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Abstract

Wind energy plays a significant role in the energy consumption reduction of the sail-assisted vessels. During the navigation process, how to select the ideal airfoil sails is crucial for the vessel safety and wind energy conversion efficiency. We resolve the airfoil sails selection problem by utilizing computational fluid dynamics simulation. Within the computational fluid dynamics simulation approach, with shear-stress transport k–ω turbulence model, we analyze the performance of the three typical airfoil sails including NACA23012, NACA0012, and NACA0018 in the wind field from the perspective of force condition, lift and drag coefficients, and lift–drag ratio under generous wind speeds and angles of attack. And we investigate the pressure contours of the airfoil sails. Then, we can determine the aerodynamic performance of the airfoil sails promptly and identify suitable sails for the sail-assisted vessels under the given wind field.

Keywords

Computational fluid dynamics airfoil hard sail lift coefficient drag coefficient

Introduction

With the globalization of the world economy, the seaborne trade grows steadily and accounts for $75 %$ of the world merchandise trade. Following with the boom of the seaborne trade, the number,^1,2 the types, and the tonnage of the vessels are increased remarkably.³ Due to the burning of heavy oil, the air pollution quantity generated by vessels is considerable. Especially, the emission of $S O_{x}$ is up to 6.34 million tons per year and contributes to $4 %$ of the global total emissions, which can be referred to the document released by the International Maritime Organization (IMO).^4,5 To limit emissions of sulfur oxides and other pollutants, IMO has established four global emission control zones, including Baltic, North Sea, North America, and Caribbean during the last decade. Meanwhile, as pointed in the future shipping industry report presented by DNV GL Group,⁶ the safety and sustainable development of the shipping industry consist of six solutions; one solution involves the low-carbon energy concept. Continuous air pollution emissions caused by worldwide shipping activities urge effective regulations and technologies, including clean energy and energy big data, to reduce the fuel consumption significantly.^6–8 Consequently, clean energy, including solar and wind power, can be employed to diminishing the fuel consumption of vessels⁸ and improve their energy management system. To efficiently achieve wind energy utilization, we focus on identifying the feasible hard sails for sail-assisted vessels from the perspective of aerodynamic characteristics under certain navigation environment.

The sail has been employed in aid of the vessel navigation for quite a long history.⁹ There are more than 10 kinds of mainstream sails with different shapes, operating principles, and aerodynamic characteristics.¹⁰ Generous sails including flying jib,¹¹ square sails, Princeton sails,¹² Magnus roll sails¹³ and wing sails have been adopted for sail-assist propulsion of vessels.¹⁴ Flying jib is often used in sailboats for recreation and competition.^11,15 Mainly relying on drag force,¹⁶ wind energy utilization efficiency of square sails is low. Because the canvas is around the mast, the maintenance costs of Princeton sails are quite high.¹⁴ Within the principle of Magnus sail, its cylinder rotates vertically around the rotary axis on deck, and the workload can be regulated by varying drum speeds. The reliability of Magnus sail is relatively high, while it consumes additional energy.¹⁷

The ideal sails for sail-assisted vessel are characterized by excellent aerodynamic performance and economical maintenance cost. Structure of wing sail is similar to an airplane wing with airfoil cross-section.¹⁸ Featured by much better lift-to-drag ratio than conventional sails, wing sails have been extensively adopted in contemporary sail-assisted vessels.^3,8,16,18 The most representative wing sail can be the series of the NACA airfoil developed by the National Advisory Committee for Aeronautics (NACA).¹⁹ NACA has constructed a considerable database for airfoils. Referring to NACA airfoil, its aerodynamic performance precedes other sails and it has been employed in aviation and navigation for many years. In the field of sail-assisted vessel navigation, the airfoils amounted on the vessel can be treated as the wings of an airplane. Consequently, we select three classical airfoils named NACA23012, NACA0012, and NACA0018 from NACA database and present the way to compare and select the feasible airfoils for vessel under certain navigation environment from the perspective of aerodynamic performance.

