Optimal control of growth of instabilities in Taylor–Couette flow

The present work aims to achieve optimal control of instabilities in a standard Taylor–Couette flow. motivation the study is reduce disturbance growth and delay transition process turbulence. We numerically employ using stability modifier, namely, wall transpiration. In non-modal framework, we form state-space model employing actuation by means periodic suction/blowing fluid from walls. conducted for two cases flow rotations: (i) counter-rotating cylinders (ii) stationary outer cylinder with inner rotating. parametric was performed varying radii ratios, Reynolds numbers (Re), axial (α), azimuthal (n) wavenumbers. time evolution governing equation written terms perturbation velocities radial (r) (θ) directions. feedback obtained linear quadratic regulator controller feed backed system maximum kinetic energy taken as measure amplification disturbances used cost function be minimized. use Chebyshev spectral collocation method discretize equations variational calculate growth. studied four different ratios (η=r1r2= 0.1, 0.25, 0.5, 0.75), angular velocity (Ω2Ω1) ratio fixed μ=−1 μ = 0. choose subcritical wavenumbers that led transient corresponding number ≈ 0.65 times critical case counter-rotation. For cylinder, showed effect modal analysis framework. presented technique resulted 72% reduction rate typical energy.