Numerical Investigation of Aerodynamic Characteristics of Biomimetic Wingsails for Unmanned Surface Vehicles

Abstract

The aerodynamic characteristics of wingsails on unmanned surface vessels (USVs) play a crucial role in enhancing propulsion performance. Two-dimensional wingsail airfoils of owl wings, merganser wings, seagull wings, and teal wings were obtained through biomimetic design. Then a numerical investigation was conducted on the four biomimetic airfoils using the SST k-ω turbulence model to evaluate their aerodynamic performance. The results demonstrate that the bionic merganser airfoil exhibits the most superior lift performance, achieving a maximum lift coefficient of 3.21 across angles of attack ranging from 0° to 60° among the four biomimetic wingsails, and the bionic seagull airfoil is second, while the bionic teal airfoil shows the weakest lift characteristics. As the angle of attack increases, flow separation emerges at the trailing edge of the biomimetic airfoils, leading to the formation of separation vortices. For example, the backflow zone on the suction surface of the biomimetic merganser wingsail, caused by unsteady flow, persists at an angle of attack of 16 degrees. The vortex structure at the trailing edge of the biomimetic merganser wingsail periodically generates, develops, detaches, and dissipates, which affects the backflow of the suction surface of the wingsail and interferes with its lift coefficient. The study provides an excellent reference for selecting high-performance USV wingsails.

1. Introduction

The wingsail is a key power equipment for achieving unlimited endurance of unmanned surface vehicles (USVs), and it is also one of the main factors affecting the safety of USVs navigation [1]. It plays a key role in meteorological monitoring, unmanned surface vehicle route planning, and autonomous navigation, directly affecting unmanned surface vehicle performance parameters such as navigation attitude, speed, and endurance mileage [2,3]. NEWSROOM [4] reported that the “SURVEYOR” USV had been developed by the American company Wind Power, powered by wind energy, with a speed of 5 km per hour as shown in Figure 1. It is particularly suitable for conducting marine surveys, meteorological monitoring, or military reconnaissance activities in severe weather conditions. The aerodynamic characteristics of wingsails determine the energy consumption, speed, and endurance of USV, directly affecting their ability to cope with complex sea conditions, ensure navigation safety, and achieve remote meteorological monitoring.

The biggest obstacle to the aerodynamic performance of wingsails at present is how to further improve the propulsion force of the sails at different wind angles [5]. According to the principles of bionics, drawing on the structural configuration of some bird wings can effectively improve the aerodynamic performance of wingsails. The wings of birds such as seagulls, owls, mergansers, and teals [6,7,8,9] have undergone long-term biological evolution to help them fly efficiently. Therefore, the structure of their wings became the focus of attention in the design of biomimetic sails in this study.

Indeed, the application of biomimicry to airfoil design is widespread in aerodynamic studies. Research by Fish et al. [10,11] revealed that humpback whale flippers facilitate rapid roll maneuvers and sudden course changes beneath the surface. Stemming from this research, bioinspired designs replicating the tubercle-like bumps characteristic of humpback flippers were developed and implemented on wind turbine blades [12,13,14], airfoil models [15,16,17], and rudders [18,19], significantly postponing the onset of stall.

Many aquatic and aerial organisms have evolved non-smooth surface structures featuring protrusions or depressions—exemplified by dolphin skin, shark dermal denticles, and the tergal plates of certain terrestrial insects [20]. Based on these biological paradigms, researchers have developed three categories of biomimetic non-smooth surfaces: compliant walls [21], groove or riblet arrays [22], and dimpled surfaces [23]. Dimpled surfaces primarily harness internal separation vortices to elevate the kinetic energy within the boundary layer, advancing the boundary layer transition location and consequently enhancing its resistance to flow separation [24,25,26]. Classic applications include golf ball dimple patterns for optimized flight and underbody dimple configurations for automotive drag reduction. Currently, dimpled blades are used in high-speed and high-load diffuser cascades to reduce aerodynamic losses [27,28,29].

During investigations into centrifugal fan noise, researchers noted the characteristically soft and fluffy nature of long-eared owl wing feathers [30]. By studying the acoustic dampening attributes of these surfaces, the biomimetic snail shell has been designed, which significantly reduces noise levels [31,32]. Additionally, inspired by the sawtooth pattern prevalent along the trailing edges of avian wings, scientists implemented analogous serrations on wind turbine blades and propeller trailing edges, resulting in a marked decrease in blade noise generation [33,34,35].