Generally, the wind tunnel test is often employed to identify the airfoil performance.^3,16 Li et al.³ tested the performance of cascade hard sails under the scale wind tunnel environment and found that the performance of the cascade sails closely linked to the distance between sails. He et al.¹⁶ was primarily concerned with the aerodynamic performance of a sail by employing the wind tunnel test, and the stability of sail-assisted vessels from the perspective of stability criteria calculation. However, confined to the expensive experiment expenditure and unstable results, the wind tunnel test is generally replaced by computational fluid dynamics (CFD) simulation^20–23 when selecting hard airfoil sails. Consequently, we tend to conduct fluid simulation modeling of the airfoil hard sail for the sail-assisted vessel by adopting CFD.

Some highlights of our paper are as follows: (1) CFD is applied for fluid simulation modeling of the airfoils mounted on the sail-assisted vessels; (2) and performance of the NACA airfoil sails are analyzed in detail including lift and drag coefficients under generous angles of attack and wind conditions, the pressure contours are analyzed in detail. Finally, new sights into the airfoil hard sail selection for the sail-assisted vessel are presented using our developed approach.

Airfoil hard sail modeling and force analysis

Nomenclature related to airfoil hard sail
$NACA$	National Advisory Committee for Aeronautics
$T$	Thrust generated by the airfoil hard sail on the vessel
$H$	Lateral force generated by the airfoil hard sail on the vessel
$F_{L}$	Lift force that perpendicular to the direction of the wind field
$F_{D}$	Drag force that along the direction of the wind field
$C_{T}$	Thrust coefficient generated by the airfoil hard sail on the vessel
$C_{H}$	Lateral force coefficient generated by the airfoil hard sail on the vessel
$C_{l}$	Lift coefficient
$C_{d}$	Drag coefficient
$l / d$	Lift–drag ratio
$ϕ$	Angle of attack
$ρ$	Air density
$v$	Relative wind speed
$A_{S}$	Wind area
$SST k - ω$	Shear pressure transmission mode
$CFD$	Computational fluid dynamics
$t$	Air temperature at a measurement position
$v_{mp}$	Wind velocity at a measurement position
$\vec{g}$	Gravitational acceleration
$P$	Pressure
$\bar{\bar{τ}}$	Stress tensor

Airfoil hard sail modeling in the wind field

Figure 1 shows the two-dimensional diagram of three NACA sails, NACA0012, NACA0018 and NACA23012. It can be found that the structure of the first two sails is symmetrical, and that of the third sail is asymmetrical. The corresponding part drawings of the airfoil hard sails are presented in Figure 2.

Figure 1.

Two-dimensional diagram of three NACA sails: (a) NACA0012, (b) NACA0018, and (c) NACA23012.

Figure 2.

Part drawing of the airfoil hard sails (a) NACA0012, (b) NACA0018, and (c) NACA230012 with CATIA.

The airfoil hard sail modeling in airfoil field is illustrated below. First, export the data from the airfoil hard sail database in the form of a txt file and set the value of the Z-axis to 0 mm. Then, import the txt file into the software SolidWorks and transform the airfoil data into an entity reference. And connect the tail of the airfoil as shown in Figure 3.

Figure 3.

Tail connection.

Following that, after connecting the fore and aft of the airfoil using a straight line, the reached line can be treated as the airfoil center line. The determined center line is presented in Figure 4.

Figure 4.

Center line determination.

Third, stretch the two-dimensional (2D) airfoil and convert it into a three-dimensional (3D) model and then save the 3D model as the part drawing of the airfoil hard sails. Figure 5 shows the 3D model of the airfoil hard sail.

Figure 5.

Three-dimensional model of airfoil hard sail.

By modifying the shape of the airfoil hard sail in the air flow field and rotating the airfoil model as shown in Figure 6, we can adjust the angle of attack of sails correspondingly.

Figure 6.

Rotation of airfoil model.

Finally, suppose the airfoil material is smooth, and check the closure of the airfoil. Based on the airfoil hard sail modeling process, we can develop the airfoil model for numerical simulation accordingly.

Force analysis of airfoil hard sail

Figure 7 demonstrates the force analysis of the airfoil hard sails that mounted on the sail-assisted vessel. Within the $XOY$ coordination system, suppose $OX$ is the fore direction of the sail-assisted vessel, $OY$ is the starboard beam of the vessel, $θ$ is the turning angle of the sail related to $OX$ , $ϕ$ is the angle of attack of the sail, $v$ denotes the relative wind speed, and $φ$ is the relative wind direction and equals to $θ + ϕ$ . Generally, when $φ$ is given, $ϕ$ is varying with the adjustment of $θ$ . The dynamic value of $φ$ , $ϕ$ , and $θ$ can be collected by sensors mounted on the sail-assisted vessels. The origin $O$ is set as the reference point of moments.

