Optimal perturbation control in plane Poiseuille flow using stability modifier

In this article we have numerically attained the optimal perturbation control in plane Poiseuille flow using stability modifier (wall transpiration). In two different test cases -one with single wall and another with combined both wall transpiration, the control effect on optimal perturbations in plane Poiseuille flow is studied. In non-modal stability structure, a state-space model is formulated which incorporates control effort as oscillatory pump in/out of fluid through boundaries, known as wall transpiration. In local stability framework, Chebyshev spectral method is utilized to discretize the wall boundary normal direction. The variational method is followed to calculate the optimal disturbance in the system. Linear Quadratic Regulator (LQR) is constructed by assuming the notion of full state and feedback is given accordingly to mitigate the maximum amplification of optimal growth of disturbances and the associated temporal growth of instabilities. After applying control, it has been found that the maximum amplification of optimal growth (for supercritical case Re = 8000, α = 1,β = 0) is suppressed approximately thirty five percent through compounded effect via both wall transpiration as compared to the single wall transpiration.