On the Stability and Control of Two-Dimensional Channel Flow

Abstract

A direct numerical simulation is used to solve the two-dimensional plane Poiseuille flow for three different stability cases; specifically, they are a supercritical case at a Reynolds number of 10,000, a critical-stable case at a Reynolds number of 5772.22, and subcritical case at a Reynolds number of 1000. The perturbations are developed using the eigenfunctions of Orr–Sommerfeld equation's solution. In many applications, the flow was required to be fully laminar. As a result, a model-based controller is developed for stabilizing the flow field using unsteady strong suction and blowing technique, through distributed slots on the two walls of the channel. This technique is introduced to cancel the propagating wave in the boundary-layers near the two walls. Promising results are achieved for the unstable and critical-stable cases. The stable case is tested. Slight improvements in its growth rate are recorded. In turn, a faster response for the flow field is achieved.