A three-equation turbulence model for high-speed flows

Adding a new equation to the two-equation K-ω turbulence model framework, this paper proposed a three-equation turbulence model to determine the density variance for high-speed aero-optics and high-speed compressible turbulent flows. Simulations were performed with the new model for supersonic and hypersonic flat-plate turbulent boundary layer and hypersonic ramp flows. The results showed that the prediction with the present model agrees well with the experimental data and is significantly better than the Lutz’s model in predicting the density variance for the flat-plate flows. Furthermore, the present model can produce more accurate skin pressure and skin heat flux distributions than the original K-ω model in simulating hypersonic compression ramp flows with separation and reattachment and shock/boundary layer interactions. Without introducing a variety of ad hoc wall damping and wall-reflection terms, the proposed three-equation turbulence model is applicable to high-speed aero-optics and turbulent flows of real vehicles of complex configuration.