Numerical Investigation of a Two-Element Wingsail for Ship Auxiliary Propulsion

Journal of Marine Science and Engineering

Article Numerical Investigation of a Two-Element Wingsail for Ship Auxiliary Propulsion

Chen Li 1,2,3,*, Hongming Wang 2,3 and Peiting Sun 1

1 Marine Engineering College, Dalian Maritime University, Dalian 116026, China; [email protected] 2 College of Marine, Electrical and Intelligent Engineering, Jiangsu Maritime Institute, Nanjing 211170, China; [email protected] 3 Jiangsu Ship Energy-Saving Engineering Technology Center, Nanjing 211170, China * Correspondence: [email protected]

Received: 16 March 2020; Accepted: 1 May 2020; Published: 9 May 2020

Abstract: The rigid wingsail is a new type of propulsion equipment which greatly improves the performance of the sailboat under the conditions of upwind and downwind. However, such sail-assisted devices are not common in large ships because the multi-element wingsail is sensitive to changes in upstream flow, making them difficult to operate. This problem shows the need for aerodynamic study of wingsails. A model of two-element wingsail is established and simulated by the steady and unsteady RANS approach with the k-ω SST turbulence model and compared with the known experimental data to ensure the accuracy of the numerical simulation. Then, some key design and structural parameters (camber, the rotating axis position of the flap, angle of attack, flap thickness) are used to characterize the aerodynamic characteristics of the wingsail. The results show that the position of the rotating shaft of the flap has little influence on the lift coefficient at low camber. When stall occurs, the lift coefficient first increases and then decreases as the flap axis moves backward, which also delays the stall angle at a low camber. At the high camber of AOA = 6◦, the lift coefficient always increases with the increase of the rotating axis position of the flap; especially between 85% and 95%, the lift coefficient increases suddenly, which is caused by the disappearance of large-scale flow separation on the suction surface of the flap. It reflects the nonlinear coupling effect between camber of wingsail and the rotating axis position of the flap

Keywords: wingsail; aerodynamics; numerical simulation

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 m2 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 (Figure1). 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

J. Mar. Sci. Eng. 2020, 8, 333; doi:10.3390/jmse8050333 www.mdpi.com/journal/jmse 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 ρ The density of the air [kg/m3] ρz The densityheight of of wingsail the air [kg/m in the3] vertical direction[m] hz TheWingsail height height of wingsail [m] in the vertical direction[m] Lh WingsailLift force[N] height [m] DL LiftDrag force[N] force [N] Dv DragThe velocity force [N] of inflow [m/s]

Xvr The positionvelocity of inflowflap rotation [m/s] axis in the direction of

Xr Thethe wing position chord of flap[-] rotation axis in the direction of the wing chord [-] 1. Introduction 1. IntroductionThe rigid wingsail is a common auxiliary propulsion device. Due to its characteristics of environmentalThe rigid protectionwingsail is and a commonenergy saving, auxiliary the rigipropulsiond wingsail device. has been Due applied to its to characteristics various types of 2 environmentalships. In 1980, twoprotection rectangular and energy rigid wingsails saving, the with rigi ad total wingsail sail area has ofbeen 194.4m applied on to"Shin various Aitoku types Maru of" ships.were installedIn 1980, twoin Japan, rectangular which rigidwas thewingsails world's with first a moderntotal sail sail-assisted area of 194.4m commercial2 on "Shin tanker.Aitoku Maru After" werefour yearsinstalled of actual in Japan, sailing, which oil wastankers the canworld's save first8.5% modern a year comparedsail-assisted with commercial conventional tanker. ships[1]. After fourAlthough years theof actualinternational sailing, oiloil pricetankers fluctuates can save grea 8.5%tly, a yearthe research compared on withsail-assisted conventional vessels ships[1]. varies Althoughfrom country the tointernational country. In oil2018, price China fluctuates Shipbuil greadingtly, Group the research delivered on the sail-assisted world's first vessels Very variesLarge fromCrude country Carrier to (VLCC),country. In“Kai 2018, Li”, China with Shipbuil wingsailsding (Figure Group delivered1). The trial the world'sresults firstshow Very that Large the Crudeenergy-saving Carrier efficiency(VLCC), of“Kai the VLCCLi”, with is obvious wingsails [2]. At(Figure the same 1). time,The trialthe wingsails results showhave alsothat been the energy-savingrapidly developed efficiency in the of field the VLCCof unpowered is obvious navigation. [2]. At the sameParticularly time, the in wingsails2010, BMW have Oracle also beenwas rapidlypowered developed by a 60-meterhigh, in the field multi-element of unpowered wingsail, navigation. which Particularly won the in33rd 2010, America's BMW Oracle Cup. wasThe poweredflexible size by anda 60-meterhigh, excellent performance multi-element of the wingsail, wingsail whichhas rekindled won the the 33rd interest America's of the Cup. shipping The flexibleindustry size [3]. andHowever, excellent due performance to the phenomenon of the wing of sailflow has separation rekindled or the stal interestl on the of surface the shipping of the industrywingsail, [3].the propulsionHowever, dueperformance to the phenomenon of the wingsail of flowwill be separation deteriorated, or stal whichl on will the seriouslysurface of affect the J.wingsail,the Mar. stability Sci. Eng.the of 2020propulsion the, 8 ,ship. 333 The performance New Zealand of the Chiefs[4 wingsail] suffered will be deteriorated, a shipwreck whichin the 35thwill seriouslyAmerica's affect2 Cup of 15 the(Figure stability 2). Therefore, of the ship. it Theis very New important Zealand toChiefs[4 find an] suffered effective a methodshipwreck to controlin the 35th flow America's separation Cup or (Figuredelay stall. 2). Therefore, it is very important to find an effective method to control flow separation or of the ship. The New Zealand Chiefs [4] suffered a shipwreck in the 35th America’s Cup (Figure2). delay stall. Therefore, it is very important to find an effective method to control flow separation or delay stall.

FigureFigure 1.1.“Kaili”“Kaili” VLCC VLCC with with wingsail. wingsail. Figure 1.“Kaili” VLCC with wingsail.

Figure 2. Capsizing accident of sailboat. Figure 2.Capsizing accident of sailboat. In order to improve the stallFigure characteristics, 2.Capsizing di accidentfferent of flow sailboat. control methods are used, which can be dividedIn order into to improve active control the stall and characteristics, passive control. different The active flow control control methods method hasare used, been appliedwhich can to thebe divided controllableIn order into to active loopimprove sail control [the5], fluidstall and characteristics, passive injection control. [6,7], turbinedi Thefferent active sail flow [control8], control Magnus method methods sail has [9], are trailingbeen used, applied flap which [ 10to , can11the], leadingbecontrollable divided slat into [loop11, 12active ],sail etc. [5],control The fluid passive and injection passive method [6,7], control. is alsoturb Theine applied activesail [8], to control di Magnusfferent method types sail [9], ofhastechnologies, trailing been applied flap such[10,11], to the as Walkercontrollableleading sailsslat [11,12], [loop13], deformedsail etc. [5], The fluid flapspassive injection [14 method] and [6,7], leading-edge is alsoturb appliedine sail tubercles [8],to different Magnus [15], etc. types sail [9],of technologies, trailing flap such[10,11], as leadingWalkerInrecent sailsslat [11,12], [13], years, deformed etc. the The flap passiveflaps setting [14] method of and the leading-edge wingsail is also applied is considered tubercles to different [15], to be etc.types a very of feasible technologies, active such control as methodWalker sails to control [13], deformed the flow flaps separation. [14] and Thisleading-edge idea has tubercles been applied [15], inetc. 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 (Figure3), so as to improve the propulsion performance and delay stall. Many scholars have also carried out research on theJ. Mar. aerodynamic Sci. Eng. 2019, characteristics.7, x FOR PEER REVIEW 4 of 16

