THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St., New York, N.Y

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1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St., New York, N.Y GT-8 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. Papers are available from ASME for 5 months after the meeting. Printed in U.S.A. Copyright 993 by ASME HEAT TRANSFER IN FILM-COOLED TURBINE BLADES Vijay K. Garg and Raymond E. Gaugler Turbomachinery Flow Physics Branch Internal Fluid Mechanics Division NASA Lewis Research Center Cleveland, Ohio ABSTRACT In order to study the effect of film cooling on the flow and heat transfer characteristics of actual turbine blades, a three-dimensional Navier-Stokes code has been developed. An existing code (Chima and Yokota, 99) has been modified for the purpose. The code is an explicit finite difference code with an algebraic turbulence model. The thin-layer Navier-Stokes equations are solved using a general body-fitted coordinate system. 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, thus providing an ability to study the effect of hole shape on the filmcooling characteristics. Comparison with experimental data is fair. Further validation of the code is required, however, and in this respect, there is an urgent need for detailed experimental data on actual turbine blades. NOMENCLATURE d h ho M p rre T V y p Ti sonic speed coolant hole diameter heat transfer coefficient standard value (= 35.6 W/m -K Btu/hr-ft -R) Mach number pressure coolant hole radius (= d/) Reynolds number normalized distance from the leading edge along the pressure or suction surface temperature average velocity of coolant at the hole exit dimensionless distance of the first point off the blade surface density curvilinear coordinate roughly following the flow curvilinear coordinate running blade-to-blade curvilinear coordinate running spanwise Subscripts at inlet at exit c for coolant o stagnation value w at the blade surface. INTRODUCTION It is well known from the thermodynamic analysis that the performance of a gas turbine engine is strongly influenced by the temperature at the inlet to the turbine. There is thus a growing tendency to use higher inlet temperatures, implying increasing heat loads to the turbine components. Modern gas turbine engines are designed to operate at inlet temperatures of 4-5 C, which are far beyond the allowable metal temperatures. Thus, to maintain acceptable life and safety standards, the structural elements such as the first stage blades need to be protected against the severe thermal environment. This calls for an efficient cooling system. One such cooling technique currently used for high temperature turbines is film cooling. In this technique, cooler air is injected into the high temperature boundary layer on the blade surface. Since the cooler air is bled directly from the compressor before it passes through the combustion chamber, it represents a loss in the total power output. The designer's goal is therefore to minimize the coolant necessary to insure adequate turbine life. To this end, considerable effort has been devoted into understanding the coolant film behavior and its interaction with the mainstream flow. The film cooling performance is influenced by the wall curvature, threedimensional external flow structure, free-stream turbulence, compressibility, flow unsteadiness, the hole size, shape and location, 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. A survey of work up to 97 has been provided by Goldstein (97). Ericksen (97) investigated film cooling behind a row of inclined holes, and found only a small effect of the Reynolds number. Ericksen et al. (97) proposed a simple analytical model of the effectiveness pattern produced by a jet. Pedersen (97) and Pedersen et al. (977) investigated the effect of mainstream to coolant density ratio on the film cooling effectiveness for a row of holes, and proposed correlations. Liess (973) found the effects of free stream acceleration and Mach number to be small. Lander et al. (97) measured film cooling effectiveness in a cascade so as to include realistic geometry and flow conditions including free stream turbulence. Musaka et al. (975) confirmed the additive nature of the effectiveness of multiple rows of film cooling holes. Blair and Lander (975) presented some techniques for measuring film cooling effectiveness. Presented at the International Gas Turbine and Aeroengine Congress and Exposition Cincinnati, Ohio May 4-7, 993 Downloaded From: on //8 Terms of Use:

2 Ito et al. (978) showed that the blade surface curvature influences the film cooling effectiveness particularly in the vicinity of the injection holes, with greater effectiveness on the convex surface and less on the concave surface, as compared to a flat plate case. Dring et al. (98) studied the performance of film cooling from a single hole 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. Near the endwalls on the suction surface of the blade, Goldstein and Chen (985) showed that the film cooling jets are swept away from the surface by the passage vortex, resulting in lower film cooling effectiveness. On the pressure surface, the film cooling was unaffected by endwall influences. Kruse (985) investigated the effects of hole geometry, wall curvature and pressure gradient on film cooling effectiveness downstream of a single row of holes, and found the hole spacing to be an important parameter. Schwarz and Goldstein (988) suggested that the unstable flow along the concave surface promotes lateral mixing of the film cooling jets, resulting in a two-dimensional behavior of the film effectiveness. Takeishi et al. (99) 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. Recently, Abhari and Epstein (99) 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. Bergeles et al. (98) devised a finite-difference code with a semi-elliptic treatment of the flow field in the neighborhood of the injection holes. They used the k-e model for turbulence with non-isotropic effective transport coefficients, but applied it only to film cooling on a flat plate, and found satisfactory results only beyond ten diameters behind the leading row of holes. SchOnung and Rodi (987) presented a twodimensional boundary layer model with a modification for three-dimensional elliptic flow for simulating the effects of film cooling by a single row of holes. They used the k-e turbulence model. Later, Haas et al. (99) extended SchOnung and Rodi's (987) model to account for density differences between the hot gas and the injected coolant gas. However, both the models did not account for the effects of curvature and multiple rows of holes. Tafti and Yavuzkurt (99) developed a two-dimensional injection model for use with a two-dimensional low- Reynolds number k-e model boundary layer code for film cooling applications. They introduced the threedimensional effects through an "entrainment fraction". Dibelius et al. (99) developed an elliptic procedure near the injection area but a partially parabolic procedure far downstream for film cooling. They used an eddy viscosity model for turbulence, and presented results for a flat plate. Recently Dorney and Davis (99) analyzed the film cooling effectiveness from one and two holes on a turbine vane, using Rai's (989) numerical technique. They carried out both two- and three-dimensional simulations, but represented each hole by just two grid points. Benz and Wittig (99) analyzed the elliptic interaction of film-cooling air with the main flow by simultaneously computing the coolant and main flows for film cooling at the leading edge of a turbine blade. They were, however, concerned with the region surrounding the hole, and presented no heat transfer results. Amer et al. (99) compared two forms each of the k-e and k-m family of turbulence models for film cooling, and found all of them to be inappropriate. Herein, an existing three-dimensional Navier-Stokes code (Chima and Yokota, 99) has been modified in order to study the effect of film cooling on the flow and heat transfer characteristics of actual turbine blades. Comparison with experimental data (Hylton et al., 988) for a C3X vane with four rows of film cooling holes is provided. Also provided are results for the grid sensitivity study.. ANALYSIS The three-dimensional, thin-layer Navier-Stokes code of Chima and Yokota (99) was modified to include film cooling effects. Briefly, the code is an explicit finite difference code with an algebraic turbulence model. The Navier-Stokes equations in a rotating Cartesian coordinate system are mapped onto a general body-fitted (gol,c) coordinate system using standard techniques, with the c-coordinate roughly following the flow, the q- coordinate running blade-to-blade, and the C-coordinate running spanwise. The governing equations are discretized