2D Sail Aerodynamics

62
A Computational Study of Upwind Sail Aerodynamics: Headsail and Mainsail Interaction of a Yacht. MSc Project By Abhipray Jain Student N 0 : 110361527 School of Marine Science and Technology Supervisor: Dr Ignazio Maria Viola Submitted: 10/08/12 In Partial Fulfilment of the Requirements for the Masters Degree in Master of Science in Naval Architecture.

Transcript of 2D Sail Aerodynamics

Page 1: 2D Sail Aerodynamics

A Computational Study of Upwind Sail Aerodynamics: Headsail and Mainsail Interaction of a Yacht.

MSc Project

By

Abhipray Jain

Student N0: 110361527

School of Marine Science and Technology

Supervisor: Dr Ignazio Maria Viola Submitted: 10/08/12

In Partial Fulfilment of the Requirements for the Masters Degree in Master

of Science in Naval Architecture.

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A Computational Study of Upwind Sail Aerodynamics:

Headsail and Mainsail Interaction of a Yacht.

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ABSTRACT

A 2D mainsail and headsail interaction in upwind condition was performed using a CFD

simulation on America`s cup 33 yacht’s sails for different camber percentages of a

headsail. Six combinations of sails were provided by the supervisor, and the headsail

cambers were 13%, 16%, 20%, 23%, 26% and 30%, but only one mainsail camber was

used. A thorough discussion regarding the effect on pressure coefficient with the change

in camber was explained. Effect in reattachment length and trailing edge separation

length of the sail was also well defined. For better understanding 3 different grids were

made namely Coarse, Medium and Fine which provided a better discussion regarding

results and validation. Different values of coefficient of lift and drag were calculated and

validated for different sail interactions and the optimum camber was selected depending

on these values. With the help of the supervisor, errors and uncertainties in the results

were discussed using a simple graphical approach. As there was no experimental data

available for this thesis, no comparison could be done between the computational results

and experimental results. However, effect of different grids in CFD and different cambers

of sail, on the sail interaction are reported clearly with remarks.

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ACKNOWLEDGEMENT

I owe a great many thanks to many people who have helped and supported me

throughout my experience as a student in Newcastle University.

First, I would like to thank my parents, Sushil Kumar Jain and Manju Jain, for providing

me with the moral support and for having confidence in me.

My special thanks to my supervisor Dr Ignazio Maria Viola for guiding me. He has taken

pain to go through every detail and make necessary correction as and when needed.

I would also thank my University and all my faculty members without whom this course

would have been a distant reality. I also extend my heartfelt thanks to my friends for

having faith in me.

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AUTHOR DISCLAIMER

The present Report is submitted for the partial fulfilment of the requirements for the

Degree of Master in Science in Naval Architecture at Newcastle University. The

undersigned, Abhipray Jain, confirms that the material presented in this project is all my

own work. References to, quotation from and the discussion of work of any other work

are correctly acknowledged/ cited within the report in accordance with university

guidelines on academic integrity.

Sign: ______________________________

Name (printed in full): Abhipray Jain

Date: 10/08/2012

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TABLE OF FIGURES

Fig 1) Flow field without circulation (Arvel Gentry, 1971) page3 ____________________________ 5

Fig 2) Applying Kutta condition gives lift (Arvel Gentry, 1971) page 3 ______________________ 5

Fig 3) Flow Regions (Gentry, 1981) page 1 ____________________________________________________ 7

Fig 4) Separation Flow Areas (Gentry, 1981) page 2 __________________________________________ 7

Fig 5) A downwind sail flow (Collie et al, 2001) page 33 ______________________________________ 7

Fig 6) Luff Separation Bubble (http://www.wb-sails.fi/news/Stallpics.HTML) _____________ 8

Fig 7) Cp Vs x/c with Camber 0% (Sulisetyono et al, 2010) page 171 ______________________ 12

Fig 8) Cp Vs x/c with Camber 0% (Sulisetyono et al, 2010) page 171 ______________________ 12

Fig 9) Schematic drawing of pressure and flow around the sails (Viola et al, 2011) Page 6.12

Fig 10) Different Geometries for Headsail and Mainsail Interaction _______________________ 17

Fig 11) Geometry, Computational Domain and Boundary Conditions in ICEM CFD _______ 18

Fig 12) A simple 2-D planar blocking strategy ______________________________________________ 19

Fig 13) Controlling number of cells and their size for better calculation of interaction. __ 20

Fig 14) Hybrid Mesh was used to reduce the total number of cells which would have been

more if same topology was used at the region away from the sails. ________________________ 21

Fig 15) Full view of the mesh showing conformal and non-conformal regions. ____________ 21

Fig 16) For creating Fine grid, scale size was increased from 1 to 1.2599. _________________ 23

Fig 17) For creating Coarse grid, scale size was reduced from 1 to 0.7937.________________ 23

Fig 18) Velocities in different directions for the inflow. _____________________________________ 24

Fig 19) Lift Convergence History _____________________________________________________________ 26

Fig 20) Drag Convergence History ___________________________________________________________ 26

Fig 21) Scaled Residuals ______________________________________________________________________ 26

Fig 22) Flowchart for Convergence Criteria. _________________________________________________ 27

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Table of Figures

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Fig 23) Wall Shear Stress _____________________________________________________________________ 29

Fig 24) Unusual Pressure contour on Mainsail. ______________________________________________ 31

Fig 25) Diffusive nature of First order Scheme. ______________________________________________ 31

Fig 26) Second order numerical method. ____________________________________________________ 32

Fig 27) Combination of First order Scheme (6000 iterations) and Second order Scheme

(more than 6000 iterations) in upwind condition. __________________________________________ 33

Fig 28) Reattachment length Vs Camber% __________________________________________________ 34

Fig 29) Separation length Vs Camber% ______________________________________________________ 35

Fig 30) Headsail Pressure distribution for varying camber _________________________________ 37

Fig 31) Headsail Pressure distribution for varying camber _________________________________ 38

Fig 32) Headsail pressure distribution for varying cambers (1a) and (1b) Coarse grid; (2a)

and (2b) Fine Grid. ____________________________________________________________________________ 38

Fig 33) Cl Vs Camber% for all grids __________________________________________________________ 40

Fig 34) Cd Vs Camber% for all grids _________________________________________________________ 41

Fig 35) Cl Vs Cd for all grids __________________________________________________________________ 41

Fig 36) Cl ratio Vs Camber% __________________________________________________________________ 43

Fig 37) Cd ratio Vs Camber% _________________________________________________________________ 43

Fig 38) Value of Cl and Cd for corresponding camber% and grid types ____________________ 44

Fig 39) Uncertainty graph - Using Factor of 3.0 56

Fig 40) Uncertainty graph - Using Factor of 3.0 when E2 > E1 56

Fig 41) Uncertainty graph - Using Factor of 3.0 when E1 > E2 56

Fig 42) Uncertainty of Cl 57

Fig 43) Uncertainty of Cd 58

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NOMENCLATURE

2d= 2 dimensional

CFD= Computational Fluid Dynamics

Cp = Pressure Coefficient

Cl = Lift Coefficient

Cd = Drag Coefficient

Xr = Reattachment Length

Xs = Separation Length

X/c = Camber/Chord

= Density

= Velocity

U+= Non dimensional velocity

Y+=Non dimension wall distance

= Wall shear stress

= Friction Velocity

= Velocity in the x direction

P = Fluid Pressure

r = Fluid Density

V = Fluid Velocity

g = Gravitational Acceleration Constant

h = Height

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TABLE OF CONTENTS

Abstract _________________________________________________________________________________________________ i

Acknowledgement ___________________________________________________________________________________ ii

Author Disclaimer __________________________________________________________________________________ iii

Table of Figures ______________________________________________________________________________________ iv

Nomenclature ________________________________________________________________________________________ vi

Chapter 1: Introduction ____________________________________________________________________________ 1

1.1 Preface _____________________________________________________________________________________ 1

1.2 Aim and Objectives _______________________________________________________________________ 2

1.3 Overview of Dissertation: _______________________________________________________________ 2

Chapter 2: Literature Review ______________________________________________________________________ 3

2.1 Introduction _______________________________________________________________________________ 3

2.2 Modern Sail Theories ____________________________________________________________________ 4

2.2.1 How a sail generates lift _______________________________________________________________ 4

2.2.2 Separation Flow areas and Turbulence ______________________________________________ 6

2.2.3 Leading Edge Separation ______________________________________________________________ 8

2.2.4 Trailing Edge Separation ______________________________________________________________ 9

2.3 Sail Interaction __________________________________________________________________________ 10

2.4 Pressure Distributions _________________________________________________________________ 11

2.4.1 Overview ______________________________________________________________________________ 11

2.4.2 Windward and Leeward Pressure Distributions __________________________________ 11

2.4.3 Headsail and Mainsail Interaction __________________________________________________ 13

2.5 Significance of Camber _________________________________________________________________ 13

2.6 Significance of Grid/Grids _____________________________________________________________ 15

Chapter 3: Computational Fluid Dynamics Methodology ___________________________________ 16

3.1 Overview _________________________________________________________________________________ 16

3.2 Geometry _________________________________________________________________________________ 16

3.3 Grid Construction _______________________________________________________________________ 18

3.4 Solver Settings __________________________________________________________________________ 23

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3.5 Post Processing _________________________________________________________________________ 25

