Suboptimal control of wall turbulence with arrayed dimple actuators for drag reduction

Direct numerical simulation of a turbulent channel flow with moving dimples at the bottom wall is carried out using the pseudo-spectral method and the curvilinear coordinate system. Suboptimal control based on the spanwise wall shear stress is applied for skin-friction drag reduction, and is implemented by the finite-size sensor-actuator system. The control law is realised in physical space by using a cross-shaped truncation of the wall shear stress information, which can be measured by the sensor. Only the information of wall shear stress inside the sensor area is utilised and that outside the sensor area is obtained by a linear reconstruction from the averaged value over the sensor. To effectively intervene the near-wall coherent structures, low-pass filtering of the spanwise wall shear stress is additionally implemented to eliminate the extra disturbances induced by the presence of dimple actuators, and the filtered stress is used as the control input. Numerical tests on the present control strategy show that the pressure form drag caused by the presence of dimples is reduced significantly as compared with the original suboptimal control, and the reduction of total drag is comparable with that of the opposition control. The underlying mechanism is further analysed by looking into the interaction between the moving dimples and the near-wall coherent structures.