Maximization of mass flow in a channel obstructed by an infinitely thin plate using a gradient-based control strategy

Abstract

The problem of maximizing the mass flow in a two-dimensional channel partially blocked by an infinitely thin flat plate is addressed using a gradient based control strategy. The state equations are the two-dimensional unsteady incompressible Navier–Stokes equations. The control is a spatially and temporally varying wall-normal velocity boundary condition subject to spatial and temporal constraints of zero mass flux, which are chosen to model realistic Micro Electronic Mechanical Systems based on the movement of small plungers or diaphragms. The control which maximizes the mass flow is found using a conjugate gradient method, where the gradient of the objective function with respect to the control variables is obtained from solving a set of adjoint equations. The effectiveness of choices for the objective function are examined along with the effect of the event horizon and the temporal constraint. Significant increases in the mass flow are obtained for certain choices of these parameters. In many cases, the increase in the mass flow was obtained with a net energy savings. The numerical issues involved with finding the control are discussed and the features of the resulting control are analyzed with the goal of understanding how it affects the mass flow.