An opposition control scheme with strengthened control input is proposed and tested in turbulent channel flows at friction Reynolds number Re τ = 180 by direct numerical simulations. When the detection plane is located at less than 20 wall units, the drag reduction rate can be greatly enhanced by increasing the control amplitude parameter. The maximum drag reduction rate achieved in the present study is around 33%, which is much higher than the best value of 25% reported in literature. The strengthened control can be more efficient to attain a given drag reduction rate. Based on the total shear stress at the virtual wall established between the real wall and the detection plane by the control, a new friction velocity is proposed and the corresponding coordinate transform is made. Scaled by the proposed friction velocity, the wall-normal velocity fluctuation and the Reynolds shear stress of the controlled flows are collapsed well with those of the uncontrolled flow in the new coordinate. Based on the similarity, a relation between drag reduction rate and the effectiveness of the virtual wall is deduced, which disclosed that the elevation and residual Reynolds shear stress at the virtual wall are the key parameters to determine the drag reduction rate. The conclusion are also validated at Reτ = 395 and 590. The decrease of the drag reduction rate with the increase of the Reynolds number is attributed to the enhanced residual Reynolds shear stress at the virtual wall.
Bibliographical noteFunding Information:
The work is supported by National Natural Science Foundation of China (grant numbers 10925210, 11322221, 11132005) and Tsinghua National Laboratory for Information Science and Technology.
- Drag reduction
- Opposition control
- Turbulent channel flow