Large Eddy Simulation of Compressible Channel Flow

A large eddy simulation method for compressible channel flow simulations is developed and validated. The method separates the resolvable scale motions from the unresolvable (subgrid) scales by applying a spatial filter to the compressible Navier-Stokes equations. The Leonard and cross terms which appear due to the filtering procedure are modeled based on a Taylor series expansion. The subgrid scale Reynolds terms are modeled using a compressible extension of an existing incompressible model for wall bounded flows. The equations are solved numerically using a modified four -step Runge-Kutta procedure in time and second or fourth -order differences in space. The method is validated by simulating a low Reynolds number, low Mach number turbulent Poiseuille flow. Various statistical comparisons are made with incompressible experimental and direct simulation data at similar Reynolds numbers, including higher-order statistics and spatial correlations. The results are seen to compare favorably with the incompressible data. A high subsonic Mach number turbulent Poiseuille flow is also simulated for comparison with the low Mach number results at nominally constant Reynolds number. The mean velocity profile is seen to depart from the low Mach number profile, corresponding to an expected dependence of the mean density and temperature profiles on Mach number. The turbulence velocity statistics are found to be reasonably independent of Mach number. Pressure fluctuation statistics are also found to scale with the wall shear stress independently of Mach number, although normalized density and temperature fluctuations increase substantially with Mach number. The density and temperature fluctuations, although small in magnitude, are observed not to be isobarically related. The current simulations have validated the algorithm in the incompressible limit and have demonstrated the ability of the method to simulate high subsonic Mach number flows. The success of these simulations suggests the utility of this method for fundamental research into many turbulent compressible flow problems.