# Moving Surface Boundary-Layer Control on the Wake of Flow around a Square Cylinder
## 1 Introduction
[PERSON] and [PERSON] [34] conducted wind tunnel tests to study the aerodynamics of a cubic structure in the presence of MSBC, using rotating circular cylindrical elements at the two adjacent vertical edges. The results revealed the significant effect of the MSBC, which changes the height of the boundary-layer separation and reattachment, thus affecting the fluid dynamical parameters. The moving surface boundary-layer control (MSBC) is also called angular momentum injection. Through numerical simulation, [PERSON] and [PERSON] [35] proposed an angular momentum injection strategy to control the wake dynamics and turbulence behind a fixed square cylinder at \(\text{Re}=200\). This study observed a new zone formation of a recirculation-free zone (RFZ) behind the cylinder at \(\zeta=1.25\). With the increase of angular momentum injection, the zones of absolute and convective instabilities (AIZ and CIZ) are diminished, and the recirculation-free zone is enhanced. Finally, the wake turbulence is completely suppressed at \(\zeta=1.5\). [PERSON] and [PERSON] [36] compared the wake characteristics of a flow past an isolated circular cylinder, with momentum injection in the subcritical Re range. The numerical flow visualization through streaklines and streamlines clearly demonstrated the effectiveness of the rotating-type actuators in modifying the turbulent vortex structures. As the ratio of the momentum input became higher, the flow tended to be smoother. [PERSON] [37] investigated the flow past a bluff body with two rotating control cylinders using two-dimensional numerical simulation. When the control cylinders rotated with a high speed, in a manner that the tip speed was five times the free-stream speed, the flow at \(\text{Re}=100\) reached a steady state. For \(\text{Re}=10^{4}\), although the flow remained unsteady, the wake was much more organized and narrower compared to the one without control. [PERSON] and [PERSON] [38] verified the efficiency of the MSBC in suppressing vortex-induced vibrations (VIV); the flow control results in a mean drag of almost 60% compared to that of the plain cylinder, reduction at \(U_{c}/U=5\). The wake is highly organized and narrower compared to the one observed in cylinders without control. In the present work, the entire process involving the flow around a fixed square cylinder and the MSBC was numerically simulated. The present numerical simulation started from the flow around a fixed square cylinder; when the alternating vortex shedding appeared and became stable, the MSBC was then activated to control the wake. Two small rotating circular cylinders were employed, which were located in the rear corners of the square cylinder, similar to [PERSON] and Wei [35], to achieve momentum injection into the flow field. In this work, we mainly study the control effectiveness of the rotation direction of the small circular cylinders, the wind angle, and the velocity ratio on the oscillating wake of the square cylinder. The aerodynamic force time histories and their statistics, the mean pressure distribution, and the vortex shedding pattern were studied to demonstrate the control effectiveness of the MSBC for different influencing factors and to explain the mechanism of the MSBC flow control method.