A data-driven wall model for the prediction of turbulent flow separation over periodic hills

Aeronautic flows are characterized by turbulence, which consists of chaotic perturbations around a time-averaged flow field. Turbulence appears in a large variety of length scales, ranging from unsteady flow features of the size of the aircraft, wing, blade down to tiny whirls, which are many orders of magnitude smaller. Turbulence has a profound impact on aerodynamic performance, but unfortunately, explicit computation of all turbulent features remains intractable for the design and analysis of real-life geometries [1]. The smallest structures, requiring the largest computational effort, are found in the so-called boundary layer near the wall. This cost can be avoided by modeling their time-averaged impact on the forces exchanged between fluid and the wall. This saving, in turn, allows for the direct computation of the largest turbulent flow features away from the wall, which govern important large-scale effects. The present work proposes the use of Deep Neural Networks (DNN) to link the wall shear stress components to volume data extracted at multiple wall-normal distances hwm and wall-parallel locations. The model focuses on separation since this phenomenon is currently not well-represented, whereas it has a huge impact on aerodynamic performance and operating range. The model is trained using a high-fidelity database of the well-known two-dimensional periodic hill flow. The conditions of this separated flow are such that it is still affordable to compute all turbulent flow features directly, using Tier-1 modern supercomputers.