Measured Adiabatic Effectiveness and Heat Transfer for Blowing From the Tip of a Turbine Blade

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1 See discussions, stats, and autor profiles for tis publication at: ttps:// Measured Adiabatic Effectiveness and Heat Transfer for Blowing From te Tip of a Turbine Blade Article in Journal of Turbomacinery April 5 Impact Factor:.9 DOI:.5/.895 CITATIONS READS 4 autors, including: Karen A. Tole Pennsylvania State University 6 PUBLICATIONS,49 CITATIONS F. J. Cuna University of Connecticut PUBLICATIONS 4 CITATIONS SEE PROFILE SEE PROFILE Available from: Karen A. Tole Retrieved on: May 6

2 Proceedings of ASME Turbo Expo 4 Power for Land, Sea, and Air June 4-7, 4, Vienna, Austria GT4-55 MEASURED ADIABATIC EFFECTIVENESS AND HEAT TRANSFER FOR BLOWING FROM THE TIP OF A TURBINE BLADE J. R. Cristopel, E. Couc, and K. A. Tole Mecanical Engineering Virginia Polytecnic Institute and State University Blacksburg, VA 46 F. J. Cuna Pratt & Witney United Tecnologies Corporation East Hartford, CT 68 ABSTRACT Te clearance gap between te tip of a turbine blade and te sroud as an inerent leakage flow from te pressure side to te suction side of te blade. Tis leakage flow of combustion gas and air mixtures leads to severe eat transfer rates on te blade tip of te ig pressure turbine. As te termal load to te blade increases, blade alloy oxidation and erosion rates increase tereby adversely affecting component life. Te subject of tis paper is te cooling effectiveness levels and eat transfer coefficients tat result from blowing troug two oles placed in te forward region of a blade tip. Tese oles are referred to as dirt purge oles and are generally required for manufacturing purposes and expelling dirt from te coolant flow wen operating in sandy environments. Experiments were performed in a linear blade cascade for two tip gap eigts over a range of blowing ratios. Results indicated tat te cooling effectiveness was igly dependent upon te tip gap clearance wit better cooling acieved at smaller clearances. Also, eat transfer was found to increase wit blowing. In considering an overall benefit of cooling from te dirt purge blowing, a large benefit was realized for a smaller tip gap as compared wit a larger tip gap. INTRODUCTION Te performance of a turbine engine is a strong function of te maximum gas temperature at te rotor inlet. Because turbine airfoils are exposed to ot gas exiting te combustion camber(s), te materials and cooling metods are of critical importance. Turbine blade designers concentrate eavily on finding better cooling scemes to increase te overall operation life of all turbine airfoils, namely te ig pressure turbine blades. Te clearance between te blade tip and te associated sroud, also known as te blade outer air seal, provides a flow pat across te tip tat leads to aerodynamic losses and ig eat transfer rates along te blade tip. Te flow witin tis clearance gap is driven by a pressure differential between te pressure and suction side of te blade, but is also affected by te viscous forces as te fluid passes troug te gap. From an operational point-of-view, engine removals from service are primarily dictated by te spent exaust gas temperature (EGT) margin caused by deterioration of te ig pressure turbine components. Increased clearance gaps accelerate effects of low cycle termal-mecanical fatigue, oxidation, and erosion as a result of increased temperatures in te turbine and decreased EGT margin. In general, tip clearances for large commercial engines are of te order of.5 mm, wic can reduce te specific fuel consumption by % and EGT by C (Lattime and Steinetz, []). Improving te blade tip durability can, terefore, produce fuel and maintenance savings over undreds of millions of dollars per year []. Te work presented in tis paper is on a realistic design for a turbine blade tip consisting of a flat tip wit te exception of a small cavity in wic two dirt oles are placed. Te location of tese oles is a direct consequence of te internal cooling passages witin te blade. Te purge ole cavity extends only over a small area in te front portion of te blade tip. Te function of te dirt purge oles includes te following: () purge oles allow centrifugal forces to expel any dirt ingested by te compressor into te turbine rater tan clogging te smaller diameter film cooling oles; and () purge oles provide a way to support te ceramic core during te lost-wax investment casting of te blade manufacturing process. Te dirt purge cavity is present to insure tat te purge oles remain open during eventual blade rubbing. Tis paper details te film-cooling and eat transfer associated wit blowing from te dirt purge oles along te tip of a turbine blade. Measurements of adiabatic effectiveness and eat transfer coefficients are studied wile varying te tip clearance and mass flux (blowing) ratios. RELEVANT PAST STUDIES Te work presented in tis paper is concerned wit te effects of injecting coolant from te tip of a turbine blade wereby te experiments were completed for a stationary, linear cascade. As suc, it is important to consider te relevance of past studies to evaluate te effects of te relative Copyrigt 4 by ASME

