Numerical and Experimental Studies of Sail Aerodynamics

Departamento de Arquitectura y Construcci´onNavales Escuela T´ecnicaSuperior de Ingenieros Navales Universidad Polit´ecnicade Madrid

PhD Thesis

Numerical and Experimental Studies of Sail Aerodynamics

By

Ms. Patricia Izaguirre Alza M.Sc. in Naval Architecture

Supervisor: Prof. Luis P´erezRojas Ph.D. in Naval Architecture Professor in Ship Theory

2012 ii Abstract

The purpose of this investigation was the determination of the aerodynamic performance of sails and gain knowledge of the phenomena involved in order to improve the aerody- namic characteristics. In this research, the airflow around different sails in four scenarios was studied.

The method to analyze these scenarios was the combination of numerical simulations and experimental tests by taking advantage of the best of each tool. Two different Com- putational Fluid Dynamic codes were utilized: the ANSYS-CFX and the CD-Adapco’s STAR-CCM+. The experimental tests were conducted in the Atmospheric Boundary Layer Wind Tunnel at the Universidad de Granada (Spain), the Twisted Flow Wind Tunnel at the University of Auckland (New Zealand) and the A9 Wind Tunnel at the Universidad Polit´ecnicade Madrid (Spain).

Through this research, it was found the three-dimensional effect of the mast on the aerodynamic performance of an IMS Class boat. The pressure distribution on a Transpac 52 Class mainsail was also determined. Moreover, the aerodynamic perfor- mance of the 43ft and 60ft Dhow Classes was obtained. Finally, a feasibility study was conducted to use a structural wing in combination with conventional propulsions systems.

The main conclusion was that this research clarified gaps on the knowledge of the aerodynamic performance of sails. Moreover, since commercial codes were not specifically designed to study sails, a procedure was developed. On the other hand, innovative experimental techniques were used and applied to model-scale sails. The achievements of this thesis are promising and some of the results are already in use by the industry on a daily basis.

iii iv

Resumen

El prop´osito de este estudio era determinar el comportamiento aerodin´amico de unas velas y mejorar el conocimiento de los fen´omenosque suceden para optimizar las caracter´ısticasaerodin´amicasde dichas velas. En esta investigaci´onse estudi´oel flujo de aire alrededor de diferentes velas en cuatro escenarios.

El m´etodo para analizar estos escenarios fue la combinaci´on de simulaciones num´ericasy ensayos experimentales mediante el aprovechamiento de las ventajas de cada herramienta. Se utilizaron dos c´odigosde din´amica de fluidos computacional: el ANSYS-CFX y el STAR-CCM+ de la empresa CD-Adapco. Los ensayos experimentales se desarrollaron en el t´unelde viento de capa l´ımite de la Universidad de Granada (Espa˜na),el t´unelde viento de la Universidad de Auckland (Nueva Zelanda) y en el t´unelA9 de la Universidad Polit´ecnicade Madrid (Espa˜na).

Mediante esta investigaci´on,se determin´oel efecto tridimensional del m´astilen un velero de la clase IMS. Tambi´ense describi´ola distribuci´onde presiones sobre una mayor de un Transpac 52. Adem´as,se obtuvo el comportamiento aerodin´amicode las clases 43ft y 60ft de los veleros Dhows. Finalmente, se llev´oa cabo un estudio de viabilidad de la utilizaci´on de un ala estructural en combinaci´on con sistemas de propulsi´on convencionales.

La conclusi´onprincipal de esta investigaci´onfue la capacidad de explicar ciertas lagunas en el conocimiento del comportamiento aerodin´amicode las velas en diferentes escenarios. Adem´as,dado que los c´odigoscomerciales no est´anespec´ıficamente dise˜nados para el estudio de velas, se desarroll´oun procedimiento a tal efecto. Por otro lado, se han utilizado innovadoras t´ecnicasexperimentales y se han aplicado a modelos de velas a escala. Los logros de esta investigaci´onson prometedores y algunos de los resultados obtenidos ya est´ansiendo utilizados por la industr´ıaen su d´ıaa d´ıa. Acknowledgments

I’m very grateful to the following people and institutions for their assistance during this research:

• Professor Luis P´erezRojas, my supervisor and boss. I will never be able to thank him enough for his support, encouragement and guidance. ¡Gracias jefe! • The members of the CEHINAV group (Juan, Paco, Rian, Ricardo A., Ricardo Z., Jorge, . . . ) . They have not only helped on the research but they have looked after me during this process. I need to highlight the contribution of Alberto Torres and Adriana Oliva, who have helped me obtaining some of the results of this research. I’m particularly grateful to Jos´eLuis Cerc´osfor his invaluable assistance in my computers. • Professor Richard G.J. Flay, David J. Le Pelley and the Yacht Research Unit of the University of Auckland (New Zealand). They gave me a warm welcome to their research group. They helped me grow as a person and as a researcher. Furthermore, they gave me the opportunity to discover New Zealand, one of the most beautiful places that I have ever visited. • Shaun Connolly, David Parr and Calibre Sails Ltd. They provided the dhow sails for free and guided me during the investigation. Thanks Shaun, for letting me meet your family and share with them the “kiwi” lifestyle. • Volker H. Rosenkranz and the EU-CargoXpress project. The collaboration with Volker and the project have allowed me not only obtaining very interesting results but traveling and meeting inspiring people. • Jos´eMar´ıaTerr´es,Jessika Garc´ıaand the Wind Engineering group of the Centro Andaluz de Medio Ambiente (Spain). I have to thank them for accepting me and opening the doors of their facilities for my investigation. They helped, support and guided me during the research.

• Sebasti´anFranchini, Javier P´erezand the Instituto Universitario de Microgravedad “Ignacio Da Riva” at the Universidad Polit´ecnicade Madrid (Spain). I’m grateful for their work on the experimental tests and their valuable suggestions.

v vi

• Professor Yutaka Masuyama. He provided me worthwhile information and his per- mission to use his experimental results.

• I have to highlight that this research has been partially funded by a PhD scholarship of the Universidad Polit´ecnicade Madrid.

• Quiero agradecer a mi aita, a mi ama, a Gloria, a toda mi familia, por el amor, el apoyo incondicional, por aguantarme, por mantenerme, por todo, eskerrik asko! Y c´omono, a Israel, mi compa˜nero, el que ha soportado cada l´agrima, cada ataque de ansiedad, cada momento de histeria y siempre ha estado a mi lado. Esta tesis ha sido posible gracias a todos vosotros. Contents

1 INTRODUCTION 1 1.1 General problem ...... 2 1.2 Motivation ...... 3 1.3 Scope ...... 4 1.4 Contributions ...... 4 1.5 Outline of the thesis ...... 5

2 SAILING CONCEPTS 7 2.1 Nomenclature ...... 7 2.2 Balance of the aero/hydrodynamic forces ...... 9 2.3 Aerodynamic Force ...... 10 2.4 Sail Interaction ...... 15 2.5 Apparent Wind ...... 16 2.6 Conclusion ...... 18

3 LITERATURE REVIEW 21 3.1 Performance Prediction ...... 21 3.1.1 Wind Tunnel Tests ...... 22 3.1.2 Full-scale Tests ...... 25 3.1.3 Numerical Simulations ...... 25 3.2 Aeroelastic Analysis ...... 33 3.2.1 Fluid Structure Interaction (FSI) ...... 34 3.3 Optimization approaches ...... 35

4 WIND TUNNEL TESTS 39 4.1 Nomenclature ...... 39 4.2 History ...... 40 4.3 Types ...... 42 4.3.1 Based on the airflow speed ...... 42 4.3.2 Based on the return circuit ...... 42 4.3.3 Based on the test section ...... 43 4.3.4 Special-purpose tunnels ...... 43 4.4 Operation and design ...... 45 4.4.1 Operation ...... 46

vii viii CONTENTS

4.4.2 Design ...... 48 4.5 Measurements and Instrumentation ...... 50

5 COMPUTATIONAL FLUID DYNAMIC SIMULATIONS 55 5.1 Nomenclature ...... 59 5.2 Mathematical Model ...... 62 5.2.1 General conservation law ...... 62 5.2.2 Levels of approximation ...... 65 5.2.3 Boundary Conditions ...... 66 5.3 Space Discretization ...... 67 5.3.1 Types ...... 68 5.3.2 STAR-CCM+ Mesh ...... 69 5.3.3 Mesh Validity and Quality ...... 70 5.4 Discretization of Equations ...... 71 5.4.1 Continuity Equation ...... 72 5.4.2 Momentum Equation ...... 75 5.4.3 RANS Turbulence Models ...... 79 5.4.4 Wall Treatment ...... 82 5.4.5 Gradient Computation ...... 84 5.4.6 SIMPLE Solver Algorithm ...... 87 5.5 Solution: Time Integration Method ...... 88 5.6 Solution: Algebraic System of Equations ...... 89

6 INFLUENCE OF THE MAST 93 6.1 Introduction ...... 93 6.2 Nomenclature ...... 95 6.3 Measurements of full-scale performance and sail shape ...... 96 6.4 Tests with ANSYS-CFX ...... 99 6.4.1 Domain and mesh ...... 100 6.4.2 Boundary conditions ...... 101 6.4.3 Numerical scheme ...... 102 6.4.4 Results and comparison ...... 102 6.5 Tests with STAR-CCM+ ...... 110 6.5.1 Domain and mesh ...... 111 6.5.2 Boundary conditions ...... 112 6.5.3 Numerical scheme ...... 113 6.5.4 Results and comparison ...... 113 6.6 Conclusions ...... 122

7 PRESSURE DISTRIBUTION ON A TP52 MAINSAIL 123 7.1 Introduction ...... 123 7.2 Nomenclature ...... 125 7.3 Transpac 52 Class ...... 125 7.3.1 Brief History ...... 127 CONTENTS ix

7.4 Experimental tests ...... 128 7.4.1 Wind tunnel description ...... 128 7.4.2 The model ...... 129 7.4.3 Experimental set-up and test description ...... 132 7.4.4 Results ...... 133 7.5 Numerical simulations ...... 136 7.5.1 Domain and mesh ...... 136 7.5.2 Boundary conditions ...... 137 7.5.3 Numerical scheme ...... 137 7.5.4 Comparison between simulations and experiments ...... 138 7.6 Conclusions ...... 141

8 AERODYNAMICS OF SAILING DHOWS 143 8.1 Introduction ...... 143 8.2 Nomenclature ...... 145 8.3 The Dhow ...... 146 8.3.1 History of the Dhow ...... 146 8.3.2 The Dhow nowadays ...... 147 8.4 Experimental Tests ...... 150 8.4.1 Wind tunnel description ...... 150 8.4.2 The model ...... 153 8.4.3 Experimental set-up and test description ...... 155 8.4.4 Results ...... 158 8.4.4.1 43ft Dhow Model ...... 158 8.4.4.2 60ft Dhow Model ...... 165 8.5 Numerical simulations ...... 169 8.5.1 Geometry ...... 169 8.5.2 Domain and mesh ...... 170 8.5.3 Boundary conditions ...... 171 8.5.4 Numerical scheme ...... 172 8.5.5 Results ...... 172 8.6 Conclusions ...... 175

9 EU-CARGOXPRESS PROJECT 177 9.1 Introduction ...... 177 9.2 Nomenclature ...... 178 9.3 Existing technologies ...... 180 9.4 The project ...... 184 9.4.1 Description ...... 184 9.4.2 Conclusions of the EU-CargoXpress Project ...... 186 9.4.3 Contribution ...... 187 9.5 Numerical simulations ...... 187 9.5.1 Geometries ...... 187 9.5.2 Domain and mesh ...... 189 x CONTENTS

9.5.3 Numerical scheme and boundary conditions ...... 190 9.5.4 Results ...... 190 9.6 Experimental Tests ...... 192 9.6.1 Wind tunnel description ...... 193 9.6.2 The model ...... 194 9.6.3 Experimental set-up and test description ...... 195 9.6.4 Results ...... 197 9.7 Feasibility study ...... 200 9.7.1 Routes ...... 200 9.7.2 Wind characteristics ...... 200 9.7.3 Energy saving ...... 202 9.8 Conclusions ...... 205

10 CONCLUSIONS 207

A Mast effect data with STAR-CCM+ 211

B Second set of tests: results 213

C Yard Stiffness Scale 215

D 43ft Dhow Model Tests 217

E 60ft Dhow Model Tests 223

F 43ft Dhow Model Results 225

G 60ft Dhow Model Results 241

H Energy Scenarios 247

I Wind tunnel results 249

J Numerical results 253 List of Figures

1.1 Volvo Ocean Race 2008-2009. Start of the Leg 1 in Alicante (Spain) . . . . 1

2.1 Force balance ...... 9 2.2 Points of sail ...... 10 2.3 Flow around a sail ...... 11 2.4 Components of the total aerodynamic force ...... 12 2.5 Flow around a mast/sail combination ...... 14 2.6 Flow around a mainsail/jib combination ...... 16 2.7 Planetary boundary layer and the twist ...... 17

4.1 Whirling arm ...... 41 4.2 Close-section, open-circuit tunnel ...... 48 4.3 Open-section, close circuit tunnel ...... 49 4.4 Pitot tube ...... 51

5.1 Post process with the STAR-CCM+ ...... 57 5.2 Polyhedral mesh with prism layers ...... 69 5.3 Trimmer mesh ...... 70

6.1 Sail dynamometer boat Fujin ...... 94 6.2 ID96092335 case mesh ...... 101 6.3 Pressure distribution (ID9807172F) ...... 105 6.4 Pressure distribution (ID9807172B) ...... 106 6.5 Pressure distribution (ID96092335) ...... 106 6.6 Plane at half of the luff of mainsail (ID9807172B) ...... 107 6.7 Two vortices downstream (ID9807172B) ...... 108 6.8 ID9807172F case mesh with a mast ...... 109 6.9 Increase of the number elements vs. elapsed time per iteration (computer 1)110 6.10 Domain of the ID9807172B case with mast ...... 112 6.11 Force coefficients ...... 114 6.12 Center of effort ...... 115 6.13 Pressure coefficient distribution (ID9807172F with mast) ...... 116 6.14 Pressure coefficient distribution (ID9807172F without mast) ...... 117 6.15 Normalized speed and streamlines (ID9807172F) ...... 117 6.16 Normalized speed (ID96092335) ...... 118

xi xii LIST OF FIGURES

6.17 Pressure coefficient (ID9807172F with and without mast) ...... 118 6.18 Pressure coefficient (ID96092335 with and without mast) ...... 119 6.19 Generation of vortices (ID9807172F) ...... 120 6.20 Maximum vorticity (ID9807172F) ...... 120 6.21 Maximum vorticity downstream, (ID9807172F, identical downstream mesh) 121

