Wing-Fai Ng

An Investigation of Heat Transfer in a Film Cooled Transonic Turbine Cascade: Part I — Steady Heat Transfer

Experiments were performed in a transonic cascade wind tunnel to investigate the film effectiveness and heat transfer coefficient on the suction side of a high-turning turbine rotor blade. The coolant scheme consisted of six rows of staggered, discrete cooling holes on and near the leading edge of the blade in a showerhead configuration. Air was cooled in order to match the density ratios found under engine conditions. Six high-frequency heat flux gauges were installed downstream of the cooling holes on the suction side of the blade. Experiments were performed with and without film and the coolant to freestream total pressure ratio was varied from 1.02 to 1.19. In order to simulate real engine flow conditions, the exit Mach number was set to 1.2 and the exit Reynolds number was set to 5×106. The freestream turbulence was approximately 1%. The heat transfer coefficient was found to increase with the addition of film cooling an average of 14% overall and to a maximum of 26% at the first gauge location. The average film cooling effectiveness over the gauge locations was 25%. Both the heat transfer coefficient and the film cooling effectiveness were found to have only a weak dependence upon the coolant to freestream total pressure ratio at the gauge locations used in this study.© 2000 ASME

Effects of Large Scale High Freestream Turbulence and Exit Reynolds Number on Turbine Vane Heat Transfer in a Transonic Cascade

This paper experimentally and numerically investigates the effects of large scale high freestream turbulence intensity and exit Reynolds number on the surface heat transfer distribution of a turbine vane in a 2D linear cascade at realistic engine Mach numbers. A passive turbulence grid was used to generate a freestream turbulence level of 16% and integral length scale normalized by the vane pitch of 0.23 at the cascade inlet. The base line turbulence level and integral length scale normalized by the vane pitch at the cascade inlet were measured to be 2% and 0.05, respectively. Surface heat transfer measurements were made at the midspan of the vane using thin film gauges. Experiments were performed at exit Mach numbers of 0.55, 0.75, and 1.01, which represent flow conditions below, near, and above nominal conditions. The exit Mach numbers tested correspond to exit Reynolds numbers of 910 5 , 1.0510 6 , and 1.510 6 based on a vane chord. The experimental results showed that the large scale high freestream turbulence augmented the heat transfer on both the pressure and suction sides of the vane as compared to the low freestream turbulence case and promoted a slightly earlier boundary layer transition on the suction surface for exit Mach 0.55 and 0.75. At nominal conditions, exit Mach 0.75, average heat transfer augmentations of 52% and 25% were observed on the pressure and suction sides of the vane, respectively. An increased Reynolds number was found to induce an earlier boundary layer transition on the vane suction surface and to increase heat transfer levels on the suction and pressure surfaces. On the suction side, the boundary layer transition length was also found to be affected by increase changes in Reynolds number. The experimental results also compared well with analytical correlations and computational fluid dynamics predictions. DOI: 10.1115/1.2952381

The Effects of Freestream Turbulence, Turbulence Length Scale, and Exit Reynolds Number on Turbine Blade Heat Transfer in a Transonic Cascade

This paper experimentally investigates the effect of high freestream turbulence intensity, turbulence length scale, and exit Reynolds number on the surface heat transfer distribution of a turbine blade at realistic engine Mach numbers. Passive turbulence grids were used to generate freestream turbulence levels of 2%, 12%, and 14% at the cascade inlet. The turbulence grids produced length scales normalized by the blade pitches of 0.02, 0.26, and 0.41, respectively. Surface heat transfer measurements were made at the midspan of the blade using thin film gauges. Experiments were performed at the exit Mach numbers of 0.55, 0.78, and 1.03, which represent flow conditions below, near, and above nominal conditions. The exit Mach numbers tested correspond to exit Reynolds numbers of 6 × 10 5 , 8 × 10 5 , and 11 × 10 5 , based on true chord. The experimental results showed that the high freestream turbulence augmented the heat transfer on both the pressure and suction sides of the blade as compared with the low freestream turbulence case. At nominal conditions, exit Mach 0.78, average heat transfer augmentations of 23% and 35% were observed on the pressure side and suction side of the blade, respectively.

3D Numerical Investigation of Tandem Airfoils for a Core Compressor Rotor

The tandem airfoil has potential to do more work as a compressor blade than a single airfoil without incurring higher losses. The goal of this work is to evaluate the fluid mechanics of a tandem rotor in the rear stages of a core compressor. As such, the results are constrained to shock-free fully turbulent flow with thick endwall boundary layers at the inlet. A high hub-to-tip ratio 3D blade geometry was developed based on the best-case tandem airfoil configuration from a previous 2D study. The 3D tandem rotor was simulated in isolation, in order to scrutinize the fluid mechanisms of the rotor, which had not been previously well documented. A geometrically similar single blade rotor was also simulated under the same conditions for a baseline comparison. The tandem rotor was found to outperform its single blade counterpart by attaining a higher work coefficient, polytropic efficiency, and numerical stall margin. An examination of the tandem rotor fluid mechanics revealed that the forward blade acts in a similar manner to a conventional rotor. The aft blade is strongly dependent on the flow it receives from the forward blade, and tends to be more three-dimensional and nonuniform than the forward blade.

