# Moving Surface Boundary-Layer Control on the Wake of Flow around a Square Cylinder
## 1 Introduction
[PERSON] and [PERSON] [24] replaced the flexible membrane material with piezoelectric material, which can achieve the dual purpose of flow control and energy harvesting. [PERSON] and [PERSON] [25] used a numerical simulation method to study the reduction effect of the aerodynamic forces and heat transfer of a control plate on a square cylinder at \(\mathrm{Re}=50-200\) based on the width of the square cylinder (\(W\)). This study shows that the optimum position and width for the control plate are a distance of \(3W\) away from the cylinder and a width of \(0.5W\) at \(\mathrm{Re}=160\), where the cylinder drag and the total drag (cylinder and plate) have a reduction of 86% and 37%, respectively, and the rms lift and drag coefficients on the cylinder have a 92% and 90% reduction compared to that of an isolated cylinder. Blowing and suction are also an effective way to control the wake of bluff bodies. [PERSON] and [PERSON] [26] investigated some aerodynamic parameters of the flow around perforated-surface square, horizontal, and diagonal cylinders at three different Reynolds numbers in a wind tunnel. The experimental results showed that the surface injections through the top-rear, rear, and all surfaces of a diagonal square cylinder reduce the drag coefficient for all the Reynolds numbers, while the injection through all surfaces only reduces the drag coefficient of a horizontal square cylinder. [PERSON] et al. [27] numerically investigated the effects of uniform suction and blowing through the surfaces of a square cylinder on the vortex shedding, wake flow, and heat transfer at low Reynolds numbers. The results show that the lift and drag fluctuations for the optimum configuration decay, and the maximum reduction on the drag force are 61%, 67%, and 72% for Re = 70, 100, 150, and respectively. [PERSON] et al. [28] and [PERSON] et al. [29] realized the passive jet flow control by attaching hollow opening pipes on the cylinder surface and opening a slit in the middle of the cylinder section. Both methods have achieved the purpose of suppressing or delaying the alternating shedding vortices in the wake of the cylinder. Based on the wind tunnel tests, the theoretical prediction, and the flow visualization, [PERSON] et al. [30] applied the MSBC to two-dimensional rectangular prisms to achieve drag reduction and suppression of flow-induced vibrations. The results indicated that the existence of the MSBC effectively eliminated the vortex resonance and galloping-type instabilities and that the maximum momentum injection corresponding to a velocity ratio of 3 was sufficient to delay boundary-layer separation and to achieve a minimum drag condition. On the basis of the existing research methods, [PERSON] et al. [31] conducted numerical simulations and analyzed the drag of two-dimensional flat plates and rectangular prisms with MSBC. Both the numerical and the flow visualization results showed narrowing of the wake as the momentum injection increased, leading to eventual suppression of the vortex shedding. [PERSON] et al. [32] studied the suppression of the aerodynamic response of square-sectioned tall structures with MSBC. The results of their study clearly showed that the boundary-layer control through the use of rotating cylinders at the leading edges of a two-dimensional square prism were effective in suppressing the vortex-excited and galloping oscillations. The rotor length and its position on the structure were the main factors affecting the effectiveness of MSBC. [PERSON] et al. [33] conducted extensive wind tunnel experiments to study the role of the MSBC in the suppression of torsional flutter of a shallow rectangular prism, which was one of the typical fundamental configurations of bridge deck sections. The results that they obtained from measurements of surface pressure distributions and aeroelastic vibration responses showed that the proposed boundary-layer control method through momentum injection was effective in suppressing the torsional flutter of a shallow rectangular prism.