Optimal flow control using unsteady sensitivity analysis

This paper describes an optimal flow control method for compressible laminar/turbulent flows utilizing discrete unsteady aerodynamic sensitivity analysis methods. Unsteady aerodynamic sensitivity codes are developed using a direct differentiation method and an adjoint method, respectively, from two-dimensional unsteady compressible Navier-Stokes equations. Optimal flow controls are conducted 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. Several flow control examples of academic interest including circular cylinder vortex shedding control and airfoil shock buffet control show satisfactory results. The present active flow control method utilizing the unsteady sensitivity analysis is robust and problem independent compared to conventional active control methods.