Inverse Design of and Experimental Measurements in a Double-Passage Transonic Turbine Cascade Model

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1 Iowa State University From the SelectedWorks of Paul A. Durbin July, 2005 Inverse Design of and Experimental Measurements in a Double-Passage Transonic Turbine Cascade Model G. M. Laskowski, Stanford University A. Vicharelli, Stanford University G. Medic, Stanford University C. J. Elkins, Stanford University J. K. Eaton, Stanford University, et al. Available at:

2 G. M. Laskowski A. Vicharelli G. Medic C. J. Elkins J. K. Eaton P. A. Durbin Flow Physics and Computation Division & Thermosciences Division, Department of Mechanical Engineering, Stanford University, Stanford, CA Inverse Design of and Experimental Measurements in a Double-Passage Transonic Turbine Cascade Model A new transonic turbine cascade model that accurately produces infinite cascade flow conditions with minimal compressor requirements is presented. An inverse design procedure using the Favre-averaged Navier-Stokes equations and k- turbulence model based on the method of steepest descent was applied to a geometry consisting of a single turbine blade in a passage. For a fixed blade geometry, the passage walls were designed such that the surface isentropic Mach number (SIMN) distribution on the blade in the passage matched the SIMN distribution on the blade in an infinite cascade, while maintaining attached flow along both passage walls. An experimental rig was built that produces realistic flow conditions, and also provides the extensive optical access needed to obtain detailed particle image velocimetry measurements around the blade. Excellent agreement was achieved between computational fluid dynamics (CFD) of the infinite cascade SIMN, CFD of the designed double passage SIMN, and the measured SIMN. DOI: / Introduction Contributed by the Turbomachinery Division of THE AMERICAN SOCIETY OF ME- CHANICAL ENGINEERS for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received by the Turbomachinery Division September 9, 2003; revised manuscript received January 12, S. A. Sjolander. Computational fluid dynamics CFD techniques are now sufficiently robust to use in both analysis and design of aircraft engine components. This is particularly true for turbine nozzles and rotors, where the generally favorable pressure gradient through the device leads to relatively thin boundary layers, making the computational results somewhat insensitive to turbulence modeling errors. However, heat transfer rates and film cooling performance are more strongly dependent on the turbulence properties, and designers must rely heavily on empirical data 1,2. In order to design more efficient and effective cooling strategies, a better understanding of the turbulent flow field is required. The effect of concave and convex streamline curvature 3, and the so-called stagnation point anomaly, or spurious buildup of turbulent kinetic energy in regions of strong irrotational strain 4 6, are two particular areas of concern for turbulence modeling in turbines. These effects have been investigated in simple flows, but detailed experiments are required to assess their importance in realistic turbine geometries. Unfortunately, acquiring the detailed turbulence measurements needed to test and calibrate turbulence models in a full rotating turbine is exceedingly difficult and expensive. Giess and Kost 7 made extensive measurements of the flow field in a rotating annular turbine cascade using L2F, pneumatic probes, and pressure taps. Lang et al. 8 measured the three-dimensional velocity field between a rotor and stator in a full rotating rig using PIV. The complexity of a rotating rig makes it nearly impossible to use optical measurement techniques to study the flow between blades. An alternative approach is to use either an annular or linear cascade. A linear cascade, with fewer blades than a full annular cascade, provides better spatial resolution for the same flow rate 9. Baughn et al. 10 showed that linear cascades provide good midspan data as compared to their rotating equivalents. Cascades consisting of multiple blades are typically utilized by the turbomachinery community to ensure periodicity about the central blade e.g., Using cascades with only one or two blade passages reduces the required flowrate and improves optical access. Ganzert and Fottner 18 conducted heat transfer measurements in a geometry consisting of three blades and two complete passages. Buck and Prakash 19 conducted film cooling effectiveness measurements in a single-passage model consisting of an entrance channel, a pressure side wall, a suction side wall, and tailboards. Suction was used to remove the boundary layers just upstream of the suction and pressure side walls and to correctly position the stagnation points. Radomsky and Thole 20 used a large-scale stator cascade to measure turbulence at low Mach numbers. Their double-passage