AYT Corporation c/o NASA Lewis Research Center Cleveland, OH 44135

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1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 L 47th St., New York, N.Y ST-221, ; The Society shall not be responsible for statements or opinions advanced in papers or discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to' photoclopy material for internal or personal use under circumstance not falling within the fair use provisions of the Copyright Act is granted by ASME to libraries and other users registered with the Copyright Clearance Center (CCC) Transactional Reporting Service provided that the base roe of $.3 per page Is paid (Greedy to the CCC, 27 Congress Street, Salem MA 197. Requests for special permission or bulk reproduction should be addressed to the ASME Technical Publishing Department. Copyright 1996 by ASME M Rights Reserved Printed In U.SA. ADIABATIC EFFECTIVENESS AND HEAT TRANSFER COEFFICIENT ON A FILM-COOLED ROTATING BLADE Vijay K. Garg AYT Corporation c/o NASA Lewis Research Center Cleveland, OH RII ABSTRACT A three-dimensional Navier-Stokes code has been used to compute the adiabatic effectiveness and heat transfer coefficient on a rotating film-cooled turbine blade. The blade chosen is the UTRC rotor with five film-cooling rows containing 83 holes, including three rows on the shower head with 49 holes, covering about 86% of the blade span. The mainstream is akin to that under real engine conditions with stagnation temperature = 19 K and stagnation pressure = 3 MPa. The blade speed is taken to be 52 rpm. The adiabatic effectiveness is higher for a rotating blade as compared to that for a stationary blade. Also, the direction of coolant injection from the shower-head holes affects considerably the effectiveness and heat transfer coefficient values on both the pressure and suction surfaces. In all cases, the heat transfer coefficient and adiabatic effectiveness are highly three-dimensional in the vicinity of holes but tend to become two-dimensional far downstream. NOMENCLATURE ; blowing parameter (.1-- (p,v,)/{ p o(rt,) 112 )] c, axial chord of the blade d coolant hole diameter h heat transfer coefficient based on (T - TO I momentum flow m mass flow rate p pressure R gas constant s distance from the leading edge along the pressure or suction surface S = Vs., on suction surface, and = - sis, on pressure surface T temperature V, average coolant velocity at the hole exit y y-coordinate of the Cartesian coordinate system with origin at the geometric stagnation point y dimensionless distance of the first point off the blade surface z z-coordinate along the span z' dimensionless distance of the first point off the hub or off the shroud ratio of specific heats Ti adiabatic effectiveness (= (T o - T)/(To - T,)] rotational speed of the blade density Subscripts aw corresponding to adiabatic condition c for coolant (average value) free-stream (external) value maximum value corresponding to uncooled blade o stagnation value at the blade surface local free-stream value 1. INTRODUCTION The quest for better performance of gas turbine engines has led to higher turbine inlet temperatures. Modem gas turbine engines are designed to operate at inlet temperatures of 18-2 K, which are far beyond the allowable metal temperatures. Under these conditions, the turbine blades need to be cooled in order to ensure a reasonable lifetime. This calls for an efficient cooling system. Discrete jet film cooling is one of the techniques used to protect the blades and endwalls that are thermally exposed. Since the injected cooler air is bled directly from the compressor before it passes through the combustion chamber, the best compromise between admissible metal temperature and aerodynamic efficiency becomes a major objective in cooled turbine blade design. A considerable effort has been devoted to understanding the coolant film behavior and its interaction with the mainstream flow. The film cooling performance is influenced by the wall. curvature, three-dimensional external flow structure, free-stream turbulence, compressibility, flow unsteadiness, the hole size, shape and location, Presented at the International Gas Turbine and Aercpengine Congress & Exhibition Birmingham, UK June 1-13,1996 Downloaded From: on 7/2/218 Terms of Use:

2 and the angle of injection. Many studies on film cooling have been confined to simple geometries, for example, two-dimensional flat and curved.plates.in.steady, incompressible flow. An excellent survey of the work up to 1971 has been provided by Goldstein (1971). While several further studies in this field have been summarized by Garg and Gangler (1993, 1994, 1995), some relevant ones are discussed here. Dring et al. (198) studied the performance of film cooling from single holes located at mid-span on the pressure and suction side of a blade in a large scale, low speed rotating facility. They concluded that the large radial displacement of the coolant jet on the pressure surface was the main cause of lower effectiveness. Graf (1985) carried out tests on a cooled gas turbine stage. However, most of the results were - provided for the first stage vane, with only metal temperature values for the first stage rotor. Talceishi et al. (1991) measured film cooling effectiveness on a rotating turbine stage; and found that on the rotor mid-span, the suction surface film cooling effectiveness is similar to that on flat plates and in cascades, while on the pressure surface, much lower values exist. Though the rotating blade had three rows of holes on the shower-head, and one row each on the pressure and suction surfaces of the blade, they measured the effectiveness values for coolant injection from individual rows of holes. Domey and Davis (1993) analyzed the film cooling characteristics from one and two rows of holes on the pressure side of a turbine blade, using Rai's (1989) numerical technique. They carried out both two- and three-dimensional simulations, but represented each hole exit by just two grid points. Their interest was in the numerical simulation of the alleviation of "hot spots" on the pressure side of the blade. Our studies have indicated that for a proper coolant jet-main flow interaction, each hole exit should be represented by about 1-15 control volumes. Abhari and Epstein (1994) measured time-resolved heat transfer on the rotor of a fully cooled transonic turbine stage and compared with data from the same uncooled geometry. They found a considerable reduction in the average suction surface heat transfer with cooling but relatively little on the pressure surface. The results were similar over the center 3/4 of the span measured, implying that the flow in this region was mainly two-dimensional. The rotor heat transfer on the suction surface was also found to be considerably less than that in a cooled cascade. Weigand and Harasgama (1994) carried out a numerical investigation of film cooling on a turbine rotor blade using Dawes (1993) code that utilizes an unstructured solution adaptive grid methodology for solving three-dimensional Navier-Stokes equations. The code uses a low Reynolds number k-a model for turbulence. The authors considered a uniform as well as a non-uniform radial temperature distribution (RTD) at inlet to the rotating blade. However, a rather academic case of blowing in the tangential direction was studied due to limitations of the code. As such, comparison with experimental data was not possible. They considered two blowing geometries; one with a single slot located at mid-span and two single holes near the hub and the tip of the blade, and another with two rows of staggered slots (total three) at mid-span and two rows of staggered holes (total six) near the hub and the tip of the blade. It was found that blowing on the pressure side of the blade resulted in some of the coolant flow being transported through the tip gap of the blade to the suction side. Also, the effect of RTD on the film cooling effectiveness is most significant near the tip of the blade. At the hub and near midspan of the blade the film cooling effectiveness distributions are very similar with or without RTD. The above survey indicates that there is relatively little information on the film cooling characteristics of a rotating turbine blade. The objective here is to fill this gap. We follow the analysis of Gars and Gaugler (1995) in order to compute the adiabatic effectiveness and heat transfer coefficient on a rotating, film-cooled rotor, specifically the UTRC rotor with five rows of film cooling holes including three rows on the shower-head. We may point out that the original UTRC rotor (Joslyn and Dring, 1989) has no film cooling holes. Thus, the film cooling holes have been somewhat arbitrarily located on the UTRC rotor for the purpose of this study. 