using a node-centered finite difference scheme. Second-order differences are used throughout; central within the domain and forward or backward at the boundaries. The multistage Runge-Kutta scheme developed by Jameson et al. (98) is used to advance the flow solution in time from an initial guess to the steady state. A spatially varying time step along with a CFL number of 5 was used to speed convergence to the steady state. Eigenvalue-scaled artificial dissipation and implicit residual smoothing are used. For the case of a film-cooled blade, it was found that a low, constant value for the implicit residual smoothing parameter on the suction surface, and a slowly increasing value on the pressure surface yielded the best convergence to the steady-state solution. 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 (generally an ellipse) is represented by several control volumes (over ) having a total area equal to the area of the hole exit, and passing the same coolant mass flow. This provides the code an ability to study the effect of hole shape on the film-cooling characteristics. Different velocity and temperature profiles for the injected gas can be specified at the hole exit. For the cases reported here, turbulent (/7th power-law) profiles were specified. The code can also handle either a specified heat flux or a variable temperature condition on the blade surface. For the cases analyzed here, the experimentally determined temperatures were specified at the blade surface, and wall heat flux was calculated. The algebraic mixing length turbulence model of Baldwin and Lomax (978) was used. This model has been used satisfactorily by Boyle and Giel (99) for heat transfer calculations on turbine blades without film cooling. For the C3X vane, fully developed turbulent flow was assumed. The in-coming flow in the experimental tests (Hylton et al., 988) had a turbulence intensity of 6.5%. Since the hole diameter on the C3X vane is.99 mm, the grid size has to be varied along the blade surface in the chord as well as the span direction. For computational accuracy, the ratio of two adjacent grid sizes in any direction was kept within.76 to.3. A periodic C-grid with up to half a million grid points was used. Normal to the blade surface is the dense viscous grid, with y' < for the first point off the blade surface, following Boyle and Giel (99). All computations were run on the Cray Y-MP computer at the NASA Lewis Research Center. The code requires about 8 million words (Mw) of storage and 4 Mw of solid state device storage. 3. RESULTS AND DISCUSSION The code was assessed against the experimental data on the C3X vane in a cascade by Hylton et al. (988). Figure shows the C3X vane with the cooling hole details, while Fig. shows the C3X vane and the 85x55 grid in the E- directions. For clarity, only a few grid lines are shown. Moreover, the same grid is stacked in the C-direction along the span. Comparisons were made with the experimental data for two rows of cooling holes on the pressure surface and two rows on the suction surface. While there were 6 holes in each row along the Downloaded From: on //8 Terms of Use:

3 span on the test vane, only one hole per row was considered for computational purposes. This is permissible since injection from the rows of holes is normal to the surface in the spanwise direction, allowing symmetry boundary conditions to be imposed at both ends of the span. This will not be true for the leading edge film cooling since injection from such holes is not normal to the spanwise direction. Details for the three grids used for computations are provided in Table. The number of grid points and the grid sizes in the q- and C-directions, arrived at following a grid-independence test, were kept the same for all three grids. In Table, d represents the diameter of the hole. Figure 3 shows the grid points on the blade surface within half the hole pitch along the chord and spanwise directions. The axes in this figure have been normalized by the coolant hole radius, r; the ordinate representing half the span considered in the analysis. A quarter of the hole-opening on the pressure and suction surfaces is also shown in Fig. 3. The grid shown repeats itself in the region of the holes, and the grid size increases slowly in the chordwise direction along the blade surface before attaining a constant value. Three experimental cases, 443, 448 and 4438, were analyzed