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An eco-friendly, alternative energy source is a key topic in all engineering fields. In the ship industry, wing-sail technology is drawing great attention as a new type of propulsion that takes full advantage of free wind energy. The purpose of our study is to numerically analyze the aerodynamic characteristics of wing-sails and optimize their shape and operation conditions in terms of the angle of attack, flap length, and deflection angle under various wind directions. A viscous Navier-Stokes flow solver is used for the numerical aerodynamic analysis. A design optimization framework using an evolutionary algorithm and the Kriging surrogate model is developed and finds the optimum operation condition for multiple wing-sails to maximize the resultant propulsive force. First, the exact response surfaces of Cl and Cd are created for a single wing-sail, and a simple trade-off study is conducted to investigate the flap effects in terms of its deflection angle and flap length. Next, the proposed design optimization framework is applied to find the optimum shape and operating conditions for multiple wing-sails, which have three identical wing-sails in a row. A total of nine design variables are employed, including the angle of attack, flap length and deflection angle for each wing-sail, and relative wind direction, which is allowed to vary from 45° to 90° and 135°. Although the design is carried out using a two-dimensional topology, mostly because of the high computational cost related to the nature of gradient free optimization algorithms, the design results are validated using a high-fidelity three-dimensional Computational Fluid Dynamics analysis. Predicted improvement in two-dimensional analysis of the averaged thrust by 14~22% of the baseline values turned out to be slightly lower and becomes 10~17% in full three-dimensional flow analysis. Although an initial set of the angle of attack values is varied from 8° to 9.5° to investigate the effects of the initial angle of attack, the trends of the design optimization are preserved. In summary, multiple wing-sails can enhance a ship's propulsion system by more than 10%.

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Aerodynamic Design Optimization of Wing- Sails

Yeongmin Jo

, Hakjin Lee2, and Seongim Choi3

Korea Advanced Institute of Science and Technology , Daejeon, Republic of Korea

An eco-friendly, alternative energy source is a key topic in all engineering fields. In the

ship industry, wing-sail technology is drawing great attention as a new type of propulsion

that takes full advantage of free wind energy. The purpose of our study is to numerically

analyze the aerodynamic characteristics of wing-sails and optimize their shape and

operation conditions in terms of the angle of attack, flap length, and deflection angle under

various wind directions. A viscous Navier-Stokes flow solver is used for the numerical

aerodynamic analysis. A design optimization framework using an evolutionary algorithm

and the Kriging surrogate model is developed and finds the optimum operation condition for

multiple wing-sails to maximize the resultant propulsive force. First, the exact response

surfaces of Cl and Cd are created for a single wing-sail, and a simple trade-off study is

conducted to investigate the flap effects in terms of its deflection angle and flap length. Next,

the proposed design optimization framework is applied to find the optimum shape and

operating conditions for multiple wing-sails, which have three identical wing-sails in a row.

A total of nine design variables are employed, including the angle of attack, flap length and

deflection angle for each wing-sail, and relative wind direction, which is allowed to vary

from 45° to 90° and 135°. Although the design is carried out using a two-dimensional

topology, mostly because of the high computational cost related to the nature of gradient-

free optimization algorithms, the design results are validated using a high-fidelity three-

dimensional Computational Fluid Dynamics analysis. Predicted improvement in two-

dimensional analysis of the averaged thrust by 14~22% of the baseline values turned out to

be slightly lower and becomes 10~17% in full three-dimensional flow analysis. Although an

initial set of the angle of attack values is varied from 8° to 9.5° to investigate the effects of the

initial angle of attack, the trends of the design optimization are preserved. In summary,

multiple wing-sails can enhance a ship's propulsion system by more than 10% .

Nomenclature

CL = Lift coefficient

CD = Drag coefficient

Cfx = Thrust coefficient along x-direction

Cfx.ave = Averaged thrust coefficient along x-direcion

CP = Surface pressure coefficient

α = AoA (Angle of attack)

δ = Flap angle

θ = Wind direction

I. Introduction

nergy is becoming a pressing issue in industry and academia because energy consumption has been growing

continuously and is focused mainly on fossil fuels, which create environmental pollution. An eco-friendly

energy source as an alternative to fossil fuels is actively sought in all engineering fields.

In the ship industry, a conventional propulsion system also greatly relies on fossil fuels and the emission of

pollutants causes great problems in the ocean system. Therefore, new propulsion technologies have been developed

Ph.D. Candidate, Dept. of Aerospace Engineering, AIAA Member

2Ms.D. Candidate, Dept. of Aerospace Engineering, AIAA Member

3Assistant Professor, Dept. of Aerospace Engineering, AIAA Member, Corresponding Author

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31st AIAA Applied Aerodynamics Conference

June 24-27, 2013, San Diego, CA AIAA 2013-2524

American Institute of Aeronautics and Astronautics

that can replace existing reciprocating and turbine engines, and use eco-friendly alternative energy sources. One of

these uses wind energy as an additional propulsive force. In fact, it has always been the main source of propulsion

for sailing ships. The basic concept is to enhance the existing propulsion efficiently by using aerodynamic

propulsion provided by sails or "wing -sails," which utilize the same shape as the wing of an airplane rather than

conventional sails made of fabric. Recent research results reached the conclusion that more than 50% of the existing

propulsion force can be replaced with wing-sails, leading to a saving of an equivalent proportion of fossil fuels 1 .

Research on wing-sails has been conducted by many groups. Kazuyuki Ouchi et al. performed aerodynamic and

structure analyses of multiple wing-sails using numerical methods1. Toshifumi Fujiwara et al. studied the

aerodynamic characteristics of multiple wing-sails with respect to the angle of the boom and slot2. Furthermore,

Toshifumi Fujiwara et al. carried out a wind tunnel experiment to reveal the sail-sail and sail-hull interaction effects

of a hybrid sail3. Takuji Nakashima et al. conducted a wind tunnel measurement and numerical simulation to clarify

the aerodynamic interaction phenomena between wing-sails in a new conceptual wind-driven vessel4. However,

most of these studies focused only on an aerodynamic analysis of the wing-sails and depended on wind tunnel

experiments. Not much attention has been given to the design aspect of multiple wing-sails. In the present study, we

conduct a high-fidelity based design optimization, which is tightly coupled with numerical analysis and optimization

algorithms.

In this study, we perform a high-fidelity aerodynamic analysis using Computational Fluid Dynamics (CFD) flow

solvers to investigate the aerodynamic characteristics of multiple wing-sails, and the highly accurate flow analysis is

directly used for aerodynamic design optimization in consideration of flow interactions in the multiple wing-sails. A

key advantage of our work is conduction of a trade-off study of the design parameters that are known to be effective

in improving the wing-sail performance. We find the optimum topology of the multiple wing-sails in terms of the

operation conditions and flap configuration. First, we conduct an aerodynamic analysis to investigate the effects of

the flow interactions and aerodynamic characteristics of the multiple wing-sails. A viscous Navier-Stokes solver is

used with an unstructured mesh topology for both two- and three-dimensional numerical analyses of the multiple

wing-sails. The turbulence model of Spalart-Allmaras (SA) is employed. The magnitude of the propulsive force is

investigated for the wing-sails both with and without the flap, while the wind direction is allowed to vary from 0° to

360° in 15° steps. To validate the accuracy of the CFD solver for the current flow conditions of the wing-sails, a

two-dimensional flow analysis is conducted around the NACA0012 airfoil, and the results are compared with the

experimental values. Next, an aerodynamic design optimization framework for multiple wing-sails is developed.

This framework uses evolutionary algorithms and the Kriging surrogate model. The optimization framework is fully

automated.

The evolutionary algorithm of the genetic algorithm (GA) is particularly attractive because it does not require

gradient-based sensitivity information and is very robust and effective at finding the global optimum. Furthermore,

the GA searches the entire design space and is less likely than a gradient-based method to get stuck at the local

optimum. However, the GA requires a large number of function evaluations in each generation. To alleviate the

computational cost of the optimization algorithm related to the large number of function evaluations, we employ the

Kriging surrogate model, which is an interpolation-based surrogate model. A surrogate model, known as an

approximate model or meta model, is an efficient way of alleviating an expensive computing burden. The Kriging

surrogate model is created by evaluating an initial sampling set of function evaluations through high-fidelity Navier-

Stokes flow solutions. We also carry out the high-fidelity CFD-based design optimization using a continuous adjoint

method tightly coupled with the CFD solver and adjoint solver. Because we consider the operating condition as well

as the flap configuration as design variables, it is difficult to smoothly handle the mesh deformation.

