Abstract
AbstractFlow control is of interest in many open and wall‐bounded shear flows in order to reduce drag or to avoid sudden large fluctuations that may lead to material failure. An established means of control is the application of suction through a porous wall. Here, we combine suction with a feedback strategy whereby the suction velocity is adjusted in response to either the kinetic energy or the shear stress at the bottom wall. The control procedure is then used in an attempt to stabilize invariant solutions and to carry out direct numerical simulations with a prescribed value of the friction coefficient.
Highlights
We consider a plane Couette setup with a fluid located in the gap between two infinitely extended parallel plates at a distance 2d
Where p is the pressure divided by the constant density ρ and Re0 = U0d/ν the Reynolds number based on the velocity of the top plate, the half-height of the domain and the kinematic viscosity of the fluid
The feedback control procedure is based on a control variable R, here related to the suction velocity Vs by Vs/U0 = R/R02, and an observable A, e.g. the L2-norm u 2 or the friction factor Cf = τw/(ρU02), where τw is the shear stress at the bottom wall
Summary
We consider a plane Couette setup with a fluid located in the gap between two infinitely extended parallel plates at a distance 2d. For large gap widths and a constant suction velocity −Vs in the wall-normal y-direction through the bottom plate, this system is often used to emulate the asymptotic suction boundary layer (ASBL).
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