Hersh et al. [36] first published the results of noise reduction in blades modified according to the comb structure of owl wings. Liu et al. [6] employed three-dimensional laser scanning to analyze the aerodynamic properties of bird wings including those of seagulls, owls, mergansers, and teals during flapping-wing flight. They subsequently designed a biomimetic flapping-wing structure inspired by these avian models and conducted preliminary analyses of its aerodynamic characteristics, achieving promising results. Klän et al. [37] designed a biomimetic wing based on the geometric shape of an owl’s wings, where the feather structure of an owl’s wings is approximately a velvet-like surface. The purpose was to study the influence of feather surface filaments on the overall flow field of the wing configuration. Zhu et al. [8] applied this bioinspired model to propeller design, demonstrating its significant efficacy in suppressing bubble formation on propeller surfaces and enhancing propulsion efficiency. Wang et al. [38] and Chattaraj et al. [39] introduced the application of biomimetic wings in the aerodynamic design of flapping wings and achieved good results.

Biomimetic design of wingsails has also become a research focus for scholars in recent years. Richard [40] designed a biomimetic sail based on the thin-film surface of fly wings. The biomimetic sail incorporated the retractable mechanism of bat forelimbs and achieved favorable energy-saving effects. Nippon Yusen Kabushiki Kaisha (NYK) drew on the bionic structure of insect wings and proposed installing eight retractable arc-shaped outer-edge blades on the NYK2030 Super Eco Concept Ship, allowing the blades to be retracted under heavy sea conditions. Horiuchi et al. [41] developed a foldable kite sail named “Manta” by mimicking the structure of kites, which consisted of a pair of delta wings and a supporting strut. Based on the design, Germany’s Beluga Group and SkySails [42] developed a rectangular kite sail to propel ships. It is predicted that after equipping the bulk carrier MV Beluga SkySails with this kite sail, the ship’s fuel consumption can be reduced by an average of 10–35% per year, with a maximum fuel saving of up to 50%. However, studies on wingsails designed by biomimicking bird wings remain scarce.

Based on prior studies, the biomimetic wing models derived from seagulls, owls, mergansers, and teals were adopted to design the wingsail for USVs. Through analysis of its aerodynamic performance and flow field, an optimal biomimetic wingsail was identified, thereby further improving the propulsion efficiency of wingsails.

2. Numerical Model

2.1. Conventional Wingsail

In 2010, wingsail propulsion with exceptional aerodynamic performance further accelerated the adoption of wingsails in small vessels such as USVs [43]. Subsequent developments include the A-Tirma G2 prototype vessel [44], the Atlantis catamaran [45], the Submaran S10 USV [46], and the Datamaran catamaran [46]. NACA airfoils remained dominant in the wingsails on USVs. Therefore, the NACA0018 airfoil was selected as the baseline configuration.

The Delft University Wind Tunnel Laboratory in the Netherlands [47] conducted comprehensive experiments on the NACA 0018 airfoil at low-to-moderate Reynolds numbers, yielding detailed experimental data on lift and drag. Based on the geometric parameters, the NACA0018 airfoil was constructed as shown in Figure 2.

2.2. Avian Wing Model

Birds flying at low altitudes have evolved wing configurations that enable efficient and quiet flight through natural selection. Consequently, numerous researchers have investigated avian wing structures. Liu et al. [6] measured surface characteristics of seagull, merganser, teal, and owl wings. Figure 2 summarizes two-dimensional airfoils derived from seagull, merganser, teal, and owl wings, revealing significant differences in thickness and camber compared to the conventional NACA airfoil.

Table 1. Comparison of operating Reynolds number ranges between wingsails and bird flight.

Airfoil Type	Operating Reynolds Number Range
USV Wingsail	1 × 105–10 × 105
Seagull wing	0.5 × 104–3 × 105
Merganser wing	0.6 × 105–3 × 105
Teal wing	0.5 × 105–2 × 105
Owl wing	0.4 × 105–0.6 × 105

summarizes the comparison of the Reynolds number ranges between wingsails and bird flight. The results show that the Reynolds numbers of both are of the same order of magnitude and both fall within the low Reynolds number regime. Therefore, applying biomimetic bird wing profiles to the design of wingsails can, on the one hand, optimize the wingsail airfoil and significantly improve the thrust that conventional symmetric wingsails do not possess. On the other hand, it can limit the side thrust generated by the wingsail airfoil, thereby reducing the heel and roll of the unmanned surface vehicle.

In the investigation, the geometric features measured by Liu et al. [6] for seagull, merganser, teal, and owl wings were applied to study the wingsail sections of USVs.