Figure 7.

Force analysis of the airfoil hard sail.

The force of the airfoil hard sail can be divided into the drag force $F_{D}$ and the lift force $F_{L}$ that is along with and perpendicular to the direction of the airfoil, respectively. And $F_{L}$ and $F_{D}$ can be

F_{L} = C_{l} ρ v^{2} A_{S} / 2

(1)

F_{D} = C_{d} ρ v^{2} A_{S} / 2

(2)

The thrust $T$ generated by the airfoil hard sail on the vessel and the lateral force $H$ generated by the airfoil hard sail on the vessel can be

T = F_{L} \sin φ - F_{D} \cos φ

(3)

H = F_{L} \cos φ + F_{D} \sin φ

(4)

Suppose $l / d$ represents the lift-drag ratio of the airfoil hard sail. After dimensionless process, then

C_{T} = C_{l} \sin φ - C_{d} \cos φ

(5)

C_{H} = C_{l} \cos φ + C_{d} \sin φ

(6)

C_{l} = \frac{2 F_{L}}{ρ v^{2} A_{S}}

(7)

C_{d} = \frac{2 F_{D}}{ρ v^{2} A_{S}}

(8)

\frac{l}{d} = \frac{F_{L}}{F_{D}} = \frac{C_{l}}{C_{d}}

(9)

Numerical simulation approach

Governing equations Shear-stress transport k–ω model

Referring to the shear-stress transport (SST) $k - ω$ model proposed by Menter,²⁴ it accounts for the effect of the transport of the principal turbulent shear stress and has been widely used in computational fluid dynamic simulations.²⁵ Thus, SST $k - ω$ model is employed to control the flow field of the airfoil hard sail. Within SST $k - ω$ model, its continuity equation is

\frac{\partial ρ}{\partial t} + \nabla \cdot (ρ \vec{v_{mp}}) = 0

(10)

And momentum equation is

\frac{\partial}{\partial t} (ρ \vec{v_{mp}}) + \nabla \cdot (ρ \vec{v_{mp}} \vec{v_{mp}}) = - \nabla P + \nabla \cdot (\bar{\bar{τ}}) + ρ \vec{g}

(11)

Details of the model can be referred to Menter,²⁴ Mao et al.,²⁵ and Wilcox.²⁶

Simulation flow for airfoil hard sail

By employing our constructed airfoil sail model, with the aid of the software SolidWorks, we can calculate the lift and drag coefficients $C_{l}$ and $C_{d}$ for the given sails NACA23012, NACA0012, and NACA0018. The simulation flow is demonstrated concisely as follows:

Import the sail model into flow simulation of SolidWorks, and suppose the flow field is the external flow field of the airfoil hard sails.

Referring to the selection of flow medium, we choose air as the external flow field of the airfoil hard sails.

Set the velocity and the turbulence intensity of the air flow field.

Select the 2D computational domain for airfoil hard sails, and the domain should be large enough to contain the airfoils.

Present the global variables, and set the variables, including $C_{l}$ and $C_{d}$ .

Start the calculation with the solver embedded in the software and obtain the results.

Simulation results and discussions

To probe into the insights of the airfoil hard sails that adopted for sail-assisted vessel, we carry out several numerical simulations under generous scenarios. Suppose the relative wind speed $v$ can be 5, 10, and 15 m/s, and the angle of attack $ϕ$ ranges from $10 \circ$ to $90 \circ$ with a step size of $10 \circ$ . As demonstrated in Figure 7, when $ϕ$ is around $90 \circ$ , the thrust $F_{L}$ generated by sail would turn out to be the lateral force for the sail-assisted vessel, and $F_{l}$ would manifest itself as a force that opposes the motion of the vessel referring to $ϕ > 90 \circ$ . Consequently, we mainly focus on the combination of $v$ and $ϕ$ ( $ϕ < 90 \circ$ ) listed above during the CFD simulation. Results and discussions are presented below in details.

