Flow control using unsteady aerodynamic sensitivity analysis

Abstract

The present paper deals with a method for the active flow control of compressible laminar/turbulent flows utilizing discrete aerodynamic sensitivity analysis. Unsteady discrete aerodynamic sensitivity equations are formulated. Unsteady sensitivity code and adjoint code are then developed by hand-differentiation from a two-dimensional unsteady covpressible Navier-Stokes solver via direct differentiation method and adjoint method, respectively. An algebraic turbulence model is also differentiated by hand for the accurate computation of sensitivity derivatives in turbulent flows. Active flow controls are efficiently carried out by minimizing an unsteady objective function defined at an instant instead of integrating a response for a period of time. Unsteady sensitivity derivatives of the objective function are calculated by the unsteady sensitivity codes, and optimization is conducted utilizing a linear line search method at every physical time step. Flow control of several unsteady problems including the vortex shedding control from a circular cylinder and airfoil shock buffet control shows very satisfactory results. The computed results validate that the present active flow control method utilizing unsteady sensitivity analysis is robust and problem-independent compared to previous approaches.