Recurrent Neural Network for End-to-End Modeling of Laminar-Turbulent Transition

Abstract

Accurate prediction of laminar-turbulent transition is a critical element of computational fluid dynamics simulations for aerodynamic design across multiple flow regimes. Traditional methods of transition prediction cannot be easily extended to flow configurations where the transition process depends on a large set of parameters. In comparison, neural network methods allow higher dimensional input features to be considered without compromising the efficiency and accuracy of the traditional data driven models. Neural network methods proposed earlier follow a cumbersome methodology of predicting instability growth rates over a broad range of frequencies, which are then processed to obtain the N-factor envelope, and then, the transition location based on the correlating Nfactor. This paper presents an end-to-end transition model based on a recurrent neural network, which sequentially processes the mean boundary-layer profiles along the surface of the aerodynamic body to directly predict the Nfactor envelope and the transition locations over a two-dimensional airfoil. The proposed transition model has been developed and assessed using a large database of 53 airfoils over a wide range of chord Reynolds numbers and angles of attack. The sequence-to-sequence transduction model proposed herein provides a more direct approach for accurate predictions of the transition location than the earlier neural network methods, which predict the local amplification rate of a single instability mode at a fixed location along the airfoil. The large universe of airfoils encountered in various applications causes additional difficulties. As such, we provide further insights on selecting training datasets from large amounts of available data. Impact StatementThe recurrent neural network (RNN) proposed here represents a significant step toward an end-to-end prediction of laminar-turbulent transition in boundary-layer flows. The general yet greatly simplified workflow should allow even nonexperts to apply a physics-based strategy for predicting transition due to a variety of instability mechanisms, which is a significant advantage over traditional direct computations of the stability theory. The sequence-to-sequence mapping enabled by the RNN faithfully represents the amplification of flow instability along the surface, exemplifying the embedding of physics in scientific machine learning. Finally, we use a very large dataset of stability characteristics of airfoil boundary layers for the training process and present an extensive study into the selection of training data and its effects on the prediction accuracy. These investigations provide important insights and best-practice guidance toward the practical deployment of neural-network-based transition models in engineering environments.