Aerodynamic Aspects and Cooling Techniques of Turbine Blade; Numerical Studies using LES, SAS, SST, SA and k-e

Abstract

Numerical investigations of turbine blade are carried out using large-eddy simulation (LES), Scale Adaptive Simulation (SAS), k-e with extended wall function, Spalart-Allmaras (SA), and Shear Stress Transport (SST). The goal of the present studies is to investigate the turbine blade aerodynamics and blade cooling techniques. The simulations are performed for a Reynolds number, Re = 3.67 x 10 6 , based on the chord, c, of the airfoil and free-stream velocity. The computational results reveal the dissipative nature, of SAS, associated with the turbulence modeling. I. Introduction HE boundary layer for the flow through a Low-Pressure Turbine (LPT) cascade is transitional in nature and the transition location is not known a-priori. Furthermore, the separation process is highly unsteady with a wide variation in the separation location. Both these factors tend to limit the predictive capability of the RANS approach for this flow. Furthermore, conventional RANS simulations provide information only about the mean flow field, and only limited insight regarding the dynamics of the unsteady separation process can be gained from these simulations. Developments in computer technology hardware as well as in advanced numerical algorithms have now made it possible to perform very large-scale computations of these turbine flow fields. Numerical methodologies based on the large-eddy simulation (LES) technique have emerged as a viable means of investigating the transitional flow through a LPT. In LES, the large-scale motion is simulated accurately, and the so-called subgrid-scales (SGS) are modeled. Recent numerical studies of flow in a LPT used LES in conjunction with upwind-biased schemes. Fujiwara et al. (2002) investigated the unsteady suction side boundary layer of a highly loaded low-pressure turbine blade, TL10. Simulations were performed using a low-Reynolds number k-e model and also compressible LES with the Smagorinsky SGS model. The numerical computations, using the low Re k-e model, were assumed to be two-dimensional and steady, whereas the large-eddy simulations were three-dimensional and unsteady. For LES, the three-dimensional compressible Navier-Stokes equations were solved by evaluating the convective terms using a third-order upwind biased scheme and evaluating the viscous terms using a second-order central-difference scheme. The study concerned the Reynolds number effect on the blade aerodynamics. Reynolds number, based on the axial chord and exit velocity, varied in the range (0.99 ÷ 1.76) x10 5 . The study showed that LES can predict the boundary layer separation and reattachment process, and its Re-number dependence, while the 2D steady simulation with a k-e model cannot capture these flow phenomena. However, some difference between LES and experimental data were observed at the reattachment point. Raverdy et al. (2003) employed the monotonically integrated large-eddy simulation (MILES) approach to predict the transition process and its interaction with the wake dynamics for a subsonic turbine blade configuration. The three-dimensional unsteady filtered Navier-Stokes equations were solved using the finite-volume solver FLU3M, developed by ONERA. No explicit sub-grid scale model was used. However, the numerical dissipation of the modified AUSM + (P) upwind scheme used to discretize the Euler fluxes was assumed to transfer the energy from large scales to the small scales at a rate nearly equivalent to the one