630 J. AIRCRAFT VOL. 13, NO. 8

Predicting Exit Temperature Profile from GasTurbine Combustors

George B. Cox Jr.*Pratt & Whitney Aircraft, Florida Research and Development Center, West Palm Beach, Fla.

An analytical model has been developed for predicting exit radial temperature profile from gas turbine engineannular primary combustors. The model assesses the effect of changes in dilution or cooling air distribution,changes in combustor aft end geometry, or changes in combustor operating conditions. The description of thedilution air mixing process includes the effects of mixing in confined flows, closely spaced dilution jets, andelongated dilution ports, the interaction of opposing rows of dilution jets, and the effect of flow area con-vergence, including nonsymmetric convergence. The cooling air mixing process description includes the effectsof combustor turbulence, multiple louvers, and flow area convergence. Comparison of measured exit tem-perature profile shifts, with the predictions of the analytical design system, shows good agreement in predictingthe effects of both dilution and cooling air shifts within the combustor aft end.

NomenclatureA =areaC = coefficientD = diameterH = height/ — momentum flux ratioM = blowing parameter (mass flux ratio)S = spacing, gapT = temperatureV = velocityW =flowrateX — downstream distanceY = penetration distanced —exit temperature profile = local minus exit average

temperature7 = heat/momentum diffusivity ratiop = density<t> = temperature profile thickness

Subscripts

ADWBCCACSCENTdDAEQFSIDJfMMaxMidODP

-- adiabatic wall= burner front-end= thermal penetration centerline= cooling air= coolant supply= center plane of dilution port^discharge= dilution air= equivalent= freestream= inner diameter-jet= louver= turbulent mixing= maximum= mid-way between dilution ports= outer diameter

Submitted September 29, 1975; presented as Paper 75-1307 at theA1AA/SAE l l t h Propulsion Conference, Anaheim, Calif., Sept. 29-Oct. 1, 1975; revision received November 26, 1975.

The author wishes to thank T.A. Trovillion for his assistance in for-mulating many of the procedures used in the design system; and J.E.Smith, for his help in writing the computer programs used in thedesign system.

Index category: Airbreathing Propulsion, Subsonic and Supersonic.*Senior Design Engineer, Analytical Design Department.

ST = staggeredT = totaloo = infinite or freestream condition

Introduction

CURRENT and future aircraft gas turbine enginesoperate at high turbine inlet temperatures in order to

operate at high engine bypass or compression ratios. Thisgives higher specific thrust (thrust per unit inlet airflow) andlower engine specific fuel consumption (fuel consumption rateper unit thrust or power). Typical average turbine entry tem-peratures for current (1975) high bypass ratio commercial air-craft engines or high thrust/weight military engines are at the1400°C level. Consequently, increasingly stringent limitationsare placed upon the temperature profile at the entrance to theturbine, as shown in Fig. 1. Hot-gas temperature profilesmust be matched carefully to the turbine blade stress levels iflong turbine life is to be attained. For example, an increase inhot-gas temperature at a particular radial location on the tur-bine first blade of as little as 28 °C can either reduce the life ofthe blade by half, or require an additional- !/2°7o engine air-flow for turbine cooling, to maintain acceptable blade life.Each 1% additional turbine cooling air can, for example,decrease takeoff thrust by as much as 214 %.

Historically, the process of designing and building a gasturbine engine primary combustor has always involvedguesswork and resulting costly development testing to achievethe desired exit temperature profile. This development testingwas required because the analytical tools to describe thevarious air mixing processes within the combustor were at bestrudimentary.

<

DESIREDPROFILE

LIMIT FOR VANE

EXCEEDING DESIREDPROFILE HURTS LIFE

BLADE LIFE X

LIMIT(S)FOR BLADES

TEMPERATUREFig. 1 Turbine life limits set radial profile requirements.

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 12,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/3.5

8694

AUGUST 1976 EXIT TEMPERATURE PROFILES FROM TURBINE COMBUSTORS 631

100

80

PERCENTVANESPAN 40

20

PRIMARYZONE EXITDILUTION- — —

_ AFT ENDCOOLING —"™COMBUSTOR__

_ EXIT

-300 -200 -100 0 +100 +200 +300

TEMPERATURE DEVIATION FROM AVERAGE - °C

5.1 cm

Fig. 2 Temperature profiles contributing to turbine inlet profile.

DILUTION PORT (£

Fig. 3 Dilution zone mixing study test section geometry.

