3.2.2. Streamlines

boundary layer.

As for the wingsails with different rotating axis positions of the flap at α = 15◦ and *d* = 15◦ , the streamlines on the mid-span of wingsail are depicted in Figure 15. It can be found that a small separation vortex appears in the wake of the wing and a large separation vortex appears in the regions over the suction surface of the flap at X<sup>r</sup> = 90%. *J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 11 of 16

**Figure 15.** Streamlines at mid-span of the wingsail at (a) Xr=75% (b) Xr=85% (c) Xr=90% and (d) Xr=95% with *α*=15°, *d*=15°. **Figure 15.** Streamlines at mid-span of the wingsail at (**a**) X<sup>r</sup> = 75% (**b**) X<sup>r</sup> = 85% (**c**) X<sup>r</sup> = 90% and (**d**) Xr = 95% with α = 15◦ , *d* = 15◦ .

Figure 16 shows the limiting streamline and static pressure contours on suction surface for two-element wingsail at different rotating axis positions of the flap. With the backward movement of the rotating axis position of the flap, the flow separation of the suction surface of the wing expands from the blade root to the top, and the return area becomes larger for the low camber wingsail. The flow separation line appears on the suction surface of the wing at Xr=85%. It explains that the forward movement of the rotating axis position of the flap increases the fluid flow through the slot, delays the flow separation of the suction surface of the wing, or delays stall of the wingsail. An obvious separation helix appears on the suction surface of the wing at Xr=95%, which indicates that the vortex has been formed. When the rotating axis position of the flap is moves backward from 90% to 95%, the flow separation on the suction surface of flap disappears. We guess the fluid flowing through the smaller gap does not supplement the wake of the wing, but flows along the flap Figure 16 shows the limiting streamline and static pressure contours on suction surface for two-element wingsail at different rotating axis positions of the flap. With the backward movement of the rotating axis position of the flap, the flow separation of the suction surface of the wing expands from the blade root to the top, and the return area becomes larger for the low camber wingsail. The flow separation line appears on the suction surface of the wing at X<sup>r</sup> = 85%. It explains that the forward movement of the rotating axis position of the flap increases the fluid flow through the slot, delays the flow separation of the suction surface of the wing, or delays stall of the wingsail. An obvious separation helix appears on the suction surface of the wing at X<sup>r</sup> = 95%, which indicates that the vortex has been formed. When the rotating axis position of the flap is moves backward from 90% to 95%, the flow separation on the suction surface of flap disappears. We guess the fluid flowing through the smaller gap does not supplement the wake of the wing, but flows along the flap boundary layer.

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(**e**) Xr = 95%

**Figure 16.** Limiting streamline and static pressure contours on suction surface for the two-element wingsail at (a) Xr=75% (b) Xr=80% (c) Xr=85% (d) Xr=90% and (e) Xr=95% with *α*=15°, d=15°. **Figure 16.** Limiting streamline and static pressure contours on suction surface for the two-element wingsail at (**a**) Xr = 75% (**b**) Xr = 80% (**c**) Xr = 85% (**d**) Xr = 90% and (**e**) Xr = 95% with α = 15◦ , d = 15◦ .

#### 3.2.3. Velocity Magnitude Contours 3.2.3. Velocity Magnitude Contours

It can be seen from Figure 17 that the suction surface of the wing has a large flow separation at *α*=15° with low camber. At Xr=85%, the fluid flowing through the slot complements the flow It can be seen from Figure 17 that the suction surface of the wing has a large flow separation at α = 15◦ with low camber. At X<sup>r</sup> = 85%, the fluid flowing through the slot complements the flow separation of the wing wake and the flap suction surface. There is no vortex in the mid-span of the wingsail. The slot jet can be observed clearly at X<sup>r</sup> = 90%. As a result of the reduced slot width due to the rotating axis position of the flap backward, the slot jet only divides the vortex of the wing wake and there is a large-scale flow separation on the suction surface of the flap, which causes deep stall of the

experiment in 2016.

