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Journal ofHeat Transfer Technical Note

This section contains shorter technical papers. These shorter papers will be subjected to the same review process as that for full papers

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Film Effectiveness Downstreamof a Row of Compound AngleFilm Holes

M. E. Taslim and A. KhanichehMechanical and Industrial Engineering Department,Northeastern University, Boston, MA 02115

Effects that two different compound-angle film-hole configuratihave on film cooling effectiveness are investigated. Effectivemeasurements have been made downstream of a single rocompound-angle cylindrical holes with a diameter of 7.5 mm, aa single row of compound-angle, diffuser-shaped holes withinlet diameter of 7.5 mm. Both geometries were inclined wrespect to the coverage surface at an anglea of 25 deg. Thecylindrical holes, however, were oriented perpendicular to thigh-temperature airflow direction while the diffuser-shaped hohad a compound angle of 45 deg with respect to the high tempture air flow direction. Both geometries were tested over a bloing ratio range of 0.7 to 4.0 Surface temperatures were measualong four longitudinal rows of thermocouples covering the dowstream area between two adjacent holes. The results showedthe best overall protection over the widest range of blowing ratwas provided by the diffuser-shaped film cooling holes, partilarly at high blowing ratios. The increased cross-sectional areathe shaped hole exit lead to a reduction of the momentum fluthe jet exiting the hole. Therefore, the penetration of the jet ithe main flow was reduced, resulting in an increased coolingfectiveness. CFD analyses were also performed to study thecooling effectiveness downstream of the row of holes. Compsons between the test and numerical results showed a reasonagreement between the two, thus CFD can be considered a vtool to predict the cooling performance of different film coolinconfigurations in a parametric study.@DOI: 10.1115/1.1865222#

IntroductionFor film cooling with compound-angle injection, higher an

more uniform film cooling effectiveness is expected due toreduced axial momentum and the enhanced lateral momentuthe secondary flow. Ligrani et al.@1,2# tested cases off530 degandf550.5 deg for both a single row and staggered double rof holes with compound-angle injection. Their results showed tthe compound-angle injection configuration significantly improved the film cooling protection. Studies by Ekkad et al.@3,4#,Sen et al.@5#, and Schmidt et al.@6#, provided film cooling effec-tiveness and heat transfer coefficient distribution over a flat

Contributed by the Heat Transfer Division for publication in the JOURNAL OFHEAT TRANSFER. Manuscript received by the Heat Transfer Division February2004; revision received December 15, 2004. Associate Editor: P. M. Ligrani.

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face with one row of inclined holes for different compounangles. Similar to previous studies, they found that compouangle injection provides higher effectiveness values than injecwithout a compound angle. In another attempt to further improthe cooling process, attention has been turned to adapting shholes, such as holes with enlarged exits. Using these shaped hbetter cooling performance can be obtained due to the reductiopenetration of coolant jets into the hot gases and improved latspread of coolant. Overall improvements in film effectivenewere found in the studies conducted by Goldstein et al.@7,8#,Papell@9#, Makki and Jakubowski@10#, and Gritsch et al.@11#, fora variety of shaped holes. These studies have shown that exping the exit of the cooling hole improves film cooling performanrelative to that for a cylindrical hole. One further step in improing the performance of film cooling is the combination of compound angle holes with shaped holes producing noncylindrholes oriented away from the streamwise direction. Less workdocumented film cooling effectiveness for the compound-anshaped hole. In a recently published paper, Bell et al.@12# inves-tigated the film cooling effectiveness and the Stanton number rdownstream of different cooling hole configurations, such aslindrical, round, simple angle; laterally diffused, simple angle; lerally diffused, compound angle; forward-diffused, simple angand forward-diffused, compound angle. The best overall protion was provided by laterally diffused, compound-angle holfollowed by forward diffused, compound-angle holes. Early coputational studies of film cooling were limited to simplified gometries with coarse grids. Bergeles et al.@13# used a finite dif-