2. ANALYSIS The three-dimensional Navier-Stokes code of Arnone et al. (1992) for the analysis of turbomachinery flows was modified by Garg and Gaugler (1994) to include film cooling effects. Briefly, the code is an explicit, multigrid, cell-centered, finite volume code with an algebraic turbulence model. The governing equations solved are the conservative form of the Reynolds averaged Navier-Stokes equations in a curvilinear coordinate system in terms of the absolute velocity and specific total energy. The perfect gas law is used as the equation of state. Variation of viscosity with temperature is assumed to follow Sutherland's law (Schlichting, 1979). The four-stage Runge-Kutta scheme developed by Jameson et al. (1981) is used to advance the flow solution in time from an initial guess to the steady state. To accelerate convergence the code employs the Full Approximation Storage (FAS) multigrid method originally devised by Brandt (1979) and Jameson (1983). Variable coefficient implicit smoothing of the residuals is performed to improve further the rate of convergence. A three-dimensional extension of eigenvalue scaling of the artificial dissipation terms, first devised by Martinelli (1987), was adopted to prevent odd-even decoupling and to capture. shocks. Further details of the numerical scheme and implementation of the boundary conditions are given in Amone (1993) and Amone et al. (1992). The effects of film cooling have been incorporated into the code in the form of appropriate boundary conditions at the hole locations on the blade surface. Each hole exit is represented by several control volumes (about 1-2) having a total area equal to the area of the hole exit, and passing the same coolant mass flow. Different velocity and temperature profiles for the injected gas can be specified at the hole exit. For the cases reported here, turbulent profiles (1nth power-law) for the coolant velocity (relative to the blade) and temperature distribution at the hole exit were specified. This is in conformity with the observation of Leylek and. Zerkle (1994) if the hole-length to diameter ratio is greater than 3.. Leylek and Zerkle (1994) found that for high hole-length to diameter ratios (2 3.) and high blowing ratios (2 1.), the velocity profile at the hole exit is akin to the 117th powerlaw profile. The blade surface was considered either adiabatic or isothermal in order to compute either the adiabatic effectiveness or the heat transfer coefficient. Similar boundary conditions were applied to the hub and shroud. Moreover, the boundary layer thickness on both the hub and shroud was taken to be 7% of span for the incoming flow. The algebraic mixing length turbulence model of Baldwin and Lomax (1978) was used. This model was designed for the prediction of wall bounded turbulent shear layers, and may not be appropriate for flows with massive separations or large vortical structures. Thus, this model is likely to be invalid in a number of turbomachinery applications, but for turbine blades, the boundary layers generally experience a favorable pressure gradient whereby this model is more likely to be valid. It has 2 Downloaded From: on 7/2/218 Terms of Use:

3 been used satisfactorily by Boyle and Giel (1992), Amen i and Amone (1994a, b), and Boyle and Amen (1994) for heat transfer calculations on rotating turbine blades without film cooling, by Hall et al. (1994), and Garg and Gaugler (1994, 1995) on planar cascades with film cooling, and by Garg and Abhari (1996) on a film-cooled rotating ' blade row. In fact, Amen and Arnone (1994b) compared the Baldwin- Lomax model and Coakley's q-oi model (Coakley, 1983) against the experimental data of Graziani et al. (198), and found that the algebraic model was able to produce many of the flow features better than the two-equation model. They further state that this conclusion is strengthened when one takes into account the relative economy of computations with the algebraic model. It is known (Amer et al., 1992) that two-equation models are also not satisfactory in the presence of film cooling. Perhaps the multiple-time-scale turbulence model of Kim and Benson (1992) may be more appropriate. However, use of this model is computationally very expensive since it involves solving four more partial differential equations in addition to the five at present, all coupled. 