cascade consisted of a single full blade and two half-blades comprising the outer walls of the test section. Again, suction was used to remove the upstream boundary layers. The correct design of suction bleeds is tedious 21 and can lead to serious difficulties in comparing CFD to experiments. Also, suction systems interfere with optical access for laser-based instrumentation. Tailboards also cause a number of difficulties 22, especially under transonic conditions. The present work was motivated by the desire to build a double-passage turbine cascade that correctly represents the flow around the blade without using suction. The passage should have continuous solid walls to facilitate comparison to CFD, while still replicating all of the flow features in an infinite cascade of blades. In the transonic flow of a modern turbine, those features include regions of very strong acceleration, shock waves, and boundary layers. We have developed a CFD-based optimization technique to design such double-passage cascades. The technique has been tested using the blade shape from a modern jet engine high-pressure turbine. Initially, the flow field for an infinite cascade was computed using the Favre-averaged Navier-Stokes equations to determine the desired surface isentropic Mach number SIMN distribution. Streamlines extracted from the infinite-cascade simulation were used as the initial guess for the solid outer walls of the double-passage apparatus. However, because of the presence of the boundary layers on these walls, this initial wall shape does not produce the desired SIMN distribution, and results in separated flow along the pressure side wall. The optimization scheme was Journal of Turbomachinery Copyright 2005 by ASME JULY 2005, Vol. 127 / 619

3 Fig. 1 Schematic of double-passage nozzle and test section then used to modify the wall shape until two-dimensional CFD simulations predicted the desired SIMN distribution with attached flow along both walls. The apparatus designed using the procedure was then built and tested. In this paper, we present the design methodology with an emphasis on the construction of the cost function. The setup of the experimental rig is discussed, and results from the infinite cascade and double-passage CFD simulations are compared with measurements obtained in the rig for the initial design and the final design. After several design attempts, excellent agreement was achieved when comparing the SIMN among the CFD simulations of the infinite cascade, the double passage design, and the experimental measurements. Inverse Problem Definition Figure 1 shows a schematic of the desired apparatus configuration. The flow in a pressurized wind tunnel passes through a turbulence generation grid, then into a contraction that thins the boundary layers. Flow with a nearly uniform velocity profile enters the rectangular passage approaching the double passage. After passing through the cascade, the flow exits into a large plenum chamber comprising the inlet of a noise suppression system. The challenge is to shape the Plexiglass walls, shown in gray, to produce the correct flow around the blade. In order to design the passage walls such that the flow in the double passage was representative of the flow in an infinite cascade, it was necessary to define a cost function that was also representative of the overall flow field. In doing so, we followed the practice used in airfoil design, and initially decided to match the surface pressure in the form of surface isentropic Mach number SIMN of the blade in the passage to that of the blade in an infinite cascade. Thus, the design optimization problem statement is min j,u :E,U =0 1 where j is the cost function, are the control variables, U is the state variable vector, and E is the set of governing equations to be solved. The global cost function is defined as I j = i i U 2 i=1 where is a set of weights to be determined heuristically, I is the number of cost function components constituting the global cost Fig. 2 Initial geometry and definitions of terminology used not to scale function, and i are the cost function components. Initially I was taken to be 1, 1 was set to 1, and 1 was defined as 1 = s M M* ds 3 blade Here s is a step-function scaling factor, M is the SIMN distribution double passage, and M * is the target SIMN distribution infinite cascade, with the isentropic Mach number defined as 1 4 M = 2 1 P t P 1/ where P t is the stagnation pressure, P is the static pressure, and is the ratio of specific heats, which is taken to be 1.4 for air. The cost function was minimized by the method of steepest descent. The control variable in 1 is updated as k+1 i = k i c j k i 5 until the minimum of 2 is achieved. In 5, c is the step size, which was either held constant or computed using a line search based on a parabola fit. The latter is analogous to a response surface method. A simple backward difference was used for the gradient computations j k i = j i k + j k i 6 where represents a perturbation to the control variable. Control Variables. Since the objective was to shape the passage walls in order to achieve the correct SIMN distribution along the blade, a natural choice for the control variables was a set of spline points used to construct the wall shapes. Figure 2 presents representative spline and control point locations as well as definitions of terminology used throughout. Furthermore, three additional definitions are presented for clarification: CFD-IC is the CFD of the infinite cascade; CFD-DP is the CFD of the double passage; and EM-DP are the experimental measurements in the 620 / Vol. 127, JULY 2005 Transactions of the ASME

