Fully local amplification factor transport equation for stationary crossflow instabilities

The traditional linear stability analysis for transition prediction includes the following steps: solving velocity profiles using boundary-layer equations or a computational fluid dynamics solver, guessing and searching operations for the eigenvalues, computing the linear perturbation equations, and integrating the amplification factor N. It is difficult to implement into modern computational fluid dynamics solvers with parallel computations because it requires many nonlocal variables and coordinate system transformations. In this Paper, an amplification factor transport equation, which can be coupled with a modern computational fluid dynamics parallel solver, is established based on the analysis results through linear stability theory for stationary crossflow instabilities. According to the analysis results of Falkner–Skan–Cooke similarity velocity profiles using linear stability theory analysis, the source term of the present transport equation is formulated locally to describe the growth of stationary crossflow waves in the laminar boundary layer. This new equation is added to the N_TS equation proposed by Coder and Maughmer for Tollmien–Schlichting instabilities. Finally, coupling of these two amplification factor transport equations and Menter’s shear stress transport turbulence model completes an effective transition turbulence model. Comparisons between the present predictions, wind tunnel experiments and the standard linear stability theory analysis on an NLF(2)-0415 infinite swept wing, Petzold’s sickle-shaped wing and 6:1 inclined prolate spheroid validate the reasonable establishment of the present amplification factor transport equation for stationary crossflow instabilities.