Gas-Kinetic Scheme Coupled with Turbulent Kinetic Energy Equation for Computing Hypersonic Turbulent and Transitional Flows

ABSTRACT

For simulation of hypersonic turbulent and transitional flows at high Reynolds numbers, a gas-kinetic scheme (GKS) strongly coupled with the turbulent kinetic energy equation in shear stress transport (SST) k−ω turbulence model is developed. To extend the current method to transitional flows, Langtry-Menter $\gamma -R{e}_{\theta }$ transition model is added together with SST k−ω turbulence model. Comparisons among the numerical solutions from current GKS method coupled with turbulent kinetic energy equation, GKS method uncoupled with turbulent kinetic energy equation, Reynolds-Averaged Navier-Stokes (RANS) solutions with turbulence/transition models, and experimental data are conducted. It is concluded that the current method can significantly improve the accuracy of numerical results.

KEYWORDS:

• Hypersonic flow
• gas-kinetic scheme
• $k-\omega$ SST turbulence model
• $\gamma -R{e}_{\theta }$ transition model
• STBLI

Acknowledgement

This research was funded by National Numerical Wind Tunnel Project (grant nos. NNW2019ZT3-A08, NNW2018-ZT1B01) and National Natural Science Foundation of China (grant nos. 6162790014, 12002306).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China: [Grant Number 6162790014,NNW2019ZT3-A08,National Numerical Wind Tunnel Project].