A.A. AmeriAYT Corporation, Brook Park, Ohio

D.L. RigbyDynacs Inc., Brook Park, Ohio

A Numerical Analysis of Heat Transferand Effectiveness on Film CooledTurbine Blade Tip Models

NASA/CR—1999-209165

July 1999

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A.A. AmeriAYT Corporation, Brook Park, Ohio

D.L. RigbyDynacs Inc., Brook Park, Ohio

A Numerical Analysis of Heat Transferand Effectiveness on Film CooledTurbine Blade Tip Models

NASA/CR—1999-209165

July 1999

National Aeronautics andSpace Administration

Glenn Research Center

Prepared under Contract NAS3–98106

Prepared for the14th International Symposium on Air Breathing Enginessponsored by the International Society for Air Breathing EnginesFlorence, Italy, September 5–10, 1999

Available from

NASA Center for Aerospace Information7121 Standard DriveHanover, MD 21076Price Code: A03

National Technical Information Service5285 Port Royal RoadSpringfield, VA 22100

Price Code: A03

This report is a preprint of a paper intended for presentation at a conference. Becauseof changes that may be made before formal publication, this preprint is made

available with the understanding that it will not be cited or reproduced without thepermission of the author.

NASA/CR—1999-209165 1

ABSTRACT

A computational study has been performed topredict the distribution of convective heat transfercoefficient on a simulated blade tip with cooling holes.The purpose of the examination was to assess the abilityof a three-dimensional Reynolds-averaged Navier-Stokessolver to predict the rate of tip heat transfer and thedistribution of cooling effectiveness. To this end, thesimulation of tip clearance flow with blowing of Kim andMetzger was used. The agreement of the computedeffectiveness with the data was quite good. Theagreement with the heat transfer coefficient was not asgood but improved away from the cooling holes.Numerical flow visualization showed that the uniformityof wetting of the surface by the film cooling jet is helpedby the reverse flow due to edge separation of the mainflow.

NOMENCLATURE

b width of the cooling hole

Cp constant pressure specific heat

D hydraulic diameter of the experimental

tunnel (4.63b)

G mass velocity (ρ V)

H height of the channel

h heat transfer coefficient, eq.(1)

M blowing parameter Gf/Gm

Nu_D Nusselt number based on hydraulic diameter

Pr Prandtl number

q wall heat flux

R gas constant

Re Reynolds number GmDh/µT temperature

Tu turbulence intensity

V channel bulk velocity

X distance downstream of cooling holes

dimensionless distance from a wall,

film cooling effectiveness, eq. (2)

µ viscosity

ν kinematic viscosity

Subscripts

f film value

m main flow

R reference value

w wall value

INTRODUCTION

The tips of unshrouded rotor blades in axial turbinestages are exposed to high free stream temperatures andlarge convective heat transfer rates. As a result, tips ofblades are prone to early failure. Film cooling is oftenemployed to provide protection against tip burn-out andcorrosion. In a typical engine the tip leakage flow issomewhere near 3% of the primary flow and the tipinjection mass flow is nearly half that amount (Chen et al.1993). Therefore efficient use of this cooling air is quiteimportant.

The ability to accurately compute the rate of heattransfer and cooling effectiveness on the tip surface canform the basis of a system enabling the design of efficienttip cooling schemes. Numerical models would enable thedesigner to design cooling schemes that use the coolingair efficiently thus producing the desired effect ofprotecting the blade tip without the side effect ofcontributing to the losses. We have in the past shown thatit is possible to predict the rate of blade tip heat transfer(Ameri and Steinthorsson, 1995, 1996 and Ameri et al.1997, 1998). More recently comparisons were made witha complete map of experimentally measured tip surfaceheat transfer rates with favorable agreement (Bunker etal. 1999 and Ameri et al. 1999).

