Stability and Control of the Flow in a Porous Channel

Abstract

In this article, optimally amplified growth of instabilities have been attenuated in porous channel flow through the standard wall transpiration technique (stability modifier). We have numerically investigated both modal and non-modal stability of the flow with underlying boundary condition as constant suction or injection through porous walls. The motivation behind this work is to delay the transition process in the porous channel flow. We formulate the state space model which includes control actuation as periodic suction/blowing of fluid through walls (wall transpiration). Variational method is used to compute the optimal growth of the system in the non-modal stability framework. We apply controls for both symmetric and non-symmetric base flow solutions (namely type I, type II and type III). Assuming the knowledge of full state, a linear quadratic regulator (LQR) is synthesized and an appropriate gain is feed-backed to the system to suppress the maximum amplification of optimal growth of the instabilities in the porous channel flow, which could be beneficial delaying the transition process in the flow.