Spatially Developing Supersonic Turbulent Boundary Layer with a Body-Force-Based Method

Abstract

A method to obtain a spatially developing equilibrium supersonic turbulent flat-plate boundary layer suitable for direct numerical simulations or large-eddy simulations of viscous/inviscid interactions is described. A steady counterflow actuator with properties based on a dielectric barrier discharge is employed to trip an incoming laminar boundary layer. The resulting unstable shear layer transitions rapidly and breaks down to generate the desired turbulent boundary layer. A fifth-order bandwidth and order optimized weighted essentially nonoscillatory scheme using Roe fluxes is used along with sixth-order viscous terms to simulate this process. The properties of the boundary layer are exhaustively analyzed on meshes of 65, 37, and 20 million grid points. The fine-grid solution agrees with the mean flow and statistical properties observed in the literature, and is used as a truth model to investigate results on smaller meshes. The medium-grid solution reproduces the fine-grid behavior with modest differences in some quantities. The coarse-grid solution shows delayed transition and reproduces some flow quantities with significant discrepancies in others. Anticipated coherent structures are observed to exist on all grids. An examination of the length scale and timescale of the turbulence shows no signature of the tripping mechanism.