Results of $C_{l}$ and $C_{d}$

Tables 1, 3 and 5 show the drag force coefficient $C_{d}$ of airfoil hard sails NACA23012, NACA0018, and NACA0012 under generous angles of attack $ϕ$ with relative wind velocity $v = 5, 10, and 15 m / s$ , respectively. Meanwhile, Tables 2, 4, and 6 list the lift force coefficient $C_{l}$ of airfoil hard sails NACA23012, NACA0018, and NACA0012 under generous angles of attack $ϕ$ with relative wind velocity $v = 5, 10, and 15 m / s$ , respectively.

Table 1.

Drag force coefficient $C_{d}$ of three airfoil hard sails under generous angles of attack $ϕ$ and relative wind velocity $v = 5 m / s$ .

Sail	$10 \circ$	$20 \circ$	$30 \circ$	$40 \circ$	$50 \circ$	$60 \circ$	$70 \circ$	$80 \circ$
NACA23012	0.096	0.237	0.479	0.721	0.757	0.776	0.934	1.478
NACA0018	0.079	0.224	0.417	0.698	0.579	0.750	0.869	0.921
NACA0012	0.070	0.246	0.445	0.642	0.592	0.759	0.919	1.092

Table 2.

Lift force coefficient $C_{l}$ of three airfoil hard sails under generous angles of attack $ϕ$ and relative wind velocity $v = 5 m / s$ .

Sail	$10 \circ$	$20 \circ$	$30 \circ$	$40 \circ$	$50 \circ$	$60 \circ$	$70 \circ$	$80 \circ$
NACA23012	0.461	0.683	0.704	0.764	0.835	0.427	0.360	0.263
NACA0018	0.336	0.599	0.610	0.682	0.470	0.434	0.363	0.257
NACA0012	0.441	0.480	0.606	0.750	0.456	0.410	0.363	0.209

Figures 8 –10 demonstrate the drag force coefficient $C_{d}$ versus the angle of attack $ϕ$ , the lift force coefficient $C_{l}$ versus $ϕ$ , and the lift–drag ratio $l / d$ versus $ϕ$ of the airfoil hard sails under $v = 5, 10, and 15 m / s$ , respectively.

Figure 8.

(a) $C_{d}$ , (b) $C_{l}$ , and (c) $l / d$ of the airfoil hard sails NACA23012, NACA0018, and NACA0012 under relative wind speed $v = 5 m / s$ .

Figure 9.

(a) $C_{d}$ , (b) $C_{l}$ , and (c) $l / d$ of the airfoil hard sails NACA23012, NACA0018, and NACA0012 under relative wind speed $v = 10 m / s$ .

Figure 10.

(a) $C_{d}$ , (b) $C_{l}$ , and (c) $l / d$ of the airfoil hard sails NACA23012, NACA0018, and NACA0012 under relative wind speed $v = 15 m / s$ .

In Table 1, the minimum $C_{d}$ of NACA23012, NACA0018, and NACA0012 are 0.096, 0.079, and 0.070, respectively, and achieved at $ϕ = 10 \circ$ , and the maximum $C_{d}$ of NACA23012, NACA0018, and NACA0012 are 1.478, 0.921, and 1.092, respectively, and achieved at $ϕ = 80 \circ$ . Whereas in Table 2, the minimum $C_{l}$ of NACA23012, NACA0018, and NACA0012 are 0.263, 0.257, and 0.209, respectively, and achieved at $ϕ = 80 \circ$ , and the maximum $C_{l}$ of NACA23012, NACA0018, and NACA0012 are 0.835, 0.682, and 0.750, respectively, and achieved at $ϕ = 50 \circ$ , $ϕ = 40 \circ$ , and $ϕ = 40 \circ$ , respectively. As shown in Figure 8, $C_{d}$ is positively correlated with $ϕ$ in Figure 8(a), and in Figure 8(b), the relationship between $C_{l}$ and $ϕ$ is positive if $ϕ$ is less than $40 \circ - 45 \circ$ and negative when $ϕ > 45 \circ$ , and the lift–drag ratio $l / d$ of three hard sails is negatively corrected with $ϕ$ , as depicted in Figure 8(c).