Figure 3. The geometry and simplified simplified configurationconfiguration of the two-element wingsail. In 1996, Daniel [11] designed a high-performance, three-element wingsail. The experimental Table 1. Parameterization of wingsail. 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◦, andc the0.35m thrust in the whole operation area is also improved. At the most efficient wind direction angle ofh the wingsail,0.7m the thrust is increased by 83%. This proves the superiority of multi-element wingsailRe in propulsion5×105 characteristics. In 2003, Fujiwara [16,17] switched from a triangular sail to a rectangulard one.0–25° Its propulsion performance is superior to that of Nojiri’s hybrid dynamic sail. In 2015, heα cooperated 0–20° with Qiao Li [14] to modify the hybrid sail, g 2.4%

Xr 75%–95%

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

2.2. The Grid Structure 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 anti-slip walls.

J. Mar. Sci. Eng. 2020, 8, 333 3 of 15 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.

2. Methods

2.1. The Geometry of the Wingsail The geometry is a simplified configuration of a two-element wingsail with 1/20th model-scale (as Figure3 and Table1). The nondimensional number for characterizing the flow of fluid Reynolds number is defined by Equation (1): ρvc Re = (1) µ where µ is the viscosity coefficient of air. The results of naca0018 airfoil with Re = 5 105 (the wind × speed is assumed to be 20 m/s) are compared with the existing experiments to ensure the accuracy of the numerical results. The general view of the geometry and its characteristic parameters are as follows:

Table 1. Parameterization of wingsail.

c 0.35 m h 0.7 m Re 5 105 × d 0–25◦

α 0–20◦ g 2.4%

Xr 75%–95%

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 Figure4. 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 Figure4. 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 wingsail will be r1.5t1815 X85g2.4α6 d15, for α = 6◦, d = 15◦. J. Mar. Sci. Eng. 2020, 8, 333 4 of 15 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 5 of 16

Figure 4. Wingsail geometry and parameterization. J. Mar. Sci. Eng. 2019, 7, x FOR PEERFigure REVIEW 4. Wingsail geometry and parameterization. 5 of 16 2.2. The Grid Structure 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 (Figure5). AOA is adjusted by rotating the direction of the airflow. The chord of the wingsail is 0.35 m and the span 0.7 m. 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 computationalFigure 4. Wingsail domain geometry are defined and asparameterization. anti-slip walls.

Figure 5. Box domain for the freestream simulation.

Mesh Details. The quality of grid determines the accuracy of numerical results. Particular attention has been paid to refine the mesh in the slot, being a region of interaction between the wake of the wing, flow from the slot and the flap boundary layer. Mesh resolution close to the slot has been encrypted as shown in Figure 6. In addition, the mesh size of the flap leading-edge curve is set as 0.4545% (in the case of mesh number 9.86M). In order to ensure the accurate simulation of the flow field near the wall, the height of the first grid cell closest to the wall should be suitable. The nondimensional wall distance for a wall-bounded flow y+ is defined by Equation (2): Figure 5. Box domainρρ forτ the freestream∂ simulation. Figure 5. Box+ yudomainτ yufor thewall freestream simulation. yy== = () (2) νμρ μ∂y Mesh Details. The quality of grid determines the accuracy of numericaly=0 results. Particular attention Mesh Details. The quality of grid determines the accuracy of numerical results. Particular has been paid to refine the mesh in the slot, being a region of interaction between the wake of the wing, attentionwhere y ishas the been distance paid to from refine the the first mesh mesh in the cell slot, to beingthe nearest a region wall. of interactionIn this paper, between y is thespecified wake flow from the slot and the flap boundary layer. Mesh resolution close to the slot has been encrypted as ofas2.871×10 the wing,−5c flowon the from wingsail the slot surface. and theIn this flap case, bounda the profilery layer. of Meshthe dimensionless resolution close wall to distance the slot y +has on shown in Figure6. In addition, the mesh size of the flap leading-edge curve is set as 0.4545% (in the beenthe surface encrypted of the as wingsail shown in with Figure AOA 6. In=6° addition, is shown the in meshFigure size 7. It of can the be flap seen leading-edge that the value curve of yis+ seton case of mesh number 9.86M). In order to ensure the accurate simulation of the flow field near the wall, asthe 0.4545% sail surface (in theis about case 1,of ensuring mesh number the accuracy 9.86M). of In numerical order to calculationensure the results.accurate The simulation growth ratio of the of the height of the first grid cell closest to the wall should be suitable. The nondimensional wall distance flowthe prism field layernear isthe 1.2.The wall, thetotal height number of theof nodes first gridin the cell grid closest is about to the9.86 wall million. should be suitable. The for a wall-bounded flow y+ is defined by Equation (2): nondimensional wall distance for a wall-bounded flow y+ is defined by Equation (2): s ρρr τ ∂ + +yuτyuτ ρy yuτwallwall ρ ∂u y =yy=== == y ()( ) (2)(2) ν νμρµ ρ μµ∂y∂y y=0 y=0 where y is the distance from the first mesh cell to the nearest wall. In this paper, y is specified where y is the distance from the first mesh cell to the nearest wall. In this paper, y is specified as as2.871×10−55c on the wingsail surface. In this case, the profile of the dimensionless wall distance y++ on 2.871 10− c on the wingsail(a) surface. In this case, the profile of the dimensionless(b) wall distance y on the surface× of the wingsail with AOA =6° is shown in Figure 7. It can be seen that the value of y++ on the surface of the wingsail with AOA = 6◦ is shown in Figure7. It can be seen that the value of y on the sail surface is aboutFigure 1,6. Theensuring encrypted the accuracymesh in (a of) mid-span numerical and calculation (b) bottom results.wallof the The slot. growth ratio of the prism layer is 1.2.1.2.The The total total number number of of nodes nodes in in the the grid grid is is about about 9.86 9.86 million. million.

(a) (b)

Figure 6.The encrypted mesh in (a) mid-span and (b) bottom wallof the slot.

J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 5 of 16

Figure 4. Wingsail geometry and parameterization.

Figure 5. Box domain for the freestream simulation.

+ yu ρρyuτ ∂ yy==τ wall = () νμρ μ∂ (2) y y=0 where y is the distance from the first mesh cell to the nearest wall. In this paper, y is specified as2.871×10−5c on the wingsail surface. In this case, the profile of the dimensionless wall distance y+ on the surface of the wingsail with AOA =6° is shown in Figure 7. It can be seen that the value of y+ on J. Mar. Sci. Eng. 2020, 8, 333 5 of 15 the sail surface is about 1, ensuring the accuracy of numerical calculation results. The growth ratio of the prism layer is 1.2.The total number of nodes in the grid is about 9.86 million.

J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 6 of 16 (a) (b) J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 6 of 16 FigureFigure 6. 6.TheThe encrypted encrypted mesh mesh in in (a ()a mid-span) mid-span and and (b ()b bottom) bottom wallof wallof the the slot. slot.

