**1. Introduction**

The rigid wingsail is a common auxiliary propulsion device. Due to its characteristics of environmental protection and energy saving, the rigid wingsail has been applied to various types of ships. In 1980, two rectangular rigid wingsails with a total sail area of 194.4 m<sup>2</sup> on "*Shin Aitoku Maru*" were installed in Japan, which was the world's first modern sail-assisted commercial tanker. After four years of actual sailing, oil tankers can save 8.5% a year compared with conventional ships [1]. Although the international oil price fluctuates greatly, the research on sail-assisted vessels varies from country to country. In 2018, China Shipbuilding Group delivered the world's first Very Large Crude Carrier (VLCC), "Kai Li", with wingsails (Figure 1). The trial results show that the energy-saving efficiency of the VLCC is obvious [2]. At the same time, the wingsails have also been rapidly developed in the field of unpowered navigation. Particularly in 2010, BMW Oracle was powered by a 60-meterhigh, multi-element wingsail, which won the 33rd America's Cup. The flexible size and excellent performance of the wingsail has rekindled the interest of the shipping industry [3]. However, due to the phenomenon of flow separation or stall on the surface of the wingsail, the propulsion performance of the wingsail will be deteriorated, which will seriously affect the stability

*ρ* The density of the air [kg/m3]

*ρ* The density of the air [kg/m3]

*v* The velocity of inflow [m/s]

*v* The velocity of inflow [m/s]

the wing chord [-]

the wing chord [-]

*h* Wingsail height [m]

*h* Wingsail height [m]

*L* Lift force[N] *D* Drag force [N]

*L* Lift force[N] *D* Drag force [N]

**1. Introduction** 

**1. Introduction** 

*z* The height of wingsail in the vertical direction[m]

*z* height of wingsail in the vertical direction[m]

Xr The position of flap rotation axis in the direction of

Xr position of flap rotation axis in the direction of

of the ship. The New Zealand Chiefs [4] suffered a shipwreck in the 35th America's Cup (Figure 2). Therefore, it is very important to find an effective method to control flow separation or delay stall. (Figure 2). Therefore, it is very important to find an effective method to control flow separation or delay stall. delay stall.

the stability of the ship. The New Zealand Chiefs[4] suffered a shipwreck in the 35th America's Cup

(Figure 2). Therefore, it is very important to find an effective method to control flow separation or

*J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 2 of 16

*J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 2 of 16

The rigid wingsail is a common auxiliary propulsion device. Due to its characteristics of environmental protection and energy saving, the rigid wingsail has been applied to various types of ships. In 1980, two rectangular rigid wingsails with a total sail area of 194.4m2 on "*Shin Aitoku Maru*" were installed in Japan, which was the world's first modern sail-assisted commercial tanker. After four years of actual sailing, oil tankers can save 8.5% a year compared with conventional ships[1]. Although the international oil price fluctuates greatly, the research on sail-assisted vessels varies from country to country. In 2018, China Shipbuilding Group delivered the world's first Very Large Crude Carrier (VLCC), "Kai Li", with wingsails (Figure 1). The trial results show that the energy-saving efficiency of the VLCC is obvious [2]. At the same time, the wingsails have also been rapidly developed in the field of unpowered navigation. Particularly in 2010, BMW Oracle was powered by a 60-meterhigh, multi-element wingsail, which won the 33rd America's Cup. The flexible size and excellent performance of the wingsail has rekindled the interest of the shipping industry [3]. However, due to the phenomenon of flow separation or stall on the surface of the

The rigid wingsail is a common auxiliary propulsion device. Due to its characteristics of environmental protection and energy saving, the rigid wingsail has been applied to various types of ships. In 1980, two rectangular rigid wingsails with a total sail area of 194.4m2 on "*Shin Aitoku Maru*" were installed in Japan, which was the world's first modern sail-assisted commercial tanker. After four years of actual sailing, oil tankers can save 8.5% a year compared with conventional ships[1]. Although the international oil price fluctuates greatly, the research on sail-assisted vessels varies from country to country. In 2018, China Shipbuilding Group delivered the world's first Very Large Crude Carrier (VLCC), "Kai Li", with wingsails (Figure 1). The trial results show that the energy-saving efficiency of the VLCC is obvious [2]. At the same time, the wingsails have also been rapidly developed in the field of unpowered navigation. Particularly in 2010, BMW Oracle was powered by a 60-meterhigh, multi-element wingsail, which won the 33rd America's Cup. The flexible size and excellent performance of the wingsail has rekindled the interest of the shipping industry [3]. However, due to the phenomenon of flow separation or stall on the surface of the wingsail, the propulsion performance of the wingsail will be deteriorated, which will seriously affect