Using this design framework, we find the optimal setup for the multiple wing-sails to maximize the averaged

thrust coefficient and thus increase the overall propulsive force. A total of nine design variables are employed, and

each wing-sail has design parameters for varying the angle of attack of the wing-sail and the flap configurations in

terms of the length and its deflection angles. In our previous study, we only considered the variation in the angle of

attack of each wing-sail as design variables that could be rotated up to ±15° independently5,6. However, in this study,

we consider not only the angle of attack but also the flap length and deflection angle of each wing-sail as design

variables. Finally, the optimal design variables are obtained to maximize the averaged thrust performance of the

multiple wing-sails, and the wind direction is allowed to vary from 45° to 90° and 135°. We initially perform the

design optimization at an angle of attack of 8° and later at 9.5°, because a 9.5° angle of attack is closer to a stall

condition. As a result, we achieve a thrust improvement of approximately 14~22% at the initial angle of attack of

AoA = 8° and 10~12% at AoA = 9.5°. Although the design is carried out based on the two-dimensional flow

analysis, mostly because of the expensive computational cost, a validation is carried out with the complete three-

dimensional wing-sails using a CFD analysis to determine whether the thrust improvement achieved from the two-

dimensional assumption is valid. The results show that the thrust performance improvement in the multiple wing-

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sails becomes slightly lower in the three-dimensional analysis (10~17% at AoA = 8° and 9~11% at AoA = 9.5°),

which is very predictable considering the three-dimensional aerodynamic effects, including cross-flows.

In conclusion, our work has advantages of providing information useful for understanding the aerodynamic

characteristics of wing-sails and of determining the optimum setup for multiple wing-sails under various operation

conditions. Our work indicates that the concept of wing-sails is a valid and viable tool that can serve as an efficient

alternative propulsion system in the ship industry.

The outline of this paper is as follows. Section II introduces the concept of wing-sails, topology of multiple

wing-sails, and force relation for evaluating the thrust performance. Sections III and IV respectively describe the

aerodynamic analysis method and design optimization framework. Section IV discusses the Kriging approach for

surrogate modeling, as well as the GA employed in this study. Section V explains the aerodynamic characteristics

and flow interaction of multiple wing-sails. Section VI then shows the results of the aerodynamic design

optimization, initially at an angle of attack of 8° and then at 9.5° in consideration of the flow interaction, as

mentioned in Section V. Section VII concludes this paper.

II. Concept of Wing-Sails

A sailing ship is an eco-friendly and fuel-efficient vessel that uses wing-sails to support an existing fossil fuel-

based propulsion system. The wing-sail technology uses the free wind energy available at sea to produce an

additional thrust force. As shown in Fig. 1 (left), the "Shin - Aitoku Maru" was the first sailing ship to use a wing-

sail propulsion system. It was introduced by JAMDA Japan in the 1970s. At first, simple flat-type sails were applied.

Then, the sailing ship shown in the right-hand illustration of Fig. 1 was developed, which utilized sails with an

airfoil shape instead of the flat-type of sail6. This considerably improved the aerodynamic performances of the wing-

sails.

Fig. 1 Examples of wing-sail ships: Shin-Aitoku Maru (left)7 and UT Wind Challenger ship (right) 8

The wing-sails are located in the limited space available on the main deck8. The number of wing-sails is

generally determined by the size of the ship. In a previous study, a wing-sail system with a total of six sails was

considered for a cargo ship in the 100-K DWT (Dead Weight Tons) class5,6. In this study, we consider a wing-sail

system with three sails for a cargo ship in the 50-K DWT class. The reduction in the number of wing-sails in the

present study is based on the observation that the most dynamic flow interaction occurs in the area of the first three

wing-sails. Fig. 2 shows a schematic of the wing-sail system being considered here. Each wing-sail has a chord

length of 10 m, height of 20 m, and aspect ratio of 2 without any taper. In addition, the interval between the wing-

sails is 15 m, which is 1.5 times the chord length. The three wing-sails are arranged along the x direction. The wing-

sails can rotate to face various wind directions, and the axis of rotation is located at 40% of each chord length. The

sectional shape of the wing-sails is an NACA 0012 airfoil, which is symmetric and does not have a camber. The

reason for selecting the symmetric airfoil is to prevent any negative effects on the aerodynamic performance because

the wind direction can vary from 0° to 360° during a cruise mission. To improve the aerodynamic performance of

the wing-sails, as shown in Fig. 2, a flap system is considered as a high-lift device.

As shown in Fig. 2, if the wing-sails are constructed as multiple arrangements in a row to generate more thrust, a

flow interaction occurs among them, and it has a significant effect on the aerodynamic performance of the multiple

wing-sails. Therefore, in order to estimate the thrust of multiple wing-sails, the effect of this flow interaction should

be considered. In our previous study5,6, to investigate the effect of the flow interaction and the flow characteristics

around multiple wing-sails, we performed a three dimensional aerodynamic analysis of six sails using a high-fidelity

numerical analysis.

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Fig. 2 Schematic view of multiple wing-sails

Fig. 3 shows a force diagram representing the sail direction, relative wind direction, and force coefficients acting

on the wing-sail. Consider that the direction that the ship is being propelled in is parallel to the x direction. Then, the

resultant force along the x-direction, which is thrust vector Cfx, can be calculated using Eq. (1). The formulation of

the thrust vector can be defined as a function of the wind direction (

) and aerodynamic coefficients (

) of

the wing-sails. It is assumed that the resultant force along the y direction is canceled out by the rudders of a thrust

vectoring system, such as azimuth thrusters, and we do not consider any side components of the force other than the

propulsive force. The thrust generation principles are applied to each wing-sail. The thrust coefficients along both

the x and y directions can be calculated using Eq. (1) and Eq. (2). For multiple wing-sails, the average thrust is

considered to be a performance indicator, and it is an average thrust coefficient divided by the number of wing-sails.

In this study, a wing-sail system with three sails is considered; thus, the average thrust is defined as Eq. (3).

Fig. 3 Resultant force relation

sin( ) cos( )

fx L D

C C C





(1)

cos( ) sin( )

fy L D

C C C





(2)

(3)

III. Aerodynamic Analysis Methods

In order to investigate the flow phenomena, an appropriate CFD flow solver must be selected. SU 2_CFD is fluid

dynamics software for simulations in a parallel computation environment, along with a module for partitioning the

volumetric grid as a pre-processor in parallel flow computations. SU2_CFD solver can provide direct flow solutions

and adjoint solutions for potential, Euler, Navier-Stokes, and Reynolds Averaged Navier-Stokes (RANS) governing

equations. It uses a Finite Volume Method (FVM) for spatial discretization. Both explicit and implicit methods are

available for time integration, and central difference or upwind methods can also be used for spatial discretization.

To improve the robustness and convergence of the flow solution, the advanced numerical techniques of residual

smoothing and agglomeration multi-grid methods are also available9 .

For the numerical analysis, we solve the two- and three-dimensional compressible RANS governing equations,

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American Institute of Aeronautics and Astronautics

which describe the conservation of mass, momentum, and energy in a viscous fluid. These governing equations have

the following structure10 :

tU F F Q        

(4)

where

is the time and

is the domain.

denotes the vector of state variables;

are the convective fluxes

(inviscid fluxes);

are the viscous fluxes; and

is a source term.

Eqs. (5) and (6) give a brief description of the physics involved for each component of the governing equations:

 

1 2 3

, , , , T

U v v v E

    



(5)

cii

vv P

F vv P

vv P

























j ij tot p i

v C T

















(6)

where

is the density;

is the static pressure;

is the total energy per unit mass;

is the fluid enthalpy; and

is the flow velocity vector in a Cartesian coordinate system. In these formulations, the static

pressure

could be derived from the state equation with the assumption of an ideal gas.

2 2 2

1 2 3

( 1)[ ( )]

P E v v v



    

(7)

(8)

where

is the temperature;

is the specific heat ratio; and

is a gas constant.

is the specific heat at a

constant pressure, and

is the Kronecker delta function. For the viscous flux term of Eq. (6), the viscous stresses

can be written as Eq. (9). The viscosity is defined by Stokes' assumption.

