IMECE 2018-87876 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. INTRODUCTION In a gas turbine engine, the upper and lower walls (casing and hub, respectively) that contain the flow also result in the generation of boundary layers. These boundary layers reduce the overall performance of the turbomachine and generate complex flow patterns in the airfoil passage, known as secondary flow. Secondary flow consists of several interconnected flow features. When the endwall boundary layer encounters the blockage of a turbine airfoil, it will separate and form coherent vorticity known as the horseshoe vortex, with two legs that wrap around the airfoil. Within the passage, strong flow turning causes development of a passage vortex that travels from the pressure to suction side. This often merges with the pressure side leg of the horseshoe vortex which has the same sense of rotation. The strong streamwise vorticity sweeps up endwall boundary layer fluid in the passage, as well as airfoil suction side boundary layer fluid as it encounters and climbs the airfoil suction side. The entrainment of endwall and suction side boundary layer fluid results in significant mixing and entropy generation, which leads to reduced aerodynamic performance. Furthermore, the sweeping action of the passage vortex can locally enhance heat transfer and remove cooling flow from the endwall. Prediction of this behavior remains challenging due to the complex nature of the vortex evolution, possible unsteadiness, and transitional behavior of the endwall boundary layer inside the passage. As such, turbulent-scale-modeling computational approaches such as Reynolds-averaged Navier-Stokes (RANS) suffer from deficiencies. Higher-fidelity approaches such as large eddy simulation (LES) can be more accurate, but much more costly. It is of interest to evaluate what kinds of improvement in accuracy might be achievable with high-fidelity methods. NOMENCLATURE CCaaaa axial chord of blade