3 motion between te blade tip and outer sroud. It is also relevant to consider tests wereby tip blowing as been investigated. Regarding te effects of blade rotation, te first work to address te flow field effects was tat by Morpis and Bindon [] wo found tat teir static pressure measurements across te blade tip in an annular turbine cascade were not affected by te relative motion at te tip. Tey concluded tat te basic nature of te flow structures remained uncanged wit and witout relative motion. In contrast, te studies by Tallman and Laksminarayana [] and Yaras and Sjölander [4] sowed tat te leakage flow troug te gap was reduced along wit te leakage vortex in te case of a moving wall relative to a fixed wall. Tey attributed tis difference to te passage vortex being convected towards te suction surface by te moving wall and postulated tat te passage vortex position can alter te driving pressure troug te tip gap. Altoug tere are apparent effects of a moving wall on some of te reported flow field studies, tip eat transfer studies generally indicate relatively minor to non-existent effects of a moving wall. Te reason for tis relatively minor effect was first ypotesized by Mayle and Metzger [5], wo evaluated te effects of relative motion on te eat transfer in a simple pressure-driven duct flow. Tey derived and also sowed experimentally tat for a flow pat lengt wit less tan times te clearance gap, te flow can be considered as developing duct flow. As suc, te boundary layers on eac surface do not merge and terefore te effect of te relative wall (sroud) movement is inconsequential. Tis range is relevant to te assessment given tat te lengt of te flow pat along te blade tip relative to te clearance gap ranges between.5 near te trailing edge for te smallest gap to 5 near te leading edge (tickest part of te airfoil) for te largest gap. Lending furter credibility to te ypotesis of Mayle and Metzger are te works of Cyu et al. [6] wit a sroud surface moving over a simple rectangular cavity and Srinivasan and Goldstein [7] wit a moving wall over a turbine blade. In particular, te work of Srinivasan and Goldstein sowed only small effects of te wall motion on teir measured Serwood numbers (eat-mass transfer analogy) in te leading edge region were te pat lengt to clearance gap was larger () tan te criterion stated by Mayle and Metzger () for te smallest clearance gap tat tey studied. For te largest gap in teir study, tey saw no noticeable effect of te wall motion. Te only reported tip blowing studies were tose completed by Kim and Metzger [8] and Kim et al.[9], wo used a two-dimensional cannel wit a number of different injection geometries, and by Kwak and Han [,], Acarya, et al. [], and Holfeld, et al.[], wo all used blade geometries. Four tip blowing geometries were investigated by Kim et al. tat included te following: discrete slots located along te blade tip, round oles located along te blade tip, angled slots positioned along te pressure side, and round oles located witin a cavity of a squealer tip. For a given coolant flow, te best cooling performance was obtained using te discrete slot configuration wereby an optimum blowing ratio was discerned. In general, Kim et al. reported iger effectiveness accompanied by iger eat transfer coefficients wit iger injection rates. Kwak and Han [,] reported measurements for varying tip gaps wit cooling oles placed along te pressure surface at a breakout angle, relative to te pressure surface, and on te tip surface for an unsrouded [] and srouded [] tip. For te unsrouded (flat) tip, Kwak and Han found increases in te eat transfer coefficients and adiabatic effectiveness occurred wit increased coolant injection and increased gap eigts. Tis is in contrast to te work presented by Kim et al., wo identified an optimum blowing ratio. For te srouded tip, Kwak and Han indicated a benefit of aving a sroud in tat tere was a reduction of te eat transfer coefficients and an increase in adiabatic effectiveness levels wen compared to te flat tip. Heat transfer measurements on flat tips wit no cooling ave been presented by many autors, including Bunker et al. [4], Kwak and Han [], and Jin and Goldstein [5]. Tese studies ave sown tere to be a region of low eat transfer located near te tickest portion of te blade. Morpis and Bindon [] and Bindon [6] ave also sown tere to be a separated region followed by a reattacment wit ig eat transfer coefficients along te pressure side of te blade tip in te entry region (Bunker et al. [4]). Tere ave also been only a relatively few computational predictions for a tip gap wit blowing including tose by Acarya et al. [] and Holfeld et al. []. Acarya et al. found tat film coolant injection lowered te local pressure ratio and altered te nature of te leakage vortex. Hig film cooling effectiveness and low eat transfer coefficients were predicted along te coolant trajectory. Bot studies indicated tat for te smallest tip gap, te coolant impinged directly on te sroud, but as te gap size increased, predictions indicated tat te coolant jets were unable to impinge upon te sroud. In summary, only one experimental study as addressed blowing in te tip gap of a turbine blade. Te objectives of te work presented in tis paper are to present te benefits of filmcooling of a blade tip using coolant exausted from dirt purge oles. In particular, bot te effectiveness levels and eat transfer coefficients were measured and combined using a net eat flux reduction to evaluate te benefits. EXPERIMENTAL FACILITY AND METHODOLOGY Te experiments were conducted in a large-scale, lowspeed, closed-loop wind tunnel tat provided matced engine Reynolds number conditions. Te flow conditions and relevant geometry are summarized in Table wit a diagram of te wind tunnel and test section sown in Figure and Figure. Results reported in tis paper include adiabatic wall temperature measurements and eat transfer coefficients along te tip. Table. Geometry for te Blade Tip Model Parameter Scaled Model Scaling Factor X Axial cord, B x (% Span) 6 True Cord, C (% Span) 96. Pitc, P (% Span) 78 Re. x 5 Inlet Angle, θ 6.5 Coolant-Mainstream Temperature Ratio.9 Small tip gap, (% Span).5 Large tip gap, H (% Span).6 Copyrigt 4 by ASME

