Data-Driven Turbulence Modeling

Abstract

Computational Fluid Dynamics (CFD) is the main tool to use in industry and engineering problems including turbulent flows. Turbulence modeling relies on solving the Navier-Stokes equations. Solving these equations directly takes a lot of time and computational power. More affordable methods solve the Reynolds Averaged Navier-Stokes (RANS) equations.
The most commonly used RANS models rely on Linear Eddy Viscosity Models for the Reynolds stress closure. However, this type of modeling does not provide satisfactory accuracy in general problems, which include curvature, impingement and separation. The rapid developments of Machine Learning (ML) in fluid dynamics and the increase of available high fidelity data of turbulent flows led to the introduction of data-driven RANS turbulence modeling. ML-augmented RANS models are promising but often lack generalisability or does not meet the preference of being interpretable. In this thesis, a sparse symbolic regression method has been used to generate interpretable algebraic equations for the non linear anisotropic Reynolds stress. These equations are built from a library of candidate functions of which the best fitting functions are selected by solving a sparse regression problem.
A deeper understanding of this methodology is achieved by creating models using different input features, including a wall damping function to improve near-wall behaviour of the model. Furthermore, different sparse regression problems are investigated, including constrained regression problems for which physical knowledge is used. The discovered models are propagated in a CFD solver to obtain a corrected velocity field.
Most of the discovered models improve the prediction of the Reynolds stress and its anisotropy compared to the $k-\omega$ RANS model. A small number of the discovered models are able to improve the prediction of the streamwise velocity compared to the RANS model. By analysing the discovered models, it is recognised that a specific term in the algebraic model is the basis of an inadequate prediction of the velocity. Furthermore, it is observed that a considerable amount of the implemented models provide an unconverged solution, which is visible as instabilities in the flow variables. Suggestions are given to improve the stability of the models. The discovered models, which include more physical knowledge by applying physical constraints to the regression problem or by including near-wall treatments, give promising results.