()

ij tot j i i j ij

v v v

  

     

(9)

(10)

The dynamic viscosity (molecular laminar viscosity)

is derived using Sutherland's Law11 , and the turbulent

viscosity

is calculated using a turbulence model.

and

are the Prandtl numbers for laminar and turbulent

flows, which have values set at

and

, respectively. In the present paper, we use the one-equation turbulence

model of Spalart-Allmaras (SA) to compute turbulent viscosity

The spatial terms of the governing equations are discretized using the cell-vertex (node) based Finite Volume

Method (FVM with a median-dual control volume technique. The inviscid and viscous flux terms are evaluated

using the central difference scheme, which is second-order accurate in space. For a high-resolution solution, we use

the Jameson-Schmidt-Turkel (JST) scheme as an artificial viscosity term12. To obtain a steady-state solution, we

perform pseudo-time integration using the Lower-Upper Symmetric Gauss Seidel (LU-SGS)13 scheme. The SA

turbulent model is used to consider turbulent eddies.

In this study, the flow around the multiple wing-sails has a very low speed. In this velocity region, it is important

to consider the viscous effect for a more accurate flow solution. Because of the viscous effect on the wall, a

boundary layer flow is developed and has to be accurately captured. Correspondingly, a high-resolution mesh is

required near the wall with the value of y+ close to unity. In the unstructured grid methodology, mixed grids (2D:

quadrangle + triangle, 3D: hexahedron + tetrahedron) are generally utilized for the viscous computation. A mixed

grid of quadrangles and triangles is used in the two-dimensional mesh, and a combination of hexahedrons and

tetrahedrons is used for the three-dimensional mesh topology. The mixed grid topology for our multiple-wing-sail

configuration is shown in Fig. 4. The size of the computational domain is 25 × 10 × 5 times the chord length.

Downloaded by Seongim Choi on July 9, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2013-2524

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Fig. 4 Computational domain of mixed grid system around multiple wing-sails

In order to consider the viscosity effects, a no-slip boundary condition is used as a wall boundary condition on

the wing-sail surface. A nonreflecting, far-field boundary condition using Riemann invariants is imposed on the far-

field boundary condition, and the symmetry condition is used for the root plane of the wing-sails. The far-field

boundary condition prevents reflected disturbances from coming back within the boundaries. In addition, because of

the symmetry plane boundary condition, there is no flow across the boundary at the root plane of the wing-sails.

IV. Design Optimization Framework

In addition to the aerodynamic analysis of the multiple wing-sails, we developed a design optimization

framework, which is tightly coupled with the high-fidelity flow analysis and gradient-free optimization algorithms.

In this section, we explain two components of the current design optimization framework: Kriging surrogate model

and GA. We also introduce a fully automated design optimization framework that integrates the geometry kernel,

mesh generation and deformation, flow solution, and optimization algorithm.

A. Kriging surrogate model

Gradient-free optimization algorithms such as the GA are known to be easy and robust methods for design

optimization. However, the objective function should be evaluated for every member in the population at each

generation. If we have to perform a high-fidelity CFD computation for the function evaluation, it is practically

impossible to apply GA directly to a design problem, because a single function evaluation may take a couple of

hours, even with parallel computation. For this reason, a surrogate model or response surface method is introduced

in order to substitute the function evaluation for the fit evaluations. The surrogate model, known as an approximate

model, is an efficient way of alleviating the expensive computation burden. To construct the surrogate model, the

function evaluation is required only for the initial experimental sample points, which are randomly selected in the

design space. After the surrogate model is constructed, we can obtain any approximated value of the objective

function without additional function evaluations.

There are two types of surrogate models. The polynomial-based regression type usually uses a least-squares

method to emulate the trend of a real function. This regression technique focuses on estimating the relationships

among function values and the trend of these values. Therefore, this approach is very sensitive to the distribution of

data and does not guarantee that the resulting regression surface passes through all the sample data points 14. On the

other hand, another surrogate model method uses a data-fitting technique, which is known as interpolation. This

interpolation-based surrogate model can construct a response surface that always passes through all the initial

sampling points by using interpolation between the data points. For this reason, the interpolation-based surrogate

model is known to be good for noisy and nonlinear functions such as CFD simulation. In this study, we use the

Kriging surrogate model, which is popularly used in combination with the gradient-free methods. The Kriging

surrogate model is defined as the sum of the mean and deviation terms, as shown in Eq. (11). The mean represents

an approximate trend of the real function. The deviation term is a quantified value that is the difference between the

real function and the approximated function. In other words, it is an error term.

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( ) ( ) ( )

krig

y x f x Z x 

(11)

The mean term can be rewritten as a combination of the basis function and its coefficients, as shown in Eq. (12).

( ) ( ) ( )

krig j j

y x f x Z x









(12)

The Kriging model can be classified as an ordinary, universal, or Taylor-Kriging model depending on the

method used to formulate the mean term using polynomial equations. If we can predict the trend of the real function,

the universal and Taylor-Kriging models are very useful approaches. However, in general engineering problems,

because we do not know the exact trend for the real function, the ordinary Kriging model is mainly used. In the

ordinary Kriging model, the polynomial term in Eq. (11) is considered to be a constant, namely, the 0th-order

polynomial equation. Therefore, the ordinary Kriging model has the advantage of robust behavior for any

problem15,16 .

The deviation term in Eq. (11) is represented by a normal distributed Gaussian process, which refers to the bias

or uncertainty in the mean prediction. It is important to define the deviation term in the covariance relation, as in Eq.

(13), which denotes the influence exerted by two points on each other.

1 2 1 2

( ( ), ( )) [ ( , )]

Cov Z x Z x R x x



R

(13)

In Eq. (13), a correlation function

can be defined as a correlation matrix, which is used to interpolate between

two points on a Kriging response surface. Therefore, how smoothly the Kriging surrogate model expresses any two

points depends on what one is trying to define with the correlation function. Here, we consider a Gauss function as

the correlation function. This function deals with the relation between two data sets by scaling their distance

exponentially. Then, we apply an exponential correlation function, as shown in Eq. (14).

1 2 1 2

( , ) exp( | |) k

R x x x x





  



(14)

As can be seen in Eq. (14), when the distance between

and

is further increased, the value of the correlation

function approaches zero. In other words, the extent of influence between any two sample points is exponentially

decreased. Furthermore, θ and p are parameters in the correlation function, and both are positive real variables.

Because these parameters determine the rate of correlation of each independent variable, appropriate methods should

be used for their accurate prediction. The magnitude of θ determines how fast the influence is weakened by the

distance.

To construct the Kriging surrogate model, we need the initial sample points. These sample points can be

extracted by using a Design of Experiment (DOE) technique. In this study, we employed a Latin Hypercube

Sampling (LHS) method17, which is known to be suitable for Kriging surrogate model. In order to improve the

accuracy and robustness of the Kriging surrogate model, we added adaptive sampling through a statistical Mean

Square Error (MSE) estimation. After the Kriging surrogate model is constructed, it may be important to validate its

accuracy. Therefore, the accuracy of th is model should be verified by comparing the exact value from the function

evaluation and the estimated value from the model.

B. Evolutionary algorithm

Evolutionary algorithms (EAs) are state-of-the-art techniques for optimization. EAs were inspired by the

processes involved in the natural evolution of humans, including inheritance, mutation, selection, and crossover.

Because EAs do not require gradient information, they are used widely for many problems in which gradient

information is very difficult to compute. The GA, memetic algorithm, and neuroevolution are typical examples of

EAs.

The Genetic Algorithm (GA) is one of the most popular EAs. When the design space is defined, the GA

randomly selects a population set, which includes optimal solution candidates. Then, the function evaluation must be

performed for every individual population. After all the function values are compared, the genetic operators select

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better candidates as an inheritance set for the next generation. In the process of evolving to the next generation, the

genetic operators apply mutation and crossover to evolve the optimum candidates, depending on the mutation

probability specified by the user. Through the generations, the more evolved gene will survive among the

populations. After many generations, the best one is chosen as the optimal solution. Commonly, these iterative

generations are repeated until either a fixed number of generations is reached, or the optimal solution is found that

satisfies the termination criteria.

In this study, Hybrid Genetic Algorithm (HGA) was used. In order to speed up the design procedure, the

function values were evaluated using Kriging surrogate model. Fig. 5 shows the design procedure for multiple wing-

sails. A brief description of the design procedure is as follows. To construct the Kriging surrogate model, we need

initial sample points. The initial sample points for the response surface are randomly extracted by using Latin

Hypercube Sampling (LHS) method, which is known to be suitable for the Kriging surrogate model. The surface

geometries and corresponding computational meshes are automatically generated by the journaling systems. In this

study, we employed the SU2_CFD solver, which is an unstructured mesh-based CFD flow solution method, to

evaluate the aerodynamic performance of these initial sample points. Using a Kriging-based surrogate model and the

derivative-free GA optimization method, we searched for the optimal candidate that maximizes the average thrust

coefficient of multiple wing-sails. This optimal candidate was validated by making a comparison between the exact

value from the function evaluation and the estimated value from Kriging surrogate model through SU 2_CFD, which

is a high-fidelity computational analysis. If differences between the estimated and validated performances are

sufficiently small, the design optimization is terminated. Otherwise, the validated optimum is considered to be an

additional point, and the response surface is reconstructed. This design procedure proceeds iteratively to find the

optimal solution.