0,Fig. 1 Schematics of the test apparatus

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ference scheme with a ‘‘partial parabolic’’ scheme of flowfieldthe neighborhood of the injection holes with poor agreementtween numerical results and experimental data. Much fimeshes, as well as more accurate discrete schemes, were nto improve the accuracy of results. Demuren@14# showed that foridentical grid meshes a higher-order discretization schemeformed better than a first-order hybrid scheme. Leylek and Ze@15# showed that the computational model must include the fihole and plenum regions to capture the physics of the jet crflow interaction accurately. Of the recent investigations that eploy numerical techniques, Walters and Leylek@16#, McGovernand Leylek@17#, Hyams and Leylek@18#, and Brittingham andLeylek @19# performed computational simulations with compa

Fig. 2 Film-hole geometries

Journal of Heat Transfer

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son to experimental data to obtain the effects of streamwise intion and compound angle with cylindrical and shaped holes.

In this study, film cooling effectiveness distributions are mesured downstream of two different hole geometries: a row wcompound-angle cylindrical hole configuration and a row wcompound-angle, shaped holes. To the best of the authors’ knedge, no similar comparisons of experimental data exist inopen literature. Thus, there is significant need for experimefilm effectiveness measurements downstream of thesecompound-angled geometries, both for the design of gas turcomponents, as well as for the development of numerical modA numerical study was also conducted and numerically calculafilm effectiveness distributions are compared with the correspoing measured results.

Experimental SetupFigure 1 shows the schematics of the test apparatus, consi

of hot and cold air circuits. The mainstream air was directed to

Fig. 4 Schematics of the mesh arrangements for the shapedfilm hole

Fig. 3 Thermocouple arrangement downstream of the film holes

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Fig. 5 Film effectiveness versus normalized distance downstream of the compound-angle cylindri-cal film holes

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electric heater where its temperature was raised to about 5then into a plenum chamber as two opposing jets for proper ming, through a wire mesh and then to the mainstream channea bell-mouth opening. The film cooling air was directed to a drand then to a copper coil immersed in an ice-water box in ordereduce its temperature to about 0°C, and then into the cooplenum chamber. The mainstream plenum and channel were mof an aluminum shell with polyurethane-slab inserts. A removatest piece, made out of a 7.62-cm-thick polyurethane slab of rtively low conductivity (k50.35 W/mK), was the part of the tesapparatus that had the relevant film-hole geometry for each testhis study, two instrumented test pieces with two different copound angle film hole configurations were tested: a single rowfive compound-angle cylindrical holes, and a single row of ficompound-angle forward-lateral-diffused holes. Coolant wasjected through these cooling holes from a fiberglass plenwhich was installed on the back of the test piece. Details ofhole geometries are shown in Fig. 2. All holes had a diamete7.5 mm at their inlet, and were separated 5.56 diameters in

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lateral direction~center-to-center!. The total axial length of eachhole was eight times its inlet diameters. Both film hole geometrmade a 25 deg angle with the coverage surface. Cylindrical hwere oriented perpendicular to the high temperature airflow wthe shaped holes had a compound angle of 45 deg with respethe hot air flow. Surface temperatures were measured at disclocations using 74K-type thermocouples mounted flush with thcoverage surface. The thermocouples were oriented alonglongitudinal rows covering the downstream area between twojacent holes. Figure 3 shows the thermocouple arrangemdownstream of the cylindrical film holes. Similar arrangemewas set for the shaped holes. A rake of 10 thermocouples oriein a plane immediately upstream of the film hole outlets and ppendicular to the hot air flow measured the hot air temperaprofile. These thermocouples were unevenly spaced with mthermocouples close to the coverage surface. The first oneabout 0.2 mm above the surface. Air temperature variation acthe hot air channel was insignificant. Coolant temperature wmeasured immediately upstream of the film hole outlet. Two cr

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Journal of H

Fig. 6 Film effectiveness versus normalized distance downstream of the compound-angle forward-lateral-diffused film holes

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cal venturis measured the hot and cold air mass flow rate.each test, the blowing ratios~M! was varied between 0.7 and 4Film effectiveness was calculated directly from the experimendata as:

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Experimental uncertainties for the film effectiveness valufollowing the method of Kline and McClintock varied from62%around the film-hole exit to about67% for the last thermocoupleon each row. Blowing ratio uncertainty varied from62% to64.3%. To account for the conduction losses, a solid model oftest piece for each film-hole geometry was meshed and solvethe test boundary conditions@20#. It was found that only for thecylindrical hole case, due to a shorter conduction path, thetwo thermocouple readings on each row had to be corrected fmaximum error of 1.2°C. The shaped hole conduction analyshowed insignificant errors in thermocouple readings.

