Computation of Hypersonic Turbulent and Transitional Flows Using an Extended Gas-Kinetic Scheme

In this paper, an extended Gas-Kinetic Scheme (GKS) is developed to predict the hypersonic turbulent and transitional flows. By using an extended Maxwellian distribution function together with a BGK-type equation, the extended GKS method is obtained. The main innovation is the addition of the turbulent kinetic energy term into the gas distribution function. To be specific, the turbulent kinetic energy term is treated similar to an internal energy term and is added to the Maxwellian distribution function. This allows the current GKS scheme to couple the molecular motion of the gas with its turbulent kinetic energy in one probability density function. GKS is coupled with turbulent kinetic energy (TKE) equation in SST k-ω turbulence model to compute hypersonic turbulent flows and with the TKE equation in Langtry-Menter four equations SST k – ω-γ-Re_θ transition model for computing hypersonic transitional flows. In order to demonstrate the high accuracy and numerical stability of the proposed method, several hypersonic turbulent and transitional flow cases are computed. The results from the current method are compared with the standard finite-volume solutions of Reynolds-Averaged Navier-Stokes (RANS) equations and experimental data; an excellent agreement between the current method and experimental data is obtained.