可压缩湍流的非平衡输运机理及模式研究

Study on compressible turbulence has mainly focused on mechanism analysis and modeling of compressibility of simple uniform and shear turbulent flows for nearly 30 years, established compressible turbulence models can not meet urgent needs of aerospace vehicles for complex compressible turbulence models. By studying the effect of the turbulent properties of non-equilibrium transport on structural changes of the flowfields, compressible turbulence models taking into account the turbulent properties of non-equilibrium transport are proposed in this project, combined with the mechanism analysis of non-equilibrium transport effect on compressible turbulent flows. At first, the equilibrium and non-equilibrium transport mechanism is going to be studied by analyzing turbulent quantities of turbulence kinetic energy, turbulence dissipation rate, Reynolds stress, anisotropy dimensionless Reynolds stress tensor based on the DNS database. Then, under the boundary layer approximation, the parameters describing the non-equilibrium transport mechanism will be investigated through the methods of theoretical analysis and dimensional analysis。Again, functional relationships of the parameters of the non-equilibrium transport properties with turbulence modeling are to be developed. Finally, the two-equation eddy-viscosity turbulence model and the Reynolds stress models are to be proposed. The aims of this project is to reveal the non-equilibrium transport mechanism of compressible turbulent flows, establish the eddy-viscosity and Reynolds stress models by taking into account the turbulent properties of non-equilibrium transport, and to lay the foundation for engineering applications.

近30年的可压缩湍流研究大多集中于简单的均匀湍流或剪切湍流的可压缩性机理分析及建模研究，所建立的可压缩湍流模型不能满足航空航天飞行器复杂的可压缩流动对湍流模型的迫切需求。本项目提出通过研究可压缩湍流的非平衡输运特性对流场结构变化影响，结合可压缩湍流非平衡输运效应的机理分析，建立计及非平衡输运特性的可压缩湍流模型。首先，基于DNS数据库，研究可压缩湍流的湍动能、湍动能耗散率、雷诺应力、无量纲的雷诺应力各向异性张量等各湍流量的平衡及非平衡输运机制。其次，在边界层近似下应用理论分析与量纲分析，DNS数据分析，研究可压缩湍流非平衡输运的描述参数。再次，构建可压缩湍流非平衡输运特性参数与湍流建模的函数关系。最后，研究计及可压缩湍流非平衡输运特性的二方程涡粘模型及雷诺应力模型。本项目旨在揭示可压缩湍流非平衡输运机理、建立计及可压缩湍流非平衡输运特性的涡粘模型及雷诺应力模型，为工程应用奠定基础。

揭示可压缩湍流非平衡输运特性机制并在此基础上建立能够精确预估飞行器复杂流场的湍流模型是高速飞行器研究中的关键问题之一。首先，本项目应用可压缩平板及压缩拐角等的直接数值模拟结果，研究了湍流的平衡及非平衡输运机制，指出了可压缩非平衡湍流的影响参数为湍动能生成与其耗散的比值以及湍流马赫数，并在此基础上修正了计及湍流非平衡影响的k-omega湍流模型的系数，使之为非平衡参数的函数，对跨声速及超声速多个算例的计算表明，所提出的修正模式正确计及了湍流非平衡的影响，模拟精度与SST k-omega相当或有所提高。其次，发现SST k-omega模型中的Bradshaw数在跨及超声速细长体大攻角分离流动中并非常数，并修正了其在此类流动的中数值，数值计算结果表明改进的SST k-omega比原模型在模拟近壁极限流线、壁面压强及空间总压分布等方面优越。再次，根据可压缩湍流非平衡的机理分析结论，利用得到的非平衡刻画参数，修正了SST k-omega模型和基于omega方程的雷诺应力模型，对不同马赫数及雷诺数的压缩拐角、入射激波/湍流边界层干扰流动及平板绕流流动的计算表明，所修正了SST k-omega模型和基于omega方程的雷诺应力模型在模拟壁面压强及壁面热流等具有更高的精度。另外，应用SST k-omega模型对复杂外形的波瓣射流掺混机制进行了研究。最后，把不可压缩流动的对流传热场协同原理推广到可压缩流动及高超声速化学/热化学非平衡流动中，研究结果表明，对可压缩及高超声速化学/热化学非平衡流动，壁面热流取决于当地单位体积的动量与总焓梯度的协同。