flap. This phenomenon has also been observed and described in Biber [27] and Chapin [18]. Because of the smaller slot width at X<sup>r</sup> = 95%, the slot jet only flows along the boundary layer of the flap, which has little effect on the separation flow of the wing wake. If the slot is further reduced or not set, the flap setting may aggravate the separation of the wing wake, such as the research of the hybrid sail designed by Qiao Li [14]. However, the forward movement of the rotating axis position of the flap is limited by the flap deflection angle. As shown in Figure 18, when the rotating axis position of the flap moves forward from 90% to 85% at α= 6 ◦ , the large-scale flow separation occurs on the suction surface of the flap, as the phenomenon seen by Fiumara [19] in the two-element sail experiment in 2016. the flap. This phenomenon has also been observed and described in Biber [27] and Chapin [18]. Because of the smaller slot width at Xr = 95%, the slot jet only flows along the boundary layer of the flap, which has little effect on the separation flow of the wing wake. If the slot is further reduced or not set, the flap setting may aggravate the separation of the wing wake, such as the research of the hybrid sail designed by Qiao Li [14]. However, the forward movement of the rotating axis position of the flap is limited by the flap deflection angle. As shown in Figure 18, when the rotating axis position of the flap moves forward from 90% to 85% at *α*= 6°, the large-scale flow separation occurs on the suction surface of the flap, as the phenomenon seen by Fiumara [19] in the two-element sail experiment in 2016. and there is a large-scale flow separation on the suction surface of the flap, which causes deep stall of the flap. This phenomenon has also been observed and described in Biber [27] and Chapin [18]. Because of the smaller slot width at Xr = 95%, the slot jet only flows along the boundary layer of the flap, which has little effect on the separation flow of the wing wake. If the slot is further reduced or not set, the flap setting may aggravate the separation of the wing wake, such as the research of the hybrid sail designed by Qiao Li [14]. However, the forward movement of the rotating axis position of the flap is limited by the flap deflection angle. As shown in Figure 18, when the rotating axis position of the flap moves forward from 90% to 85% at *α*= 6°, the large-scale flow separation occurs on the suction surface of the flap, as the phenomenon seen by Fiumara [19] in the two-element sail

*J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 13 of 16

separation of the wing wake and the flap suction surface. There is no vortex in the mid-span of the wingsail. The slot jet can be observed clearly at Xr = 90%. As a result of the reduced slot width due to

separation of the wing wake and the flap suction surface. There is no vortex in the mid-span of the

*J. Mar. Sci. Eng.* **2019**, *7*, x FOR PEER REVIEW 13 of 16

and there is a large-scale flow separation on the suction surface of the flap, which causes deep stall of

the rotating axis position of the flap backward, the slot jet only divides the vortex of the wing wake

Figure 17. Velocity magnitude contours at mid-span of wingsail at (a) Xr= 85% (b) Xr= 90% and (c)Xr= 95% with α=15°,d=15° **Figure 17.** Velocity magnitude contours at mid-span of wingsail at (**a**) X<sup>r</sup> = 85% (**b**) X<sup>r</sup> = 90% and (**c**)Xr = 95% with α = 15◦ , d = 15◦ (**c**) Xr = 95% Figure 17. Velocity magnitude contours at mid-span of wingsail at (a) Xr= 85% (b) Xr= 90% and (c)Xr= 95% with α=15°,d=15°

(**b**) Xr = 90% **Figure 18.** *Cont.*

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**Figure 18.** Velocity magnitude contours at mid-span of wingsail at (a) Xr= 85% (b) Xr= 90% and (c)Xr= 95% with α=6°,d=25°. **Figure 18.** Velocity magnitude contours at mid-span of wingsail at (**a**) X<sup>r</sup> = 85% (**b**) X<sup>r</sup> = 90% and (**c**) Xr = 95% with α = 6 ◦ , d = 25◦ .

#### **4. Conclusions 4. Conclusions**

**References** 

By studying the influence of flap geometric parameters on the aerodynamic characteristics of two-element wingsail under steady and unsteady conditions, two-dimensional and three-dimensional related parameters were simulated using the same Reynolds number (*Re* =5×105). By studying the influence of flap geometric parameters on the aerodynamic characteristics of two-element wingsail under steady and unsteady conditions, two-dimensional and three-dimensional related parameters were simulated using the same Reynolds number (*Re* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup><sup>5</sup> ).

