Machine learning building-block-flow wall model for large-eddy simulation

A wall model for large-eddy simulation (LES) is proposed by devising the flow as a combination of building blocks. The core assumption of the model is that a finite set of simple canonical flows contains the essential physics to predict the wall shear stress in more complex scenarios. The model is constructed to predict zero/favourable/adverse mean pressure gradient wall turbulence, separation, statistically unsteady turbulence with mean flow three-dimensionality, and laminar flow. The approach is implemented using two types of artificial neural networks: a classifier, which identifies the contribution of each building block in the flow, and a predictor, which estimates the wall shear stress via a combination of the building-block flows. The training data are obtained directly from wall-modelled LES (WMLES) optimised to reproduce the correct mean quantities. This approach guarantees the consistency of the training data with the numerical discretisation and the gridding strategy of the flow solver. The output of the model is accompanied by a confidence score in the prediction that aids the detection of regions where the model underperforms. The model is validated in canonical flows (e.g. laminar/turbulent boundary layers, turbulent channels, turbulent Poiseuille-Couette flow, turbulent pipe) and two realistic aircraft configurations: the NASA Common Research Model High-lift and NASA Juncture Flow experiment. It is shown that the building-block-flow wall model outperforms (or matches) the predictions by an equilibrium wall model. It is also concluded that further improvements in WMLES should incorporate advances in subgrid-scale modelling to minimise error propagation to the wall model.