2.3. Biomimetic Wingsail

The design of biomimetic wingsails constitutes a critical component of the research. Given that the study focuses exclusively on the impact of blade cross-sectional profiles on aerodynamic performance, the primary geometric features of the biomimetic wingsails align with those of conventional wingsails. For example, their chord length was 0.35 m. Their differences were only reflected in the shape of the airfoil profile. According to Liu et al. [6], the thickness near x/c = 1.0 for merganser and owl wings can be approximated as zero. To facilitate the design and analysis of the biomimetic wingsail geometry, a minor thickness was intentionally added in this region. When the chord length of the airfoil is 1, the airfoil profile data points for merganser wingsail are listed in

Table 2. Airfoil profile data sets for merganser wingsail.

Suction Side-Merganser Wingsail		Pressure Side-Merganser Wingsail
X-axis coordinate	Y-axis coordinate	X-axis coordinate	Y-axis coordinate
0.02	0.061224	0.95	0.040626
0.04	0.091109	0.9	0.070991
0.06	0.115921	0.8	0.093725
0.1	0.148805	0.7	0.090888
0.15	0.176184	0.6	0.079676
0.2	0.192857	0.5	0.064543
0.3	0.209123	0.4	0.046026
0.32	0.210176	0.32	0.027552
0.4	0.213624	0.3	0.022495
0.5	0.21128	0.2	−0.00688
0.6	0.20028	0.15	−0.02201
0.7	0.175536	0.1	−0.03502
0.8	0.132766	0.06	−0.04083
0.9	0.072745	0.04	−0.04035
0.95	0.040626	0.02	−0.03385
1	0	0	0

. Figure 2 illustrates the two-dimensional geometries of biomimetic airfoils based on morphology data from seagull, merganser, teal, and owl wings. For clarity, the biomimetic wingsail adopting a seagull wing structure is abbreviated as the “seagull wingsail”, while the remaining three configurations are designated as the “merganser wingsail”, “teal wingsail”, and “owl wingsail”, respectively.

2.4. Computational Domain and Meshing

The computational domain for the wingsail is illustrated in Figure 3. To mitigate boundary effects on the external flow field, the domain extended 12c upstream, 20c downstream, and 12c laterally, forming a rectangular region (32c × 24c). The front and lower boundaries were configured as velocity inlets with a turbulence intensity of 1% and a turbulent viscosity ratio of 7. The turbulence model was the Transition SST k-ω turbulence model [48], and the intermittency factor for fully turbulent conditions was set to 1. The outlet boundary was defined as a pressure outlet with a total pressure of 101,325 Pa. The airfoil surface adopted the no-slip wall boundary condition. For unsteady simulations, the time step was set to 1.6 × 10⁻⁴ s to maintain a CFL number (CFL = vΔt/Δx) of 1 [49]. Convergence can be achieved by iterating no more than 10 times per step length. The convergence residual criterion for the grid calculation was 1 × 10⁻³.

In CFD computations, mesh quality directly determines numerical accuracy and computational efficiency. Unstructured meshes for the 2D computational domain were generated using ANSYS ICEM 18.2 as shown in Figure 4. To satisfy turbulence model requirements for boundary layer resolution (ensuring y⁺ ≤ 1), the first-layer grid height on the wingsail surface was set to 0.85 × 10⁻⁵c, featuring the boundary layer growth rate of 1.05 with 20 layers. The total mesh count approximated 1.24 × 10⁶. The Reynolds number was 2.4 × 10⁵. Since the wingsail operates in the low Reynolds number regime, the working fluid can be assumed to be incompressible.

The simulation software used in this study was FLUENT 18.2. This is because FLUENT is based on the conservative finite volume method in the numerical simulation of aerodynamic flows. It is equipped with both density-based and pressure-based solvers, a complete series of aerodynamic turbulence models, high-order shock-capturing schemes, and high-precision boundary layer meshing. It also fully supports unsteady flow and fluid–structure interaction, ensuring accuracy and stability in aerodynamic analysis.

2.5. Mesh Independence Check

To ensure that the number of mesh does not affect the aerodynamic characteristics of the wingsail, four distinct mesh resolutions (6.3 × 10⁵, 9.5 × 10⁵, 1.24 × 10⁶, and 1.54 × 10⁶) were evaluated with the Transition SST k-ω turbulence model. Figure 5 presents the lift and drag coefficients of the wingsail airfoil under Re = 2.4 × 10⁵. As shown in Figure 5, the drag coefficient remains nearly constant with increasing mesh density, while the lift coefficient exhibits minor fluctuations within 0.5%, meeting numerical accuracy requirements. Considering the computational cost associated with higher mesh counts, the optimal mesh count of 1.24 × 10⁶ was selected for the 2D computational domain in this study.

