Direct Numerical Simulation and Large-Eddy Simulation of Supersonic Channel Flow

Abstract

Compressible isothermal-wall channel flows are studied with direct numerical simulation and large-eddy simulation tools. Computations are carried out using a high-order, low-dissipation, bandwidth-optimized weighted essentially nonoscillatory numerical scheme to describe the hyperbolic terms of the Navier–Stokes equations. Periodic supersonic channel flow direct numerical simulation (, , , and ) is used to validate the procedure and the numerical scheme; a new subgrid term contribution based on pressure drop is proposed for the driving term required in momentum and energy equations for large-eddy simulation. Coherent structures of the flowfield are analyzed with scatter plots, criterion, and vorticity fields. As expected, the strong Reynolds analogy is not valid for this nonadiabatic flow. Streaks and horseshoe-like structures are highlighted and detailed. The authors propose a scenario for the formation of horseshoe-like structures. With large-eddy simulation tools, a dynamic procedure to evaluate the turbulent Prandtl number is required because results are found more accurate and computations more stable. Wall temperature and pressure impact are also emphasized on the normalized van Driest velocity profile in the logarithmic region. The classical log law is recovered: with , and a constant depending on and . An analog law is also recovered for the normalized temperature with the maximum of the Prandtl number . An a priori study on mesh requirements determination for a large range of pressure levels is realized through highly near-wall resolved large-eddy simulation.