Chapter 4: Results __________________________________________________________________________________ 28

4.1 Method ___________________________________________________________________________________ 28

4.1.1 Overview ______________________________________________________________________________ 28

4.1.2 Formulae Used _______________________________________________________________________ 28

4.2 Discretization and Error Handling during Post Processing: _____________________ 30

4.3 Effect of Camber on reattachment length (Xr) and Trailing Edge Separation

length (Xs) for Fine, Medium and Coarse grids. ________________________________________ 33

4.3.1 Overview ______________________________________________________________________________ 33

4.3.2 Effect on camber on Xr _______________________________________________________________ 33

4.3.3 Effect of different Grids on Reattachment length (Xr) ____________________________ 34

4.3.4 Effect on camber on Xs ______________________________________________________________ 35

4.3.5 Effect of different Grids on Trailing Edge Separation Length (Xs) _______________ 36

4.4 Effect of camber on Pressure Coefficient (Cp) _____________________________________ 36

4.5 Effect of camber on Drag (Cd) and Lift Coefficients (Cl) __________________________ 39

4.5.1 Lift Coefficient (Cl) ___________________________________________________________________ 39

4.5.2 Drag Coefficient (Cd) _________________________________________________________________ 40

4.6 Effect of grids on Cl and Cd ____________________________________________________________ 42

4.7 Uncertainty ______________________________________________________________________________ 44

4.7.1 Overview ______________________________________________________________________________ 44

4.7.2 Method ________________________________________________________________________________ 45

4.7.3 Cl and Cd uncertainties ______________________________________________________________ 47

Chapter 5 Conclusion _______________________________________________________________________________ 49

5.1 Summary _________________________________________________________________________________ 49

5.2 Recommendations ______________________________________________________________________ 50

References: ___________________________________________________________________________________________ 51

Bibliography: ________________________________________________________________________________________ 52

Appendix 53

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Chapter 1: Introduction

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CHAPTER 1: INTRODUCTION

1.1 PREFACE

To design efficient sails, more and more researches have been done throughout the

history and many methods have been employed. From the start of the sail design, an

insight and knowledge have been the first means of designing sails. Insight and

knowledge still play a major role in sail design as there is no database available which

defines the maximum efficiency of a certain camber of a sail for a particular yacht. From

an insight, prototype sails can be built to perform experiments and simulations.

Also, wind tunnel testing can be done with model sails to observe and study the flow

around sails on a smaller scale.

Today, computers have become a means of calculating a lot of information in short

amounts of time. The digital computer with an integration of mathematical models, have

given a new sight to the aerodynamics called as Computational Fluid Dynamics (CFD). In

its simplest terms, CFD is the process of taking a physical flow problem, breaking it down

into a suitable set of equations, and solving them on a digital computer. As the use of CFD

grew in the field of aircraft industries in the past years, it has been proved that CFD is a

quite cost effective method which doesn’t have any approximations present. CFD had also

been used and still being used for sail aerodynamics because it doesn’t allow any

approximations which are present in the wind tunnel tests for yachts, thus decreasing the

design processing time.

Therefore, this paper presents the experiences of the author in exploring the use of CFD

on sails. Early explorations were quite significant as they led to the correct explanation

for the headsail-mainsail interaction problems (Gentry, 1971). CFD technology was

applied to the problems of several camber profiles of headsail with only one mainsail

camber interaction. The sections of the sail have been taken from AC33 yacht’s section

(Viola et al, 2011). This project reviews some earlier work done on sail of yachts and gives

a brief explanation regarding effect of camber on the lift and drag of a sail and also the

effect of grid on the results obtained by the solver.

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1.2 AIM AND OBJECTIVES

The main objective of this research is to understand the aerodynamics of sail. To improve

its performance, a maximum optimum lift force is required. Also minimum drag is

required so as to reduce resistance losses. After running the simulations for different

grids, the maximum lift coefficient has to be found for a camber, which will be an

optimum camber profile of a headsail. Also, a good argument about the sensitivity of

camber of the headsail to the lift coefficient is required to be made. Discussion regarding

how a change in number of elements for a mesh can change the results is to be made. At

last a validation of CFD results is needed to be done so as to get an idea regarding the

probability of error in the results.

1.3 OVERVIEW OF DISSERTATION:

The dissertation has been organized in a way that chapter 2 outlines a simple and

comprehensive review about the evolution of sail aerodynamic theory. Here, the

fundamental concepts are explained and more emphasis is given on the latest researches

of the leading edge bubble, flow separation, flow reattachment and trailing edge

separation. The trend in pressure distribution around sails is also discussed.

In chapter 3, remarks are made regarding the geometry dimensions, the generation of

mesh, solver setup and boundary conditions used. A simple explanation is been given

about the mesh quality and its sensitiveness. Chapter 4 deals with the results section,

which provides all the basic elements which defines forces in the sail aerodynamics. Thus,

coefficient of lift and drag are explained in this section with a statement regarding on

different values obtained for different grids and cambers used. To understand the flow

around the sails, pressure coefficient and flow separation has been discussed. Verification

and validation has been presented in this section so as to define a certain level of accuracy

in the results.

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Chapter 2: Literature Review

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CHAPTER 2: LITERATURE REVIEW

2.1 INTRODUCTION

During the period of 3000 BC – 900 AD, the first sail which was used by the sailors was in

a form of a square shape. This square shaped boat was used for thousands of years in the

river Nile, by the sailors, despite the limitations of the wrong design of the sail. The square

sails were pushed by the wind and the boat could only sail windward. Thus, all of the

forces were in the same direction. People soon realised the mistakes they were doing and

about two thousand years ago triangular sails came into the picture. Due to the better

design and orientation of these sail, a forward thrust could be generated even if the wind

angle wasn’t perpendicular to the sail, which was expected to be present in the square

shaped sail. Sail could be pulled or pushed, but pulling force was more than the push

force. There was no physical understanding of the pulling force but during 18th century it

was identified as Lift and the explanation behind this pulling force was based on two basic

theories namely BERNOULLI and EULER lift theories.

Square Sail Triangular Sail

Aerofoil Yacht Sail

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Bernoulli’s Equation: P + 1/2rV^2 + gh = C

Bernoulli’s equation was based on the energy conservation in a fluid system, thus energy

being constant. It can be assumed that the gravitational force is negligible, when increase

in velocity and thus decrease in pressure is considered. The streamlines separate at the

leading edge of the airfoil and meet again at the trailing edge. The pressure above is lower

than the pressure below, creating a lifting force.

Many other theories came into existence during 19th and 20th century but a major turn in

sail aerodynamics came when Arvel Gentry, an aerodynamicist at Boeing Commercial

Airplane Company proved the majority of the earlier theories wrong. As research was

already going on in aircraft industry, people had several myths regarding sail

aerodynamics because they integrated aerofoil aerodynamics to sail aerodynamics as a

whole. They didn’t realise that airplanes have long and smooth, only slightly cambered,

thick wings which are designed for specific speeds and operational conditions. Where

sails are of lower aspect ratio, highly cambered, thin and twisted, and have to operate in a

variety of conditions and wind speeds in a turbulent layer of air above the sea surface. For

the underwater hull & fins, lessons learned from airplanes were more valid than for sails.

In the last few years, advances in CFD (Computer Fluid Dynamics) have changed the way

we perceive sail aerodynamics. Old beliefs are proven wrong and new features found.

2.2 MODERN SAIL THEORIES

2.2.1 HOW A SAIL GENERATES LIFT

Arvel Gentry, an aerodynamicist in 1971 founded that the basic explanations regarding

lift generation for sail were all wrong. He explained that lift generation doesn’t depend on

the sail’s/aerofoil’s shape. It was believed by many people that air flows faster on the

upper surface of the aerofoil than the lower surface, as at the upper surface it has to travel

more distance. This is not in case of sail as upper and lower surfaces are almost of the

same distance. To verify this, an experiment was done on an aerofoil. The figure (1) below

shows the resulted streamlines on an aerofoil section where all the governing

equations were satisfied but the results showed that aerofoil hasn’t got any lift. In reality

the streamlines shouldn’t be as it’s shown but the flow around the trailing edge should

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change, as the air begins to move past the aerofoil so that it leaves the aerofoil in the same

direction on the top and bottom.

Fig 1) Flow field without circulation Fig 2) Applying Kutta condition gives lift

(Arvel Gentry, 1971) page3 (Arvel Gentry, 1971) page 3

He applied Kutta condition as shown in figure (2), to the sail in order to create his theory

of generation of lift and he performed several experiments on the sail interaction where

he found out different pressure and velocity distributions on the sail geometry. All his

experiments and findings gave the basic knowledge of modern sail aerodynamics to the

sailors and to the aerodynamicists all over the world. Since then research in this field

using modern sail aerodynamics is being done which has been successful.

Fossati, another researcher in 2009, identified the significance of the camber and aspect

ratios of the sail on the aerodynamics behaviour. The research was done on a cambered

plate for checking the effect of resistance on aviation equipments with in a period of 1904

to 1910. In this piece of research it was shown that a shell plate with zero angle of attack

can also generate a minimum amount of lift. As we know that this doesn’t hold true for

sail, as at zero angle there is no pressure at the windward side of the sail which makes it

collapse and doesn’t allow to retain its cambered shape anymore. This also proved to be a

better vision to learn and practise aerodynamics as it was proved that a certain degree of

angle is needed to generate lift on a sail.

