There are many gas turbine flows that are subsonic but still at speeds where gas compresses and the assumptions made in a low-Mach formulation are inadequate. In particular, a low-Mach spectral element solver, NEK5000, was used to perform a LES study of a film cooling hole at a blowing ratio and density ratio of 1.0 and 1.5, respectively. Due to a lack of real compressibility effects in the formulation, the simulation over-predicted the velocity in the hole, leading to large coolant lift-off and poorer film cooling performance than expected. Recently, the capabilities of NEK5000 have been extended to solve the compressible Navier-Stokes equations using the discontinuous Galerkin spectral element method (DGSEM). In this paper, details of the new algorithm are given, and results of the new simulation show vast improvements over the low-Mach code and compare well to previous experimental results.
Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier–Stokes Equations
