Adjoint Approaches For Optimal Flow Control

Abstract

In many engineering applications, aerodynamic behaviour is significantly influenced by flow separation. A promising concept for improving the aerodynamic design is to manipulate the separated flow using active flow control. This is often realised by blowing and suction, whereby gradient-based optimisation methods can help to find an optimal set of excitation parameters. In the present paper, three methods for calculating the gradient are compared: Finite Differences, a continuous adjoint approach and a discrete adjoint method based on Automatic Differentiation (AD). The methods have been applied to the flow around a rotating cylinder at Reynolds numbers of Re = 100 and Re = 5000 to calculate the derivative of the drag coefficient with respect to the revolution rate of the cylinder. The results of these computations are used for a detailed comparison of the methods in terms of consistency, numerical efficiency and accuracy with special emphasis on the treatment of turbulence to demonstrate the superiority of the discrete adjoint approach.