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LINEAR PROPORTIONAL-INTEGRAL CONTROL OF TURBULENT CHANNEL FLOW FOR DRAG REDUCTION

Euiyoung Kim
School of Mechanical and Aerospace Engineering Seoul National University Seoul 151-744, KOREA

Haecheon Choi
Department of Mechanical & Aerospace Engineering Seoul National University 1, Gwanak-ro, Gwanak-gu, Seoul 08826, Korea

Sinopsis

Choi, Moin and Kim (1994) applied the opposition control, vw = − vS+~10, to turbulent channel flow and obtained about 25 % drag reduction, where vw is the blowing and suction at the wall, and v is the wall-normal velocity, and ys is the sensing location above the wall. From the classical control theory, the opposition control by Choi et al. (1994) is a proportional (P) control with a fixed feedback gain. In the present study, we investigate the performance of proportional-integral (PI) control in reducing the skin friction in a turbulent channel flow. The PI control is defined as vw = −α vys − β ∫ vysdt, where α and β are the proportional and integral feedback gains, respectively. The direct numerical simulation (DNS) and linear systems approach are conducted. In the effective sensing region, the PI control results in slightly more drag reduction and lower transient energy growth rate than the P control. The sensing velocity fluctuations, considered as an error in the control, approach zero with the PI control, while they do not go to zero with the P control.