This paper describes a method of predicting the gas turbineengine primary combustor exit temperature profile by predic-ting the temperature profiles produced by all of the air ad-mission processes. The approach limits the analytical descrip-tion to the aft end, or dilution zone, of the combustor. The aftend is considered to be the portion of the combustor betweenthe leading edge of the dilution holes and the exit of the com-bustor. Newly developed correlations for describing themixing of the dilution air1 '2 form the basis of the analyticalmodel. These correlations are combined with anothercalculation procedure which determines the contribution ofthe aft end liner cooling air. An additional contributor to thecombustor exit temperature profile is the temperature profileentering the dilution zone from the primary zone. Figure 2shows, on a representational basis, how the profiles fromthese separate processes combine to form e.g., the combustorexit radial average temperature profile.

Conceptual FormulationThe generation of the detailed Aft End Design System

(AEDS) followed a building-block approach. Each step in thedesign system is based on a set of empirical correlations whichpredict one aspect of the dilution and cooling air mixingprocesses. The temperature profiles resulting from each of thetwo air-admission processes are calculated independently. Thefinal step consists of combining these separate profiles intoone combustor aft end exit temperature profile.

The primary-zone exit temperature profile is treated deduc-tively. The analytical model uses measured combustor exittemperature profile data to derive a primary zone exit profile.This deduced profile is then resubmitted to the design systemin order to predict combustor exit temperature profile shiftsresulting from changes to the combustor aft end geometry orto the combustor operating conditions.

Sources of Data for Analytical CorrelationsSingle-Row Dilution Jet Mixing

The National Aeronautics and Space Administrationfunded an experimental test program (NASA Contract NAS3-15703) to supply the data needed to describe the dilutionprocess by a single row of closely spaced dilution jets.3 Asingle row of closely spaced dilution jets was used to.injectambient-temperature air into a heated crossflow confinedwithin a rectangular duct.

Major operation point variables were the diluent jet-to-mainstream density ratio and the diluent jet-to-mainstreamvelocity ratio. These in turn give the momentum flux ratio

(1)

Geometric variations were obtained by varying the dilutionport diameter, D, and the spacing of the ports in the row, Sp.

These in turn describe the geometry in terms of the ductheight-to-port diameter ratio, H/D, and the port spacing-to-port diameter ratio, SP/D. The range of geometric variablesand the experimental operating points are representative ofcurrent design practice for Gas Turbine Engine (GTE)combustors.Dilution-Zone Dilution Jet Mixing

Generation of the procedures for describing the mixing ofopposing rows of opposed or staggered dilution jets, in amixing section with a converging cross-sectional flow area, isbased upon the test data from another NASA test program.4

Figure 3 illustrates the configuration of the test section. Thetest section featured a rectangular inlet section whichdischarged -heated air into a converging mixing section. Themixing section, in turn, discharged into a rectangularmeasurement section. The convergence, as shown by Fig. 3,was not symmetric. One wall remained straight, and the entireconvergence was formed by the opposite wall. Temperaturedata for the experimental test program were taken using afixed thermocouple array.

Dilution air was injected through a series of in-terchangeable orifice plates located at the start of the con-vergent mixing section. The orifice plates used rectangular in-jection slots, and were built so as to be able to test eitherstaggered or directly opposed dilution jets. Testing used a farmore limited range of dilution injector geometries than didthe test program in Ref. 3.

The major flow variable for the test program was thedilution jet/crossflow velocity ratio; the density ratio wasconstant at approximately 2. The range of velocity ratio testedincluded mostly values which were lower than typical GTEdesign practice. Only one test condition for each geometry ex-ceeded the minimum velocity ratio required, which is 2.5.Cooling Air Mixing

There are only a few sources of data that deal with the gastemperature profile downstream of a louver cooling slot. Theapproach taken was to link an approximate profile with themuch better documented cooling efficiency data. The mainassumption made is that the profile is Gaussian. This has ex-perimental justification in the work of Wieghardt.5'6Although the experimental data were taken under less severeconditions than are found in combustors, this appears to be areasonable approximation. Also required is some velocityprofile associated with this temperature profile. This wasfound in the work of Reichardt,7'8 who derived a semiem-pirical relation between the velocity and temperature profileusing the ratio of coefficients for heat and momentumtransfer. This gives a velocity profile which is Gaussian buthas half the width of the temperature profile.