4 Te wind tunnel, sown in Figure, includes a 5 Hp fan tat drives te flow troug a primary eat excanger to obtain a uniform temperature profile. Te flow is divided into tree passages. Te main passage, located in te center, as a eater used to acieve a ot mainstream gas, wile te flow in te two outer passages provided a single row of normal jets used to generate an inlet turbulence level to te cascade of % and an integral lengt scale of cm. To quantify te integral time scale, velocity fluctuations were measured using a ot-wire anemometer. Tese jets were uneated (due to a facility constraint) and were injected one cord upstream of te blade. Te mass flow of te injected jets represented 4.% of te core mass flow and ad a momentum flux ratio of 8. Because of te ig turbulence generated, te termal field entering te cascade was quite uniform. Te main features of te linear cascade test section, sown in Figure, were an instrumented center blade, two outer blades, sidewall bleeds, and adjustable tailboards. Tese components were required to ensure periodic flow conditions. Coolant flow for te blade tip was provided to a plenum inside te center blade from an independent pressurized air supply. Te pressure drop across a venturi meter was used to quantify te coolant flowrate wile te incoming velocity to te test section was measured wit a pitot probe at several locations across te blade pitc. Figure sows te details of te plenum for te blade tip, te dirt purge cavity and te dirt purge oles. Te removable portion of te tip was 8% of te span (total span was 55 cm) and was specifically molded to allow for a number of different tip geometries to be studied. A two-part foam mixture tat exotermically expanded was used to mold te blade tip. Te Figure. Scematic of te wind tunnel facility used for te testing of te blade tips. Bleed Gate IR Window Locations Instrumented Blade cm Bleed Gate Figure. Te corner test section of te wind tunnel oused tree blades tat formed two full passages..9d 4.d.6d (/)H 7.d d.5d Plenum.9d Figure. Te blade tip included a plenum tat supplied coolant to te dirt purge oles. termal conductivity of tis foam was quite low at.6-.4 W/mK dependent upon te foam properties after expansion; tereby allowing for an adiabatic surface on te blade tip. Only te foam surface (no eater) was present during te effectiveness tests. For te adiabatic effectiveness tests, te experiments were conducted suc tat te coolant was nominally 5ºC lower tan te mainstream. Tis termal equilibrium required about 4 ours for eac test. For te eat transfer measurements, separate experiments were performed wit a constant eat flux surface installed on te tip surface. For tese tests, te coolant and mainstream temperatures were typically kept to witin.5ºc of one anoter. Two separate eaters were necessary because of te dirt purge cavity on te tip. Te dirt purge cavity was eated wit one strip of Inconel tat was.5 mm tick and ad a surface area of 7. cm. Te main eater covered an area of 6. cm and consisted of a serpentine Inconel circuit. As sown in Figure 4, te circuit consisted of te Inconel sandwiced between insulating Kapton and ten covered wit a very tin (. mm) layer of copper on bot sides. Bot eaters were attaced to a foam blade tip using double-sided tape tat was.64 mm tick. Te nominal eat flux for bot eaters was set to 7 W/m wic provided a maximum temperature difference between te mainstream and blade surface of 8ºC. Te two eaters were controlled independently to witin.67% of one anoter during all tests. Te current supplied to eac eater was known by placing a precision resistor (R =. Ω ±.%) in eac circuit and measuring te voltage drop across eac resistor wit a digital multimeter. Te eater power was ten determined from te supplied current and known eater resistance. Equation was used wen calculating te eat transfer coefficients. '' '' = ( qtot qr ) ( Tw T ) [] In tis equation, q '' tot represents te total eat flux output from te resistive eaters and q r '' represents te energy lost to radiation. Typically, radiation losses were less tan % wit te maximum for all cases being.4%. Conduction losses were found to be negligible since te eaters were placed on te low termal conductivity foam. For te surface temperature measurements along te tip, an infrared (IR) camera was used to take four separate images tat were ten assembled to provide te entire surface temperatures of te tip. Te image locations are sown in Figure. Te IR camera was positioned to look directly at te blade tip and required te use of a zinc selenide window placed along te outer sroud tat permitted 8- micron wavelengts to pass troug. Eac of te four IR camera images covered an area tat was. cm by 6 cm wit te area being divided into Copyrigt 4 by ASME

5 (a) (b) by 4 pixel locations. Te camera was located approximately 55 cm from te tip, resulting in a spatial resolution of.6 mm, wic is over 6 times smaller tan te dirt purge diameter. At eac viewing location five images were acquired and averaged at eac pixel location to give an overall image of te tip. Te calibration process for te camera involved direct comparisons of te infrared radiation collected by te camera wit measured surface temperatures using eiter termocouple strips placed on te tip surface (for te adiabatic effectiveness measurements) or termocouple beads placed underneat te eater (for te eat transfer measurements). For bot experiments, termocouples were placed on te blade surface using a bonding agent wit a ig termal conductivity of.6 W/mK. For te termocouples placed underneat te main tip eater, a ºC temperature adjustment was applied during calibration to account for te termal resistivity of te eater at te nominal Inconel eater in te dirt purge cavity was found to be negligible and no correction was needed for tis area of te blade tip. After te experiments were completed, te infrared images were processed wereby adjustments of te surface emissivity and background temperature (irradiation) were made until te image and termocouple temperatures matced. Tis process resulted in an agreement between all of te termocouples and infrared temperatures to witin ±. C ( η = ±.4). A ceck on te calibration process is tat te four individual images matced up well to form one entire blade contour witout any jumps in measured values between images. Static pressure taps were located near te mid-span of te central blade and tufts were located near te stagnation locations of all te blades to ensure periodic flow troug te passages was acieved. Te measured static pressure distribution around te center blade was compared wit an inviscid CFD simulation using periodic boundary conditions, as sown in Figure 5. Tis pressure loading is representative of a modern, ig pressure turbine blade. Overall uncertainties