Data-driven Augmentation of Turbulence Models for Complex Fluid Flows

Turbulent flows are broadly investigated using physical experiments and/or computational fluid dynamics (CFD) where the accuracy, level of fidelity, and associated costs play competing roles. For practical CFD analyses such as design and analysis of aircraft, there is a heavy reliance on the Reynolds-averaged Navier–Stokes (RANS) simulations due to their relative simplicity and low computational cost. This comes at the cost of limited accuracy for complex flows. A number of data-driven techniques have emerged that augment RANS-based turbulence models using high-fidelity data. The novel contributions of this thesis in data-driven augmentation of RANS-based turbulence models, categorised under two themes, are: 1) the data in adjoint-based data assimilation, and 2) developing and employing neural network-augmented turbulence models for automated aerodynamic design optimisation.

Firstly, we develop a novel sensor placement approach for generating sparse experimental data for data assimilation. It leverages systematic eigenspace perturbations of the Reynolds-stress tensor to identify regions of flow where RANS turbulence modelling assumptions are most erroneous and concentrate measurements in these areas using a novel greedy algorithm. Results show that the error reduction using our placement strategy is close in accuracy to the instances where two to three orders of magnitude more data points than the placed sensors. We further investigate fusing data for multiple quantities (e.g. velocity and surface pressure measurements) to perform data assimilation, and investigate the relative importance of various physical quantities on the flow reconstruction.

Secondly, we employ the field inversion and machine learning technique to augment an existing turbulence model for aerodynamic shape optimisation. As a proof-of-concept we apply the framework to a separated periodic hill flow. Our investigations highlight the role of the turbulence model on the optimal shapes achievable, with the neural network-augmented turbulence model achieving approximately 4-times more drag reduction compared to the baseline model.