7.1 TP52 Class yacht Balearia (2005) ...... 126 7.2 Atmospheric boundary layer wind tunnel at CEAMA ...... 128 7.3 The model ...... 129 7.4 Sections and sensors ...... 131 7.5 The model in the wind tunnel ...... 133 7.6 Pressure coefficients, first set of tests ...... 135 7.7 Midsection plane mesh ...... 137 7.8 Computed pressure coefficient distribution (windward) ...... 138 7.9 Wind tunnel data vs CFD results ...... 140

8.1 A 43ft dhow racing ...... 144 8.2 A 60ft dhow sailing in Dubai ...... 148 8.3 The Twisted Flow Wind Tunnel at the University of Auckland ...... 150 8.4 Plan of the wind tunnel ...... 152 8.5 The model fitted with the 43ft rigging and winches ...... 153 8.6 43ft dhow model during a test with stiffeners ...... 157 8.7 43ft model, CX ...... 159 8.8 43ft model, CMX ...... 160 8.9 43ft model, CX/CMX ...... 161 8.10 43ft model, CX vs HA ...... 162 8.11 43ft model, CMX vs HA ...... 162 8.12 43ft model, Optimum Trimming Test, CX and CMX (AWA=60◦) . . . . . 163 8.13 43ft model, Optimum Trimming Test, CX/CMX (AWA=60◦) ...... 163 8.14 43ft model, Bending Test, CX and CMX ...... 164 8.15 43ft model, Bending Test, CX/CMX ...... 165 8.16 43ft model, Yard Stiffness Test, CX/CMX ...... 166 8.17 60ft model, Basic Test, CX, CMX and CX/CMX ...... 167 8.18 60ft model, Basic Test with mizzen, CX and CMX ...... 168 8.19 60ft model, Optimum Trimming Test, CX, CMX and CX/CMX ...... 168 8.20 Flying shapes: experimental, original and customized ...... 171 8.21 Pressure coefficient distribution ...... 173 8.22 Pressure coefficient ...... 174 8.23 Normalized speed at the midsection ...... 174 8.24 Vortices downstream ...... 175

9.1 Solar Albatros ...... 181 9.2 Buckau ...... 182 9.3 Alcyone ...... 183 LIST OF FIGURES xiii

9.4 Beluga-SkySails ...... 184 9.5 EU-CargoXpress Project ...... 185 9.6 First (red), second (blue) and third geometry (green) ...... 188 9.7 The third geometry in the numerical domain ...... 189 9.8 Force coefficients ...... 191 9.9 Saved power at 15knots of vessel speed (second and third geometries) . . . 192 9.10 A9 IDR/UPM wind tunnel ...... 193 9.11 Pressure model ...... 194 9.12 Sensor distribution, leeward(left) and windward(right) (Dimensioning in mm) ...... 195 9.13 Models of the third geometry ...... 196 9.14 Force coefficients ...... 197 9.15 Pressure coefficient, experimental vs numerical results ...... 199 9.16 Effective power (EHP) compare to the expected power (Psail) ...... 204 B.1 Pressure coefficient, second set of tests ...... 213

F.1 43ft model, Basic Test: CX vs AWA...... 225 F.2 43ft model, Basic Test: CMX vs AWA...... 225 F.3 43ft model, Basic Test: CX/CMX vs AWA...... 226 F.4 43ft model, Basic Test: CD vs AWA...... 226 F.5 43ft model, Basic Test: CL vs AWA...... 226 F.6 43ft model, Basic Test: CX vs HA...... 227 F.7 43ft model, Basic Test: CMX vs HA...... 227 F.8 43ft model, Bent Yard Test: CX vs AWA...... 227 F.9 43ft model, Bent Yard Test: CMX vs AWA...... 228 F.10 43ft model, Bent Yard Test: CX/CMX vs AWA...... 228 F.11 43ft model, Bent Yard Test: CD vs AWA...... 228 F.12 43ft model, Bent Yard Test: CL vs AWA...... 229 F.13 43ft model, Bent Yard Test: CX vs HA...... 229 F.14 43ft model, Bent Yard Test: CMX vs HA...... 229 F.15 43ft model, Optimum Trimming Test: CX vs HA (AWA=40◦) ...... 230 F.16 43ft model, Optimum Trimming Test: CMX vs HA (AWA=40◦) ...... 230 F.17 43ft model, Optimum Trimming Test: CX/CMX vs HA (AWA=40◦) . . . . 230 F.18 43ft model, Optimum Trimming Test: CX vs HA (AWA=60◦) ...... 231 F.19 43ft model, Optimum Trimming Test: CMX vs HA (AWA=60◦) ...... 231 F.20 43ft model, Optimum Trimming Test: CX/CMX vs HA (AWA=60◦) . . . . 231 F.21 43ft model, Optimum Trimming Test: CX vs HA (AWA=80◦) ...... 232 F.22 43ft model, Optimum Trimming Test: CMX vs HA (AWA=80◦) ...... 232 F.23 43ft model, Optimum Trimming Test: CX/CMX vs HA (AWA=80◦) . . . . 232 F.24 43ft model, Bending Test: CX vs AWA...... 233 F.25 43ft model, Bending Test: CMX vs AWA...... 233 F.26 43ft model, Bending Test: CX/CMX vs AWA...... 233 F.27 43ft model, Yard Stiffness Test: CX vs AWA (HA=0◦) ...... 234 xiv LIST OF FIGURES

F.28 43ft model, Yard Stiffness Test: CMX vs AWA (HA=0◦) ...... 234 F.29 43ft model, Yard Stiffness Test: CX/CMX vs AWA (HA=0◦) ...... 234 F.30 43ft model, Yard Stiffness Test: CD vs AWA (HA=0◦) ...... 235 F.31 43ft model, Yard Stiffness Test: CL vs AWA (HA=0◦) ...... 235 F.32 43ft model, Yard Stiffness Test: CX vs AWA (HA=5◦) ...... 235 F.33 43ft model, Yard Stiffness Test: CMX vs AWA (HA=5◦) ...... 236 F.34 43ft model, Yard Stiffness Test: CX/CMX vs AWA (HA=5◦) ...... 236 F.35 43ft model, Yard Stiffness Test: CD vs AWA (HA=5◦) ...... 236 F.36 43ft model, Yard Stiffness Test: CL vs AWA (HA=5◦) ...... 237 F.37 43ft model, Yard Stiffness Test: CX vs AWA (HA=10◦) ...... 237 F.38 43ft model, Yard Stiffness Test: CMX vs AWA (HA=10◦) ...... 237 F.39 43ft model, Yard Stiffness Test: CX/CMX vs AWA (HA=10◦) ...... 238 F.40 43ft model, Yard Stiffness Test: CD vs AWA (HA=10◦) ...... 238 F.41 43ft model, Yard Stiffness Test: CL vs AWA (HA=10◦) ...... 238 F.42 43ft model, Yard Stiffness Test: CX vs AWA (HA=15◦) ...... 239 F.43 43ft model, Yard Stiffness Test: CMX vs AWA (HA=15◦) ...... 239 F.44 43ft model, Yard Stiffness Test: CX/CMX vs AWA (HA=15◦) ...... 239 F.45 43ft model, Yard Stiffness Test: CD vs AWA (HA=15◦) ...... 240 F.46 43ft model, Yard Stiffness Test: CL vs AWA (HA=15◦) ...... 240

G.1 60ft model, Basic Test: CX vs AWA (with and without mizzen) ...... 241 G.2 60ft model, Basic Test: CMX vs AWA (with and without mizzen) . . . . . 241 G.3 60ft model, Basic Test: CX/CMX vs AWA (with and without mizzen) . . . 242 G.4 60ft model, Basic Test: CD vs AWA (with and without mizzen) ...... 242 G.5 60ft model, Basic Test: CL vs AWA (with and without mizzen) ...... 242 G.6 60ft model, Basic Test: CX vs HA ...... 243 G.7 60ft model, Basic Test: CMX vs HA ...... 243 G.8 60ft model, Basic Test: CX vs HA (without mizzen) ...... 243 G.9 60ft model, Basic Test: CMX vs HA (without mizzen) ...... 244 G.10 60ft model, Optimum Trimming Test: CX vs HA ...... 244 G.11 60ft model, Optimum Trimming Test: CMX vs HA ...... 244 G.12 60ft model, Optimum Trimming Test: CX/CMX vs HA ...... 245 G.13 60ft model, Optimum Trimming Test: CD vs HA ...... 245 G.14 60ft model, Optimum Trimming Test: CL vs HA ...... 245

H.1 Energy balance ...... 248 List of Tables

6.1 Sail dimensions ...... 97 6.2 Sail shapes ...... 98 6.3 Sailing conditions ...... 98 6.4 Measured data ...... 99 6.5 Comparison of results, reference vs present study ...... 103 6.6 Comparison of results, with and without a mast ...... 109

7.1 Main dimension limits ...... 126 7.2 Pressure tap location ...... 130 7.3 The tests ...... 134

8.1 Model-scale hull dimensions ...... 154 8.2 The rigging dimensions ...... 154 8.3 The yards dimension ...... 158 8.4 Summary of the conducted tests ...... 159 8.5 Comparison of results ...... 172

9.1 Main characteristics ...... 186 9.2 Main dimensions of the three geometries ...... 188 9.3 Routes and areas ...... 201 9.4 Relationship between waves and wind speed ...... 201 9.5 Annual probabilities for different wave heights ...... 202 9.6 Annual probabilities for different wind directions for wave height less than 4m...... 202 9.7 Third geometry, sail power obtained with CFD data ...... 203 9.8 Third geometry, comparison between numerical (CFD) and experimental (WT) results (13 knots of vessel speed) ...... 203

A.1 Results of the simulations with and without the mast ...... 211

C.1 Yard data ...... 216

D.1 43ft model: Basic Test(BT) ...... 217 D.2 43ft model: Bent Yard Test(BYT) ...... 218 D.3 43ft model: Optimum Trimming Test(OPT) ...... 219

xv xvi LIST OF TABLES

D.4 43ft model: Yard Stiffness Test (YST) ...... 220 D.5 43ft model: Bending Test (BEN) ...... 222

E.1 60ft model: Basic Test(BT) with and without mizzen ...... 223 E.2 60ft model: Optimum Trimming Test(OPT) ...... 224

I.1 Pressure tap position and pressure coefficient ...... 249

J.1 Pressure coefficient ...... 253 Chapter 1

INTRODUCTION

The sport of sailing is of prime importance for Spain. It is the sport which has achieved more Olympic (17) and gold (11) medals than any other sport in this country. The interest increased when the 32nd and 33rd America’s Cup races were held in Valencia in 2007 and 2010, respectively. Moreover, the start of the Volvo Ocean Race 2008/2009 and 2011/2012 also contributed to the media and economic impact.

The America’s Cup is one of the world’s most important sports event and the oldest of the modern age. This race is not only sport but due to its special features and high media profile, it has become a first order economic phenomenon. As an example, and according to [1], “the holding in Valencia of the America’s Cup 2007 involved an injection of expenditure of such magnitude that it translated into an annual increase during three years of around 1% of the Gross Domestic Product (GDP) and employment of the Valencia Region, generating an accumulated total of 5,748 million of output, 2,724 million of value added and 73,859 jobs over the period 2004-07”. Another figure of the America’s Cup 2007: the budget of the Spanish Challenge in that race was about 60 millions.

The Spanish sailing has also gotten involved in the Volvo Ocean Race. In 2008, the

Figure 1.1: Volvo Ocean Race 2008-2009. Start of the Leg 1 in Alicante (Spain)

1 2 CHAPTER 1. INTRODUCTION

race start was held in Alicante (see figure 1.1) and two Spanish boats participated. It was estimated that the 2008/2009 race involved 80 millions of economic impact and generated 1,500 direct and indirect employments. Furthermore, the media impact was valued in 180 million euro and a million visitors at the Village. In 2011, the race start was held in Alicante as well and there was also an Spanish challenge. Again, the next race starts will be held in Alicante (2014 and 2017).

These figures highlight that sailing is not just a sport but a profitable industry. Spain is getting involved and providing this sport with funds and resources. Nowadays, sailboats present high technology advances, a leading edge engineering and the use of the latest tools. There is a continuous research on sail aerodynamics but there are some gaps which this thesis tries to explain.

1.1 General problem

The knowledge of the airflow around the rigging of a sailboat is indispensable for the resulting performance, and therefore, increased attention is being paid to this problem in order to gain a thorough understanding of the phenomena involved.

Up to now, the sail designing has been mainly based on the experience of the designers and on experimental tests. The scientific community have considered that wind tunnel tests are more adequate to analyze the flow around sails despite some drawbacks such as the scale effect or the difficulty to measure some parameters. For example, it is trouble- some to obtain the pressure distribution over the sail for different apparent wind angles or the vorticity downstream. Several complex devices are needed which are usually intrusive.

The use of numerical tools to study the aerodynamic of sails is recent and it is on the increase since it is cheaper and faster comparing to experimental tests. Ad- ditionally, unlike in wind tunnel testing, numerical codes can provided, with simple models, a high amount of parameters on the sails and around them. The main disad- vantage to trust on numerical results is that first, codes and procedures must be validated.

Therefore, it is reasonable that numerical tools do not substitute experimental tests but complement them in order to develop an efficient and trustworthy design methodology. The thread of this thesis is the combination of experimental tests and numerical simulations in four different scenarios (IMS Class, Transpac 52 Class, Dhows and structural wings) to understand the sail performance. 1.2. MOTIVATION 3

1.2 Motivation

Numerical codes are widely used but the procedure and the results are not easily disclosed. This is due to the excessive secrecy of the high performance sailboat industry. There is a lack of information to validate new codes and the methodology that designers may use. Most of the publications of reference provide qualitative results instead of quantitative values. Moreover, commercial numerical codes are not specifically developed to study the aerodynamics of sails. There are some difficulties such as the analysis of lifting surfaces without thickness, the complex geometry of the rigging and the elasticity of sails.

During this thesis four different scenarios have been emerged with the same phi- losophy: combine experimental tests with numerical codes to better understand the phenomena involved near the sails. Next, the motivations for each of the four investiga- tions are described.

