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

Abstract

In 2021, the European Union adopted measures in its European Green Deal to reach the target of carbon neutrality by 2050. As an intermediate milestone for 2030, it aims for a reduction of greenhouse gas emissions by at least 55% compared to levels of 1990. The need to reduce emissions is also felt in aviation. One of the most impactful factors is the reduction of viscous drag, which itself is heavily influenced by the boundary-layer state. A crucial design parameter in this context is the position of laminar-turbulent transition. In order to assess the transition location, the semi-empirical e^N-method is commonly used, which relies on stability characteristics of the laminar boundary layer computed based on the linear stability theory (LST). Transition is predicted, where the integrated growth rate of disturbances modes, the N-factor, reaches an experimentally derived critical limit. However, the transition prediction based on LST is so far mostly used by expert users only. To open the accessibility of this method to a broader user spectrum and to profit from enhanced performance, different strategies to construct an according surrogate model, such as lookup tables, have been proposed in the past. After having proven their strong potential in different branches and fields of application, artificial neural networks (ANN) have lately gained again attention as a suitable candidate for surrogate models for boundary-layer stability predictions. In the present work, an ANNbased approach for surrogate modelling of LST-based stability computation is presented for threedimensional compressible boundary layers. Within the scope of this work, two different instability mechanisms, two-dimensional (2D) Tollmien-Schlichting waves (TS) and stationary cross-flow instability (CFI), are covered.