Fig. 5 Design framework for multiple wing-sails

V. Aerodynamic Characteristics of Wing-Sails

A. Validation of CFD flow solver

In order to examine the computational accuracy of the CFD flow solver, we performed a solver validation. By

comparing the results of the numerical analysis and the experimental data, we confirmed the accuracy of the solver.

As a validation model, we used the NACA0012 airfoil, which is a symmetrical and no-camber type of the 4-digit

series of NACA airfoils. The aerodynamic experiment on the NACA0012 airfoil was conducted at Re = 9.0 M18.

The numerical analysis for NACA0012 was performed at Re = 10.0 M, which is the design condition for multiple

wing-sails. The Reynolds number based on the chord length of the wing-sail was 107. The relative wind speed

between the true wind speed and the ship cruse speed was 14 knots (7 m/s). For the solver validation, a mixed grid

was generated, as shown in Fig. 6. The far field of the computational domain had a boundary, which was a radius of

20 times the airfoil chord length and a value of y+ close to unity near the solid wall. The total numbers of nodes and

elements in the computational grid are listed in Table 1.

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In Fig. 7 , although the drag coefficients predicted by the numerical analysis differed slightly from the

experimental drag coefficients, the lift coefficients are considerably similar until an angle of attack of 16°. In

addition, even though the numbers of drag counts have differences, the trends are very similar. Therefore, it is

expected that the flow characteristics can be captured using the CFD flow solver. Thus, the results of the numerical

analysis are sufficiently accurate.

Table 1 Numbers of nodes and elements in grid system

Fig. 6 Computational grid system around NACA0012

Fig. 7

-α curve (left) and drag polar (right) of NACA0012

B. Aerodynamic characteristics of multiple wing-sails

Prior to investigating the effect of the flow interaction of multiple wing-sails, we carried out an aerodynamic

analysis for a single wing-sail to reveal the effect of the flap. The angle of attack of a single wing-sail is allowed to

vary from 9° to 21° in steps of 3°. As mentioned before, the single wing-sail is a rectangular wing with an aspect

ratio of 2. The two-dimensional cross section shape is an NACA0012 airfoil with and without a trailing edge flap,

which can be deflected up to an angle of 15°. The length of the flap is 20% of the chord length. In Fig. 8, we

compare the values of the aerodynamic coefficients Cl and Cd between the single wing-sail cases with and without a

flap. It can be seen that the single wing-sail with the flap has approximately 20~50% higher lift and drag coefficients

Single wing-sail in 2D analysis

Multiple wing-sails in 3D analysis

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in comparison to the one without the flap. If we employ the trailing edge flap, the effective camber of the airfoil is

increased, and the pressure gradient from the stagnation point to the suction peak point is increased. This results in

increased velocity at the suction peak (low-pressure region on the upper surface), which causes a larger pressure

difference between the upper and the lower surfaces of the wing-sail. For these reasons, the single wing-sail with a

flap can have better aerodynamic performance than the one without a flap. Furthermore, we can observe from Fig. 8

that the stall angle of the wing-sail without the flap was about 15°, whereas that of the wing-sail with the flap was

about 12°.

To investigate the effect of the flow interaction, which has a significant effect on the aerodynamic performance of

multiple wing-sails, we performed a numerical aerodynamic analysis for multiple wing-sails by varying the wind

direction from 15° to 165° in intervals of 15°. Even though the wind direction varied, the angle of attack of each

wing-sail, which is a relative angle between the wing-sails and the wind direction, was fixed at 12°. The value of 12°

was obtained by examining the Cl - α curve in Fig. 8. The maximum lift of the single wing-sail with a flap was

obtained at that angle.

As indicated in Fig. 9, because of the camber effect of the flap, the thrust performance of multiple and single

wing-sails with a flap is superior to those without a flap. Furthermore, we considered how much thrust is increased

or decreased by the flow interaction in multiple wing-sails by comparing the results with the thrust of a single wing-

sail. In the comparison of the thrust coefficients of a single wing-sail and multiple wing-sails, both with and without

flaps, the thrust coefficients of the multiple wing-sails were smaller by about 21~43% (with flap case) and 24~37%

(without flap case) than those of the single wing-sail. However, in the multiple wing-sails, the average thrust

coefficient is divided by the total area of the wing-sails. Therefore, the total area should be considered to obtain the

total thrust force. As a result, the total thrust force of multiple wing-sails is about six times that of a single wing-sail.

From these results, we conclude that the flow interaction between the wing-sails results in decreased aerodynamic

performance. As a result, the thrust coefficients of multiple wing-sails are lower than that of a single wing-sail at all

wind directions. The mechanism of the flow interaction that causes the decreased aerodynamic performance in

multiple wing-sails is as follows. If the wing-sail is set with a positive angle of attack, a stagnation point is located

on the lower surface of the wing-sail instead of at the leading edge. Furthermore, a suction peak point, which is a

very low pressure region, is located on the upper surface of the wing-sail. The front wing-sail, which is located

further upstream in the wind direction, causes the stagnation point on the rear wing-sail to shift toward the leading

edge ; "the head effect." Then, the strength of the suction peak point of the rear wing -sails is considerably reduced.

Because the pressure gradient from the stagnation point to the suction peak point is also decreased, the flow velocity

is less accelerated (the suction peak velocities are reduced). For these reasons, on the upper surface of the rear wing-

sail, the recovery adverse pressure gradient is also lower. Then, the rear wing-sails can be operated at a higher angle

of attack without flow separation and stall. As a result of the above, although the each angle of attack of the multiple

wing-sails is set to be the same, the effective angle of attack of the rear wing-sail is reduced because of the flow

interaction effect19.

Fig. 8 Aerodynamic coefficient comparison between single wing-sails with and without flap

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Fig. 9 Cfx comparison between single and multiple wing-sails without flap (left), and

Cfx comparison between single and multiple wing-sails with flap (right)

VI. Design Applications and Results

In this section, we show the design optimization results for single and multiple wing-sails. For a single wing-sail,

we constructed the exact response surfaces based on aerodynamic performances and selected the optimum solution

visually. In contrast, the design optimization framework was used for multiple wing-sails under various wind

direction conditions. In order to speed up the design procedure, we performed the design optimization in two

dimensions (2D) and validated the design results in three dimensions (3D).

A. Design problem formulation

In the previous study, we considered only the angle of attack of each wing-sail as design variables5,6 . Therefore,

the geometric deformation of the wing-sails was not considered. However, in this research, we found the optimum

shape and operating condition for multiple (three) wing-sails. A total of nine design variables are employed,

including the flap length, deflection angle, and angle of attack, in terms of the flap configuration and operating

condition. The initial flap length and deflection angle were set at 20% of the chord length and 15°, respectively. In

the previous study, we set the initial angle of attack at 12°. However, this initial angle of attack is too high to find a

steady-state solution because it causes flow separation on the head wing-sail, which was the first wind-sail in the

wind direction. Therefore, in this study, 8° and 9.5° were chosen as the initial angles of attack of each wing-sail. Fig.

10 shows a schematic diagram of the design variables for the design optimization of the multiple wing-sails. The

angle of attack is the relative angle between the wing-sail direction and the wind direction. Constraints on the design

variables, called design bounds, were set from +15° to –15° (angle of attack), from +5° to +25° (flap deflection

angle), and from 0.05c to 0.3c (flap deflection length).

In a parameter study of a single wing-sail, because no flow interaction occurs, the angle of attack remains

constant at 8°. In other words, we consider that the design variables are only the deflection angle and flap length.

Therefore, we are able to construct the exact response surface with a 30 × 30 resolution, which is an output,

corresponding to two input variables (deflection angle and length). After the exact surfaces were organized using

900 function evaluations, the optimum setup of the flap geometry was selected visually. On the other hand, for the

design optimization of multiple wing-sails, we considered a total of nine design variables (three design variables for

each wing-sail × three wing-sails). Therefore, we employed the design framework, which tightly coupled the high-

fidelity CFD and gradient-free optimization algorithms.