This leaves only the wall value of the temperature profile tobe determined. A correlation derived by Juhasz and Marek9

proved to give satisfactory results and was simple to use.Their experiment was done under conditions similar to those

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 12,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/3.5

8694

632 G.B.COXJR. J. AIRCRAFT

found in combustors, which set it apart from numerous ex-periments done under low turbulence wind tunnel type con-ditions. The change in turbulence conditions made markedchanges in the value of their mixing coefficient.

A report by Carlson and Talmor1() considers the effect ofturbulence level and mainstream hot-gas acceleration on thedecay of the film cooling under conditions like those found incombustors. Both these effects are important in combustors,but the correlating parameter used is very complicated and ex-tremely difficult to use. It also did not lend itself to program-ming and so was used as a check of the Juhasz and Marekcorrelation.

Dilution Jet Mixing AnalysisCorrelation of experimental data on the mixing of single

rows of closely-spaced dilution jets is based upon the ex-perimental observation that the vertical temperature profilesat all axial and transverse locations are Gaussian in shape.They can be expressed in a self-similar form by the properchoice of scaling parameters. The procedures for correlatingand predicting the vertical temperature profile scalingparameters as functions of geometric and flow variables, andtheir applicability under conditions typical of gas turbineengine primary combustor design practice, have been reportedpreviously.1'2 By themselves, these correlations cannot bedirectly applied to a workable annular combustor dilutionzone design system.

First, the correlations were derived from test data usinground dilution ports/Elongated dilution ports are commonlyused in gas turbine combustors, and some procedure must bederived to analyze their effect. Contrary to previous ex-perience with single, elongated dilution jets, closely spaced,elongated dilution jets were found to have reducedpenetration compared with round ports of the same area.3

Second, many gas turbine annular combustors inject dilutionair through both the inner and outer liners, with the jetsmeeting in some fashion within the combustor. Third, thecombustor annular height required for good ignition and ef-ficient combustion is usually larger than the turbine inlet an-nulus height, and so some degree of flow area convergence isrequired.

Corrections for Elongated Dilution PortsThe procedures for correcting the calculated temperatures

from single rows of dilution jets for elongated dilution portsuse an equivalent jet diameter defined by

DEQ=(4Ap/ir)[

with

(2)

(3)

This equivalent jet diameter is substituted in all the correlatingequations in place of the jet diameter for round dilution ports.Many of the correlating equations require additional correc-tion using correlations of the form

Corrected quantityUncorrected quantity

(4)

where F and /are functions of the dilution port aspect ratio.The ratios of the corrected to uncorrected correlatingparameters to reduce to identical unity for round ports (aspectratio of 1). These correcting functions are based upon testdata from the NASA-sponsored test program.3

Correlation Procedures for Opposite-Wall InjectionAnnular combustors used in gas turbine engines

customarily inject the dilution air through both the inner andouter liners, although burners have been tested successfully

MOMENTUM-BALANCESPLIT PLANE(FICTITIOUS WALL)

PENETRATION-CORRECTEDSPLIT PLANE

I OD

Fig. 4 Correction for opposite-wall injection.

using dilution air injected through one liner only. Theprocedures, which predict the temperature field produced by asingle row of dilution jets, must be adapted to predict the tem-perature field from rows of dilution jets injected through op-posite liners in the burner.

The mutual interaction of dilution jets, which enter the bur-ner through opposing, single rows of multiple jets, requiresthe treatment of three separate aspects of behavior. First,penetration of each row of jets restricts the distance to whichthe other row can penetrate, and thus results in each row ofjets being influenced by an equivalent height, HEQ, which isless than the total height, //. Second, the jets from opposingliners can be either directly opposed or staggered with respectto jets from the opposite liner. Third, the temperature fieldsproduced by each row of jets must be combined in such a wayas to give an overall temperature field which is close to theaverage temperature.

Equivalent Height FormulationFor the particular case of two equal-strength directly op-

posing single jets, the plane of symmetry between the two hasbeen shown to have the same effect as an opposite wall at thesaine location.n This observation leads to the followingprocedure for analyzing directly-opposing multiple jets: 1) theplane of symmetry between the opposing jets acts as an op-posite wall at the same location, and 2) the location of this fic-titious wall within the burner is obtained by a momentum fluxbalance between the opposing multiple jet rows.

