Drag reduction by active control for flow past cylinders

Abstract

The main objective of this article is to investigate computational methods for the active control and drag optimization of incompressible viscous flow past cylinders, using the two-dimensional Navier-Stokes equations as the flow model. The computational methodology relies on the following ingredients: space discretization of the Navier-Stokes equations by finite element approximations, time discretization by a second order accurate two step implicit/explicit finite difference scheme, calculation of the cost function gradient by the adjoint equation approach, minimization of the cost function by a quasi-Newton method à la BFGS. The above methods have been applied to predict the optimal forcing-control strategies in reducing drag for flow around a circular cylinder using either an oscillatory rotation or blowing and suction. In the case of oscillatory forcing, a drag reduction of 31% at Reynolds number 200 and 61% at Reynolds number 1000 was demonstrated. Using only three blowing-suction slots, we have been able to completely suppress the formation of the Von-Karman vortex street up to Reynolds number 200 with a significant net drag reduction. We conclude this article by an appendix describing a bisection method which allows very substantial storage memory savings at reasonable extra computational time when applying adjoint equation based methodologies to the solution of control problems modeled by time dependent equations.