were calculated for non-dimensional temperature and eat transfer (η and Nu values) according to te partial derivative metod described in Moffat [7]. Te total uncertainty of all measurements was calculated as te root of te sum of te squares of te precision uncertainty and te bias uncertainty. Te precision uncertainty for measurements made wit te Sroud q '' = 7 W/m. Te termal resistance of te Tip Leakage Flow M tape Foam Copper (. mm) Combined Inconel/Kapton (.778 mm) Copper (. mm) Termocouple Figure 4. Main tip eat transfer surface sowing serpentine passages (a) and detail of main tip eater as placed on te blade surface (b). C p S/S max Computational Exp - no gap Exp - small gap Exp - large gap Figure 5. Measured and predicted static pressures at te blade mid-span. infrared camera was determined troug an analysis of five calibrated images taken in succession on one portion of te tip at constant conditions. Te precision uncertainty was calculated to be. C, wic is te standard deviation of te five readings based on a 95% confidence interval. Te camera manufacturer reported te bias uncertainty as.% of te full scale. Te largest scale used in tis study was C toug some images could be captured on a C range. A bias error of ± C was considered for te camera calibration. Te termocouples measuring te freestream and coolant temperatures were reported by te manufacturer to read witin ±. C. Te total uncertainty in effectiveness was found to be δη = ±.46 at η = and δη = ±.46 at η =.. Te total uncertainty in eat transfer measurements was 6% at Nu D = 45 and.5% at Nu D = Note tat te uncertainty is iger in te immediate vicinity of te dirt purge oles were te eat flux is not uniform. Te non uniformity of te eat flux does not effect te ratios of te eat transfer coefficients wit and witout blowing, owever, since tis effect is canceled. EXPERIMENTAEST CASES Tis series of experiments focused on investigating te effect of tip gap eigt and blowing ratio as indicated in Table. Wit regards to te tip gap eigt, two different gaps relative to te span were investigated including gaps tat were.54% () and.6% (H) of te span. Troug te remainder of tis paper tese two tip gaps will be referred to as small and large tip gaps. Wit regards to te blowing from te dirt purge oles, cases at eac tip gap eigt were measured wit a coolant flow rate tat ranged from.% to.8% of te primary core flow. Note tat tese flow rate ranges were cosen to simulate engine conditions. A baseline case was also considered for eat transfer measurements tat ad te dirt purge cavity present, but no oles. Measurements were performed at bot gap eigts for te baseline case. Te global and local ratios of mass and momentum fluxes were calculated for te blowing cases and are also given in Table. Te global mass and momentum flux ratios were based on te incident inlet velocity to te blade passage wile te local mass and momentum flux ratios were based on te local 4 Copyrigt 4 by ASME

6 Table. Matrix of Experiments and Blowing Ratios Holes and Coolant (% Passage Flow) Tip Gap Small, Large Small, Large Small, Large Small, Large Hole Hole Global M Global I Local M Local I Local M Local I tip flow conditions for eac of te two dirt purge oles. To compute te local external velocity for te dirt purge ole exits, te local static pressure for te dirt purge oles was taken as te average of te predicted static pressures for te pressure and suction surfaces at te 95% blade span location. Te blade locations of tese pressures were at % and 5% of te total surface distance measured from te stagnation location for dirt purge oles and, respectively. Te coolant velocity was calculated directly from measured coolant flow rates. As seen in Table, te local blowing (and momentum) ratio for ole, wic is te ole closest to te leading edge, is significantly iger tan ole, due to te lower local velocity present at te ole location. ADIABATIC EFFECTIVENESS RESULTS Te dirt purge oles serve te functional purpose of expelling dirt from te blade tat migt oterwise block smaller film cooling oles. Any cooling from te dirt purge oles is of potential benefit for cooling te leading edge region. Te cooling effects of te dirt purge jets are presented as adiabatic effectiveness levels tat were measured only in te leading edge alf of te blade. No coolant from te dirt purge oles was measured along te downstream portion of te blade tip, and as suc, only te front portions of te tip were measured. Figure 6 presents te measured adiabatic effectiveness contours for te small tip gap case at four different blowing ratios, ranging from.% to.8% (percents based on passage flow). At te lowest blowing ratio, te dirt purge oles cool only a portion of te tip downstream of te oles. Tere is very little cooling measured witin te dirt purge cavity. Tere is a dramatic increase in te measured adiabatic effectiveness levels as te coolant flow is increased for te small tip gap. Te maximum effectiveness for te lowest blowing ratio was.86 wile a maximum value of η =. was reaced for te.9%,.9%, and.8% blowing ratios. For coolant injection greater tan te.9% case, a completely cooled region was measured to extend from te pressure side of te tip to te suction side. Interestingly, te coolant is also present upstream of te dirt purge oles suc tat at te igest blowing ratio, te coolant extended to te leading edge of te tip. Tis is because te coolant exiting te dirt purge oles impacted te sroud and ten propagated outward in all directions. Tese very ig effectiveness levels in te leading edge region indicate a saturation of te coolant witin te tip gap. In general, tis is consistent wit field run ardware were tis portion of te airfoil as little evidence of tip oxidation. Figure 7 presents te measurements of adiabatic effectiveness contours for te large tip gap. Results indicate a significantly reduced benefit of te coolant exiting te dirt purge oles as compared wit te small tip gap. As te coolant is increased, te experiments sow a muc broader cool region downstream of te cavity. Tis spreading of te coolant for te iger blowing ratio cases is caused by an impingement of te jets onto te sroud. At te.8% coolant injection tere is coolant present wit te dirt purge cavity and upstream of te cavity. Tis is more similar to te small tip gap were coolant is filling te entire gap. Te camber line of te blade is used to compare data and is defined in Figure 8. Tis line extends troug te mid-section of te blade. Effectiveness data was taken along te camber line of te blade, sown in Figure 9, to furter illustrate te differences between te cases tested. Te vertical lines on bot plots indicate te location of te dirt purge oles. For te small tip gap sown in Figure 9a, te.