Large Eddy Simulation of Pseudo-Shock Waves Using Wall Model

Abstract

A supersonic turbulent flowfield involving the pseudo-shock waves in an isolator of a supersonic combustion ramjet is computed using two different LES codes which are a high-order upwind finite volume scheme, and a sixth order compact differencing scheme utilizing the localized artificial diffusivity method for stabilizing shock waves and employing a wall model to enable the use of coarse mesh. In the validation study where a supersonic turbulent boundary layer flow over a flat plate is examined, both LES codes are well validated using velocity profile in the boundary layer given by the hot-wire anemometry and normal stress given by the laser Doppler anemometry. In particular, the sixth order compact differencing scheme gives closer agreements with these experimental data. Then, the validated LES codes are applied to solve the Mach number 2.5 supersonic turbulent flowfield involving the pseudo-shock waves. It is shown that typical features of unsteady flowfield of the pseudo-shock waves are well obtained by both schemes. Again, it is indicated that the sixth order compact differencing scheme gives closer agreements with the existing velocity data obtained by particle image velocimetry and pressure fluctuation data on the wall surface. Besides, the computational cost of the compact differencing scheme is found to be 1/7 of that for the upwind finite volume scheme, even though a wall model is solved at each grid point on the wall surface. Therefore, the obtained results in the present study allow recommending the sixth order compact differencing scheme with a wall model for simulating supersonic turbulent flowfield in an isolator involving the pseudo-shock waves.