Massively-Parallel DNS and LES of Turbine Vane Endwall Horseshoe Vortex Dynamics and Heat Transfer

Higher turbine inlet temperatures enable increased gas turbine efficiency but significantly reduce component lifetimes through melting of the blade and endwall surfaces. This melting is exacerbated by the horseshoe vortex that forms as the boundary layer stagnates in front of the blade, driving hot gasses to the surface. Furthermore, this vortex exhibits significant dynamical motions that increase the surface heat transfer above that of a stationary vortex. To further understand this heat transfer augmentation, the dynamics of the horseshoe vortex must be characterized in a 3D time-resolved fashion which is difficult to obtain experimentally. In this paper, a 1st stage high pressure stator passage is examined using a spectral element direct numerical simulation at a Reynolds number Re = U_∞C/v = 10,000. Although the Re is lower than engine conditions, the vortex already exhibits similar strong aperiodic motions and any uncertainty due to sub-grid scale modeling is avoided. The vortex dynamics are analyzed and their impact on the surface heat transfer is characterized. Results from a baseline case with a smooth endwall are also compared to a passage with film cooling holes. Higher Reynolds number simulations require a Large Eddy Simulation turbulent viscosity model that can handle the high accelerations around the blade. A high-pass-filter sub-grid scale model is tested at the same low Reynolds number to test its effectiveness by direct comparisons to the DNS. This resulted in a significant drop in turbulence intensity due to the high strain rate in the freestream, resulting in different dynamics of the vortex than observed in the DNS. Appropriate upstream engine conditions of high freestream turbulence and large integral length scales for all cases are generated via a novel inflow turbulence development domain using a periodic solution of Taylor vortices that are convected over a square grid. The size of the vortices and grid spacing is used to control the integral length scale, and the intensity of the vortices and upstream distance is used to control the turbulence intensity. The baseline DNS exhibits a bi-modal horseshoe vortex, and the presence of cooling-holes qualitatively increases the number of vortex cores resulting in more complex interactions.