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Numerical ModelsThe computational model simulated a row of compound-an

cylindrical film cooling holes and a row of compound-anglforward-lateral-diffused film cooling holes using the assumptof repeating boundary conditions between holes. For accurateresentation of the jet crossflow interaction, it is necessarymodel the hot channel, film cooling hole, and cold plenum regiosimultaneously. Figure 4 shows this representative domain forcompound angle, forward-lateral-diffused film cooling hole geoetry and details of the numerical grid. The CFD analysis wperformed using theFluent/UNS solver by Fluent, Inc., apressure-correction-based, multiblock, multigrid, aunstructured/adaptive solver. The standardk-« turbulence modelin conjunction with the generalized wall function was usedturbulence closure. Other available options, short of the two-lamodel which required a remeshing of the numerical models, wtried without any significant changes in the final results. Meindependence was achieved at about 350,000 cells for compo

APRIL 2005, Vol. 127 Õ 437

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angle cylindrical configuration, and at about 450,000 cells forcompound angle, forward-lateral-diffused configuration with tmajority of cells in the film cooling hole and near the bottom wchannel. Cells in both models were entirely hexagonal, a prefechoice for CFD analysis, and were varied in size bigeometricfrom the boundaries to the center of the computational domaiorder to have finer mesh around the film-hole boundaries. M

Fig. 7 Laterally averaged film effectiveness for small „a…, me-dium „b…, and large „c… blowing ratios

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size for the first row of cells on the wall was varied such thatoverall averagey1 for the first row of cells was less than 20. Aboundary conditions matched the experimental values. Massrate boundary conditions were specified at the inlet of thechannel and the cold plenum. At both the hot channel and theplenum inlet planes, turbulence intensity was set to 1%, andlength scale was taken as 1/10th of the hydraulic diameter ofinlet. Adiabatic boundary conditions were assumed for all wallsconstant pressure condition was applied at the outlet, withother flow variables upwinded.

Results and DiscussionFigure 5 shows the film effectiveness versusx/d for all four

rows of thermocouples downstream of the cylindrical film holeRepresentative results for five blowing ratios, ranging from 0.7to 3.83, show that beyondx/d58 the film effectiveness decreaseas the blowing ratio increases. This is an indication of the coopenetration into the main flow as its momentum increases withincreasing blowing ratio. A local increase in film effectivenewith the blowing ratio, consistently observed in the interval btween x/d53 and x/d58 depending on spanwise location,attributed to the coolant jet reattachment to the surface aftedetachment immediately downstream of the film hole exit.

Representative results of the measured film effectiveness foshaped film holes are shown in Fig. 6 for the same blowing raas those for the cylindrical film holes. Several observationsmade. Film effectiveness values, especially further downstreamthe film holes are higher than those of the cylindrical holes. Fthe same amount of coolant, increased exit area has reducecoolant momentum and increased the coverage area both conuting to the increased film effectiveness. Contrary to the cylindcal film holes, for these shaped holes, the film effectivenesscreases with the blowing ratio. Again, increased exit area reduthe coolant exit velocities to levels much lower than those ofcylindrical film holes, thus reducing the rate of penetration of tcoolant into the mainstream. Local peaks in film effectivenessthe first and second rows of the thermocouples in the vicinityx/d54 – 8 is again attributed to the reattachment of the coolanthe surface after its initial detachment immediately downstreamthe exit area.

Figure 7 compares the laterally averaged film cooling effectiness in the mainstream direction for the two film hole geometrResults are presented for three blowing ratios. As expected byindividual row results of Figs. 5 and 6, the shaped holes are pducing much higher film effectiveness, especially at high blowratios. The improvement in laterally averaged film cooling effetiveness when using shaped film holes is caused mainly byincreased lateral spreading of the injected cooling air and becoverage of the surface. Compared with the cylindrical film holthe laterally averaged film effectiveness of the shaped film hoincreased by about 25% for the lowest blowing ratio, 35% formedium blowing ratio, and up to 45% for the highest blowinratio.

