Feedback control to delay or advance linear loss of stability in planar Poiseuille flow

Abstract

By using linear stability theory, we demonstrate theoretically that the critical Reynolds number for the loss of stability of planar Poiseuille flow can be significantly increased or decreased through the use of feedback control strategies which enhance or suppress disturbance dissipating mechanisms in the flow. The controller studied here consists of closely packed, wall mounted, shear stress sensors and thermoelectric actuators. The sensors detect flow instabilities and direct the actuators to alter the fluid’s viscosity by modulating the adjacent wall temperature in such a way as to suppress or enhance flow instabilities. Results are presented for water and air flows.