2.6. Model Validation

Prior to simulating the biomimetic airfoil, the fundamental verification of the numerical methodology was conducted. In this study, the accuracy of the Transition SST k-ω turbulence model for predicting performance metrics and capturing flow field details was validated with the NACA0018 airfoil. Experimental data from Delft University’s Wind Tunnel Laboratory [48] corresponding to the NACA0018 airfoil was employed for model validation. The experimental Reynolds number was 1.6 × 10⁵, which is the same as that used in the numerical validation. The mesh topology adhered to the same specifications as those used for the biomimetic airfoil model.

Figure 6 compares the lift and drag characteristics between the experimental data [47] and numerical results for the NACA0018 airfoil at Re = 1.6 × 10⁵. As shown in Figure 6, the lift and drag coefficients predicted by the Transition SST k-ω turbulence model exhibit good agreement with the experimental data. At higher angles of attack, the experimental lift coefficient slightly falls below the numerical predictions, while the drag coefficient displays fluctuations. This discrepancy arises because increased angles of attack significantly influence boundary layer transition and flow separation due to factors such as freestream turbulence intensity and surface roughness. The Transition SST k-ω model, incorporating two additional transport equations, effectively captures the boundary layer transition process, yielding results closely aligned with the experimental values [47,50]. It demonstrates the accuracy of the adopted numerical methodology in predicting aerodynamic performance. In the present numerical study, the Reynolds number employed was 2.4 × 10⁵. Although the two values differ, they both fall within the low Reynolds number range, and the results obtained using the same numerical simulation method are considered reliable.

Figure 7 illustrates the correspondence between the laminar separation bubble location predicted by the Transition SST k-ω model and Nakano’s experimental results [51] at α = 0°. From Figure 7, the model predicts the laminar separation point (S point) at 0.512c and the reattachment point (RA point) at 0.78c. Although Nakano’s experimental measurements report relatively larger chord-length positions, the locations of the separation and reattachment points for the NACA0018 airfoil generally align with the Transition SST k-ω model predictions. It indicates that it is relatively accurate to predict the positions of laminar separation bubbles and boundary layer transitions by the Transition SST k-ω turbulence model.

3. Results and Discussions

3.1. Aerodynamic Performance of Wingsail Airfoil

To demonstrate the aerodynamic performance of biomimetic wingsails, the NACA0018 airfoil was selected for comparison, and the aerodynamic performance curves are shown in Figure 8. The aerodynamic performance parameters of the five wingsail airfoils at different angles of attack are shown in

Table 3. Comparison of aerodynamic performance parameters of five wingwail airfoils at different angles of attack.

	Merganser Wingsail			Owl Wingsail			Seagull Wingsail			Teal Wingsail			NACA0018 Wingsail
α	CL	CD	CL/CD	CL	CD	CL/CD	CL	CD	CL/CD	CL	CD	CL/CD	CL	CD	CL/CD
0	1.40	0.09	15.79	0.09	0.04	2.22	1.07	0.04	25.56	0.70	0.05	15.00	0.07	0.05	1.39
4	1.89	0.10	18.33	0.36	0.07	5.57	1.28	0.06	22.24	0.91	0.09	9.85	0.16	0.02	6.56
8	2.33	0.11	21.74	1.15	0.09	12.94	1.38	0.10	14.39	0.98	0.11	8.75	0.75	0.02	32.58
12	2.78	0.18	15.66	1.92	0.10	18.27	1.89	0.18	10.25	1.61	0.19	8.41	1.03	0.03	30.04
16	3.10	0.24	13.04	2.40	0.17	14.31	2.19	0.36	6.14	1.89	0.27	6.98	0.98	0.08	12.01
20	3.31	0.33	10.09	2.17	0.57	3.78	2.33	0.51	4.55	2.24	0.40	5.58	1.33	0.48	2.79
24	3.06	0.79	3.85	2.31	0.75	3.09	2.57	0.78	3.28	2.51	0.57	4.42	1.45	0.70	2.07
28	3.13	1.07	2.91	2.45	0.84	2.92	2.66	0.96	2.78	2.26	0.70	3.23	1.63	0.79	2.06
32	3.03	1.26	2.41	2.38	0.98	2.43	2.61	1.07	2.43	2.24	1.17	1.92	1.70	1.07	1.59
36	2.92	1.52	1.92	2.45	1.12	2.19	2.57	1.24	2.08	1.96	1.54	1.27	1.87	1.06	1.75
40	2.80	1.73	1.62	2.57	1.24	2.08	2.66	1.45	1.84	2.10	1.68	1.25	2.19	1.91	1.15
44	2.89	1.96	1.48	2.68	1.54	1.74	2.47	2.01	1.23	2.10	2.10	1.00	2.38	2.19	1.09
48	2.57	2.57	1.00	2.85	2.10	1.36	2.38	2.43	0.98	1.96	2.14	0.92	2.19	2.29	0.96
52	2.19	2.43	0.90	2.94	2.57	1.15	2.19	2.57	0.85	1.91	2.41	0.79	2.10	2.57	0.82
56	2.10	2.89	0.73	2.47	2.71	0.91	2.10	2.80	0.75	1.87	2.65	0.71	2.01	2.94	0.68
60	1.96	3.27	0.60	2.24	3.03	0.74	2.10	3.03	0.69	1.85	2.92	0.63	1.91	3.17	0.60