Gentry also suggested that the generation of lift requires that the fluid have some

viscosity. He performed an experiment with a fluid without viscosity to prove this point

and it was shown that without viscosity there would be no lift and sailboats would not sail

(Gentry, 2006). He also suggested the significance of the centre of effort on the sail which

generates lift in the direction perpendicular to the direction of the angle of attack. Larsson

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and Eliasson (2000) explained that any change in angle of attack will change the position

of centre of effort on the sail. This happens because of the change of angle of attack, the

distribution of velocity and pressure over the sail changes. This changes the magnitude

and direction of the lift on the sail.

Wilkinson (2009) measured the pressure distribution along a mainsail using a rigid foil,

and found that there was separation behind the mast on the sail on both the windward

and leeward side of the sail. The sail can be divided up into a variety of different section

because of the difference in pressure distribution characteristics. The pressure

distributions shown by Wilkinson can also be used to confirm Gentry’s (1971) modern

sail theories. The aerodynamics of a Sparkman and Stephens 24-foot sailing yacht was

investigated by Viola et al (2010). Full-scale pressure measurements were performed on

the mainsail and the genoa in upwind condition and compared against the modern sail

theory. Pressure taps were adopted to measure the pressures on three horizontal sections

on the windward and leeward sides of the two sails (Viola et al, 2010). The results

showed that as the angle of attack was changed, it caused the pressure distribution over

the sails to change, which caused trailing and leading edge separation at high angles of

attack. The results showed a correlation between the modern sail theory and Wilkinson’s

theories.

2.2.2 SEPARATION FLOW AREAS AND TURBULENCE

Turbulent Transition was first studied by Osborne Reynolds (1883). He did an

experiment observing turbulent transition in a glass walled tank where he proved that in

order to have a transition, disturbance in a flow needs to be present. He also provided the

information about the stresses magnitude being higher in the turbulent area than in the

laminar area for the same Reynolds number (Collie et al, 2001).

In 1970’s Gentry’s modern sail theory also stated different divisions of flow on a sail area

as shown in figure (3, 4). He stated that air is a viscous medium and it reflects its viscosity

in the region of boundary layer. He explained that the laminar boundary layer is more

susceptible to separation that the turbulent boundary layer. In some cases, as he

explained, the separated flow will reattach to the surface of the sail. In separated laminar

boundary case a small separation bubble forms due to the same phenomenon and

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reattaches itself to the turbulent boundary layer. Also, if no reattachment of the flow

happens, the condition is called a stalled condition where lift doesn’t increase but

gradually decreases (Gentry, 1971).

Fig 3) Flow Regions (Gentry, 1981) page 1 Fig 4) Separation Flow Areas (Gentry, 1981) page 2

Collie et al (2001) also showed the leading edge separation phenomenon on a downwind

sail flow. As shown in figure (5) the flow accelerates around the leading edge and forms a

recirculation region while separating. They also told that when the sail stalls, there is no

reattachment of the separation at the leading edge but a disrupt flow occurs. Also, they

told about interdependency of flow over each sail in an interaction as shown.

Fig 5) A downwind sail flow (Collie et al, 2001) page 33

Wilkinson (2009) also discovered there would be separation at the leading edge on the

windward and leeward side, when there was a mast in front of the sail. Thus, confirming

the modern sail theory of Gentry which talks about the laminar and turbulent separation

at the ends of the sail.

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2.2.3 LEADING EDGE SEPARATION

There are two types of leading edge separation which takes place, a short bubble and a

long bubble. A short bubble is generally seen on a conventional airfoil with rounded nose

shape where as a long bubble appears on thin aerofoils with tapered or sharp leading

edges like in a yacht sail, turbine blades etc ( Viola et al, 2011).

Gentry (1976) did an experiment on a mast shape of a sail. He placed a mast at the leading

edge of the mainsail and tried to see its interaction with the jib. He managed to evaluate

that mast’s shape can change the magnitude of the leading edge separation and thus,

separation by the mast was needed to be reduced. Also, he mentioned that not only the

mast’s shape can change the separation but jib’s trim also affects the separation caused by

the mast on the sail. Wilkinson (2009) also defined the change in leading edge separation

caused by the mast’s shape. He told that the intensity of the pressure increase at the

turbulent boundary layer depends on the mast shape. As the pressure increase is

intercepted by the shape of the mast and sail, the flow reattaches and forms a separation

bubble. If sail and mast integrated pressure doesn’t intercept the pressure increase at the

turbulent boundary, flow remains separated and no separation bubble forms. A

separation bubble behind the mast on the leeward side of the sail has been shown in the

figure (6).

Fig 6) Luff Separation Bubble (http://www.wb-sails.fi/news/Stallpics.HTML)

In 1950’s, aeronautical industries discovered another type of bubble which was longer

thinner separation bubble at the leading edge. This was done to achieve high speed for an

aircraft using thin airfoils so as to get more lift and since then research started on thinner

longer separation bubbles. Crompton and Barrett (2000) found out that bubble separates

due to the laminar separation and to find this they conducted an experiment on a flat

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plate. They investigated that the adverse pressure, forces the shear layer to separate and

vortices to shed and dissipate into an unstable layer that moves along an elliptic track.

This track is the upper boundary of the leading edge bubble. The shear layer passes

through a transition from turbulent to laminar flow and at some distance downstream

reattaches to the sail. Crompton and Barrett used laser Doppler anemometer (LDA),

which was believed to give a better insight to the flow phenomena rather than just the

numerical calculation. Viola et al also found that as the angle attack increases on a sail it

will cause lower pressure on the leeward side of the sail which will lead to the leading

edge bubble increasing in length (Viola et al, 2011).

Collie, Gerritsen and Jackson (2008) looked into the leading edge bubble on a flat plate

with a low angle of incidence of 3˚. Since this time, CFD use for identifying the separation

bubble on sail was in used at a major scale. In spite of having more accurate data from the

Crompton and Barrett research, Collie et al weren’t able to predict the secondary leading

edge bubble. It was concluded as the problem with the model, which Collie et al made, for

validation with the wind tunnel tests done by Crompton et al as the software (CFD) didn’t

seem to understand the flow separation regions within the model made or probably the

model was wrong.

2.2.4 TRAILING EDGE SEPARATION

Gentry (1971) found that the area of turbulent separation occurs because of the pressure

change around the sail profile. As the flow increases around the leeward side of the sail,

pressure decreases and separation occurs. Then when the velocity slows it causes the

pressure to increase causing the flow to become turbulent and the shear layer to separate

from the surface of the sail.

Viola et al (2011) also mentioned the change in pressure distribution with the trim angle

increase. When the angle of attack increases, there is a lower pressure area formation

which causes separation to occur earlier along the chord. Also, a sail with a shorter chord

experiences quick slow down in velocity when put at a higher angle of attack. This causes

the flow to become unstable earlier, which results in early turbulent separation.

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2.3 SAIL INTERACTION

Headsail and mainsail interaction with each other has been an extensive area of research

since many years for aerodynamicists and sailors. When the two sails are close to each

other, air flow distribution around the sails tends to change depending on the position of

the two sails. Gentry (1971) explained how presence of headsail causes the stagnation

point of the mainsail to shift to leading edge, which in turn reduces the suction velocities

on the mainsail. These interactions between the two sails suggest that mainsail can be

used with higher angle of attacks with less possibility of separation happening on it. Also,

as air flows first on headsail and then on mainsail, this would affect the flow on the

mainsail altogether. This happens as the flow has to circulate from the top of the headsail

profile to the mainsail, which doesn’t happen in reality, thus affecting the flow over

mainsail.

The upwash (flow on the upper side of the sail) of the mainsail shifts the stagnation point

of the headsail towards the windward side of the sail. This prevents the headsail to stall

on the leeward side of it. To increase the efficiency of the headsail, it was identified that if

the headsail is in the high velocity regions of the mainsail trailing edge, then velocity at

the trailing edge of the headsail increases.

Viola et al (2011) also did an investigation on the sail interaction and found out that as the

trailing edge of the headsail is the suction for the mainsail, trailing edge of the headsail is

at low pressure during the interaction. Thus pressure decreases at the leeward side of the

headsail with the interaction with mainsail.

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2.4 PRESSURE DISTRIBUTIONS

2.4.1 OVERVIEW

Pressure distribution around sails is usually presented in the form a pressure coefficient

(Cp) defined as the normalised difference between the pressure at the sail (p) and the

free-stream dynamic pressure (p∞).

As it has been discussed before, we expect a formation of a thin separation bubble at the

leading edge of the headsail (Crompton et al, 2000). Also, laminar separation is supposed

to occur from leading edge which forms a secondary separation bubble. Following the

phenomenon, the flow will go through a transition phase before turning into a turbulent

flow.

2.4.2 WINDWARD AND LEEWARD PRESSURE DISTRIBUTIONS

In viscous flows the stagnation point of a flat plate was found by Crompton et al (2000).