for comparison. The values of various parameters for these cases are given in Table. In this table, the derived film cooling parameters are based upon the assumption of one-dimensional compressible flow through the hole. The case 448 represents the maximum while the case 443 represents the minimum coolant mass flow rate for the experimental data. In terms of the coolant temperature, the case 448 represents the coolest while the case 4438 represents the warmest coolant. Figure 4 shows the non-uniform experimentally determined temperature on the blade surface for the case 4438, and is typical of the cases studied. These temperature values were specified as the boundary condition for the blade surface temperature in the code as well. In this and later figures, s represents the normalized distance along the pressure or suction surface of the blade. Besides the somewhat erratic temperature variation over IsI >.5, there is a sharp drop in temperature at each end of the insulated portion of the blade (Isl.5). Figures 5 through 7 provide a comparison of the normalized heat transfer coefficient at the blade surface with experimental data (Hylton et al., 988) for the case 4438 using the three different grids. The heat transfer coefficient was normalized by h. = 35.6 W/m -K, an arbitrary value used by Hylton et al. (988). There is no data given for about 5% of surface length on either side of the leading edge since this portion contained the plenum chambers for injection of the colder gas and was insulated from the rest of the blade in the experimental tests (cf. Fig. ). The /7th power-law velocity and temperature profiles were used for the injected gas at each hole exit. Due to lack of experimental data on the mean temperature of the injected gas at the hole exit, it was necessary to estimate it based on a one-dimensional compressible flow through the hole. Despite this estimate, the comparison is fairly good, specially for the 85,65x3 grid. The fluctuations in the data are due to the non-uniform blade surface temperature in the experimental data. Strangely enough, the coarsest grid in the t- direction yields the best comparison with experimental data for this case. The difference between the heat transfer coefficient values obtained with the 85x5543 and 36,6543 grids is much larger than that between the 36x5543 and 634x55x3 grid results. This implies convergence of results with respect to the grid size. However, to ensure grid-independent values of the heat transfer coefficient, a denser grid in the c-direction should be tried. This may invite the problem of roundoff error besides being computationally expensive. The temperature values at the first and second point away from the blade surface in the q-direction differ by less than.5% based upon the three grids, but the viscous grid spacing in the direction normal to the blade surface is of the order of 4x -5. Thus, the very small differences in temperature values from the three grids are blown up in the computation of the temperature gradient at the blade surface. It may be pointed out that when the iterative procedure for solution of the governing equations is assumed to converge for each grid, the maximum error in any of the variables is of the order of -4. Further iterations produced no change in the heat transfer coefficient. The rest of the results are presented for the 36x5543 grid only, since they differ little from those for the 634,55x3 grid for all the cases analyzed. Clearly, results with the 36,65x3 grid take only half the CPU time per iteration required by those with the 634x55x3 grid. Moreover, the finer the grid, the larger is the number of iterations required for convergence. Figure 8 shows a comparison of the static pressure distribution on the blade surface with the experimental data for the case 448. The comparison is fairly good. It may be noted that for all the experimental cases (443, 448 and 4438) analyzed here, the pressure distribution is almost identical, and all three grids yield the same result. Figure 9 shows the distribution of y* for the first point off the blade surface for the case The wiggles in the curve near Isl.5 are due to the coolant injection. Clearly y+ < over the whole blade surface, as required for accurate heat transfer calculations (Boyle and Giel, 99). Figures and provide a comparison between the present computations and experimental data for the normalized heat transfer