Large-eddy simulations of low pressure turbine endwall flow and heat transfer

Turbine airfoils are subject to strong secondary flows that produce total pressure loss and high surface heat transfer in the airfoil passage. The secondary flows arise from the high overall flow turning acting on the incoming boundary layer, as well as the generation of a horseshoe vortex at the leading edge of the airfoil. Prediction of the effects of secondary flows on endwall heat transfer using steady Reynolds-averaged Navier-Stokes (RANS) approaches has so far been somewhat unsatisfactory, but it is unclear whether this is due to unsteadiness of the secondary flow, modeling assumptions (such as the Boussinesq approximation and Reynolds analogy), strongly non-equilibrium boundary layer behavior in the highly skewed endwall flow, or some combination of all. To address some of these questions, and to determine the efficacy of higher-fidelity computational approaches to predict endwall heat transfer, a low pressure turbine cascade was modeled using a wall-modeled Large Eddy Simulation (LES) approach. The result was compared to a steady Reynolds-stress modeling (RSM) approach, and to experimental data. Results indicate that the effect of the unsteadiness of the pressure side leg of the horseshoe vortex results in a broad distribution of heat transfer in the front of the passage, and high heat transfer on the aft suction side corner, which is not predicted by steady RANS. However, the time-mean heat transfer is still not well predicted due to slight differences in the secondary flow pattern. Turbulence quantities in the blade passage agree fairly well to prior measurements and highlight the effect of the strong passage curvature on the endwall boundary layer, but the LES approach here overpredicts turbulence in the secondary flow at the cascade outlet due to a thick airfoil suction side boundary layer. Overall, more work remains to identify the specific model deficiencies in RSM or wall-modeled LES approaches.