Modeling and Distributed Control of Transition in Plane Poiseuille Flow

Abstract

Recently a mathematical model for flow transition control in 2-D channels has been proposed that is in interconnected systems representation. The model is valid for all spatial frequencies and can be used for the synthesis of controllers for flow transition control problems in channels of infinite length. In this brief the model is validated against known features of plane Poiseuille flow and against the response of a nonlinear simulation at Reynolds number 2000. Based on this model a distributed control scheme is then synthesized for Reynolds number 10 000 using a recently proposed approach for interconnected systems. The controller is designed to stabilize the otherwise spatially unstable flow. This instability causes the transition from laminar to turbulence. Furthermore, a desired closed loop frequency response is obtained by tuning the weighting filters. The designed controller is then tested in a nonlinear simulation and closed-loop results are presented. The approach proposed here does not make any assumption on the periodicity of the channel, as is the case in most of previously published work. The control scheme can be implemented on microelectro-mechanical systems (MEMS)-based control systems. Such systems are spatially discrete in nature which is taken into consideration in the controller synthesis phase.