Multi-task Gaussian process regression for active drag reduction in turbulent boundary layer flows

As environmental goals and rising energy costs pose technological and economic challenges to air travel, aerodynamic improvements are needed to reduce energy demand, cost, and environmental impact. A promising technique to actively reduce the aerodynamic viscous drag are spanwise traveling transversal surface waves to manipulate the near-wall turbulent boundary layer. Given the flow conditions the goal is to choose the actuation parameters, such that the drag reduction and the net power savings are optimized, while other essential aerodynamic properties, such as the lift-to-drag ratio for airfoils, are neutrally or positively affected.

The partially conflicting objectives, i.e., drag reduction and net power savings, are evaluated by wall-resolved large-eddy simulations (LESs) using the structured finite volume solver of the in-house solver framework m-AIA. Facing computational cost of LESs and the design space of actuation parameters, surrogate modeling is key for surrogate-based optimization to efficiently achieve a satisfactory optimum, insightful data and interpretative knowledge. In this study, Gaussian process regression (GPR) based multi-task learning models with different level of architectural complexity are analyzed. These multi-task Gaussian process regression (mGPR) models are compared in terms of their effectiveness in incorporating prior knowledge and in transferring insights from one prior-dense objective, i.e., relative drag reduction, to the other prior-sparse objective, i.e., relative net power savings, in terms of prediction quality.