First, the three-dimensional effect of the mast on the aerodynamic performance of an IMS Class boat has been studied. There are several two-dimensional studies that deal with the mast influence but there is a lack of three dimensional results.

Second, the pressure distribution on a Transpac 52 Class mainsail has been de- termined. As far as this author can tell, when this investigation began, pressure distributions on three-dimensional upwind model-scale sails had never been published. This encouraged the author to carry out this research.

Third, the aerodynamic performance of the 43ft Dhow Class has been obtained as well as the performance of the 60ft Dhow Class. This research has come up from the interest shown by different sailmakers and the Yach Reseach Unit (University of Auckland, New Zealand) on the performance of sailing dhows. As far as it is known, there haven’t been conducted any aerodynamic nor hydrodynamic tests of these boats. It has been impossible to find any technical article or report which describes dhows.

Fourth, a feasibility study has been conducted to use a structural wing in combination with conventional propulsions systems. Due to the increase of the fuel cost and the environmental concern, the shipping industry has high requirements on propulsion technologies using offshore wind which is an endless energy source, free of charge, powerful at seas and renewable. The EU-CargoXpress project deals with this problem and the aerodynamic performance of different structural wings have been analyzed under the context of this thesis. 4 CHAPTER 1. INTRODUCTION

1.3 Scope

The principal objective of this research is to establish a procedure to study the sail aerodynamics by combining the use of numerical viscous codes and experimental tests. Moreover, the specific objectives for each of the scenarios are:

• Evaluate the effect of the mast on the sail performance of an IMS Class rigging.

• Measure the pressure distribution on a Transpac 52 Class mainsail.

• Characterize the main parameters that affect the sail performance of sailing Dhows.

• Study the viability of using a structural wing to reduce the fuel consumption and emissions on the EU-CargoXpress Project.

1.4 Contributions

One of the main contributions of the research is the study of the three-dimensional effect of a mast on sail performance. Numerical results have been compared with full scale data. This investigation has been partially disclosed in the papers “Computational Study of Sail Performance of a Racing Yacht” presented at the 47◦ Congreso de Ingenier´ıa Naval e Industria Mar´ıtima in 2008 [2] and “The Effect of the Mast on Sail Performance” prestented at the IV International Symposium on Yacht and Motor Boat Design and Production [3] in 2010.

The pressure distribution on the three-dimensional upwind model-scale Transpac 52 Class mainsail have been measured in a wind tunnel. The experimental technique that has been used is widely spread in civil wind engineering but it is innovative in sail aerodynamics. Moreover, the tests have been reproduced with a numerical code.

Another relevant achievement of this research is to be the first that has scientifically studied sailing dhows. These tests lay the grounds of future investigations. Both experimental and numerical tests have been conducted. The results of the experimental tests have been partially disclosed by the author in the report “Aerodynamics of Sailing Dhows” [4].

A methodology to study the viability of using structural wings combined with conventional propulsion systems has been also developed within the EU-CargoXpress Project. The aerodynamic performance of three different geometries have been compared numerically and then, the results have been validated with wind tunnel tests. The results of this investigation have been partially disclosed by the author in the paper “Viability Study of Sailing Propulsion combined with a Conventional System” presented at the XXII Congreso Panamericano de Ingenier´ıa Naval, Transporte Mar´ıtimo e Ingenier´ıa 1.5. OUTLINE OF THE THESIS 5

Portuaria [5]. The author also collaborated on the report “Proposal for sustainable energy elaborated” of the Universidad Polit´ecnicade Madrid [6]. Moreover, the paper “EU-CargoXpress: Wind Propulsion Concept” [7], written by this author and presented at the Transport Research Arena - Europe 2012, won the Best Paper Award. This highlights the relevance of this project and in particular, the innovative achievements of this author to the concern of the shipping industry.

1.5 Outline of the thesis

The remainder of this thesis is the following. In chapter 2 the context is set. Chapter 3 puts the reader in the picture. The tools that have been used in this research are described in chapters 4 and 5. The four scenarios are presented in chapters 6, 7, 8 and 9. Finally, the conclusions are summarized in chapter10.

Chapter 2 Sailing Concepts. In this chapter the basic ideas to understand the aerody- namics of sailing are presented. It is included an explanation of the aero/hydrodynamic balance of forces, the sail interaction, the apparent wind concept, as well as the nature of the aerodynamic force.

Chapter 3 Literature review. Here, the research on sail aerodynamics is described. The tools to predict the performance of a sailboat, such as numerical simulations, wind tunnel and full scale tests, are presented. It is also included a description of the investigations related to aeroelastic studies and optimization approaches.

Chapter 4 Wind tunnel tests. The history and types of wind tunnels are described in this chapter. Moreover, the operation and design are explained. It is also included a summary of the most common measurements that are acquired in wind tunnels and the instrumentation needed for those measurements.

Chapter 5 Computational fluid dynamic simulations. In this chapter the basic con- cepts to understand a Computational Fluid Dynamic code are included. Furthermore, a description of the formulation and methodology used by the CD-Adapco’s STAR-CCM+ code are described. This chapter is particularized to the study of sail aerodynamics.

Chapter 6 Influence of the mast. First, the reference full-scale tests are described as well as the sail shapes and the results for comparison. Then, the numerical simulations carried out with ANSYS-CFX are included. In the next section, the simulations per- formed with the CD-Adapco’s STAR-CCM+ code are presented. Finally, the conclusions are summarized.

Chapter 7 Pressure distribution on a TP52 mainsail. First, the Transpac 52 Class is described. Then, the experimental test conducted at the Atmospheric Boundary Layer 6 CHAPTER 1. INTRODUCTION

Wind Tunnel (Universidad de Granada, Spain) are included. In the next section, the numerical simulations are presented as well as the comparison of results. Subsequently, the conclusions are summarized.

Chapter 8 Aerodynamics of sailing dhows. In this chapter, a description and the history of dhows are presented. Next, the experimental tests conducted at the Twisted Flow Wind Tunnel (University of Auckland, New Zealand) are described as well as the numerical simulations carried out with the STAR-CCM+ code. In the last section, there is a summary of the conclusions.

Chapter 9 EU-CargoXpress project. First, the existing technologies are indicated. Next, the EU-CargoXpress project is briefly summarize. Then, the numerical simulations and the experimental tests are presented. These tests have been conducted at the A9 Wind Tunnel (Universidad Polit´ecnicade Madrid, Spain). Subsequently, the feasibility study is described. In the last section, there is a summary of the conclusions that have been drawn.

Chapter 10 Conclusions. In the last chapter of this thesis, the main conclusions are drawn. Chapter 2

SAILING CONCEPTS

In this chapter, the basic sailing concepts are explained in order to better understand the studies that are described in this thesis.

2.1 Nomenclature

β Apparent wind angle

δm Trim angle of the mainsail

A Angle between lift (L) and total aerodynamic force (FT ) γ True wind angle

λ Leeway angle

µ Air dynamic viscosity

ρ Air density

∆ Displacement

Θ Heel angle

D Drag force

FH Total heeling force

FHlat Horizontal heeling force

FR Driving force

FS Total side force

FSlat Horizontal side force

7 8 CHAPTER 2. SAILING CONCEPTS

FT Total aerodynamic force

FV Vertical aerodynamic Force

FVW Vertical hydrodynamic force g Gravity

L Lift force or cross wind force

Lc Characteristic length

MH Heeling moment

MPA Aerodynamic pitching moment

MPW Hydrodynamic pitching moment

MR Righting moment

MYL Hydrodynamic yawing moment

MYW Aerodynamic yawing moment

R Water resistance

Re Reynolds number

V Wind speed

VA Apparent wind

VS Boat speed

VT True wind

W Weight z Height, vertical distance zref Reference height z0 Roughness length

Abbreviations

CE Center of effort 2.2. BALANCE OF THE AERO/HYDRODYNAMIC FORCES 9

2.2 Balance of the aero/hydrodynamic forces

How does a sailing yacht navigate with a constant speed? This phenomenon is the consequence of the balance of the aerodynamic, hydrodynamic, buoyancy and gravity forces. As stated by [8], these forces, in turn, depend on the wind strength, the shape of sail, type of rig and control gadgets, the size and shape of the hull, displacement of the boat and distribution of weight, sea conditions and the crew’s level of expertise. The easiest and most common method to study the balance is to consider the forces acting separately and then, include the effect among them. In figure 2.1 (obtained from [9]) the components of these forces are illustrated, as well as the moments produced.

Figure 2.1: Force balance

The force/moment balance can be simplified to the resolution of six simple equations as presented in [9]:

• Driving force (FR) = Water resistance (R)

• Horizontal heeling force (FHlat) = Horizontal side force (FSlat)

• Vertical aerodynamic force (FV ) = Vertical hydrodynamic force (FVW ) 10 CHAPTER 2. SAILING CONCEPTS

• Aerodynamic pitching moment (MPA) = Hydrodynamic pitching moment (MPW )

• Heeling moment (MH ) = Righting moment (MR)

• Aerodynamic yawing moment (MYM ) = Hydrodynamic yawing moment (MYL)

The difficulty arises when determine the components of the forces. In our case, the problem is focused on the aerodynamic force which depends not only on the wind strength but on the sail, the rig, mast and hull. It is also important to highlight that the aerodynamic force behaves differently depending on the angle between the wind and the boat. This concept is named “point of sail” as presented in figure 2.2 (obtained from [10]).

Figure 2.2: Points of sail

When a boat is sailing upwind, the angle of incidence of the apparent wind (concept explained in section 2.5) to the sail is small. The sails are pulled tight to the boat, the camber is small and the flow is mainly attached. In these conditions, sails act like traditional airfoils. The typical sloop-rig sailing boat uses the mainsail and a bow sail such as a genoa.

If the angle of incidence of the apparent wind is larger, the point of sail is named “reach”. In this case, the mainsail is hoisted together with the gennaker or spinnaker. The flow is more complex since there is large scale separation. At the highest angles of incidence, the point of sail is called downwind (or run). The sails hoisted are the mainsail and the spinnaker. Here the flow is completely detached and becomes unsteady. The traditional airfoil theory cannot be applied in this situation. Therefore, the method to calculate the aerodynamic force depends on the point of sail in study, due to the different behavior of the flow in each case.

2.3 Aerodynamic Force

But, where does the aerodynamic force come from? The sails have a profile around with the air flows. Due to the camber of the sail, the air on the leeward side has a higher 2.3. AERODYNAMIC FORCE 11

velocity comparing to the air on the windward side in order to verify the continuity of the field. According to the Bernoulli’s principle, the high speed flow provokes a reduction of pressure and therefore a suction comparing to the windward side of the sail. The aerodynamic force of a sail is a combination of the suction on leeward side and the pressure on windward side.

Figure 2.3: Flow around a sail

In figure 2.3 (obtained from [11]) the flow around a sail is plotted together with the pressure distribution on both sides. The aerodynamic force is the difference between the two curves (the pressure on each side). It can be seen that the major contribu- tion to the force comes from the suction on the leeward side of the sail, as explained in [11].

In chapter 7, the pressure distribution on the windward side of a mainsail will be measured. In chapter 9, the pressure distribution on a rigid sail is calculated on both sides.

The total aerodynamic force can be decomposed in two ways. The first method considers the driving (FR) and heeling (FH ) components of the total force. This is used when studying the balance of the aero-hydrodynamic forces. But, when the aerodynamic behavior is analyzed by its own, it is a common practice to decompose the aerodynamic force in its lift (L) and drag (D) components as plotted in figure 2.4 (obtained from [9]). Drag has the direction of the apparent wind whereas the lift is perpendicular. Equation 2.1 shows the simple trigonometrical relation between the two methods of decomposition which depends on the apparent wind angle (β). 12 CHAPTER 2. SAILING CONCEPTS

Figure 2.4: Components of the total aerodynamic force

F = L sin β − D cos β R (2.1) FH = L cos β + D sin β It is obvious that the goal is to maximize the driving force and simultaneously minimize heeling force. When beating against the wind, the contribution of the drag is negative not only because it increases the heeling force but reduces the driving forces. The ratio L/D (or the angle between the lift and the total aerodynamic force) serve as an index of the aerodynamic efficiency. Therefore, in this point of sail, the objective is to maximize the lift and minimize the drag.

As the apparent wind angle increases through the reaching point of sail, the contri- bution of the drag to the driving force becomes more important. At the last stage, when downwind, the maximum driving force will be equivalent to maximum drag.

It can be seen that the study of the behavior of the drag is essential to understand the overall aerodynamic sail performance. Theory and experiments indicate that the drag (D) of a given rig is made up of four components: induced drag, friction drag, form (or pressure) drag and additional drag.

Induced Drag

Induced drag is produced in every lift-generating device and is manifested on the tip vortices. It is a rotating mass of air that is trailed behind sails and produces a continuous loss of wind kinetic energy. In chapter 6 the vortices are obtained with a numerical code 2.3. AERODYNAMIC FORCE 13

and the plot is included.

The vortices are generated due to the difference of pressure on windward and leeward sides near the edges, foot and head. In those edges, the high pressure air on windward flows to the suction side on leeward, producing the tip vortices. Since the lift and the induced drag have the same origin this drag cannot be avoided but it can be reduced.

Sail designers control the induced drag by three parameters. The first is the aspect ratio. Is is known that the higher the aspect ratio, the smaller the induced drag. This general statement should be considered together with other aspects than can be negative. For example, the heeling moments increase with the aspect ratio and the point of sail as mentioned before. The second parameter is the sail planform. An elliptic shape has low induced drag values whereas traditional triangular planforms have high values. Latest versions of high performance sails have a trapezoid shape with large heads. It has been proven that this shape has the benefits of the ellipctic shape not being detrimental to downwind sailing. The last parameter to control the induced drag is the gap between the boom and the deck. The boom can be lowered, or made wider or sim- ply, the gab can be sealed. The objective is to prevent the air from flowing around the foot.

Friction Drag

The origin of the friction drag is the viscosity even though the direct effect is small. The problem arises because the viscosity generates the “boundary layer”. The layer, though thin, plays a crucial part in flow studies due to the shear stresses.

Even for an incoming laminar flow, the shear stress provokes this flow become turbulent and increase the friction drag. In order to analyze if the transition from laminar to turbulent flow would occur, the Reynolds number (Re) is calculated (see equation 2.2, where ρ is the air density, µ is the air dynamic viscosity, V is the wind speed and Lc is the characteristic length which can be the camber of a section or the boom length, for example). It has been measured that the transition occurs approximately at Reynolds numbers around 5 · 105.

