Control of optimal growth of instabilities in Jeffery-Hamel flow

In this article, we present an active control of optimal growth of instabilities in Jeffery-Hamel (JH) flow through the standard wall transpiration control technique. The motivation behind this work is to delay the transition process in converging/diverging JH flows with small angles. We formulate the governing equations and the control model for the JH flow with the parallel flow approximations. In the non-modal stability framework, we have constructed a state space model which incorporates control actuation as periodic suction/blowing of fluid through walls (wall transpiration). The variational method is used to compute the optimal growth of the system. An optimal feedback control gain is obtained (assuming the knowledge of the full state) through linear quadratic regulator (LQR) and feed-backed to the system to suppress the maximum amplification of optimal growth of the instabilities in the flow. We found that the optimally amplified growth in both converging as well as diverging JH flow is reduced after applying controlled wall transpiration. The present study could be the starting step towards the control of non-parallel global instabilities.