An improved four-equation transition-turbulence model for high-speed flows: Transition prediction and physical insight

In this paper, two major improvements are first proposed to break the bottleneck of conventional $k$-$\omega$-$\gamma$-${\widetilde{Re}}_{\theta t}$ transition-turbulence model for simulation of high-speed flows. One is reformulation of the correlation for maximum ratio between vorticity Reynolds number and momentum thickness Reynolds number derived from the self-similar solutions of compressible boundary layer. The other is modification of the empirical correlation for critical momentum thickness Reynolds number in consideration of the compressibility and nose bluntness effects. Then, these improvements are applied to the original $k$-$\omega$-$\gamma$-${\widetilde{Re}}_{\theta t}$ model for prediction of high-speed flow transition and investigation of underlying physics. Three configurations, including flat plate, sharp straight cones at different Reynolds numbers, and blunt straight cones with several nose bluntness, are adopted to fully validate the new developed model. Numerical results manifest that the transition trend given by the improved $k$-$\omega$-$\gamma$-${\widetilde{Re}}_{\theta t}$ model is basically consistent with that observed in experiments, considerably overcoming the disability of its original counterpart. In addition, several physical mechanisms are highlighted, such as the compressibility signatures, effects of Reynolds number/nose bluntness on transition, and applicability of generalized Reynolds analogy.