Figure 7.Wall y+ contour on wingsail surface (AOA=6 deg). Figure 7. Wall y+ contour on wingsail surface (AOA = 6 deg). Mesh Independence.Figure It 7.isWall considered y+ contour a on necessary wingsail surface step (AOA=6to analyze deg). the influence of grid Mesh Independence. It is considered a necessary step to analyze the influence of grid characteristics. characteristics. When Re =5×105, four different grid numbers (including 2.57, 4.22, 9.86 and 14.4M) WhenMeshRe Independence.= 5 105, four It diisff erentconsidered grid numbers a necessary (including step 2.57,to analyze 4.22, 9.86 the and influence 14.4M) are of used grid to are used to estimate× the grid sensitivity. In the case of AOA = 6°, the grid independence analysis is characteristics.estimate the grid When sensitivity. Re =5×10 In5, four the casedifferent of AOA grid= numbers6 , the grid (including independence 2.57, 4.22, analysis 9.86 isand carried 14.4M) out carried out with steady Reynolds Average N-S equation◦ and AOA=15° with URANS. Figure 8 arewith used steady to estimate Reynolds the Averagegrid sensitivity. N-S equation In the andcase AOAof AOA= 15 = 6°,with the URANS. grid independence Figure8 reports analysis the liftis reports the lift and drag coefficients of the unmodified sail model.◦ As shown in Figure 8, the number carriedand drag out coewithfficients steady of Reynolds the unmodified Average sail N-S model. equation As shown and inAOA=15° Figure8 ,with the numberURANS. of Figure grids has8 of grids has a great influence on the lift coefficient, and the error of lift coefficient is less than 0.3% reportsa great the influence lift and ondrag the coefficients lift coefficient, of the and unmodi the errorfied ofsail lift model. coeffi Ascient shown is less in than Figure 0.3% 8, the between number 9.86 between 9.86 and 14.4M. Based on these calculations, the increase in the number of grids (relative to ofand grids 14.4M. has a Basedgreat influence on these calculations,on the lift coefficient, the increase and in the the error number of lift of coefficient grids (relative is less to than the case0.3% of the case of 9.86M) results in a small change in lift. And the drag coefficient, whose change can be between9.86M) 9.86 results and in 14.4M. a small Based change on inthese lift. calculations, And the drag the coe increasefficient, in whose the number change of can grids be considered (relative to as considered as acceptable. Therefore, the grid number of 9.86M is used in this study. theacceptable. case of 9.86M) Therefore, results the in grid a small number change of 9.86M in lift. is And used the in this drag study. coefficient, whose change can be considered as acceptable. Therefore, the grid number of 9.86M is used in this study. 1.6

1.6 0.3 AOA=6o d=15o AOA=15o d=15o 1.4 0.3 AOA=6o d=15o o o 1.4 AOA=15 d=15 o o [-] [-] AOA=6 d=15 l

d 0.2 o o C C AOA=15 d=15

1.2 o o [-] [-] AOA=6 d=15 l

d 0.2 o o C C AOA=15 d=15 1.2 0.1

1 0.1 0 5E+06 1E+07 1.5E+07 0 5E+06 1E+07 1.5E+07 1 Number of mesh [-] Number of Mesh [-] 0 5E+06 (a) 1E+07 1.5E+07 0 5E+06 (b) 1E+07 1.5E+07 Number of mesh [-] Number of Mesh [-] FigureFigure 8. 8.Convergence Convergence(a) of of ( a()a) lift lift and and (b (b) drag) drag coe coefficientsﬃcients as as a a function function(b) of of mesh mesh number. number.

In orderFigure to 8. Convergencefurther verify of the(a) liftreliability and (b) dragof the coefficients grid with as URANS, a function the of meshinfluence number. on the flow field with different grid sizes is also analyzed when Re=5×105 and AOA =15°. For four different grids In order to further verify the reliability of the grid with URANS, the influence on the flow field (including 2.57, 4.22, 9.86 and 14.4M), the velocity vector on the x–y plane is shown in Figure 9. It can with different grid sizes is also analyzed when Re=5×105 and AOA =15°. For four different grids be observed that there is a large separation vortex on the suction surface of the flap and a small (including 2.57, 4.22, 9.86 and 14.4M), the velocity vector on the x–y plane is shown in Figure 9. It can vortex on the wake of the wing, which is generated by grids of 9.86 and 14.4M, respectively, but be observed that there is a large separation vortex on the suction surface of the flap and a small there is no obvious flow separation for grids of 2.57 and 4.22M. There was no significant difference vortex on the wake of the wing, which is generated by grids of 9.86 and 14.4M, respectively, but in the flow profile between 9.86 and 14.4M. Therefore, the grid number of 9.86M is suitable for the there is no obvious flow separation for grids of 2.57 and 4.22M. There was no significant difference research of wingsail 3D. in the flow profile between 9.86 and 14.4M. Therefore, the grid number of 9.86M is suitable for the

research of wingsail 3D.

J. Mar. Sci. Eng. 2020, 8, 333 6 of 15

In order to further verify the reliability of the grid with URANS, the influence on the flow field with different grid sizes is also analyzed when Re = 5 105 and AOA = 15 . For four different grids × ◦ (including 2.57, 4.22, 9.86 and 14.4M), the velocity vector on the x–y plane is shown in Figure9. It can be observed that there is a large separation vortex on the suction surface of the flap and a small vortex on the wake of the wing, which is generated by grids of 9.86 and 14.4M, respectively, but there is no obvious flow separation for grids of 2.57 and 4.22M. There was no significant difference in the flow profile between 9.86 and 14.4M. Therefore, the grid number of 9.86M is suitable for the research of wingsail 3D. J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 7 of 16

(a) 2.57M

(b) 4.22M

(d) 14.4M

FigureFigure 9. Flow9. Flow proﬁles profiles on on the the mid-span mid-span of wingsail of wingsail with with diﬀ erentdifferent grid grid numbers numbers of (a )of 2.57M, (a) 2.57M, (b) 4.22M, (b) (c) 9.86M and (d) 14.4M (AOA4.22M,= 15 (c) deg). 9.86M and (d) 14.4M (AOA=15 deg).

2.3. Computational Approach 2.3. Computational Approach ω NumericalmethodNumericalmethod.. MenterMenter[ 20[20]] established established the the k- k-turbulenceω turbulence model model of shear of shear stress stress transport transport (SST). ε Hassan(SST). Hassan[21] compared [21] compared the numerical the numerical predicted predicted results of results standard, of standard, RNG and RNG realizable and realizable K- , standard K-ε, ω ω andstandard SST K- andmodels SST K- withω models the experimental with the experimental data, and found data, that and the found K- thatSST the model K - isω theSST most model accurate is the predictionmost accurate model. prediction So the steady model. Reynolds So the steady Averaged Reynolds Navier–Stokes(RANS) Averaged Navier–Stokes(RANS) equations are solved equations thanks toare ANSYS solved Fluentthanks ﬁnite-volume to ANSYS Fluent solver finite-volume with low angle solv ofer attack with low before angle stall of occurs; attack then,before the stall unsteady occurs; ω Reynoldsthen, the Averageunsteady N-SReynolds equation Average is used N-S based equation on the is SST used K- basedmodels on whenthe SST physical K-ω models instabilities when exist [22,23]. As the low Reynolds number is based on the chord of the wingsail (Re = 5 105), the physical instabilities exist [22,23]. As the low Reynolds number is based on the chord of the× wingsail ﬂuid(Re=5×10 is considered5), the fluid as is incompressible considered as (the incompressible Mach number (the of Mach the inlet number is about of 0.062).the inlet These is about models 0.062). are These models are assigned solvers which control the number of the time step. The selected time step size is computed in the case of CFL=V△t/△x=1. The impact of time models on the aerodynamic performance of the wingsail is investigated at Re=5×105(i.e., V=20.87 m/s), and the mesh size of the leading-edge curve of the flap is taken as the length interval (i.e., △x=5×10−4m). Therefore, the magnitude of the time step △t is set at a value of 2.5×10−5s in this simulation investigation. The turbulence intensity at inlet is 1%. The discrete format is quick. Simple algorithm is adopted for the pressure velocity coupling scheme [24]. Model validation. In order to verify the numerical results, the lift coefficient of the two-dimensional wingsail model in a free flow environment is compared with the experimental results, as shown in Figure 10. Daniel [11] had carried out experimental research on the lift/drag characteristics of naca0018 wing.