He explained the stagnation point to be located at the leading edge for a range of angle of

attack close to the ideal angle of attack. Sulisetyono et al (2010) described the behaviour

of sails in the fluid dynamics analysis. Only mainsail design was tested using CFD for

various drafts, cambers and angle of attacks of the sail. Figure (7, 8) shows the

dependency of camber profile with the coefficient of pressure distribution along the sail.

He tried to explain that when the angle of attack becomes more the transition point

becomes smaller and opposite the stagnation point becomes bigger (Sulisetyono et al,

2010).

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Fig 7) Cp Vs x/c with Camber 0% Fig 8) Cp Vs x/c with Camber 0%

(Sulisetyono et al, 2010) page 171 (Sulisetyono et al, 2010) page 171

It was identified that with 0% camber there was no bubble separation occurred while a

camber 5% has a trailing edge separation with the decrease in pressure from the

reattachment point. Viola et al (2011) found out the pressure distribution for the mainsail

and headsail interaction which is shown in figure (9).

Fig 9) Schematic drawing of pressure and flow around the sails (Viola et al, 2011) Page 6.

It was found out that the windward side of both the sails was a low speed region (Viola et

al, 2010). Therefore, Cp was found out to be same (Cp=1.0) across the whole section.

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Then, it initially decreases and after that initial decrease, sail curvature causes the

pressure to increase with a maximum around half chord length. At the trailing edge Cp

tends to take negative values to meet the pressure at the leeward side of the sail. Also, for

low angle of attacks of the sail a recirculation bubble was formed and kept on decreasing

in size as angle of attacks became greater. Something opposite was found out on the

leeward side which was a particular length of a bubble for an ideal angle of attack which

started to increase with the increase in angle of incidence.

2.4.3 HEADSAIL AND MAINSAIL INTERACTION

Referring figure (9), a suction peak at the leading edge was seen on the leeward side of

the headsail. This was recovered by a quick pressure increase with a local minimum

suction of around 10% of the chord (Viola et al, 2010). This happened because of the

formation of laminar separation bubble behind the sharp edge of the headsail which

reattaches after the turbulent transition (Crompton and Barret, 2000). Downstream of the

reattachment the pressure decreases because of the headsail’s shape and curvature. Just

after this, trailing edge separation occurs and pressure becomes nearly constant.

For the mainsail, the leeward side shows similar trends to what was found for the

headsail. The major differences were that the laminar separation occurred at the mast and

turbulent separation occurred at around 10% of the mainsail chord (Viola et al, 2011).

Between the turbulent reattachment and the initial suction, the pressure seemed to be

almost constant whereas during the reattachment a smooth curve was obtained than it

was in case of a headsail.

2.5 SIGNIFICANCE OF CAMBER

Camber refers to the curvature of the sail. An efficient camber results in a very less drag,

and thus, requiring less thrust to produce lift. Therefore, camber has an effect on lift in

addition with the reduction of drag. Back in 19th century this was proved by Daniel

Bernoulli, referred to as the Bernoulli’s principle, that the cambered wings generate

efficient lift rather than flat wings. As we studied in the former part of this research, sail

behaves almost like an aerofoil; the Bernoulli’s principle seemed to work on sails.

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It has been found out that cambered sail, even at zero angle of attack, creates a pressure

differential between upper and lower surfaces. As the camber of the sail increases, more

lift is produced but unfortunately, high cambers produce high drags too. Therefore, there

is a limit to the camber which gives more lift than drag. As drag is counter-productive to

the performance of the sail and its yacht, it is formed when high-pressure air on the

windward side of the sail tries to escape to the low pressure, leeward side. When this air

escapes it becomes turbulent and gets distributed over the smooth flow of sail. When this

happens the air slows and stalls from the sail thereby reducing lift. Therefore, the balance

for boat performance is maximum lift and minimum drag.

Lasher et al (2005) presented a paper on symmetric spinnakers where they have several

models of spinnakers with varying cambers, aspect ratios etc. and they tried to find out

the affect of these, on the force coefficients like lift and drag coefficients. They concluded

that the effect of camber depends on the aspect ratio of the sail. It was found that for

cambered sail there was a less increase in lift for lower aspect ratios than for higher

aspect ratio sails. This increase in lift was compared with respect to the model of a flat

sail.

As research for the significance of camber on force coefficients has been a concise study,

we haven’t achieved a substantial amount of data, to perform a validation which may give

precise results of its effectiveness. Some of the experimental data which we have today is

from the study of mast and sail pressure distribution by Wilkinson (1990). It provided us

with a local wall measurement around the mast and the sail. More recently others have

investigated the effect of camber on sails (Lopes et al, 2008) but results haven’t provided

any better knowledge of the effect of camber of force coefficients. Also, there is no

research papers published, which describes the effect of very high cambered sail on

forces.

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2.6 SIGNIFICANCE OF GRID/GRIDS

Not only parameters like camber, aspect-ratio, boundary conditions etc. for the sail, affect

the simulations but also the meshing which has been done can change the results

significantly. A meshing sequence was used while forming a grid in ICEM CFD, which was

further used for running the simulations in Fluent v6. We know that cells near the sail

should be many in number and of square shape, so as to calculate the velocity and

pressures effectively, as Velocity/Pressure is more turbulent near the wall of the sail than

away from it. Therefore, to maintain the integrity of the mesh to be made, more number of

cells are used near the sail region than away from it. This certainly gives the required

result when simulated in a solver, but to check the uncertainty of the solution different

grids namely fine, medium and coarse were prepared.

Bentaleb et al (2004) found out that the values of CL and CD were reduced linearly for the

three meshes. Also, CL and CD converged towards a rather narrow range of values for

medium and fine grids. Fathi et al (2010) found out that accuracy is penalized when high

residuals of the unstructured mesh were found out in areas with large flow gradients.

They also told that although the structured grids being more complex to generate rather

than unstructured, they get hold of improved numerical accuracy to the simulation (Fathi

et al, 2010). It was also believed that while comparing results between the different grids,

if there is a large difference between grid A and grid B but small relative difference

between grid B and grid C, than resolution of the grid C (finest grid) is suitable to be used

for calculation purposes ( Ramponi et al, 2012) .

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CHAPTER 3: COMPUTATIONAL FLUID

DYNAMICS METHODOLOGY

3.1 OVERVIEW

As the user was new to the software Ansys, learning the basic working of the software

was one of the tasks which were performed for a certain period of time. In this section a

detail description of the method employed for carrying out the simulations is described.

The procedure involves use of Fluent v6 software for carrying out simulations (post

processing) while blocking and meshing is done on ICEM CFD, both software being a part

of Ansys 13.0. The process can be summarized as –

Geometry Creation

Meshing

Solver Setting

Post processing

3.2 GEOMETRY

A cluster of geometries was provided by the supervisor which consists of the two sail

sections namely headsail and mainsail, with different geometries configurations. The

outer rectangular boundary is defined as a domain for different headsail geometries in

combination with a single geometry of mainsail. As the geometry was designed in

AutoCad its dimensions were changed from millimeters to meters in ICEM CFD and its

axis was changed from x-y to y-x. This was done to carry out sail aerodynamics in the

right axis so as to make, the input velocity direction corresponding to the sail geometries,

almost perpendicular to the sails. This was done to obtain the right angle of attack as

needed.

As shown in figure (10), different headsail camber profiles can be seen, whose interaction

with the mainsail is needed to be checked for obtaining maximum lift. Thus, each camber

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of headsail has different chord lengths minimum being 0.3 meters and mainsail chord

length is 0.5 meters. For headsail, different ratios between camber to chord length from

the bottom to the top sail are 13%, 16%, 20%, 23%, 26%, 30%, 33%, 36%, 40%, 43%,

46%, and 50%. The mainsail camber has not been changed for all the cases. During the

simulations it was found that the maximum lift occurred for lower percentages of the

Camber/Chord length ratios. Thus to make the work less tedious, it was suggested by the

supervisor to work on lower Camber/Chord length ratios being 13%, 16%, 20%, 23%,

26%, and 30% for the headsail. However, simulations for all the camber profiles were

done by the author, to get the better insight of the problem. These sail were designed for

the America’s Cup class yacht ‘AC33’ and rigid model-scaled sails of the ‘AC33’ were tested

at the Yacht Research Unit of the University of Auckland (Viola et al, 2011).

Fig 10) Different Geometries for Headsail and Mainsail Interaction

To solve the Navier-Stokes equations, proper boundary conditions are required on all

calculation domain frontiers. At wall boundary (headsail and mainsail), the no-slip

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condition is applied. An outlet boundary condition is applied at the right computational

domain boundary. A velocity inlet boundary condition is applied on other part of the

computational domain (inlet, up and down) as shown in figure (11).

Fig 11) Geometry, Computational Domain and Boundary Conditions in ICEM CFD

3.3 GRID CONSTRUCTION

The process of developing mesh is called Mesh or Grid Generation and is considered the

most important phase as successful simulations depend on the quality of mesh generated.

Grid creation involves blocking the model creating various surfaces on the sails of yacht. A

simple 2-D planar blocking strategy was done in ICEM. Different blocking strategies were

tried out and the one in the figure (12) was used, keeping in mind, that the cell formations

near the edges of the sail will be square shaped. This was done so that velocity can be

monitored accurately as near the edges, velocity can be in different directions due to high

interactions between sail and the air.

