Boundary layer transition is a hot research topic in fluid mechanics and aerospace engineering. In low-speed flows, two-dimensional Tollmien-Schlichting (T-S) waves always dominate the flow instability, which has been modeled by Coder and Maughmer from 2013. However, in supersonic flows, three-dimensional oblique Tollmien-Schlichting waves become dominant in flow instability. Inspired by Coder and Maughmer’s amplification factor transport equation for two-dimensional Tollmien-Schlichting waves in low-speed flows and Kroo and Sturdza’s linear stability theory (LST) analysis results for oblique Tollmien-Schlichting waves in supersonic flows, a new amplification factor transport equation for oblique Tollmien-Schlichting waves has been developed based on LST. The compressible Falkner-Skan similarity equations are introduced to build the relationships between nonlocal variables and local variables so that all the variables used in the present model can be calculated using local variables. Applications of this new transport equation to the flows over supersonic flat plate, 3% thick biconvex airfoil, and one modified supersonic laminar airfoil show promising results compared with the standard LST analysis results.

中文翻译：

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超音速边界层中倾斜Tollmien-Schlichting波的CFD兼容放大因子传输方程

边界层过渡是流体力学和航空航天工程领域的研究热点。在低速流中，二维托尔米-施利希特（TS）波始终占主导地位，这是由Coder和Maughmer从2013年开始建模的。但是，在超音速流中，三维斜向Tollmien-Schlichting波成为主导。流量不稳定。受Coder和Maughmer's的启发二维Tollmien-Schlichting波在低速流动中的放大因子传递方程以及Kroo和Sturdza的超声速倾斜Tollmien-Schlichting波的线性稳定性理论（LST）分析结果，一种新的Tollmien-Schlichting倾斜的放大因子传递方程基于LST开发了wave。引入可压缩的Falkner-Skan相似性方程来建立非局部变量和局部变量之间的关系，以便可以使用局部变量来计算本模型中使用的所有变量。与标准的LST分析结果相比，该新的输运方程在超音速平板，3％厚的双凸翼型和一种改良的超音速层流翼型上的流动中的应用显示出令人鼓舞的结果。