3. UTRC ROTOR The UTRC rotor chosen for the present simulation was tested, without any film cooling holes, in the 5 ft (1.524 m) diameter low speed rotating rig at United Technologies Research Center (Joslyn and Dring, 1989). The rig has a.8 hub/tip ratio. There are 28 blades with an axial chord of.161 m. Figure 1 shows the UTRC rotor geometry at the hub, tip and mid-span sections. For the present study, three staggered rows containing 49 cooling holes were located around the leading edge at s/d =, ±4.. These holes were angled at 35 from the radial direction and drilled in a plane normal to the blade surface. The coolant injection from these holes could be directed towards the hub or towards the tip or towards both. One row containing 17 holes was located on the suction side at s/d values varying from 32.4 near the hub to 28.4 near the tip, and another row containing 17 holes was located along the pressure side at s/d values varying from near the hub to near the tip. These holes were inclined at 3' with respect to the local blade surface and drilled in a plane normal to the span. All the 83 holes are cylindrical with a diameter of 2 mm, and the spanwise pitch is 8 mm. The hole center closest to the hub is located at 7.4% of the blade span, while the hole center closest to the blade tip is located at 92.3% of the span. Figure 2 shows the unfolded part of the blade containing the holes. The ordinate in Fig. 2 denotes the distance along the blade surface in the spanwise direction, while the abscissa denotes the distance, measured from the leading edge, along the blade surface in the streamwise direction, both normalized by the hole diameter, d. The shape and orientation of the hole openings in Fig. 2 is a direct consequence of the angles the holes make with the spanwise or streamwise direction. 4. COMPUTATIONAL DETAILS Since the cylindrical hole diameter is 2 mm (-1.25% of the axial chord), the grid size has to be varied along the blade chord. For computational accuracy, the ratio of two adjacent grid sizes in any direction was kept within.76 to 1.3. A periodic C-grid with over 2,, grid points was used The grid used was 225x45x21 where the first number represents the number of grid points along the main flow direction, the second in the blade-to-blade direction, and the third in the span direction. 'This grid was arrived at following numerical experimentation with a coarser grid 133x41x11, and discussions with co-workers. Normal to the blade surface is the dense viscous grid, with y c 1.5 for the first point off the blade surface, following Boyle and Giel (1992), and Hall et al. (1994). Normal to the hub and shroud also is a dense grid, with e c 2.5 for the first point off the hub or off the shroud. Also, the tip clearance region was taken to be I% of the blade span with 24 grid points within it. The tip clearance region is handled by imposing periodicity conditions across the airfoil. Computations were run on the 16-processor C-9 supercomputer at NASA Ames-Research Center. The code requires about 12 million words (Mw) of storage and takes about 4 s per iteration (fullmultigrid) on the C-9 machine. For a given grid the first adiabatic blade case requires about 2 iterations to converge, while subsequent cases (corresponding to different values of the parameters) for the same grid require about 1 iterations starting with the solution for the previous case. 5. RESULTS AND DISCUSSION The code has been validated on the rotating film-cooled ACE rotor (Garg and Abhari, 1996), on stationary, film-cooled turbine vanes and blades (Garg and Gauzier, 1995), and on rotating UTRC and other rotors without film cooling,(amert, 1994; Ameri and Arnone, 1994a). Due to lack of experimental data on the rotating film-cooled UTRC blade, however, no comparison can be provided at present. Present results were obtained for air (y = 1.4) with inlet total pressure, p. = 3 MPa, inlet total temperature, T.= 19 K, blade speed = 52 rpm, exit relative Mach number = 1., and exit relative Reynolds number based on the axial chord = 5.8 x 1 6. The coolant temperature, T was taken to be.5 T. so that the density ratio is about 2., as in an engine. For heat transfer coefficient computations, the isothermal blade, hub and shroud surfaces were taken to be at.7 To. Three orientations for the coolant injection from the shower-head holes were analyzed. These are: Case (i): all shower-head holes inject towards the hub, Case (ii): all shower-head holes inject towards the tip, and Case (iii): same as Case (ii) except that eight holes on the suction side of shower-head holes between the hub and mid-span inject towards the hub. The blowing parameter, B r- was adjusted so that the ratio of coolant mass flow to inlet mass flow (mirn.) varied from about 3.6% to 7.4%, and the coolant momentum flow to inlet momentum flow (1i1.) varied from 3.5% to 14.2%. For each case, ; was specified the same value for all holes. We may point out that for film cooling on a turbine blade, it is better to use the blowing parameter than the usual blowing ratio (defined as p cvip_v_) since the latter is based on the local free-stream velocity and density that change all over the airfoil. For injection at the stagnation line, for example, the blowing ratio is infinite, while the blowing parameter is finite. The term "blowing ratio" perhaps originated with fundamental studies of a jet in crossflow for which the blowing ratio is akin to the blowing parameter. In the following, we discuss results for the adiabatic effectiveness and heat transfer coefficient separately. 