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Fig 12) A simple 2-D planar blocking strategy

A certain type of mesh generation is a critical step in the process of RANS simulation for

many reasons. First of all, it is very time consuming to create geometry on ICEM CFD or

export geometry from CAD model and try to mesh it using CFD topology. Secondly, the

mesh can manipulate results on typical sails configurations and should be carefully

calculated and a restricted choice of a mesh size in the important flow regions should be

considered as an important factor. Boundary layers have to be well resolved on all bodies

(headsail and mainsail) and this inflicts a decisive factor on mesh size in the normal

direction to walls. But this well-known criterion is not enough to have a good flow

description and results independent to mesh. All flow gradients have to be well resolved

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and this is not a simple task on typical sails because of the zero thickness and the

subsequent leading-edge pressure gradient when angle of attack is not ideal.

Another important feature of mesh is their flexibility to different kind of geometries.

Therefore, a good quality meshes should be generated in the boundary layers regions of

each body without any use of too high aspect ratio cells and with a good control in the

interaction regions which may be small (mainly between headsail and mainsail figure 13).

To respect these topologic constraints, a good candidate is hybrid meshes. However, the

author hasn’t used the hybrid mesh but have tried to decrease the cell ratio which can be

seen on figure (14) with eventually conformal interface between the inner structured

region around sails and the outer structured region around the interacting structured

domain being non conformal as shown in figure (15).

Fig 13) Controlling number of cells and their size for better calculation of interaction.

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Fig 14) Hybrid Mesh was used to reduce the total number of cells which would have been more if

same topology was used at the region away from the sails.

Fig 15) Full view of the mesh showing conformal and non-conformal regions.

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Thus, the mesh was generated for one combination of headsail and mainsail profile which

was copied onto the other combinations. This was done to prevent any anomaly in the

results as different meshes may give different results. Also, numbers of elements in the

mesh were kept same for the first bunch of grids.

Turbulence is modelled using the SST k − ω turbulence model which is taken as the most

suitable model for high-lift aerodynamic applications. Validation studies carried out by

the researchers for highly cambered sail sections have indicated that the SST model is

indeed the most suitable turbulence model in CFD for computing the flow past upwind

sails.

To analyse the sensitivity of mesh with the results, number of elements were increased

and decreased by changing the scale factor in ICEM CFD (Fig. 16, 17) so as to make Fine

grid and Coarse grid respectively. The first bunch of meshes which were made were

named as Medium grid and kept as a reference. Therefore, numbers of grids were 6 for

medium, 6 for Fine and 6 for Coarse making total number of grids as 18 in number.

Different meshes have different number of elements being 68612,106884, and 170036 for

Coarse, Medium and Fine grids respectively. To make sure the simulation were accurate

in the sub layer a Y+ <=1 was used. Where a non-dimensional wall distance for a wall-

bounded flow can be defined as -

Where is the friction velocity at the nearest wall, is the distance to the nearest wall

and is the local kinematic viscosity of the fluid. In order to achieve a y+ of

approximately 1.0 the near wall spacing was set at c. Particular care was taken to

provide high quality cells around the leading and trailing edges and in these regions the

cells have an aspect ratio of 1: 1. Further along the sail, very high aspect ratio cells are

used in order to resolve the large flow gradients normal to the wall.

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Fig 16) For creating Fine grid, scale size was increased from 1 to 1.2599.

Fig 17) For creating Coarse grid, scale size was reduced from 1 to 0.7937.

3.4 SOLVER SETTINGS

After generating the mesh of the desired quality it is converted to unstructured mesh and

then it is modified to match the solver settings. In this case the solver which being used is

Fluent v6. So we generate an unstructured fluent mesh using the output solver settings in

Ansys Design Modeler. Once we convert the generated mesh to unstructured mesh we can

start using this mesh in fluent for simulation.

We begin the simulation process by reading the meshes in solver and then assigning the

operating and boundary conditions. As we know, the numerical solution of the Navier–

Stokes equations for turbulent flow is extremely difficult, and due to the significantly

different mixing-length scales that are involved in turbulent flow, the stable solution of

this requires such a fine mesh resolution that the computational time becomes

significantly infeasible for calculation. Attempts to solve turbulent flow using a laminar

solver typically result in a time-unsteady solution, which fails to converge appropriately.

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To counter this, time-averaged equations such as the Reynolds-averaged Navier–Stokes

equations (RANS), supplemented with turbulence models, are used in practical

computational fluid dynamics (CFD) applications when modelling turbulent

flows.Therefore, the turbulence model used was k-omega with SST option and Low

Reynolds number corrections as it is considered to be one of the best models for turbulent

flows.

Once the turbulent model is selected the velocity inlet condition are specified as shown in

figure. Where, the free stream velocity has a magnitude of 7.3426 m/s in the x and 0.0314

m/s in the y direction (Figure 18). The turbulent Intensity and Viscosity ratio was

recommended by the supervisor as 3% and 10 respectively. This was done to maintain

the same conditions as they were for the AC33 yacht’s section (Viola et al, 2011).

Fig 18) Velocities in different directions for the inflow.

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Reference values were taken as:

Area = 0.83695 m2 Length = 0.83695 m

Density = 1.225 kg / m3 Pressure = 0

Depth = 1 m Temperature = 288.16 k

Enthalpy = 0 Viscosity = 1.7894 e-05

The solution method for all the simulations used was:

Pressure Velocity

Coupling scheme

= SIMPLE Momentum = Second Order

Upwind

Gradient = Least square cell

based

Turbulent

kinetic energy

= Second Order

Upwind

Pressure = Second order

Specific

dissipation rate

= Second Order

Upwind

3.5 POST PROCESSING

Once the required boundary conditions and operating conditions are set on the model in

fluent, simulations are carried out. The simulation process continues till the desired

convergence criteria are achieved for the continuity equation. Required convergence had

not been taken into consideration only by the residual plot alone, but also with the

coefficient of lift and coefficient of drag history together as shown in the figure (19, 20

and 21).

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Fig 19) Lift Convergence History

Fig 20) Drag Convergence History

Fig 21) Scaled Residuals

Some of the important points which should be kept in mind while looking for the

convergence criteria are:

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The solution may not be converged if the residuals have met the convergence

criteria specified, but still decreasing.

If residuals are no longer decreasing but have not reached the convergence

criteria, also if lift and drag plots are not changing, the solution has converged.

Residuals are not the solution. Other solution monitors like lift and drag

coefficients monitors should also be taken into consideration. Also, low residuals

don’t mean a right answer and high residuals don’t mean a wrong one.

The flowchart in figure (22) below explains the convergence criterion further. Therefore,

during the simulation the nature of forces and contours of flow, drag, lift and velocity are

also checked regularly, to be on the safer side, in order to ascertain that we get the correct

results.

Fig 22) Flowchart for Convergence Criteria.

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Chapter 4: Results

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CHAPTER 4: RESULTS

4.1 METHOD

4.1.1 OVERVIEW

As referred in 3.1 of this thesis, 6 different cases were tested for different headsail and

mainsail combinations. Also, 3 different grid types were formed namely coarse, medium

and fine for all the 6 grids. Thus, total number of different grids, whose simulations were

performed, was 18. For each grid, wall shear stress was plotted so as to identify the

reattachment length and separation length for the headsail. It was kept in mind that all

the calculation was done only for headsail; however, being an interaction between

headsail and mainsail, mainsail affected headsail performance which will be shown

further during discussion.

Lift and drag coefficients were found out and plotted for all the different cambers and

grids. Also, reattachment length and separation length were plotted and compared with

the coefficients. Proper justification of results was done and the optimum camber profile

for the headsail was found out which generates the maximum lift and the minimal drag.

Significance of grid type on the results was understood and explained. Further in this

thesis, we would try to investigate the results and do the verification.

4.1.2 FORMULAE USED

(i) The position of reattachment and separation was found out by plotting the x-wall

shear stress which is defined as

at y=0.

Where,

μ is the dynamic viscosity

u is the x-velocity parallel to the wall ; y is the distance to the wall.

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As the value of wall shear stress depend on the velocity. Thus, a change of direction in µ

would change the sign value of the x-wall shear stress. Therefore the intersection point of

x-wall shear stress with the x-axis is considered to be the reattachment and separation

point. At typical plot of wall shear stress against x/c figure (23) is shown for 13% camber.

The reattachment and separation points are taken were τw becomes zero. The values of

reattachment and separation length presented in the further sections are found by linear

interpolation from the τw readings.

Fig 23) Wall Shear Stress

(ii) Lift and drag coefficients are defined in equation 1 and 2. As lift and drag force are

directly proportional to the respective coefficients, only coefficients were plotted against

Camber/chord length to get the idea of the maximum lift to minimum drag which can be

produced.

-2

-1.5

-1

-0.5

0

0.5

1

0 0.2 0.4 0.6 0.8 1 1.2

Wal

l Sh

ear

Str

ess

(P

a)

X/c

Wall shear stress 13% Camber

(1)

(2)

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4.2 DISCRETIZATION AND ERROR HANDLING DURING POST PROCESSING:

The strategy of CFD is to replace the continuous problem domain with a discrete domain

using a grid. In the continuous domain, each flow variable is defined at every point in the

domain whereas in the discrete domain, each flow variable is defined only at the grid

points.

