2023 UK Fluids Conference, Glasgow

Reynolds-averaged Navier-Stokes equations with turbulence models continue to be the workhorse for predictions of complex flows despite their limitations. An area of interest for us is adjoint-based aerodynamic shape optimisation at off-design conditions where the flows exhibit complex behaviour, such as separation, poorly predicted by RANS models. Using higher fidelity methods (e.g. DNS, LES), or even unsteady RANS simulations, for iterative shape optimisation is prohibitively expensive as many function evaluations are required. To tackle this challenge, we propose the use of machine learning techniques trained on high-fidelity data for a relatively small parameter space to enhance the RANS-based models and then using the augmented model for shape optimisation, at a computational cost similar to the existing RANS-based approaches. We employ the field inversion and machine learning technique to enhance the k-omega SST model. First, the PDE(s) of the turbulence model is modified with a corrective field which is then optimised to reduce the error between the model output and data. This process is repeated for geometries/flow conditions sufficiently representative of the design space. Next, neural networks are employed to predict the corrective fields for unseen geometries and/or flow conditions. Aerodynamic shape optimisation is then performed with the machine learning enhanced turbulence model. As a proof-of-concept we apply the framework to a separated periodic hill flow with the goal of drag reduction on the hill wall. The FIML training is performed on a set of parameterised geometries with DNS data. Shape optimisation is performed using both the baseline and the FIML-enhanced turbulence models. The optimal shape output by each model is then verified with the hybrid RANS/LES method in terms of flow prediction accuracy. Preliminary results show the ML-augmented model achieves more drag reduction with a good flow prediction agreement against the IDDES results.