4 double passage. In order to keep the number of degrees of freedom to a minimum, cylindrical coordinates were used with the origin placed at the leading edge of the blade, and only the radial location of the control points was varied refer to Fig. 2. Thus, = r, = const Once the control points were moved, either due to a perturbation or due to a gradient update, a piecewise cubic spline was fit through the points. Governing Equations. Since the viscous boundary layers are critically important, the Favre-averaged Navier-Stokes equations were solved with the Chen two-layer k- model in order to determine the flow field in the passage. Referring back to Eq. 1, the state variable vector U=, u, v, e, k, and E U is where e t t + u i =0 x i u i t + u iu j + eu j = iju i = ij + q ij = u i + u j x i 2 3 u k x k p ij q =, e = c v where = L + T and = L + T represent the sum of the molecular and turbulent viscosity, and thermal conductivity, respectively. The two-equation Chen k- model 23 was selected based on the turbulence model assessment of 5 to compute T. The model does not account for transition, and the boundary layer that develops along the passage walls and blade surface is assumed to be turbulent, which follows the work of 5. The two-layer model was used along the blade surface, and wall functions were used along passage walls. The governing equations were solved using STAR-CD, a finite-volume commercial CFD package developed by Adapco 23. The SIMPLE algorithm with second-order monotone advection residual scheme MARS for the spatial flux computations was used. Algorithm The infinite cascade simulation for the blade was conducted at transonic conditions. The SIMN and stagnation streamlines were extracted, the former to be used as the initial cost function definition, and the latter to be used as the initial guess for the wall shapes. Once the stagnation streamlines were offset by the pitch, a set of points was extracted to be used as both spline and control points for subsequent wall shape definitions. An algebraic grid generator was used to generate the grid for the blade-wall geometry and the CFD simulation was run until convergence was achieved. A script controlling the perturbations, spline fits, grid generation, flow field computations, and cost function evaluations was written to loop sequentially through the control points for each global iteration. Experimental Setup The experimental apparatus shown in Fig. 1 was attached to an existing high-pressure wind tunnel. The rig was designed so that the passage walls could be replaced with walls of a different shape, allowing for an iterative approach for the design optimization. A 4.6:1 area ratio nozzle was fabricated to reduce the wind tunnel cross section to the appropriate dimensions of the passage, 7 Table 1 with thin boundary layers at the passage inlet. A turbulencegeneration section upstream of the nozzle allows for the placement of turbulence grids to create turbulence intensities ranging from 5 6 % at the nozzle inlet. The two-dimensional doublepassage shape was given a depth of approximately one blade chord, allowing the apparatus to operate at full-scale Mach numbers using the 1 kg/s flow provided by the lab compressor. The flow geometry and conditions are summarized in Table 1. The passage walls were CNC machined from transparent plexiglass and polished to allow for transmission of laser light. One of the aluminum end walls is fitted with two optical-quality glass windows for PIV imaging, one to study the inlet conditions and one to examine the flow around the blade. The blade itself was manufactured from a block of stainless steel using wire EDM electrical discharge machining, and slides into a pocket in the far end wall that holds it in place. A simple free-flow exhaust muffler is attached to the cascade exit to enable supersonic flow in the passage. Static Pressure Measurements. The blade was equipped with 17 static pressure taps. Holes with a diameter of 0.58 mm were drilled perpendicular to the blade surface midspan and were connected to a Scanivalve model SSS-48C-MK4 through vinyl tubes extending out the far end wall. The blade surface pressure was measured relative to the flow stagnation pressure at the cascade inlet using a Kiel