Friction Drag Reduction On A Turbulent Boundary Layer Based On A Proportional-Derivative Control Scheme

The surface friction of vehicles is closely related to the coherent structure in the turbulent boundary layer.With the rapid global energy consumption and environmental pollution problems becoming increasingly prominent,how to control these coherent structure in an active and effective way,while increasing the drag reduction and improving the control efficiency is an urgent problem to be solved.In this paper,A feedforward proportional-derivative(PD)control scheme is developed based on the dielectric barrier discharge(DBD)plasma actuators for friction drag reduction in a turbulent boundary layer(TBL)over a flat plate when momentum Reynolds number is 1450.The fluctuating wall-pressure upstream of the actuators is used as the feed-forward signal in the control system.A technique called vibration-noise-cancellation,where two microphones and a Kalman filter are deployed,is used to capture the "true" wallpressure fluctuations.The force balance is used to measure the spatial average drag reduction in the area of 1333.3 × 333.3 at 100 wall units downstream of the plasma actuators.A hot wire is used to measure the velocity signal at 166.7 wall units downstream of the plasma actuators,and the burst frequency is analyzed by VITA(Variable Interval Time Average)technique.Finally,the flow field structures changes are displayed by smoke-wire flow visualization in a plane parallel to the wall.In the PD control system,15 proportional coefficients Kp(1?Kp?25)and 17 differential coefficients Kd(0.01?Kd?1)are combined to achieve the maximum average drag reduction;as a result,the PD control achieves of is-16%,marginally less than that-18%under the open-loop control.Further,the control efficiency ? of the PD control is 31.1%larger than that of the open-loop control.The PD control is found to manipulate the voltage E fluctuations at a pronounced frequency of 40 Hz.The streamwise velocity u at y+ =5 fluctuates at the same frequency as shown in the PSD.The PD control adversely influences urms near the wall(y+<17),as a result;the urms and burst intensity are only decreased by 9.06%and 15.11%,respectively,which are 10.7%and 5.6%,respectively,less than the open-loop control at(x+,y+,z+)=(166.7,5,100).Under PD control,the low-speed streaks in R3 region is not as stable as those in open-loop control,so ?cf under PD control is slightly lower than that in open-loop control.By analyzing the instantaneous pressure signal Pe,voltage signal E and downstream velocity signal u+captured simultaneously,it is found that the voltage E will increase its amplitude for control when there is a large pressure fluctuation(|Pe|>0.016 Pa).The input power Pin for PD control is reduced,therefore,the ?2 of PD control is higher than that of open-loop control.