Direct numerical simulation of compressible homogeneous turbulence using natural initial conditions

Abstract

Reynolds averaged Navier Stokes (RANS) solvers have become the workhorse for simulating turbulent flows for most practical purposes. While the incompressible turbulence models used with RANS equations have improved considerably in their predictive capability, significant breakthrough has not been achieved for their compressible counterparts. With the advancement in computing power, high resolution direct numerical simulation (DNS) of low Reynolds number turbulent flows has become feasible. DNS of simple turbulent flows provides a detailed database which can be used for developing and testing turbulence models. In this work, we perform DNS of compressible homogeneous turbulence—decaying isotropic turbulence and homogeneous shear flow—for a range of initial turbulent Mach numbers, (M_{t 0} = 0.05–0.4) using the more natural initial conditions. Simulations were performed on grids with 128³ and 256³ points. Compressibility effects on the evolution of turbulent kinetic energy were studied. We found negligible compressibility effects for decaying isotropic turbulence, while homogeneous shear flow demonstrated compressibility effects in the growth rate of turbulent kinetic energy. Compressibility corrections to turbulence models in the form of the ratio &epsis;_d/&epsis; _s, have been tested with the results from the simulations. For decaying isotropic turbulence a [special characters omitted] scaling was found to be better than [special characters omitted] while for homogeneous shear flow it was the opposite. The small value of the ratio &epsis;_d/&epsis;_s in decaying isotropic turbulence makes the [special characters omitted] scaling less relevant. Based on the DNS results of homogeneous shear flow, a new correction parameterized by the gradient Mach number, M_g, is proposed. The parameter C_μ, which is assumed constant for incompressible two equation eddy viscosity models, is computed explicitly from the DNS data. An M_g, dependence of the parameter, C_μ, is proposed.