probe and a Setra model 204D pressure transducer. The Kiel probe was also connected to a Bourdon tube manometer Wallace & Tiernan FA 145, to ensure that the inlet stagnation pressure in the passage matched that of the infinite cascade, and to double-check the transducer calibration. Voltage signals were acquired using a National Instruments PC-MIO- 16E-4 board, and controlled using LabVIEW software. The resulting pressure measurements were then used to calculate the SIMN distribution, using Eq. 4. Results Geometric and flow conditions for experiment Inlet total temperature 293 K Inlet total pressure Pa Inlet Mach number 0.3 Exit Mach number 1.7 Flow inlet angle 0.0 Flow exit angle deg a Re c 660,000 Mass flow 0.63 kg/s a The Reynolds number is based on inlet conditions and blade axial chord. Infinite Cascade Simulations. Figure 3 shows the computational grid used for the simulation of the infinite cascade. The O grid consisted of 180 points in the circumferential direction, with 51 points in the transverse direction. The inlet and the exit of the O grid were extended with an H grid. Sixteen grid points were used for the entrance section, while 24 points were used for the exit section. The maximum value of y + for the nearest grid point to the blade was 0.9. Stagnation pressure and temperature corresponding to the val- Fig. 3 Computational grid used in infinite cascade simulations not to scale Journal of Turbomachinery JULY 2005, Vol. 127 / 621

5 Fig. 4 Mach number contours for infinite cascade simulation not to scale Fig. 5 SIMN corresponding to Fig. 4 plotted against the blade surface coordinate nondimensionalized by the blade axial chord where 0\ +s/c xl is the blade suction side from the stagnation point to the trailing edge and 0\ s/c xl is the blade pressure side from the stagnation point to the trailing edge ues in Table 1, as well as the direction cosine 0.488,0.873, turbulence intensity 5%, and turbulent length scale m were set at the inflow boundary to coincide with the experiment. The static pressure was set to atmospheric at the outflow boundary, with a zero gradient boundary condition for turbulence quantities and temperature. Periodic boundary conditions were set at the upper and lower boundary, along the midpitch line. Finally, adiabatic no-slip with two-layer k- was invoked at the blade surface. Convergence was achieved when all residuals dropped at least eight orders in magnitude. Figure 4 presents the Mach number contours resulting from the converged solution, depicting the shock locations and stagnation streamlines. The flow stagnates at the leading edge and undergoes strong acceleration through the upper passage. An oblique shock forms near the blade midchord and interacts with the trailing-edge shock from the pressure side of the adjacent blade forming a -shock pattern. The flow continues to undergo weak acceleration up to the trailing edge where a terminal shock forms at the blade trailing edge. Along the suction side blade surface, the turbulent boundary layer remains attached up to the trailing edge. Through the lower passage, the flow undergoes very mild acceleration at first, and eventually goes supersonic near the blade trailing edge, thus resulting in another trailing-edge oblique shock, which, when combined with trailing edge oblique shock emanating from the suction surface, forms the well-known fish-tail shock structure for airfoils operating in transonic conditions. From this converged solution, the SIMN distribution was extracted Fig. 5, which was used as the target distribution in the optimization M * in Eq. 3. Furthermore, the stagnation streamlines were extracted and replaced with solid walls for the double-passage simulation. The stagnation streamlines were then linearly extrapolated to match the contraction exit and muffler entrance of the experimental rig, a pseudoconstraint Fig. 2. Double-Passage Simulations. The grid used in the infinite cascade simulation was modified for use in the double-passage simulation. Grid refinement studies showed that at least 70,000 cells were required for the simulations. The same inflow and outflow conditions as those used in the infinite cascade simulation were used, and the inflow conditions coincide with the experiment. Noslip adiabatic wall with the two-layer k- model was specified at the blade surface, whereas adiabatic walls with wall functions were used for the passage walls. This was done in order to keep the number of grid cells to a minimum, and it was determined that wall functions along the passage walls did not degrade the overall results. The grid was constructed, and the results were monitored, to ensure that all values of y + for the nearest cell to the blade surface were well within the viscous sublayer, and within the log layer along the passage walls. Figure 6 demonstrates the SIMN resulting from the initial geometry, using stagnation streamlines shown in Fig. 2. Obviously, the initial geometry does