y+

y+

yv

*

ν-----=

η

A NUMERICAL ANALYSIS OF HEAT TRANSFER AND EFFECTIVENESS ON FILMCOOLED TURBINE BLADE TIP MODELS

A.A. AmeriSenior Research Engineer, AYT Corporation

Brook Park, OH, USA

D. L. Rigby*Senior Research Engineer, Dynacs Inc.

Brook Park, OH, USA

* Member AIAA

In a previous numerical work Chen et al. (1993)showed, by employing two-dimensional simulations andcomparison with experimental measurements the variationof the discharge coefficients with parameters such as thetip flow Reynolds number, isentropic Mach number, lengthof the flow path along the tip gap and the positive effect ofthe utilization of squealer tips in conjunction withsecondary jets issuing into the tip gap thus reducing thedischarge coefficient of the tip leakage flow. Obviouslytwo-dimensional simulations pose severe limitations onthe range of geometries that can be considered. Inaddition, due to the lack of three-dimensional structuressuch as streamwise vortices, the penetration of the freestream into the film cannot be simulated.

Experimentally, tip cooling has been investigated byKim et al.(1995) and Kim and Metzger (1995) for flat andrecessed tips and for cooling holes of different shapes andissuing from different locations. We have focused ourattention on the flat tip case as will be discussed in theensuing sections.

In this work we seek to determine the suitability oftypical CFD methods to tip heat transfer predictions in thepresence of the cooling holes. We will also attempt todetermine the suitability of the scheme for prediction ofcooling effectiveness. This would be the first workaddressing tip cooling using numerical simulations.

EXPERIMENTAL SETUP OF KIM AND METZGER

Kim and Metzger set out to study the heat transferproblem as shown in Fig. 1. The tip of the blade is exposedto high velocity flow of hot air. The flow runs from thepressure to suction side of the blade following the pressuregradient. Cooling air is injected through the holes (shownas white dots) over the tip to provide a film of cooler air toprotect the blade tip against burnout. A physical model ofthe blade tip was constructed by Kim and Metzger as

b

w

x0 x

Fig. 2Details of the test surface of Kim and Metzger(1995)

H

Test Surface

Calming Section

Fig. 3Schematic of the testing tunnel

Fig. 1 Typical turbine blade with tip cooling holes

NASA/CR—1999-209165 2

shown in Figs 2 and 3. Figure 2 shows the detailsof the test surface of the experiment. In thisexperimental model the primary flow is supplied toa narrow channel simulating the clearance gapabove a plain blade tip and the secondary film flowis supplied to the tip surface through a line array ofdiscrete normal injection holes near the upstreamor pressure side. Figure 3 shows the schematic ofthe tunnel and manner in which the main streamand secondary air stream are introduced. The filmis injected into the main flow near the channelentrance and is discharged downstream thussimulating the pressure side to suction flow in thetip region of a blade with injection near the edge onthe pressure side. The upper wall is adjustable suchthat the ratio of H/b can be adjusted.

It should be noted that the type of flowconsidered here is quite sensitive to the sharpnessof the corner as has been stressed by many authorsincluding Chen et al. (7). It is believed thatmodeling the corners as sharp is appropriate for theexperiment of Kim and Metzger (9)

The available runs are for values of H/b of 1.5and 2.5 and for main stream Reynolds numbers of15000, 30000 and 45000 and blowing ratios (M)ranging from zero to 0.9. The no blowing case wasperformed without covering the hole.

In this work numerical calculations for theReynolds number of Re=45,000, H/b=2.5 and M ofzero and 0.3 were made.