. From Table 3 and Figure 8a, it can be observed that among the four biomimetic wingsails, the merganser wingsail exhibits the highest lift coefficient within an angle of attack (AOA) range of 0–45°, reaching a maximum value of 3.21, which highlights its excellent lift performance. When the AOA exceeds 45°, the lift coefficient of the merganser wingsail decreases rapidly but remains second only to that of the owl wingsail. The seagull wingsail demonstrates relatively stable changes in its lift coefficient, with the smallest reduction rate at the initial stall stage (at α = 28°) being merely 1.77%. After the stall occurs, the seagull wingsail still maintains a high lift coefficient, closely approaching those of the merganser and owl wingsails. At small angles of attack, as the AOA increases, the lift coefficient of the owl wingsail rises more quickly. Following the stall occurrence, although there is a slight drop initially, a significant increase follows subsequently. Specifically, it peaks at 2.95 when the AOA reaches 52°, marking the highest value among all four biomimetic wingsails under identical conditions.

Among these biomimetic wingsails, the teal wingsail shows the poorest lift performance. After stall (within an AOA range of 24–36°), the teal wingsail exhibits the largest reduction in lift coefficient, which amounts to 21.86%. When the AOA surpasses 40°, the lift coefficient of the teal wingsail falls below that of the NACA0018 wingsail. Therefore, within the AOA range of 0–60°, the merganser wingsail delivers superior lift performance followed by the seagull wingsail, while the teal wingsail performs worst.

Figure 8b presents the curve of the drag coefficient with angle of attack for the biomimetic wingsails. As shown in Table 3 and Figure 8b, within the AOA range of 0–60°, four biomimetic wingsails exhibit a generally consistent trend in drag coefficient. At small angles of attack, the drag coefficients are relatively low and vary only slightly. However, once the AOA exceeds 20°, the drag coefficient increases rapidly with increasing AOA. Among them, the merganser wingsail maintains the higher drag coefficient, whereas the owl wingsail demonstrates more pronounced fluctuations in its drag coefficient.

Figure 8c illustrates the lift-to-drag ratio (C_L/C_D) as a function of AOA for the biomimetic wingsails. From Table 3 and Figure 8c, it can be observed that within the AOA range of 0–24°, both the seagull and teal wingsails show a decreasing trend in lift-to-drag ratio when AOA increases. And the teal wingsail exhibits the lowest lift-to-drag values among the designs. In contrast, the lift-to-drag ratio of the merganser and owl wingsails increases first and then decreases with the increase in AOA. At the same time, the merganser wingsail achieves a higher lift-to-drag ratio compared to the others. When the angle of attack exceeds 24°, all four biomimetic wingsails follow a similar declining trend in lift-to-drag ratio with further increases in AOA.

It can be seen that before the stall occurs, the lift coefficient of the biomimetic wingsail dominates. After the stall occurs, the drag coefficient increases sharply. As the angle of attack increases, the lift-to-drag ratio gradually decreases, and the lift coefficient and drag coefficient become more balanced. Therefore, when the angle of attack is 0–24°, the propulsion performance of biomimetic wingsails should be mainly based on the lift coefficient. When the angle of attack is between 24° and 60°, the propulsion performance of biomimetic wingsails should consider both lift and drag coefficients. It is because the drag coefficient increases rapidly with the increase in angle of attack.

To more clearly analyze the effects of lift and drag generated by the wingsail on its thrust and side thrust acting on the USV, a force analysis diagram of the wingsail on the USV is constructed, as shown in Figure 9. The positive direction of the X-axis is the bow direction, and the positive direction of the Y-axis is the starboard direction of the vessel. The wind speed relative to the vessel is defined as v₀, and the angle between the wind direction and the bow is defined as the relative wind angle, denoted by θ. For instance, the relative wind angle is 0° when the wind is from the bow direction, increases counterclockwise when viewing the vessel from above, and reaches 180° when the wind is from the stern direction. By resolving the combined force of lift F_L and drag F_D, the thrust F_x along the vessel’s heading and the side thrust F_Y perpendicular to the vessel’s heading are obtained.