Thus in a CFD solution, one would directly solve for the relevant flow variables only at the

grid points. The values at other locations are determined by interpolating the values at

the grid points. There are several methods which explains discretization in Fluent like

First Order Upwind Scheme, Power Law Scheme, Second Order Upwind Scheme etc but

here we will talk about Second Order Upwind as this discretization method was used for

our simulation.

Unfortunately, during one of the simulations, for 16% Camber/Chord length of a headsail,

for the fine grid, the results were not as it was expected. We found that for 16% camber,

coefficient of lift obtained by simulating Coarse and Medium grids gave a value of around

1.74 while the finer grid gave a value of 1.6638. As such a difference shouldn’t be present

and is not accepted, the data was verified in the following manner. At first, all the

variables values were cross checked with the other data, which was saved and used for all

other simulations. After coming to the conclusion that all variables match, its convergence

criteria was checked but everything seemed correct. Then the pressure contours were

plotted and some unusual behavior was seen above the mainsail while pressure contours

over the headsail seemed right as shown in figure (24), which wasn’t present in other

grids. As the maximum pressure, shown in red color, is below the sails, it maintains the

sails shape and prevents them to be in a stall condition. Whereas on the mainsail, it can be

seen that more than 2 separation bubbles were formed, which were not present in any

other simulations, thus it was confirmed that something went wrong with this particular

simulation. It was suggested by the supervisor to first run the simulation with first order

upwind scheme and then after around 6000 iterations, run it on second order upwind

scheme. This model was taken from the by Viola et al 2011, and it was recommended to

run simulations using second order upwind scheme so as to match the numerical method

based conditions in the paper.

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We used first order upwind scheme to run initial iterations because it was believed that

this scheme is easier to be implemented which makes the model more stable. Full

simulation was not done using this scheme as results can be diffusive in nature, for

example see figure (25). Thus to omit any diffusion, we have used second order upwind

scheme for more than 6000 iterations.

Fig 24) Unusual Pressure contour on Mainsail.

Fig 25) Diffusive nature of First order Scheme.

.

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We understand that second order upwind scheme is more accurate than first order

upwind scheme; still we got the wrong result. Question is why this happened? Why wrong

result for only this model? It can be demonstrated using the figure (26) as shown.

Fig 26) Second order numerical method.

In regions with strong gradients second order upwind scheme can result in face values

that are outside of the range of cell values. It is then necessary to apply limiters to the

predicted face values or to make the model stable in nature. We made the model stable,

using first order upwind scheme and provided a right path to the simulation so that the

face values remain inside the range of cell values. As far as other simulations were

concerned, we got the satisfactory values of coefficient of lift and drag, using the second

order upwind scheme itself. Thus, we can say that other models were more stable than

this one. As we using software for simulations, we can’t actually define or calculate what

went wrong during the simulation or where the model became unstable. Therefore, this

was taken as an unusual behavior of the software and was rectified using combined

schemes technique. It was confirmed by the supervisor that the method worked and right

value for coefficient of lift was obtained using a combination of schemes as discussed

above. The pressure contours of the combined scheme simulation looks better than

before as shown in figure (27).

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Fig 27) Combination of First order Scheme (6000 iterations) and Second order Scheme (more than

6000 iterations) in upwind condition.

4.3 EFFECT OF CAMBER ON REATTACHMENT LENGTH (XR) AND TRAILING

EDGE SEPARATION LENGTH (XS) FOR FINE, MEDIUM AND COARSE GRIDS.

4.3.1 OVERVIEW

In this section, the author has tried to differentiate between the results obtained for

several camber profiles of the Headsail and effect of these profiles on the Xr and Xs. Also, a

descriptive explanation has been given regarding effect of different grids on the results.

4.3.2 EFFECT ON CAMBER ON XR

For the ideal angle of attack of the headsail, flow of air acts tangentially on the sail profile.

Therefore for high cambers, this tangential flow helps the flow over the headsail and

prevents any detachment from the sail. It’s one of the reasons why headsail with the low

camber profiles has more length of a leading edge bubble than for high cambers. This is

because as the tangential air flow hits the sail, the pressure increases at the leeward side

and separation occurs, which reattaches soon due to the presence of a boundary layer.

This reattachment is seen for low cambers but not for the large cambered headsail as flow

follows the sails curvature due to its initial tangential direction. In figure (28), we can see

the exponential decrease in the Xr lengths, thus a smaller leading edge separation bubble,

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with an increase in the camber percentage. We can see that the Xr is zero for 26% camber

of the headsail which signifies that higher percentage of the camber results in no leading

edge bubble and thus zero Xr. An interesting fact which is seen in the graph is for 30%

camber of the headsail. As shown, the Xr increases from 0 to 0.03 from 26% to 30%

camber respectively. This signifies that after a particular increase in camber, further

increase results in the formation of a small leading edge bubble. Thus, this formation of a

short length leading edge bubble (Xr= 0.03) doesn’t reflect any influence on the Lift and

Drag characteristics of the headsail.

Fig 28) Reattachment length Vs Camber%

4.3.3 EFFECT OF DIFFERENT GRIDS ON REATTACHMENT LENGTH (XR)

Referring figure (28), it can be seen that results depend on the number of cells used in

different grids. The distribution around all the cambered sails seems aligned as far as

different grids are taken into consideration. However, there is an increase of 28% in Xr for

23% Camber, for Medium and Fine grids. As for the Medium and Fine grids the graph

contours match, we tried to find the difference using these grids as our reference grids.

This explains the sensitivity of the grid generation which signifies that as the number of

cell increases, an improved result can be obtained. This significant change for 23%

Camber is believed to be the result of the abrupt curvature on it.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

30 26 23 20 16 13

Xr

as %

of

cho

rd le

ngt

h

Camber %

Headsail Xr Vs Camber %

Fine

medium

coarse

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As the initial grid was generated and named as Medium grid, the same grid was used for

all the cambers. For generating Fine and Coarse grids the same grid was used but only the

number of cells were increased and decreased as explained in 3.1. At 23% camber, flow

around the maximum camber could be very turbulent and it is this reason why we faced a

difference in results between different grids. The shape of the cell near the camber was

rectangular and the cell size was big for the Coarse grid because of which the turbulent

flow might not have been measured appropriately. In Medium and Fine grids, more

number of cells near the camber would have eliminated this effect by calculating the

turbulent flow in each small cell, an integration of which, gave an accurate answer.

4.3.4 EFFECT ON CAMBER ON XS

The trailing edge separation length (Xs) follows an opposite pattern than Xr. As the

camber increases or leading edge bubble decreases, the trailing edge separation

increases. For small cambers, the flow reattaches at the leading edge and remains

attached followed by a late separation downstream. Whereas for high cambers, due to the

momentum energy, low viscosity of air and no reattachment, the flow tries to maintain its

direction and therefore separates quite earlier from the sail boundary than expected.

Thus, for the highest camber (30%) flow separates earliest around the mid-chord length

(fig 29).

Fig 29) Separation length Vs Camber%

0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

30 26 23 20 16 13

Xs

as %

of

cho

rd le

ngt

h

Camber %

Headsail Xs Vs Camber %

Fine

Medium

Coarse

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4.3.5 EFFECT OF DIFFERENT GRIDS ON TRAILING EDGE SEPARATION LENGTH

(XS)

Referring figure (29), we understand the effect of grids on the trailing edge separation

characteristics. Altogether there is an exponential increase in the separation length as

camber is increasing, however, a small divergence was found in the separation lengths for

high camber profiles of headsail. For 26% camber, an increase of 3.6% of separation

length (Xs) can be seen for Fine grid when compared with the other two grids. It is

believed that more number of cells at the trailing edge for the Fine grid helped the solver

to calculate the précised flow direction. This must have not happened in other two grids

where big and less numbers of cells were present. As shown in figure (29), the separation

occurs more earlier for the Fine grid than it occurs for other two grids. For very high

camber profiles like 26% and 30%, in real scenario, the separation should occur earlier

because of the abrupt change in curvature. However, deciding whether Fine grid provided

the right results than the Medium or the Coarse grid, depends on the investigation and

verification with the wind tunnel experiments which has not been done for these sail

profiles. Therefore, commenting on the nature of results, as far as grids are concerned, is

erroneous.

4.4 EFFECT OF CAMBER ON PRESSURE COEFFICIENT (CP)

To understand the effect of camber on the Pressure Coefficient a graph was plotted

between Cp and X/c of headsail as shown in figure (30, 31). Medium mesh has been taken

as a reference mesh to explain the effect of Cambers on Cp. The results discussed for the

Xr and Xs above matches the changes in Cp for different cambers. For Fine and Coarse

grids graphs are represented in the figure (32).

For low cambers (fig 30), there is a suction peak at the leading edge of the headsail. This

defines the formation of the leading edge bubble, whose length reduces as the camber is

increased. Same can be seen from the graph, as the camber increases the suction peak

reduces or the bubble length reduces and thus for high cambers the bubble totally

vanishes. Xr for the 26% camber was zero, can be explained referring figure (31) in which

it can be seen that there is no suction peak at the leading edge. The second suction peak is

observed where curvature of the sail plays the role. As the camber increases the second

suction peak also increases (figure 30). On the contrary, there is no second suction peak

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Chapter 4: Results

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observed for highest camber of 26% and 30%. This happens due to the curvature of these

high cambers, which makes the separation to occur earlier than expected because of

which no second suction peak forms. For the high cambers, the leeward side is at a high

pressure region compared to the pressure for the low cambers which increases the

possibility for a sail to go in a stall condition.

