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SUBOPTIMAL CONTROL OF WALL TURBULENCE WITH MOVING DIMPLES

Weixi Huang
Department of Engineering Mechanics Tsinghua University Beijing 100084, PR China

Wuyang Zhang
Department of Engineering Mechanics Tsinghua University Beijing 100084, PR China

Ming-Wei Ge
Department of Engineering Mechanics, School of Aerospace Tsinghua University, Beijing 100084, P. R. China

G. Yang
Mechanical Engineering Department, Florida International University The State University of Florida at Miami, Miami, FL 33199, USA; Department of Engineering Mechanics Tsinghua University Beijing 100084, China

Chunxiao Xu
Department of Engineering Mechanics Tsinghua University Beijing 100084, PR China

Résumé

Direct numerical simulation of a turbulent channel flow with moving dimples at the bottom wall was carried out using the spectral method. Suboptimal control based on the wall information of the spanwise wall shear stress was applied for skin-friction drag reduction. The average reconstruction scheme together with the spanwise stripped truncation of the weighting function was found to be effective for realization of the control law in physical space. Both the linearized approximate and real no-slip boundary conditions were tested. It was found that the approximate boundary condition overestimates the drag reduction rate. For the real no-slip condition, low-pass filtering of the wall shear stress was additionally implemented for the control input to eliminate the fluctuations due to the presence of dimples. Drag reduction was successfully obtained by reducing the pressure form drag as compared with the original suboptimal control.