Wei Liao, Old Dominion University


Gas Kinetic Scheme for DNS of Decaying Compressible Turbulence


Abstract: Technical feasibility of hypersonic flight, to an important degree, depends on our ability to understand and predict transition and turbulence in hypersonic flows with non-equilibrium thermo-chemistry. In non-thermochemical-equilibrium (NTE) turbulence, however, the Kolmogorov paradigm, which forms the basis of most equilibrium turbulence models, is questionable. Hence, physics-based modeling of NTE turbulence must start from fundamental first principles. At the same time, the simulation of highly NTE-turbulent flows is a challenge to the conventional computational fluid dynamics (CFD) based on the Navier-Stokes equation, because in the non-equilibrium flows, the assumption of linear constitutive laws and even the basic premises of continuum mechanics begin to break down. As a result, the kinetic methods, which are derived from the Boltzmann equation as opposed to conventional CFD methods based on direct discretizations of the Navier-Stokes equations, have been attracting more and more attention in the recent years. There are a number of kinetic methods, of which the LBE and GKS methods are specifically designed as numerical methods for CFD: the former is for low-Mach-number flows while the latter is for fully compressible flows. The final goal of our work is to develop a physics-based multiscale GKS for direct numerical simulations (DNS) and large eddy simulations of nonequilibrium turbulent gas flows. In this study, we apply GKS for DNS of compressible decaying homogeneous isotropic turbulence (DHIT). In compressible DHIT, the gas compressibility admits the production of random shocklets, which is not observed in incompressible decaying turbulence. We apply the GKS for DNS of the compressible DHIT to obtain the detailed results and statistics on grids 128^3 and 256^3. Based on our DNS results, we make the following observations: 1) With initial Taylor microscale Reynolds number fixed, increase of initial turbulent Mach number (Mt) leads to the increase of dissipation rate at the initial stage. 2) Change of the Mt has no effect on kinetic energy and the asymptotics of energy dissipation. 3) At the lower Mt (=0.1), intermittency persists; while at higher Mt (=0.5), intermittency quickly dies, the probability density function (PDF) of the two-point longitudinal velocity difference becomes Gaussian independent of the separation distance. 4) The PDF's of both shock strength and the local Mach number all appear to follow some scaling laws.

Advisor: Dr. Li-Shi Luo (Old Dominion University)