For opposing jet rows, wherein the individual jets arestaggered with respect to the jets from the opposing rows, theprocedure as given above must be modified. Figure 4 shows atypical contour plot of the temperature field from a single rowof jets at a particular axial location. The penetration distancefor a particular isotherm is, as expected, greater in the jet cen-ter plane-of symmetry. A jet from one row will thus see agreater equivalent height than if it were penetrating into thejet center plane-of-symmetry of the jets from the oppositerow.

The procedure selected to handle this equivalent heightbegins by defining an effective height for directly opposedjets. It then defines two additional increments to the effectiveheight, based upon the ratio of penetration between the jetcenter and midspan planes-of-symmetry, for a particularisotherm or penetration parameter.

The equivalent heights for opposed jets are given by

ff\r> = -

HOD = '

( A j J ) l D + (AjJ)OD

(AjJ)OD

( A j J ) [ D + (AjJ)OD

x H

x H

(5a)

(5b)

Extension of this procedure to the case of staggered jetsfollows from the conceptual formulation previously outlined.

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 12,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/3.5

8694

AUGUST 1976 EXIT TEMPERATURE PROFILES FROM TURBINE COMBUSTORS 633

-0.04

RA

DIA

L LO

CA

TIO

N S

PA

N -

% ^

NJ

JS.

O)

00

Co

o

o

o

o

c

9 MEASURE

x*"^OPPOSED JETS

D TEMPERATURES ̂

——— --

b INLET

.^

1

^^ V-CALCULATED• T E M P E R A T U R E

ppncn c

/EXIT AREA 3ATIO = 2.25

0.04

Fig. 5

-0.02 0 0.02DIMENSIONLESS TEMPERATURE PROFILE

Substantiation for opposing rows of dilution jets, and for

100

2 80<

|60h-

840

< 20Q<c o

STAGGERED JETSMEASURED TEMPERATURES

INLET/EXIT AREA RATIO = 2.25

-0.04 -0.02 0 0.02DIMENSIONLESS TEMPERATURE PROFILE

0.04

converging flow area.Fig. 6 Substantiation for opposing rows of dilution jets, and forconverging flow area.

Temperature Field CombinationThe procedure for combining the separate temperature

fields produced by the opposing rows of dilution jets, whichwas found to give the best results, involves first thecalculation of each separate temperature field. For directlyopposed jets, the region occupied by each temperature fieldextends from the liner from which the jets entered, up to themomentum-balance fictitious wall. The separate fields areplaced together with the dimensionless temperature ratio atthe fictitious wall obtained by averaging. For staggered jets,the temperature field for each row of jets is calculated overthe entire burner height. The jets are assumed to overlap bet-ween their respective centerlines, and the dimensionless tem-perature ratios in the overlap region are obtained byaveraging. Outside of this overlap region, the dimensionlesstemperature ratios are those of the respective jets.

Calculation Procedures for Flow-Area ChangeMost gas turbine engine primary combustors have some

degree of flow-area convergence, from the inlet to the dilutionzone, to the inlet to the turbine. Two major effects are seen.The first results from the acceleration of the flowfield as theflow area is decreased. The length of time the mixing gasesremain in the burner is less than if the flow area were con-stant, hence, less mixing will occur. Further, the assumptioncan be made that both the hot and cold streams will be ac-celerated uniformly once the jets enter the hot-gas flowfield.This latter assumption results in the determination that thecontrolling momentum flux ratio, for calculation purposes, isat the plane of dilution jet injection. The second is the effectof nonuniform convergence is that, the case wherein one wallof the burner has a greater flowpath change than the otherliner.

The appropriate means by which to determine the effect ofaccelerating flowfield has been found by defining anequivalent mixing length, XEQ, which is the volume of theburner between the dilution jet inlet plane and the burner exitplane, divided by the burner cross-sectional area at thedilution jet inlet plane. This definition of an effective lengthhas been used with success in performance calculations formixing-limited rocket engine combustion chambers. The tem-perature profiles at the exit of the combustor are obtained bynondimensionalizing the vertical (or radial) locations at theheight at the combustor inlet plane.

The effect of a nonuniform convergence considers the non-symmetric turning of the cross-flow to be reflected in a dif-ferent equivalent burner height for each separate row of jets.These different equivalent heights depend upon whether theOD or ID jets are those which see the greatest amount ofconvergence.

SubstantiationComparisons between experimentally measured and

anlytically predicted dimensionless temperature ratios areshown as transverse averages, plotted in the form of locally

measured (or calculated) values, minus the average dimen-sionless temperature ratio.

