# Aerodynamic Characteristics of a Square Cylinder with Vertical-Axis Wind Turbines at Corners
## 1 Introduction  
Techniques to reduce wind-induced vibration of high-rise buildings have practical significance for ensuring structure safety and occupant comfort. In general, there are two traditional strategies, mechanical strategies and aerodynamic modifications, to reduce wind-induced vibrations. The tuned mass damper (TMD) installed inside tall buildings is one of the most effective mechanical strategies. In order to achieve an ideal vibration control effect, the mass of the damper normally needs to reach about 0.5-3% of the building mass. As a result, the damper not only occupies a large amount of building space, but also requires a stronger structure system to support such a heavy device. Furthermore, aerodynamic modification strategies, including rounding corners [1; 2; 3] and recessing corners [4; 5; 6], have also been studied. Wind tunnel model testing results demonstrate that slotted corners and chamfered corners can cause significant reductions in both along-wind and cross-wind responses [7; 8]. Drag forces on a cylinder can also be reduced by adding a splitter plate behind it [9]. Although these strategies are very effective, they sacrifice the valuable space of tall buildings for the sole purpose of reduction in wind loading and wind-induced vibrations. To further achieve the purpose of reducing drag, many researchers use the moving surface boundary layer control method (MSBC) to inject momentum into the flow field to prevent the formation of boundary layers. In [10], experimental research was conductedon the aerodynamic characteristic of a square cylinder under the momentum injection method. The results show that in the presence of MSBC, the drag of the square cylinder is considerably reduced at all angles of attack. In research reported in [11], a rectangular prism with two rotating cylinders was studied in a wind tunnel, and the effects of different rotation speed and modes on the aerodynamic characteristic were analyzed. Previous scholars mainly relied on the rotation of the small cylinder to inject momentum into the flow field. We consider replacing the small cylinder with wind turbines to increase its possibility and value in engineering applications. Compared to the sole purpose of aerodynamic modification strategies to suppress wind-induced vibrations of tall buildings described in previous studies, it is desirable to develop effective aerodynamic devices for not only suppressing the wind-induced vibrations but also harvesting wind energy. Extensive studies aimed at making wind energy more efficient have also been carried out. The authors of [12] added two small diameter cylindrical rods on both sides of the cylinder to significantly improve the efficiency of a vortex-induced vibration energy collection system. Wind turbines have been installed in various positions of tall buildings, such as rooftop and through opening and channel between two buildings. The authors of [13] used the scale model to evaluate the wind speed amplifications in the tunnels for wind-power generation through the installation of wind turbines. To obtain optimal environmental benefits, the optimizing design of wind turbines installed on the tall buildings is also discussed [14; 15]. Because previous studies have only focused on the energy-saving benefits of installing wind turbines on structures, we consider that installation of the wind turbine at the corners of the square cylinder will not only enhance structural safety but also exploit wind energy simultaneously. This is a preliminary study to investigate the aerodynamic characteristics of a square cylinder with Savonius wind turbines and attempts to explain the reason why this kind of structure can suppress wind-induced vibrations. Numerical models, including numerical method, computational configuration and mesh arrangement, grid size and time step configuration, and simulation cases are illustrated in Section 2.