Direct numerical simulation of spatially developing turbulent boundary layers with opposition control

Abstract

Opposition control of spatially developing turbulent boundary layers for skin friction drag reduction is studied by direct numerical simulations. The boundary layer extends 800θ0 in the streamwise (x) direction, with θ0 denoting the momentum thickness at the flow inlet. The Reynolds number, based on the external flow velocity and the momentum thickness, ranges from 300 to 860. Opposition control applied in different streamwise ranges, i.e. and as well as the uncontrolled case, are simulated. Statistical results and instantaneous flow fields are presented, with special attention paid to the spatial evolution properties of the boundary layer flow with control and the underlying mechanism. It is observed that a long spatial transient region after the control start and a long recovery region after the control end are present in the streamwise direction. A maximum drag reduction rate of about 22% is obtained as the transient region is passed, and an overshoot in the local skin friction coefficient (Cf) occurs in the recovery region. A new identity is derived for dynamical decomposition of Cf. Reduction of Cf by opposition control and overshoot of Cf in the recovery region are explained by quantifying the contributions from the viscous shear stress term, the Reynolds shear stress term, the mean convection term and other terms.