Active proportional feedback control of turbulent flow over a circular cylinder with averaged velocity sensor

Abstract

In the present study, we perform an active proportional (P) feedback control of laminar and turbulent flows over a circular cylinder with an averaged velocity sensor to reduce its drag and lift fluctuations. As a sensor for the feedback control, we adopt an averaged transverse velocity on the centerline of the wake. For the averaging of the transverse sensing velocity, we consider both temporal averaging over a finite period and spatial averaging in the spanwise direction. As a control input, the blowing/suction actuation is provided on the cylinder surface near the flow separation, and its magnitude is linearly proportional to the averaged transverse sensing velocity. With the control, the fluctuations of the transverse sensing velocity are significantly reduced and the vortices right after the cylinder and the K\'{a}rm\'{a}n vortex shedding in the wake are weakened, resulting in substantial reductions of the mean drag and lift fluctuations. Furthermore, it is shown that the adoption of the averaged sensing velocity makes the P control successful for a wider range of sensing locations in laminar flow at $Re=100$, and is essential for the success of the P control in turbulent flow at $Re=3900$. With the optimal control parameters, the reductions of the mean drag and lift fluctuations for turbulent flow at $Re=3900$ are about 11\% and 61\%, respectively. The present P control maintains the magnitude of the blowing/suction actuation less than $1\%$ of the free-stream velocity, and thus the control input power is very small, leading to an excellent control efficiency.

Prediction of Near-Wake Velocity in Laminar Flow over a Circular Cylinder Using Neural Networks with Instantaneous Wall Pressure Input

“…The transverse velocity in the near-wake of the cylinder is a useful information indicating the status of the Kármán vortex shedding. Thus, various feedback controls applied to flow over a circular cylinder measure the transverse velocity in the wake as sensors and aim to reduce its amplitude to weaken the strength of the Kármán vortex shedding [27][28][29][30][31]. However, it would not be practical to measure the transverse velocity in the wake in real applications of these control methods.…”

“…However, it would not be practical to measure the transverse velocity in the wake in real applications of these control methods. Therefore, we believe that incorporating the present neural networks with feedback control methods would be an effective control strategy to improve its practical applicability because this approach does not need to measure the velocity and only measures the wall pressures as a sensor of feedback controller [27].…”

“…The second-order central difference scheme is used for spatial discretizations in each term of Equations ( 1) and ( 2). We note that the numerical details described above have been implemented through our own in-house code, and its accuracy has been proven in predicting various complex flow configurations [7,9,26,27]. Figure 1a,b shows the computational domains for Re = 60 and 300, respectively.…”

“…In this study, we aim to predict the near-wake transverse velocity in laminar flow over a circular cylinder by using a neural network with instantaneous wall pressures on the cylinder surface as the input variables. The transverse velocity in the wake of a circular cylinder has been considered a good indicator for the state of Kármán vortex shedding [27][28][29][30][31]. In this regard, one of the motivations for constructing neural networks to predict the transverse velocity is to further integrate them, in future studies, with active feedback control methods such as proportional-integral-derivative (PID) control [27,29], whose control purpose is to mitigate the strength of the Kármán vortex shedding.…”

“…The transverse velocity in the wake of a circular cylinder has been considered a good indicator for the state of Kármán vortex shedding [27][28][29][30][31]. In this regard, one of the motivations for constructing neural networks to predict the transverse velocity is to further integrate them, in future studies, with active feedback control methods such as proportional-integral-derivative (PID) control [27,29], whose control purpose is to mitigate the strength of the Kármán vortex shedding. Figure 1 shows learning dataset domains for neural networks at Re = 60 and 300.…”