Figure 5 shows a comparison, using the data of Ref. 4, forthe case of directly opposed dilution jets. Although equalamounts of diluent were injected through each liner, the exittemperature profile is nonsymmetric because of thenonuniform convergence of the test section. The analyticalprocedures accurately assess the effect of this nonuniformconvergence and give a predicted profile in good agreementwith the measured data.

Figure 6 shows a comparison for the case of staggereddilution jets. Again, the exit dimension temperature profile isnonsymmetric, and the analytical profiles reflect this non-symmetry.

Cooling Air Mixing AnalysisSingle Slot Analysis

To obtain a gas temperature profile from a single louvercooling slot, the following procedure was developed to give asemiempirical approximation. The main assumption made inthis procedure was that the profiles downstream of the louverwere all of the same Gaussian form

T-Tk7\nw — 7 =exp -(-Y]

4 \ 6 > J(6)

To determine the temperature of the profile (7) requires thatvalues be found for the adiabatic wall temperature (7"ADW)and the temperature profile thickness ( < / > ) . To determine thewall temperature, the empirical film cooling correlation ofJuhasz and Marek is used.

(7)

To determine the temperature profile thickness, the assump-tion is made that the enthalpy under the profile remains con-stant from the initial conditions at the louver lip where theprofile is assumed to be a step function.

(8)profile enthalpy = I p ( Y ) V (Y) (T-TFS)dA

The density (p( Y)) is found by ratioing it to the freestreamvalue, which then becomes the inverse of the temperatureratio. An assumption is then made to relate the velocityprofile ( V ( Y ) ) to the temperature profile. Reichardt hasderived the following semiempirical relation for free turbulentconditions which is appropriate for the major part of theprofile

(9)

Here, the temperature and velocity scales are adjusted so thattheir zeros coincide. The ratio of heat to momentum dif-

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 12,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/3.5

8694

634 G.B.COXJR. J. AIRCRAFT

fusivity (7) has been experimentally determined to be about 2under turbulent conditions. This gives the velocity a Gaussianprofile with half the width of the temperature profile, but thevelocity at the wall, which is the maximum, is the one un-determined value. To arrive at this value, the assumption ismade that the mass defect in the profile is constant and thevelocity profile at the louver lip is a step function.

ivspanprofilemass= [p(Y) V(Y)-pFSVFS} dA

' J 0(10)

These assumptions and equations are then sufficient to deter-mine the temperature profile thickness. Combining theassumptions, the conservation equations are then solvedsimultaneously for the thickness and wall velocity.

The success of this profile prediction system depends on theprediction of the wall temperature by the film coolingcorrelation. In using the Juhasz and Marek correlation givenpreviously, it was necessary to modify it slightly so that theprediction of the wall temperature would not go below thetemperature of completely mixed flow. If it should, theprocedure would be unable to find a real profile width tosatisfy the equations. The following equation assumes that thetemperature at infinity in the correlation should be the com-pletely mixed temperature in the duct.

- 7>5 = / + (Wcs/ WB) CM(X/MS()*-7>s ~ 1 + CM(X/MS()

(11)

Correlation Procedures for Flow-Area ChangeThe preceding analysis neglects the effect of a converging

duct where the mass flux ratio (M) is changing with distance(X). All that is given,is that the mixing coefficient (Cm) hasa value of about 0.15 for turbulent combustor type con-ditions. By using the Carlson and Talmor correlation whichwill handle accelerating flow, it was found that the samemixing coefficient gives a good approximation if the massflux for the freestream, at the location where the profile iscalculated, is used in determining the mass flux ratio (M).Since the Carlson and Talmor correlation was difficult to useand did not lend itself to programming, this modified form ofthe Juhasz and Marek correlation was used.

Multiple-Louver Combined ProfilesThe above procedure gives a good profile for a single

louver. These must then be combined at the end of the com-bustor. The approach taken is to separate the profile intoseparate gases at freestream and coolant temperature. Theratio of the mass of these two gases at each point in the profileis given by

(12)

The assumption is then made that the mass of freestreamtemperature gas is the same at the same profile location for allthe profiles to be summed, and also that the ratio of the twogases is the same as in the original profile. The finalsummed profile is then found by

TCA = T>s- + ( TVs ~~ TV's ) , . v ,1 + L ((13)

This approach will not arrive at temperatures less than thecoolant temperature or greater than the freestream tem-perature. It is therefore a physically reasonable approach.

