INFLUENCE OF 3D HOT STREAKS ON TURBINE HEAT TRANSFER. Karen L. Gundy-Burlet NASA Ames Research Center Moffett Field, CA

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1 THE AMERICAN SOCIETY OE MECHANICAL ENERNEERS 1,.! 97;4'142 : The Society ehedrien be reeciet:stile for etetearritior opinions advanced in papersor discussion at meeilngs loetqe Socletior 4ol its Divisions or: Secllons or printed in Its publications Discussion Is Minted only If the priperis'published in -anasme JournaCAuthorlititiori to photocopy i;. materiel lei Internal Or personaluse:undercircumstance not telling within the fair use provisions of MeCieydgitt Act is gieted by ASiASto S libraries eirdinher usciriiegistereb with dry ddpiright0eirthicebenbir(ccc),triniedlional Reporting SeMce.pioylded that the bee fee of $0304 ',,, per page Is aide 'thready to the cdd, 27.Congreati Street, Salim MA : Requests for apatite pierinissied or IxilkreroduCtie ;held addreesed. '.. ' Copyright 0,1(10 by ASME,,sJlRlghtsReseived Printed In U.S.A.', INFLUENCE OF 3D HOT STREAKS ON TURBINE HEAT TRANSFER Karen L. Gundy-Burlet NASA Ames Research Center Moffett Field, CA Daniel J. Dorney Pratt & Whitney East Hartford, CT ABSTRACT Experimental data have shown that combustor temperature non-uniformities can lead to pressure side burning on firststage turbine rotor blades. Although most modern turbines operate in an environment with significant heat transfer, the majority of hot streak experiments and simulations during the last decade have assumed adiabatic flow. This assumption can cause errors in the prediction of turbine cooling requirements. In the present investigation, three-dimensional unsteady Navier- Stokes simulations have been performed for a 1-1/2 stage highpressure turbine geometry operating in subsonic flow. Combustor hot streaks and heat transfer effects at the airfoil surfaces were included in the simulations. The predicted aerodynamic (pressure) data shows close agreement with the available experimental data. The predicted heat flux results agree with experimental observations. NOMENCLATURE - Speed of sound - Static pressure - Heat Flux per unit area, q = - x, y, z components of flux - Vector of flow variables - Static temperature - x, y, z components of velocity - Rotor velocity - Density - Viscosity - Rotor rotational speed its Subscripts - Hot streak - Inviscid quantity - Mid-span value - Normal direction - Stagnation quantity, time derivative - Turbulent quantity - Viscous quantity s, y, z - First derivative with respect to x, y, z 1 - First Stator inlet quantity 2 - Rotor inlet quantity 3 - Rotor exit quantity 4 - Second stator exit quantity oo - Free stream quantity INTRODUCTION Hot streaks are known to have a significant impact on the wall temperature distributions of first-stage turbine rotors. The experimental geometry most often employed to simulate hot streak migration is the Large-Scale Rotating Rig (LSRR) turbine model used by Butler et at. (1989) and Roback and Dring (1992). The LSRR is a large-scale, low-speed, rotatingrig wind-tunnel facility designed to simulate the flow field in an axial-flow turbine. The migration of hot streaks through the LSRR has been simulated by many researchers including Krouthen and Giles (1988), Rai and Dring (1990), Takahashi and Ni (1990,1991), Dorney et al. (1992,1993,1996). While these numerical simulations have produced significant insights into the mechanisms controlling hot streak migration they have (for the most part) neglected surface heat transfer, which can be important in high-pressure turbines. The design of efficient Presented at the International Gas Turbine & Aeroengine Congress & Exhibition Orlando, Florida June 2,5,1997

2 blade cooling schemes requires a knowledge of both the hot streak migration path and the local heat transfer coefficients. The focus of the present effort has been to study the combined effects of a combustor hot streak and heat transfer in a three-dimensional viscous flow environment. To this end, threedimensional unsteady Navier-Stokes simulations have been performed for the 1-1/2 stage configuration on the LSRR turbine. The predicted aerodynamic data (time-averaged surface pressures) have been compared with the available experimental data. The time-averaged and unsteady temperature data has been used to analyze the effects of the hot steaks on the airfoil heat transfer. PHYSICAL AND MATHEMATICAL MODELS The governing equations considered in this study are the time dependent, three-dimensional Reynolds-averaged Navier- Stokes equations: Qt +(Fe+ F,): + (Gi +G,)v + (Hi +H) = 0 (1) The viscous fluxes are simplified by incorporating the thin layer assumption (Baldwin