not produce the correct pressure distribution. First, the acceleration over the leading-edge suction side of the blade is too low, leading to low values of SIMN for x/c xl = Second, the shock structure is completely misrepresented as well. This geometry produces a very weak oblique shock followed by strong acceleration up to the trailing-edge fish-tail shock. The agreement along the pressure side of the blade is better, but there is an obvious shift in the SIMN predictions. Finally, the stagnation point location for CFD-DP is in error by 3.8% of the blade chord. Initial Design. Modifying the suction wall had no discernable effect on the pressure-side pressure distribution, and vice versa. As such, the two walls were optimized simultaneously and independently for different definitions of Eq. 3. Furthermore, it was observed that the pressure wall needed to be divided into two distinct sections, a subsonic region upstream of the throat, and a downstream supersonic region. Thus, Eq. 3 takes the form Fig. 6 SIMN for the initial geometry using stagnation streamlines refer to Fig. 5 for explanation of the abscissa axis 622 / Vol. 127, JULY 2005 Transactions of the ASME

6 Fig. 7 SIMN for the initial geometry with separation along pressure wall refer to Fig. 5 for explanation of the abscissa axis where M M* ds + 2 inlet throat M 1 = 1 M M* ds throat M 1 = 2 M M* ds + 3 M M* ds throat throat exit 2 1 and 2 3 Furthermore, the step size in Eq. 5 was held fixed. The suction wall solution converged very quickly, and only 5 6 global iterations were required to match the SIMN along the pressure-side blade. This can be attributed to two factors. First, the flow is completely subsonic in the lower passage up to the terminal fish-tail shock. Second, the favorable pressure gradient negates the difficulty of having to deal with flow separation issues along the suction wall. The pressure wall, on the other hand, proved to be a much stiffer problem than the suction wall. There was a region of separated flow in the region of high curvature on the pressure wall. As the optimization routine changed the passage shape, improving the SIMN, the size of the separation region increased slightly. The existence of a separation region was deemed unacceptable, since it was likely to produce unsteadiness in the experiment and possibly affect the turbulence measurements. After achieving good agreement for the SIMN distribution Fig. 7, the wall shape was manually modified, such that the dividing streamline around the separation bubble was replaced with a solid wall Fig. 8. After doing so, the iteration process was continued until a reasonable SIMN distribution was achieved. The first version of the experimental apparatus was built to test the concept. Figure 9 presents the initial and final wall shapes for the initial design. Figure 10 shows the corresponding SIMN compared to that of the infinite cascade and the experimental measurements. It can be seen that the agreement between CFD-DP and EM-DP is very good up to the shock location. However, the shock structure resulting from the CFD-DP simulations is in very poor agreement with the experimental measurements. While the CFD-DP simulation predicted an oblique shock, the measurements in the passage clearly indicate a strong normal shock. This was not too surprising, as similar shock structures were observed in the optimization procedure while converging to the initial design geometry. Changes of less than 0.1 mm in the wall position in the Fig. 8 Separation along pressure wall not to scale supersonic region produced entirely different shock structures. These results showed that the basic methodology works, but that considerable care is needed in the supersonic region. Agreement was quite good for the pressure side of the blade between CFD-IC, CFD-DP, and EM-DP. Furthermore, there is a small error over the suction side of the blade between CFD-IC and CFD-DP. The agreement, however, between CFD-DP and EM-DP is excellent up to the shock. Final Design. To seek an improved design, the cost function was modified in order to penalize the method for separated flow along the pressure wall, thus doing away with the need for manual fixes b 2 = ds w w 8 pwall where w b is a lower bound on the shear stress to ensure that the boundary layer does not tend toward separation. Furthermore, the wall shear stress along the blade surface was also included as a Fig. 9 Initial versus final wall geometries for the first design not to scale Journal of Turbomachinery JULY 2005, Vol. 127 / 623

