Control of turbulent flow for drag reduction

Abstract

A suboptimal boundary control in the stochastic Burgers equation has been studied to review the suboptimal control methodology. The control laws are formulated based on the continuous adjoint operators. Several case studies have been attempted to test the control performances. A systematic analysis is made of suboptimal control for drag reduction. The influence of the amplitude of actuation (A) and the time scale of actuation $(\Delta t^+_a)$ is evaluated. Two wall sensing variables are employed $(∂w/∂y|_w and ∂p/∂z|_w)$, with two actuations ($\phi_2 and \phi_3$). To test the suboptimal control, direct numerical simulations of turbulent channel flow at $Re_\tau =100$ are performed in a spectral domain. It is found that the effect of A and $\Deltat^+_a$ on the drag reduction rate $(D_r)$ is significant. The near-wall behaviors of flow structure are analyzed to characterize the drag reduction. An optimal time scale is obtained at $\Deltat^+_a \simeq 1$ and $\Deltat^+_a$ should be less than $Deltat^+_a \sim 100$. The size effect of the sensor/actuator is examined. Additionally, a weakly nonlinear formulation for the suboptimal control has been derived. In order to consider the nonlinear convection term, two stages of the discretized Navier-Stokes equations are introduced. These feedback control laws are formulated based on the wall shear-stress only. A suboptimal control law in turbulent pipe flow is derived and tested. Two sensing variables $∂p/∂θ|_w$ and $∂_vθ/∂r|_w$ are applied with two actuations $\phi_θ$ and $\phi_r$. To test the suboptimal control law, direct numerical simulations of turbulent pipe flow at $Re_\tau=150$ are performed. When the control law is applied, a 13~23% drag reduction is achieved. The most effective drag reduction is made at the pair of $∂_v\theta/∂r|_w$ and $\phi_r$. An impenetrable virtual wall is observed by the controlled wall suction and blowing. The virtual wall concept is useful for analyzing the near-wall behavior of the co...