Since the profiles are to be summed after being calculatedindividually, the single calculations must ignore the con-tribution of the other louvers. Therefore, the temperature atinfinity used in the calculation of the profile from each slot isthe average exit temperature with the enthalpy from all of thelouver cooling air removed. But in the calculation of the mass

-0.20 -0.16 -0.12 -0.08 -0.04 0 0.04DIMENSIONLESS TEMPERATURE PROFILE

Fig. 7 Calculated combustor cooling air profile.

0.08

GEOMETRY ANDOPERATINGCONDITIONS

r^DILUTE

CALCULATES DILUTIONAIR TEMPERATURE

PROFILE

FORWARDCALCULATES COMBUS-

TOR EXIT TEMPER-ATURE PROFILE

COOLCALCULATES COOLING

AIR TEMPERATUREPROFILE

"

BACKWARDDEDUCES PRIMARYZONE EXIT TEMPER-

ATURE PROFILE

I1111

CALCULATEDPROFILE

USER - INVOLVED ITERATIONUSING TEST DATA

Fig. 8 AEDS computation flow chart.

flux ratio, the mass contribution of the other louvers isconsidered.

SubstantiationThe substantiation for the procedure used to derive the

cooling air profile is very limited. Figure 7 shows a calculatedcooling air temperature profile for representative combustorcooling airflows. A significant point of the analysis is thechoice of the mixing coefficient for the efficiency correlation.The value chosen for the coefficient has an important effecton the profile so that with the range of values possible there isenough variation to calibrate the prediction system to achievea reasonable profile for a general combustor. So far, a mixingcoefficient of 0.15 has given good agreement between predic-ted and measured profile shifts.

Design System SynthesisApproach

Formulation of the unified design system consists of com-bining the independently generated dilution air temperatureand cooling air profiles into the combustor aft end exit tem-perature profile. Procedures for calculating the contributionof the combustor primary zone to the exit temperature profileare not presently available. Combination of the dilution andcooling air profiles includes a way to deduce the primary zoneprofile contribution from test data.

Figure 8 shows the overall computation flow charts.DILUTE calculates the dilution air temperature profile;COOL, the cooling air temperature profile. These, in turn,supply their calculated temperature profiles to the finalcalculation procedure, herein lumped into a FORWARDpackage and a BACKWARD package.

The FORWARD package accepts the calculated dilutionand cooling air temperature profiles, plus a primary zone tem-perature profile contribution, and calculates the aft end exittemperature profile. The primary zone temperature profilemay be input as a constant value or as a deduced temperature

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 12,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/3.5

8694

AUGUST 1976 EXIT TEMPERATURE PROFILES FROM TURBINE COMBUSTORS 635

array. The constant value would be used at the beginning ofthe design process, before test data become available. Oncetest data are taken, they are used to deduce the primary zonetemperature profile contribution.

The BACKWARD package handles this process ofdeducing the primary zone profile contribution. It accepts asinput the calculated dilution and cooling air temperatureprofiles plus the measured combustor exit temperatureprofile, and returns the deduced primary zone profile con-tribution.

Calculation of Exit Temperature ProfilePreviously, all analyses were for rectangular ducts, and set-

ting the jet spacing was straightforward. In an actual annularcombustor having, for example, the same number of ID andOD dilution jets, the ID jets are physically closer togetherthan are the OD jets. The ID jets spread apart on penetratingoutward into the combustor. The OD jets converge onpenetrating inward into the combustor. Definition of the jetspacing for use in the mixing correlations is no longer ob-vious. The equivalent spacing for the ID dilution jets is basedupon an equivalent surface, area-weighted between the IDliner and the momentum-balance split plane. A correspondingdefinition holds for the OD jets.

The procedure used to obtain the combined, combustor exittemperature profile from the individually generated coolingand dilution air temperature profiles is the algebraic additionof the separate profiles. Because the cooling air in the aft endof the combustor is a small fraction, 14 or less, of the totalcombustor airflow, and because the cooling air is con-centrated near the combustor liners, the ''first-order" ap-proximation for the profile calculations neglects the effect ofthe dilution and cooling air upon each other.