and Lomax, 1978). In the current study, viscous terms are retained in the direction normal to the hub and shroud surfaces, and in the direction normal to the blade surfaces. To extend the equations of motion to turbulent flows, an eddy viscosity formulation is used. The turbulent viscosity, pp, is calculated using the two-layer Baldwin-Lomax (1978) algebraic turbulence model. The numerical algorithm used in the three-dimensional computational procedure consists of a time-marching, implicit, finite-difference scheme. The procedure is third-order spatially accurate and first-order temporally accurate. The inviscid fluxes are discretized according to the scheme developed by Roe (1981). The viscous fluxes are calculated using standard central differences. An alternating direction, approximate-factorization technique is used to compute the time rate changes in the primary variables. In addition, Newton sub-iterations are used at each global time step to increase stability and reduce linearization errors. For all cases investigated in this study, two Newton subiterations were performed at each time step. Further details on the numerical procedure can be found in Gundy-Burlet (1992). The Navier-Stokes analysis uses 0- and H-type zonal grids to discretize the rotor-stator flow field and facilitate relative motion of the rotor. The 0-grids are body-fitted to the surfaces of the airfoils and generated using an elliptic equation solution procedure. They are used to properly resolve the viscous flow in the blade passages and to easily apply the algebraic turbulence model. Algebraically generated El-grids are used to discretize the rest of the passage in the vicinity of the airfoil. BOUNDARY CONDITIONS The theory of characteristics is used to determine the boundary conditions at the inlet and exit of the computational domain. For subsonic inlet flow four quantities are specified and one is extrapolated from the interior of the computational domain. In particular, the total pressure, v and in velocity components, and the downstream running Riemann invariant, = u (or the total temperature Ti), can be specified as a function of the radius. The upstream running Riemann invariant, R2 =u 1497, is extrapolated from the interior of the computational domain. For simulations containing inlet hot streaks, the boundary conditions within the hot streak must be modified. Within the hot streak the inlet flow variables used to define the specified boundary conditions can be written as uh, wh, = woon,firco TF oh, = /l eo V7,77-1., Tt Vhs = Vog 1 /1,00 Ph. = Pco (2) Ph. = pcol(th,it,) where 7Th, is the temperature within the hot streak and T oo is the temperature of the undisturbed inlet flow. The static and total pressure within the hot streak are assumed to be equal to that of the undisturbed inlet flow. In the current investigation, the temperature profile within the hot streak is based on a hyperbolic-tangent distribution with the center located at 40% of span. This distribution is consistent with the experimental geometry of Butler et al. (1989). For subsonic outflow one flow quantity is specified and four are extrapolated from the interior of the computational domain. The v and w velocity components, entropy, and the downstream running Riemann invariant are extrapolated from the interior of the computational domain. The pressure ratio, P4/Pi1 specified at mid-span of the computational exit and the pressure at all other radial locations at the exit is obtained by integrating the equation for radial equilibrium. Periodicity is enforced along the outer boundaries of the H-grids in the circumferential (9) direction. For viscous simulations, no-slip boundary conditions are enforced along the surfaces of the stator and rotor airfoils. Absolute no-slip boundary conditions are enforced at the hub and tip end walls of the stator regions, along the surface of the vane, and along the outer casing (tip end wall) of the rotor blade. Relative no-slip boundary conditions are imposed at the hub and along the surface of the rotor blade. It is assumed that the normal derivative of the pressure is zero at solid wall surfaces. In addition, a specified temperature distribution is held constant in time along the solid surfaces. The flow variables of Q at zonal boundaries are explicitly updated after each time step by interpolating values from the adjacent grid. The zonal boundary conditions are nonconservative, but for subsonic flow this should not affect the accuracy of the final flow solution. GEOMETRY AND GRID GENERATION The three-dimensional turbine model is based on the Large Scale Rotating Rig (LSRR) geometry used in the experiments performed by Dring, et al. (1986a,1986b) and Joslyn and Dring (1989). The LSRR is a 1-1/2 stage turbine with a 27-inch midspan radius, 6-inch span and airfoil aspect ratios of approximately unity. The turbine hub and casing are at constant radii. The axial gap between the first stator and rotor is approximately 50% of the first-stage average axial chord, while the gap between the rotor and the second stator is approximately 67% of their 2

