Proposition of Engineering Turbulence Modeling for Direct Numerical Simulation of Compressible Flow

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High-speed flows in aerospace phenomena, which often accompany large changes of fluid density, are of very high Reynolds numbers and are beyond the scope of the direct numerical simulation of the primitive fluid dynamical equations. As a results, some kind of turbulence model accounting for compressibility effects is indispensable for supplementing the process of energy disspation.In this study, the direct numerical simulation was performed to increase our understanding of compressible turbulence and to aid the development of turbulence models. The simulation results showed that the conventional two-equation turbulence models cannot predict the compressibility effects precisely. To overcome this deficiency, there-equation model was proposed by the authors, which shows good agreements with the direct simulation data of compressible turbulence. The proposed model was also applied to the isotropic turbulence interacting with a normal shock wave, providing good predictions of the compressibility effects on tubulence.