NUMERICAL SIMULATIONS

COMPUTATIONAL METHODThe simulations in this study were performed

using a multi-block computer code called Glenn-HT, previously known as TRAF3D.MB(Steinthorsson et al. 1993) which is based on asingle block code designed by Arnone et al. (1991).This code is a general purpose flow solver designedfor simulations of flows in complicated geometries.The code solves the full compressible Reynolds-averaged, Navier-Stokes equations using a multi-stage Runge-Kutta based multigrid method. It usesthe finite volume method to discretize theequations. The code uses central differencingtogether with artificial dissipation to discretize theconvective terms. The overall accuracy of the codeis second order. The present version of the code(Rigby et al. 1996, 1997 and Ameri et al. 1998a)employs the k-ω turbulence model developed byWilcox (1994a,1994b) with modifications byMenter (1993). The model integrates to the wallsand no wall functions are used. For heat transfer aconstant value of 0.9 for turbulent Prandtl number,Prt,and 0.72 for Pr were used. Viscosity is afunction of temperature through a 0.7 power law(Schlichting, 1979) and is taken to be aconstant.

Cp

(a)

(b)

Fig. 4Various views of the computational grid

(c)

NASA/CR—1999-209165 3

The problem considered is a three temperatureproblem, involving the main flow fluid temperature, thefilm temperature and the wall temperature. Kim andMetzger define:

(1)

Where TR is a reference temperature that rendershindependent of the temperature andTw is the walltemperature as long as temperature differences are nottoo high and fluid property variations can be reasonablysmall. Both h and TR are unknowns. The coolingeffectiveness is defined as:

(2)

If the wall temperature is the only parameter that isvaried (density ratio held constant), thenTR is constantand simultaneous solution of eq. (1) for two runsprovides h andTR and the effectiveness is obtained fromeq.(2).

THE GRID AND THE BOUNDARY CONDITIONSFigure 4 shows the grid built for the model problem.

Figure 4(a) shows the total view of the problem. Figure4(b) shows the details near the edge and the injectionhole while 4(c) shows more clearly the details of the gridaround and into the hole. The spanwise symmetrybetween the holes and within the holes is used tominimize the size of the computational domain andsymmetric boundary conditions are used along thoseboundaries. The grid is refined to resolve gradient nearthe walls. The resolution is such that the average value ofy+ is around 0.25, The total number of cells for this gridwas 655488 cells. No slip boundary condition is appliedto all the walls except to the left wall of the reservoir inFig. 4(a). This was done to relieve some of the griddensity requirement. At the two inlets, total temperatureand the average normal momentum were specified.

RESULTS AND DISCUSSION

GENERAL REMARKSFirst for validation purposes the case of fully

developed pipe flow is presented. This is followed byclearance flow simulations. The case of Re=45,000, H/b=2.5, with the blowing parameter M of zero and 0.3were chosen for study.

FULLY DEVELOPED PIPE FLOWAs a check on the accuracy of the results we

performed two simulations to predict the rate of heattransfer for a fully developed pipe flow. For this wechose two cases of Reynolds numbers of 17,000 and33,000. The pipes were 65 diameters long. Thecalculations were done on a longitudinal slice withperiodic boundary conditions in the tangential direction.

qw h TR Tw–( )=

ηTR Tm–( )T f Tm–( )

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

0.0 5.0 10.0 15.0 20.0X/b

0.0

100.0

200.0

300.0

Nu

_D

Data of Kim and Metzger(1995)Fully Developed, Dittus−Boelter corr.Fine grid Solution (T.I.)Coarse grid (C.I.)Coarse grid (T.I.)

0.0 5.0 10.0 15.0 20.0X/b

0.0

100.0

200.0

300.0

Nu_

D

Fine GridMedium Coarse

Fig. 6 Comparison of the data and numerical simulationsfor the no blowing case.

Fig. 5Grid resolution study

A 5x49x49 grid was used. The results were compared withthe commonly used Dittus-Boelter correlation (Boelter etal.(1945))

(3)

The following table contains the results of thatcomparison.

Both of the above cases were run using a constant walltemperature 1.1 times the total inlet temperature.

NO BLOWING CASEFor this case in the experiment the supply of injection

air into the tip gap was shut off but the hole was notcovered. Similarly, for the simulations it was still necessaryto model and grid the injection pipe but the inlet to theinjection pipe was closed by assigning a slip boundarycondition to that surface.