Looking at the windward side of the headsails, there is a sudden small increase in

pressure (which maintains the sail shape) and altogether a constant pressure till 60% of

the chord length of the sail. After 60% of the length, a gradual and small decrease in

pressure occurs, going towards the leeward side of the sail to maintain a balance. We can

see from the figure (31) that as the camber% increases there is a small reduction in the

initial pressure and also at 20% of the chord length, on the windward side. For the highest

cambers (26% and 30%), the pressure has reduced to its maximum which resulted in no

further increase in pressure at the windward side of the 30% camber.

Fig 30) Headsail Pressure distribution for varying camber

-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1 1.2

Cp

X/c

Cp for Varying Cambers (Headsail - Medium Mesh)

13%Camber

16%Camber

20%Camber

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Chapter 4: Results

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Fig 31) Headsail Pressure distribution for varying camber

Fig 32) Headsail pressure distribution for varying cambers (1a) and (1b) Coarse grid; (2a) and (2b)

Fine Grid.

-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1 1.2

Cp

X/c

Cp for Varying Cambers (Headsail - Medium Mesh)

23%Camber

26%Camber

30%Camber

-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1 1.2

X/c

Cp

Cp for Varying Cambers (Headsail - Coarse Mesh)

-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1 1.2

X/c

Cp

Cp for Varying Cambers (Headsail - Coarse Mesh)

-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1 1.2

Cp

X/c

Cp for Varying Cambers (Headsail - Fine Mesh)

-5

-4

-3

-2

-1

0

1

0 0.2 0.4 0.6 0.8 1 1.2

X/c

Cp

Cp for Varying Cambers (Headsail - Fine Mesh)

(1a) (1b)

(2a) (2b)

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Chapter 4: Results

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4.5 EFFECT OF CAMBER ON DRAG (CD) AND LIFT COEFFICIENTS (CL)

As the purpose of this thesis is to study the interaction between headsail and mainsail,

another important factor comes into picture which is the effect of camber on the Lift and

Drag forces. As we already know that minimum drag and maximum lift is required to

achieve the high level of performance standards for a yacht sail, the author has tried to

identify the best camber profile which would provide these parameters. Figure (33, 34

and 35) gives a detailed information regarding change in lift and drag coefficients (thus

change in lift and drag forces) with the change in camber%.

4.5.1 LIFT COEFFICIENT (CL)

It can be seen from figure (33), that maximum lift is given by the camber with an X/Chord

ratio of 20%. Increasing camber% after 20%, doesn’t not provide any increase in lift,

however, 23% camber generates a little high lift than 16%. This doesn’t mean that 16%

camber is less effective in performance than 23% camber but one should take drag

coefficient into consideration as well, while measuring the performance. As we can see the

more drag is being produced by the 23% camber as compared to 16% camber (fig. 34,

35), and as drag act as a resistance to the movement of the sail, the 16% camber profile

should provide the better performance characteristics. Therefore, increasing any

camber% further doesn’t provide any increase in lift force.

A certain pattern of increase and decrease in the lift coefficient value with the camber% is

noticeable. While lowest and highest camber profiles fail to provide the best combination

of lift and drag, the lift intends to increase and then decrease with the increase in camber.

A 3% of increase in lift can be seen from 13% to 16% of the camber increase, whereas,

from 16% to 20% this increase in lift is little. This happened because with the increase in

camber the suction peak pressure curvature became more high, which delayed the

separation due to the boundary layer effect. However, a slight decrease in lift was noticed

from 20% to 23% of camber followed by a sudden decrease, as camber% increased. This

was an effect of early separation which wasn’t able to provide long interaction time over

the headsail. Also, figure (35) gives the idea of the sail which gives maximum lift and

minimum allowable drag. It can be seen that after 23% camber, lift decreases and drag

increases.

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Chapter 4: Results

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4.5.2 DRAG COEFFICIENT (CD)

An exponential increase can be seen in the Cd for increase in camber% in figure (34, 35).

Maximum drag is for the highest camber and the ratio of the maximum lift to minimum

drag for a camber profile is highest between 16% to 23% camber. The ratio of the

maximum lift to the minimum profile drag tends to increase with the increase in camber

till 23%, but decreases significantly if camber is further increased (fig. 35). Low camber%

of the headsail has less value of drag coefficients; this is because for low cambers (below

23%) the greater portion of the camber is dedicated to the laminar flow. This reduces the

separation length over the sail which in turn produces less drag. However, for large

cambers (above 23%) the turbulent flow occurs quite early than for low cambers which

results in more drag and ultimately less lift. Figure (34) also signifies that even if a flat sail

was used instead of a cambered sail drag wouldn’t have been zero as there is always some

resistance to motion, drag always increases with the increase in camber. Therefore to

reduce drag, one needs to identify the airflow separation and try to reduce the low

pressure wake that gets created by that separation. This can be done using cambered

profiles but again simply increasing camber doesn’t always mean increase in lift but also

an increase in drag, thus, a good combination of both should be chosen which in this case,

is a 20% camber headsail.

Fig 33) Cl Vs Camber% for all grids

30 26 23 20 16 13

medium 1.6243229 1.6928683 1.75195 1.7538806 1.7455721 1.7067898

fine 1.6184205 1.6894207 1.7494963 1.7568469 1.7452865 1.7009468

coarse 1.6338303 1.696023 1.7515448 1.752029 1.7444661 1.7030694

1.6

1.62

1.64

1.66

1.68

1.7

1.72

1.74

1.76

Cl

Cl Vs Camber%

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Chapter 4: Results

110361527 Page 41

Fig 34) Cd Vs Camber% for all grids

Fig 35) Cl Vs Cd for all grids

30 26 23 20 16 13

medium 0.181521 0.13096857 0.082468565 0.062696619 0.046114466 0.046301234

fine 0.19440913 0.13714268 0.088292307 0.060947919 0.047030005 0.045954602

coarse 0.17304823 0.13178692 0.086307521 0.066402395 0.04885772 0.047998763

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Cd

Cd Vs Camber%

1.6

1.62

1.64

1.66

1.68

1.7

1.72

1.74

1.76

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Cl

Cd

Cl Vs Cd

Medium

Fine

Coarse

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Chapter 4: Results

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4.6 EFFECT OF GRIDS ON CL AND CD

Figure (36, 37) shows graphs which demonstrate the effect of different types of grids on

the results. As previously mentioned for Xr and Xs, more or less number of elements in

different grids does cause significant changes in the results. However, there is not much

difference between the values of Cl and Cd for different grids (figure 38), but a certain

pattern of values can be seen. Where lift coefficient is maximum for the 20% camber, drag

coefficient is maximum for the maximum camber which is 30%

Figure (36, 37) shows the ratio of Cl and Cd for different grids, where fine grid was taken

as a reference denominator whose numerator was coarse and medium grids. As seen in

the figure, most of the Cl and Cd values for the ratio between coarse and fine grids are

more than the ratio between medium and fine grids. This is simply because the values of

Cl obtained from the coarse grid are less as compared to medium (figure 38), and the

most for fine grid. The question comes why the values differ with the number of

elements?

As fine mesh has more number of elements in it, though it increases the simulation time

but it provides us a more detailed result. However, coarse and medium grids have

correctly established the main features of the flow around the sail and thus have provided

approximately same values of lift and drag. It’s been seen in the simulation contours that

fine grid shows a sharper image with a greater resolution, while the medium and coarse

grids shows unfocused results. This happens because a grid with less number of elements

deals with the averaged properties over a large volume space which subsequently blurs

the results. A single cell from the coarse model in real represents 2.5 cells from the fine

model and 1.56 cells from the medium model. Thus this single cell has to represent

average lift and drag coefficients across all 2.5 fine cells and 1.56 coarse cells. This

procedure of averaging makes the solution more accurate which differs from the coarse

and medium grids. An anomaly can be seen for higher camber % where medium grid

gives more value of Cl than coarse grid does. This can be due to various factors like

increase in camber, early separation, short leading edge bubble etc. which does affect the

performance of the simulation and can provide ambiguous results. Same pattern can be

seen for Coefficient of drag in figure (37) with a constant difference between the coarse

and medium Cd values with reference to fine grid. There is a sinusoidal pattern of Cd ratio

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Chapter 4: Results

110361527 Page 43

values which shows the dependence of results on the mesh type, as previously in figure

(34) we saw that exponential increase in drag coefficient with the camber which isn’t

same while comparing different grids. Where in the table in figure (38) maximum Cd is for

the maximum camber% (30%), in graph it can be seen that the maximum camber ratio is

coming for 20% camber. Also, this maximum value is near the value of 1, which signifies

that at this camber the value of Cd matches for medium and fine grid. However, all the

values are under a range of 0.9 to 1.1 which states the overall difference of 20% error

between the values obtained from the medium/ fine and coarse/ fine grid ratios.