J. Mar. Sci. Eng. 2020, 8, 333 7 of 15 assigned solvers which control the number of the time step. The selected time step size is computed in the case of CFL = V∆t/∆x = 1. The impact of time models on the aerodynamic performance of the wingsail is investigated at Re = 5 105(i.e., V = 20.87 m/s), and the mesh size of the leading-edge curve × of the flap is taken as the length interval (i.e., ∆x = 5 10 4 m). Therefore, the magnitude of the time × − step ∆t is set at a value of 2.5 10 5 s in this simulation investigation. The turbulence intensity at inlet × − is 1%. The discrete format is quick. Simple algorithm is adopted for the pressure velocity coupling scheme [24]. Model validation. In order to verify the numerical results, the lift coefficient of the two-dimensional wingsail model in a free flow environment is compared with the experimental results, as shown inJ. Figure Mar. Sci. 10 Eng.. Daniel2019, 7, x [ FOR11] hadPEER carriedREVIEW out experimental research on the lift/drag characteristics 8 ofof 16 naca0018 wing.

1.2 0.3

CFD Test CFD Test 0.8 0.2 [-] [-] l d C C

0.4 0.1

0 0 0 5 10 15 20 0 5 10 15 20 AOA [deg] AOA [deg] (a) (b)

FigureFigure 10. 10.Comparison Comparison of of lift lift coe coefficientﬃcient (a) ( anda) and drag drag coe coefficient(ﬃcient (b)b between) between test test and and CFD. CFD.

5 In the case of Re = 5 105 , the RANS method is verified. Before stall (AOA < 15 ), the numerical In the case of Re=5×10× , the RANS method is verified. Before stall (AOA < 15°),◦ the numerical calculationcalculation results results of of the the lift lift coe coefficientfficient and and drag drag coe coefficientfficient are are close close to to the the experimental experimental values, values, and and thethe estimation estimation error error is lessis less than than 5%. 5%.At At the the same same time, time, the the prediction prediction of the of the position position of the of stallthe stall angle angle is accurate.is accurate. Although Although the results the results of numerical of numerical prediction prediction are di ffareerent different from the from experimental the experimental values aftervalues stall,after it isstall, acceptable it is acceptable that the 2Dthat numerical the 2D numerical calculations calculations used for theused qualitative for the qualitative study of the study lift/drag of the characteristicslift/drag characteristics of the wingsail. of the wingsail.

3. Numerical Results 3.Numerical Results 3.1. Two-Dimensional Wingsail Configurations Study 3.1. Two-Dimensional Wingsail Configurations Study The lift force and drag force are converted into dimensionless lift coefficient CL and drag coefficient The lift force and drag force are converted into dimensionless lift coefficient CL and drag CD, respectively. They are defined as follows: coefficient CD, respectively. They are defined as follows: L C = L (3) LC = 2 L 0.5ρvρ A2 R (3) 0.5 vAR

DD CDC== (4) D 0.5ρvρ2A2 (4) 0.5 vAR R where L and D are the lift force and drag force of the wingsail, respectively. AR is the aspect area of where L and D are the lift force and drag force of the wingsail, respectively.AR is the aspect area of wingsail, include the wing and flap. The lift coefficient and drag coefficient characteristics of wingsail wingsail, include the wing and flap. The lift coefficient and drag coefficient characteristics of with different geometric parameters are compared. wingsail with different geometric parameters are compared. Camber and the rotation axis of the flap effect: as the key parameter, the rotating axis position of the Camber and the rotation axis of the flap effect: as the key parameter, the rotating axis position of the flap in the direction of the wing chord Xr is selected as 75% and 85%; five cambers (d = 5◦, 10◦, 15◦, flap in the direction of the wing chord Xr is selected as 75% and 85%; five cambers 20 , 25 ) have been selected as Figure 11. (◦d=5°,10°,15°,20°,25°)◦ have been selected as Figure 11. When Xr is 85%, the stall does not occur advance with the increase of flap deflection angle at low camber as Xr is 75%. It can be illustrated that the slot width with Xr=75%exceeds that with Xr=85%due to the coupling between the camber of the wingsail and the slot width (as Figure 12). The fluid through the slot is enough to supplement the loss of the wing wake, then delay the stall. When the flap deflection angle is more than 15°, the stall angle begins to reduce, which is caused by flow separation of the wing wake, then the flap stalls. The maximum lift coefficient of the wingsail is 2.29 when the flap deflection angle is 20° with AOA=12°. However, due to the reduction of stall angle, the comprehensive performance of the wingsail with d=20° is not as good as that with d=15°. When the flap deflection angle adds to 25°, the lift coefficient decreases in the range of full angles of attack, which may be caused by the stalls. Therefore, it is necessary to consider the rotating axis position of the flap, flap deflection angle and slot width when choosing flap geometry parameters.

J. Mar.J. Mar. Sci. Sci. Eng. Eng.2020 2019, 8, 3337, x FOR PEER REVIEW 8 of 9 of 15 16

2.4 2.4

2 2

1.6 1.6 [-] [-] l l

C 1.2 C 1.2

o o d=5 Xr=75% d=5 Xr=85% o o 0.8 0.8 d=10 Xr=75% d=10 Xr=85% o o d=15 Xr=75% d=15 Xr=85% o o d=20 Xr=75% d=20 Xr=85% o o d=25 Xr=75% d=25 Xr=85% 0.4 0.4 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 9 of 16 0 4 8 12 16 0 4 8 12 16 AOA [deg] AOA [deg]

2.4 (a) Xr=85% 2.4 (b) Xr=75%

FigureFigure2 11. 11.ConvergenceConvergence of of lift lift coecoefficientsfficients as a a function function of2 of AOA AOA and and flap flap deflection deflection angle angle with with (a) (a)Xr = 85% and (b)Xr = 75%. Xr=85% and (b) Xr=75%.