5.1 Adiabatic Effectiveness Figure 3 shows the adiabatic effectiveness contours over a stationary as well as a rotating (S2 r: 52 rpm) blade for Case (i) corresponding to B, =.5 (intim. = 2.84% for Q =, and mirn. = 3.65% for = 52 rpm) and 13, = 1. (mint. = 7.4%). In this and later figures, three views of the blade surface are presented for clarity. While the middle view shows the entire pressure surface and a part of the suction surface, the view in the lower left corner shows the part of 3 Downloaded From: on 7/2/218 Terms of Use:

4 the suction surface from the leading edge holes to the gill holes on the suction surface, and the view on the right shows the suction surface from the gill holes to the trailing edge. The term, gill holes, denotes the location of holes on a blade similar to that of gills on a fish. Also, the contours are shown at intervals of.5 except in the view in the lower left corner where the interval is.1. Figure 3a for the stationary blade shows that n is close to zero between the shower-head holes and gill holes on the pressure side, and in the boundary layers near the blade hub and tip. Such low values of n imply hot spots on the blade surface. The tip boundary layer is fairly thick on the suction surface, and near the trailing edge on the pressure side. A strong spanwise variation in n values is also discernible downstream of the holes, especially on the suction surface, in the form of a finger-like distribution of n. Comparison between Figs. 3a and 3b shows that rotation of the blade does improve the effectiveness in general. However, there arc sail some regions near the tip between the gill holes on the pressure and suction sides, and near the hub between the shower-head and gill holes on the pressure side where the values of 1 are still low, leading to hot spots on the blade. The tip region downstream of gill holes on both the pressure and suction sides does not have as low an effectiveness value as that upstream of the gill holes due to cross-over of flow from the pressure to the suction side. The flow cross-over starts downstream of gill holes on the pressure side. In an effort to improve the effectiveness over the blade surface, the coolant mass flow rate was increased. Figure 3c shows the adiabatic effectiveness over the rotating blade for Case (i) corresponding to B p = 1. and = 52 rpm. Unfortunately, the situation is worse overall than that in Fig. 3b; regions of low effectiveness have strengthened and increased in extent. The increased coolant momentum (about four times that in Fig. 3b) results in coolant jet lift-off. This leads to exposure of the blade surface to the hot freestream resulting in hot spots. An intermediate value of B p =.75 was also analyzed, but it results in an 1-distribution between those in Figs. 3b and 3c, and is not shown here for brevity. The low rt values on the pressure surface between the showerhead and gill holes are a consequence of the lift-off of the coolant jet from the blade surface as evidenced from Fig. 4 in terms of static temperature ratio (Ta o) contours for case (i). These contours are shown at intervals of.2. The right-hand portion of this figure shows the UTRC rotor with five rows of holes located by their centerlines drawn in black, and two more locations (where temperature contours are displayed) shown in gray. The static temperature ratio contours in the y-z plane are shown at two spanwise locations represented by the index i = 84 and 9 for two coolant flow rates. It is clear from Fig. 4a that for the lower coolant flow rate (m,./m = 3.65%), there is a fairly uniform blanket of coolant over the blade surface all along the span except near the hub where coolant was not injected. However, for the higher coolant flow (Rim. = 7.4%), Fig. 4b clearly shows that at i = 9, some hot gas pockets have opened up near the blade surface in the mid-span and tip regions, and further downstream at i = 84, hotter gas has migrated near the blade surface due to lift-off of the coolant jet