coefficient for the cases 448 and 443, respectively. In general, the agreement is qualitative. Though at a somewhat different level quantitatively, the theory seems to follow the fluctuations in the data, which are again due to the nonuniform blade surface temperature, similar to those in Fig. 3 for the case We may point out that experimentally, the heat transfer coefficients on the blade (inner) surface were calculated from a finite element analysis of conduction within the blade, with the known (measured) blade surface temperatures. The present study computes the heat transfer coefficients on the blade (outer) surface from the three-dimensional Navier- Stokes analysis. 4. CONCLUSIONS A relatively good comparison with experimental data suggests that the thin-layer Navier Stokes analysis is able to predict the heat transfer characteristics of a film-cooled turbine blade. There is, however, an urgent need for detailed experimental data on actual turbine blades for further validation of the code. Results for the near-hole region could not be compared due to lack of such experimental data. Grid sensitivity studies showed that heat transfer is sensitive to the grid density. While the temperature values at corresponding points within the boundary layer near the blade surface can be computed very accurately, obtaining grid-independent heat transfer coefficients requires very dense grids that may not be practical. Use of a denser grid also invites the problem of modeling the turbulence properly while it is known that no satisfactory model for turbulence in the presence of film cooling exists at present. ACKNOWLEDGEMENTS This work was done when the first author held a National Research Council - NASA Research Associateship at the NASA Lewis Research Center. Helpful discussions with R.J. Boyle, R.V. Chima and F.F. Simon of the NASA Lewis Research Center are gratefully acknowledged. REFERENCES Abhari, R.S. and Epstein, A.H., 99, "An Experimental Study of Film Cooling in a Rotating Transonic Turbine," ASME Paper 9-GT-. Amer, A.A., Jubran, B.A. and Hamdan, M.A., 99, "Comparison of Different Two-Equation Turbulence Models for Prediction of Film Cooling from Two Rows of Holes," Numer. Neat Transfer, Vol., Part A, pp Downloaded From: on //8 Terms of Use:

4 Baldwin, B.S. and Lomax, H., 978, "Thin-Layer Approximation and Algebraic Model for Separated Turbulent Flows," AIAA Paper Benz, E. and Wittig, S., 99, "Prediction of the Interaction of Coolant Ejection with the Main Stream at the Leading Edge of a Turbine Blade: Attached Grid Application," Proc. Intl. Symp. Heat Transfer in Turbomachinery, Athens, Greece. Bergeles, G., Gosman, A.D. and Launder, B.E., 98, "Double-Row Discrete-Hole Cooling: an Experimental and Numerical Study," J. Eng. Power, Vol., pp Blair, M.F. and Lander, R.D., 975, "New Techniques for Measuring Film Cooling Effectiveness," J. Heat Transfer, Vol. 97, pp Boyle, R.J. and Giel, P., 99, "Three-Dimensional Navier Stokes Heat Transfer Predictions for Turbine Blade Rows," AIAA Paper Chima, R.V. and Yokota, J.W., 99, "Numerical Analysis of Three-Dimensional Viscous Flows in Turbomachinery," AIAA J., Vol. 8, pp Dibelius, G.H., Pitt, R. and Wen, B., 99, "Numerical Prediction of Film Cooling Effectiveness and the Associated Aerodynamic Losses with a Three-Dimensional Calculation Procedure," ASME Paper 9-GT-6. Dorney, D.J. and Davis, R.L., 99, "Numerical Simulation of Turbine Hot Spot Alleviation Using Film Cooling," AIAA Paper Dring, R.P., Blair, M.F. and Joslyn, H.D., 98, "An Experimental Investigation of Film Cooling on a Turbine Rotor Blade," J. Eng. Power, Vol., pp Ericksen, V.L., 97, "Film Cooling Effectiveness and Heat Transfer with Injection Through Holes," Ph.D. Thesis, Univ. of Minnesota. Ericksen, V.L., Eckert, E.R.G. and Goldstein, R.J., 97, "A Model for the Analysis of the Temperature Field Downstream of a Heated Jet Injected into an Isothermal Crossflow of an Angle of 9," NASA CR 799. Goldstein, R.J., 97, "Film Cooling," Advances in Heat Transfer, Vol. 7, pp Goldstein, R.J. and Chen, H.P., 985, "Film Cooling on a Gas Turbine Blade Near the End Wall," J. Eng. Gas Turbine & Power, Vol. 7, pp. 7-. Haas, W., Rodi, W. and SchOnung, B., 99, "The Influence of Density Difference Between Hot and Coolant Gas on Film Cooling by a Row of Holes: Predictions and Experiments," ASME Paper 9-GT-55. Hylton, L.D., Nirmalan, V., Sultanian, B.K. and Kaufman, R.M., 988, "The