Bayesian Optimisation of Wall-Normal Blowing Control for Skin-Friction Drag Reduction in a Turbulent Boundary Layer*

Skin-friction drag is a key contributor to inefficiencies across a broad range of industries. Strategies aimed at minimising skin friction, therefore, have the potential to significantly reduce operating costs and assist in meeting emission targets. Active flow control techniques are among the most promising approaches to robust and effective skin-friction drag reduction. However, they are difficult to design and optimise. Furthermore, the drag reduction must be weighed against the energy required to power the control. Bayesian optimisation is a derivative-free, non-intrusive optimisation technique that is well-suited to problems with a moderate number of input dimensions and where the objective function is expensive to evaluate, such as with high-fidelity computational fluid dynamics simulations. With this in mind, the present work explores the potential of low-intensity wall-normal blowing for skin-friction drag reduction in turbulent boundary layers by combining a high-order flow solver (Incompact3d) with a Bayesian optimisation framework. The control is composed of streamwise-varying wall-normal blowing, parameterised by a cubic spline. The inputs to the optimiser are the amplitudes of the spline knots, whereas the objective function is the net-energy saving (NES), which accounts for both the skin-friction drag reduction and the input power for the control (which is estimated from a real-world device). The results are mixed, with significant drag reduction reported but no improvement in NES over the canonical case. Selected cases are chosen for further analysis and the drag reduction mechanisms are highlighted. The results demonstrate that low-intensity wall-normal blowing is an effective strategy for skin-friction drag reduction and that Bayesian optimisation is a useful tool for optimising such strategies. Furthermore, the results show that even a minor improvement in the blowing efficiency of the device used in the present work will lead to meaningful NES.