% case as significantly lower effectiveness values tan te oter coolant levels. For te.9%,.9%, and.8% cases, tere is ardly any difference in peak values between te cases, but tere is increased spreading in te leading edge region wit increased blowing. Also, at te iger blowing ratios, te camber line sows tat.%.9%.9% % Figure 6. Adiabatic effectiveness contours taken along te tip wit dirt purge blowing for te small tip gap..9%.%...9% % Figure 7. Adiabatic effectiveness contours taken along te tip wit dirt purge blowing for large tip gap. Camber Line S/Smax x/c Figure 8. Definition of te blade camber line. 5 Copyrigt 4 by ASME

7 te effectiveness reaces a value of one almost all te way to te stagnation point (x/c = ). For te large tip gap sown in Figure 9b te effectiveness steadily increases wit eac blowing case as was discussed for te contour levels. Bot te peak values and spreading in te leading edge are increased wit eac increase in blowing rate. However, tere appears to be no benefit of nearly doubling te coolant flow from.% to.9% at te large tip gap until downstream of te second ole after wic tere is more spreading of te coolant for te iger coolant flow. Also, te overall effectiveness levels are lower at te large tip gap relative to te small tip gap. For all cases sown in Figures 9a and 9b, te results indicate η values tat are above zero outside of te region affected by te dirt purge blowing. Te reason for tis non-zero effectiveness level is due to a termal boundary layer effect. As was discussed in te experimental section of tis paper, te eaters for te main gas pat are located significantly upstream of te test section. As te flow progresses troug te contraction of just upstream of te test section, te flow near te wall is sligtly cooler tan te mid-span temperature resulting in non-zero effectiveness levels. All of te effectiveness measurements for dirt purge cases are summarized by considering an area average tat was calculated for a region defined from te leading edge to a location along te pressure side of s/c =.. A line drawn normal to te pressure side extending to te suction side defines te area. Tese area averages, wic represent effectiveness averages over 46% of te total blade tip area are sown in Figure. Overall tere is a dramatic difference between te small tip gap and te large tip gap at eac blowing ratio. Te small tip gap sows te average effectiveness increases wit blowing ratio, but is leveling off at te iger injection levels. Te area averages for te large tip gap case sow tat te effectiveness only sligtly increases wen te blowing ratio is increased from.% to.9% wit larger increases being measured beyond.9% injection levels. HEAT TRANSFER RESULTS As discussed, separate experiments were performed to measure eat transfer for baseline cases wit no blowing and for te blowing cases at bot tip gap eigts. Tese measurements were completed using a constant eat flux boundary condition on te tip surface. Baseline studies wit no blowing were used to validate te current experiments wit previous ones by comparing wit a fully developed cannel flow correlation. Te eat transfer for te blowing cases was normalized by te baseline cases to provide te eat transfer augmentation associated wit eac blowing case considered. Also, te results from te adiabatic effectiveness experiments were combined wit tese eat transfer measurements to quantify te overall blade termal loading for eac of te blowing cases. η % Coolant Flow.9% Coolant Flow.9% Coolant Flow.8% Coolant Flow (a) Baseline Cases No Blowing Previous studies ave compared flow in a turbine blade tip gap to tat of a fully developed cannel flow correlation for turbulent flow in a duct. Te correlation tat was used for comparison was developed by Gnielinski [8]. Gnielinski s correlation is given in equation and as been reported in te literature to provide accuracy to witin 6% as reported by Kakaç [9] for a large Reynolds number range ( 4 < Re < 6 )..8.4 Nu fd =.4(Re ) Pr [] Mayle and Metzger [5] furtered tis correlation for a tip gap by adding an augmentation factor to account for te overwelming entry region effects of tin blade tips. Tis augmentation factor, wic was taken from Kays and Crawford η η x / C Figure 9. Effectiveness taken along te blade camber line for te small (a) and large (b) tip gaps. (b). Small, Exp Large, Exp % Coolant Figure. Area-averaged effectiveness of te tip at various coolant blowing levels. 6 Copyrigt 4 by ASME

8 [], allows blade designers to relate overall blade tip eat transfer (for a given blade tickness and tip gap) to an overall eat transfer expected in a fully developed cannel as sown in equation. Equation, as pointed out by Mayle and Metzger, accounts for te fact tat only one side of te cannel (blade tip) was eated. Nu / Nu fd = + [] L t / D Comparisons ave been made to te data of Jin and Goldstein [5] and Bunker et al. [4] tat confirm tis augmentation factor approac. Altoug Mayle and Metzger [5] first noted te augmentation factor, teir data as not been included in tis comparison because only experiments performed on airfoil sapes were considered. Tis is because te plotting variables were based on blade exit velocity, of wic tere is no equivalent in te Mayle and Metzger tests. Figure sows Nusselt number values based on te ydraulic diameter of te tip gap ( or H) plotted as a function of te blade Reynolds number based on te exit velocity and ydraulic diameter. Te