For calculation of the dilution-air mixing, the first-orderapproximation uses a mixed temperature based upon the totalcombustor airflow, minus the aft-end cooling airflow. Thedilution jet temperature is the shroud air temperature. Thecombustion temperature of the combustor front end is basedupon the fuel/air ratio up to the leading edge of the dilutionslots and assuming 100% combustion efficiency at this point.For calculation of the cooling-air mixing, the first-order ap-proximation replaces the freestream temperature, TFS, by themixed temperature defined previously.

Algebraic addition of the separate profiles gives the com-bustor exit temperature profile about the mixed temperature.The combustor exit profile, relative to the turbine inlet tem-perature, is then obtained by adding the difference betweenthe mixed temperature and the turbine inlet average tem-perature.

SubstantiationSubstantiation of the Aft End Design System is based

upon comparison of predicted and measured profiles for alow bypass ratio military augmented turbofan and a highbypass ratio commercial turbofan. The substantiationprocedure, which was followed, was the same in both cases. Abaseline test was used to deduce the primary zone exit tem-perature array. This deduced array was then input, and the ef-fect of combustor dilution zone hardware changes was predic-ted. The predicted exit average radial temperature profiles arecompared with the measured profiles.

Military Turbofan TestingThe military turbofan testing was directed toward im-

provement of the exit average radial profile by shifts in thedilution air from the OD liner to the ID liner. The test shifted10% of the combustor air from the OD to the ID. Since thedilution air is roughly 40% of the combustor airflow, thisamounted to decreasing the OD dilution airflow, and in-creasing the ID dilution airflow by 50%.

Figure 9 shows the measured exit average radial tem-perature profile in the form of a dimensionless temperature

PREDICTEDTEMPERATURESAFTER CHANGE

I I

-0.18 -0.16 -0.12 -0.08 -0.04 0 0.04 0.08 0.12DIMENSIONLESS EXIT TEMPERATURE PROFILE

Fig. 9 Predicted profile shift from 10% dilution air shift on amilitary turbofan engine.

BEFORE CHANGE

AFTER CHANGE

A

5.1

3.7

B

3.5

3.7

C

.1.17

0.62

D

0.98

0.51

TOTAL

10.75

8.53

Fig. 10 Cooling air changes in a commercial turbofan engine.

for the baseline geometry. This profile was obtained fromTemperature Sensitive Paint (TSP) applied to the first-stageturbine blades, extrapolated back to combustor exit con-ditions. The combination of TSP measurements and ex-trapolation gives a temperature error band. This profile wasinput to the AEDS to deduce the primary zone exit tem-peratures.

Figure 9 also shows the comparison between the predictedexit average radial temperature profile and the measuredprofile band. Qualitative agreement is quite good. The AEDScorrectly predicts a profile peak shift toward the OD and anincrease in peak temperature. Quantitative agreement is alsogood. The greatest deviation between the measured andpredicted value is about 0.050, at the 36% span location. Theaverage deviation between measured and predicted tem-peratures is about 0.022.

The "notch" at the 36% and 64% span locations resultsfrom the mixing analysis procedures for the dilution airprofiles. Further improvements to the mixing analyses requireadditional development and better test data on the dilution airmixing process.

Commercial Turbofan EngineThe commercial turbofan engine testing examined the ef-

fect of changes in the cooling airflows through the final threeID and OD louvers, and in the turbine platform cooling air-flow. Profile changes were measured using instrumented first-stage turbine vanes. The changes in the airflow distributionare shown in Fig. 10. Figure 11 shows the measured exitaverage radial temperature profile for the baseline geometry.

Analysis of the exit temperature profile shifts was com-plicated by the geometry of the dilution injection ports on theOD liner. The combustor injects the dilution air throughdirectly-opposing rows of jets, with 40 jets/row on the ID and80 jets/row on the OD. The OD jets are in pairs, inlineaxially, and spaced approximately two hole diameters apart.Each pair of OD jets directly opposes an ID jet.

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 12,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/3.5

8694

636 G.B. COX JR. J. AIRCRAFT

PREDICTED TEMPERATURESAFTER CHANGE

-0.08 -0.04 0 0.04 0.08DIMENSIONLESS EXIT TEMPERATURE PROFILE

0.12

Fig. 11 Predicted profile shift from 2% cooling air shift on a com-mercial turbofan engine.

The AEDS, as currently formulated, cannot directly handlemore than one row of dilution ports per liner. However, Ref.3 reports that pairs of jets behave like a single row of portshaving the same open area and transverse spacing, formoderate-to-high momentum flux ratios.