In Table 3, the minimum $C_{d}$ of NACA23012, NACA0018, and NACA0012 are 0.070, 0.075, and 0.050, respectively, and reached at $ϕ = 10 \circ$ , and the maximum $C_{d}$ of NACA23012, NACA0018, and NACA0012 are 1.488, 0.925, and 1.060, respectively, and reached at $ϕ = 80 \circ$ . Whereas in Table 4, the minimum $C_{l}$ of NACA23012, NACA0018, and NACA0012 are 0.265, 0.258, and 0.195, respectively, and reached at $ϕ = 80 \circ$ , and the maximum $C_{l}$ of NACA23012, NACA0018, and NACA0012 are 0.879, 0.701, and 0.750, respectively, and reached at $ϕ = 50 \circ$ , $ϕ = 40 \circ$ , and $ϕ = 40 \circ$ , respectively. As shown in Figure 9, $C_{d}$ is positively correlated with $ϕ$ in Figure 9(a) expect that $C_{d}$ of NACA0018 is negatively correlated with $ϕ$ when $ϕ$ exceeds $70 \circ$ , and in Figure 9(b), the relationship between $C_{l}$ and $ϕ$ is positive if $ϕ$ is less than $30 \circ - 35 \circ$ and negative when $ϕ > 35 \circ$ , and the lift–drag ratio $l / d$ of three hard sails is negatively corrected with $ϕ$ , as presented in Figure 9(c).

Table 3.

Drag force coefficient $C_{d}$ of three airfoil hard sails under generous angles of attack $ϕ$ and constant wind velocity $v = 10 m / s$ .

Sail	$10 \circ$	$20 \circ$	$30 \circ$	$40 \circ$	$50 \circ$	$60 \circ$	$70 \circ$	$80 \circ$
NACA23012	0.070	0.232	0.439	0.743	0.755	0.768	1.477	1.488
NACA0018	0.075	0.220	0.417	0.712	0.876	0.955	0.904	0.925
NACA0012	0.050	0.243	0.441	0.636	0.714	0.756	0.921	1.060

Table 4.

Lift force coefficient $C_{l}$ of three airfoil hard sails under generous angles of attack $ϕ$ and relative wind velocity $v = 10 m / s$ .

Sail	$10 \circ$	$20 \circ$	$30 \circ$	$40 \circ$	$50 \circ$	$60 \circ$	$70 \circ$	$80 \circ$
NACA23012	0.631	0.687	0.710	0.783	0.879	0.423	0.265	0.265
NACA0018	0.396	0.604	0.605	0.701	0.467	0.259	0.318	0.258
NACA0012	0.306	0.479	0.602	0.750	0.458	0.408	0.363	0.195

In Table 5, the minimum $C_{d}$ of NACA23012, NACA0018, and NACA0012 are 0.074, 0.070, and 0.057, respectively, and obtained at $ϕ = 10 \circ$ , and the maximum $C_{d}$ of NACA23012, NACA0018, and NACA0012 are 1.472, 0.925, and 1.090, respectively, and obtained at $ϕ = 80 \circ$ . Whereas in Table 6, the minimum $C_{l}$ of NACA23012, NACA0018, and NACA0012 are 0.265, 0.259, and 0.202, respectively, and obtained at $ϕ = 80 \circ$ , and the maximum $C_{l}$ of NACA23012, NACA0018, and NACA0012 are 0.810, 0.701, and 0.726, respectively, and obtained at $ϕ = 50 \circ$ , $ϕ = 40 \circ$ , and $ϕ = 40 \circ$ , respectively. As given in Figure 10, $C_{d}$ is positively correlated with $ϕ$ in Figure 10(a), and in Figure 10(b), the relationship between $C_{l}$ and $ϕ$ is positive if $ϕ$ is less than $30 \circ - 40 \circ$ and negative when $ϕ > 40 \circ$ , and the lift–drag ratio $l / d$ of three hard sails is negatively corrected with $ϕ$ , as demonstrated in Figure 10(c).

Table 5.

Drag force coefficient $C_{d}$ of three airfoil hard sails under generous angles of attack $ϕ$ and relative wind velocity $v = 15 m / s$ .

Sail	$10 \circ$	$20 \circ$	$30 \circ$	$40 \circ$	$50 \circ$	$60 \circ$	$70 \circ$	$80 \circ$
NACA23012	0.074	0.222	0.436	0.725	0.752	0.775	0.933	1.472
NACA0018	0.070	0.209	0.414	0.711	0.729	0.748	0.906	0.925
NACA0012	0.057	0.247	0.444	0.627	0.756	0.763	0.917	1.090

Table 6.

Lift force coefficient $C_{l}$ of three airfoil hard sails under generous angles of attack $ϕ$ and relative wind velocity $v = 15 m / s$ .

Sail	$10 \circ$	$20 \circ$	$30 \circ$	$40 \circ$	$50 \circ$	$60 \circ$	$70 \circ$	$80 \circ$
NACA23012	0.611	0.792	0.709	0.765	0.810	0.400	0.361	0.265
NACA0018	0.526	0.648	0.615	0.701	0.434	0.435	0.319	0.259
NACA0012	0.512	0.482	0.607	0.726	0.450	0.411	0.363	0.202

Results of contours of statistic pressure

Figures 11 –13 plot the pressure contours of NACA23012, NACA0012, and NACA0018 under varied angles of attack $ϕ$ and constant wind velocity $v = 10 m / s$ , respectively. The angles of attack are $10 \circ$ , $20 \circ$ , $30 \circ$ , $40 \circ$ , $50 \circ$ , $60 \circ$ , $70 \circ$ , and $80 \circ$ .

Figure 11.

Pressure contours of the airfoil hard sail NACA23012 under varied angles of attack $ϕ$ and constant wind velocity $v = 10 m / s$ : (a) φ = 10°, (b) φ = 20°, (c) φ = 30°, (d) φ = 40°, (e) φ = 50°, (f) φ = 60°, (g) φ = 70°, and (h) φ = 80°.

Figure 12.

Pressure contours of the airfoil hard sail NACA0012 under varied angles of attack $φ$ and constant wind velocity $v = 10 m / s$ : (a) φ = 10°, (b) φ = 20°, (c) φ = 30°, (d) φ = 40°, (e) φ = 50°, (f) φ = 60°, (g) φ = 70°, and (h) φ = 80°.

Figure 13.

Pressure contours of the airfoil hard sail NACA0018 under varied angles of attack $ϕ$ and constant wind velocity $v = 10 m / s$ : (a) φ = 10°, (b) φ = 20°, (c) φ = 30°, (d) φ = 40°, (e) φ = 50°, (f) φ = 60°, (g) φ = 70°, and (h) φ = 80°.

The vertical bar scale with different colors on the left part in Figures 11 –13 indicates the pressure value. Red color of the bar means the pressure of this part is markedly higher than standard atmospheric pressure, and the airfoil hard sail would encounter a large wind pressure under which condition the sail is prone to damage. The blue part signifies that its pressure is navigate and significantly lower than standard atmospheric pressure, and stall phenomenon would be generated when sail located in this region. Green color implies that the pressure of this part is close to standard atmospheric pressure, and the sail would experience a relative small force in the wind field corresponding to the green color.

New insights into airfoil hard sail selection for sail-assisted vessel

Generally, referring to $v = 5 m / s$ , we can find the following new insights from Figure 8: (1) $C_{d}$ and $C_{l}$ of NACA23012 are larger than the values of the other two airfoil hard sails observably; (2) $C_{d}$ of NACA0018 and NACA0012 overlap each other till $ϕ = 70 \circ$ , and $C_{l}$ of NACA0018 is larger than $C_{l}$ of NACA0012 within the ranges of $20 \circ \leq ϕ \leq 45 \circ$ and $70 \circ \leq ϕ \leq 80 \circ$ ; (3) the values of $l / d$ in three sails sorted from large to small are NACA0012, NACA23012, and NACA0018 orderly if $10 \circ \leq ϕ \leq 37 \circ$ and are NACA23012, NACA0018, and NACA0012 in sequence if $ϕ \geq 37 \circ$ .

When the relative wind speed $v$ increased to 10 m/s as illustrated in Figure 9, we detect some new sights as follows: (1) Till $ϕ = 60 \circ$ , the sequence of $C_{d}$ ranked from greatest to petty is NACA0018, NACA23012, and NACA0012; (2) $C_{l}$ of NACA23012 is far greater than $C_{l}$ of the other two sails expect $ϕ \geq 75 \circ$ , and $C_{l}$ of NACA0018 is larger than that of NACA0012 if $ϕ \leq 36 \circ$ and $ϕ \geq 75 \circ$ ; (3) $l / d$ of NACA230012 is larger than that of the other two sails if $ψ \leq 20 \circ$ and 40 $\circ \leq ψ \leq 60 \circ$ , and in the remaining intervals l/d of the three sails are coincide.

Referring to $v = 15 m / s$ , similar insights can be gained in Figure 10: (1) $C_{d}$ and $C_{l}$ of NACA23012 are larger than $C_{d}$ and $C_{l}$ of the other two airfoil hard sails; (2) $l / d$ of three sails overlaps to a large extent.

Consequently, when we probe into the phenomenon in Figures 8 –10, new insights can be achieved as follows: (1) $C_{d}$ of three airfoil hard sails is positively linear correlated with $ϕ$ and most parts of $C_{d}$ overlap with each other, and $l / d$ of the sails overlaps closely; (2) $C_{l}$ is varied with the increasement of $ϕ$ , $C_{l}$ would increase evidently if $ϕ \leq 20 \circ - 35 \circ$ , and maintain a fixed relative high value when $ϕ$ falls in $[30 \circ 40 \circ]$ , and be negatively linear correlated with $ϕ$ if $ϕ \geq 40 \circ$ ; (3) referring to the aerodynamic performance of the excellent airfoil hard sail, it should be with smaller $C_{d}$ , and larger $C_{l}$ and $C_{d}$ as depicted in former section, then if set $ϕ \leq 60 \circ$ , the ideal airfoil hard sail can be NACA230012. By employing similar deduction, the proper airfoil hard sail can be selected for the sail-assisted vessel at the given $ϕ$ .

From the perspective of the pressure contours of the airfoil hard sails, we find the following new insights from in Figures 11 –13. (1) For one certain airfoil hard sail operating at the given relative wind velocity $v$ , the larger the angle of attack $ϕ$ , the greater the stress that the sails encountered; (2) the leading edge that the sails against the wind is covered with deep red region, and this part of the sail is prone to damage due to higher pressure; (3) on the leeward side of the sails, the deep blue region is also enlarged observably when $ϕ \geq 70 \circ$ .

Since the pressure value in the deep blue region is below 0, the energy saving efficiency by employing the airfoil hard sails is low. Therefore, it is all utterly senseless and pointless using the sails for sail-assisted vessel under those similar situations. Correspondingly, to ensure the performance of the airfoil hard sails in the wind field, it is necessary to enhance the structural strength of the sails especially on the part of its leading edge. Furthermore, to fulfill the ideal energy saving efficiency for the sail-assisted vessel, it is significant to equip with flexible gears on the vessel in order to drive the sails to the reasonable angle of attack $ϕ$ promptly.

Conclusion

By employing the CFD simulation approach, several new insights have been found referring to the ideal airfoil hard sail selection for the sail-assisted vessel. Within our proposed approach, the critical factors including lift and drag coefficients, lift–drag ratio, and pressure contour of the candidate sails are investigated thoroughly. The performance of the airfoil hard sails has been demonstrated in detail. Numerical simulations under multiple scenarios have been developed. Accordingly, we present the deep new insights, including ways to select the ideal sails for the sail-assisted vessel, the appropriate time to use the sails, and the damage-avoidance instructions during sail operation. In the near future, with the aid of techniques including energy big data and path planning,^27–29 we would develop the operational intelligent sail selection system for the shipping industry application.

Footnotes

Handling editor: Zhixiong Li

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors are partially supported by the National Science Foundation of China (51579202, 51309186, 61673223, 71501151, 61773401) and China Postdoctoral Science Foundation Funded Project (2015T80848 and 2014M560633).

ORCID iD

Yong Ma

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New insights into airfoil sail selection for sail-assisted vessel with computational fluid dynamics simulation

Abstract

Keywords

Introduction

Airfoil hard sail modeling and force analysis

Airfoil hard sail modeling in the wind field

Force analysis of airfoil hard sail

Numerical simulation approach

Governing equations Shear-stress transport k–ω model

Simulation flow for airfoil hard sail

Simulation results and discussions

Results of C l and C d

Results of contours of statistic pressure

New insights into airfoil hard sail selection for sail-assisted vessel

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References

Results of $C_{l}$ and $C_{d}$