1.6 1.6 When X is 85%, the stall does not occur advance with the increase of ﬂap deﬂection angle at

[-] r [-] l l C C low camber1.2 as Xr is 75%. It can be illustrated that the slot1.2 width with Xr = 75% exceeds that with

o o X = 85% due to the coupling between the camber of the wingsail and the slotd=5 widthXr=75% (as Figure 12). r d=5 Xr=85% o o 0.8 0.8 d=10 Xr=75% d=10 Xr=85% o o d=15 X =75% d=15 X =85% r The fluid through the slot is enoughr to supplement the loss of the wing wake, theno delay the stall. o d=20 Xr=75% d=20 Xr=85% o o d=25 Xr=75% d=25 Xr=85% When the0.4 flap deflection angle is more than 15◦, the stall angle0.4 begins to reduce, which is caused by

flow separation0 of4 the wing8 wake,12 then16 the flap stalls. The0 maximum4 lift coe8 fficient 12 of the16 wingsail AOA [deg] AOA [deg] is 2.29 when the flap deflection angle is 20◦ with AOA = 12◦. However, due to the reduction of stall Figure 12. The slot width with Xr=85% and 75%. angle, the comprehensive performance of the wingsail with d = 20◦ is not as good as that with d = 15◦. (a) Xr=85% (b) Xr=75% When the flap deflection angle adds to 25◦, the lift coefficient decreases in the range of full angles Camber and flap thickness effect: Nine selected simulations are summarized in Table 2 to illustrate of attack,Figure which 11.Convergence may be caused of lift bycoefficients the stalls. as a Therefore, function of it AOA is necessary and flap todeflection consider angle the with rotating (a) axis the coupling between the camber (flap deflection) and the thickness of the flap. It can be seen that the position of the flap, flap deflection angleX andr=85% slot and width (b) Xr=75%. when choosing flap geometry parameters. flap thickness (e2/c2) has little effect on the lift and drag coefficients of d= 5° and 15° (low camber), but has significant effect on d= 25° (high camber) which shows the nonlinear coupling between flap thickness and flap deflection angle. For high camber, 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. It emphasizes the complexity of the slot flow of a two-element wingsail through the strong coupling between flap deflection, thickness and slot width. The slot effect may be useful to recall some famous papers with Gentry [25] and Smith [26] which illustrate the complex effect among the wing wake, Figure 12. The slot width with Xr = 85% and 75%. the leakage flow from the Figureslot and 12. theThe flap slot widthboundary with Xlayerr=85% as and may 75%. be seen in Figure 13. Therefore, theCamber slot of the and wingsail flap thickness includes effect: a Ninestrong selected design simulationsconstraint which are summarized include the inrotating Table2 axis to illustrate position of Camber and flap thickness effect: Nine selected simulations are summarized in Table 2 to illustrate thethe coupling flap, flap between deflection, the camber flap thickness (flap deflection) and slot width. and the thickness of the flap. It can be seen that the the coupling between the camber (flap deflection) and the thickness of the flap. It can be seen that the flap thickness (e2/c2) has little effect on the lift and drag coefficients of d = 5◦ and 15◦ (low camber), flap thickness (e2/c2) has little effect on the lift and drag coefficients of d= 5° and 15° (low camber), but but has significant effectTable on 2.dResults= 25 (highfor α=6° camber) with the which SST transiti showsonal the turbulence nonlinear model. coupling between flap has significant effect on d= 25° (high◦ camber) which shows the nonlinear coupling between flap thickness and flap deflection angle. thickness andConfigurations flap deflection angle. e2/c2 d CL CD L/D For high camber, the thickening flap leads to an increase of the leading-edge radius which decreases For r1.51815x0.85g2.4high camber, theα 6d5thickening flap leads15% to an increase5° of 1.005the leading-edge 0.0213 radius which47.16 the pressure coefficient suction peak and has postponed the stall of the wingsail. It emphasizes the decreasesr1.51815x0.85g2.4 the pressure coefficientα6d15 suction peak15% and has15° postponed 1.724 the stall of0.0338 the wingsail.50.94 It complexity of the slot flow of a two-element wingsail through the strong coupling between flap emphasizesr1.51815x0.85g2.4 the complexityα6d25 of th e slot flow of15% a two-element 25° wingsail1.951 through the0.06 strong coupling32.53 deflection, thickness and slot width. The slot effect may be useful to recall some famous papers with betweenr1.51812x0.85g2.4 flap deflection, thicknessα6d5 and slot width.12% The slot effect5° may1.002 be useful to recall0.0207 some famous48.5 Gentry [25] and Smith [26] which illustrate the complex effect among the wing wake, the leakage papers withr1.51812x0.85g2.4 Gentry [25] αand6d15 Smith [26] which12% illustrate the15° complex1.73 effect among0.0336 the wing wake,51.47 flow from the slot and the flap boundary layer as may be seen in Figure 13. Therefore, the slot of the the leakager1.51812x0.85g2.4 flow from theα 6d25slot and the flap boundary12% layer25° as may 1.606be seen in Figure0.1628 13. Therefore,9.87 wingsail includes a strong design constraint which include the rotating axis position of the flap, flap the slot ofr1.51810x0.85g2.4 the wingsail includesα6d5 a strong design10% co nstraint which5° include1.002 the rotating0.0208 axis position48.22 of deflection, flap thickness and slot width. the flap,r1.51810x0.85g2.4 flap deflection, flapα6d15 thickness and slot10% width. 15° 1.74 0.0337 51.59 r1.51810x0.85g2.4α6d25 10% 25° 1.649 0.1649 10 Table 2.Results for α=6° with the SST transitional turbulence model.

Configurations e2/c2 d CL CD L/D r1.51815x0.85g2.4α6d5 15% 5° 1.005 0.0213 47.16 r1.51815x0.85g2.4α6d15 15% 15° 1.724 0.0338 50.94 r1.51815x0.85g2.4α6d25 15% 25° 1.951 0.06 32.53 r1.51812x0.85g2.4α6d5 12% 5° 1.002 0.0207 48.5 r1.51812x0.85g2.4α6d15 12% 15° 1.73 0.0336 51.47 r1.51812x0.85g2.4α6d25 12% 25° 1.606 0.1628 9.87 r1.51810x0.85g2.4α6d5 10% 5° 1.002 0.0208 48.22 r1.51810x0.85g2.4α6d15 10% 15° 1.74 0.0337 51.59 r1.51810x0.85g2.4α6d25 10% 25° 1.649 0.1649 10

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Table 2. Results for α = 6◦ with the SST transitional turbulence model.

Conﬁgurations e2/c2 d CL CD L/D

r1.51815x0.85g2.4α6d5 15% 5◦ 1.005 0.0213 47.16 r1.51815x0.85g2.4α6d15 15% 15◦ 1.724 0.0338 50.94 r1.51815x0.85g2.4α6d25 15% 25◦ 1.951 0.06 32.53 r1.51812x0.85g2.4α6d5 12% 5◦ 1.002 0.0207 48.5 r1.51812x0.85g2.4α6d15 12% 15◦ 1.73 0.0336 51.47 r1.51812x0.85g2.4α6d25 12% 25◦ 1.606 0.1628 9.87 r1.51810x0.85g2.4α6d5 10% 5 1.002 0.0208 48.22 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW ◦ 10 of 16 r1.51810x0.85g2.4α6d15 10% 15◦ 1.74 0.0337 51.59 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 10 of 16 r1.51810x0.85g2.4α6d25 10% 25◦ 1.649 0.1649 10

