative agreement with the data,
show temperature gradients that are too steep, especially in
Inthe numerical model used in the studies by Srinivasan, the uansverse direction. Under-prediction of the mixing was
Reynolds, Berry, Ball, Johnson, & Mongia (1983) and seen inthe single-jet calculations by Clans(1983) also, where
it was shown thatthe k-e type of turbulence model under-
Reynolds &White (1987), the governing equations were rep-
resented by finite difference approximations on a staggered estimated the intensity. The re.suitin Fig. 7 is typical of the
numerical model calculations shown inthis paper.
grid system. Hybrid differencing was used for convective
terms with centraldifferencing ofallotherterms. Thevelocity-
For the sanall-orifice case a coarse-grid calculation using
pressure coupling used the SIMPLER algorithm (Patankar,
1980). Uniform velocities, and mass flow rateswere speci- less than 6000 nodes was also performed. The numerical
fied at all in-flow boundaries. Standardvalues of the con- results inFig. 7 illustrate the significant influence gridselec-
tion can have on the solution obtained, and the smearing of
stants CD,C1,and C2 were used (i.e., CD=0.09, C_ - 1.44,
C2- 1.92). The RMS turbulence intensity was chosen to be the profiles which can occur because of numerical diffusion.
7.5 percent of the local mean velocity, the inlet lengthscale Even the fmer grid calculations by Srinivasan, Reynolds,
was 2 percent ofthe jet diameter and the ductheightforthe jet Ball, Berry,& Johnson(1983) andReynolds &White (1987)
andmainstream respectively, and the turbulentPrandtlNum- were notclaimed tobe gridindependent; in fact, latexcalcu-
ber was 0.9 for all calculations. lations by Claus & Vanka (1990) that used over 2.4million
nodes fora single jet-in-erossflow did not appearto be grid
Re_ult,sand Discussion independent. (Although the calculated coarse-grid profiles
in Fig. 7 are in better quantitative agreement with the
The following paragraphsdescribe the experimental results experimental data than the freer-grid solution, this result
and compare them with empirical and numerical model should be considered fortuitous.) In general, the finest
affordabgleridshouldbeusedunlesgsridindependenccaen At alldownstream locations, the profiles for symmetric
bedemonstrated.
convergence (Fig. 10(b)) are more uniform than the cone-
spoudlng straight duct Wofiles. An evm greater effect was
Couvled spacing and momentum-flux ratio.--It was observed when all of the turning was on the injection walL
observed by Holdeman, Walker, & Kors (1973) thatsimilar These profiles (Fig. 10(c)) aremuchmete unifmm inboththe
jet penetration was obtained over arange of momentum-flux uansvme and]atend directions. Although detalkd analysis
ratios, independent of ofifw_ diameter, when the odfi_ spac- _ not mdmakm, Hoidmm_ $dntmm_ md Betcafeld
ing and the square-root of the momenuan-flux ratio were (1984) hylx_l_bed that _ mixing in _verging
inversely _. ThisisapparentintheexperimenUd xaiom omld result from the mew.hl_ ot the straq dual-
datashown inF_g.8 fromtheexperimentsby Srinivaum, vortex field typ/cal of • jet-in-cnmflow (c.f. _o Stevens &
Berenfeld, & Mongia (1982) (see also Holdeman & Walker, Carrotte, 1988).
1977; Holdeman, 1983; Hoideman, Sriuivasan, & Bexenfeld,
1984). Forexample, low momentum-flux ratiosrequirelarge, Sqm_ ho_s.--A_e teswtm pe_med byS_dvmn,
widely spaced holes, whereas smallerclosely spacedholes are Coleman, & Johnson(1984) with the couventional circular
forhighmomenann-flux ratios,asshown inFig. 8. holes replaced with squareholes to identify the effect of this
The duct cross-section is shown to the right of the three- change in ¢rifiee shape ee the mixing. Sqea_ ed_:es were
dimensional oblique and isotherm contour plots for each chosen to represent the approximation often made in multi-
configuration. Note thatthejet penetrationand thecenterplane dimensional numerical modeling due to limitations ou the
profiles aresimilafror all cases,butthat the circumferential nmnber of grid nodes available. Figure 11_ three-
nonuniformity increases as the spacing increases. Itfollows dimensional obfique plots of the temperature distribution for
that for low momentum-flux ratios (large spacing) a greater equal-area sqnareandmund holes with SMo" Iand H0/D=4
axial distance is required for equivalent mixing. (The atintermediate momentum-flux ratios (slightly less than25).
experimental resultsinSriuivasan,Berenfeld, &Mongia (1982) Themean temperaturedistributions are nearlyidentical atall
suggest thatcircumferential nonuniformities (as inFig. 8(a)) downstream locations.