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Fig. 10 Design variables for multiple wing-sails

B. Parameter study using single wing-sail

Using 900 function evaluations, the two exact response surfaces for the lift and drag were constructed, which are

shown in Fig. 11. We chose a flap deflection length of 0.2914c, and a flap deflection angle of 24.3103° as the

optimum for a single wing-sail, which generated the maximum aerodynamic performance. In Fig. 11, the airfoil with

the larger flap length and angle (red circle) has a stronger suction peak on the upper surface of the wing-sail

compared to those of the airfoil with the smaller flap length and angle (black circle). These have a larger "camber

effect," which makes the lift force more effective. Based on this result, it can be inferred that the design for multiple

wing-sails points in the direction of a larger flap length and angle.

The thrust is the resultant force of the lift and drag forces. It can be calculated using Eq. (1) along the wind

direction, and the results are listed in Table 2. Because no flow interaction occurs with a single wing-sail, the lift and

drag coefficients remain constant with respect to the wind direction. However, the thrust coefficient in a wind

direction of 135° is larger than the thrust coefficients in the other wind directions. In addition, the thrust coefficient

is maximized in the wind direction of 90°. This can be proved using Eq. (1). When the wind direction is varied from

0° to 90°, the sign of the drag is positive. It generates a negative thrust, which is the opposite to that of the lift. Thus,

the resultant force becomes smaller. When the wind direction is varied from 90° to 180°, both the lift and the drag

have positive signs, which cause the resultant force to become larger. In a wind direction of 90°, the drag does not

generate any thrust, and only the lift contributes to the thrust. This is why the maximal thrust occurs in a wind

direction of 90°.

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Fig. 11 Exact response surfaces of Cl (left) and Cd (right) for single wing-sail

Table 2 Parameter study results for single wing-sail

C. Design results of multiple wing-sails at angle of attack of 8°

As mentioned before, for the design optimization of multiple wing-sails, we considered a total of nine design

variables, which included the angle of attack, flap deflection length, and angle of each wing-sail. Therefore, we

employed the gradient-free optimization algorithms and Kriging surrogate model. A total of 90 sample points were

estimated for constructing the Kriging response surfaces for each wind direction case. In addition, some adaptive

sampling procedures and the regeneration of the response surface were performed to improve the accuracy of the

Kriging response surface. To evaluate the sample points, which were extracted by using LHS method, we generated

a computational grid with 49,258 nodes and 72,556 elements.

1. Design with respect to varying wind direction

The results of the design optimization are listed in Table 3. In Table 3, the variation of the angle of attack( △

)

refers to the amount of change from the initial angle of attack to the optimum angle of attack. The sign of the

changing angle follows the "right hand rule." If the sign is positive, the angle of attack becomes larger than the

initial angle of attack, whereas the angle of attack becomes smaller with a negative sign.

• Case of wind direction θ = 45°

As seen in Table 3, the three types of design variables were gradually increased, which gradually improved the

aerodynamic performances. It is notable that the angle of attack of wing-sail #1 was decreased, whereas those of

wing-sails #2 and #3 were increased. We confirmed the header effect, as discussed previously. On the baseline

results, the stagnation point gradually moved toward the leading edge of each wing-sail because of the flow

interaction. Then, the effective angles of attack were decreased. This phenomenon contributed to the strength

variation of the suction peak and the flow separation. A larger effective angle of attack led to a stronger suction

peak and flow separation. In a comparison between the baseline and the design results, the strength of the suction

peak on wing-sail #1 was decreased slightly. This is because the angle of attack of wing-sail #1 was reduced to

prevent flow separation at the trailing edge flap. Therefore, the flow separation almost disappeared. This was also

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caused by the reduced flap length and angle. As a result, the design variables of the head wing-sail, which was the

first wind-sail in the wind direction, were reduced (decreased angle of attack and deflection angle, and shortened

flap length) to prevent the flow separation. On the other hand, the design variables of wing-sails #2 and #3 were

gradually increased (increased angle of attack and deflection angle, and lengthened flap length) to improve the

aerodynamic performance. For these reasons, the strengths of the suction peaks were increased. In addition, the

pressure differences between the upper and lower surfaces of wing-sails #2 and #3 were significantly increased, as

shown in Fig. 12. Fig. 12 shows the pressure contour, streamline, and surface pressure coefficient distribution

around the wing-sails. The "blue circle" shows the stagnation region of each wing - sail, and the "red circle" shows

the flow separation on the upper surface of the flap of each wing-sail. As can be seen in Fig. 12, in a comparison

of the baseline and optimized flow fields, the stagnation point shifted from the lower surface of the wing-sail to

the leading edge, and the flow separation disappeared.

• Case of wind direction θ = 90°

In Table 3, there are no trends for the same types of design variables. It is thought that relatively less flow

interaction occurred in a wind direction of 90°. In the previous study, the smallest flow interaction was observed

in a wind direction of 90°. The overall angles of attack of the wing-sails were increased to enhance the

aerodynamic performance. For wing-sail #2, the flap deflection length is very small in comparison with the other

wing-sails. Therefore, to compensate for the shorter deflection length, the angle of attack and deflection angle of

wing-sail #2 are considerably greater than those of the other wing-sails. In a wind direction of 90°, because little

flow interaction occurred, each wing-sail was optimized independently to find the optimal setup of the design

variables. As a result, we obtained an improvement in the aerodynamic performances of the wing-sails that was

caused by an increased angle of attack.

• Case of wind direction θ = 135°

As shown in Table 3, the design trends were the reverse to the trends in the case of a wind direction of 45°,

because wing-sail #3 is the head wing-sail instead of wing-sail #1. However, the angle of attack of the head wing-

sail (wing-sail #3) is slightly increased. Thus, it is thought that this case has less flow interaction than that with a

wind direction of 45°. As a result, the angle of attack, deflection length, and angle of attack of the rear wing-sail,

which is located further downstream, were gradually increased to compensate for the header effect.

Table 3 Design optimization results for multiple wing-sails at initial angle of attack of 8°

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Fig. 12 Comparison of flow fields at 45° wind direction using two-dimensional analysis:

pressure contour and streamline around baseline (top) and optimized (center) wind-sails,

and surface pressure coefficient distribution of both baseline and design results (bottom)

Fig. 13 Cfx comparison between baseline and optimized results using two-dimensional analysis

For a comparison of the three cases, the averaged thrusts of the baseline and optimized results are plotted in Fig.

13 with respect to the varying wind direction. In addition, the values of each averaged thrust are listed in Table 4. As

we described, in a wind direction of 90°, the maximum averaged thrust was obtained in both the baseline and

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optimized results, and the improvements in the averaged thrust are similar in the wind directions of 90° and 135°.

The relative improvements are the largest in the case of a wind direction of 45°, which caused very strong flow

interactions. The overall improvements in the averaged thrust were 14~22%, which are very successful design

results.

Table 4 Cfx improvement in multiple wing-sails using two-dimensional analysis

2. Validation of design results using three-dimensional CFD analysis

The design results were based on a two-dimensional analysis. We carried out a three-dimensional numerical

analysis to determine whether the design results achieved with the two-dimensional assumption were preserved. We

generated a full three-dimension computational grid using the same mixed grid topology. The numbers of nodes and

cells in the grid were 1,217,710 and 6,541,622, respectively, as shown in Table 1. The same flow conditions as used

in the two-dimensional analysis were used in the three-dimensional analysis.

In aerodynamic characteristics of aircraft, a geometrical finite wing causes a "3D effect," in other words, "a

wing-tip vortex." This is driven by the pressure difference between the upper and lower surfaces of the wing. In

general, the fluid moves from a high-pressure region to a low-pressure region. If the wing has a positive angle of

attack, the high-pressure region is distributed on the lower surface, whereas the low-pressure region is distributed on

the upper surface of the wing. Therefore, the fluid moves from the lower surface to the upper surface at the wing tip.

This phenomenon generates the vortex, which results in a downwash flow. As a result, the effective angle of attack

is reduced around the wing tip because of the wing-tip vortex, which results in decreased lift and increased drag.

Because this flow phenomenon occurs in actual wing-sails, it should be considered.