The calculation formulas for the propulsive force F_x and side force F_Y are as follows:

$$F_{\mathrm{X}}=F_{\mathrm{L}}sin\theta -F_{\mathrm{D}}cos\theta$$

(1)

$$F_{\mathrm{Y}}=F_{\mathrm{L}}cos\theta +F_{\mathrm{D}}sin\theta$$

(2)

The propulsive force coefficient C_X and the side force coefficient C_Y of the wingsail are respectively given by

$$C_{\mathrm{X}}={\displaystyle \frac{F_{\mathrm{X}}}{0.5\rho v_0^{2}c}}=C_{\mathrm{L}}sin\theta -C_{\mathrm{D}}cos\theta$$

(3)

$$C_{\mathrm{Y}}={\displaystyle \frac{F_{\mathrm{Y}}}{0.5\rho v_0^{2}c}}=C_{\mathrm{L}}cos\theta +C_{\mathrm{D}}sin\theta$$

(4)

Based on the lift coefficient and drag coefficient data of the merganser wingsail in Table 3,

Table 4. Maximum thrust coefficient and corresponding performance parameters of the wingsail at different relative wind angles.

θ (°)	α (°)	CL	CD	CX_max	CY	θ (°)	α (°)	CL	CD	CX_ max	CY
0	0	1.4	0.09	−0.09	1.4	95	20	3.31	0.33	3.3262	0.0403
5	8	2.33	0.11	0.0935	2.3307	100	20	3.31	0.33	3.317	−0.2498
10	12	2.78	0.18	0.3055	2.769	105	28	3.13	1.07	3.3003	0.2234
15	16	3.1	0.24	0.5705	3.0565	110	44	2.89	1.96	3.3861	0.8534
20	16	3.1	0.24	0.8347	2.9951	115	44	2.89	1.96	3.4476	0.555
25	20	3.31	0.33	1.0998	3.1393	120	48	2.57	2.57	3.5107	0.9407
30	20	3.31	0.33	1.3692	3.0315	125	48	2.57	2.57	3.5793	0.6311
35	20	3.31	0.33	1.6282	2.9007	130	48	2.57	2.57	3.6207	0.3168
40	20	3.31	0.33	1.8748	2.7477	135	60	1.96	3.27	3.6982	0.9263
45	20	3.31	0.33	2.1072	2.5739	140	60	1.96	3.27	3.7648	0.6005
50	20	3.31	0.33	2.3235	2.3804	145	60	1.96	3.27	3.8028	0.2701
55	20	3.31	0.33	2.5221	2.1689	150	60	1.96	3.27	3.8119	−0.0624
60	20	3.31	0.33	2.7015	1.9408	155	60	1.96	3.27	3.792	−0.3944
65	20	3.31	0.33	2.8604	1.6979	160	60	1.96	3.27	3.7432	−0.7234
70	20	3.31	0.33	2.9975	1.4422	165	60	1.96	3.27	3.6659	−1.0469
75	20	3.31	0.33	3.1118	1.1754	170	60	1.96	3.27	3.5607	−1.3624
80	20	3.31	0.33	3.2024	0.8998	175	60	1.96	3.27	3.4284	−1.6675
85	20	3.31	0.33	3.2686	0.6172	180	60	1.96	3.27	3.27	−1.96
90	20	3.31	0.33	3.31	0.33

and Figure 10 were plotted to show the maximum thrust coefficient C_{X_max} and the corresponding side thrust coefficient C_Y generated by the merganser wingsail on the USV. It can be seen from Table 4 and Figure 10 that when the relative wind angle is below 25°, the maximum thrust coefficient produced by the wingsail increases with the rise in the angle of attack, while the corresponding side thrust coefficient also increases, which will intensify the heeling of the USV. When the relative wind angle ranges from 30° to 100°, the thrust coefficient of the wingsail is optimal at an angle of attack of 20°, and the maximum thrust coefficient keeps increasing with the rise in the relative wind angle, whereas the corresponding side thrust coefficient decreases continuously. The maximum thrust coefficient reaches 3.33 at a relative wind angle of 95°, with the side thrust coefficient close to 0, indicating the best comprehensive propulsion performance of the wingsail.