Figure 13. The streamlines in the slot region (URANS). Figure 13. The streamlines in the slot region (URANS). Figure 13. The streamlines in the slot region (URANS). 3.2.3.2. Three-DimensionalThree-Dimensional StudyStudy aboutabout EEffeffectct of of Flap Flap Rotation Rotation Axis Axis Position Position 3.2. Three-Dimensional Study about Effect of Flap Rotation Axis Position 3.2.1.3.2.1. AerodynamicAerodynamic PerformancePerformance 3.2.1. Aerodynamic Performance TheThe three-dimensional three-dimensional flow flow around around the the wingsail wingsail at low at low camber camber (d = 15(d◦=) and15°) highand camberhigh camber(d = 25 (d◦)= is25°) studied Theis studied three-dimensional in detail. in detail. In order In orderflow to better aroundto better study the study the wingsail etheffect effect ofat thelow of rotating the camber rotating axis (d= axis position15°) positionand ofhigh the of camber flapthe flap on the( don= aerodynamic25°)the aerodynamicis studied characteristics in detail.characteristics In order and delayed andto better delayed stall study of stall the the of wingsail, effect the wingsail, of wethe analyzed rotating we analyzed theaxis lift position the characteristics lift ofcharacteristics the flap of theon wingsailtheof theaerodynamic wingsail when the when characteristics rotating the rotating axis of and the axis delayed flap of isthe located stall flap of is at thelocated di ffwingsail,erent at positionsdifferent we analyzed ofpo thesitions wingthe oflift chord the characteristics wing (Xr = chord75%, 80%,of(X ther=75%, 85%, wingsail 80%, 90% 85%,andwhen 95%) 90% the atandrotatingα =95%)6◦ andaxis atα=6° 15of◦ the.and flap 15° 。is located at different positions of the wing chord (Xr=75%,FigureFigure 80%, 14 14 shows85%, shows 90% the the and lift lift characteristics 95%) characteristics atα=6° and for di15°forff。erent different rotating rotating axis positions axis positions of the flap. of the The flap. position The ofposition flapFigure rotating of flap14 shows axisrotating has the littleaxis lift has echaracteristicsffect little on effect lift coe on ffifor liftcient different coefficient at α = rotating6 ◦at(stall α=6° axis has(stall notpositions has yet not occurred) yet of occurred)the flap. with with lowThe camper.positionlow camper. of The flap The lift rotating coelift fficoefficientcient axis firsthas first little increases increases effect andon and lift then coefficientthen reduces reduces at with αwith=6° the (stallthe position position has not of ofyet flap flap occurred) rotation rotation with axis axis movinglowmoving camper. backward; backward; The lift especially especially coefficient from from first 80% 80%increases to to 85%, 85%, and it it drops thendrops suddenlyreduces suddenly with at atα the =α=15°(stall15 position◦ (stall has hasof flap occurred).occurred). rotation ItIt axis cancan bemovingbe illustratedillustrated backward; thatthat thethe especially changechange isfromis causedcaused 80% bybyto the85%,the flowflow it drops separationseparation suddenly ofof thethe at wingαwing=15°(stall wakewake has andand occurred). thethe flapflap suctionsuction It can surfacebesurface illustrated fromfrom FigurethatFigure the 16. 16. change AtAtα α= =6°is6 caused◦ withwith high highby the camber, flow separation the lift coecoefficient offfi thecient wing increasesincreases wake withandwith the thethe flap positionposition suction ofof thesurfacethe flapflap from rotating rotating Figure axis axis 16. moving moving At α=6° backward, back withward, high especially especially camber, from fromthe lift 85% 85% coefficient to to 95%. 95%. ItIt increases cancan bebe explainedexplai withned the from fromposition FigureFigure of 17bthe17b flap that that rotating the the flow flow axis separation separation moving on onback the theward, suction suction especially surface surface offrom of the the 85% flap flap to has has 95%. disappeared. disappeared. It can be explai ned from Figure 17b that the flow separation on the suction surface of the flap has disappeared. 2 AOA=6o d=15o 2 AOA=15o d=15o o o AOA=6AOA=6o d=15d=25o o o 1.5 AOA=15 d=15 AOA=6o d=25o 1.5 [-] l

C 1 [-] l

C 1

0.5

0.7 0.8 0.9 1

Xr/c1 [-] 0.7 0.8 0.9 1 X /c [-] Figure 14. Lift coefficient versus flap rotation axisr 1 position of the wingsail in low and high camber Figure 14.Lift coefficient versus flap rotation axis position of the wingsail in low and high camber configuration. Figureconfiguration. 14.Lift coefficient versus flap rotation axis position of the wingsail in low and high camber configuration.

3.2.2. Streamlines 3.2.2. Streamlines As for the wingsails with different rotating axis positions of the flap at α=15°and d=15°, the streamlinesAs for theon wingsailsthe mid-span with ofdifferent wingsail rotating are depict axised positions in Figure of 15.the Itflap can at be α =15°andfound that d=15°, a small the streamlinesseparation vortexon the appearsmid-span in ofthe wingsail wake of are the depict winged and in aFigure large 15.separation It can be vortex found appears that a insmall the separationregions over vortex the suction appears surface in the of wake the flap of theat X rwi=90%.ng and a large separation vortex appears in the regions over the suction surface of the flap at Xr=90%.

J. Mar. Sci. Eng. 2020, 8, 333 10 of 15

3.2.2. Streamlines

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 overJ. Mar. the Sci. suctionEng. 2019, surface 7, x FOR ofPEER the REVIEW flap at Xr = 90%. 11 of 16

(a) Xr = 75%

(b) Xr = 85%

(d) Xr = 95%

FigureFigure 15. 15.Streamlines Streamlines at at mid-span mid-span of of the the wingsail wingsail at at ( a(a))X Xr r==75%75% (b) (b )XXr=85%r = 85% (c) X (cr=90%)Xr = and90% (d) and

(d)Xr = 95% with α = 15◦, d = 15◦. Xr=95% with α=15°, d=15°.

Figure 16 shows the limitinglimiting streamlinestreamline andand staticstatic pressurepressure contourscontours onon suctionsuction surfacesurface forfor two-elementtwo-element wingsailwingsail atat didifferentfferent rotating rotating axis axis positions positions of of the the flap. flap. With With the the backward backward movement movement of theof the rotating rotating axis axis position position of the of flap, the theflap, flow the separationflow separation of the suctionof the suct surfaceion ofsurface the wing of the expands wing fromexpands the bladefrom rootthe toblade the top,root and to thethe returntop, and area the becomes return larger area forbecomes the low larger camber for wingsail. the low The camber flow separation line appears on the suction surface of the wing at X = 85%. It explains that the forward wingsail. The flow separation line appears on the suction surfacer of the wing at Xr=85%. It explains movementthat the forward of the movement rotating axis of the position rotating of theaxis flap position increases of the the flap fluid increases flow through the fluid the flow slot, through delays thethe flowslot, delays separation the flow of the separation suction surfaceof the suction of the wing,surface or of delays the wing stall, or of delays the wingsail. stall of the An wingsail. obvious separation helix appears on the suction surface of the wing at X = 95%, which indicates that the vortex An obvious separation helix appears on the suction surface ofr the wing at Xr=95%, which indicates hasthat beenthe vortex formed. hasWhen been formed. the rotating When axis the position rotating ofaxis the position flap is movesof the flap backward is moves from backward 90% to from 95%, the90% flow to 95%, separation the flow on separation the suction on surface the suction of flap surface disappears. of flap Wedisappears. guess the We fluid guess flowing the fluid through flowing the smallerthrough gap the does smaller not supplementgap does not the supplement wake of the wing,the wake but flowsof the along wing, the bu flapt flows boundary along layer. the flap boundary layer.

J. Mar. Sci. Eng. 2020, 8, 333 11 of 15 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 12 of 16

(a) Xr = 75% (b) Xr = 80%

(e) Xr = 95%

Figure 16. Limiting streamline and static pressure contours on suction surface for the two-element Figure 16. Limiting streamline and static pressure contours on suction surface for the two-element wingsail at (a)X = 75% (b)X = 80% (c)X = 85% (d)X = 90% and (e)X = 95% with α = 15 , d = 15 . wingsailr at (a) Xr=75%r (b) Xr=80% r(c) Xr=85% (d)r Xr=90% and (e) Xr=95%r with α=15°, d=15°.◦ ◦ 3.2.3. Velocity Magnitude Contours 3.2.3. Velocity Magnitude Contours It canIt be can seen be seen from from Figure Figure 17 17 that that the the suction suction su surfacerface of of the the wing wing has has a large a large flow flowseparation separation at at α =α15=15°◦ with with low low camber. camber. AtAt XXr r=85%,= 85%, the the fluid fluid flowing flowing through through the the slot slot complements complements the theflow 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 Xr = 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 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 13 of 16 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.separation The of theslot wingjet can wake be observed and the clearlyflap suction at Xr =su 90%.rface. As There a result is no of vortexthe reduced in the slot mid-span width dueof the to J.thewingsail. Mar. rotating Sci. Eng.The axis2020 slot ,position8 jet, 333 can be of observedthe flap backward, clearly at Xther = slot90%. jet As only a result divides of the the reduced vortex ofslot the width wing due12 wake of to 15 andthe rotatingthere is aaxis large-scale position flow of the separation flap backward, on the suctthe slotion surfacejet only of divides the flap, the wh vortexich causes of the deep wing stall wake of theand flap.there This is a large-scalephenomenon flow has separation also been on observed the suction and surface described of the in flap, Biber wh ich[27] causes and Chapin deep stall [18]. of flap. This phenomenon has also been observed and described in Biber [27] and Chapin [18]. Because Becausethe flap. ofThis the phenomenonsmaller slot width has also at X beenr = 95%, observed the slot and jet only described flows alongin Biber the [27]boundary and Chapin layer of [18]. the of the smaller slot width at Xr = 95%, the slot jet only flows along the boundary layer of the flap, which flap,Because which of the has smaller little effect slot onwidth the atseparation Xr = 95%, flow the slotof the jet wingonly flowswake. along If the theslot boundary is further layerreduced of the or has little effect on the separation flow of the wing wake. If the slot is further reduced or not set, the flap notflap, set, which the flaphas littlesetting effect may on aggravate the separation the separation flow of the of wingthe wing wake. wake, If the such slot asis thefurther research reduced of the or setting may aggravate the separation of the wing wake, such as the research of the hybrid sail designed hybridnot set, sailthe designedflap setting by mayQiao aggravate Li [14]. However, the separation the forward of the movementwing wake, of such the asrotating the research axis position of the by Qiao Li [14]. However, the forward movement of the rotating axis position of the flap is limited by ofhybrid the flapsail designedis limited byby Qiao the flapLi [14]. deflection However, angl thee. Asforward shown movement in Figure of18, the when rotating the axisrotating position axis the flap deflection angle. As shown in Figure 18, when the rotating axis position of the flap moves positionof the flap of theis limited flap moves by the forward flap deflection from 90% angl to 85%e. As at shownα= 6°, thein Figurelarge-scale 18, whenflow separationthe rotating occurs axis forward from 90% to 85% at α= 6 , the large-scale flow separation occurs on the suction surface of the onposition the suction of the surfaceflap moves of the forward flap,◦ as from the phenomen90% to 85%on at seen α= 6°, by the Fiumara large-scale [19] inflow the separation two-element occurs sail flap, as the phenomenon seen by Fiumara [19] in the two-element sail experiment in 2016. experimenton the suction in 2016.surface of the flap, as the phenomenon seen by Fiumara [19] in the two-element sail experiment in 2016.

(a) Xr = 85% (a) Xr = 85%

(b) Xr = 90% (b) Xr = 90%

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

(a) Xr = 85% (a) Xr = 85%

(b) Xr = 90%

Figure 18. Cont.

J. Mar. Sci. Eng. 2020, 8, 333 13 of 15 J. Mar. Sci. Eng. 2019, 7, x FOR PEER REVIEW 14 of 16

Figure 18. VelocityVelocity magnitude magnitude contours contours at at mid-span mid-span of ofwingsail wingsail at at(a) ( aX)Xr= 85%r = 85% (b) X (rb=)X 90%r = and90% (c)X andr= (c)Xr = 95% with α = 6◦, d = 25◦. 95% with α=6°，d=25°.

4. Conclusions Conclusions By studying the influenceinfluence of flapflap geometric parametersparameters on the aerodynamic characteristics of two-element wingsailwingsail under under steady steady and unsteady and conditions,unsteady two-dimensionalconditions, two-dimensional and three-dimensional and related parameters were simulated using the same Reynolds number (Re = 5 105). three-dimensional related parameters were simulated using the same Reynolds× number (Re =5×105). The 2D simulation resultsresults showshow that, that, when when the the rotating rotating axis axis position position of of the the flap flap is is located located at at 85% 85% of ofthe the wing wing chord, chord, the thickening the thickening flap leads flap to leads an increase to an ofincrease the leading-edge of the leading-edge radius which radius decreases which the pressuredecreases coe theffi pressurecient suction coefficient peak and suction has postponed peak and thehas stall postponed of the wingsail the stall for of high the wingsail camber. Itfor reflects high camber.the nonlinear It reflects coupling the nonlinear effect between coupling wingsail effect camberbetween and wingsail flap thickness. camber and When flap the thickness. rotating axisWhen of the rotating flap is located axis of at the the flap 75% is oflocated the wing at the chord, 75% theof the stall wing angle chord, is delayed the stall with angle the is increase delayed of with the flapthe increasedeflection of anglethe flap at lowdeflection camber. angle When at low selecting camber. the When geometric selecting parameters the geometric of the parameters flap, factors of such the flap,as the factors position such of theas the flap position rotation of axis, thethe flap flap rota deflectiontion axis,angle, the flap and deflection the flap thicknessangle, and need theto flap be thicknessconsidered need comprehensively. to be considered comprehensively. The 3D simulation mainly studies the influence influence of the flap flap rotating axis position and the flap flap deflectiondeflection angle angle on on the the stall stall characteristics characteristics of of the the wingsail. wingsail. When When stall stall has hasnot notyet occurred yet occurred with with low camber,low camber, the therotating rotating axis axis position position of the of the flap flap has has little little effect effect on on the the lift lift coefficient, coefficient, while while stall stall has occurred, the lift coefficient coefficient increases firstfirst and then re reducesduces with the rotating axis position of the flap flap moving backward. The The flow flow separation separation of of the the suctio suctionn surface of of the wing expands from the root to the top and the return area becomes larger, especiallyespecially from the 80% to the 85%, the lift coecoefficientfficient drops suddenly. This is caused by the flowflow separationseparation between the wing wake and the flapflap suction surface. At high camber withwith AOAAOA=6°,= 6◦ the, the lift lift coef coeficientfficient always always increases increases with with the the position position of the flapflap rotation axis,axis, especiallyespecially from from 85% 85% to to 95%, 95%, the the lift lift coe coefficientfficient suddenly suddenly rises, rises, which which is caused is caused by theby thedisappearance disappearance of large-scale of large-scale flow flow separation separation of the of flapthe flap suction suction surface. surface. Therefore, the slot width is an important factor affecting affecting the flowflow separation of the wing wake and the suction surface of the flap, flap, where size is affe affectedcted by the rotating axis position of the flapflap and the flap flap deflectiondeflection angle. When When the the flap flap deflection deflection an anglegle is is adjusted adjusted to to obtain obtain a a large large lift lift coefficient, coefficient, the restriction of the rotating axis position of the fl flapap must be considered to ensure a reasonable stall angle range.