In Fig. 14 , the "red circle" shows the suction peak region on the upper surf ace of the wing-sail. The top of the

figure shows the flow fields of the baseline, whereas the center of the figure shows the flow fields of the design

result. The overall flow characteristics around the three-dimensional wing-sail are similar to those for the two-

dimensional wing-sail. However, the pressure differences between the upper and lower surfaces of each wing-sail

are relatively smaller than the flow fields in Fig. 12. In addition, no flow separations occurred on the flap surfaces in

three dimensional analyses. This means that even though the angle of attack was set to be the same (8°) in the two-

and three-dimensional analyses, the flow characteristics around the multiple wing-sails were slightly different

because of the 3D effect. To investigate whether the 2D improvements were valid in three dimensions, we plot the

averaged thrust coefficients along the wind direction for both the baseline and the optimized results in Fig. 15. The

averaged thrusts were improved in all wind directions. The improvements in the averaged thrusts can be confirmed

in Table. 5. The overall improvements are 10~17%, which are smaller than the improvements in the 2D design

optimization. The differences between the improvements in the 2D and 3D design optimizations were 2~5%, which

is very predictable considering the 3D effect. Therefore, we concluded that the developed design optimization

framework for multiple wing-sails, which was based on the 2D de sign optimization, could be utilized for 3D design

optimization. Furthermore, we confirmed that the design optimization trends in two dimensions were still preserved

in three dimensions.

Table. 5 Cfx improvement in multiple wing-sails using three-dimensional analysis

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Fig. 14 Comparison of flow fields in 45° wind direction using three-dimensional analysis at Y/C = 5%:

pressure contour and streamline around baseline (top) and optimized (center) wind-sails, and

surface pressure coefficient distributions of both baseline and design results (bottom)

Fig. 15 Cfx comparison between baseline and optimized results using three-dimensional analysis

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D. Design results for multiple wing-sails at angle of attack of 9.5°

1. Design with respect to varying wind directions

• Case of wind direction θ = 45°

In this study, we also performed the design optimization for multiple wing-sails to improve the average-thrust

performance in the case of an initial angle of attack of 9.5°. This operating condition is closer to the stall

condition, which results in the flow separation. The part of the flow that separates from the boundary layer is

called the separation bubble flow and is a recirculating flow. This flow cannot move along the streamline. After

the flow goes farther downstream, it eventually attaches to the wall again, which is called the reattached flow. As

can be seen in Fig. 16, unlike the case of an angle of attack of 8°, a separation bubble occurs on the upper surface

of wing-sail #1. In a comparison between the baseline and optimized results, by decreasing the angle of attack of

wing-sail #1, the region of the separation bubble was considerably reduced. However, in the case of wing-sails #2

and #3, to compensate for the angle of attack reduction by the flow interaction, each angle of attack was increased.

As a result, as compared with the baseline, the aerodynamic performance of all the wing-sails was improved. This

can be confirmed from the surface pressure distribution graph in Fig. 16.

• Case of wind direction θ = 90°

Similar to the case of an initial angle of attack of 8°, there were no trends for the same types of design

variables. It is thought that relatively less flow interaction occurred in this case. Therefore, because the effect of

the flow interaction was smaller than that in the other wind directions, each wing-sail was optimized to improve

its aerodynamic performance. Furthermore, because the wing-sails in the wind direction of 90° have little flow

interaction with each other as compared to those in the other wind directions, the maximum thrust of the wing-

sails is generated in a wind direction of 90°.

• Case of wind direction θ = 135°

In this case, the design trends were very similar to the trends in a wind direction of 135° for an initial angle of

attack of 8°. However, unlike the case of an angle of attack of 8°, the angle of attack of the head wing-sail (wing-

sail #3) was reduced to prevent the flow separation. It is thought that this initial angle of attack is too high. The

angles of attack, flap lengths, and deflection angles of wing-sails #1 and #2 were gradually increased to improve

the aerodynamic performance of the multiple wing-sails in consideration of their flow interaction.

Table. 6 Design optimization results for multiple wing-sails at initial angle of attack of 9.5°

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Fig. 16 Comparison of flow fields in 45° wind direction using two-dimensional analysis:

pressure contour and streamline around baseline (top) and optimized (center) wind-sails, and

surface pressure coefficient distribution of both baseline and design results (bottom)

Fig. 17 Cfx comparison between baseline and optimized results using two-dimensional analysis

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In summary, in the wind directions of 45° and 135°, the angle of attack of the front wing-sail, which is located

further upstream in the wind direction, was reduced and the other angles of attack of the wing-sails were gradually

increased. On the other hand, in a wind direction of 90°, all of the angles of attack of the wing-sails were increased.

In the wind directions of 45° and 135°, because a strong flow interaction occurred and the initial angle of attack was

too high, the angle of attack of the head wing-sail (when the wind direction was 45°, the head wing-sail was wing-

sail #1, and when it was 135°, the head wing-sail was wing-sail #3) was reduced slightly to prevent flow separation,

which results in a reduction in the aerodynamic performance of the wing-sail. On the other hand, the angles of attack,

flap lengths, and deflection angles of the other wing-sails were gradually increased to improve the aerodynamic

performance.

In a wind direction of 90°, because a weak flow interaction occurred, we could not confirm a distinct design

trend. Therefore, the design variables of each wing-sail were varied independently to improve the aerodynamic

performance. We could conclude that the maximum thrust of the wing-sails was generated in a wind direction of 90°,

because the wing-sails in a wind direction of 90° had little flow interaction with each other as compared to those in

the other wind directions.

As can be seen in Fig. 17, we were able to obtain an overall improvement in the averaged thrust of

approximately 10~12%, depending on the wind direction and corresponding detailed flow characteristics.

Table. 7 Cfx improvement in multiple wing-sails using two-dimensional analysis

2. Validation of design results using three-dimensional analysis

A high-fidelity CFD analysis was carried out to validate the design results in three dimensions. The validation

results show that the average thrust performance of optimized multiple wing-sails was improved in all wind

directions in comparison with the baseline multiple wing-sail. As can be seen in Table. 8, we were able to obtain an

actual improvement of 9~11%, depending on the wind direction.

As shown in Fig. 18, we plotted the streamline and pressure contour around multiple wing-sails at a y/c of 5%. A

comparison of the baseline and optimized results shows that the strength of the suction peak point of each wing-sail

was increased, except for wing-sail #1. In the case of the head wing-sail (wing-sail #1), which is located at first in

the wind direction, the angle of attack was decreased to prevent flow separation in two dimensions. However, as can

be seen in Fig. 18, flow separation did not occur for any of the wing-sails because of the 3D effect, which is driven

by the pressure difference between the upper and lower surfaces of the wing. Therefore, the aerodynamic

performance of the optimized head wing-sail was worse than the baseline. However, in the case of wing-sails #2 and

#3, the strength of the suction peak was distinctly increased, which was caused by increasing the angle of attack.

Then, the flow was more accelerated from the stagnation point to the suction peak, which resulted in increased lift

and drag performances. This can also be confirmed from the surface pressure distribution graph in Fig. 18.

Table. 8 Cfx improvement in multiple wing-sails using three-dimensional analysis

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Fig. 18 Comparison of flow field in 45° wind direction using three-dimensional analysis at Y/C = 5%:

pressure contour and streamline around baseline (top) and optimized (center) wind-sails, and

surface pressure coefficient distribution of both baseline and design results (bottom)

Fig. 19 Cfx comparison between baseline and optimized results using three-dimensional analysis

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VII. Conclusion and Future work

In this research, we focused on an aerodynamic analysis and design optimization of multiple wing-sails. For the

aerodynamic analysis, we solved the two/three-dimensional (2D/3D) compressible Navier-Stokes governing

equation with a Spalart-Allmaras turbulence model. To more exactly predict the viscous flow, we used a mixed grid

topology. Using the gradient-free optimization method of Genetic Algorithms (GAs) and Kriging Surrogate model

method, we found the optimal setup for multiple wing-sails that maximizes the thrust performance. In a previous

study, we only dealt with the angle of attack of each wing-sail as design variables. Namely, the shape deformation of

the wing-sails was not considered. However, in this study, we set the angle of attack, flap deflection angle, and

deflection length of individual wing-sails as design variables. The total number of design variables was nine.

Until now, studies on wing-sails depended on aerodynamic analyses using wind tunnel experiments. In this study,

we developed a design framework for multiple wing-sails to improve the aerodynamic performance that tightly

coupled high-fidelity computational fluid dynamics (CFD) and gradient-free design optimization algorithms.

Prior to the design optimization, we performed an aerodynamic analysis to reveal the effect of flow interaction

and the flow characteristic around multiple wing-sails. For the numerical analysis, we used the SU2_CFD solver. We

investigated the effect of the flap of a wing-sail. The results showed that a wing-sail with a flap has about 20~50%

larger lift and drag coefficients than a wing-sail without a flap with respect to the angle of attack. In multiple wing-

sails, the effect of their interaction should be considered so as to estimate their thrust. In a comparison between a

single wing-sail and multiple wing-sails, the thrust coefficients of the multiple wing-sails were worse than those of a

single wing-sail by about 21~43%, depending on the wind direction, because of the flow interaction, which

decreased the effective angle of attack of the wing-sails located further downstream in the wind direction.