from the blade surface. The coolant jet is thus no longer effective in cooling parts of the blade surface. This is due to the secondary flow within the coolant jet, and the resulting entrainment of the hot gas from the outer region towards the blade surface between the adjacent jets. The lift-off is a jet-cross-flow interaction based upon pressure fields and momentum balances (Haas et al., 1991). The penetration of the coolant jet depends mainly on the injection angle, on the momentum ratio (py, 2)/(p eve2), and on the pitch-to-diameter ratio. Much better distribution of adiabatic effectiveness over the blade is found in Fig. 5 for Case (ii) with B p =.5 (mitrip = 3.65%) and B p = 1. (mjm,, = 7.4%), and f2 = 52 rpm. Comparison between Figs. 3b and 5a shows that the effectiveness has improved everywhere on the blade except within the hub boundary layer between the showerhead and gill holes on the suction surface. The region between the shower-head and gill holes on the pressure side is fairly well cooled compared to that in Fig. 3b. The region of very high effectiveness values downstream of gill holes on the preisure side has been reduced but the ii values in this region (Fig. 5a) are still high. The objective is to cool the blade reasonably well over the entire surface, and not to overcool it in some regions leaving others with hot spots. Recall that the only difference between the two cases in Figs. 3b and 5a is the orientation of coolant jets from the shower-head holes. Thus, the coolant jet orientation is an important factor. Comparison between Figs. 5a and 5b shows higher effectiveness values in the tip region around the whole blade for the higher coolant flow. However, n values are lower within the hub boundary layer between the showerhead and gill holes on both the suction and pressure sides due to coolant jet lift-off. Also, n values are lower over most of the suction surface in Fig. 5b than those in Fig. 5a, though they are still tolerable, being Comparison between Figs. 3c -and 5b shows the beneficial effects of the orientation of the coolant jet from the shower-head holes towards the tip, except in the hub region between the shower-head and gill holes on the suction side. In order to improve effectiveness values in this region, Case (iii) was analyzed in which eight shower-head holes between the hub and mid-span on the suction side were oriented towards the hub, while the rest of shower-head holes injected towards the blade tip. Figure 6 shows the adiabatic effectiveness over the rotating blade for Case (iii) corresponding to Bp =.5 (mjrna = 3.65%) and B c, = 1. (mime = 7.41%), and = 52 rpm. Comparison between Figs. 5a and 6a shows that the blade pressure surface is almost unaffected. On the suction surface, the extent of low 1 values near the hub between the shower-head and gill holes has been reduced, as desired. However, the blade suction surface downstream of the gill holes has lower effectiveness values near the hub in Fig. 6a as compared to that in Fig. 5a. Also, owing to the split of coolant injection from shower-head holes on the suction side towards the hub and tip, there is a small band of somewhat lower n values (though still.4) near the mid-span on the suction side in Fig. 6a as compared to that in Fig. 5a. In comparison to the results in Fig. 6a, the higher coolant momentum in Fig. 6b results in lift-off of the coolant jet near the hub between the shower-head and gill holes on the pressure side, leading to lower 1 values. Also, the effectiveness values are lower on the suction surface, especially near mid-span, while the tip region is cooler than that in Fig. 6a since the extent of cooled flow crossing from the pressure to suction side through the tip clearance region has increased. This also results in slightly lower values of n near the mid-span-trailing-edge on the pressure side. Overall, Fig. 5a represents the best distribution of adiabatic effectiveness over the blade surface. Table 1 provides a summary of the above results in terms of the average values of adiabatic effectiveness over the blade pressure and suction surfaces for the various cases analyzed. These values are of interest to the blade designer. While Case (ii) with mini, = 3.65% is the best one, it is little different from Case (iii) with mfrn, = 3.65%. However, one cannot discern local variations from an average value. 4 Downloaded From: on 7/2/218 Terms of Use:

5 5.2 Heat Transfer Coefficient For computing the heat transfer coefficient, the blade, hub and shroud surfaces were assumed isothermal at.7 T r,. In Figs. 7 and 8, contours are actually provided for h/h at intervals of.2, where h. is the heat transfer coefficient with no film cooling. Since (1 - Wh y) represents the net benefit from film cooling, values of h/h closer to zero are desirable. Figure 7 shows the normalized heat transfer coefficient (h/h) contours for the rotating blade (C/ = 52 rpm) for case (i) with B p =.5 (mime = 3.64%) and B,, = 1. (maim. = 7.39%). Presence of negative values of h/h p at some locations simply implies that the direction of heat transfer is reversed at these locations due.to. specification of the isothermal wall boundary condition (Tif p =.7 here) and coolant temperature (T/F Ø =.5 here). From this figure, we observe that the heat transfer coefficient, like the adiabatic effectiveness, is a strong function of the streamwise as well as the spanwise location. Also, a finger-like distribution of IA, similar to that of is observed immediately downstream of the film-cooling holes. Figure 7a shows that the tip region between the gill holes on the pressure and suction surfaces, and part of the pressure surface between the shower head and 11 holes has little benefit from film cooling; the latter is due to jet lift-off. Moreover, increasing the blowing parameter, as in Fig. 7b, worsens the situation considerably in both the above-mentioned regions as well as on the suction surface. Figure 8 shows the normalized heat transfer coefficient (a) for the rotating blade (Cl = 52 rpm) for case (iii) with B p =.5 (m./rn, = 3.64%) and 13,, = 1. (nndrrip = 7.4%). In comparison to Fig. 7, the situation is much better here for both the lower and higher values of the blowing parameter. However, values of h/h a are still high, and thus only a little benefit from film cooling is evident on the pressure surface upstream of the gill holes due to coolant jet lift-off. Moreover, the situation worsens with increase in the coolant mass or momentum flow. 6. CONCLUSIONS It is found that the adiabatic effectiveness is higher for a rotating blade as compared to that for a stationary blade. Also, the direction of coolant injection from the shower-head holes affects considerably the effectiveness and heat transfer coefficient values on both the pressure and suction surfaces. Moreover, different effects are observed on the pressure and suction surfaces of the blade. Clearly, studies on a flat plate or a stationary blade cannot reveal these differences. In all cases, the adiabatic effectiveness and heat transfer coefficient are highly three-dimensional in the vicinity of holes but tend to become two-dimensional far downstream. ACKNOWLEDGEMENTS The author wishes to thank Dr. Raymond Gaugler, Chief, Turbomachinery now Physics Branch, and Mr. Peter Banerton, Manager, Advanced Subsonic Technology Program at the NASA Lewis Research Center for their support of this work. REFERENCES Abhari, R.S and Epstein, A.H., 1994, "An Experimental Study of Film Cooling in a Rotating Transonic Turbine," J. Turbomachinny, Vol. 116, pp Amer, A.A., Jubran, BA. and Hamdan, M.A., 1992, "Comparison of Different Two-Equation Turbulence Models for Prediction of Film Cooling from Two Rows of Holes," Numer, Heat Transfer, Vol. 21, Part A, pp Aineri, A.A., 1994, "Transition Modeling Effects on Turbine Rotor Blade Heat Transfer Predictions," NASA CP 3282, Vol. II, pp Amen, A.A. and Arnone, A., I994a, 'Transition Modeling Effects on Turbine Rotor Blade Heat Transfer Predictions," ASME Paper 94- GT-22. Ameri, A.A. and Arnone, A., 19941,, "Prediction of Turbine Blade Passage Heat Transfer Using a Zero and a Two-Equation Turbulence Model," ASME Paper 94-GT-122. Amone, A., 1993, "Viscous Analysis of Three-Dimensional Rotor Flow Using.a Multigrid Method," ASME Paper 93-GT-I9. Amone, A., Liou, M.-S. and Povinelli, L.A., 1992, "Navier-Stokes Solution of Transonic Cascade Rows Using Non-Periodic C-type Grids," J. PropuL & Power, Vol. 8, pp _ Baldwin, B.S. and Lomax, H., 1978, "Thin-Layer Approximation and Algebraic Model for Separated Turbulent Flows," AIAA Paper Boyle, R.I. and Ameri, A.A., 1994, "Grid Orthogonality Effects on Predicted Turbine Midspan Heat Transfer and Performance," ASME Paper 94-CT-l23. Boyle, R.J. and Giel, P., 1992, "Three-Dimensional Navier Stokes Heat Transfer Predictions for Turbine Blade Rows," AIAA Paper Brandt, A., 1979, "Multi-Level Adaptive Computations in Fluid Dynamics," AIAA Paper Coakley, T.J., 1983, "Turbulence Modeling Methods for the Compressible Navier-Stokes Equations," AIAA Paper Dawes, W.N., 1993, "The Extension of a Solution-Adaptive