Computation of Hypersonic Transitional Flows Over Cones Using Gas-Kinetic Scheme Coupled with the Turbulence Model

Accurate prediction of the laminar-turbulent transition with the aerodynamic force and heat in hypersonic boundary flows is essential for the design of a hypersonic vehicle. However, subject to the complex boundary layer mechanism of the angle of attack (AOA) effects, the numerical prediction with high accuracy of hypersonic transitional flows over a cone at a small AOA is still a challenging job in current computational fluid dynamic (CI-D) modeling. In this paper, our objective is to improve the prediction accuracy of the traditional turbulent model in the boundary layer flow problems. We employ a gas-kinetic scheme (GKS) strongly coupled with the turbulent kinetic energy equation in the shear stress transport (SST) turbulence model. Langtry-Menter's two-equation transition model is also implemented under the GKS framework. The turbulent relaxation time obtained from the turbulence model is also implemented into the kinetic equation of the BGK model as an enhanced particle collision time related to turbulent fluctuation. We further validate this method for several classic cases of the hypersonic transitional flows over cones with various free-stream conditions at zero AOA. We also compare the numerical solutions by the current GKS coupled with the turbulent kinetic energy equation and traditional Reynolds-Averaged Navier Stokes (RANS) method. The numerical results confirm the consistency of the transition onset locations predicted by the proposed method with the experiments. The new coupled method also significantly improves numerical accuracy. The heat flux is also in good agreement with the experimental data. The hypersonic flows past a sharp cone are also computed at various small angles of attack ranging from 2 to 4, where the numerical results agree with the existing experimental data. Using our results we also analyze the impact of AOA on a sharp cone.