Furthermore, compared to the other wind directions, the wing-sails in a wind direction of 90° showed little flow

interaction with each other and had the best aerodynamic performance.

To confirm the relation of the design variables, which were the flap deflection length and angle in two

dimensions, we constructed an exact response surface for the aerodynamic performance of a single wing-sail. We

performed the numerical analysis 900 times. Through the exact response surface, it was possible to select the

optimum point. The optimal setup for the two-dimension single wing-sail was a flap length of 0.2914c and a flap

angle of 24.3103° at a fixed angle of attack. Furthermore, using the developed design framework, optimal design

variables were obtained that maximize the averaged thrust performance of multiple wing-sails with respect to the

wind direction. We carried out design optimization for initial angles of attack of 8° and 9.5°. With multiple wing-

sails, the 9.5° angle of attack was closer to the stall condition. As a result, we acquired thrust increases of

approximately 14~22% and 10~12%, respectively, in two dimensions. A high-fidelity CFD analysis was carried out

for complete three-dimensional wing-sails to determine whether the thrust improvement achieved from the two-

dimensional assumption was preserved. The results showed that the thrust performance of the multiple wing-sails

was improved by 10~17% and 9~11%, respectively, in three dimensions. Although the thrust increments were

reduced because of the 3D effect, these were still good. Thus, it was concluded that the design optimizations were

successful when using the design framework.

We plan to conduct advanced research on wing-sails that can be applied practically to an actual bulk ship using a

stability analysis and structural analysis. Furthermore, future studies will consider various aspects such as the

interaction between the wing-sails and the ship and the optimization of wing-sails in three dimensions using efficient

optimization methods. Establishing a wing-sail system based on the results of these studies is expected to contribute

to the development of more efficient eco-friendly ships.

Acknowledgments

We acknowledge the financial support from the Ministry of Science, ICT & Future Planning, subjected to the

project EDISON (EDucation-research Integration through Simulation On the Net, Grant No.: NRF-2011 -0020 565)

and Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the

Ministry of Science, ICT & Future Planning(NRF-2011-0014722) . This work was also supported by grant No.

EEWS-2011 -N01130029-02 from the EEWS Research Project of the office of KAIST EEWS Initiative. (EEWS:

Energy, Environment, Water, and Sustainability)

Downloaded by Seongim Choi on July 9, 2013 | http://arc.aiaa.org | DOI: 10.2514/6.2013-2524

American Institute of Aeronautics and Astronautics

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... For most of the studies [20] [30] [21], the overall interaction effects on the aerodynamic performance of several Rigid Wing Sails are not beneficial. According to [30], when having interaction, each Wing Sail produces thrust coefficients smaller by about 21-43% (with flap) and 24-37% (without flap) than those of the single Wing Sail. The mechanism of the flow interaction that causes the overall average altered aerodynamic performance in a jib-main sail configuration is based on an circulation differential following The Venturi effect and the so-called "slot effect". ...

Martina Reche-Vilanova

Wind-assisted cargo ships can play a key role in achieving the IMO 2050 targets on reducing the total annual GHG emissions from international shipping by at least 50%. The present project deals with the development of a 6 degrees of freedom Performance Prediction Program for wind-assisted cargo ships aimed at contributing knowledge on the performance of this technology. It is a fast and easy tool able to predict, to a good level of accuracy and low computational time, the performance of any commercial ship with three different Wind-Assisted Propulsion Systems (WAPS) installed: Rotor Sails, Rigid Wing Sails and DynaRigs; with only ship main particulars and general dimensions as input data. The program is based on semi-empirical methods and a WAPS aerodynamic database created from published data on lift and drag coefficients. All WAPS data can be interpolated with the aim to scale to different sizes and configurations such as number of units and different aspect ratios.

... The works of Jo et al. (2013) and Lee et al. (2016) are also related to the sail cascade concept proposed in the "Wind Challenger" project. In these studies, the authors made use of a CFD code connected to a genetic algorithm to optimize the angle of attack, the flap length and the flap deflection angle of three identical wingsails set 1.5 chord lengths apart. ...

... The works of Jo et al. [22] and Lee et al. [23] are also related to the sail cascade concept proposed in the "Wind Challenger" ...

Wind-assisted propulsion has recently attracted attention as one viable option to drastically reduce pollutant emissions produced by ships. Despite its potential, there is still a substantial lack of understanding of the physical aspects proper of wind-assisted ships, leading to unreliable fuel-saving claims. In the context of the development of a performance prediction program for such type of hybrid ships, the research presented herewith deals with the aerodynamic interaction between two rigid sails. Wind-tunnel experiments were carried out on a single sail and on a two-sail arrangement, during which force and pressure measurements were taken on each sail. For the two-sail arrangement, two gap distances between the sails were investigated and the tests were performed at apparent wind angles ranging all typical sailing conditions. The results show that for an extended interval of moderate apparent wind angles the aerodynamic interaction has a positive effect on both sails. On the contrary, at smaller and at larger angles the interaction effects are detrimental for the downstream sail. The outcome of the present work indicates that the number of sails employed and their gap distance are important parameters to determine the aerodynamic interaction effects.

... Capsizes of the American and the Swedish teams have shown the difficulty to maneuver the wing without causing stability problems. However, the possibility of its usefulness even in domains different from the sporting one has recently rekindled the interest for new concept design of wind driven vessel in the era of low carbon society [1] [2]. ...

This paper is devoted to the study of a 1/20-scale model of wingsail in a wind tunnel environment. This study deals with the methodology to achieve accurate comparisons between numerical and experimental data. A particular care is brought in the numerical simulation to reproduce the wind tunnel effects on the model. The experimental results did not match with preliminary numerical simulations performed in a freestream domain. The reason is that the wind tunnel domain introduces some modifications in the flow field, around the wingsail, especially near the tip. As a consequence, a study has been done first to set the correct configuration to model the real vein conditions. Then numerical simulations based on a RANS approach have been run to study the flow around the wing in the wind tunnel environment, at different operating conditions in terms of inlet flow angles and wingsail cambers. A comparison of the numerical predictions with experimental data established the accuracy of the selected approach. The numerical results were then used to complete the investigations done during the experimental campaign.

... Blakeley & al. (2012) have done one of the first windtunnel tests of a two-dimensional wingsail section with pressure measurements for lift and pressure drag estimation. Recently a new interest on wingsail emerges for concept design of wind driven vessel in the era of low carbon society (Nakashima & al. 2011, Jo & al. 2013). ...

Abstract. this paper is devoted to the numerical study of a 1:20th model-scale wingsail typical of America's Cup yachts like AC72, AC62, AC45 or any C class catamaran to gain insight in its complex aerodynamic behavior and to prepare a wind-tunnel campain. This rigging has still not been much studied and needs more knowledge. This study is based on CFD simulations of the flow around the wingsail by resolving Navier-Stokes equations. Two modeling issues are investigated: the Unsteady Reynolds Average Navier-Stokes (URANS) and the Large Eddy Simulation (LES). These numerical approaches are used to characterize the wingsail aerodynamic behavior and variations with some key design and trim parameters (camber, slot width, angle of attack, flap thickness). Unsteady modeling are used to characterize the stall behavior and improve our understanding of the flow physics that may occur in such configurations. The analysis of the results shows transition phenomena due to a laminar separation bubble and strong interaction of boundary layers of main and flap in the slot region. LES results give flow physics understanding and qualitative elements of validation of the URANS simulations. Both URANS and LES results emphasized the central role of the slot geometry and its associated leakage flow in the onset of stall. Some key parameters of the wingsail are identified. The stall behavior for low and high camber (through flap deflection) is characterized showing differences in both configurations. These differences are related to the leakage flow in the slot where a non-linear coupling between flap deflection, slot width and flap thickness takes place. These results illustrate the complex aerodynamic of multi-element wingsail and that a better knowledge of its behavior is necessary to open roads for better design and enhanced performances for future multihull yachts and foilers.