ρ · V · L Re = c (2.2) µ In the air (ρ ≈1.2 kg/m3 y µ ≈1.810−5 Ns/m2) the Reynolds number is approximately 5 Re=Lc · V · 0.67 · 10 . For example, at 15knots of boat speed (7.7m/s), the transition from laminar to turbulent would occur at 65cm from the leading edge. Therefore, it is natural to think that in most cases, sails produce turbulent flow and consequently, an increase of the friction drag.

But friction drag depends not only on the Reynolds Number but also on the smoothness of the sail surface. This affects the selection of the sailcloth. Thus, in order 14 CHAPTER 2. SAILING CONCEPTS

to control the magnitude of the friction drag it is important to study the design, the trim when sailing and the sailcloth.

Form (or pressure) Drag

The form drag could be included in the friction drag since the origin of both is the air viscosity. But, it is convenient to consider both separately. This pressure drag arises from the separated flow which exists over some parts of a body (sail) in an air stream. It is named “form” because it is a consequence of the shape of the body. For example a large camber provokes flow detachment as well as the presence of a mast.

The mast has a great influence in the speed performance since it disturbs the incoming flow to the sail. It generates turbulence and detachment. The flow can be attached again but the loss of energy would have already been produced.

Figure 2.5: Flow around a mast/sail combination

In figure 2.5 (obtained from [11]) the flow around a mast-sail configuration is shown. Three zones of separation can often be distinguished. As explained in [11], two are immediately behind the mast, to windward and leeward, respectively, while the third zone is on the aft part of the leeward side. This third zone depends on the forward separation and the loading of the sail.

The main objective is always to improve the airflow pattern and thus to maximize the pressure differences between the windward and leeward sides of the mast-sail configuration. The adverse effect of a mast can be reduced by profiling it carefully, eliminating the gap between the mast and the sail, reducing the diameter and introducing turbulence stimulator. Moreover, the negative influence of the mast can be reduced by the sail sheeting. There is an optimum gab between sails that can reduce the form drag. In chapter 6 more information of the mast effect is included.

Additional Drag 2.4. SAIL INTERACTION 15

The total area above waterline can be divided into two areas: sail and residual. This last generates the additional aerodynamic drag. Here the forces generated by the wind on the hull, rigging, mast and crew are taken into account. The impact of the additional drag to the total aerodynamic forces depends on the ratio between the sail and residual areas.

The contribution of the additional drag is positive when sailing downwind but it does not compensate the losses that produces when sailing upwind. It is usually desirable to reduces as much as possible the effect of the parasitic area. Due to an appropriate design of the rigging, hull and superstructure, the additional drag can be reduced even though it will never be eliminated.

2.4 Sail Interaction

When two or more sails are hoisted together, the interaction among them must be studied since their performance is not the sum of their contributions by their own. In figure 2.6 the easiest configuration is presented. There are two sails without the mast and sailing upwind. The thin lines are the streamlines for the single mainsail whereas the thick lines are the streamlines of the two sails in combination as presented in [11]. In the lower part of the figure the pressure curves are plotted.

As it can be observed, the streamlines vary depending on the configuration. In the two-sail case the jib gets the load while the mainsail is unloaded, comparing to the single sail case. It is also observed that the presence of the jib modifies the suction side of the mainsail. The contribution of the mainsail to the total aerodynamic forces is reduced but there is a larger increase of the contribution of the jib.

There are two theories that explain what happens between the two sails, which is called the “slot effect”. The traditional theory states that there is an increase of the airflow speed between the sails due to the Venturi effect. Recently, the second theory has demonstrated that the airflow speed decreases when reaching the gap between the sails. This makes the combination of the two sails behave as a single airfoil. If there is a suitable trimming, the lift generation of the combination of both sails is greater than the sum of each forces by their own.

As mentioned in the previous section, the interaction between sails can also reduce the negative effects of the mast and prevent the flow from detaching. 16 CHAPTER 2. SAILING CONCEPTS

Figure 2.6: Flow around a mainsail/jib combination

2.5 Apparent Wind

In real life, the onset flow onto a sail of a yacht (apparent wind, VA) is not uniform. The flow has a vertical speed gradient and twist since the speed and direction of the flow change with height. This complex flow structure results from the vertical speed gradient in the atmospheric boundary layer (true wind, VT ) combined with the movement of the yacht (boat speed, VS). In figure 2.7 (obtained from [12]) the true wind gradient is plotted in the left site while the apparent wind structure is presented on the right side.

At sufficiently great heights above the surface of the earth, the influence of the friction of the wind along the ground becomes negligible. This region is called the free atmosphere. Within the atmospheric or planetary boundary layer the wind velocity is slowed down by the friction along the ground. The atmospheric boundary layer depth is typically between several hundred and 3km depending on the wind intensity, roughness of the terrain and angle of latitude. When considering yacht sails, only the lower portion 2.5. APPARENT WIND 17

Figure 2.7: Planetary boundary layer and the twist

of the boundary layer up to about 100m above the ground is of interest. The atmospheric wind in relation to sailing is called “true wind” (VT ).

Extensive research has been conducted over the years to measure and describe the velocity profiles in boundary layers. In relation to the atmospheric boundary layer, the first representation of the wind profile in a horizontally homogeneous terrain was the power law proposed in 1916. Initially, it was assumed that the entire boundary layer depth could be approximated with a constant exponent. However, a number of experiments and real life observations have shown that only the lower fraction (∼ 10%) of the atmospheric boundary layer can be accurately described by a logarithmic velocity profile. In order to define the whole atmospheric boundary layer, empirical velocity profiles have been developed from theory and experiments, which are a combination of the logarithmic and power laws where the exponent varies with height.

For the application to yacht sails the influence of the non-logarithmic terms can be ignored since the logarithmic law is known to hold well up to a height of at least 100m. Providing that the characteristic height of the sail is not larger than 100m, the true wind speed (VT ) at the height z can thus be calculated from the equation 2.3 where z0 is the terrain roughness length.

ln(z/z0) VT (z) = VT (zref ) (2.3) ln(zref /z0)

For open waters, the roughness length (z0) is a function of the wave height, which again, it is a function of the wind speed. Cook [13] thus gives the roughness length as equation 2.4 where zref is 10m above the water and g is the acceleration due to gravity. 18 CHAPTER 2. SAILING CONCEPTS

V (z )2 z ≈ 5 · 10−5 T ref (2.4) 0 g

According to this equation, for typical true wind speeds between 5m/s and 20m/s, the roughness lengths would range from 0.13mm to 2.04mm. Clearly, ocean waves are larger than these roughness lengths, but their crests are rounded enough for the flow to follow the curvature without separating, which reduces the friction and in turn, the roughness length. Moreover, ocean waves travel in the direction of the wind, which reduces the speed differential, friction and roughness length. This expression for z0 is gen- eralized. If not fully developed waves are to be considered, then an enhanced expression would be required. Similarly, the logarithmic law only applies for homogeneous terrain and gradient wind. For winds close to shore, another expression could be more convenient.

As mentioned before, the variation of true wind speed with height affects the apparent wind velocity in magnitude and direction for each sail section. The apparent wind angle and speed for different heights resulting from the constant yacht speed and the logarithmi- cally increasing true wind speed is shown in figure 2.7, as mentioned before. It can be seen that both the apparent wind speed and angle increase with height above the water. The apparent wind angle (β) and speed (VA) can be calculated from the geometric relationship at any height z with equations 2.5 and 2.6, where λ is the leeway angle (which is usually ignored in the wind tunnel) and VT varies logarithmically with z as shown in equation 2.3.

V (z) sin(γ + λ) β(z) = tan−1 T − λ β[0, 180◦] (2.5) VT (z) cos(γ + λ) + Vs

p 2 2 VA(z) = Vs + VT (z) + 2VSVT (z) cos(γ + λ) (2.6)

The structure of the apparent wind is relevant to the problem of deliberate twisting of the sails. It is recommended that each section of the sail should operate at the same effective angle of incidence relative to the apparent wind. Furthermore, rolling and pitching should be taken into account due to their influence on the apparent wind strength and direction, because of the associated movements of the mast and sails. The effect is greatest toward the top of the mast, where the motion is more violent.

2.6 Conclusion

It can be concluded that there are many factors affecting aerodynamic forces: sail setting (sheeting), heel angle, wind velocity and turbulence, mast, sail interaction, sail 2.6. CONCLUSION 19

planform and cloth (elasticity), heading, sail camber and twist, etc. In order to quantify the aerodynamic forces and investigating the influence of the aforementioned factors on an specific sailing yacht, prediction performance analysis, aeroelastic studies and optimization techniques must be applied. These three research fields are described next.

For further information about “sailing concepts”, the author recommends [11] [9] and [8], from which most of the information of this chapter has been obtained. 20 CHAPTER 2. SAILING CONCEPTS Chapter 3

LITERATURE REVIEW

The research on sail aerodynamics can be divided in three main fields: performance prediction (section 3.1), aeroelastic analysis (section 3.2) and optimization approaches (section 3.3). Each field studies the same physical problem with a different point of view.

In this chapter, the state of the art in these investigations is presented. Applied methods such as wind tunnel tests, full-scale tests and numerical simulations, are described. Performance Prediction Programs (VPP) and Fluid-Structure Interaction (FSI) programs are also explained.

3.1 Performance Prediction

When designing a sailing yacht, the main objective is finding the optimal aerodynamic performance to beat the hydrodynamic features of the yacht and sail as fast as possible. A Velocity Prediction Program (VPP) is one of the most important tools in this field. These computer codes predict speed, heel angle, leeway angle and many other parameters under different wind conditions. The first VPP was developed by Kerwin in the mid 70’s for the International Measurement System (IMS) handicapping formula [14].

VPPs are used for predicting the performance of a sailing boat by balancing the aerodynamic and hydrodynamic forces and moments so that the vessel sails in equilibrium. This occurs, as explained in [11], when the forces and moments in each of the three directions cancel each other: driving force/hydrodynamic resistance; aerodynamic side force/hydrodynamic side force; vertical force/buoyancy; heeling moment/righting moment; pitching moment/restoring moment; and aerodynamic yawing moment/hydrodynamic yawing moment (see section 2.2). Both aerodynamic and hydrodynamic forces and moments are calculated from coefficients for each condition.

The program runs through a set of given true wind speeds and for each speed, a set of wind directions. The result of the VPP is often presented in the form of a polar plot.

21 22 CHAPTER 3. LITERATURE REVIEW

Each curve represents the boat speed for a constant true wind speed.

Traditional VPPs are based on a steady-state equilibrium between aero- and hy- drodynamic forces. But, in the last decade, there have been several investigations to include the dynamic behavior of the yacht. These programs are now called DVPP (Dynamic Velocity Prediction Programs). These can include unsteady conditions due to seakeeping and maneuvering. For example, in 2002, Day et al.[15] developed a tool for time-domain simulation of yacht performance in waves. In 2008, Binns et al.[16] presented a velocity prediction program which was used to simulate the steady state force balance based on towing tank and wind tunnel experiments. Then, they considered the dynamic terms of the equations by systematic series of full scale tests.

Another development in VPPs, apart from the dynamic consideration, is the depow- ering technique. The traditional method uses the trim parameters “reef” and “flat” as introduced by Kerwin [14] to model the depowering. More recently, a third trim parameter named “twist” was introduced by Jackson [17]. Nowadays, the depowering is obtained from wind tunnel tests such as in [18], [19] and [20]. Instead of considering the force coefficients as curves, they can be treated as surfaces where the influence of trim parameters are included.

It can be stated that the most important part of a VPP is the quality of the force and moment coefficients. According to [18], prior to the 2000 America’s Cup, many, if not most VPP’s used upwind and downwind aerodynamic models that were essentially similar to the approach first developed by Kerwin [14]. Nowadays a good VPP has the aerodynamic force and moment coefficients of the specific boat in study. These coefficients can be determined in several ways: wind tunnel tests, full-scale measurements and numerical simulations. Which tool or combination of techniques is used depends on the particular case and, of course, the resources available.

3.1.1 Wind Tunnel Tests Wind tunnel tests are carried out not only to obtain the aerodynamic coefficients but to have a real-time aerial view of the flying shape of sails. Forces are usually measured with a 6-component balance located below or inside the model. Furthermore, smoke can be used to efficiently visualize the streamlines. The flexible scaled sails can be trimmed remotely. Therefore, the change of forces and streamlines with the sail trim can be acquire immediately. In most of the wind tunnels where sail aerodynamics is investigated, special devices allow the flying shapes to be detected. Thus, forces and flying shapes are recorded simultaneously.

The first wind tunnel testing of sailing yacht rigs were performed in the late 1950’s at the Southampton University. The work of the Yacht Research Group and Tony Marchaj [9] has been continued by the Wolfson Unit for Marine Technology. While the wind 3.1. PERFORMANCE PREDICTION 23

tunnel used for the first tests has remained substantially the same, measuring devices and techniques have been gradually refined.

Although the general set-up of a wind tunnel has remained substantially the same since the first tests, there was an important development in the mid 90’s when the concept of twisted flow wind tunnel (TFWT) was introduced. It was originally developed by Flay [21] for the New Zealand America’s Cup Challenge in 1995 at the University of Auckland. The TFWT is unique in that it was developed specifically for the testing of yacht sails. This facility can reproduce the twisted flow generated by the true wind profile and the boat speed. More recently, other wind tunnels have incorporated the flow twisting concept, including the Politecnico di Milano in Italy and the University Applied Science Kiel in Germany.

Advantages and drawbacks

The main advantage of the wind tunnel testing is that the trimming process is similar in the wind tunnel and full-scale since flexible sails are used on the model. Model-scale sails are trimmed remotely and the aerodynamic forces are displayed to the operator in real-time. When the optimum trim is achieved, the aerodynamic forces are recorded. This procedure allows different trims to be investigated easily.

Wind tunnel testing is also a cost effective tool comparing to full-scale tests and it is much less time consuming. Moreover, wind tunnel measurements have a good repeatability thanks to the steady and controllable test environment. These advantages make this tool useful in early stages of the design process.

The fundamental disadvantage of wind tunnel testing is the inaccurate extrapolation from model scale to full scale values. Results are not completely reliable due to the difficulty of simulating the elasticity of the sails and rigging. To overcome this problem some investigations have been conducted with rigid scaled sails which reproduce the flying shape. There is a good insight of the phenomena involved in the flow around sails and rigging but the trimming process is withdrawn.