3 HjuUflI STATOR 1 a_e ,01# _11 911,... _ = : : : , 1 1_ \.4 ROTOR I STATOR 2 Figure 1: Zonal grid topology. average chord. The rotor tip clearance is approximately 1% of span. A large experimental database exists for this turbine, including time-averaged pressures at several span wise locations on each airfoil, traverse data behind each airfoil, and surface flow visualizations. The experimental configuration has 22 airfoils in the first stator row and 28 airfoils in each of the rotor and second stator rows for a total of 78 airfoils. A three-dimensional computation of the flow through the complete turbine configuration would be prohibitively expensive. To reduce the cost of the computation, the number of stators in the first row was increased to 28 and the size of the stators was reduced by a factor of 22/28 to maintain the same blockage. The flow is then assumed to be periodic from passage to passage, thereby allowing a reduction to a single blade or vane in each of the rows. The grids used to describe the hub and airfoil surfaces of the turbine are shown in Fig. 1. The stator 0-grid contains 214 points in the wrap-around direction, 26 points in the surfacenormal direction and 51 points in the radial direction. The rotor 0-grid contains 214 in the wrap-around direction, 45 points in the surface-normal direction and 51 points in the radial direction. The additional points in the rotor grid exist to discretize the rotor tip region. The dimensions of the H-grids vary, but average 123 points in the axial direction, 81 points in the circumferential direction and 51 points radially. The dimensions of the H-grids used to disaetize the inlet and outlet regions of the turbine stage are 34 by 81 by 51. These relatively fine grid dimensions were arrived through the use of a two-dimensional code to evaluate the grid density needed to support the convection of the wakes with minimal dissipation. The total number of grid points used for the grid system was approximately 2.7 million grid points. NUMERICAL RESULTS The inlet Mach number to the first-stage stator was 0.07 and the inlet flow was assumed to be axial. The rotor rotational speed was 410 rpm. The free stream Reynolds number was 39,370/cm. The midspan pressure coefficient 14% of chord aft of the second-stage stator trailing edge of Cp. = (used to set the exit boundary condition) was determined from the inlet total pressure and the static pressure measured in the second-stage stator trailing-edge plane. In this investigation Cy, is defined as _ (3) 0.5* pi. fg., The airfoil surfaces were assumed to be at 267 degrees Kelvin while the free stream temperature was 295 degrees Kelvin. The surface temperature was chosen to simulate the surface temperature to freestream temperature ratios encountered in engine operation. A hot-streak was introduced at the inlet which was directly in line with the first-stage stator (see Dorney and Gundy-Burlet, 1996, for the importance of the relative position between the hot streak and first-stage stator, and the effects on rotor heating). A hot streak temperature of 1.2 times that of the surrounding inlet flow was chosen for this investigation. Actual hot streak temperatures 1.1 to 1.6 of free stream are typical of engine operating environments (Takahashi, 1996). The numerical simulations were run at 2000 time steps (with 2 Newton sub-iterations at each time step) per cycle on the Cray Co supercomputer at NASA Ames Research Center. A cycle corresponds to the rotor blade rotating through an angle of 2rn/N where n is the number of stator blades (i.e., it = 1) used in the simulation and N is the number of stator airfoils in the modeled machine (i.e., N = 28). The code operates at 31p-secs/it./grid point and 384 Mtlops on the Cray C90. Figures 2, 3 and 4 show the time-averaged pressure coefficient and pressure coefficient amplitude distributions for the midspan of the first-stage stator, first-stage rotor and second- 3