mix much more rapidlywith inc_g downstream distance
thando radialnonuniformities (such asshown in Fig. 6(a)). Slots and holes.--Figure 12 shows three-dimensional i
obfiqne Odisuibutions for equally spaced equiva_nt-_
Generally,jet penetration and centerplane profiles aresimi- streamlined, bluff, and slanted slots with S/Ho=0.5 andHot
lar when the orifice spacing and the square root of the D =4. These slots had an aspect ratio (length/width) of 2.8,
momemum-flux ratio areinversely proportional, i.e.,: with their major axes aligned with, perpendkular to, and
slanted at45° tothe mainstream flow direction. All profiles
C ffi(S/H0)_Y (3)
comparison shown in this figure are for intermediate
For single-side injection, the centerplane profiles are momentum-flux ratios.
approximately centered across the duct height and approach
an isothermal distribution in the minimum downstream dis- The streamlined slots (Fig.12(a)) have deeper jet penetra-
tance when C =2.5. This appears to be independent of tioncompared totheequal-area circularholes shown inFig. 2.
orifice diameter, as shown inb_th the calculated andexperi- Figure 12(b)shows that,for x/H0< l,jets from bluffslots are
mental profiles inFig. 9. Values of C in Eq.(3) which are moretwo-dimensional acrossthe orifice centerplane,andtheir
a factor of two or more smaller or larger thanthe optimum penetration isslightly less thanforstreamlined slots orround
_d to under-penetratiou or over-penetration respec- holes. Farther downslream, both of the slot configurations,
tively (see Figs. 6 and 7 and Table 1). A summary of the and the circular holes give very similar mixed temperature
ggtctng and momentum-flux ratio relationships for single- distributions.
side injoction isgiven inTable 4.
Figure 12(c) shows the temperature distribution thatresults
Flow area convergence.--The effect of flow area conver- when the same slotisslantedat45°tothe mainflow direction.
gence onthetemperatureWof'flesfor S/H0=0.5and H0/D- 4 The three-dimensioual figures suggest thatthe asymmetry of
with J- 26isshown inFig. I0. Theprofiles inFig. 10(a) are the orifices with respect to the main flow directicmpromotes
fromthestraightduct,whereas those inFigs. 10(b) and(c) are the development of one vortex of the pair,but_ the
fortestsections thatconverge symmetrically andasymmetri- other. Thepenetration of the jets is noticeably _ for
cally, respectively, to one-half of the injection plane height, this case, and the mixing does not appear to be any better.
H0,inadownstream distance _ to H0(i.e., dH/dx =0.5). Thus, theredoesnotseem tobeany advantage tothisceafigu-
Note thatthe ordinate in these figures isnondimensionalized ration in a rectangular duct, at least at the optimum orifice
bythe local height of the duct,so the gradients areless steep spacing and momentum-flux ratio relationship for round
thanthey would be in physical space. holes.
6
Furtherinsight intothe mixing inthiscase isprovided by the Densiw mtio.--It was suggested by Holdeman, Walker, &
isotherm contours in Fig. 13(a) for circular holes and in Kors (1973) thatthe density ratio did not need to be consid-
Fig. 130>) for the 45° slanted slots. Note thatat the closest ered independently from themomentum-flux ratio. This was
location (x/H0=0.25) the isotherms for the flow from the confirmed over abroaderrange ofdensity ratios intheexp,-
slanted slots are inclined compared to those for jets from meritsby Srinivasan,Berenfeld, &Mongla (1982). Theresults
circular holes. The influence of the adjacent image vorticies from these expedme_ inFigs. 17and 18sbow the effect of
in this flow would be to laterally shift the jet ceaterplanes abedmsity ratiom the Odism3aaiom for (marly) matebed
with increasing down.qream distance, as can be observed in jet-to-ma_ velocity, mass-flux, and momentum-
both Figs. 12(c) and 130>). Comparing the contours at flux ratios. Tbe I_ftles tnFig. 17arefor anodflce configu-
XlH0=0.5 tothose at x/H0=0.25 suggesttshatthe distribu- ratica with S/H0=0.5 sad HoB) =8 (plate A inPig. 3) for
tion hasrotated fartheraswell as shifted. Thisalso supports thr_ different flow conditions. For each of these, prof'des
the observation made from the oblique plots thatthe vorticies are shown at downstream distances of x/I-lo-0.5, l, and 2
_ to beof unequal suength. from left to tight. _ Im3ffles in Pig. 17(•) are for hot
jets and an ambient temperature mainstream, whereas
Figure 14 shows experimental and calculated those in partsb and c are for ambient jets and • heated
three-dimensional oblique 0 distributionsforslanted slots at mainstream.
