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

航空航天中的高速流动往往伴随着流体密度的大幅度变化，具有很高的雷诺数，超出了原始流体动力学方程直接数值模拟的范围。因此，某种考虑可压缩性影响的湍流模型对于补充能量耗散过程是不可或缺的，本研究通过直接数值模拟来加深我们对可压缩湍流的理解，并帮助湍流模型的发展。模拟结果表明，传统的双方程湍流模型不能准确预测可压缩性效应。为了克服这一不足，作者提出了三方程模型，该模型与可压缩湍流的直接模拟数据吻合较好。该模型也适用于各向同性湍流与正激波相互作用，提供了很好的预测压缩性对湍流的影响。

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.