4 stage stator, respectively. The pressures are time-averaged and the minimum and maximum pressures are determined over one rotor-passing cycle. The time-averaged results from the numerical analysis are represented as a solid line, while the experimental suction side results are shown as squares and the pressure side results are indicated by drdes. The comparison between the time-averaged computational results and the experimental data (Dring et al. 1986a,1986b) is good. Neither the hot streak nor the constant surface temperature significantly affect the pressure field. Figures 5-13 illustrate the surface heat flux within the turbine. In these figures, the time-averaged heat flux on the suction surface is a solid line and the suction-surface unsteady heat flux envelope is denoted by dashed lines. The chain-dot line is the time-averaged pressure-surface heat flux while the dotted lines show the pressure-surface unsteady heat flux envelope. Figures 5-7 present the surface heat of the first-stage stator at the 12.5%, 50.0% and 87.5% span locations, respectively. The influence of the hot steak can be seen in the heat transfer. The raidspan heat transfer is generally high with a peak at the leading edge where the hot streak impacts the first-stage stator. The radial migration of the hot streak combined with slow pressureside convection rates results in high heat transfer on the pressure surface near the hub trailing edge. There is uniform unsteadiness over the majority of the blade span because of the equal blade count ratios modeled in the simulation. Figures 8-10 contain the surface heat flux of the first-stage rotor at the 12.5%, 50.0% and 87.5% span locations, respectively. The peak unsteadiness in the heat flux occurs on the suction surface near raidspan and is caused by the rotor sweeping through a hot streak entrained in the shedding first-stage stator wake. The imprint of the rotor passage vortices can be seen at approximately the 10 cm axial position on both the 12.5% and 87.5% span stations. The passage vortex causes a distinct increase in heat transfer aft of this point. On the pressure side, time-averaged heat transfer increases near the trailing edge as the hot streak moves radially toward the tip. At the midspan station, the heat transfer is greater on the suction surface than on the pressure surface until approximately 90% of the axial chord. Dorney and Gundy-Buzlet (1996) showed that the rotor pressure and suction surface temperatures were approximately equal for an adiabatic computation with the hot streak fully impinging on the first-stage stator. However, when the hot streak was aligned with the mid-passage of the first-stage stator, the temperature on the rotor pressure surface was substantially higher than that of the suction surface. It is surmised that if the mid-passage hot streak case were recomputed with heat-transfer effects at the surface, the pressure surface would show substantially more heat transfer than in the current full-impingement calculation. Figures show the surface heat flux of the second-stage stator at the 12.5%, 50.0% and 87.5% span locations. The figures show generally higher levels of heat transfer and unsteadiness on the suction surface of the second-stage stator. The imprint of the passage vortex at the hub can be seen at approximately mid-chord at the 12.5% span station. Because of the full impingement of the hot streak on the first-stage stator, the hot ca Figure 2: First-stage stator midspan pressures, Figure 3: First-stage rotor midspan pressures Figure 4: Second-stage stator midspan pressures

5 Figure 5: First-stage stator heat transfer, 12.5% span Figure 8: First-stage rotor heat transfer, 12.5% span 40 " ' ra. 20 g 15 Sucdte Sofro An. 10 Pass= Sado Avg i Figure 6: First-stage stator heat transfer, 50.0% span 40 Figure 9: First-stage rotor heat transfer, 50.0% span ao 'A SSad= Avg. - - Name Surf= An, Figure 7: First-stage stator heat transfer, 87.5% span Figure 10: First-stage rotor heat transfer, 87.5% span 5

6 the hot streak has largely mixed out by the time it reaches the second-stage stator. Heat transfer effects on the second-stage stator are minimixed in this case. Figure 14 shows time-averaged heat-transfer contours over each of the pressure and suction surfaces in the turbine. In this figure, blue indicates low heat flux, red indicates high heat flux and the color scale is the same for all of the surfaces. The flow is from left to right for each of the surfaces. The path of the hot streak over the surface of the first-stage stator is readily apparent. The highest levels of heat flux are at the leading edge suction surface where the hot streak expands over the stator and at the trailing edge pressure surface. The imprints of the passage vortices on the suction surfaces of each airfoil are accentuated by the higher heat flax in those regions. The rotor shows the highest heat flux near the midspan leading edge although the hub passage vortex and the tip leakage