intermediate momentum-flux ratios. The empirical model
calculations includeamodification toaccount forthe observed In Figs. 17(a) and 0>)the momentum-flux ratios arenearly
centerplane shift, butdonotmodel theasymmetry (Holdeman, equal and the profdes arequite similar alflmugh the density
Srinivasan, Coleman, Meyers, &White, 1987). Incontrast to ratio is 0.65 in Fig. 17(•) and 2.2 inFig. 170>). The slightly
this,boththe mmslation androtation ofthe mixing patternare smaller 0 levels in 17(a) result from the smaller jet-
apparentinthe numerical calculations, althoughthe gradients to-mainstream mass flow ratio in the case of hot jets. In
inthese appear tobetoo steep asarethose inalmost allof the coneast, theprofilesinFig. 17(c)show ove:-peneeation, which
numerical calculations shownherein. appears tobe the result of an almost quadrupledratio of the
jet-to-mainstream momentum-flux. Note, however, that the
Inthesame study,a limitendumber oftestswereper- jet-to-malnst_vme_locity ratios, R. are about the same for
formedwithtwo-dimensionasllotsinplaceoftherow of thehot-jets andambient mainstream case shown in 17(a), and
discreet orifices. Figures 15(a) and 16(a) show.the results for, the ambientjets and hot mainstream _ in 17(c).
respectively, a wide continuous slot (Aj/Am=0.I) ata low
momentum-flux ratio (J- 6.7) and a narrowcontinuous slot Figure 18shows • similar compadscm for an m-ifice plate
(Aj/Am=0.05) at a high momentura-flux ratio (J= 105.4). with thesameratiosoforifice spacingtoductheight(S/HO)but
Distributions for closely spaced (S/D ,-2) circl_lar holes are with largerholes. Thehotjets and ambient mainstream case
shown in Figs. 150>)and 160>),and centerplane profdcs for and ambient jets and hot mainstream case in Figs. 18(a) and
the circular andcontinuous slot jets areshown in Figs. 15(c) 0>),respectively have nearly equal jet-to-mainslream mass-
and 16(c). The similarity inthe penetration shown by these flux ratios, M, but note that the jets in Fig. 180>) do not
profiles is surprising, since the two-dimensional slot flow penetrate nearly as far into the mainstream apparently as a
completely blocks the maintoP, whereas the discreet jetflow result of their lower momentum-flux ratio. Theexperimental
ishighly three-dimensional. Inthe latter case the mainslream profiles foracase with aheated mainstream flow, butwith a
flow isdeflected around,aswell asover, the jets, creating the slightly smaller momentum-flux ratiothanthatforthehotjets
well known vortexpairand kidney shaped mixing pattern. case inFig. 18(•), isshownin Fig. lO(a)here andinFig. 50>)
The increased blockage in the slot-jet cases result in less in paper AIAA-90-1201 (see Holdeman, Srinivasan, and
mixing and higher temperatures inthe wake region of these Berenfeld, 1984).
flows compared toequal-area closely-spaced holes.
Variable temperature matnsueam.--The influence of a
Experimental profiles for the narrow slot at intermediate nonisothermal mainstream flow on the profdes forintermedi-
momentum-flux ratiosare similar tothose shown inFig. 15(a) atemomentum-flux ratioswith S/Ho =0.5, Ho/D =4isshown
for the wide slot ata low momentum-flux ratio, and profiles in Fig. 19. The isothermal mainstream case is showninthe
for the wide slot at an intermediate momentum-flux ratio are toprow. Inthe center row inthe figure, the upstreamprofile
similar to those shown in Fig. 16(a) forthe narrow slot at a (left frame) is coldest nearthe injection wall, whereas in the
high momentum-flux ratio(Srinivasan, Coleman, &Johnson, bottom row, the upstream profde Oeft frame) is coldest near
1984). Thecorresponding circular hole cases arealso similar, the opposite wall. In thisfigure, the hottest temperatareinthe
as expected since thecorresponding values of C =(S/H0)(_) mainstream for each case was used as Tm in the definition
are also similar. of 0.
