Convolutional neural networks for surrogate modeling of linear stability analysis of three-dimensional compressible boundary layers

Abstract

The reduction of viscous drag plays a key role in the necessary reduction of carbon emissions in aviation and is heavily dependent on the boundary-layer state. Therefore, the point of laminar-turbulent transition is of crucial interest. Its estimation is based on the analysis with linear stability theory (LST), which typically requires expert-level knowledge. Thus, in this work we use artificial neural networks (ANNs) as suitable surrogate models for this task. The talk will report about progresses of the work presented at last year's workshop. ANNs are used to predict the stability characteristics of 2D Tollmien-Schlichting instabilities (TSI) and stationary crossflow instabilities (CFI). Training of the networks relies on a database of stability results for these two instabilities for compressible Falkner-Skan-Cooke basic flows, a family of locally self-similar boundary-layers. Whilst the results presented one year ago only investigated multilayer-perceptron-like (MLP) network architectures, which take scalar input quantities describing the boundary layer and showed promising prediction quality already, we now employ neural networks using information about whole boundary-layer profile in terms of the velocity components. This profile information is processed via 1D convolutional layer and the networks are consequently referred to as CNNs in the following. For both instability types, a comparison of stability results for test cases from a DLR ATTAS flight test campaign between LST, the MLP and the CNN networks is made, also in terms of derived n-factors, the crucial parameter for the determination of the transition point. Further, we try to find correlations between the latent variables, found by the CNNs' encoding of the boundary-layer profiles, and physically motivated quantities typically used for characterization of boundary-layer properties.