Gnielinski correlation as been plotted for several /D ratios as sown on te plot. Note tat represents te maximum tickness of te blade. As known for turbulent cannel flow, fully developed conditions generally occur for L/D > (Kays and Crawford []). Te correlations given in Figure indicate similar trends to te experimental data despite very different blade sapes wit te largest outliers occurring for te (Jin and Goldstein) occurring at te lowest blade Reynolds numbers (not tip gap Reynolds number). It sould be noted tat te /D ratios are based on te maximum blade tickness and te Nusselt numbers are te average values calculated for te tip surface. Terefore, tis ratio is not a perfect representation of a blade profile. More experiments sould be performed to furter verify tis trend. Te baseline results are presented as contour plots of Nusselt number (based on cord) in Figure. Note tat te cord rater tan ydraulic diameter was used for tese contour plots to illustrate te differences in te eat transfer coefficients along te blade tip for bot tip gaps. Also, it is important to recognize tat te eat flux is not uniform in te immediate vicinity of te dirt purge oles. Results at bot gap eigts sow similar trends, owever, te large tip gap sows iger Nusselt numbers at te blade trailing edge relative to te small tip gap. Tis increase in eat transfer at te larger tip gap trailing edge is a result of te increased entry region effect relative to te small tip gap. Wit smaller L/D values (for te large tip gap), te entry region is expected to ave a greater effect, as mentioned at te beginning of tis section. For te large tip gap, te L/D is as low as across te trailing edge of te tip surface, wereas for te small tip gap te L/D is.5. Te area-averaged Nusselt numbers are given for eac case to quantify te increase in eat transfer wit gap eigt. For tese cases, te Nusselt number at te large tip gap is. times tat of te small tip gap wen based on te exit velocity and ydraulic diameter. By using Reynolds number scaling for a turbulent cannel flow, te large tip gap is expected to ave.4 times te eat transfer of te small tip gap. Tis larger tan expected increase results from te overwelming entry region effects, wic serve to greatly increase te tip eat transfer. As sown in Figure, tere are regions of low eat transfer immediately downstream of te dirt purge cavity for bot tip gap eigts. Tis is near te tickest portion of te blade and represents te area of lowest eat transfer on te blade tip. Tis region was first pointed out by Bunker et al. [4] and as been confirmed by oter autors. Witin te dirt purge cavity, tere are ig eat transfer coefficients resulting from low velocity flow re-circulation in te cavity. Overall, te leading edge region experiences relatively low eat transfer outside of te dirt purge cavity relative to te trailing edge. Nu D Current Study /D =.5 /D = 4.5 Bunker et al. () /D = 6.5 /D =. /D = 7.5 / D = 9 / D = 5 Jin & Goldstein () /D = 6.5 /D = 8. /D = 4. /D =. / D = 4 Fully Developed, / D > 4 Re 5 ex,d Figure. Comparison of experimental data to a fullydeveloped correlation. (a) Nu Nu =, C, D = (b) Nu Nu, C =, D = 54 Figure. Baseline Nusselt number contour plots for te small (a) and large (b) tip gap eigts. Also seen on tese contour plots are regions of ig eat transfer along te pressure side tat begin around S/S max =. and extend until te trailing edge. Tese regions of ig eat transfer ave been noted by Morpis and Bindon [] and Bindon [6] to be te separation-reattacment region tat forms along te pressure side due to mainstream and leakage flow interaction. Tis region occurs witin te entry region and is more dominant at te large tip gap tan at te small tip gap, and extends over a large region of te tip for te large tip gap. Heat Transfer Augmentation wit Blowing By comparing te eat transfer wit blowing to tat of te baseline cases, te augmentation associated wit tip blowing can be studied. Te camber line plots for te dirt purge blowing 84 Nu,C Copyrigt 4 by ASME

9 are sown in Figure a and b for te small and large tip gaps, respectively. For bot tip gaps, te eat transfer is increased wit blowing for te region of < x/c <.5. Beyond x/c =., tere is no difference between any of te cases because te dirt purge blowing does not affect eat transfer in tis area. In comparing Figure wit Figure 9, tere are striking differences between te two data sets. Te film cooling effectiveness (Figure 9) extends furter down te blade tan does te eat transfer augmentation. For te small tip gap, te film-cooling remains near η = out to x/c =.5 for te igest blowing ratio wereas te eat transfer augmentation is at a value of one at tat location. Tis sows tat for te small tip gap, te dirt purge oles are impinging upon te sroud and effectively spreading coolant flow wile te eat transfer increase is localized around te ole exits. For te large tip gap, tere are localized peaks of film-effectiveness for eac of te tree igest blowing ratios located at x/c =.5 for te.9% case, and near x/c =. for te.9% and.8% cases. Tese peaks of film effectiveness correspond to peaks of eat transfer. At te.9% and.8% cases, te peaks are located at te same position, suggesting tat te coolant flow as impinged upon te sroud and returned back to te tip. For te.9% case, owever, te peaks are not co-located. Instead, te peak in eat transfer is located downstream of te peak in filmeffectiveness. Tis suggests tat at tis particular blowing ratio, te dirt purge jet is causing flow vortices to form near te jet wic do not cause ig film-effectiveness but do increase te eat transfer. 4.% Coolant Flow.9% Coolant Flow.9% Coolant Flow.8% Coolant Flow CFD results by Holfeld [] predicted tese voritices. Coolant flow streamlines for te large tip gap are sown in Figure 4. At te igest blowing ratio (.8%), te coolant is spread in all directions after itting te sroud. At te.9% case te first dirt purge ole is split by te second ole suc tat part of te flow rolls into a vortex around te rigt side of te second ole jet. Tis vortex extends te full gap eigt and is wat causes te peak in eat transfer to be located furter downstream tan te peak in film-effectiveness for tis case. Te.