Development of A Two-Equation Turbulence Model for Hypersonic Shock Wave and Turbulent Boundary Layer Interaction

For hypersonic compressible turbulence, the correlations with respect to the density fluctuation must not be neglected. A Reynolds averaged K-epsilon model is proposed in the present paper to include these correlations, together with the Reynolds averaged Navier-Stokes equations to describe the mean flowfield. The K-equation is obtained from Reynolds averaged single-point second moment equations which are deduced from the instantaneous compressible Navier-Stokes equations. Under certain hypotheses and scales estimation of the compressible terms, the K-equation is simplified. The correlation terms of the fluctuation field appearing in the resulting K-equation, together with a conventional form of the epsilon-equation, are thus correlated with the variables in the average field. The new modeling coefficients of closure terms are optimized by computing the hypersonic turbulent flat-plate measured by Coleman and Stollery [J. Fliud Mech., Vol. 56 (1972), p. 741]. The proposed model is then applied to simulate hypersonic turbulent flows over a wedge compression corner angle of 34 degree. The predicting results compare favorably with the experimental results. Also, comparisons are made with other turbulence models. Additionally, an entropy modification function of Harten-Yee's TVD scheme is introduced to reduce artificial diffusion near boundary layers and provide the required artificial diffusion to capture the shockwaves simultaneously.