Recent Investigations

Next, it is presented a list of some of the latest publications related to sail aerodynamic research in which wind tunnel tests are conducted.

• Lasher et al. [22] built twelve parametric spinnaker models and tested them in a wind tunnel. In these models, five sail shape parameters were varied (cross-section camber ratio, sail aspect ratio, sweep, vertical distribution of camber, and vertical distribution of sail width). Lift and drag forces were measured for a range of angles of attack and the results were analyzed for three points of sail. 24 CHAPTER 3. LITERATURE REVIEW

• A symmetrical spinnaker was also tested in [23] for the validation of a fluid-structure interaction program. The model was tested in the Kiel’s Twisted Flow Wind Tunnel (TFWT).

• In 2008, Fossati et al. [24] presented an experimental database to provide the scientific community for numerical simulation benchmarking activities, concerning upwind sail aerodynamics. They included some results concerning the relationship between upwind flying shapes and the aerodynamic performance at different appar- ent wind angles and sail trim settings. The tests were performed in the Politecnico di Milano Twisted Flow Wind Tunnel using a typical IMS cruiser-racer 1/10th scaled model.

• Most DVPPs use aerodynamic forces which are calculated from quasi-steady theory. The paper of Gerhardt et al.[25] discusses whether this assumption of quasi-steady aerodynamics can be justified and also analyzes the error introduced by such quasi- steady analysis. In order to validate the unsteady potential flow theory for a thin sail-like aerofoil, experiments with an oscillating 2D mainsail model were carried out in the University of Auckland’s Twisted Flow Wind Tunnel. The researchers conclude that if the performance of the yacht is to be predicted on a time-scale shorter than the pitching period, this can be achieved better with an unsteady aerodynamic model rather than with a quasi-steady model.

• There are also some recent DVPPs which allow studying the behavior of a yacht while tacking. The aerodynamic models used in these codes usually suffer from a lack of available data on the behavior of the sail forces at very low apparent wind angles where the sails are flogging. In [26] measured aerodynamic force and moment coefficients for apparent wind angles between 0 degrees and 30 degrees are presented. Tests were carried out in the University of Auckland’s Twisted Flow Wind Tunnel in a quasi-steady manner for stepwise changes of the apparent wind angle.

• Fossati et al. [27] characterize the aerodynamic behaviour of a 48’ yacht rig scale model by means of experimental tests in the Politecnico di Milano Twisted Flow Wind Tunnel. The experiments allowed to characterize the aerodynamic forces and to study the aeroelastic behaviour of the sailplan.

• More recently, Viola et al. [28] presented a paper to provide a benchmark set of pressure distributions for the validation of numerical codes. Modern upwind sails were built at 1/15th-scale and tested in the Twisted Flow Wind Tunnel at Yacht Research Unit (University of Auckland).

In chapter 4 more information related to wind tunnel testing is included. 3.1. PERFORMANCE PREDICTION 25

3.1.2 Full-scale Tests Full-scale tests are conducted at sailing dynamometer boats in which the aerodynamic forces can be measured. Some of these boats carry special devices to measure the flying shapes. Thus, forces and flying shapes can be recorded simultaneously as in wind tunnel tests.

In 1988 the first full scale sailing dynamometer boat was built [29]. The system, named MIT Sailing Dynamometer, was a 35-foot boat containing an internal frame connected to the hull by six load cells configured to measure all forces and moments acting on the sails. At the same time, the sail shapes were measured and used for the input data of CFD analysis. In 1997 Masuyama and Fukasawa built the sail dynamometer boat Fujin that was similar to the MIT dynamometer. The results using IACC and IMS type sail were reported in different papers such as [30], [31] and [32]. One of the most recent project was initiated in Germany in which the 10-meter full scale sail force dynamometer was named DYNA. It was based on a 33ft IMS cruiser/racer ([33], [34], [35]).

The main advantage of full-scale testing is that the real behavior of sails and rigging is studied. Other tools such the wind tunnels and numerical simulations are simplified techniques of a complex phenomenon. For example, the full-scale testing include the dynamic movements of the yacht and besides, there is no need to simulate the atmospheric boundary layer and turbulence of the true wind. Furthermore, the problems of accuracy of the extrapolation from model to full-scale are eliminated.

Apart from the cost of full-scale testing, the main drawback of this technique is the large uncertainty in the results. The dynamic effects of the real environment such as the time dependent wind flow and seakeeping, make the measuring process difficult and it leads to a poor repeatability. The actual flow cannot be measured and the flying shape is troublesome to be acquire with precision.

The latest publications related to full-scale tests are focused on full-scale pressure measurements. In [36] the aerodynamics of a Sparkman & Stephens 24-foot sailing yacht was investigated. Full-scale pressure measurements were performed on the mainsail and the genoa in upwind condition. Pressure taps were adopted to measure the pressures on three horizontal sections on the windward and leeward sides of the two sails. Several trims and apparent wind angles were tested. Moreover, in [37], the downwind condition was studied too. Pressure distributions were measured on an asymmetric spinnaker at three apparent wind angles and several sail trims.

3.1.3 Numerical Simulations As stated by Gentry [38] “in its simplest terms, CFD (Computational Fluid Dynamics) is the process of taking a physical flow problem, breaking it down into a suitable set of 26 CHAPTER 3. LITERATURE REVIEW

equations, and solving them on a digital computer”. In CFD simulations, the governing equations of fluid flow are solved numerically with the aid of computers rather than solving them analytically.

In the past few decades, numerical codes have become the most commonly used research tool for sails thanks to the increasing performance of hardware and software. In the 31st America’s Cup (2003) in New Zealand, only a few racing syndicates applied CFD programs as a common design tool. By the 32st America’s Cup (2007) in Spain, almost all the teams highlighted the importance of the computational research together with traditional experimental tests.

One of the advantages of CFD applications is that it can provide not only global quantities like sail forces and moments but also detailed flow information useful for the design of a sail system. It is believed that CFDs are cost-effective tools for the performance prediction of a sailing yacht; it can save a lot of efforts in experiments. But these advanced tools have two major drawbacks: the high computational time and the need of continuous validation with physical experiments.

Numerical codes can be divided in two types: potential (or inviscid) codes and viscous codes. At the same time, viscous codes are divided in: Direct Numerical Simulations, Large Eddy Simulations, Detached Eddy Simulations and Reynolds-Averaged Navier- Stokes Equations Simulations.

Direct Numerical Simulation (DNS) resolves the entire range of turbulent length scales. It is widely considered to be as accurate as a full-scale measurement. DNS is intractable for flows with complex geometries or flow configurations.

Large Eddy Simulation (LES) is a technique in which the smallest scales of the flow are removed through a filtering operation and their effect is modeled using subgrid scale models. This allows the largest and most important scales of the turbulence to be resolved, while greatly reducing the computational cost provoked by the smallest scales. This method requires greater computational resources than RANS methods, but is far cheaper than DNS.

Detached Eddy Simulation (DES) is a modification of a RANS model in which the model switches to a subgrid scale formulation in regions fine enough for LES calculations. Regions near solid boundaries and where the turbulent length scale is less than the maximum grid dimension are assigned the RANS mode of solution. As the tur- bulent length scale exceeds the grid dimension, the regions are solved using the LES mode.

Nowadays DNS cannot be used in sail aerodynamics, even when very large compu- tational resources are available. On the other hand, according to Viola et al [39], LES and DES techniques will commonly be used in sail aerodynamics but they are not widely 3.1. PERFORMANCE PREDICTION 27

used yet. There is a recent publication [40] in which a steady-state RANS approach is compared with a transient DES approach for a downwind condition. It is concluded that the ability of DES to capture the transient and separated flows could be outstanding in the accurate modeling and performance prediction of yachts for the near future.

Reynolds-Averaged Navier-Stokes Equations Simulations (RANS or RANSE) are the oldest approach to turbulence modeling. A set of the governing equations is solved, which introduces new apparent stresses known as Reynolds stresses. This adds a second order tensor of unknowns for which various models can provide different levels of closure. Among the numerical codes, this is the most common type for studying sail aerodynamics together with the potential codes. This method is explained in chapter 5.

On upwind sailing, the flow is mainly attached and therefore, potential codes can be used. On the other hand, on downwind sailing, the flow is separated and to properly predict the aerodynamic forces and the detachment of the flow, RANS codes are used. Nonetheless, if large computational resources are available, RANS codes are preferable even for upwind condition since they are more accurate. During the next paragraphs both potential and RANS codes are described as well as the state of the art in both methods.

Inviscid (or potential) Methods

Traditional inviscid methods, such as panel and Vortex Lattice Methods (VLM) assume that the flow is inviscid, irrotational and steady. The simulated flow does not include all the characteristics of flows that are encountered in the real world. For example, potential flow excludes turbulence, which is commonly encountered in nature. Moreover, potential flow cannot account for a boundary layer.

As mentioned before, potential codes can compute aerodynamic forces with a reason- able accuracy in upwind conditions. But this approach is computationally efficient until separation occurs; which is a far more common phenomenon than was previously believed.

The first numerical method for calculating lift and induced drag of sails was performed in 1968 by Milgram [41] [42] at the Massachusetts Institute of Technology. The method involved the representation of the sails by vortex lattices and flat wakes.

A development of traditional methods includes the influence of viscous flow by means of a coupling scheme between the potential method and an integral boundary layer equation. For example, in [43], a simple strip-based integral boundary layer is coupled to a potential code to give an estimation of the profile drag level on the sails. The code also includes a special treatment of leading-edge bubbles for sails without masts, and a simple treatment of the initial boundary layer development downstream of a mast. 28 CHAPTER 3. LITERATURE REVIEW

Next, some of the latest publications related to sail aerodynamic research which include potential codes are presented.

• The main goal of the work presented in [44] was the investigation of non linear behavior of sail rig under aerodynamic load. First, a potential code was developed to perform the viscous aerodynamic analysis of a multi-sail system. The code was based on 3D vortex lattice method coupled to 2D boundary layer solution. The aerodynamic problem was faced using vortex rings. The integral boundary layer equations, including the separation bubble model, were used to evaluate viscous effects (including mast effect) on the inviscid pressure distribution. Then the potential code was coupled to a finite element code in order to perform the structural analysis. In the same way, [45] coupled a vortex lattice model to a structural nonlinear finite element model to perform an aeroelastic analysis of sails.

• In [46], a method for predicting the flying shape and performance of yacht sails in upwind conditions is presented. The method includes an advanced vortex lattice method for sails. Then, a coupled inverse boundary layer analysis is applied on all surfaces including both sides of each sail membrane; this computes the skin-friction drag and the source displacement effects of the boundary layers and wakes, including bubble and leeward side “trailing-edge” type separations.

• In [32] a database of full-scale three-dimensional sail shapes is presented with the aerodynamic coefficients for the upwind condition of International Measurement System (IMS) type sails. Three-dimensional shape data were used for the input of numerical calculations and the results are compared with the measured sail perfor- mance. The sail shapes and performance were measured using sail dynamometer boat Fujin. Numerical calculations were run with a RANS code and a Vortex Lattice Method code.

• In [28] modern upwind sails were built at 1/15th scale and tested in a wind tunnel. The paper aims to provide a benchmark set of sail pressure distributions for the validation of numerical codes. To verify the capability of the present database to provide suitable benchmarks for numerical codes, all the test conditions were modeled with a numerical code based on the Vortex Lattice Method (VLM). The code has been based on the work of Werner, 2001 [47].

RANS Codes

This is a numerical model which describes the dynamic of fluids around bodies based on the resolution of the Reynolds-Averaged Navier-Stokes (RANS) equations. 3.1. PERFORMANCE PREDICTION 29

These codes allow for extensive flow visualization and quantitative results from complex realistic scenarios including separation. The use of RANS provides a powerful tool when analyzing, for example, sail and mast interaction as explained in chapter 6.

An important part of RANS codes is the selection of the turbulence model. This can influence the results obtained quite considerably but it is necessary to provide the closure of the set of equations. As mentioned before, more information related to RANS codes and turbulence models is included in chapter 5.

RANS solvers saw their first practical application to upwind and downwind sail design during the 29th America’s Cup (1995). Since then, several applications of RANS have been made to the study of sails. In the next list, the most relevant publications which include RANS simulations applied to sail aerodynamic investigations are presented.

• Hedges et al. 1996 [48]. In 1993, Hedges reported in her M.E. thesis the first downwind RANS application. She utilized a finite-volume RANS solver named CFDS-FLOW3D as in this publication. Here, the solver was used to model the flow around a spinnaker/mainsail combination. The sail shapes used were those designed by North Sails NZ Ltd for the Whithbread 60 yacht Winston. The sails were modelled in a uniform flow at apparent wind angles from 70◦ to 180◦ at intervals of 10◦.

• Caponneto et al. 1999 [49]. The numerical simulations conducted for the Swiss Team preparing the 30th America’s Cup are described. The three-dimensional geometries of both upwind and downwind configurations were simulated using the RANS commercial software FLUENT/UNS. Tests of three million cells took 5 hours to converge on 64 processors of the Silicon Graphics Origin 2000. Quantitative results are not included in the article due to the need of secrecy in America’s Cup teams.

• Lasher 1999 [50]. The results of computations for two-dimensional blocked flow normal to a flat plate are presented. The basis of RANS is reviewed, and both quasi-steady and transient computations described.

• Jones et al. 2001 [51]. It is presented the RANS code used for all the Amer- icaOne design simulations, preparing the 30th America’s Cup. The code is named FANS (Finite-Analytic NAvier-Stokes). It is an unsteady, incompressible, three-dimensional RANS solver with extensive validation on a wide range of high-Reynolds number flows. 30 CHAPTER 3. LITERATURE REVIEW

• Collie 2001-2006

Collie et al. 2001 [52]. This document looks at various modern turbulence models and considers their suitability for modeling sail flows. Two-dimensional sections of downwind sails were investigated. The intention of the research was to find a model suitable to solving sail flows, while using the minimum computational resources. The results showed that some turbulence models provide reasonable levels of accuracy for predicting force coefficients, but none of the models fully capture separation, reattachment and reformation of the boundary layer.

Collie et al. 2002a [53]. The flow past upwind yacht sails was simulated using the commercial RANS software FLUENT. Two-dimensional horizontal cross section of a genoa and mainsail combination was reproduced at three apparent wind angles. The meshes had around two million cells. Special atention was paid to the turbulence models.