When the relative wind angle ranges from 100° to 135°, the maximum thrust coefficient continues to increase with the rise in the angle of attack, and the side thrust coefficient basically stays between 0 and 1, maintaining a small heeling moment; thus, the wingsail also achieves favorable propulsion performance. When the relative wind angle exceeds 130°, the maximum thrust coefficient first increases and then decreases with the increase in the relative wind angle, reaching the optimum at 150°, where the side thrust coefficient is close to 0.

3.2. Pressure Load Distribution of Bio-Wingsail Airfoil

To analyze the reasons for differences in lift coefficient among biomimetic wingsails, Figure 11 presents the pressure load distributions of the biomimetic wingsails at different angles of attack, compared with the NACA0018 airfoil. As shown in Figure 11 the merganser wingsail exhibits the largest area with the pressure coefficient curve at α = 4°, indicating that it generates the highest lift force, followed by the seagull wingsail. In contrast, the owl wingsail demonstrates the higher pressure coefficient on its suction surface than on its pressure surface at the rear-middle section, resulting in significant adverse pressure gradients and consequently the lowest lift coefficient. Additionally, the maximum negative pressure coefficient of the teal wingsail occurs at the mid-chord section of its suction surface, which correlates with its specific airfoil configuration (as illustrated in Figure 2).

As the AOA increases to 8°, the pressure coefficient area of the merganser wingsail further expands, with its most negative pressure coefficient reaching −3.23 near the leading edge of the suction surface, substantially enhancing its lift coefficient. Meanwhile, the negative pressure coefficient of the owl wingsail also rapid increase (up to −2.8) at the leading edge of its suction surface. And the previously observed adverse pressure gradients diminish at the rear-middle section. Consequently, the pressure coefficient area of the owl wingsail surpasses that of the teal wingsail. At α = 12°, the pressure coefficient area of the owl wingsail exceeds that of the seagull wingsail, highlighting its exceptional sensitivity to changes in angle of attack regarding lift performance.

At α = 16°, although the merganser wingsail still maintains the largest pressure coefficient area, the owl wingsail begins to show favorable pressure loading characteristics along the leading edge. However, a pronounced negative pressure emerges at the trailing edge of the suction surface of the owl wingsail, suggesting susceptibility to early stall due to strong adverse pressure gradients. On the other hand, the negative pressure coefficient of the suction surface of the seagull wingsail showed significant fluctuations at the rear-middle section, but its pressure coefficient area remained relatively large, exhibiting delayed stall phenomena to demonstrate good stall performance.

When the angle of attack increased to 20°, there was a significant change in the pressure load on the suction surface of the four biomimetic wingsails. At the trailing edge of the airfoil, both the suction and pressure surfaces of the merganser wingsail experience sharp increases in negative pressure, effectively eliminating any lifting contribution from this region and resulting in a stall phenomenon of the merganser wingsail. Combined with Figure 8, it can be observed that at an angle of attack of 20°, the cambered trailing-edge configuration of the merganser wingsail airfoil leads to early stall of the overall airfoil. Conversely, the owl wingsail exhibits a marked reduction in negative pressure at the trailing edge of its suction surface, which greatly enhances the pressure load on the trailing edge of the airfoil. It is corroborated by the corresponding shifts in the lift coefficient curves presented in Figure 8a.

In contrast, the NACA0018 airfoil exhibits a gradual stall phenomenon across the range of angles of attack, which is related to its symmetric airfoil. However, its overall pressure loading is relatively low, indicating inferior lift performance.

3.3. Unsteady Flow Characteristics of Bio-Wingsail Airfoil

The unsteady flow simulations were conducted by the Transition SST k-ω turbulence model, with convection terms discretized employing high-resolution schemes and temporal terms handled via second-order Euler implicit time integration. The computation was initialized from a converged steady Reynolds-Averaged Navier–Stokes (RANS) solution to accelerate convergence in the subsequent transient phase. After achieving statistical stationarity, data sampling commenced for an additional 5000 time steps at intervals of every 14 steps within appropriate time windows to capture transient characteristics effectively. As the angle of attack increases, flow separation emerges near the trailing edge of biomimetic wingsails, leading to vortex shedding that induces pronounced unsteady fluctuations in both lift and drag coefficients. Figure 12 illustrates the periodic variation in the lift coefficient of the merganser wingsail during a time period.

