Evaluation of Massively-Parallel Spectral Element Algorithm for LES of Film-Cooling

Abstract

A blind Large-Eddy Simulation (LES) of film-cooling heat transfer is performed on a canonical cylindrical cooling hole geometry using a massively-parallel, geometrically-flexible, open-source spectral element solver NEK5000. The simulation is for a blowing-ratio of 1.0, density-ratio of 1.5, and Reynolds-number Reθ = 4,300 based on boundary layer momentum thickness and ReD = 32,000 based on hole diameter. A low-Mach ideal gas formulation is used to match the density ratio. A spectral-damping LES subgrid model is used which does not restrict time-stepping, allowing CFL numbers of 5–10 through characteristics time-integration. The numerical mesh resolves the boundary layer and coarsens to acceptable LES sizing in the free stream, resulting in 88 million grid points (410,464 elements at 5th order polynomial). For this blowing ratio, the coolant hole Mach number is too large for the low-Mach formulation (> 0.3). This results in faster hole velocities as opposed to fluid compression, effectively changing the momentum ratio leading to coolant lift-off as compared to experiment. The film-cooling effectiveness along centerline and spanwise locations of x/D = 2 and 8 are lower than experiment. Ideal parallel scaling is shown up to 256 processors and estimated to continue at ideal scaling to 2048 processors.