Collie et al. 2002b [54]. In this publication, turbulence models were also studied but in this case, for downwind configuration and using the commercial code CFX5. The results were validated with wind tunnel experiments carried out at the Yacht Research Unit (University of Auckland). Here again, the simulations were limited to two-dimensional analysis.

Collie 2006 [55] and Collie et al. 2006 [56]. The practical application of RANS simulations to downwind sail design is investigated. Simulations were again per- formed with the commercial code CFX5. The research focuses on the performance of the SST and K-Omega turbulence models which were judged to be the most appropriate turbulence models for downwind sail flows.

• Richter et al. 2003 [57]. This is known as the first downwind RANS computation with tetrahedras. This work also presented an innovative aeroelastic coupling between the RANS code FLUENT and the North Sails’ finite element code MemBrain but no experimental comparison was presented.

• Chapin et al. 2005 [58] and Chapin et al. 2006 [59]. In [58] it is presented the preliminary study of the complex and largely unknown Yves Parlier Hydraplaneur double rig. Two and three-dimensional RANS simulations were conducted using the commercial code FLUENT6. These include two wing masts, two mainsails, and eventually arms of the boat. The finest mesh for upwind conditions contained around 2 million cells. 3.1. PERFORMANCE PREDICTION 31

The second publication, [59], is the enhancement of the first work. Here, an integrated approach with wind tunnel and RANS simulations is presented. This approach was developed to investigate in more details the double rig concept. This paper is focused on the interaction between multiple sails and what can be done to optimize their design.

• Clauss et al. 2005 [35]. As mentioned bejore, DYNA is a full-scale research vessel, a dynamometer boat. It is equipped with a measuring system capable of capturing the flying shape of the sails. This article presents the CFD analysis that was performed on real flying shapes using the commercial RANS code ANSYS-CFX. Both two and three dimensional studies were performed. Good agreement was found between RANS results and full-scale measurement.

• Yoo and Kim 2006 [60]. In this paper the three-dimensional flow around a jib-mast-main sail configuration is investigated using the RANS code WAVIS. This software was developed at KRISO/KORDI. Lift, drag and thrust forces are calculated for various conditions of gap distance between the two sails and the center of effort of the sail system is obtained. Wind tunnel experiments are also carried out to measure aerodynamic forces acting on the sail system and to validate the computations.

• Ciortan et al. 2007 [61]. Airflow around upwind yacht sails with imposed final geometry is simulated using the commercial RANS code ANSYS-CFX. The simulations were reproduced on experimental tests carried out in a wind tunnel. Two configurations were considered: one, mast-main sail and the other, mast-jib- main sail. In the second case, the total number of elements was of about one million.

• Querard et al. 2007 [62]. The commercial RANS code ANSYS-CFX10 is used here to compare with wind-tunnel experiments of a ORMA60’ rig in upwind condition. Two mainsails of different tip chord length and a head sail are tested. The flying shapes are acquired by a digital camera to feed the numerical model with the same geometry that has been used in the experiments. The three-dimensional mesh used were made of around 2 million cells.

• Masuyama et al. 2007 [31] and 2009 [32]. A database of full-scale three-dimensional sail shapes are presented with the aerodynamic coefficients for the upwind condition of IMS type sails. The full-scale tests were performed at the sail dynamometer boat Fujin. Then, the measured geometries were simulated on two CFDs and the sail performance was compared. The calculation methods were a RANS code and a Vortex Lattice Method (inviscid code). The RANS 32 CHAPTER 3. LITERATURE REVIEW

code was developed by Yusuke Tahara (FLOWPACK version 2005). It is a multi-block method which is capable of predicting viscous flows and aerodynamic forces for complicated sail configurations for upwind as well as downwind conditions.

• Lasher et al. 2007 [63] and Lasher et al. 2008 [10]. In [63], RANS simulations are compared to experimental data for three-dimensional spinnakers in an atmospheric boundary layer. Three models for America’s Cup Class spinnakers were tested in a wind tunnel with a simulated atmospheric boundary layer. These experiments were reproduced using the commercial RANS solver FLUENT 6 with three different turbulence models. The results suggest that RANS codes can be used as a design tool for optimizing spinnaker shapes.

In [10] the numerical simulations of 12 spinnakers with six different turbulence models are described. The spinnakers had already been tested at a wind tunnel, consequently in this article, a comparison of numerical and experimental results is presented.

• Viola 2009 [64]. A RANS solver was applied to an America’s Cup Class yacht to investigate sailing performance in a downwind configuration. The code was the commercial software ANSYS-FLUENT 6. A mainsail with an asymmetrical spinnaker was tested at three apparent wind angles with four different turbulence models. Numerical results were compared to wind tunnel data. Moreover, a large investigation on the dependence of the solution on mesh size and topology is also included in this article. In particular, meshes up to 37 M elements were tested. Numerical results are in good agreement with wind tunnel data. The nu- merical/experimental ratios of the coefficients are less than 8% for both lift and drag.

• Paton et al. 2009 [65]. This paper presents the effects of interaction between the foresail and the mainsail on a sailing vessel. A RANS code provides the flow visualisation and quantitative analysis. The effect of the foresail sheeting angle upon a sailing rig’s performance is compared and discussed. Simulations were limited to two-dimensional geometries. The commercial RANS code ANSYS-CFX 10 and the SST turbulence model were used for all the simulations presented in this paper.

• Viola et al. 2011 [39] This article presents the comparison of results of full-scale tests, wind tunnel tests and numerical analysis. Pressure measurements were obtained from both full-scale tests and wind tunnel tests, in upwind and down- wind conditions. The upwind condition was modelled using an inviscid method, whilst the downwind condition using the RANS code CD-Adapco’s STAR-CCM+ 3.2. AEROELASTIC ANALYSIS 33

5.04.004. The flying shapes in the wind tunnel were detected using photogrammet- ric techniques, and then, the geometries were introduced into the CFD. Mesh sizes of 1.5 millios were used in the RANS code.

3.2 Aeroelastic Analysis

The flexible behavior of sails should be also investigated. Therefore, aeroelastic sim- ulations which can deal with large displacements are studied. There are mainly two methods to reproduce the elasticity of the sailcloth. One is based on a strings network model and the other one, on a flexible membrane model.

The model based on the strings network was developed by O. Le Maˆıtre et al. [66]. The sail is considered to be an ideally flexible structure, having the behav- ior of a network of stress unilateral strings: all the internal efforts are traction efforts. The strings network approximation is a simplified form of the nonlinear membrane model.

An example of the use of this model in sail aerodynamic is the paper of Maskew et al. [46], where Vortex Lattice Method is coupled with a strings network model. The aim of the investigation is predicting the flying shape and performance of yacht sails in upwind conditions.

The structural analysis of sails as flexible membranes started in the 1960s with a two-dimensional model. A special feature of the structural analysis of sails is that the geometric nonlinearities should be taken into account. However, since the strains remain small, constitutive laws for the material can be considered to be linear, with the result that the tension in the structure is a linear function of the local deformation [67].

This flexible membrane model was used in [68], where aeroelastic responses of three-dimensional flexible sails were investigated by means of numerical simulations. An incremental finite displacement theory using the Finite Element Method was implemented to describe the structural behavior of the sail. Deformations and stresses of the sail in a steady flow were calculated.

In [69] the model was also applied. This work describes the investigation to improve the performance of sails by using non-linear modeling, numerical experimentation and optimization methods. The sail is represented by a triangular structure made of composite materials modeled by an orthotropic membrane behavior. Under the wind pressure, the sail is submitted to large displacements and small strains. Initial pre-tension load which ensures that the surface is reasonably free of wrinkles is required.

Wrinkles are an important feature of the structural deformations. They are induced by the aerodynamic loading to relieve compression. The highly non-linear nature of the 34 CHAPTER 3. LITERATURE REVIEW

formation of these wrinkles makes the model more complex. In [70], the author details some techniques for improving accuracy in the computation of structural membranes. The paper describes the way that wrinkling interacts with the kinematics of the element grid. Results are presented demonstrating the effects of varying grids, with and without the modeling of wrinkling.

3.2.1 Fluid Structure Interaction (FSI) A thorough aeroelastic modeling is conducted coupling structural and aerodynamic computations. This codes are named FSI (Fluid Structure Interaction). This can be done by combining the stiffness, damping, mass and loading from both structure and aerodynamics into one system of equations. But usually, it is done by iterating between separate steady-state structural and aerodynamic codes. That is, forces from flow simulation are used to predict the deformed shape of the sail, while in turn the deformed shape is used to predict the flow forces. Both inviscid and viscous CFDs can be coupled.

In the next list, the latest publications which include FSI codes are presented.

• Shankaran et al. 2002 [71] and Jameson et al. 2003 [72]. The pressure loading obtained with a 3D unstructured incompressible Euler solver is transferred to the structural package NASTRAN, which computes the deflected shape of the sail. This methodology is applied to improve the flying shape and forces on America’s Cup sails.

• Richter et al. 2003 [57]. It studies the flow around a spinnaker by coupling a RANS solver with a membrane programe.

• Ranzenbach et al. 2004 [73] and 2005 [74]. A Finite Element Analysis (FEA) of the sail structure and a Computational Fluid Dynamics (CFD) model of the aerodynamic field are combined. They are iteratively solved to compute the actual flying shape, the stress-strain behavior of the sail membrane, the integrated aerodynamic forces and the loads on sheets, halyards, etc. The aerodynamic code is a potential program named S2KV which was originally developed at the MIT. It is based upon a vortex lattice method formulation. The FEA in this study is a modified version of commercially available software.

• Paton et al. 2008 [75]. This paper looks at the creation of a FSI solution and its application to the accurate modelling of racing yacht sails. In the present scheme the codes RELAX and ANSYS-CFX are coupled together. RELAX is a structural code based on a flexible membrane model developed by Peter Heppel Associates. 3.3. OPTIMIZATION APPROACHES 35

As mentioned before, the code ANSYS-CFX is a RANS solver.

• Renzsch et al. 2008 [23] and Renzsch et al. 2010 [76]. The FSI described in these publications couple a RANS solver for flow analysis and a Finite Element Method for the structural investigation of the sail modeled as a membrane. The aerodynamic code is the again the commercial flow solver ANSYS-CFX 12.0. The results obtained from the FSI are validated with twisted flow wind tunnel tests.

• Malpede et al. 2008 [45]. This paper presents a method to predict external forces and improve the performance and quality of custom-made fiber-membrane sails by tailoring the material that it is made of in a timely, cost-effective, flexible, and quality manner. The method performs the aeroelastic analysis through the interaction of a structural nonlinear finite element model with a vortex lattice aerodynamic model. The structural model considers large displacements and small strains and takes into account a comprehensive set of structural components like the sail rig, the sail with isotropic/anisotropic material models and sail battens.

3.3 Optimization approaches

The aim of any engineering project is to achieve the optimum performance for a set of restrictions. Two main decisions should be made before a systematic optimization technique is developed. First, the control parameters which are to be optimized must be chosen; for example, the sail geometry. The second decision is the election of the objective (or merit) function which defines the aspect of the performance to be mini- mized or maximized; for example, maximize the drive force for a constant heeling moment.

Several strategies can be used to optimize the sail performance varying in degrees of robustness and computational intensity. Here, four groups are presented: parametric studies, gradient-based cost function minimization, adjoint optimization approach and evolutionary algorithms.

a) Parametric approaches

These are the easiest methods to implement since they manually adjust the control parameters in a trial-and-error fashion. In this case, the parameters are simple such as camber, draft or sheeting angle.

b) Gradient-based cost function minimization

In this approach, a cost (or merit) function is minimized with respect to one or more control parameters. The iterative procedure requires the calculation of the sensitivity 36 CHAPTER 3. LITERATURE REVIEW

derivatives (gradient) of the cost function with respect to each of the control parameters in each iteration step. These derivatives determine the direction of improvement.

The calculation of the gradients is the critical point of these methods. There are a variety of approaches to compute the gradient information but the finite-difference method is the most used technique. However, it is not only computational expensive but it can produce inaccurate gradient approximations unless carefully monitored.

A gradient-based cost function minimisation approach is implemented in [71]. In this case, the method combines the commercial CFD package FLUENT with a gradient-based approach. The sheeting angles for the rig of a three masted clipper yacht have been optimized for two merit functions: the ratio of the driving to heeling force coefficient and the reciprocal of the driving force coefficient.

c) Adjoint optimization methods or control theory approaches

The third optimization group is the adjoint optimization approach. In this method, the sensitive derivatives (gradients) are obtained via the solution of the adjoint of the equations describing the fluid flow. This control theory approach is much more efficient because the expense incurred in the calculation of the gradient is effectively independent of the number of design variables. It has computational cost advantages when compared to any of these methods. The cost of the adjoint solve is comparable to the cost of the flow solution.

There are two main categories of control theory methods depending on the way the adjoint fiel is solved: continuous and discrete. In the discrete approach, the discretized flow equations are assembled to obtain the gradient, therefore different adjoint systems need to be formulated for different discretizations. In the continuos approach, the original flow equations in partial difference form is used to estimate the gradients eliminating the need to reformulate the adjoint equations. Some studies concluded that there is no particular benefit in using either one of these approaches.

Adjoint optimization methods were developed in [67] and applied to sail aerodynamic studies. They were used to induce changes to the camber distribution of the mainsail. The objective was to reduce the leading edge suction peaks that were considered to be detrimental to the growth of the boundary layer. The design process resulted in an camber distribution that allowed smooth entry of the flow through the leading edge of the main sail thereby, reducing the leading edge suction peaks.

d) Evolutionary algorithms

Evolutionary algorithms imitate the process of natural evolution. They use a population (set of solutions) to find the optimal designs. 3.3. OPTIMIZATION APPROACHES 37

This optimization technique is clearly explained in [77]: A population of individual parameter sets is generated at random, and the objective function evaluated for each parameter set. The values obtained are treated as “fitnesses” and are then used as a basis on which the parents for the next generation may be selected. “Breeding” then occurs by an operation known as “crossover”. In order to allow the populations to explore the whole solution space, the possibility of “mutation” is introduced. The objective function is then evaluated for the new generation of individuals created in this manner, and the process is repeated, until convergence is achieved.

One particular advantage of this technique is that they avoid local extrema and numerical noise in aerodynamic optimization. Moreover, these algorithms are essentially parallel rather than sequential in operation; therefore if a number of solutions with similar fitnesses are far apart in the solution space the algorithm will usually find many or all of them.