7
Experimenteaml,piricaal,ndnumericarelsultfsorthe top- The influence of theleading row onthe temperature distri-
coldcase areshown inFig. 20. Theempirical calculations are butionsisevident inFig. 21(o")also, where distributions from
from a supeqxe;ition of the upstream prot'de and the corre- a double row of staggered jets (Sx/H0=0.5) is shown for
sponding jets-in-an-isothermal mainsCeam distribution comparisonwiththeotherco_guradons. Thejetsfromthe
OIoideman, Srinivasan, & Berenfeld, 1984). Although this leading row penetrate fardgr acroa the duct than do those
gives a good fL,'St-orderapproximation, itshould benotedthat bornthe single row, as would be expected due totheirlarger
•with • variable temperature mainstream there can be cross- qa_g, buttbepew_ratinaofthejm fromthemuli_ rowis
mmun thermal transportbecause of the flow of nudnseeam mppmmd, ixob_y bythevomx fieldfromtbeleadingrow.
fluidarcumi thejets (and heace todifferent y locations), and l_rther downsmmn thisdisu-tbuflm wu _ni_r mthatfmm
this is not 4_x.ounted for in superimposing the distributkms. asinglerow atono-half the spacing oftbe lead row. This flow
This becomes apparent if the local mainstream temperature, was modeled empirically by superimposing separate calcula-
T.(y), isused in the definition of 0 in Eq.(1). tions of each tow, butnote that this appmac.h significantly
ovcffiestimates the jet peaetration for very retail axial dis-
Inthe variable temperaturemainstream case the numerical lances, Sx/Ho,between the rows (see Ho_ &Sriniv_n,
model results agree well with the experimental data, espe- 1986b).
cially on the jet centerplane, but the Iransver_ mixing is
under-predicted, as in the corresponding isothermal main- Oooosin_ Rows of Jets
stream case shown in Fig. 90>).
Tae next three sections show results for _ injeetioa
Double Rows of Holes from_rowsofjets, witlz (1)thejet centettines ontop
and bottom directly opposite each other; and (2) the jet
Figure21 shows three-dimensional oblique and isotherm centerlines on topand bottom staggered in the z (_er-
contour plots at x/I-I0- 0.5 for a single row Ofroundholes ential) direction. The experimen_ results are shown and
and several equal-area double-row circular bole configura- compared with the single-side results in Figs. 24 and 26. In
tions atintermediate momentum-flux ratios. The single row these figures, aductcross-section isshown toscale tothe left
(configuration CinFig. 3)isshown in Fig. 21(a); flow down- of the data.
stream from two rows of orifices with centerlines atignecl
(configuration M) is shown in Fig. 210>); two rows of jets Opposed rowsof in-line jets.--Figure 24shows acompari-
with adifferent hole diameter andspacing in each row (con- son between single-side and opposed jet injection cases for
figuration N) areshown in21(c); andastaggered double-row intermediate momentum-flux ratios. For these momentmn-
(configuration O) is shown in Fig. 21(d). Forthe double row fluxratios, anappropriate orifice spacing to ductheightratio
cmfigurations, x/H0=0 was midway between'the rows. for optimum single-side mixing is approximately 0.5 (see
Eq.(3)), as confirmed by the profiles in Fig. 8.
Figure 22 shows both experimental and calculated tem-
perature distributions for a double row of in-line holes (Sx/ Foropposed jet injection, withequalmomentum-flux ratios
H0=0.5). Itwas observed from the experimental profiles in on both sides, the effective mixing height is half the duct
Holdeman, Srinivasan, Coleman, Meyers, & White (1987) height, based on the result in Kamotani & Greber(1974) that
that the two configurations have very similar temperature the effect of an opposite wall issimilar to thatof the planeof
dis_butions, and thisisseen in thecalculated profiles aswell. symmetry in an opposed jet configuration (c.f. also Wittig,
In this case the empirical model calculations arederived by Elbshar, & Noll, 1984).
superimposing the distributions from the two rows.
"Innstheapwowiate orifice spacing toductheight ratio for
Bothexperimental andcalculated temperature distributions opposed jet injection at these intermediatemomentum-flux
areshown in Fig. 23for adouble-row configuration with Sx/ ratios would be about SMo =0.25. Dimensionless tempera-
H0 =0.25 wherethe trailingrowhastwice as manyorifices as ture dis_butions downstream of jets with this spacing are
the lead row. Note that the orifice areais the same for both shown in the bottom row of Fig. 24; and the two streams do
rows. "l'nesimilarity inthe profiles sbows the dominance of indeed mix very rapidly. Note that since the orifices in
the leadrow inestablishing thejet penetration andfLrst.order Figs. 24(a) and 0>)are the same size, the jet to mainstream
profile shape (Holdeman, Srinivasan, Coleman, Meyers, & flow ratio isfourtimes greater inthe opposed jet case thanin
White, 1987). The same conclusion is supported by the the single-side case. Ifit isdesired to maintain an equal flow
empiricalandnumerical calculations. As with the double row rate, the orifice diametermust be halved, since there is injec-
of in-line holes, the empirical calculations forthis case were tion from both sides, and the opposed jet cases requiretwice
obtained by superimposing separate calculations for the two asmany boles in the row comparedtothe optimum single-
side case.
rows.