Application of the adjoint multi-point and the robust optimization of shock control bump for transonic aerofoils and wings

Abstract

A shock control bump (SCB) is a flow control method which uses a local small deformation in a flexible wing surface to considerably reduce the strength of shock waves and the resulting wave drag in transonic flows. Most of the reported research is devoted to optimization in a single flow condition. Here, both equally and variably weighted multi-point optimization and a robust adjoint optimization scheme are used to optimize the SCB. The numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm are used to find the optimum location and shape of the SCB for two benchmark aerofoils. A multi-point optimization method under a constant-lift-coefficient constraint is implemented to find the optimum design of a two-dimensional (2D) SCB and it is observed that the general results are similar to other optimization algorithms. To show that these results are extendable to real three-dimensional (3D) cases, a 3D bump model with 11 parameters is introduced, and it is optimized using both single- and multi-point optimization procedures. Although the 3D flow structure involves much more complexity, the overall results are shown to be similar to the 2D case.