They have some drawbacks. The population normally must be large, requiring many flow calculations and thus, a large CPU requirements. Also, the technique is not based in physics and therefore it may be unattractive for engineers.

There have been published articles which describe the implementation of genetic algorithms to optimize sail aerodynamics such as [77], [78], [59], [79] and [80]. 38 CHAPTER 3. LITERATURE REVIEW Chapter 4

WIND TUNNEL TESTS

A wind tunnel is a research facility designed for studying the aerodynamic interaction between a flow and an object. It can be analyzed the effect of a fluid moving around the object (buildings, bridges...) or, on the other hand, an object moving through the still fluid (airplanes, boats, cars...).

The core of the facility is a controlled air-stream which is flown through a “tube” where the aerodynamic behavior of an object is reproduced. Inside the tube, the scaled model is placed in the test section where properties such as pressure, velocity or forces can be measured. Then, the measurements are extrapolated to obtain the full-scale performance of the object.

In the previous chapter the state of the art on wind tunnel testing of sails has been presented. Hereafter, the history of these facilities, types of wind tunnels, operation, design and instrumentation will be described. More information regarding wind tunnels can be found in [81], [82], [83] and [84].

4.1 Nomenclature

µ Dynamic viscosity

ρ Density a Sound speed k Constant

L Characteristic length

Ma Mach number p Pressure or stagnation pressure

39 40 CHAPTER 4. WIND TUNNEL TESTS

p0 Static pressure

Re Reynolds number

V Speed of the flow full Referred to full-scale mod Referred to model-scale

4.2 History

As early as in the fifteenth century, Leonardo da Vinci designed airplanes based on bird watching. The first attempts by inventors to design flying machines used moving wings powered by humans. But in the beginning of the seventeenth century, they realized that the bird flight did not provide the information they needed. Researchers required a mechanism which allowed them study the flow around the airplanes and understand the physics involved.

It was soon accepted that aerodynamic forces depend on the relative velocity between the fluid and the model. Therefore, researchers thought of either move the model or move the air. Firstly, the atmospheric wind was used as the moving air, but the rapidly changeable behavior of natural winds made the researchers opt to develop the second method. The simplest device was to place the model on a whirling arm which was powered by pulleys and weights. In 1746, Benjamin Robins (1707-1751) employed the first whirling arm (see figure 4.1). It was 1.22m long and spun by a weight hanging on a pulley. He mounted different shaped objects and found out that shape and orientation affect the drag. This conclusion revealed that the aerodynamic theory was not complete at that time.

Sir George Cayley (1773-1857) built a whirling arm which was longer (1.5m) and faster (5m/s) than Robin’s device. He measured the drag and lift of airfoils. Prior to his investigations, airplane’s wings moved like birds trying to both propel and lift. Cayle was the first to propose the new design philosophy: wings should generate lift and something else should provide thrust.

Between 1866 and 1889, Otto Lilienthal (1848-1896) built several whirling arms. He focused his research on lifting surfaces. At the same time, Samuel Langley (1834-1906) built a large whirling arm which was 18m long and reached speeds of 160km/h. The device was installed outdoor and this led to large errors in the measurements due to the environmental disturbances and the self-induced wind around the arm at such high speeds.

The whirling arm was the first serious attempt in aerodynamic facilities and it provided a great amount of data through the end of the nineteenth century. However, the 4.2. HISTORY 41

Figure 4.1: Whirling arm

results were not reliable since the device had some drawbacks. On one hand, centrifugal forces appear and the model was always flying in its own wake. The true wind speed and angle were unknown as well as the effect of the wake in the performance. On the other hand, it was challenging to design an appropriate set-up to measure the performance of a model which was continuously rotating.

Consequently, researches opt to developed the second method: instead of moving the model through still air, move the air past a stationary model. The wind tunnel was the answer to their problems. In 1971, Francis Herbert Wenham (1824-1908) invented, designed and operated the first enclosed wind tunnel. It was 3.7m long and 45.7cm square. A steam-powered fan flew the air through a duct to the test section where the model was mounted. The maximum air speed was 65km/h. Wenham tested several shapes in the wind tunnel and measured the lift and drag forces. He studied concepts such as aspect ratio, angle of incidence or lift-to-drag ratio. Sir Hiram Maxim (1834-1906) also built a wind tunnel when he found out the drawbacks of his whirling arms. His tunnel was slightly larger than Wenham’s facility. In this case, he installed two fans that could move the air up to 80km/h. He also studied lifting airfoils and was the first to study the interference concept.

In 1893, William Charles Kernot (1845-1909) was the first to study aerodynamic forces on buildings in his open-circuit open-test section wind tunnel. A year later, Johan Irminger used the flow in a flue of a chimney to study wind pressures on some basic shapes.

Contemporary to the aforementioned researchers, Osborne Reynolds (1842-1912) demonstrated that the flow around a model would be equivalent to the full-scale object if a certain parameter was the same in both scales. Nowadays, this parameter is known as Reynolds Number. 42 CHAPTER 4. WIND TUNNEL TESTS

In 1901, Wilbur (1867-1912) and Orville (1871-1948) Wright built a wind tunnel to study the effect of airflow over various shapes while developing their Wright Flyer. They first built a small tunnel but the results were so encouraging that they built a larger tunnel. Here, they obtained the critical data they needed for their first manned and powered airplane.

During the first decades of the twentieth century, especially during and between the two World Wars, wind tunnels for aeronautical applications developed rapidly. As an example of this achievements, Germans used large natural caves as wind tunnels and tested in high speed regimes which gave a boost to their aeronautical industry. By the end of the Second World War Germany had, at least, three different supersonic wind tunnels.

Lately, the aeronautical and civil engineering has gained importance which has extraordinary increased the necessity of wind tunnels. But now, there is broad diversity of vehicles and objects to study. This has led to develop different types of wind tunnels depending on the purpose. It can be stated that wind tunnels have turned into the core of the experimental facilities in aerodynamic research.

4.3 Types

There is a wide variety of wind tunnels and they can be classified according to the speed range, arrangement or purpose.

4.3.1 Based on the airflow speed Depending on the air-stream speed, wind tunnels can be: subsonic (0≤Ma<0.7), transonic (0.7≤Ma<1.2), supersonic (1.2≤Ma<5) or hypersonic (Ma≥5). Where Ma is the Match number which is defined in the next section. Hereafter, if the type is not explicitly mentioned, it is referred to subsonic wind tunnel which is the most common and versatile type.

4.3.2 Based on the return circuit Depending on the arrangement of the return duct, the wind tunnels can be open- or close-circuit tunnels.

In Open-circuit tunnels (figure 4.2, page 48) the air returns to the inlet through the room where the tunnel is located. Also, the air can be obtained and discharged directly from and to the atmosphere. These are the main characteristics of this type of 4.3. TYPES 43

wind tunnel: low manufacturing costs; low energy efficiency; noisy; if directly connected to the atmosphere, they rely on weather conditions; appropriate to test combustion engines; flow visualization test with smoke can be easily conducted; and, if the wind tunnel/room size ratio is large, this arrangement may require excessive screening at the inlet to get high-quality flown, thus, reducing even more the efficiency.

Close-circuit tunnels (figure 4.3, page 49) have an specific and close return duct. It can be a single return or more than one ducts can be connected. The main characteristics of this type are: high manufacturing costs; more efficient because there is no discharge of kinetic energy at exit, although there are high frictional losses; not as noisy as the open-circuit tunnel; better control of the flow parameters; the air should be periodically renewed; for long testing periods, the air should be cooled; and, more than one test section with different characteristics can be incorporated.

4.3.3 Based on the test section The subsonic wind tunnels, regardless of the return circuit, can have an open- or close- test section.

Open-section (figure 4.3). There are no walls on the test section, apart from the cover of the balance. With this arrangement, testing ground devices such as buildings, bridges, ground-planes, etc., is more difficult. Moreover, if the size of the tunnel is large, it can be also difficult changing the model.

The experimental tests explained in chapter 8 have been conducted in an open-circuit open-section wind tunnel at the University of Auckland.

Close-section (figure 4.2). Most tunnels have a closed section, which means that the test section has solid walls. Specifically, rectangular shaped close-section is the most common arrangement since it facilitates the handling of the model. The experimental tests explained in chapters 7 and 9 have been conducted in two different open-circuit close-section wind tunnels.

4.3.4 Special-purpose tunnels For many years, different types of wind tunnels have been built for specific purpose. Some of them have already been dismantled or adapted. Now, there is a tendency to use a general purpose tunnel and modify the arrangement conveniently. The following classification is partially based on [82] and includes most of the wind tunnels that have been built, even if they are not in operation currently. 44 CHAPTER 4. WIND TUNNEL TESTS

Atmospheric Boundary Layer tunnels (Environmental Tunnels). These tunnels are designed to simulate the earth’s natural boundary layer. These tunnels are used to determine wind loads on buildings, boats, study air pollution or soil erosion. The experimental tests explained in chapter 7 were conducted by the author at the Boundary Layer Wind Tunnel of the Universidad de Granada (Spain).

It is always desirable to test sails in this type of wind tunnels since it is possible to reproduce the wind profile and in some facilities, the wind twist. It has been demonstrated that both aspects (profile and twist) have a remarkable effect in sail performance. The wind tunnel which can reproduce the twist of the flow is named Twisted Flow Wind Tunnel (TFWT). As mentioned before, the concept of the TFWT was originally developed by Flay et al.[21] for the New Zealand America’s Cup Challenge in 1995.

Automobile tunnels. There are two types of automobile tunnels: external and climatic wind tunnels. In external flow tunnels the aerodynamic flow around the vehicle is studied. The aim of these tests is to evaluate the automobile’s performance, stability and try to reduce the power required to move the vehicle at a given speed. In many automobile external flow wind tunnels the model is at full scale. In these tests, the interaction between the automobile and the road is very important. It should be either taken into account in the extrapolation or reproduced the relative movement in the wind tunnel, as it is done nowadays.

In climatic wind tunnels it can be studied: the drive system, air conditioners, door and window seals...These facilities have the capability to generate rain, heat and cool the flow, to create radiation conditions and to have the model running for long periods.

High Reynolds Number tunnels. These are pressurized tunnels to reproduce high Reynolds numbers. These tunnels usually have an annular close-return duct which is the arrangement with requires the least amount of steel.

Free-flight tunnels. The dynamic behavior of airplanes is studied in these tunnels. The model flies in the test section under the influence of gravity. The tunnels have an open-return close-section arrangement. Test are conducted at very low speeds.

Spin tunnels (Vertical Wind Tunnels). These tunnels are vertical in which the air flows upwards, sucked by a fan near the top. In these tunnels, the recovery from a spin is studied. (Spin: “a maneuver in which an airplane descends in a vertical direction along a helical path of large pitch and small radius at an angle of attack greater than the critical angle, dangerous when not done intentionally or under control”, [85]).

Stability tunnels. These tunnels had two test sections were the airplane’s stability was studied. In one of them, the swirl in the upstream was created by rotating 4.4. OPERATION AND DESIGN 45

vanes. In the other test section, the turning flight was reproduced. Nowadays, they are not built anymore since similar test can be conducted in general purpose wind tunnels.

Propeller tunnels. These tunnels have an open round cross test section where propellers are studied.

Propulsion tunnels. These tunnels are used to study aircraft engines and therefore, the flight velocity, the atmospheric pressure and the temperature are simulated. These tunnels can have an open circuit or close circuit, but in this case, the air must be removed from the tunnel and renewed continuously. It is also required low density and a refrigeration system.

Icing tunnels. It is a conventional low-speed closed return tunnel with a refrigeration system which reduces the air temperature to -40◦C and a water drop generation system.

Low-turbulence tunnels. The main parts of these tunnels are the honeycombs and screens which damp out the turbulence. These tunnel also have a wide angle diffuser before the settling area and a large contraction ratio to reduce turbulence.

V/STOL wind tunnels. Obviously, in these tunnels the V/STOL (“vertical short takeoff and landing”, [86]) is studied. These tunnels have large test sections so that the wake produced by the powered lift systems can develop. The velocity in the transition (takeoff or landing) is low which facilitates the simulation.

Two-dimensional tunnels. They are used for testing airfoil sections. They can be open circuit or closed return types. Also, they are high Reynolds number tunnels and low-turbulence type.

Smoke tunnels. They are used primarily for flow visualization. Usually these tunnels are of the open-return, low-turbulence type.

Aeroacoustic wind tunnels. In these tunnels it is studied the flow-generated noise from submarines, ships, appendages and their wake distributions.

4.4 Operation and design

This section is focused on subsonic tunnels and specially, the atmospheric boundary layer wind tunnels. 46 CHAPTER 4. WIND TUNNEL TESTS

4.4.1 Operation In order to reproduce the aerodynamic performance of an object in a wind tunnel, obviously, there should be identical geometric similarity. But not only. It should be taken into account the kinematic, dynamic and manufacturing similarities too. These can be achieved by making equal certain dimensionless parameters related to the flow, fluid, geometry and material in both scales. The most important dimensionless parameters in aeronautics are the Reynolds number (Re) and the Math number (Ma). When testing sailing boats in a wind tunnel there are also other parameters that could be important, such as the Froude number, the membrane mass ratio, membrane elasticity ratio, membrane fold height ratio and the weight/pressure ratio.

The Match number (eq. 4.1) is a relation between the inertial forces and the compressibility of the fluid. In the equation, V is the flow speed and a is the sound speed for a given conditions of pressure and temperature. This parameter is very important when the variation of density due to dynamic pressures is relevant. This takes place in high speed flows. Apart from some special high speed aeronautic vehicles, the most common reproduced flows are in a low speed range and in this case, the compressibility of the fluid is negligible.

V Ma = (4.1) a The Reynolds number (eq. 4.2) relates the inertial forces and the friction forces. In the equation, V is the flow speed, ρ is the density of the fluid, L is the characteristic length of the object and µ is the dynamic viscosity. If λ is the scale of the model then Lfull = λLmod. It is clear that if the Reynolds numbers are equal both in model and full scale, Vmod = λVfull. This means that if the fluid in the wind tunnel is the same as the one in full scale, it is impossible to match both parameters Re and Ma.

V ρL Re = (4.2) µ There are two ways of matching both parameters simultaneously: first, simulate with the same fluid, scale and speed (full-scale tests). The second way, is modifying the fluid which is very expensive. Therefore, the usual procedure is selecting the most important parameter depending on the physical phenomena involved in the case of study. It is analyzed whether the nature of the simulation is compressible or not and then, it is tried to reproduce the parameter that influences the most. In the case of testing aircrafts, the wind tunnels should be large and the speed high, since both parameters are important. This makes these tunnels very expensive and difficult to built.