Generalized conjugate-gradient methods for the Navier-Stokes equations

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Steady and Unsteady Heat Transfer in a Transonic Film Cooled Turbine Cascade

This paper reports on an investigation of the heat transfer on the suction side of a transonic film cooled turbine rotor blade in a linear cascade. Heat transfer coefficient and film effectiveness are first determined for steady conditions. The unsteady effects of a passing shock on the heat transfer are then investigated. The film cooling pattern used is a showerhead design with three rows on the suction side, one row at the stagnation point and two rows on the pressure side. The experiments were performed at engine representative temperature and pressure ratios using air as coolant. Heat transfer measurements are obtained using a Heat Flux Microsensor, and surface temperature is monitored with a surface thermocouple. Static pressure is monitored with a Kulite pressure transducer. The shock emerging from the trailing edge of the NGV and impinging on the rotor blades is modeled by passing a shock wave along the leading edges of the cascade blades. The steady-state heat transfer coefficient is 8% higher with film cooling than without film cooling. Shock heating of the freestream flow is determined to be the major contribution to the unsteady variation of heat flux, leading to an increase of about 30°C to 35°C in recovery temperature and adiabatic wall temperature.Copyright

Upwind relaxation methods for the Navier-Stokes Equations using inner iterations

An upwind line relaxation algorithm for the Navier-Stokes equations which employs inner iterations is applied to a supersonic and a subsonic test problem. The purpose of using inner iterations is to accelerate the convergence to steady-state solutions, thereby reducing the overall CPU time. A convergence criterion is developed to assist in automating the inner iterative procedure. The ability of the line inner iterative procedure to mimic the quadratic convergence of the direct solver method is confirmed in both test problems, but some of the non-quadratic inner iterative results were more efficient than the quadratic results. In the supersonic test case, the use of inner iterations was very efficient in reducing the residual to machine zero. For this test problem, the inner iteration method required only about 65% of the CPU time which was required by the most efficient line relaxation method without inner iterations. In the subsonic test case, poor matrix conditioning forced the use of under-relaxation in order to obtain convergence of the inner iterations, resulting in an overall method which was less efficient than line relaxation methods which employ a more conventional CPU savings strategy. 23 refs., 9 figs.

An Experimental Investigation of Showerhead Film Cooling Performance in a Transonic Vane Cascade at Low and High Freestream Turbulence

This experiment investigates the effects of blowing ratio on the film cooling performance of a showerhead-cooled first-stage turbine vane at low freestream turbulence (Tu = 2%) and an integral length scale normalized by vane pitch (Λx /P) of 0.05. The exit Reynolds number based on vane true chord is 1.1 × 106 . The effect of freestream turbulence at high Mach number (Mex = 0.76) and blowing ratio (BR = 0, 1.5, 2.0) is also explored by comparing results with high freestream turbulence measurements (Tu = 16%) previously performed in the same cascade. To characterize film cooling performance, platinum thin-film gauges were used to measure Nusselt number and film cooling effectiveness distributions at the midspan of the vane. Net heat flux reduction is also addressed. The primary effects of coolant injection were augmentation of Nusselt number and reduction of adiabatic wall temperature on the vane surface. In general, increasing blowing ratio showed increases in Nusselt number augmentation over the vane surface and an increase in film cooling effectiveness as well. Both Nusselt number and film cooling effectiveness trends were influenced by a strong favorable pressure gradient and resulting flow acceleration on the suction surface. Comparing low freestream turbulence results with high freestream turbulence measurements showed that large-scale, high freestream turbulence can decrease heat transfer coefficient and film cooling effectiveness downstream of injection.© 2009 ASME

M. J. Hartmann Memorial Session Paper: Turbulence Characteristics in a Supersonic Cascade Wake Flow

The turbulent character of the supersonic wake of a linear cascade of fan airfoils has been studied using a two-component laser-doppler anemometer. The cascade was tested in the Virginia Polytechnic Institute and State University intermittent wind tunnel facility, where the Mach and Reynolds numbers were 2.36 and 4.8 × 10 6 , respeclively. In addition to mean flow measurements, Reynolds normal and shear stresses were measured as functions of cascade incidence angle and streamwise locations spanning the near-wake and the far-wake. The extremities of profiles of both the mean and turbulent wake properties were found to be strongly influenced by upstream shock-boundary-layer interactions, the strength of which varied with cascade incidence. In contrast, the peak levels of turburlence properties within the shear layer were found to be largely independent of incidence, and could be characterized in terms of the streamwise position only

Preconditioned Conjugate Gradient methods for low speed flow calculations

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.