A CFD-Compatible Amplification Factor Transport Equation for Oblique Tollmien-Schlichting Waves in Supersonic Boundary Layers

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 NTS 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.