Fig 36) Cl ratio Vs Camber%

Fig 37) Cd ratio Vs Camber%

0.996

0.998

1

1.002

1.004

1.006

1.008

1.01

1.012

13 16 20 23 26 30

Rat

io o

f C

l

Camber%

Cl ratio Vs Camber%

CL coarse/ cl fine

cl medium/cl fine

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

30 26 23 20 16 13

Rat

io o

f C

d

Camber%

Cd ratio Vs Camber%

Cd Coarse/ Cd Fine

Cd Medium/ Cd Fine

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Chapter 4: Results

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Fig 38) Value of Cl and Cd for corresponding camber% and grid types

4.7 UNCERTAINTY

4.7.1 OVERVIEW

An obtained solution, which may have a potential deficiency in any part of the modeling

or simulation process, may be a wrong solution and can be called as an uncertain solution.

Main aim of using CFD analysis, for the presented model, is to find a single solution which

identifies the maximum lift obtained using a certain camber profile out of a bunch of

headsail profiles. However, obtaining a deterministic solution for a single grid is

impossible due to many factors. First, the model which has been used might contain

errors and uncertainties which compromise the accuracy of the results. Second, all

parameters used in the simulation process might have a certain level of accuracy, which

should be taken into consideration. Thirdly, human error may occur which reduces the

reliability of the system as a whole.

Roache et al initiated the work by proposing uncertainty due to grid (Roache et al, 1998)

as a part of Verification and Validation, which was further discussed by Fred et al (2005).

As it’s a vast topic to be discussed and performed, the author has tried to narrow it down

to the most possible extent and has tried to identify the key points relevant to this thesis.

To do so, a private discussion was done with the supervisor and a certain compact

method of finding out the uncertainties was discussed.

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Chapter 4: Results

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4.7.2 METHOD

Author has tried to find out the uncertainty based on different grids rather than based on

the accuracy of the simulations i.e. Fluent, CFD etc. For finding uncertainties in the values

of Cl and Cd, graphs between Cl Vs 1/number of cells were plotted for every camber. Then

the error was found out based on the location of the points and based on the error, the

deflection was taken. The deflection is multiplied with the certain factor which provides

the uncertainty.

As shown in the figures (39, 40, and 41), where there is no relationship between the

points (fig. 39) the maximum deflection is taken with a factor of 3.0. However, if some

relationship if found between the points the error is checked and if E2 > E1, then again

factor of 3.0 is used (fig. 40). However, if E1 > E2, then the deflection is taken as shown in

fig. (41), and a factor of 1.5 is used to calculate the deflection.

Uncertainty is calculated as:

Uncertainty (U) = Factor X Deflection (where factor can be 3.0 or 1.5 depending on the

type of graph obtained)

Also, this has to be kept in mind that while plotting the uncertainties for Cl and Cd, a fine

mesh values should be used. This is because the above mentioned method has been

described for the fine mesh, thus the factor depends on the type of mesh we use to define

uncertainties. Using a fine mesh doesn’t mean that the information regarding the other

meshes has not been taken into consideration as while calculating uncertainties, the

author has used the values of Cl and Cd for all the meshes.

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Chapter 4: Results

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Fig 39) Uncertainty Graph – Using Factor of 3.0

Fig 40) Uncertainty Graph – Using Factor of 3.0 when E2 > E1

Fig 41) Uncertainty Graph – Using Factor of 1.5 when E1 > E2

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Chapter 4: Results

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4.7.3 CL AND CD UNCERTAINTIES

Overall, prediction of lift coefficient Cl seems quite accurate as compared to drag

coefficient Cd. As can be seen in figure (42), the minimum uncertainty of Cl is for the 16%

camber while the maximum is for 26%, however, all uncertainties beyond 23% and below

13% camber seems to be quite significant. This implies that the value of uncertainty is

less for the cambers which is the optimum camber or the cambers behaving equivalent to

the optimum camber. Thus, a comment can be made that a too low camber and a too high

camber, gives more probability of error to sustain in a solution, thus becoming more

uncertain to be accurate. As we know that the Cl of 20% is the highest it holds the best

camber profile to be suited for a yacht sail, but, its uncertainty value (1.45%) is

approximately 4 times bigger than the value for 16% camber (0.33%).

While calculating the best camber suited for the interaction, we now need to consider the

uncertainties values and the Cl values and try to find out the best combination of both. Cl

value for 23% camber is the second highest with an uncertainty of 0.74%, but 16%

camber, of which the third highest value of Cl, can be taken as a best solution as accuracy

of this result is 99.67% certain.

Fig 42) Uncertainty of Cl

0.000

0.500

1.000

1.500

2.000

2.500

3.000

3.500

4.000

13 16 20 23 26 30

Fin

e M

esh

Cl

Camber%

Uncertainty of Cl Vs Camber%

Cl Values

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Chapter 4: Results

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Considering Figure (43) a very precise observation can be made. Figure shows the

increasing values of uncertainties as the camber increases and after a certain point is

becomes as high as 6.4% for the maximum camber of 30%. The minimum uncertain value

is obtained for 20% camber with 0.29% uncertainty. For the first 3 camber the

uncertainties are almost negligible which again signifies the accurate results obtained for

or near the optimum camber profiles.

Large uncertainty values for bigger cambers can be explained by understand the flow

around the big camber profiles. We know that for big cambers, the separation point move

upstream and keep moving upstream as the camber increases which make the turbulent

boundary to shift upstream as well. Due to this early trailing edge separation flow

remains disturbed for the more length of the sail, and this turbulent flow when calculated

using a solver, may not be as accurate as the less turbulent flow which was calculated for

the lower cambers. As there is not much difference between the drag values from 13% to

20% cambers, we opt for the Cd of 20% as its uncertainty is only 0.29%. Also, a minimum

drag doesn’t always mean a minimum drag; some amount of drag is always required and

is present in the real scenario. Thus, the Cd value of 0.061 for 20% camber seems

reasonable.

Fig 43) Uncertainty of Cd

-1.000

-0.500

0.000

0.500

1.000

1.500

2.000

2.500

13 16 20 23 26 30

Fin

e M

esh

Cd

Camber%

Uncertainty of Cd Vs Camber%

Cd Values

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Chapter 5: Conclusion

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CHAPTER 5 CONCLUSION

5.1 SUMMARY

In the present report the computational results for 2D headsail/mainsail geometry were

presented. Different values for coefficient of lift and drag was obtained from different

cambered profile of the sail interaction. The flow around the sail was understood better

with the help of reattachment length and trailing edge separation length on the sail.

Different flow regions were understood and discussed and emphasis was given on the

turbulent region near the separation end which can cause change in results for different

grids.

There was no comparison done between any experimental data and the computational

data as there was no experiment done on the current report. Therefore, author tried to

find out all the possible and relevant causes and explanation for the results provided in

the paper. A good combination of lift and drag was found out. If no uncertainty is

considered then the best combination is provided by the 20% camber, however, we saw

after considering some error in the simulation process and for the coarser grids, the best

combination suited was for 16% camber profile. It was discussed that 23% camber gives

the allowable drag, but as it has to be one camber we finally chose 16% camber, as

difference between the drag values is not large in the three cases (16%, 20% and 23%).

A good agreement between results found out using different grids was discussed, and the

author tried to explain how the results get affected if a coarser grid is used rather than a

finer grid. In this report, emphasis was given over the pressure distributions around the

sail, as good combination of pressure and velocity defines the forces like lift and drag

forces. Also, a simulation error was discussed in the report which enhanced the

knowledge regarding the software and discretization methods, it is believed that this

error affects the whole system.

As the author tried to do a brief validation and verification of the results, it is his belief

that the results and the uncertainties obtained may have some errors. Therefore, a

detailed study regarding validation and verification should be done to find out the true

values so that a better understanding and knowledge can be gained.

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Chapter 5: Conclusion

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5.2 RECOMMENDATIONS

The current author would like to make the reader aware of possible recommendations for

future pieces of research that could be linked with the current piece of research to help in

validation and to understand the performance of sails.

More number of simulations can be done by using different mainsail cambers and

using one headsail camber which can provide a better understanding of the sail

interaction.

Camber percentage increase in camber should be reduced so as to better

understand the effect of increasing camber and the optimum region for the

cambers.

Sail with large angle of incidence can be used to understand the effect of cambers.

An experiment should be done in the wind tunnel test only for the optimum

cambers so as to differentiate better between the computational and software

results.

A 3D simulation can be done to understand more about the software and

interaction of sails. Also, 3D and 2D results can be compared and analysed.

More study can be done by changing sail shape and angle which may change the

angle of attack of the sail and thus cause change in results.

As there was no effect of mast in the present work, it can be added to see the

change in results and which will provide a better understanding in the subject.

Mesh refinement can be performed on the sails which may affect the results.

A hull form for the sails can be tested so as to get the exact idea about the

performance of the yacht as a whole.

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Appendix

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use in Sail flow Analysis. School of Engineering Report No. 603

Collie. S, Gerritsen. M and Jackson ., 2008. Performance of two equation turbulence

models for Flat Plate flows with Leading Edge Bubbles, Journal Fluid Engineering

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Crompton M.J and Barrett R.V., 2000. Investigation of the separation bubble

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Appendix

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P. Lopes, C. Ciortan & C. Guedes Soares ., 2008. Computational study on the

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