Prediction method for stationary crossflow instability transition in supersonic boundary layers based on multi-layer perceptron

Crossflow vortices induced transition is one of the most important instability types in supersonic aircraft boundary layers. While the traditional linear stability theory (LST)-based e^N method demonstrates satisfactory predictive capabilities for this kind of transition, its practical implementation faces inherent limitations: the requirement of first- and second-order wall-normal derivatives of boundary layer velocity/temperature profiles, the need for initial eigenvalue guesses, and the computational burden of solving eigenvalue problems. To address these challenges, this study develops a multi-layer perceptron (MLP) model tailored for linear stability analysis of three-dimensional compressible boundary layers based on the artificially defined quasi-three-dimensional non-similar boundary layer solutions. The boundary layer edge flow parameters and perturbation characteristics are mapped to eigenvalues or local growth rates of the envelop curves through fully connected layers. This architecture eliminates the need for computing wall-normal derivatives of velocity/temperature profiles, initial eigenvalue estimation, and direct eigenvalue problem solving. Extensive validation across varying operational conditions and geometries (airfoils and swept wings) demonstrates exceptional agreement between the MLP’s predictions (eigenvalues and disturbance amplification factors) and traditional LST results. Furthermore, the model’s transition prediction capability is rigorously verified using National Aeronautics and Space Administration’s supersonic swept-wing crossflow-dominated transition benchmark, incorporating both stability analysis and flight test data. Results confirm the model is an efficient and reliable computational framework for transition prediction in three-dimensional finite-span wings.