The question of the minimum grid resolution requiredto obtain grid independence was first addressed by runningour problem at three different grid levels, namely, coarse,medium and fine levels. The medium grid was obtained bydiscarding alternate grid points from the generated fine grid

Re Eq. 3 CFD

33000 85.08 88.20

17000 48.86 53.47

Nu 0.023Pr0.4

Re0.8

=

NASA/CR—1999-209165 4

and the coarse was subsequently generated from themedium grid in the same manner.

Figure 5 shows the distribution of the span averagedNusselt number downstream of the hole and theexperimental data. The Nusselt number is based on thehydraulic diameter of the experimental channel which inthe present case is 4.63 times the hole diameter. Themedium and the fine grid results differ by less than 3%away from the hole and less than 10% within twodiameters of the hole. Given that the fine grid has 8times as many cells as the medium grid we decided thatthe fine level grid was resolved enough for our purposes.The current grid resolution will be used for the blowingcases as well to be discussed later.

Figure 6 compares the simulation results with theexperimental measurements of Kim and Metzger(1995)where the data is somewhat over-predicted. It wasspeculated by the experimenters that the flow mighthave relaminarized. Numerical experimentation usingthe coarse grid showed that the flow inside the channelcould be laminar, semi-laminar (upper wall turbulentand the lower wall laminar) or turbulent depending onthe state of the incoming flow. The calm inlet (C.I.) andthe turbulent inlet (T.I.) solutions are presented on thesame figure to bolster this point. Since the solutionsusing clam inlet condition are unsteady and difficult toconverge and more importantly the true state of the flowin turbine environments is seldom laminar, it wasdecided to run all the cases using the (T.I.) conditions.Considering the very complex nature of the flow nearthe edge and the presence of the hole and the reported8% error band on the data we deem the comparisonsatisfactory.BLOWING CASE

To test the calculation technique discussed earlier,three cases (instead of two) with differing walltemperatures or total inlet film temperatures were runkeeping the film to main temperature ratio closetogether to avoid differences due to density ratio. Thiswas done using a coarse grid. The results of thecomputations were post-processed pairwise and theresulting heat transfer coefficient and coolingeffectiveness distributions were calculated and found tobe identical. Having convinced ourselves of theaccuracy of the technique, using a fine grid two cases ofdiffering wall temperatures for the case of M=0.3 andRe=45,000 and H/b=2.5 were run. The film to main flowtemperature ratio for both cases was 0.85 and the wall tomain flow temperature ratios were 0.85 and 0.9.

Figure 7 show the flow near the hole. In Fig. 7 (a) itcan be seen that the coolant air has covered the tipsurface immediately downstream of the hole. Due to theflow separation and backward flow of the main streamair the fluid emerging out of the hole flows upstream(fig. 7(b)) and spills out the sides of the hole thuscovering the surface between holes. This action appearsto help the spanwise uniformity ofh andη . Thus theproximity of the hole to the pressure side edge of the

blade in addition to the ones already considered hereappears to be an important factor in tip film cooling. InFig. 7 (c) the distribution of cooling effectiveness overthe entire surface is shown where the relative uniformityis evident. In the experiment of Kim and Metzger theresulting effectiveness was completely uniform.

Figure 8 shows the comparison between thecomputed spanwise averaged cooling effectiveness andthe experimentally measured values. The overallagreement is quite good and improves with distancefrom the hole. In Fig. 8 the distribution obtained from

(a)

(b)

Fig. 7 (a) Top view of the blowing hole showing thecooling fluid distribution on the surface and (b)

interpolated on a uniform grid velocity vectors on thehole’s minor plane of symmetry and (c)cooling

effectiveness distribution over the surface

0.60.5 0.4

0.3

0.2

0.8

10.6

0.15

(c)