% case is sown to verify tat tere are no vortices at tis case, but rater flow exiting te oles and immediately flowing out of te gap region. Peaks of eat transfer are seen immediately around bot of te dirt purge oles in Figure. Te reason for tis is because te oles cut-out of te foil eater ad ig current gradients very near to te oles resulting in ig eat transfer coefficients. Area-averages of te eat transfer augmentation for bot tip gaps are sown in Figure 5. Again, tese averages are over te forward 46% of te blade tip area, so tat only te area affected by te blowing is considered. Tese results sow tere to be te same eat transfer augmentation for te lowest blowing ratios at bot tip gaps. As te blowing ratio increases, owever, te small tip gap sows increasingly iger augmentation tan te large tip gap. Tis iger augmentation is because of te influence of te tree-dimensional vortices formed as te jets exit te dirt purge oles. As was discussed in te adiabatic results section, flow from te dirt purge oles for te small tip gap can flood te leading edge gap region, causing very good cooling over most of te leading edge. At te large tip gap, te flow is blowing off te tip surface and impinging on te sroud. Because of tis, te augmentation is iger at te small tip gap tan te large tip gap for te same blowing ratio. f / θ.% (a) 4.9% f / (b).8%... x / C..4.5 Figure. Camber line data for f / for te small (a) and large (b) tip gaps. Figure 4. CFD predictions of dirt purge streamlines for te large tip gap (Holfeld []). 8 Copyrigt 4 by ASME

10 . Small Tip Gap Large Tip Gap.5..% / f.9%.9%.8% % Coolant Figure 5. Area-averaged eat transfer augmentation for te small and large tip gaps. Net Heat Flux Reduction Combining te eat transfer measurements wit te film effectiveness measurements can give te overall cooling benefit in te form of a net eat flux reduction (NHFR). Sown in equation 4, NHFR is an establised metod of evaluating te overall effect of a cooling sceme on a surface (Sen et al. []). [4] NHFR = ( f )[ η θ )] All variables ave been measured experimentally except for θ, wic was assumed to be.6 based on previous literature []. Tis value corresponds to a cooling effectiveness of 6.5%. As tis equation sows, wen ig eat transfer augmentation is not accompanied by ig film cooling, te NHFR can become negative. A negative NHFR means tat an increased eat load to te blade surface, wic is undesirable. Te NHFR values were calculated locally for eac case and are sown in Figure 6. Te NHFR is always iger at te small tip gap relative to te large tip gap. Tis can be attributed to te muc iger film cooling effectiveness and only sligtly iger eat transfer augmentation of te small tip gap relative to te large tip gap. At te small tip gap, te NHFR always increases wit blowing. For te large tip gap, te area downstream of te dirt purge cavity sows increased NHFR values wit increased blowing, owever, for te entire leading edge region, te.9% case appears to be lower tan te.% case. Tis is because of te sligtly negative NHFR downstream of te second dirt purge ole. Tis region is caused by te vortices created by te dirt purge blowing tat are not seen in any of te oter cases, as was previously discussed. NHFR values along te camber line are sown in Figure 7 for te small and large tip gaps. For te small tip gap (Figure 7 a), tere is increased spreading of te NHFR in te region < x/c <. as blowing increases. Te igest blowing case (.8%) sows a large spike at te first dirt purge ole. Tis is caused by ig eat transfer immediately surrounding te dirt purge ole, were te uncertainly is iger due to non-uniform eat flux, as discussed previously. For te large tip gap, tere is generally increased NHFR wit increased blowing wit te exception of te region around x/c =.. Around tis area, te.9% case actually sows lower NHFR tan te.% case due to te decreased film effectiveness. 4 Figure 6. Contour plots of NHFR for te small (top) and large (bottom) gap eigts at all blowing ratios. Area-averages of te NHFR values were calculated for te forward part of te blade. Te results, sown in Figure 8, indicate te NHFR is always iger for te small tip gap. For te small tip gap, te NHFR levels increase nearly linearly wit blowing ratio. For te large tip gap, owever, te lowest blowing ratio sows iger NHFR values tan te.9% case, altoug increases in blowing ratio result in increased NHFR. 4.% Coolant Flow.9% Coolant Flow.9% Coolant Flow.8% Coolant Flow NHFR (a) - 4 NHFR (b) -... x/c..4.5 Figure 7. NHFR taken along te camber line for te small (a) and large (b) gap eigts. 9 Copyrigt 4 by ASME

11 NHFR Small Tip Gap Large Tip Gap % Coolant Figure 8. Area-averaged NHFR for bot gap eigts. CONCLUSIONS Intended to prevent dirt and dust particles from clogging smaller film cooling oles, dirt purge oles can provide significant cooling to te leading edge of a blade tip. Note tat in an engine design, te entry corner and trailing edge regions also need to be cooled. Te dirt purge jets provided a significant amount of cooling for te leading edge area particularly for te small tip gap. From te contours and profiles on te tip for te small gap case, it was apparent tat tere was an overcooling of te leading edge area for coolant injections tat were greater tan.9% of te main passage flow. Increased blowing resulted in a larger cooling benefit for te large tip gap as compared wit te small tip gap, altoug te small tip gap always sowed iger overall effectiveness for te same blowing ratio. For te large tip gap, wic is most likely to occur for operating engine conditions, te lower coolant injection rates of.% and.9% of te passage flow, te coolant was only effective witin te dirt purge cavity and just downstream of te cavity. As te coolant injection was increased to.9% and.8% for te large tip gap, cooling was evident witin, upstream, and downstream of te purge cavity. Heat transfer measurements indicate tat eat transfer augmentation wit blowing is increased wit iger blowing ratios for bot gap eigts tested. Also, te augmentation seen for te small tip gap tends to be iger tan tat of te large tip gap. By combining te adiabatic effectiveness and eat transfer measurements, te large tip gap experienced less benefit tan te small tip gap of te dirt purge cooling. For te large tip gap, te NHFR decreased from te.