Effects of Leading Edge and Downstream Film Cooling on Turbine Vane Heat Transfer," NASA CR 833. Ito, S., Goldstein, R.J. and Eckert, E.R.G., 978, "Film Cooling of a Gas Turbine Blade," J. Eng. Power, Vol., pp Jameson, A., Schmidt, W. and Turkel, E., 98, "Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes," AIAA Paper Kruse, H., 985, "Effects of Hole Geometry, Wall Curvature and Gradient on Film Cooling Downstream of a Single Row," AGARD-CP-39, Paper 8. Lander, R.D., Fish, R.W. and Suo, M., 97, "External Heat Transfer Distributions on Film Cooled Turbine Vanes," J. Aircraft, Vol. 9, pp Liess, C., 973, "Film Cooling with Ejection from a Row of Inclined Circular Holes, An Experimental Study for the Application to Gas Turbine Blades," von Karman Institute for Fluid Dynamics, Tech. Note 97. Musaka, J.F., Fish, R.W. and Suo, M., 975, "The Additive Nature of Film Cooling From Rows of Holes," ASME Paper 75-WA/GT-7. Pedersen, D.R., 97, "Effect of Density Ratio on Film Cooling Effectiveness for Injection Through a Row of Holes and for a Porous Slot," Ph.D. Thesis, Univ. of Minnesota. Pedersen, D.R., Eckert, E.R.G. and Goldstein, R.J., 977, "Film Cooling with Large Density Difference Between the Mainstream and the Secondary Fluid Measured by the Heat Mass Transfer Analogy," J. Heat Transfer, Vol. 99, pp Rai, M.M., 989, "Three-Dimensional Navier-Stokes Simulations of Turbine Rotor-Stator Interaction; Part I - Methodology," AIAA J. Propul. & Power, Vol. 5, pp SchOnung, B. and Rodi, W., 987, "Prediction of Film Cooling by a Row of Holes with a Two-Dimensional Boundary-Layer Procedure," J. Turbomachinery, Vol. 9, pp Schwarz, S.G. and Goldstein, R.J., 988, "The Two- Dimensional Behavior of Film Cooling Jets on Concave Surfaces," ASME Paper 88-GT-6. Tafti, D.K. and Yavuzkurt, S., 99, "Prediction of Heat Transfer Characteristics for Discrete Hole Film Cooling for Turbine Blade Applications," J. Turbomachinery, Vol., pp Takeishi, K., Aoki, S., Sato, T. and Tsukagoshi, K., 99, "Film Cooling on a Gas Turbine Rotor Blade," ASME Paper 9-GT-9. Total No. of grid points No. of grid points on TABLE Grid Sizes Used min - max grid size No. of control volumes within a hole c-dir n-dir C-dir the blade along blade along span Press-Surf Suct-Surf in - direction d-.8d.d-.35d d-.4d.d-.35d d-.6d.d-.35d 3 4 Downloaded From: on //8 Terms of Use:

5 TABLE Parameter Values for the Cases Analyzed Main Flow Parameters (Experimental) Case p, (kn/m ) T, (K) M Re M, Re, x x x5.89.x x x5 Film Cooling Parameters (Experimental) Case Poc/P. Tog/To Surf. Surf. Surf. Surf Film Cooling Parameters (Derived) Case (Pc7/(Poc) Tc/T Surf. Surf. Surf. Surf ROWS OF HOLES 35' ANGLE CHORDWISE ACTIVE PART OF BLADE STAGNATION POINT ROWS OF HOLES ' ANGLE CHORD WISE HOLE DIA. d =.99 mm 4d ROW SPACING 3d SPANWISE SPACING Fig. C3X vane and cooling hole details. Fig. C3X vane and grid. 5 Downloaded From: on //8 Terms of Use:

6 - - 5 ' T 85x55x3 or 36x55x3 grid _ I- I... A - I- A - Surface Hole - I- -4 o 3 s/r a.8 s - o (bo86 66 o % cb % db AP cci i i i ( 634x55x3 grid Surface Hole -4. _ LII I LIII l_ijlj. 3 4 s/r T " " All three grids Fig. 4 Blade surface temperature for the Case ,,, Surface Hole LI_I I I II I I j I i Fig. 5 Normalized heat transfer coefficient on the 3 4 blade surface (Case 4438)., present computation;, experimental data (Hylton et al., 988). s/r Fig. 3 Grid points within and near a hole on the blade surface. 6 Downloaded From: on //8 Terms of Use:

7 . -C - c- DO 36 x 55 x 3 grid I Ili! i C Fig. 6 Normalized heat transfer coefficient on the Fig. 8 Static pressure distribution on the blade blade surface (Case 4438)., present surface (Case 448)., present computation; computation;, experimental data (Hylton et, experimental data 77IYIton et al., 988). al., 988)...8 -C x 55 x 3 grid I C Fig. 7 Normalized heat transfer coefficient on the blade surface (Case 4438)., present computation;, experimental data (Hylton et al., 988). Fig. 9 y+ of the first point off the blade surface for the Case Downloaded From: on //8 Terms of Use:

8 I -93"ft349 fibiguipia4inge - 36 x 55x 3 grid - h = 35.6 W/m -K _ Fig. Normalized heat transfer coefficient on the blade surface (Case 448)., present computation;, experimental data (Hylton et al., 988). Fig. Normalized heat transfer coefficient on the blade surface (Case 443)., present computation;, experimental data (Hylton et al., 988). 8 Downloaded From: on //8 Terms of Use: