ABSTRACTCalculationswereperformedto simulatethe tip flow andheat

transferontheGE-E3 first stageturbine,whichrepresentsamoderngas turbine bladegeometry. Casesconsideredwere a smoothtip,2% recess,and 3% recess.In addition a two-dimensionalcavityproblemwascalculated.Goodagreementwith experimentalresultswasobtainedfor thecavity calculations,demonstratingthatthek-ωturbulence model used is capableof representingflows of thepresenttype.In therotorcalculations,two dominantflow structureswere shown to exist within the recess.Also areasof large heattransferratewereidentifiedon thebladetip andthemechanismsofheat transfer enhancementwere discussed. No significantdifferencein adiabaticefficiency was observed for the three tiptreatments investigated.

INTRODUCTIONThe tips of turbine bladesin gas turbinesexperiencelarge

thermalloadswhichcanleadto tip burnout.Thelargethermalloadon bladetips is dueto hot gasesflowing throughthe gap betweenthe bladetip andthe shroud.The flow acceleratesdueto pressuredifferencebetweenthe pressureand suction sides,causingthinboundarylayersandhighheattransferrates.Theflow acrossthetipis also undesirablefrom the perspective of efficiency since itincreases the losses in the flow.

A commonstrategy to reducethe flow on the tip is to usearecessedtip, alsoknown asa squealertip. By usinga squealertip,the tip gap canbe madesmallerwithout the unacceptablerisk ofcatastrophicfailure should the tip rub against the shroudin thecourseof turbineoperation.The smallergap reducesthe flow ratethroughthe tip clearance,which leadsto smallerlossesandlowerheattransfer. It is believed that the tip recessalsoactsto increasethe resistance to the flow (Metzger et al. ,1989).

In orderto studytheeffectsof a squealertip geometryon heattransferand losses,Metzgeret al. (1989),andChyu et al. (1989)performedexperimentsusingcavitiesof varyingdepthto width andgapto width ratios.As a resultof theseexperimentsMetzgeret al.made a number of important conclusions.In particular, theyconcludedthat for a givenpressuredifferenceacrossthegap thereis an optimum value of depth to width ratio beyond which nofurther flow reduction will occur. They also concluded that

althoughtherateof heattransferonthecavity floor is lower thanthat on a flat tip, the reductionin heattransferis offset by thehigh heattransferin the redevelopingflow on the downstreamgap andby the additionalheattransferareacreatedon the sidewalls. Thus, they recommendedthat shallow cavities arepreferredif overall heattransferreductionon the cavity wall isthe goal.

The experimentalstudiescited above provide insight intothe natureof the flow field aroundthe squealertip. However,actual turbine blades differ greatly from the idealizedexperimentalsetup.Theflow in thebladetip andgaparehighlythree-dimensional.The relevant parameters,namely, depth towidth andclearancegapto width ratiosof therecessvarywidelyalongthegap.Thepressuredifferenceacrossthe tip alsovarieswidely alongthe blade.Thusit is unlikely that a simplemodelwill provide designerof a turbine bladewith the informationneededto understandthe flow in the tip region. At the presenttime neither experimentaldata nor numericalsimulationsareavailable in openliteraturethat shedlight on the detailsof theflow and heat transferon a squealertip flow. Also, with theexceptionof the heat transferdataof Yang and Diller (1995)which wastaken at a singlepoint on the cavity floor of a rotorblade,thereare no dataavailable on heattransferon squealertips. In this paperwe conducta numericalstudyof heattransferon a squealertip of a genericmoderngas turbine blade.Thisnumericalsimulationalsoallows insight into the natureof theflow within the cavity and its effects on efficiency. The bladechosenfor thisstudyis theGeneralElectricE3 designdetailedintwo NASA reports(Halila et al., 1982 and Timko1982).Thenumericalsimulationsof the heattransferwithin the simplifiedsquealertip model used by Metzger et al. (1989) are firstperformed with a view to demonstratethe ability of thenumericalmodelto accuratelypredicttheflow andheattransferas well as to forewarn us as to the possiblelimitations of theanalysis.

In the sectionto follow we will give a brief descriptionofthe numericalmethodusedin the simulations,the turbulencemodel and the numericalboundaryconditions.Afterwardswewill present the results of heat transfer predictions and

1

EFFECT OF SQUEALER TIP ON R OTOR HEAT TRANSFER AND EFFICIENCY

A. A. Ameri AYT Corporation, Brook Park, Ohio

E. SteinthorssonInstitute for Computational Mechanics in Propulsion (ICOMP)

NASA Lewis Research Center

David L. RigbyNYMA, Inc. NASA Lewis Group

ASME Journal of Turbomachinery, vol. 120, No. 4., Oct. 1998, pp. 753-759.

2

comparisonwith experimental data on the walls and rim oftransverse grooves used in the experiments cited above tosimulatethe squealertip. We will subsequentlyshow the heattransferresultsobtainedfor theGE-E3 turbinebladefor a flat tipandtwo recessedtip casesanddiscusstheresults.Finally wewillpresentthe calculationof efficiency and close by presentingasummary and the conclusions.

COMPUTATIONAL METHOD

The simulationsperformedin this studyweredoneusingamulti-blockcomputercodecalledTRAF3D.MB (Steinthorssonetal. 1993).This codeis a generalpurposeflow solver designedforsimulationsof flows in complicatedgeometries.The code isbasedon TRAF3D, an efficient computer code designedforsimulationsof steadyflows in turbine cascades(Arnone et al.1994). The TRAF3D.MB code solves the full compressibleNavier-Stokes equations.It usesthe finite volume method todiscretize the equations.The code uses central differencingtogetherwith artificial dissipationto discretizethe convectiveterms. The overall accuracy of the code is secondorder. TheTRAF3D.MB codewasdescribedin detailby Steinthorssonetal.(1993).The presentversionof the codewhich employs a two-equationmodelhasbeenusedin connectionwith aninternalflowcalculation of heat transfer as described by Rigby et al. (1996)

Turbulence and Transition Models

Algebraic model of Baldwin and Lomax (1978) has beenquite successfulin predictingthe rateof heattransferto turbineblades. Combining this turbulence model with other modelssimulating laminar-turbulent transition and models simulatingleading edge heat transfer enhancementhave been shown toproduceaccurateresults(Ameri andArnone1996,Boyle(1991).Whenusinga multiblock approachin connectionwith complexgeometriesinvolving many no-slipsurfaces,it is advantageoustousea turbulencemodelthat doesnot requirethe computationofthedimensionlessdistanceto thewall (y+) asis donein Baldwin-Lomax zero equationmodel and many two-equationmodels.Therefore,for thepresentcomputations,it wasdecidedto usethek-ω turbulencemodeldevelopedby Wilcox (1994a,1994b)withsubsequent modifications by Menter (1993). The modelintegrates to the walls. Chima (1996) incorporatedthe lattermodel in a Navier-Stokes solver and presentedresults of itsapplicationto turbomachineryflows andheattransfer. Below wepresenttheequationsdescribingtheturbulencein tensornotation.

(1)

(2)

where s1=k and s2=ω also µt=α* . The production sourceterms, P, of equation (1) are defined as:

(3)

whereΩ is themagnitudeof vorticity. Thedestructionterms,D, are given by

(4)

The coefficients appearing in the model are as follows:σ=2.0, β=3/40, β*=0.09Fβ, α=(5/9)(Fα/Fµ), and α*=Fµ,

where

(5)

(6)

(7)

(8)

α0=0.1,α0*=0.025,Rβ=8, Rω=2.7 and Rk=6.The turbulent thermal diffusivity is computed from:

(9)

whereρ is density. A constantvalueof 0.9 is usedfor turbulentPrandtl numberPrt.

Boundary ConditionsThe types of boundary conditions encounteredare as

follows:1) Inlet: The inlet boundary condition for axially subsonic

flows is treatedby specifyingtheinlet total temperatureandinlettotal pressure as well as the inlet angle profiles. The outgoingRiemann invariant is extrapolated to the inlet from within. Thetotal temperature and total pressure profiles are determined tomatch the law of the wall for the specified hydrodynamic andthermalboundarylayerthicknesseson thehuband/ortheshroud.For theturbulencequantitiesfor thebladerow, aninlet turbulenceintensity of 8% and a length scale of 10% of axial chord is used.These values are estimated and believed to be representative ofthe condi t i ons exi st i ng at the i nl et of the bl ade row.

2) Exit: At theexit boundary, for thesubsonicaxial flow, thepressureis specifiedand all the other conditions(including theturbulencequantities)areextrapolatedfrom within. Thepressureat theexit planefor theturbinebladeconsideredhereis computed

ρsi( ),t

ρsiu j qij+( ),j

+1ρ--- P D–( )=

qi j, µµt

σ-----+

si j, i=1,2–=

ρkω------

Pρ---

Re1–

ρ-----------µtΩ

2ui i,–

α α∗Ω2 23---ωui i,–

=

Dρ----

β∗ωk

βω2=

Fβ5 18⁄ ReT Rβ⁄( )4

+

1 ReT Rβ⁄( )4+

-----------------------------------------------=

Fαα0 ReT Rω⁄( )+

1 ReT Rω⁄( )+--------------------------------------=

Fµα0

∗ ReT Rβ⁄( )+

1 ReT Rβ⁄( )+-----------------------------------------=

ReTρkµω-------=

αt

µt

ρPrt-----------=

Ameri et al.

3Ameri et al.

by integrationof the radialequilibriumequationwith specifiedhubendwall pressure at the exit.

3) Walls: At the walls, the normal pressuregradientis set tozero, the temperatureis specified,and the no-slip condition isenforced.The density and total energy are computedfrom thepressureandthe temperature.Also thekinetic energy of turbulence(k) is setto zerowhile thespecificdissipation(ω) is calculatedusingthe following boundary conditions.

(10)

where

(11)

KR is the equivalent sand roughnessheight. Here KR=5corresponding to an hydraulic smooth surface is used.

4) Periodic boundaries are computed as interior points.

RESULTS AND DISCUSSIONWe first computethe rateof heattransferon the surfacesof a

cavity anddeterminethepressurelossesdueto sucha flow. This isdonein orderto verify theability of thenumericalprocedureandinparticular the turbulencemodel, to handlethe similar problemofpredictingthe heattransferon the rim andwithin the cavity on theblade tip for which no measured data is available.

CavityThegeometryandthedatachosenfor this testweretakenfrom

Metzgeret al. (1989).Thesketchof thegeometryusedin theexper-imentandsomeof thenomenclatureareshown in Fig. 1. Two caseswith differentcavity depthto width ratios(D/W) of 0.2and0.5wereconsidered.For both casesheattransferdatafor the rim aswell asthebottomof thecavity areavailable.For thedeepercavity theheattransferdataon thesidewalls werealsotaken.For bothcasescon-sidered,thegap to width ratio (C/W) is 0.1 andtheReynoldsnum-berbasedon gapheightandaverageinlet velocity is 15,000.Fig. 2shows a three-blockgrid used to discretizethe flow.(the grid iscoarsenedfor clarity) The blocks contain 81x65, (81x41 for theshallower case),129x41and25x41grid pointsrespectively. Coarsergrid was also usedto calculatethe flow and the resultspresented

ω SR y∂∂u

wall=

SR

50KR-------

2KR 25<,

100KR--------- KR 25≥,

=

Fig. 2 Three-blockgrid usedfor thediscretizationof theflow.

13

2

0.0 5.0 10.0

15.0X

0.0

50.0

100.0

150.0

Nu

Present AnalysisData,Bottom and Rim, Metzger et al., 1989

Fig. 4 Nusseltnumberdistribution along the rim,and the bottom of the cavity from Metzger et.al.(1989). D/W=0.2, C/W=0.1, Re=15,000.

0.0 5.0 10.0 15.0 20.0String distance

0.0

50.0

100.0

150.0

Nu

Sides

RimBottomPresent Analysis

xy

1

3 4 5 6 7 8 9 10

11 12

Fig. 1 Diagramandnomenclatureof thecavity usedinthe experiments of Metzger et. al. (1989)

wD

2

C

0.00 0.20 0.40 0.60D/W

0.00

0.02

0.04

0.06

F

C/W=0.05

C/W=0.10

C/W=0.15

C/W=0.10

Fig. 3 Nusselt number distribution along the rim,sidewallsandthebottomof thecavity from Metzgeret. al.(1989). D/W= 0.5, C/W=0.1, Re=15,000.

Fig. 5 Measured Pressure coefficient (closed symbols) ofMetzger et.al.(1989) and present computations (open

symbols).

4

c

hereinare spatially converged. Note that in the computations,thegrid in the exit region wasextendedto allow completeflow attach-ment very near the rim before exiting the computational domain.

Figure 3 presentsthe rate of heat transferas computedandmeasuredfor the deepercavity. The abscissais the string distancemeasuredalongthe rim andwalls of the cavity, startingfrom x=0,y=4. The ordinate is the Nusselt number defined as:

(12)

In Eqn. 11, h is the heat transfer coefficient basedon the inlettemperature,c is theinlet gapheightandk is thermalconductivity ofthe bulk inlet flow. The figure shows generally good agreementbetweentheexperimentalresultsandtheanalysis.However a largerise in heat transfer is predicted on the upper portion of thedownstreamside wall. A rise in the rate of heat transfer in thatregion is expectedto exist dueto flow stagnation.Thedatahoweverdo not indicate as large a rise as predicted by the analysis.

In Fig. 4 the comparisonbetweenanalysisand experimentaldatafor theshallow cavity is presented.Theexperimentaldataweretaken on the rim and the bottom of the cavity but not on the sidewalls. Again it is observed that the agreement in general is good.

Finally, in Fig. 5 themeasuredpressurelosscoefficientsdefinedas:

(13)areplottedasa function of cavity depthratio for threefamiliesofgap clearanceratios.In the above definition,L is the gap lengthinflow directionandρ andV arethe bulk densityandvelocity of theinlet flow and ∆p is the pressuredifferenceacrossthe gap. Thecalculatedvaluesof the pressurelosscoefficient for the two casesconsideredherearesuperimposedon this plot usingopensymbols.The agreement is very good.

The two computedcasesof flow in a cavity, demonstratethecapability of the presentturbulencemodel to produceresultsofreasonableaccuracy for this particulartype of flow. Although thisflow is essentiallytwo-dimensionalwhile the flow on a bladetip isthree-dimensional,theseresults lend credenceto the predictionspresentedin the following section.The turbulencemodelhasbeenshown to performquite well for flow andheattransferpredictionson turbine blades as was demonstrated by Chima(1996).

Blade TipGeometry and the grid . Thegeometryof theGE-E3 bladewith thesimulatedsquealertip is shown in Fig. 6a. The bladeshave aconstantchord length of 2.87 cm and an aspectratio of 1.39. Asquealertip thicknessof 0.030 in. (0.77 mm) was chosenfor thisstudy. Threegeometricalcaseswereconsidered,a flat tip, andtwotypical tip recessesof 2% anda 3%. The tip gapclearancewas1%for all thethreecases.Figures6b and6c show thegrid on theblade,thehubandthetip surfaces.Notethatevery othergrid line hasbeeneliminatedfor clarity. The grid topology is essentiallythe sameasgiven in Ameri andSteinthorsson(1996)with the exceptionof thegrid in the tip. For the presentgeometry, the tip grid is constructedusing two blocks. One block covers the entire tip clearanceexcludingthecavity while thesecondblock coversthespacewithinthe cavity. Grid is refinedcloseto all no-slip surfacessuchthat thedistanceof thecell centersadjacentto solid walls,measuredin wallunits (y+), is closeto unity. This aspectof the grid constructionis

Nuhck------=

f ∆pC( ) 2LρV2( )⁄=

Ameri et al.

b

a

Fig. 6 Geometry and grid distribution for the E3

blade. Alternate grid lines are eliminated for clarity.

crucial to both the solution accuracy and to convergence.Thedimensionof theC grid coveringthebladefrom hubtoshroud is 193x49x99. In the tip clearance the griddimensionis 129x57x33.In the cavity thereare129x 33x41grid pointsfor boththe2%andthe3%cases.Theflat tipcasewasrun with the samegrid in the tip as the recessedcases(129x57x 33) to allow direct comparisonof heattransferdevoid of resolutiondifferences.A singleblock of9x9x99grid points covers the entire inlet upstreamof theblade.

Flowfield. The conditions used for the numericalsimulationsarethe sameasexperimentalconditionsof thewarmrig usedby Timko (1982)for theGE-E3 turbineandare as listed in Table 1. The inlet anglevariation is taken

5

from measurementsbut thewall to total temperatureratio wassetat a typical value.

In Figure7plotsof computedvelocityvectorsin thetip regionprojected on planes normal to the machine axis for various axiallocationsareshown.Theflow is shownin therotatingbladeframe

Ameri et al.

60%

Fig. 7 View of the velocity vectors in and around the tip atvarious axial locations for the case of 3% recess.

Fig. 8 Streamlines showing the blade tip flow patterns.

Pressure side Suction side20%

40%

of reference,hencethenonzerovelocityontheshroud.Thetip flowishighly three-dimensional.Thevariationin flow patternsin thetipclearanceis apparentfrom examiningthevectorplots.Forthe20%to 60%axialdistancetheplotsshowacomplexsystemof vorticesin thetip clearance.Figure8showsthestreamlinepatternsin thetip.In thatfigureat leasttwo distinctvorticescanbediscernedto existwithin thecavity.Onevortexisaseparationvortex,generatedastheincomingflow separatesoff theinneredgeof thepressuresiderim.Thisvortexhugsthepressureside,sidewalland“spills” outof thecavitynearthetrailing edgeof theblade.Thesecondvortexwhichis apparently also a separation vortex, runs from the stagnationregionto thesuctionsideof theblade.Thesevorticesaregeneratedin addition to the separation vortex along the pressure side rim,suction side rim and the blade suction side tip flow vortex.

Thisvortexsystemapparentlyoffersadditionalblockagetotheflow throughthegap.Theflow ratethroughthetip gapfor theflattip case was calculated to be 1.98% of the mass flow through thebladerow. The2%and3%recessedbladeshadleakagemassflowratesof 1.8%and1.7%of thetotalmassflow rateequivalentto90%and 86% of that of the flat tip case.Heat Transfer The rateof heattransferis presentedin termsofStanton number defined as:

(14)

whereh is theheattransfercoefficient basedon theabsoluteinlettotal temperature.The referencevelocity is the averagerelativevelocity at a location 20% of the axial chord upstreamof theblade. The referencetemperatureis the averageabsolutetotaltemperatureandthereferencedensityis theaveragedensityat thatlocation. (The inlet relative total temperatureat the midspanis0.879 times the absolute inlet total temperature.)

Heat transfer rateson the blade surface at three spanwiselocationsaregivenin Fig. 9. Thisfigureservesasaguideasto themagnitudeof thetip heattransferascomparedto thebladesurfaceheat transfer.

The heattransferresultson the tip of the bladearegiven inFig. 10a-c.Fig. 10ashows theStantonnumberdistribution on theflat tip surface.Thepatternsof heattransfercontourson thebladetip areasexpectedandhave beenseenbeforein connectionwithour previous studies(Ameri & Steinthorsson1995 and 1996).Thosepatternsinclude,sharpentranceeffect on thepressuresideof the tip surface where the rate of heat transfer reachesamaximum due to flow reattachment;the ensuingdrop in heattransferdownstreamof that location;a large rateof heattransferaroundthe cornerfrom the bladestagnationpoint and the largeincreasein heattransferon thesuctionsideof theblade(nearthecrown). Theaveragelevel of heattransferon theflat tip is similarin magnitudeto the heattransferrateon the bladeleadingedge.For the two recessedcasestheheattransferdistribution is shownusingonefigure which shows the heattransferon the bottomofthe cavity and the rim surfaceof the squealertip anda separateFig. 11 to show the heattransferon the side-wall of the recess.Fig. 10b andc show the heattransferon the surfacesof the 2%and 3% cavity, respectively. It is observed that the rate of heattransferon thebottomof thecavity reacheshighervaluesthanisseenon the flat tip. On the rim the rate of heat transferon thepressuresideis comparableto theflat casebut is somewhathigher

Sth

ρref V ref C p----------------------------=

TABLE 1. Run conditions

Absolute pressure Ratio acrossthe Blade Row

0.44

Absolute inlet angle 69 Hub

74.5 Mid Span

78.5 Shroud

Rotation Rate 8450 RPM

Tw/Tt 0.7

°

°

°

6Ameri et al.

7

2 3

8

3 7

15

1

2%

8

3

6

14

1

2

1

3

3%

Pressure side L.E. Suction side

0.0 50.0 100.0 150.0Percent Chord

0.0

2.0

4.0

6.0

8.0

Stx

1000

Flat tip2% Recess3% Recess

Fig. 11 Heat transfer distribution on the side wall of thecavity asunwrappedabouttheminimumx locationin terms

of 1000xSt.

Fig. 12 Tangentially averaged shroud heat transfer

on thesuctionside.The large rateof heattransferon thebottomof thecavity is dueto flow impingementcontaininghot gas.Thisimpingementcan best be seen in Fig. 7 for the 20% axialdistance.

It is worth mentioning that in both the experimentalinvestigationscitedabove, therateof heattransferon thebottomof thecavity wasalwaysobservedto belessthanthaton therim.However, in their numericalcalculations,Chyu et al. (1987) doshow instanceswherethe bottomof the cavity hassubstantiallyhigher heat transfer coefficient compared to the rims.

Squealersidewall heattransferis presentedin Fig. 11. Theinside wall surface is unwrappedaround the minimum axiallocation.The ordinateis exaggeratedfor clarity. The abscissaisthe axial chord distance.Areas of large heat transferratesaregeneratedasa resultof the vortical actioninsidethe cavity. Thevorticalactionincreasesdueto flow accelerationandstretchingofthesevortices.The highestrate of heat transferis observed toexist nearthe trailing edgeof the bladeon the suctionsidewall.The causeof this increasewas found to be the impact of thevortex spillage with the side wall. As such this rise in heattransfer, althoughpresentmaybeexaggeratedaswasdiscussedinconnection with the two-dimensional cavity.

5

6

6 4

3

4

7 4 1

8

4

2

2 1

2 7

4

4

5

6

4

3

3

2

4

8

6 3 3

1

2

7

6

5

4

4

3

32% recess

3% recess

c

b

aNo recess

Fig. 10a-c Heattransferdistribution (1000xStantonnumber)onthe cavity floor and rim for no recess as well as 2 and 3% tip

recess.

-1.0 -0.5 0.0 0.5 1.0Pressure side Normalized distance Suction Side

0.0

2.0

4.0

6.0

8.0S

tx10

00

10% Span50% Span

90% Span

Fig. 9 Surface heat transfer at 10%, 50% and 90% span onthe flat tipped blade.

Vortex impact regions

Theshroudheattransferis presentedin Fig. 12.As canbeseenfrom this figure the rateof heattransferon the shroudishigher for the flat tip caseas comparedto the two recessedcases.

Finally the total tip heattransferfor the threecaseswascompared.It wasfoundthatthe2%and3%recesscases,hadanincreaseof 80%and90%respectively in total heatadditiontothe tip compared to the flat tip case of the same tip clearance.

EfficiencyAs a by-productof our heat transfercomputations,it is

possibleto computethe efficiency and the possibleeffect ofrecesson efficiency. Theexpressionfor theadiabaticefficiencyis

(15)

In Eqn.14theprimessignify relativetotalvalues,subscriptin andex, signify inlet andexit massaveragedvaluesandγ is thespecific heat ratio. The calculatedefficiency is basedon theassumptionof an ideal statorupstreamand the averageinletvaluesarecomputedat 20%axial chordupstreamof the rotor.Theexit valuesarecomputedat50%axialchorddownstreamofthe rotor. Becausethe bladesurfacetemperaturewas set at aconstanttemperatureof 0.7xtheinlet total temperature,in orderto recover adiabaticconditions,thegastotal temperatureat theexit was modified to reflect the loss of energy through heattransfer. Failure to do so leadsto an error of 5 points in theefficiecy for the presentcomputations.The changein massaveragednormalizedtotal temperatureat the exit of the bladerow can be computed as follows:

(16)

In theabove equationµ is dimensionlessviscosityandn isthe normalizeddistanceto the wall is the normalizedmassflow ratethroughthe bladepassageandA is the surfacearea.The integration is performed over all of the heat transfersurfaces.Themassaveragedvalueof theexit total temperatureis thus computed as:

(17)Theefficiency for therow of bladeswascomputedto be91.3%,91.4%and91.4%for the0%,2% and3% recesscases,in spiteof the fact that there was a 10 to 14% reduction in gap flow.

SUMMARY AND CONCLUSIONSIn this paper, resultsarepresentedfrom three-dimensional

simulationsof flow andheattransferovera turbinebladewith asquealertip. The simulationswerecarriedout usinga secondorder accuratefinite volume schemeon a multi-block gridsystemcontaining1.2million grid points.Effectsof turbulenceon the flow field were modeledusing a k-ω two-equationturbulencemodel.Theability of theturbulencemodelto predicttheheattransferin flowsof thetypeconsideredherewasverifiedby simulatingtheflow in a two-dimensionalmodelof squealertips for which experimentaldata is available. For the three-dimensional case an actual modern gas turbine geometry,namely the GE-E3 first stageturbine blade was used.Two

ηT′in T′ex–

T′in 1pex′

p′in-----------

γ 1–( ) γ⁄

–

-------------------------------------------------------------------=

∆T 'ex

(µA∫∑ T n

w) dA∂⁄∂

m RePr------------------------------------------------------=

m

T 'ex T 'unmodified ∆T 'ex+=

dominantvortical structureswere identified to exist in the recessregion.Theheattransferrateontherecesssurfaceswerefoundtobestrongly affected by theseflow structures.Especiallyhigh heattransfer rateswere observed where the vortices exit the recessregion. No significanteffect dueto the recessedtip on efficiencywasdetectedalthoughthe massflow ratethroughthe tip gap wasfound to be smallerby as much as 14% for the squealertip ascompared to flat tip of the same clearance height.

ACKNOWLEDGEMENTThe authorswish to expresstheir gratitudeto Dr. Raymond

Gaugler, Chief of the Turbine Branch, as well as to Dr. LouisPovinelli, Chief of the Turbomachineryand PropulsionSystemsDivisionof NASA Lewis ResearchCenterandDirectorof ICOMPfor their supportandencouragementof this work. Thanksarealsodueto Mr. RobertBoyle for his suggestionsandhis guidance.Thecomputationswereperformedon theCRAY-C90of NAS atNASAAmes Research Center.

REFERENCESAmeri, Ali A., and Steinthorrson,E., 1995, “Prediction of

UnshroudedRotorBladeTip HeatTransfer,” ASME 95-GT-142.Ameri,Ali A., Arnone,A., 1996,“TransitionModelingEffects

on Turbine Rotor Blade Heat Transfer Predictions,” J. ofTurbomachinery, Vol. 118,pp.307-313.

Ameri, Ali A., andSteinthorrson,E., 1996,“Analysisof GasTurbineRotorBladeTip andShroudHeatTransfer,” IGTI 96-GT-189.

Arnone,A., Liou, M. S.,andPovinelli, L. A., 1994,''ViscousAnalysis of Three-DimensionalRotor Flow Using a MultigridMethod,” J. of Turbomachinery, Vol. 116,pp.435-445.

Baldwin, B. S. and Lomax, H., 1978, “Thin LayerApproximation and Algebraic Model for SeparatedTurbulentFlows,” AIAA paper78-0257.

Boyle, R. J.,1991,“Navier-StokesAnalysisof TurbineBladeHeatTransfer,” J. of Turbomachinery, Vol. 113,pp.392-403.

Chima, R. V. 1996, “A k-ω Turbulence Model for Quasi-Three-DimensionalTurbomachineryFlows,” AIAA paper96-0248

Chyu, M.K., Moon, H.K. and Metzger, D.E., 1989, “HeatTransfer in the Tip Region of Grooved Turbine Blades,” J. ofTurbomachinery, Vol. 111,pp.131-138

Chyu, M.K., Metzger, D.E. and Hwan, C. L., 1987,“HeatTransferin ShroudedRectangularCavities,” J. of Thermophysics,Vol. 1, No.3,July1987,pp247-252.

Halila, E. E. and Lenahan,D. T., and Thomas,L. L., 1982,“Energy Efficient Engine,High PressureTurbine Test HardwareDetailedDesignReport,”, NASA CR-167955.

Menter, Florian R., 1993, “Zonal Two-Equation k-ωTurbulenceModelsfor AerodynamicFlows,” AIAA-93-2906.

Metzger, D. E., Bunker, R. S.andChyu, M. K., 1989,“CavityHeatTransferonaTransverseGroovedWall in aNarrow Channel”,J. of Heat Transfer, Vol. 111,pp.73-79.

Rigby David, L., Ameri Ali, A. and SteinthorssonE., 1996,“InternalPassageHeatTransferPredictionUsingMultiblock Gridsandk-w TurbulenceModel,” IGTI paper96-GT-188.

Steinthorsson,E., Liou, M. S., and Povinelli, L.A., 1993,“Developmentof anExplicit Multiblock/Multigrid Flow Solver forViscousFlowsin Complex Geometries,” AIAA-93-2380.

7

Timko, L.P., 1982,“Energy Efficient EngineHighPressureTurbineComponentTestPerformanceReport,”NASA CR-168289.

Wilcox, D. C., 1994a,“TurbulenceModeling forCFD,” DCW industries, Inc. La Canda, CA.

Wilcox, D. C., 1994b, “Simulation of Transitionwith a Two-Equation Turbulence Model,” AIAAJournal, Vol. 32, No.2, pp.247-255.

Yang, Timothy, T. and Diller, Thomas,E., “HeatTransferandFlow for aGroovedTurbineBladeTip in aTransonic Cascade,” ASME paper No. 95-WA/HT-29.