An Active Flow Control Approach for Spatially Growing Mixing Layer1

Abstract

A control approach is proposed in this study that controls the growth of a spatially growing mixing layer in an open loop. Due to the similarity of the mixing layer dynamics in the temporal and spatial domains, the control is exercised in the temporal domain that leads to optimization of the layer in the spatial domain. The proportional-integral-derivative (PID) control in the temporal domain uses Navier–Stokes equations as the plant model. Apart from being prohibitively expensive, control in the spatial domain presents convective time delay problems. These barriers are circumvented by solving the control problem in the temporal domain very rapidly, based on a given set point in the linear regime. Once the set point in the temporal domain is reached, the corresponding initial conditions in the temporal domain are mapped to inflow boundary conditions in the spatial domain. With these mapped inflow boundary conditions in the spatial domain, the spatial development of the mixing layer is followed, which confirms the efficacy of control in the spatial domain. The present control methodology offers a new paradigm for control of the spatially growing mixing layer.