Control of optimal growth of instabilities in Taylor-Couette flow

It is well understood that sub-critical transition may occur due to short-term algebraic growth in many flows. In this work, we study the optimal growth in standard Taylor-Couette flow and control of the optimal perturbation using wall transpiration. In the non-modal stability framework, we develop a state-space model which incorporates control actuation as periodic suction/blowing of fluid through walls. The study is carried out for different flow configurations such as radii of cylinders and their angular velocities. We explored different wave numbers as well. The Reynolds number is defined based on inner cylinder velocity and the gap between two cylinders. The time evolution of governing equation is written in perturbation velocities in radial (r) and azimuthal (θ) directions. The optimal feedback control is obtained using the linear quadratic regulator (LQR) and feed-backed to the system to reduce the maximum optimal growth of the instabilities in the flow. The perturbation kinetic energy is used as cost function. We used Chebyshev spectral collocation method to discretize the equations and the variational method to calculate the optimal growth. A significant reduction is observed in the growth of perturbation energy. It is observed that a reduction of more than 45% is achieved by this method. More detailed results will be presented at the conference.