**Figure 1.** "Kaili" VLCC with wingsail. **Figure 1.**"Kaili" VLCC with wingsail.

**Figure 2.**Capsizing accident of sailboat. **Figure 2.** Capsizing accident of sailboat.

**Figure 2.**Capsizing accident of sailboat. In order to improve the stall characteristics, different flow control methods are used, which can be divided into active control and passive control. The active control method has been applied to the controllable loop sail [5], fluid injection [6,7], turbine sail [8], Magnus sail [9], trailing flap [10,11], In order to improve the stall characteristics, different flow control methods are used, which can be divided into active control and passive control. The active control method has been applied to the controllable loop sail [5], fluid injection [6,7], turbine sail [8], Magnus sail [9], trailing flap [10,11], leading slat [11,12], etc. The passive method is also applied to different types of technologies, such as In order to improve the stall characteristics, different flow control methods are used, which can be divided into active control and passive control. The active control method has been applied to the controllable loop sail [5], fluid injection [6,7], turbine sail [8], Magnus sail [9], trailing flap [10,11], leading slat [11,12], etc. The passive method is also applied to different types of technologies, such asWalker sails [13], deformed flaps [14] and leading-edge tubercles [15], etc.

leading slat [11,12], etc. The passive method is also applied to different types of technologies, such as Walker sails [13], deformed flaps [14] and leading-edge tubercles [15], etc. Walker sails [13], deformed flaps [14] and leading-edge tubercles [15], etc. In recent years, the flap setting of the wingsail is considered to be a very feasible active controlmethod to control the flow separation. This idea has been applied in the American Cup Sailing Competition with great success. The rigid wingsail consists of two or three symmetrical wings. There is a gap between them to control the wingsail camber on starboard tack and port tack (Figure 3), so as to improve the propulsion performance and delay stall. Many scholars have also carried out research on the aerodynamic characteristics. *J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 4 of 16

**Figure 3.** The geometry and simplified configuration of the two-element wingsail. **Figure 3.** The geometry and simplified configuration of the two-element wingsail.

**Table 1.** Parameterization of wingsail. *c* 0.35m *h* 0.7m *Re* 5×105 *d* 0–25° *α* 0–20° In 1996, **Daniel** [11] designed a high-performance, three-element wingsail. The experimental results show that the maximum thrust coefficient of the three-element wingsail is increased by 68%, the stall angle is delayed between 4◦ and 6◦ , and the thrust in the whole operation area is also improved. At the most efficient wind direction angle of the wingsail, the thrust is increased by 83%. This proves the superiority of multi-element wingsail in propulsion characteristics. In 2003, **Fujiwara** [16,17] switched from a triangular sail to a rectangular one. Its propulsion performance is superior to that of Nojiri's hybrid dynamic sail. In 2015, he cooperated with **Qiao Li** [14] to modify the hybrid sail,

The aim of this paper is to understand the influence of geometric parameters on aerodynamic performance. The parametric design of the wingsail is selected and described in Figure 4. In order to simplify the general problem, it has been decided to focus on the flap deflection angle *d*, the position of flap rotation axis in the direction of the wing chord Xr, and flap thickness e2/c2. The angle of attack(*α*) of the wing represents the angle of attack (AOA) of the wingsail, as seen in Figure 4.

Based on the preliminary simulation and previous research [11,18], the initial wingsail configuration has chord ratio c1/c2= 3:2, wing thickness e1/c1= 18%, flap thickness e2/c2 = 15%, one flap rotation axis Xr/c1=85%, slot width g/c1= 2.4%. Its name will be r1.5t1815 X85g2.4. Adding the angle of attack (*α*) and flap deflection angle (*d*) after this name, and the full configuration name of the

*Computational Domain.* Before mesh generation, the calculation domain of geometric model should be determined. The computational domain of wingsail is large enough (32c×30c×10c) to consider the side effect as negligible (Figure 5). AOA is adjusted by rotating the direction of the airflow. The chord of the wingsail is 0.35m and the span 0.7m. In order to simplify the model, the atmospheric boundary layer is not considered. The boundary conditions used are velocity inlets on three sides (inlet, starboard boundary, port boundary) and a static pressure outlet equal to the far-field pressure. The velocity at the inlet is uniform, and the value is the same as the free flow velocity. The wingsail surface and the bottom surface of the computational domain are defined as

wingsail will be r1.5t1815 X85g2.4α6 d15, for *α* = 6°, *d*= 15°.

*2.2. The Grid Structure* 

anti-slip walls.

replacing the flap with a rigid plate and controlling the rotation of the wing and the plate. Therefore, the sail was also called a variable camber sail(VCS). Through simulation and test, the aerodynamic performance of the VCS was better than that of naca0021 sail and the plate sail. **Vincent** [18] carried out the simulating research of the two-element wingsail with some key design parameters (camber, slot width, angle of attack, flap thickness, etc.) The results show that the transition phenomenon of flap boundary layer occurs due to the existence of laminar separated bubbles and the interaction between the wing and flap boundary layer in the slot region. The stall is related to slot leakage flow with nonlinear coupling and the leakage flow is affected by flap deflection, slot width and flap thickness. Through PIV measurement and numerical simulation, **Alessandro** [19] explained the flow phenomena of rigid wingsails at low and high cambers in detail, especially the flow behavior near the slot between two element wings. He pointed out that the flow field in the gap is the key factor affecting the performance of the wingsail. However, the internal relationship between the change of slot size and the development of wingsail aerodynamic characteristics is still unclear. In order to better understand the aerodynamic characteristics and better control of the rigid wingsail, some numerical studies are proposed in this paper.