CFD ResultsResults from computational simulation are presented in

form of comparison with experiments for downstream lateraaveraged film effectiveness values. These comparisons shogood agreement with experiments, and served to validate the cputational method. CFD models identical to the tested geomfor each case were run on PC Pentium4™, 1.6 GHz machwith 512 MB memory. A typical case took about 2000 iteratioand about one full day to converge. Figure 8 shows the compuversus measured laterally-averaged film effectiveness vadownstream of the film holes. For the compound-angle cylindrifilm holes, the most significant disagreement occurs immediadownstream of the jet exit in the near-hole region (x/d,5). Thenumerical models consistently predicted lower effectivenessues in this region. These deviations are attributed partly to ins

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Fig. 8 Comparison between the experimental and numerical laterally averaged film effectiveness

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ficient spreading in the computations and also the limited abof creating perfectly adiabatic surfaces in the experiments. Asx/dincreases, the agreement between predicted and measuredeffectiveness values becomes very good. For the compound-aforward-lateral-diffused film hole, in the near-hole region (x/d,3) effectiveness is somewhat over-predicted, presumablycause of a hypothesized recirculation region immediately dostream of the film hole exit; the use of wall functions in the simlations does not allow the grid resolution necessary to capsuch a phenomenon. As the coolant moves further downstrethe numerical model seems to slightly overpredict the film efftiveness. The maximum difference, however, is about 10%.

ConclusionsFilm effectiveness values were measured and compared for

film-hole geometries: a single row of compound-angle cylindriholes and a single row of compound-angle forward-latediffused holes. A combination of several factors, including lesspenetration into the mainstream, cooling flow diffusion, lower v

Journal of Heat Transfer

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locity gradient because of increased exit area, increased laspreading, and greater injectant concentration near the covesurface results in a better cooling performance for the forwalateral-diffused film holes, particularly at high blowing ratioComputations were performed usingFluentsoftware to study filmcooling effectiveness downstream of the hole geometries usethe experiments. Comparisons between the experimentally msured and numerically calculated film effectiveness distributshowed that the computed results, especially for the shaped hare in good agreement with the measured results. Therefore,can be used as a viable tool to predict cooling performancesdifferent film cooling configurations in a parametric study.

Nomenclature

A 5 cross-sectional area perpendicular to the flow direction

L 5 film-hole lengthM 5 blowing ratio, (rU)c /(rU)h5(m/A)c /(m/A)hP 5 film-hole pitch

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T 5 temperatured 5 film-hole diameter in the cylindrical portionk 5 thermal conductivity

m 5 air mass flow ratex 5 distance downstream of the cooling hole in the hot

air flow direction~Fig. 3!y 5 lateral direction~Fig. 3!a 5 injection angle~angle between the film hole axis and

the coverage plane!h 5 film cooling effectiveness, (Th2Taw)/(Th2Tc)h̄ 5 laterally averaged film cooling effectivenessr 5 air densityf 5 compound angle~Fig. 2!

Subscripts

aw 5 adiabatic wallc 5 property value at injection hole~cold! conditionsh 5 property value at mainstream air~hot! conditions

References@1# Ligrani, P., Wigle, J., Ciriello, S., and Jackson, S., 1994, ‘‘Film Cooling Fro

Holes With Compound Angle Orientations, Part I: Results Downstream of TStaggered Rows of Holes With 3D Spanwise Spacing,’’ ASME J. Heat Trafer, 116, pp. 341–352.

@2# Ligrani, P., Wigle, J., Ciriello, S., and Jackson, S., 1994, ‘‘Film Cooling FroHoles With Compound Angle Orientations, Part I: Results Downstream oSingle Row of Holes With 6D Spanwise Spacing,’’ ASME J. Heat Transf116, pp. 353–362.

@3# Ekkad, S., Zapata, D., and Han, J., 1997, ‘‘Heat Transfer Coefficient OvFlat Surface With Air and CO2 Injection Through Compound Angle HoleUsing a Transient Liquid Crystal Image Method,’’ ASME J. Turbomach.,119, pp. 580–586.