Three-Dimensional Navier-Stokes Solver Toward Geometries of Arbitrary Complexity," I Turbomachinery, Vol. 115, pp Domey, Di. and Davis, R.L., 1993, "Numerical Simulation of Turbine Hot Spot Alleviation Using Film Cooling," J. PropuL & Power, Vol. 9, pp Dring, R.P., Blair, M.F. and Joslyn, M.D., 198, "An Experimental Investigation of Film Cooling on a Turbine Rotor Blade," J. Eng. Power, Vol. 12, pp Garg, V.K. and Gaugler; R.E., 1993, "Heat Transfer in Film- Cooled Turbine Blades," ASME Paper 93-GT-81. Garg, V.K. and Gaugler, RE., 1994, "Prediction of Film Cooling on Gas Turbine Airfoils," ASME Paper 94-GT-16. Garg, V.K. and Gaugler. R.E., 1995, "Effect of Velocity and Temperature Distribution at the Hole Exit on Film Cooling of Turbine Blades," ASME Paper 95-GT-2. (Also to appear in J. Turbomachinery). Goldstein, R.I., 1971, "Film Cooling." Advances in Heat Transfer, Vol. 7, pp Graf, HI., 1985, "Engine Tests on a Cooled Gas Turbine Stage," AGARD-CP-39, Paper 14, Graziani, RA., Blair, M.F., Taylor, J.R. and Mayle, R.E., 198, "An Experimental Study of Endwall and Airfoil Surface Heat Transfer in a Large Scale Turbine Blade Cascade," I Eng. Power, Vol. 12, pp Haas, W., Roth, W. and Schanung, B., 1991, "The Influence of Density Difference Between Hot and Coolant Gas on Film Cooling by a Row of Holes: Predictions and Experiments," ASME Paper 91-GT Hall, Topp, D.A. and Delaney, R.A., 1994, "Aerodynamic/Heat Transfer Analysis of Discrete Site Film-Cooled 5 Downloaded From: on 7/2/218 Terms of Use:

6 Turbine Airfoils," AIAA Paper Jameson, A., 1983, "Transonic Flow Calculations," MAE Report 1651, MAE department, Princeton University. Jameson, A., Schmidt, W. and Turkel, E., 1981, "Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes," AIAA Paper Joslyn, H.D. and Dring, It.?., 1989, "Three Dimensional Flow and Temperature Profile Attenuation in an Axial Flow Turbine," UTRC Report R Kim, S.-W. and Benson, Ti., 1992, "Calculation of a Circular Jet in Cross Flow with a Multiple-Time-Scale Turbulence Model," Intl. J. Heat Mass Transfer, Vol. 35, pp Leylek, J.H. and arkle, RD., 1994, "Discrete-Jet Film Cooling: A Comparison of Computational Results With Experiments," J. Turbonzachinery, Vol. 116, pp Martinelli, L., 1987, "Calculations of Viscous Flows With a Multigrid Method," Ph.D. Thesis, Princeton University. Rai, M.M., 1989, "Three-Dimensional Navier-Stokes Simulations of Turbine Rotor-Stator Interaction; Part I - Methodology," AIM J. Propul. & Power, Vol. 5, pp Schlichting, H., 1979, Boundary Layer Theory, 7th Ed., McGraw- Hill, New York, p Takeishi, K., Aoki, S., Sato, T. and Tsulcagoshi, K., 1991, "Film Cooling on a Gas -Turbine Rotor Blade," ASME Paper 9I-GT-291. Weigand, B. and Harasgama, S.P., 1994, "Computations of a Film Cooled Turbine Rotor Blade with Non-Uniform Inlet Temperature Distribution Using a Three-Dimensional Viscous Procedure," ASME Paper 94-GT-I5. Table 1 Average Effectiveness Values Over the Blade Surface Case f2 (rpm) ; menn, lil,, Pressure ri m Suction rim (i) % 2.2% (i) % 3.55% (i) % 7.88% (i) % 14.13% (ii) % 3.55% (ii) % 14.12% (iii) % 3.55% (iii) % 14.19% I F I I x/ca Pressure I Suction s/d Fig. 1 UTRC Rotor Geometry at Three Spanwise Locations Fig. 2 Location of Film Cooling Holes on the UTRC Rotor 6 Downloaded From: on 7/2/218 Terms of Use:

7 Tip Tip Hub Tip.2 mdmo = 2.84% lc/lot 2.2% M NO ROTATION.2.15 Tip.35 Tip H Tip mdmo = 7.4% lelo = 14.13% = 52 rpm.25 FIG. 3 ADIABATIC EFFECTIVENESS ON THE UTRC ROTOR FOR CASE (I). 7 Downloaded From: on 7/2/218 Terms of Use:

8 = co S = 84 a) mdmo = 3.65%, leflo = 3.55% Hole-row centerlines.88 in black at 1 = 77, 11, 113,125 and 152; gray planes at i = 84 & 9.84 Hub A (,) = = In V Cr/ dir b) mdmo = 7.4%, leflo = 14.13% ir\w-j r il.88,j2 Ii.8.88 Tip FIG. 4 STATIC TEMPERATURE RATIO CONTOURS AT TWO STREAMWISE LOCATIONS FOR CASE (I) WHEN D = 52 rpm Downloaded From: on 7/2/218 Terms of Use:

9 Tip Tip FIG. 5 ADIABATIC EFFECTIVENESS ON THE UTRC ROTOR FOR CASE (Ii) WHEN O. r: 52 rpm. 9 Downloaded From: on 7/2/218 Terms of Use:

10 Tip a).2 Tip ITIC/M = 3.65% id1 = 3.55% FIG. 6 ADIABATIC EFFECTIVENESS ON THE UTRC ROTOR FOR CASE (iii) WHEN CI = 52 rpm. 1 Downloaded From: on 7/2/218 Terms of Use:

11 Tip I.4.8 Ti p mc/mo = 7.39%.6 b) icno = 14.7%..p.4\; FIG.? NORMALIZED HEAT TRANSFER COEFFICIENT ON THE UTRC ROTOR FOR CASE (I) WHEN D = 52 rpm. 11 Downloaded From: on 7/2/218 Terms of Use:

12 P FIG. 8 NORMALIZED HEAT TRANSFER COEFFICIENT ON THE UTRC ROTOR FOR CASE (Iii) WHEN Q = 52 rpm. 12 Downloaded From: on 7/2/218 Terms of Use: