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

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 (M = 1.5, Re-tau = 221, T-w = 500 K, and T-c = 700 K) 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, Q 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 T-w and pressure p impact are also emphasized on the normalized van Driest velocity u(VD)(+) profile in the logarithmic region. The classical log law is recovered: u(VD)(+) = In(y(+))/kappa + C with kappa = 0.41, and a constant C depending on T-w and p. An analog law is also recovered for the normalized temperature T+ = Pr-t(max) In(y(+))/kappa + C' with the maximum of the Prandtl number Pr-t(max). 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.