% case to te.9% case, but increased wit subsequent blowing ratios. Overall, te measurements indicate tat better NHFR from te dirt purge oles can be acieved for a small tip gap as compared wit a large tip gap. ACKNOWLEDGMENTS Te autors gratefully acknowledge United Tecnologies Pratt and Witney for teir support of tis work. NOMENCLATURE B x = axial cord C = true cord of blade C p = pressure coefficient, C p = ( p pin ) [( ρ U ) / ] D = ole diameter of te dirt purge D = ydraulic diameter, always used as or H = small tip gap eigt H = large tip gap eigt f = film eat transfer coefficient = blade eat transfer coefficient wit no blowing k = termal conductivity I = local ( ρcu c ) ( ρ LU L ) or global ( ρ c U c ) ( ρ U ) momentum flux ratio L = local tickness of blade L max = max local tickness of blade = max tickness of blade overall. m = mass flowrate M = local ( ρcu c ) ( ρlu L ) or global ( ρ c U c ) ( ρ U ) mass flux ratio NHFR = net eat flux reduction, see equation 4 Nu D = Nusselt number based on ydraulic diameter, (D )/k Nu fd = Nusselt number fully developed based on ydraulic diameter, (D )/k Nu,C = baseline Nusselt based on cord, (C)/K Nu,D = baseline Nusselt based on ydraulic diameter, (D )/k P = blade pitc P o, p = total and static pressures Pr = Prandtl number q tot '' = eat flux supplied to tip surface eater q '' r = eat flux loss due to radiation R = resistance in.. Re in = inlet Reynolds, U (C)/ν Re D = Reynolds based on local velocity and ydraulic diameter, U local (D )/ν Re ex,d = Reynolds based on exit velocity and ydraulic diameter, U ex (D )/ν S = surface distance along blade T = temperature U local = local velocity U ex = exit velocity (at blade trailing edge) U = inlet velocity ( cord upstream) x = distance along blade cord Greek η = adiabatic effectiveness, (T - T aw )/(T - T c ) = denotes a difference in value ρ = density ν = kinematic viscosity ε = emissivity of tip eater surface, always set to.9. θ = dimensionless temperature, (T - T c )/(T - T w ) =.6 θ = dimensionless termal field, (T - T)/(T - T c ) Subscripts ave, = pitcwise average at a given axial location ave, = area average aw = adiabatic wall c = coolant conditions in = inlet value at C upstream of blade ms = value at blade midspan = local inviscid value w = wall temperature wit eat transfer surface b = background temperature for surface Copyrigt 4 by ASME

12 REFERENCES [] Lattime, S. B. and Steinetz, B. M.,, "Turbine Engine Clearance Control Systems: Current Practices and Future Directions," NASA TM [] Morpis, G. and Bindon, J. P., Te Effects of Relative Motion, Blade Edge Radius and Gap Size on te Blade Tip Pressure Distribution in an Annular Turbine Cascade wit Clearance, ASME 88-GT-56. [] Tallman, J. and Laksmiarayana, B.,, Numerical Simulation of Tip Leakage Flows in Axial Flow Turbines, Wit Empasis on Flow Pysics: Part II Effect of Outer Casing Relative Motion, J of Turbomacinery, vol., pp. 4-. [4] Yaras, M.I., and Sjölander, S. A., Effects of Simulated Rotation on Tip Leakage in a Planar Cascade of Turbine Blades: Part I Tip Gap Flow, J of Turbomacinery, vol. 4,. pp , 99. [5] Mayle, R. E. and Metzger, D. E., Heat Transfer at te Tip of an Unsrouded Turbine Blade, Proceedings 7t International Heat Transfer Conference, vol., pp. 87-9, 98. [6] Cyu, M. K., Moon, H. H., and Metzger, D. E., Heat Transfer in te Tip Region of Grooved Turbine Blades, J of Turbomacinery, vol., pp. -8, 989. [7] Srinivasan, V. and Goldstein, R.J., Effect of Endwall Motion on Blade Tip Heat Transfer, J of Turbomacinery, vol. 5, pp. 67-7,. [8] Kim, Y. W. and Metzger, D. E., Heat Transfer and Effectiveness on Film Cooled Turbine Blade Tip Models, J of Turbomacinery, vol. 7, pp. -, 995. [9] Kim, Y. W., Downs, J. P., Soecting, F. O., Abdel Messe, W., Steuber, G., and Tanrikut, S., A Summary of te Cooled Turbine Blade Tip Heat Transfer and Film Effectiveness Investigations Performed by Dr. D. E. Metzger, J of Turbomacinery, vol. 7, pp. -, 995. [] Kwak, J. S. and Han, J. C., Heat Transfer Coefficient and Film-Cooling Effectiveness on a Gas Turbine Blade Tip, GT--94. [] Kwak, J. S. and Han, J. C., Heat Transfer Coefficient and Film-Cooling Effectiveness on a Squealer Tip of a Gas Turbine Blade Tip, GT [] Acarya, S., Yang, H., Ekkad, S.V., Prakas, C., Bunker, R., Numerical Simulation of Film Cooling Holes On te Tip of a Gas Turbine Blade, GT--55. [] Holfeld, E. M., Cristopel, J. R., Couc, E. L., and Tole, K. A.,, Predictions of Cooling from Dirt Purge Holes Along te Tip of a Turbine Blade, GT- 85. [4] Bunker, R.S., Bailey, J.C., and Ameri, A.A., Heat Transfer and Flow on te First-Stage Blade Tip of a Power Generation Gas Turbine: Part Experimental Results, J of Turbomacinery,, pp. 6-7,. [5] Jin, P. and Goldstein, R.J., Local Mass/Heat Transfer on a Turbine Blade Tip, J of Rotating Macinery, 9, No., pp , [6] Bindon, J.P., Te Measurement and Formation of Tip Clearance Loss, J of Turbomacinery,, pp. 57-6, 989. [7] Moffat, R. J., 988, Describing te Uncertainties in Experimental Results, Experimental Termal and Fluid Science, Vol., pp. -7. [8] Gnielinski, V., New Equations for Heat and Mass Transfer in Turbulent Pipe and Cannel Flow, Int. Cem. Eng., 6, pp , 976. [9] Kakaç, S., Sa, R.K., and Aung, W., Handbook of Single-Pase Convective Heat Transfer, Jon Wiley & Sons, pp. 4-5, 987. [] Kays, W.M. and Crawford, M.E., Convective Heat and Mass Transfer, nd ed., McGraw-Hill, pp. 69-7, 98. [] Holfeld, E.H., Film Cooling Predictions Along te Tip and Platform of a Turbine Blade, Master s Tesis, Virginia Polytecnic Institute and State University, Blacksburg, VA, [] Sen, B., Scmidt, D.L., and Bogard, D.G., Film Cooling wit Compound Angle Holes: Heat Transfer, 94-GT-. Copyrigt 4 by ASME