NASA/CR—1999-209165 5

the coarse grid is also shown. The solution shown as 2/3coarse grid was obtained on a grid similar to the coarsegrid except in the normal direction from the heattransfer surfaces where the grid was as refined as thefine grid. The agreement with the experimentalmeasurements is quite similar to the fine grid solutionwhereas the true coarse grid shows agreement with thedata away from the holes. The comparison of thecalculated spanwise averaged Nu_D with the measuredvalues is shown in Fig. 9. The agreement with theexperimental data near the hole is not very good butimproves away from the hole. The agreement away fromthe holes is encouraging since the objective of filmcooling is to provide a blanket of coverage persisting fardownstream of the holes. The near hole area is generallyovercooled and not normally a failure region.Nevertheless, the near hole results if used in a designwould lead to a conservative design. Figures 8 and 9show that the effectiveness can be computed with betterreliability than the heat transfer coefficient.

SUMMARY AND CONCLUSIONS

The use of CFD code to predict the rate of heattransfer and the cooling effectiveness for tip cooling ofblades was investigated. To this end the simplifiedphysical model of Kim and Metzger and thecorresponding data were used. The three temperatureproblem was solved by setting up two cases withdiffering wall temperatures and solving forh andη. Theprocess was repeated using the two cases above with athird case pairwise to ensure the consistency of themethod.

The heat transfer coefficient required higher gridresolution than the effectiveness. There was a largevariation of the heat transfer coefficient with the griddensity. This is logical since the flow near the hole, stillunder the influence of the tip clearance entrance effect,is quite complex and nonuniform. The variation ofeffectiveness with the grid density was much reduced.The agreement of the computed effectiveness with the

data was quite good. The agreement with the heattransfer coefficient very near the holes (up to 3 to 4diameters) was not very good but improved away fromthe holes. The agreement away from the holes where theeffectiveness of cooling is diminished is encouraging.The near hole area is generally overcooled and notnormally a failure region.

Numerical flow visualization showed that theuniformity of wetting of the surface by the film coolingjet is helped by the reverse flow due to edge separationof the main flow and that the distance from the pressureside edge to the edge of the film cooling hole may be animportant variable.

REFERENCES

Ameri, Ali A., and Steinthorsson, E., 1995,“Prediction of Unshrouded Rotor Blade Tip HeatTransfer,” ASME 95-GT-142.

Ameri, Ali A., and Steinthorsson, E., 1996,“Analysis of Gas Turbine Rotor Blade Tip and ShroudHeat Transfer,” IGTI 96-GT-189.

Ameri, Ali A., and Steinthorsson, E., Rigby, DavidL., 1997, “Effect of Squealer Tip on Rotor Heat Transferand Efficiency,”Journal of Turbomachinery, Vol. 120.pp 753-759.

Ameri, A. A., Steinthorsson, E. and Rigby, D. L.1998, “Effects of Tip Clearance and Casing Recess onHeat Transfer and Stage Efficiency in Axial Turbines,”ASME paper 98-GT-369., to published in the Journal ofTurbomachinery.

Ameri, A.A. and R.S. Bunker, 1999, Heat Transferand Flow on the First Stage Blade Tip of a PowerGeneration Gas Turbine Part 2: Simulation Results,ASME paper no. 99-GT-283, to be published in theJournal of Turbomachinery.

Boelter, L. M. K., Young, G. and Iverson, H. W.,1945, “An Investigation of Aircraft Heaters. XXVII--Distribution of Heat Transfer Rate in the EntranceRegion of a Tube,” NACA TN 1451.