In order to reveal the mechanism of unsteady pressure load fluctuations in biomimetic wingsails, the instantaneous streamlines of the merganser wingsail during a time period were analyzed, as shown in Figure 13. From Figure 13, a persistent backflow zone exists on the suction surface throughout the entire period, continuously being constricted by vortical structures originating from the trailing edge region. These vortical structures undergo periodic processes including generation, growth, shedding, and eventual dissipation during their downstream evolution. At time instance t₁, an extensive backflow region occupies substantial portions of the suction surface while simultaneously featuring a nascent separation spiral point near the trailing edge. By stage t₂, this separation point expands progressively, thereby intensifying compression effects acting upon the upstream backflow region. Upon reaching phase t₃, the separation point matures into a fully developed separation vortex which subsequently detaches from the airfoil contour, causing maximum contraction of the attached backflow zone. During the transition to state t₄, the shed vortex engages with ambient wake flows through entrainment interactions, leading to gradual energy dissipation. Finally at moment t₅, complete mixing between the shedding vortex structure and the surrounding fluid medium occurs, resulting in full dissipation accompanied by restoration of original backflow dimensions comparable to those observed initially at t₁, thus completing one full cycle of unsteady dynamics.

These observations collectively demonstrate that under operating conditions involving 16° angle of attack, the rhythmic production, exfoliation, and subsequent annihilation of trailing-edge separation vortices exert decisive influence on stabilization characteristics of suction side reattachment phenomena ultimately governing lift coefficient variability exhibited by the biomimetic merganser wingsail.

Figure 14 presents the Q-criterion isosurface distributions for the merganser wingsail at α = 16° during a time period. From Figure 14, the temporal evolution of Q values throughout the period reveals the dynamic process of vortex shedding from both the separation zone of the suction side and the trailing edge region as they propagate downstream. At time instance t₁, the initial separation vortex on the suction surface begins to detach and breaks up into smaller vortical structures. By stage t₂, the small vortical structures gradually expand as they develop downstream. Upon reaching phase t₃, the magnitude of the shed vortex originating from the suction side diminishes, indicating weakened rotational strength and onset of dissipation processes, while simultaneously the trailing-edge vortex undergoes elongation along the streamwise direction. During the transition to state t₄, further degradation occurs wherein both the suction-side remnant vortex continues fading and the primary trailing-edge vortex loses intensity through viscous diffusion mechanisms. Finally at moment t₅, the spatial configuration of Q-distribution closely resembles that observed initially at t₁, signifying completion of one full vortex alternation cycle and initiation of subsequent periodic behavior.

4. Conclusions

The aerodynamic characteristics of wingsails mounted on USVs play a crucial role in enhancing propulsion performance, with the lift coefficient serving as a direct indicator of their aerodynamic efficiency. Biomimetic airfoils were developed based on owl, merganser, seagull, and teal configurations through principles derived from biological optimization. Numerical investigation was conducted using the Transition SST k-ω turbulence model to analyze the aerodynamic behavior of the four biomimetic airfoils. The results are as follows:

(1)

It can be observed that within the AOA range of 0–45°, the merganser wingsail exhibits the highest lift coefficient, achieving a peak value of 3.21 among the biomimetic wingsails. Within the broader range of 0–60° angle of attack, the merganser wingsail demonstrated superior overall lift performance, followed by the seagull wingsail, while the teal wingsail airfoil displayed comparatively inferior lift characteristics under identical conditions.

(2)

At low to moderate angles of attack (0–24°), lift generation dominates the propulsive contribution of biomimetic wingsails, which is closely related to favorable pressure distribution near the leading edge. However, beyond an angle of attack of 24° up to 60°, both lift and drag coefficients must be considered simultaneously for accurate assessment of net thrust production. This is because the drag coefficient increases rapidly with the increase in angle of attack.

(3)

As the angle of attack increases, flow separation initiates at the trailing edge of biomimetic wingsails, resulting in vortex formation that induces significant unsteady fluctuations in both lift and drag coefficients. For the merganser wingsail airfoil, a persistent recirculation zone persists along its suction surface and it is dynamically modulated by periodic interactions with coherent vortical structures shed from the trailing edge. The transient phenomena including initiation, growth, detachment, and dissipation of vortices exert substantial influence on the stability and magnitude of suction-side reattachment processes, thereby directly affecting temporal variations observed in the lift coefficient at 16° angle of attack.

In the present study, which is a numerical investigation without self-conducted experimental validation, the reliability of the numerical method was verified using other similar experimental data. Although this approach is reasonable, the results of this study have not been experimentally validated. So some deviations may exist in the data, and the research relying solely on numerical simulation methods has certain limitations.

In subsequent studies, the focus will be on the three-dimensional design of the merganser wingsail. The three-dimensional merganser wingsail will be applied in the gradient wind under the atmospheric boundary layer to evaluate its aerodynamic performance. This work will provide guidance for improving the auxiliary propulsion performance of wingsails.