7 Fig. 10 SIMN corresponding to Fig. 9, without separation along pressure wall refer to Fig. 5 for explanation of the abscissa axis way of ensuring that the boundary layer had similar characteristics to the infinite cascade 3 = w * w ds 9 blade Thus, the cost function was defined based on both an inviscid property and a viscous property. Finally, a line search was implemented for the determination of c in Eq. 5 to expedite convergence. A total of 150 global optimization iterations were initially run in order to arrive at the final design. The resulting geometry at iteration 150 was built and tested to determine if the shock agreement could be improved. The experimental tests indicated that the correct shock structure was now achieved, and more subtle refinements were then made in order to arrive at the final design. Figure 11 presents the convergence history with the redefined cost function up to iteration 150 as well as after 150 with the modifications, which are described below. Starting from iteration 150, several more control points were Fig. 12 Initial versus final wall geometries for the final design not to scale added in the downstream region of the shock, which allowed for more subtle refinements in the wall shape to improve the agreement there. Also, the pressure wall separation penalty w b in Eq. 8 was relaxed, as it was observed that this would facilitate better agreement in the SIMN along the suction side. While this resulted in a thicker boundary layer, the flow was monitored to ensure that attached flow was still achieved. Referring to Fig. 11 again, it is evident that the overall cost function dropped significantly after these changes, and Fig. 12 presents the resulting geometry, which was then manufactured, installed, and tested in the rig. Figure 13 presents the resulting SIMN distributions for the final design. Excellent agreement can be seen between the CFD-IC and CFD-DP over the entire blade section for this case. Furthermore, the experimental measurements are in very good agreement with the CFD-DP results. The only discernable discrepancy is in the peak Mach number. Whereas the CFD predicts a value of 1.52, the peak value measured was somewhat higher, with a value of 1.58 Fig. 11 Convergence history Fig. 13 SIMN corresponding to Fig. 12 refer tofig. 5forex- planation of the abscissa axis 624 / Vol. 127, JULY 2005 Transactions of the ASME

8 at the same axial location; a relative error of less than 4%. Figure 14 presents the wall shear along the blade surface resulting from the CFD simulations. Again, very good agreement is observed between the CFD-IC and CFD-DP results. It is interesting to note that the shock recovery between the two cases is slightly different, indicating a different shock boundary layer interaction. Figure 15 presents the Mach number contours for the CFD-IC and CFD-DP. Recalling the agreement in SIMN from Fig. 13, and referring to the Mach number flow field in Fig. 15, it is evident that the agreement in SIMN between CFD-DP and CFD-IC is associated with an equally similar Mach number distribution throughout the entire passage. Upon completion of the blade surface pressure validation, an additional test of the inflow conditions was conducted. Matching the inflow conditions of the CFD with the experiment is a concern, since the domain of the CFD simulations did not include the nozzle section shown in Fig. 1, where the turbulence intensity was measured. This was done in order to keep the grid sizes to a minimum. While the total pressure and total temperature specified at the inflow agreed with the values used in the experiment, the prescribed value for the turbulence intensity was an issue. Velocity and turbulent kinetic energy profiles located just downstream of the inflow boundary for the CFD simulations were extracted and compared with preliminary PIV measurements. The agreement between the measured velocity profile and the CFD velocity profile was excellent; the error was on the order of 3%. The turbulence intensities also agreed quite well. Finally, a 3D simulation was conducted for the final geometry to assess the effect of the passage aspect ratio. The 2D grid was extruded to the end wall, where the grid points were clustered to facilitate the use of the two-layer model. Only half of the passage width was simulated, and a symmetry boundary condition was specified at the passage midspan. The resulting flow field at the midspan location was nearly identical with the 2D simulations, confirming that the passage width was satisfactorily large. Fig. 14 Shear stress comparison for the final design refer to Fig. 5 for explanation of the abscissa axis Fig. 15 Comparison between CFD-IC and CFD-DP for the final design: Mach number contour comparison not to scale Conclusions A double-passage turbine cascade model was designed, built, and tested for the study of turbulent flow past a stationary turbine blade. The design was based on the Favre-averaged Navier-Stokes equations and an inverse design procedure with the objective of matching the surface isentropic Mach number SIMN of the blade in the passage with the SIMN of the blade in an infinite cascade, while maintaining attached flow along the passage walls. Excellent agreement was observed between the CFD results for the infinite cascade SIMN and the double-passage SIMN. Furthermore, the experimental measurements