Bunker, R.S., Bailey J.C. and Ameri, A.A., 1999,“Heat Transfer and Flow on the First Stage Blade Tip of

0.0 5.0 10.0 15.0 20.0X/b

0.0

0.2

0.4

0.6

0.8

1.0

CO

OLI

NG

EF

FE

CT

IVE

NE

SS Data of Kim & Metzger (1995)

Fine grid solutionCoarse grid solution2/3 coarse grid

0.0 5.0 10.0 15.0 20.0X/b

0.0

100.0

200.0

300.0

Nu_

D

Data of Kim & Metzger (1995)Fine grid solutionCoarse grid solution2/3 coarse grid

Fig. 9Spanwise averaged Nusselt numberdownstream of the cooling hole

Fig. 8Spanwise averaged cooling effectiveness

NASA/CR—1999-209165 6

a Power Generation Gas Turbine, Part 1: ExperimentalResults,” ASME paper no. 99-GT-169 to be published inthe Journal of Turbomachinery.

Chen, G., Dawes, W. N. and Hodson, H. P., 1993,“A Numerical and Experimental Investigation ofTurbine Tip Gap Flow,” AIAA paper 93-2253.

Kim, Y. W., Downs, J. P., Soechting, F. O., Abdel-Messeh, W., Steuber, G. D. and Tanrikut, S., 1995, “ASummary of the Cooled Turbine Blade Tip HeatTransfer and Film Effectiveness InvestigationsPerformed by Dr. D. E. Metzger,” Journal ofTurbomachinery, Jan. 1995, Vol. 117, pp. 1-11

Kim, Y. W. and Metzger, D. E., 1995“Heat Transferand Effectiveness on Film Cooled Turbine Blade TipModels,” Journal of Turbomachinery, Jan. 1995, Vol.117, pp. 12-21.

Menter, Florian R., 1993, “Zonal Two-Equation k-ω Turbulence Models for Aerodynamic Flows,” AIAA-93-2906

Rigby David, L., Ameri Ali, A. and SteinthorssonE., 1996, “Internal Passage Heat Transfer PredictionUsing Multiblock Grids and k-ω Turbulence Model,”IGTI paper 96-GT-188.

Steinthorsson, E., Liou, M. S., and Povinelli, L.A.,1993, “Development of an Explicit Multiblock/Multigrid Flow Solver for Viscous Flows in ComplexGeometries,” AIAA-93-2380.

Wilcox, D. C., 1994a,Turbulence Modeling forCFD, DCW industries, Inc. La Canada, CA.

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

NASA/CR—1999-209165 7

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National Aeronautics and Space AdministrationJohn H. Glenn Research Center at Lewis FieldCleveland, Ohio 44135–3191

July 1999

NASA CR—1999-209165

E–11756

13

A03

A Numerical Analysis of Heat Transfer and Effectiveness on Film CooledTurbine Blade Tip Models

A.A. Ameri and D.L. Rigby

Gas turbine; Tip clearance; Heat transfer; Film cooling; Numerical simulation

WU–523–26–13–00NAS3–98106

AYT CorporationBrook Park, Ohio 44142

Unclassified -UnlimitedSubject Categories: 02 and 34 Distribution: Nonstandard

A computational study has been performed to predict the distribution of convective heat transfer coefficient on asimulated blade tip with cooling holes. The purpose of the examination was to assess the ability of a three-dimensionalReynolds-averaged Navier-Stokes solver to predict the rate of tip heat transfer and the distribution of cooling effective-ness. To this end, the simulation of tip clearance flow with blowing of Kim and Metzger was used. The agreement ofthe computed effectiveness with the data was quite good. The agreement with the heat transfer coefficient was not asgood but improved away from the cooling holes. Numerical flow visualization showed that the uniformity of wettingof the surface by the film cooling jet is helped by the reverse flow due to edge separation of the main flow.

Prepared for the 14th International Symposium on Air Breathing Engines sponsored by the International Society for AirBreathing Engines, Florence, Italy, September 5–10, 1999. A.A. Ameri, AYT Corporation, Brook Park, Ohio 44142, andD.L. Rigby, Dynacs, Inc., Brook Park, Ohio 44142. Project Manager, R. Gaugler, Turbomachinery and Propulsion SystemsDivision, NASA Glenn Research Center, organization code 5820, (216) 433–5882.