The 2D simulation results show that, when the rotating axis position of the flap is located at 85% of the wing chord, the thickening flap leads to an increase of the leading-edge radius which decreases the pressure coefficient suction peak and has postponed the stall of the wingsail for high camber. It reflects the nonlinear coupling effect between wingsail camber and flap thickness. When the rotating axis of the flap is located at the 75% of the wing chord, the stall angle is delayed with the increase of the flap deflection angle at low camber. When selecting the geometric parameters of the flap, factors such as the position of the flap rotation axis, the flap deflection angle, and the flap thickness need to be considered comprehensively. The 2D simulation results show that, when the rotating axis position of the flap is located at 85% of the wing chord, the thickening flap leads to an increase of the leading-edge radius which decreases the pressure coefficient suction peak and has postponed the stall of the wingsail for high camber. It reflects the nonlinear coupling effect between wingsail camber and flap thickness. When the rotating axis of the flap is located at the 75% of the wing chord, the stall angle is delayed with the increase of the flap deflection angle at low camber. When selecting the geometric parameters of the flap, factors such as the position of the flap rotation axis, the flap deflection angle, and the flap thickness need to be considered comprehensively.

The 3D simulation mainly studies the influence of the flap rotating axis position and the flap deflection angle on the stall characteristics of the wingsail. When stall has not yet occurred with low camber, the rotating axis position of the flap has little effect on the lift coefficient, while stall has occurred, the lift coefficient increases first and then reduces with the rotating axis position of the flap moving backward. The flow separation of the suction surface of the wing expands from the root to the top and the return area becomes larger, especially from the 80% to the 85%, the lift coefficient drops suddenly. This is caused by the flow separation between the wing wake and the flap suction surface. At high camber with AOA=6°, the lift coefficient always increases with the position of the flap rotation axis, especially from 85% to 95%, the lift coefficient suddenly rises, which is caused by the disappearance of large-scale flow separation of the flap suction surface. The 3D simulation mainly studies the influence of the flap rotating axis position and the flap deflection angle on the stall characteristics of the wingsail. When stall has not yet occurred with low camber, the rotating axis position of the flap has little effect on the lift coefficient, while stall has occurred, the lift coefficient increases first and then reduces with the rotating axis position of the flap moving backward. The flow separation of the suction surface of the wing expands from the root to the top and the return area becomes larger, especially from the 80% to the 85%, the lift coefficient drops suddenly. This is caused by the flow separation between the wing wake and the flap suction surface. At high camber with AOA = 6 ◦ , the lift coefficient always increases with the position of the flap rotation axis, especially from 85% to 95%, the lift coefficient suddenly rises, which is caused by the disappearance of large-scale flow separation of the flap suction surface.

Therefore, the slot width is an important factor affecting the flow separation of the wing wake and the suction surface of the flap, where size is affected by the rotating axis position of the flap and the flap deflection angle. When the flap deflection angle is adjusted to obtain a large lift coefficient, the restriction of the rotating axis position of the flap must be considered to ensure a reasonable stall angle range. Therefore, the slot width is an important factor affecting the flow separation of the wing wake and the suction surface of the flap, where size is affected by the rotating axis position of the flap and the flap deflection angle. When the flap deflection angle is adjusted to obtain a large lift coefficient, the restriction of the rotating axis position of the flap must be considered to ensure a reasonable stall angle range.

**Author Contributions:** conceptualization, C.L. and H.W.; investigation, C.L. and H.W.; methodology, C.L. and P.S.; software, C.L.; writing—original draft preparation, C.L.; writing—review and editing, H.W.; supervision, P.S. **Author Contributions:** Conceptualization, C.L. and H.W.; investigation, C.L. and H.W.; methodology, C.L. and P.S.; software, C.L.; writing—original draft preparation, C.L.; writing—review and editing, H.W.; supervision, P.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China,51709165, Research **Funding:** This research was funded by National Natural Science Foundation of China, 51709165, Research Funds of Jiangsu Maritime Institute, 014070, kjcx-1907.

Funds of Jiangsu Maritime Institute,014070, kjcx-1907. **Conflicts of Interest:** The authors declare no conflict of interest. **Conflicts of Interest:** The authors declare no conflict of interest.

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