agree very well with the CFD results for the double passage in terms of the SIMN. Acknowledgment This work was funded by GE through the University Strategic Alliance Program and by AFOSR Contract No. F monitored by Thomas Beutner. Nomenclature c step size, true chord length c v specific heat at constant volume c xl axial chord length e energy E set of governing equations I number of cost function components j global cost function k turbulent kinetic energy l length scale M isentropic Mach number p pressure q heat flux Re Reynolds number s blade surface coordinate t time u velocity component U state variable vector y + nondimensional wall unit Greek weight coefficient scaling factor perturbation dissipation, convergence criteria control variable cost function component, ratio of specific heats bound of surface integral thermal conductivity viscosity temperature density shear stress Subscripts i,j,k indices Journal of Turbomachinery JULY 2005, Vol. 127 / 625

9 L laminar t stagnation condition T turbulent w wall Superscripts b bound k optimization counter number * target value Abbreviations CFD computational fluid dynamics CFD-DP CFD of the double passage CFD-IC CFD of the infinite cascade EM-DP experimental measurements of the double passage PIV particle image velocimetry RANS Reynolds averaged Navier-Stokes SIMN surface isentropic Mach number References 1 Goldstein, R., 1971, Film Cooling, Adv. Heat Transfer 7, pp Dornberger, R., Stoll, P., Buche, D., and Neu, A., 2000, Multidisciplinary Turbomachinery Blade Design Optimization, AIAA Paper No Camci, C., and Arts, T., 1985, Short-Duration Measurements and Numerical Simulation of Heat Transfer Along the Suction Side of a Film-Cooled Gas Turbine Blade, J. Eng. Gas Turbines Power 107, pp Durbin, P. A., 1996, On the k- Stagnation Point Anomaly, Int. J. Heat Fluid Flow 17, pp Medic, G., and Durbin, P. A., 2002, Toward Improved Prediction of Heat Transfer on Turbine Blades, J. Turbomach. 124, pp Medic, G., and Durbin, P. A., 2002, Toward Improved Film Cooling Prediction, J. Turbomach. 124, pp Giess, P. A., and Kost, F., 1997, Detailed Experimental Survey of the Transonic Flow Field in a Rotating Turbine Cascade, 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics Antwerpen, Belgium March Lang, H., Morck, T., and Woisetschlager, J., 2002, Stereoscopic Particle Image Velocimetry in a Transonic Turbine Stage, Exp. Fluids 32, pp Giel, P. W., Van Fossen, G. J., Boyle, R. J., Thurman, D. R., and Civinskas, K. C., 1999, Blade Heat Transfer Measurements and Predictions in a Transonic Turbine Cascade, NASA/TM Baughn, J. W., Butler, R. J., Byerley, A. R., and River, R. B., 1995, An Experimental Investigation of Heat Transfer, Transition and Separation on Turbine Blades at Low Reynolds Number and High Turbulence Intensity, ASME Paper No. 95-WA/HT Drost, U., and Bolcs, A., 1999, Investigation of Detailed Film Cooling Effectiveness and Heat Transfer Distributions on a Gas Turbine Airfoil, J. Turbomach. 121, pp Vogt, D. M., and Fransson, T. H., 2002, A New Turbine Cascade for Aero- Mechanical Testing, 16th Symp. on Measuring Techniques in Transonic and Supersonic Flow in Cascades and Turbomachines. 13 Hollon, B., and Jacob, J., 2001, Experimental Investigations of Separation on Low Pressure Turbine Blades, AIAA Paper No Dorney, D. J., Lake, J. P., King, P. I., and Ashpis, D. E., 2000, Experimental and Numerical Investigation of Losses in Low-Pressure Turbine Blade Rows, AIAA 38th Aerospace Sciences Meeting, Reno. 15 Erhard, J., and Gehrer, A., 2000, Design and Construction of a Transonic Test-Turbine Facility, ASME Paper No GT Sanz, W., Gehrer, A., Woisetschläger, J., Forstner, M., Artner, W., and Jericha, H., 1998, Numerical and Experimental Investigation of the Wake Flow Downstream of a Linear Turbine Cascade, ASME Paper No. 98-GT Casey, M., and Innotec, S., 2001, Classical Test Cases for the Validation of Turbomachinery CFD and the Relevance of QNET-CFD Cases, QNET-CFD Workshop, Athens. 18 Ganzert, W., and Fottner, L., 1999, An Experimental Study on the Aerodynamics and the Heat Transfer of a Suction Side Film Cooled Large Scale Turbine Cascade, ASME Paper No. 99-GT Buck, F. A., and Prakash, C., 1995, Design and Evaluation of a Single Passage Test Model to Obtain Turbine Airfoil Film Cooling Effectiveness Data, ASME Paper No. 95-GT Radomsky, R. W., and Thole, K. A., 2000, Flowfield Measurements for a Highly Turbulent Flow in a Stator Vane Passage, J. Turbomach. 122, pp Kodzwa, P. M., Elkins, C. L., and Eaton, J. K., 2003, Measurements of Film Cooling Performance in a Transonic Single Passage Model, 2nd Int. Conf. on Heat Transfer, Fluid Mechanics and Thermodynamics, Zambia. 22 Ott, P., Norryd, M., and Bolcs, A., 1998, The Influence of Tailboards on Unsteady Measurements in a Linear Cascade, ASME Gas Turbine and Aeroengine Congress. 23 STAR-CD Version-3.10, 1999, Methodology, Computational Dynamics Ltd. 626 / Vol. 127, JULY 2005 Transactions of the ASME