Neural Networks as a Surrogate Model for Linear Stability Analysis of Three-Dimensional Compressible Boundary Layers

Abstract

Linear stability theory (LST) is a well-established method to evaluate the susceptibility of a basic flow to instabilities and, in combination with the e^N-method, allows an estimation of the region of laminar-turbulent transition. However, using it in a more automated framework is rather challenging because the method often requires an expert to intervene in the performed analysis. This issue is remedied by making use of surrogate models for LST. This work presents artificial neural networks (ANN) for modeling the instability characteristics of two-dimensional Tollmien-Schlichting and stationary crossflow instabilities for three-dimensional, compressible flow. Training of the ANNs relies on a dataset based on compressible Falkner-Skan-Cooke basic flows. Two types of networks are compared in their predictive performance for the components of the complex-valued eigenvalues of instability modes, i.e., their wavenumbers and growth rates. One network architecture relies only on scalar boundary-layer quantities as inputs, whereas the other one also uses actual boundary-layer-profile information, which is taken into account by an adjusted network architecture comprising convolutional network layers. The models' performances are finally successfully demonstrated for one test data point of the ATTAS natural laminar flow on swept-wing flight experiment each, also in terms of integrated n-factors.