Author Contributions: Conceptualization,conceptualization, C.L. C.L. and and H. H.W.;W.; investigation, investigation, C.L. C.L. and and H.W.; H.W.; methodolo methodology,gy, C.L. and P.S.; software,software, C.L.;C.L.; writing—originalwriting—original draft draft preparation, preparation, C.L.; C.L.; writing—review writing—review and and editing, editing, H.W.; H.W.; supervision, supervision, P.S. AllP.S. 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 Funds Funding:of Jiangsu This Maritime research Institute, was 014070,funded kjcx-1907.by National Natural Science Foundation of China,51709165, Research 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.

References

1. Ishihara, M., Watanabe, T., Shimizu, K. Yoshimi, K., Namura, H. Prospect of sailequipped motor ship as assessed from experimental ship Daioh. Proceedings of the Shipboard Energy Conservation Symposium; Society of Naval Architects and Marine Engineers, New York, America 1980; pp. 181–198. 2. Available online: http://www.sohu.com/a/275284498_100091571 (accessed on 14 November 2018).

J. Mar. Sci. Eng. 2020, 8, 333 14 of 15

Nomenclature

Re Reynolds number [-] α Angle of attack of the main wing (AOA) [◦] c total chord of the wingsail [m] c1 chord of the main wing [m] c2 chord of the flap [m] CD Drag coefficient [-] CL Lift coefficient [-] d Flap deflection angle [◦] g non-dimensional slot width (g/c1) [-] e1 thickness of the main wing [m] e2 thickness of the flap [m] 2 AR The aspect area of wingsail [m ] y+ Non-dimensional wall distance [-] ρ The density of the air [kg/m3] z The height of wingsail in the vertical direction [m] h Wingsail height [m] L Lift force [N] D Drag force [N] v The velocity of inflow [m/s] Xr The position of flap rotation axis in the direction of the wing chord [-]

References

1. Ishihara, M.; Watanabe, T.; Shimizu, K.; Yoshimi, K.; Namura, H. Prospect of sailequipped motor ship as assessed from experimental ship Daioh. In Proceedings of the Shipboard Energy Conservation Symposium; Society of Naval Architects and Marine Engineers: New York, NY, USA, 1980; pp. 181–198. 2. Available online: http://www.sohu.com/a/275284498_100091571 (accessed on 14 November 2018). 3. Blakeley, A.W.; Flay, R.G.J.; Richards, P.J. Design and Optimisation of Multi-Element Wing Sails for Multihull Yachts. In Proceedings of the 18th Australasian Fluid Mechanics Conference, Tasmania, Australia, 3–7 December 2012. 4. Available online: http://k.sina.com.cn/article_6424865154_17ef3a982001001t6p.html (accessed on 20 December 2017). 5. Kind, R.J. An Experimentel Investigation of a Low- Speed Circulation Controlled Airfoil. Aero. Quart. 1968, 19, 170–182. [CrossRef] 6. Seifert, A.; Bachar, T.; Koss, D.; Shepshelovich, M.; Wygnanski, I. Oscillatory Blowing: A Tool to Delay Boundary-Layer Separation. AIAA J. 1993, 31, 2052–2060. [CrossRef] 7. Seifert, A.; Darabi, A.; Wyganski, I. Delay of airfoil stall by periodic excitation. J. Aircr. 1996, 33, 691–698. [CrossRef] 8. Kralj, D.M.; Klarin, B. Wing Sails for Hybrid Propulsion of a Ship. J. Sustain. Dev. Energy Water Environ. Syst. 2016, 4, 1–13. [CrossRef] 9. Marine, B. E-ShiP1 with Sailing Rotors to Reduce Fuel Costs and to Reduce Emissions. Available online: http://www.marinebuzz.com (accessed on 28 August 2008). 10. Borglund, D.; Kuttenkeuler, J. Active Wing Flutter Suppression Using A Trailing Edge Flap. J. Fluids Struct. 2002, 16, 271–294. [CrossRef] 11. Daniel, W.A. The CFD Assisted Design and Experimental Testing of a Wingsail with High Lift Devices; University of Salford: Salford, UK, 1996. 12. Carr, L.W.; McAlister, K.W. The eﬀect of a leading-edge slat on the dynamic stall of an oscillating airfoil. AIAA Pap. 1983, 83, 2533. 13. Available online: http://cookeassociates.com/sports/commercial,php (accessed on 6 August 2015). 14. Li, Q.; Nihei, Y.; Nakashima, T.; Iked, Y. A study on the performance of cascade hard sails and sail-equipped vessels. Ocean Eng. 2015, 98, 23–31. [CrossRef] J. Mar. Sci. Eng. 2020, 8, 333 15 of 15

15. Fish, F.E.; Battle, J.M. Hydrodynamic design of the humpback whale flipper. J. Morphol. 1995, 225, 51–60. [CrossRef][PubMed] 16. Toshifumi, F.; Koichi, H.; Michio, U.; Nimura, T. On aerodynamic characteristics of a hybrid-sail with square soft sail. In Proceedings of the International Offshore and Polar Engineering Conference, International Society of Offshore and Polar Engineers, Honolulu, HI, USA, 25–30 May 2003; pp. 2576–2583. 17. Fujiwara, T.; Hirata, K.; Ueno, M.; Nimura, T. On the development of high-performance sails for an ocean-going sailing ship. In Proceedings of the International Conference on Marine Simulation and Ship Manoeuvrability, MARSIM’03, Kanazawa, Kanazawa, Japan, 25–28 August 2003. RC-23-1–9. 18. Chapin, V.; Gourdain, N.; Verdin, N. Aerodynamic Study of a Two-elements Wingsail for High Performance Multihull Yachts. In Proceedings of the 5th High Performance Yacht Design Conference Auckland, Auckland, New Zealand, 10–12 March 2015. 19. Fiumara, A.; Gourdain, N.; Chapin, V.; Senter, J.; Bury, Y. Numerical and experimental analysis of the flow around a two-element wingsail at Reynolds number 0.53 106. Int. J. Heat Fluid Flow 2016, 62, 538–551. × [CrossRef] 20. Menter, F.R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 1994, 32, 1598–1605. [CrossRef] 21. Hassan, G.E.; Hassan, A.; Youssef, M.E. Numerical Investigation of Medium Range Re Number Aerodynamics Characteristics for NACA0018 Airfoil. CFD Lett. 2014, 6, 175–187. 22. Malan, P.; Suluksna, K.; Juntasaro, E. Calibrating the γ-Reθ Transition Model for Commercial CFD. In Proceedings of the 47th AIAA Aerospace Science Meeting, Orlando, FL, USA, 5–8 January 2009. 23. Douvi, C.E.; Tsavalos, I.A.; Margaris, P.D. Evaluation of the Turbulence Models for the Simulation of the Flow Over a National Advisory Committee for Aeronautics (NACA) 0012 Airfoil. Mech. Eng. Res. 2012, 4, 100–111. 24. Rhee, S.H.; Kim, H. A suggestion of gap flow control devices for the suppression of rudder cavitation. J. Mar. Sci. Technol. 2008, 13, 356–370. [CrossRef] 25. Gentry, A. The Aerodynamic of Sail Interaction. In Proceedings of the 3th AIAA Symposium on the Aero/Hydronautics of Sailing, Redondo Beach, CA, USA, 20 November 1971. 26. Smith, A.M.O. High-Lift Aerodynamics. J. Aircr. 1975, 12, 501–530. [CrossRef] 27. Biber, K.; Zumwalt, G. Experimental studies of a two-element airfoil with large separation. In Proceedings of the 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 6–9 January 1992. [CrossRef]

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