MEng Thesis: Towards statistical inference to improve turbulence RANS closures for multi-element aerofoils

While remaining an indispensable tool in design, predictions of turbulent flows based on computational fluid dynamics analyses continue to face challenges. High-fidelity approaches based on resolving the Navier-Stokes equations in one form or other are predicted to remain computationally intractable for the near future. This means the Reynolds-averaged Navier-Stokes models remain the workhorse of industrial CFD analyses. RANS closures are developed based on various modelling assumptions which are plagued with inaccuracies in complex physical flows such as flow separation over high-lift multi-element aerofoils, essential for takeoff and landing phases of an aircraft flight envelope. This thesis explores the application of a new paradigm in turbulence modelling which leverages high-fidelity data such as those from experiments, and machine learning algorithms to augment RANS closures. Through statistical inference a discrepancy field is generated by formulating a highly dimensional, deterministic, gradient-based optimisation problem where the goal is to minimise the error between a base RANS model and experimental data in every cell of the computational grid. The main contribution of the present work is to implement a discrete adjoint method for efficient derivative computations using open-source software. The errors in the adjoint derivative computations are about 2%. Additionally, the data-driven turbulence modelling paradigm is explored through an extensive literature survey; three multi-element aerofoils and the associated experimental data are identified for the task of statistical inference; the capabilities of two popular RANS models (Spalart-Allmaras and $k-\omega$ shear stress transport) in predicting flows around a representative three-element high-lift aerofoil are evaluated against experimental data; and to conclude, key questions and possible ways of investigating these are highlighted for future work.