flows induce significant heat transfer. The radial movement of the hot streak toward the tip of the pressure side of the rotor is also apparent. CONCLUSIONS Previous numerical and experimental studies, assuming adiabatic airfoil and end wall surfaces, have shown that combustor hot streaks can cause significant temperature increases along the pressure surface of first-stage turbine rotors. In the current investigation, the combined effects of combustor hot streaks and airfoil heat transfer have been studied. The predicted results indicate that full-impingement of the hot streak on the first-stage stator results in low levels of heat transfer on the second-stage stator. Relatively high heat transfer on the first-stage rotor is localized to the leading edge and hub vortex and tip leakage flow regions. It is expected that alignment of the hot streak with the mid-passage of the first-stage stator would result in significant pressure-surface heat transfer on the first-stage rotor. These are the areas of the rotor which have been shown experimentally to endure the greatest thermal stresses. FUTURE DIRECTIONS Hot-streak clocking studies are currently underway for other circumferential and radial positions of the hotstreak. There are plans to compare with unsteady heat transfer data from an updated version of the LSRR facility as it becomes available. BIBLIOGRAPHY Baldwin, B. S., and Lomax, H., 1978, "Thin Layer Approximation and Algebraic Model for Separated Turbulent Flow," AIAA Paper , Huntsville, AL, January. Butler, T. L., Sharma, 0. P., Joslyn, H. D., and Dring, R. P., 1989, "Redistribution of an Inlet Temperature Distortion in an Axial Flow Turbine Stage," AIAA Journal of Propulsion and Power, Vol. 5, January-February, pp Dorney, D. J., Davis, FL. L., Edwards, D. E., and Madavan, N. K., 1992, 'Unsteady Analysis of Hot Streak Migration in a ao ' or 25 - IL 2 i Suakin &due Ant Ptessore Safa MFA. Pt St Afl. Presort St Max Figure 11: Second-stage stator heat transfer, 12.5% span 40 "E' ' 2 p a Figure 12: Second-stage stator heat transfer, 50.0% span 40 I- S l0 W as Stan Stthce An. St M Pa= Surface Avg. is 4:0 is Figure 13: Second-stage stator heat transfer, 87.5% span

7 Turbine Stage," AIAA Journal of Propulsion and Power, Vol. 8, No. 2, pp Dorney, D. J., and Davis, R. L., 1993, "Numerical Simulation of Turbine 'Hot SpOt' Alleviation Using Film Cooling," AIAA Journal of Propulsion and Power, Vol. 9, No. 3, pp Dorney, D. J., and Gundy-Burlet, K. L., 1996, "Hot Streak Clocking Effects in a 1-1/2 Stage Turbine," AIAA Journal of Propulsion and Power, VO1.12, No. 3, pp Dring, R. P., Blair, M. F., Joslyn, H. D., Power, G. D., and Verdon, J. M:, 1986a "The Effects of Inlet Turbulence and Rdtor/Stator Interactions on the Aerodynamics and Heat Transfer of a Large-Scale Rotating'Turbine Model. i - Final Report,", NASA Contractor Report 4079, Contract NAS , May. Dring, R. P., Blair, M. F., Joslyn, H. D., Power, G. D., and Verdon, 3. M., 1986b, "The Effects_of Inlet Turbulence and Rotor/Slator Interactions on the Aerodynamics and Heat Transfer of a Large-Scale Rotating Turbine Model, iv - Aerodynamic Data Tabulation," NASA Contractor Report 4079, Contract NAS , May. Gundy-Burlet, K. L., 1992, "Navier-Stokes Simulations of Multistage Turbomachinery Flows," Computing Systems in Engineering, 3(1-4): Joslyn, H. D., and Dring., R. P., 1989 "Three Dimensional Flow and Temperature Profile Attenuation in an Axial Flow Turbine," AFOSR Report R , March. Krouthen, B., and Giles, M. B., 1988, "Numerical Investigation of Hot Streaks in Turbines," AIAA Paper , Boston, MA. Rai, M. M., and Dring, R. P., 1990, "Navier-Stokes Analysis of the Redistribution of Inlet Temperature Distortions in a Turbine," AIAA Journal of Propulsion and Power, Vol. 6, pp , Roback, R. J., aid Dring, R. P., 1992, "Hot Streaks and Phantom Cooling in a Turbine Rotor Passage: Part 1 - Separate Effects," ASME Paper 92-GT-75, Cologne, Germany. Roe, P. L., 1981, "Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes," Journal of Corny utational Physies, Vol. 43, pp Takahashi, R. K., and Ni, R. H., 1990, "Unsteady Euler Analysis of the Redistribution of an Inlet Temperature Distortion in a Turbine," AIAA Paper , Orlando, FL. Takahashi, R. K., and Ni, R. H., 1991, "Unsteady Hot Streak Migration Through a 1-1/2 Stage Turbine," AIAA Paper , Sacramento, CA. Takahashi, R. K., 1996, Pratt & Whitney, Private Communication, August,

8 First Stage Stator Suction Surface (left) Pressure Surface (right) ) First Stage Rotor Suction Surface (left) co Pressure Surface (right) Second Stage Stator Suction Surface (left) Pressure Surface (right) Figure 14. Time Averaged Surface Pleat Transfer