@4# Ekkad, S., Zapata, D., and Han, J., 1997, ‘‘Film Effectiveness Over aSurface With Air and CO2 Injection Through Compound Angle Holes UsingTransient Liquid Crystal Image Method,’’ASME J. Turbomach.,119, pp. 587–593.

@5# Sen, B., Schmidt, D. L., and Bogard, D. G., 1996, ‘‘Film Cooling With Compound Angle Holes: Heat Transfer,’’ ASME J. Turbomach.,118, pp. 800–806.

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@6# Schmidt, D. L., Sen, B., and Bogard, D. G., 1996, ‘‘Film Cooling With Compound Angle Holes: Adiabatic Effectiveness,’’ ASME J. Turbomach.,118, pp.807–813.

@7# Goldstein, R. J., Eckert, E. R. G., and Burggraf, F., 1974, ‘‘Effects of HoGeometry and Density on Three-Dimensional Film Cooling,’’ Int. J. Heat MaTransfer,17, pp. 594–605.

@8# Goldstein, R. J., and Jin, P., 2001, ‘‘Film Cooling Downstream of a RowDiscrete Holes With Compound Angle,’’ ASME J. Turbomach.,123, pp. 222–230.

@9# Papell, S., 1984, ‘‘Vortex Generating Flow Passage Design for IncreasedCooling Effectiveness and Surface Coverage,’’ ASME Paper No. 84-HT-2

@10# Makki, Y. H., and Jakubowski, G. S., 1986, ‘‘An Experimental Study of FilCooling From Diffused Trapezoidal Shaped Holes,’’ AIAA Paper No. AIAA86-1326.

@11# Gritsch, M., Schulz, A., and Witting, S., 1998, ‘‘Adiabatic Wall EffectiveneMeasurements of Film Cooling Holes With Expanded Exits,’’ ASME J. Tubomach.,120, pp. 549–556.

@12# Bell, C. M., Hamakawa, H., and Ligrani, P. M., 2000, ‘‘Film Cooling FromShaped Holes,’’ ASME J. Heat Transfer,122, pp. 224–232.

@13# Bergeles, G., Gosman, A. D., and Launder, B. E., 1978, ‘‘The Turbulent Jea Cross Stream at Low Injection Rates: A Three-Dimensional Numerical Trment,’’ Numer. Heat Transfer,1, pp. 217–242.

@14# Demuren, A. O., 1982, ‘‘Numerical Calculation of Steady Three-DimensioTurbulent Jets in Cross Flow,’’ Rep. SFB 80/T/129, Sonderforschungsber80, University of Karlsruhe, Germany.

@15# Leylek, J. H., and Zerkle, R. D., 1994, ‘‘Discrete Jet Cooling: A ComparisonComputational Results With Experiments,’’ ASME J. Turbomach.,113, pp.358–368.

@16# Walters, D. K., and Leylek, J. H., 1997, ‘‘A Systematic Computational Meodology Applied to a Three-Dimensional Film Cooling Flowfield,’’ ASME JTurbomach.,119, pp. 777–785.

@17# McGovern, K. T., and Leylek, J. H., 2000, ‘‘A Detailed Analysis of FilmCooling Physics: Part II Angle Injection With Cylindrical Holes,’’ ASME JTurbomach.,122, pp. 113–121.

@18# Hyams, D. G., and Leylek, J. H., 2000, ‘‘A Detailed Analysis of Film CoolinPhysics: Part III Streamwise Injection With Shaped Holes,’’ ASME J. Turboach.,122, pp. 122–132.

@19# Brittingham, R. A., and Leylek, J. H., 2000, ‘‘A Detailed Analysis of FilmCooling Physics: Part IV Angle Injection With Shaped Holes,’’ ASME J. Tubomach.,122, pp. 133–145.

@20# Khanicheh, A., 2002, ‘‘An Experimental and Computational Investigationthe Film Cooling Effectiveness of a Single Row of Cylindrical and ShapHoles,’’ Northeastern University, M.S. thesis.

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