The analysis of the two dimensional subsonic flow over a National Advisory Committee for Aeronautics (NACA) 0012 airfoil at various angles of attack and operating at a Reynolds number of 3×10 6 is presented. The flow was obtained by solving the steady-state governing equations of continuity and momentum conservation combined with one of three turbulence models [Spalart-Allmaras, Realizable   k and   k shear stress transport (SST)] aiming to the validation of these models through the comparison of the predictions and the free field experimental measurements for the selected airfoil. The aim of the work was to show the behavior of the airfoil at these conditions and to establish a verified solution method. The computational domain was composed of 80000 cells emerged in a structured way, taking care of the refinement of the grid near the airfoil in order to enclose the boundary layer approach. Calculations were done for constant air velocity altering only the angle of attack for every turbulence model tested. This work highlighted two areas in computational fluid dynamics (CFD) that require further investigation: transition point prediction and turbulence modeling. The laminar to turbulent transition point was modeled in order to get accurate results for the drag coefficient at various Reynolds numbers. In addition, calculations showed that the turbulence models used in commercial CFD codes does not give yet accurate results at high angles of attack.

This paper describes the history, objectives, structure, and current capabilities of the Stanford University Unstructured (SU2) tool suite. This computational analysis and design software collection is being developed to solve complex, multi-physics analysis and optimization tasks using arbitrary unstructured meshes, and it has been designed so that it is easily extensible for the solution of Partial Differential Equation-based (PDE) problems not directly envisioned by the authors. At its core, SU2 is an open-source collection of C++ software tools to discretize and solve problems described by PDEs and is able to solve PDE-constrained optimization problems, including optimal shape design. Although the toolset has been designed with Computational Fluid Dynamics (CFD) and aerodynamic shape optimization in mind, it has also been extended to treat other sets of governing equations including potential flow, electrodynamics, chemically reacting flows, and several others. In our experience, capabilities for computational analysis and optimization have improved considerably over the past two decades. However, the ability to integrate the resulting software packages into coupled multi-physics analysis and design optimization solvers has remained a challenge: the variety of approaches chosen for the independent components of the overall problem (flow solvers, adjoint solvers, optimizers, shape parameterization, shape deformation, mesh adaption, mesh deformation, etc) make it difficult to (a) expand the range of applicability to situations not originally envisioned, and (b) to reduce the overall burden of creating integrated applications. By leveraging well-established object-oriented software architectures (using C++) and by enabling a common interface for all the necessary components, SU2 is able to remove these barriers for both the beginner and the seasoned analyst. In this paper we attempt to describe our efforts to develop SU2 as an integrated platform. In some senses, the paper can also be used as a software reference manual for those who might be interested in modifying it to suit their own needs. We carefully describe the C++ framework and object hierarchy, the sets of equations that can be currently modeled by SU2, the available choices for numerical discretization, and conclude with a set of relevant validation and verification test cases that are included with the SU2 distribution. We intend for SU2 to remain open source and to serve as a starting point for new capabilities not included in SU2 today, that will hopefully be contributed by users in both academic and industrial environments.

Antony Jameson

The theory of non-oscillatory scalar schemes is developed in this paper in terms of the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. This principle can be used for multi-dimensional problems on both structured and unstructured meshes, while it is equivalent to the total variation diminishing (TVD) principle for one-dimensional problems. A new formulation of symmetric limited positive (SLIP) schemes is presented, which can be generalized to produce schemes with arbitrary high order of accuracy in regions where the solution contains no extrema, and which can also be implemented on multi-dimensional unstructured meshes. Systems of equations lead to waves traveling with distinct speeds and possibly in opposite directions. Alternative treatments using characteristic splitting and scalar diffusive fluxes are examined, together with modification of the scalar diffusion through the addition of pressure differences to the momentum equations to produce full upwinding in supersonic flow. This convective upwind and split pressure (CUSP) scheme exhibits very rapid convergence in multigrid calculations of transonic flow, and provides excellent shock resolution at very high Mach numbers.

In a previously reported study, wind tunnel experiments were undertaken to investigate the aerodynamic characteristics of hybrid-sails in isolation. Such sails are seen as providing a worthwhile reduction in the delivered power to the propeller and hence the engine generated thrust, with a corresponding reduction in the CO2 production of diesel engine exhaust. In this paper, wind tunnel testing is used to investigate sail–sail interaction effects for two sets of four identical hybrid-sails, and the sail–hull interaction effects for the same two sets of four identical sails in the presence of a bulk carrier hullform. The analysis presented suggests that to build a sail-assisted ship requires an appreciation of the sail–sail and sail–hull interaction effects.

This document is designed for users of the program developed at Sandia Laboratories by the authors to generate Latin hypercube samples. Latin hypercube sampling is a recently developed sampling technique for generating input vectors into computer models for purposes of sensitivity analysis studies. In addition to providing a cost-effective and reliable sampling scheme, the Latin hypercube sampling technique also provides the user with the flexibility efficiently to study effects of distributional assumptions on key input variables without rerunning the computer model. 5 figures, 2 tables.

A factorial, computational experiment was conducted to compare the spatial interpolation accuracy of ordinary and universal kriging and two types of inverse squared-distance weighting. The experiment considered, in addition to these four interpolation methods, the effects of four data and sampling characteristics: surface type, sampling pattern, noise level, and strength of small-scale spatial correlation. Interpolation accuracy was measured by the natural logarithm of the mean squared interpolation error. Main effects of all five factors, all two-factor interactions, and several three-factor interactions were highly statistically significant. Among numerous findings, the most striking was that the two kriging methods were substantially superior to the inverse distance weighting methods over all levels of surface type, sampling pattern, noise, and correlation.

An adjoint-based Navier-Stokes design and optimization method for two-dimensional multi-element high-lift configurations is derived and presented. The compressible Reynolds-Averaged Navier-Stokes (RANS) equations are used as a flow model together with the Spalart-Allmaras turbulence model to account for high Reynolds number effects. Using a viscous continuous adjoint formulation, the necessary aerodynamic gradient information is obtained with large computational savings over traditional finite-difference methods. A study of the accuracy of the gradient information provided by the adjoint method in comparison with finite differences and an inverse design of a single-element airfoil are also presented for validation of the present viscous adjoint method. The high-lift configuration design method uses a compressible RANS flow solver, FLO103-MB, a point-to-point matched multi-block grid system and the Message Passing Interface (MPI) parallel solution methodology for both the flow and adjoint calculations. Airfoil shape, element positioning, and angle of attack are used as design variables. The prediction of high-lift flows around a baseline three-element airfoil configuration, denoted as 30P30N, is validated by comparisons with experimental data. Finally, several design results that verify the potential of the method for high-lift system design and optimization, are presented. The design examples include a multi-element inverse design problem and the following problems: Cl maximization, lift-to-drag ratio, L/D, maximization by minimizing Cd at a given Cl or maximizing Cl at a given Cd (α is allowed to float to maintain either Cl or Cd), and the maximum lift coefficient, Clmax, maximization problem for both the RAE2S22 single-element airfoil and the 30P30N multi-element airfoil.

Ronald O'Rourke

General strategies for reducing the Navy's dependence on oil for its ships include reducing energy use on Navy ships; shifting to alternative hydrocarbon fuels; shifting to more reliance on nuclear propulsion; and using sail and solar power. Reducing energy use on Navy ships. A 2001 study concluded that fitting a Navy cruiser with more energy-efficient electrical equipment could reduce the ship's fuel use by 10% to 25%. The Navy has installed fuel-saving bulbous bows and stern flaps on many of its ships. Ship fuel use could be reduced by shifting to advanced turbine designs such as an intercooled recuperated (ICR) turbine. Shifting to integrated electric-drive propulsion can reduce a ship's fuel use by 10% to 25%; some Navy ships are to use integrated electric drive. Fuel cell technology, if successfully developed, could reduce Navy ship fuel use substantially. Alternative hydrocarbon fuels. Potential alternative hydrocarbon fuels for Navy ships include biodiesel and liquid hydrocarbon fuels made from coal using the Fischer-Tropsch (FT) process. A 2005 Naval Research Advisory Committee (NRAC) study and a 2006 Air Force Scientific Advisory Board both discussed FT fuels. Nuclear propulsion. Oil-fueled ship types that might be shifted to nuclear propulsion include large-deck amphibious assault ships and large surface combatants (i.e., cruisers and destroyers). A 2005 "quick look" analysis by the Naval Nuclear Propulsion Program concluded that total life-cycle costs for nuclear-powered versions of these ships would equal those of oil-fueled versions when oil reaches about $70 and $ 178 per barrel, respectively. Sail and solar propulsion. Kite-assisted propulsion might be an option for reducing fuels use on Navy auxiliaries and DOD sea lift ships. Two firms are now offering kite-assist systems to commercial ship operators.

Source: https://www.researchgate.net/publication/269047236_Aerodynamic_Design_Optimization_of_Wing-sails

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