Data-driven flow instability analysis methods for oblique T-S waves in supersonic boundary layers using CNNs and MLPs

Oblique Tollmien-Schlichting (T-S) wave instability is one of the most critical flow instability types in supersonic boundary layers. However, traditional linear stability theory (LST) analysis requires calculating the second derivatives of velocity and temperature profiles along the wall-normal direction in body-fitted orthogonal coordinate systems, guessing initial eigenvalues, and solving eigenvalue problems, which is cumbersome and hinders its engineering applications. To address these issues, this paper introduces convolutional neural networks (CNNs) and multilayer perceptrons (MLPs) to replace the traditional eigenvalue-solving process through different technical routes. The former constructs training samples for CNNs using similarity solutions of laminar boundary layers in LST analysis to predict eigenvalues of different oblique T-S waves, while the latter uses artificially constructed non-similarity solutions of laminar boundary layers in LST analysis to generate training data for MLPs to predict the envelope of the most unstable amplification factors. Validated through numerous cases with varying Reynolds numbers, Mach numbers, and airfoils (i.e., altering pressure gradients), both models achieve satisfactory predictions of perturbation amplification factors. Notably, the proposed neural network models require only one-time training and can be reused infinitely without retraining. The study also reveals that using similarity solutions of laminar boundary layers as training samples leads to significant deviations in predicting amplification factor envelopes and results in limited generality. These findings provide efficient data-driven alternatives for supersonic boundary layer transition prediction, promoting the engineering application of linear stability theory in complex flow scenarios while clarifying the applicability boundaries of different technical approaches.