Application and Extension of a Data-driven Turbulence Modeling Method using Machine Learning

Abstract

Numerical efforts to estimate turbulence in fluid flows are focused on developing turbulence models, with Reynolds Averaged Navier–Stokes (RANS) models being the most popular. RANS methods are practical to apply on complex geometries, and high Reynolds number flows, albeit at a loss of accuracy in difficult flow situations like separation and transition. In recent years, many data-driven approaches which leverage high-fidelity data have been developed to augment the performance of RANS models. The goal of this M.Sc. thesis is to apply and extend one such data-driven approach “Field Inversion and Machine Learning (FIML)” [Parish and Duraisamy,2016] to improve the negative Spalart-Allmaras (SA-neg) turbulence model, with specific application to the shock-induced separation on a 2D airfoil profile. Inversion techniques involve formulating an optimisation problem aiming to provide an improved closure for the turbulence model at the point of inversion by minimising a measure of discrepancy between the baseline model and the high-fidelity data. This results in a corrective, spatially distributed discrepancy field and is referred to as β in this work. To incorporate a general β-field for improved predictions in aRANS solver, machine learning algorithms (neural networks in this case) will be used to find a functional approximation. Machine learning (ML) algorithms will identify patterns in the training data, which is an appropriately chosen set of flow features (ηi) from the solutions of the inverse problem for multiple flow cases for the 2D airfoil over a range of Mach numbers (M), Reynolds Number (Re), and angle of attacks (Ao A). This work’s primary objectives are to identify flow features (ηi) relevant to shock-induced flow separation. The improved RANS model will be tested on unseen flow conditions to evaluate the generalisation capability of the machine learning augmentation.