This argument led to the replacement in the AEDS, of theOD dilution port pairs with a row of single ports, each porthaving the same total area. The single ports were located atthe same axial location as the upstream port in the pairs ofports. Figure 11 shows the comparison between the predictedexit average radial temperature profile and the measuredprofile following the change in combustor cooling air.Agreement is superb over almost all of the profile. This suc-cess is viewed as a confirmation of the validity of theprocedures describing the mixing of the combustor aft endcooling air, since the combustor modifications involve coolingflow changes only.

ConclusionsComparison of the analytical predictions of both the com-

ponent process analyses in the Aft End Design System and ofthe AEDS as a whole, with available test data, leads to thefollowing conclusions.

1)The procedures to predict the mixing behavior of op-posing rows of dilution jets, in geometries representative ofcurrent GTE design practice, give good agreement with thelimited amount of available data.

2) The procedures to predict the mixing behavior of thecooling air have no direct data substantiation under ideal con-ditons. The results appear to be qualitatively reasonable whencompared with profile shifts resulting from cooling airchanges in actual combustors.

3) The AEDS gives good qualitative agreement betweenpredicted and measured profile shifts resulting from dilutionor cooling air changes for a limited amount of testing. Betterqualitative agreement requires further improvements to theanalytical mixing models.

4) Testing of single rows of multiple dilution ports shouldbe done using nonround ports in a wider range of geometriesthan the testing described in Ref. 3.

5) Testing of opposing rows of multiple dilution jets shouldbe done under a wider range of geometric and flow conditionsthan the testing described in Ref. 4.

6) The analytical procedures describing the mixing of op-posing rows of multiple dilution jets could be revised and im-proved to give more reliable prediction of absolute profilelevels.

7) Testing of multiple cooling slots under high-turbulenceand accelerating flow conditions should be done to obtainmixing behavior data for single or multiple louvers for com-parison with the analytical predictions.

References!Cox, G.B. Jr. "Correlations for Predicting the Temperature Field

Produced by a Single Row of Cool Jets Penetrating into a Hot, Con-fined Crossflow," l l th JANNAF Combustion Meeting, Pasadena,Calif., Sept. 1974.

2Cox, G.B. Jr., "Multiple Dilution Jet Mixing Correlations forGas Turbine Engine Combustor Design," ASME Trans-actions—Journal of Engineering for Power, Vol. 98 Series A No. 2,April 1976, p. 265.

3 Walker, R.E. and, Kors, D.L., "Multiple Jet Study FinalReport," NASA CR-121217, June 1973.

4Norgren, C.T. and Humenik, P.M., "Dilution Jet Mixing Studyfor Gas Turbine Combustors," NASA TN D-4695, Aug. 1968.

5Advances in Heat Transfer, Vol. 7, Edited by Irvine, T.F. andHartnett, J.P., Academic Press, N.Y. 1971, pp. 336.

6Wieghardt, K., AAF Translation No. F-TS-919-RE (1946).7Schlichting, H., Boundary Layer Theory, 6th Ed., 1968, pp. 703-

705.8Reichardt, H., "Implus-und Warmeaustausch in frier Tur-

bulenz," Zeitschrift fuer Angewandte Mathematik und Mechanik,Vol.24, 1944, p. 268.

9Juhasz, A.J. and, Marek, C.J., "Combustor Liner Film Coolingin the Presence of High Free-Stream Turbulence," NASA TN D-6360,July 1971.

10Carlson, L.W. and, Talmor, E., "Gaseous Film Cooling atVarious Degrees of Hot-Gas Acceleration and Turbulence Levels,"InternationalJournal of Heat Mass Transfer, Vol. II, pp. 1695-1713.

HKamotani, Y. and Greber, I., "Experiments in Confined Tur-bulent Jets in Cross Flow," NASA CR-2392, March 1974.

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 12,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/3.5

8694

This article has been cited by:

1. E.R.G. Eckert, E.M. Sparrow, R.J. Goldstein, C.J. Scott, E. Pfender, S.V. Patankar, J.W. Ramsey. 1977. Heat transfer—a review of 1976 literature. International Journal of Heat and Mass Transfer 20:11, 1097-1125. [CrossRef]

Dow

nloa

ded

by Y

OR

K U

NIV

ER

SIT

Y L

IBR

AR

IES

on A

ugus

t 12,

201

4 | h

ttp://

arc.

aiaa

.org

| D

OI:

10.

2514

/3.5

8694