基于Reynolds平均的高超声速二方程湍流模型

 在Reynolds平均的框架下推导了可压缩湍流Reynolds应力方程和湍动能方程。根据一定的假设和尺度分析简化并封闭了所推导的湍动能方程。在均匀湍流假设下，湍动能耗散率可分解成可压缩性耗散和旋度耗散，并对其中的可压缩性耗散进行了封闭；同时认为旋度耗散不受可压缩性影响，直接引用传统的Reynolds平均不可压缩湍动能耗散率模型方程。由此构造了适用于高马赫数的二方程可压缩湍流模型。应用所发展的模型计算了高超声速平板绕流，并与若干现有模型的计算、实验与半经验公式的计算结果进行了对比，验证了所发展的模型。在此基础上，通过对压缩拐角的高超声速湍流的数值模拟，对所发展的湍流模型，以及若干现有模型进行了对比，显示了不同湍流模型及可压缩性修正在计算壁面压力分布和热流分布上的特点，说明了湍流模型可压缩修正的必要性,得到了所发展模型的计算结果最接近实验结果的结论。

A Reynolds Averaged Two-equation Turbulence Model for Hypersonic Flows

A set of compressible Reynolds stress model equations and the turbulent kinetic energy equation were derived with Reynolds average formality. A closure of the turbulent kinetic energy equation was then deduced and simplified under certain hypotheses, in conjunction with scaling analysis. A K-ε two-equation turbulence model was proposed based on the modeled turbulent kinetic energy equation and a conventional incompressible turbulent kinetic energy dissipation rate equation. The proposed model was then applied to simulate hypersonic turbulent flows over a flat-plate. The numerical results reveal that the present model would be favorable in comparison with some of the existing two-equation turbulence models, experimental data, and the estimations given by the semi-empirical formulations. Another test case on hypersonic flows over a ramp was then computed using the developed model, as well as some of the existing two-equation turbulence models. The comparative study shows that the compressibility corrections to the two-equation turbulence models are necessary for hypersonic ramp-type flows, and the numerical results by the present model are closest to the experiments simultaneously.