In most cases, the type of flow in study is determined by the critical Reynolds number which defines the transition of the boundary layer from laminar to turbulent. This point 4.4. OPERATION AND DESIGN 47

depends on the turbulence of the inflow, the shape of the object and the roughness of the surfaces in contact with the fluid. In most of the aeronautic and civil aerodynamic tests, the normal procedure is defining a flow speed as high as possible. That is, increase the Reynolds number above 105-106 which is the critical Reynolds number. In this way, even if the speed is not properly scaled, the laminar/turbulent scenario it would reproduced. It is accepted that the performance of the full scale object and the model would be equivalent if the regime is the same.

It is noteworthy that the scale of the model it is not only defined by the mentioned parameters because the size of the wind tunnel should be taken into account. The frontal area of the model is limited since the model can not produce a blockage of the flow. A typical blockage ratio (frontal area of the model/test section cross area) is 0.1. It is assumed that above this value, the flow around the model is affected by the walls of the test section and some corrections must be calculated after the tests.

Testing sails

In practice, it is impossible to match both Reynolds and Mach numbers. Mach number is not so critical due to the slow speed flow when sailing. On the other hand, the high speed required for matching the Reynolds number equivalence would also make difficult to manufacture a model which met demands on strength and deflection. A research was conducted by Hawkins [87] to investigate the influence of not matching the Reynolds number. It was shown that the effect is not of first order significant.

As mentioned before, when testing sailing boats in a wind tunnel there are also other parameters that could be important, such as the Froude number, the membrane mass ratio, membrane elasticity ratio, membrane fold height ratio and the weight-pressure ratio, as described in [88].

Froude number. This dimensionless number is very important when doing hy- drodynamic tests. For wind tunnel experiments, is only of importance when dynamic behaviors are being measured, which is not very common.

Membrane mass ratio. This ratio is related to inertial forces. Since wind tunnel tests are conducted under static loads, this ratio is not important. It is only taken into account when dynamic effects are considered.

Membrane elasticity ratio. It describes the aeroelastic effects of the sailcloth. For most testing conditions sail stretch is small and a comparable membrane elasticity ratio can be achieved by selecting the material properties of the model sail to reflect the changes in flow speed between the wind tunnel and full-scale, [88].

Membrane fold height ratio. It provides an estimation of the sailcloth stiffness. 48 CHAPTER 4. WIND TUNNEL TESTS

Figure 4.2: Close-section, open-circuit tunnel

The feasibility of the sailcloth of the model should permit the sail to adopt the scaled flying shape. The fold height ratio does not need to be matched exactly to the full-scale sail if the model sail is flexible enough to maintain its natural shape.

Weight/pressure ratio. It relates the gravitational force to the pressure loading on the sail. It has been demonstrated that as long as it is within certain values, does not need to be matched.

Obviously, the closer these ratios are to real values, the better the results will be. However, since wind tunnels test are usually conducted with a comparative purpose, matching these ratios is not strictly necessary. It can be assured that when a model behaves better in the wind tunnel it will also do better at full-scale. But in fact, it is difficult to exactly know how much will be the improvement.

4.4.2 Design The description of a multipurpose wind tunnel is presented in this section with the aid of figures 4.2 and 4.3.

Inlet (settling area) (I). This is a large section, comparing to the test section, where the honeycomb (or flow straightener) and the screens are located. The aim of this settling is to obtain a smooth air-stream, both in terms of flow direction and intensity. These stabilization elements are located in this area because the speed is lower here and therefore, the losses will be smaller (the losses are proportional to the velocity squared). 4.4. OPERATION AND DESIGN 49

Figure 4.3: Open-section, close circuit tunnel

Contraction (C). This part is located after the settling area and the aim of this section is to allow the flow reach the test section with a uniform velocity profile and low turbulence. It also increases the speed of the inflow by reducing the cross section.

Boundary layer development duct. By using a suitable combination of different types of roughness elements (blocks, planks or corrugated metal), the desired velocity and turbulence profiles can be created. This part is located between the contraction and the test section and it is usually ten times longer than the transversal length of the test section. In figure 8.4 an example of a boundary layer development duct is illustrated.

Test section (T). The characteristics of the test section are defined by the speed of air. Usually, for closed-test sections, the cross section is squared or rectangular. Even though over the years, depending on the utility of the wind tunnel, many shapes have been used for test sections, including round, elliptical, hexagonal, octagonal... The length of the test section is usually small. For example, in aeronautical wind tunnels, the length is only two times the largest dimension of the cross section. In boundary layer wind tunnels, the test section could be small but it must be located after the aforementioned boundary layer development duct. If not, the test section should be longer than usual.

Another important detail when designing a test section is the lighting. The test section should have direct light or sufficient windows to view the model during the tests. It is also important because there should be enough light when handling the model and taking pictures. 50 CHAPTER 4. WIND TUNNEL TESTS

Adaptation diffuser (A). After the test section and before the fans, the adaptation diffuser is located. The main purpose of the diffuser is adapting the cross section of the test section and the place where the fan is located, since the shapes are usually different. In this duct the speed of the flow is reduced in order not to loss energy. The principal constrain is the divergence angle that should be small to avoid the detachment of the flow.

Fan (F). It can be installed one or more fans. Obviously, the purpose of the fan is to generate the air flow. There are two arrangements depending on the location of the fan in relation to the test section. Both arrangements have been used successfully in wind engineering applications. When the fan is downstream, the air is sucked and the flow over the model is “clean”. The drawback is that there is a pressure drop across the walls and the flow, that can be a problem. In the other arrangement, the test section is downstream the fan and it is called the “blowing arrangement”. The drawback of this situation is the turbulence generated by the fan. Therefore, in this ar- rangement it is essential to properly design the honeycomb and screens of the settling area.

In picture 4.2 the air is sucked (first arrangement) whereas in picture 4.3 the air is blown (second arrangement).

Return (or second) diffuser (E). The aim of this part is decelerate the air-stream after the fan. If the air is discharged to the room after this diffuser (depending on the wind tunnel arrangement), low speeds are better to increase the pressure and improve the wind tunnel performance. If the second diffuser is after the fan and the air stream continues to the test section, it must take into account the flow separation and the nonuniform velocity distributions in this zone.

Return (R). In close-circuit wind tunnels there is a return duct with corners. To avoid losses and to maintain a relatively smooth flow through the circuit, the corner areas are equipped with vanes. Closely-spaced vertical and horizontal vanes are used to straighten out the turbulent airflow before reaching the model in the test section.

4.5 Measurements and Instrumentation

The most important measurements in a wind tunnel test are: velocity, pressure, forces, flow path and shape. The information of this section has been partially obtained from [81] and [82].

Velocity

Velocity is always measured during a wind tunnel test because, at least, the testing speed should be measured. The simplest way to measure pressure is using a Pitot tube. This simple instrument is based on the Bernoulli’s principle which relates the static 4.5. MEASUREMENTS AND INSTRUMENTATION 51

Figure 4.4: Pitot tube

pressure and the dynamic pressure along an streamline of a potential, incompressible and stationary flow: p + 1/2ρV 2 = k, where p is pressure, ρ is the density of the fluid, V is the flow speed and k is a constant. Therefore, by measuring two pressures along an streamline and the temperature of the fluid, the velocity is simply obtained by: p V = 2(p − p0)/ρ. In this case, p is the stagnation pressure and p0 is the static pressure.

The simple Pitot tube is indeed formed by two concentric tubes (see figure 4.4). The stagnation pressure is measured at the inner tube, which has a hole in the end and pointing upstream. The static pressure is measured at the outer tube which has a hole, far from the end and perpendicular to the stream. A manometer connects both tubes and measures the difference (p − p0).

According to the Bernoulli’s principle, Pitot tubes can only be used in those regions of the fluid in which the viscous or turbulent effects are negligible. In these regions the following devices can be used.

Hot wires and hot films are very accurate devices which allow measuring fast turbulent fluctuations of the velocity. Unlike other instruments, these can measure very small velocities but even in this case, the major drawback of these devices is their fragility.

The device consist of a conductive wire which is heated by an electric current. The wire is then cooled down by the flow in study. The temperature of the wire depends on the electric resistance. Therefore, if the temperature is kept constant, the electric power required to maintain it constant provides a measurement of the flow around the wire and 52 CHAPTER 4. WIND TUNNEL TESTS

consequently a measurement of the speed.

Laser Doppler Velocimeters (LDV) is a non intrusive technique to measure the velocity field. It is the most accurate technique but also, the most expensive one. LDV can be used not only to measure the velocity field but measure turbulence, vortex shedding, circulation to obtain lift, momentum losses in wakes to obtain drag, etc. It can be also used as a flow-visualization method but in this case, the precision is lower.

The LDV is a tracer method. The laser beam is split in two, which are focused to cross at the point of interest where there will be a wave interference. Then, a fringe pattern at the beam intersection is formed. A receiver collects the light from the traces crossing the fringes. The output of the measurement is a frequency that is converted to a voltage in a computer with the adequate size and speed for LDV data acquisition. Then, the voltage is converted to velocity.

Sometimes, the natural dust provides the traces needed but generally, a seed generator is needed. These seeds need an specific size and density in the flow to get adequate data and ensure that tracers are traveling at local instantaneous velocity.

The Particle Image Velocimeter (PIV) is another tracer method. The flow is seeded with tracers, then, several pictures are taken sequentially with a known interval among them. The position of the tracer in each picture is calculated and since the time between two pictures is known, the velocity field in the plane of the image is determined. Good results are obtained in small low-speed tunnels but it is still complicated to apply this technique at high speeds. If the wind tunnel has an open return arrangement, a drawback of this method is that the tracers are lost in the room where the tunnel is located and new traces must be continuously added.

Pressure

Apart from the Pitot tubes, there are several ways to measure the pressure distribu- tion over a model. The manometer is a fundamental instrument available for pressure measurements. This device determines the difference between a reference pressure (such the atmospheric pressure) and the pressure at the point in study. Manometers are often used for calibrating and checking other instruments since it is very accurate and precise.

A pressure transducer is a device that provides an electrical response to a pressure or change in pressure. These transducers are very common in wind tunnel tests and they are used to measure both flow conditions and pressures on the model. The most generally used pressure transducer is the diaphragm type transducer. In this instrument there is a thin sheet of material that deforms as the pressure across changes. By measuring the deformation, the pressure that has been applied can be determined. 4.5. MEASUREMENTS AND INSTRUMENTATION 53

Another device to measure pressure is the piezoelectric transducer. This trans- ducer has a piezoelectric element inside which generates an electrical signal in response to an applied pressure. The output signal is proportional to the applied load. This type of transducer is capable of measuring high frequency pressure fluctuation that other transducers can not. Therefore, this device is used when the pressure measurements are time-varying.

One of the most modern technique to measure pressure is coating the model, or part of it, with Pressure Sensitive Paints. The high local pressure is determined by a lowered fluorescence of the paint in that area. Pressure sensitive paints provide very high spatial density of measurements. With this technique, the cost of the model increase moderately, but the cost of the high-quality cameras needed is still enormous.

Forces

The most common method to measure forces and moments is using a six-component balance. The balance is composed of load cells which are passive transducers. These convert a force into an electrical signal. A load cell is a metallic beam with extensome- ters. When an axial load is applied, the deformation of the beam, measured by the extensometers, provide a measurement of the applied load. Any wind tunnel balance is a compromise between the required maximum load capability of all components and the accuracy required for minimum loads.

Forces and moments can be also determined by measuring the wake of the model, pressure distribution, stress distribution or the motion of the model.

Flow path

Tell telltales (cotton tufts) over the aerodynamic surfaces can be stuck to visualize the flow direction, vortex shedding, detachment of the flow, etc. Also, smoke, dye or bubbles of liquid can be introduced upstream and then, the airflow around the model can be easily photographed.

Shape

When the model is not solid, it could be useful to measure the flying shape of the model during the test. This is the case when testing sails in a wind tunnel. Usually the photogrammetry is utilized to measure the flying shape. This is a method to generate a three dimensional description of the model from a set of images taken by digital cameras as in [89], [24] or [90]. There is also the laser scanning technique to measure the shape of a model. 54 CHAPTER 4. WIND TUNNEL TESTS Chapter 5

COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

As mentioned before and stated by Gentry [38] “in its simplest terms, CFD (Compu- tational Fluid Dynamics) 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”. In CFD simulations, the governing equations of fluid flows are solved numerically with the aid of computers rather than solving them analytically. CFDs are used, besides marine field, in other industries such as aerospace, automotive, biomedical, building, chemical, electronic or turbo-machinery.

In chapter 3, the state of the art of numerical simulations applied to sail aerody- namics have been presented. Now, the steps to develop a CFD and the main equations involved are described. Furthermore, the commercial code CD-Adapco’s STAR-CCM+ is presented as well as the assumptions made in the numerical simulations conducted during this investigation. The information presented in this chapter have been partially obtained from [91] and [92].

Procedure

The steps that should be undertaken in order to develop and use a computational fluid dynamic code are the following.

First step (section 5.2). The mathematical model is selected and the level of approximation to reality that will be simulated is defined. The complete equations of fluid mechanics are extremely complicated. They form a system of nonlinear partial differential equations. One of the most relevant consequences of this nonlinearity is the existence of turbulence.

Assumptions and simplifications are defined and they are translated into a mathe- matical model. Additional laws can be set regarding the type of fluid or special physics (multiphase flows, chemical reactions...)

55 56 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

Second step. The geometrical and mathematical models are translated into num- bers. This is named the discretization phase and it encompasses the space discretization and the discretization of the mathematical equations.

In the space discretization (section 5.3), the continuity is replaced by a finite number of points in space. This is called mesh or grid. The space includes the solid bodies (sail, mast...) and the flow surrounding (air). The mesh generation is an important step in the process since the accuracy of the simulation is extremely dependent on the grid properties and quality.

The discretization of the mathematical equations (section 5.4) transforms the mathematical operators into arithmetic operations on the mesh point values, defining the numerical scheme. The most important methods to perform this conversion from derivatives to arithmetic operations are: finite difference method, finite volume method and finite element method.

Third step. Any discretization will automatically generate errors due to the replacement of the continuum model by its discrete representation. In this step the numerical scheme is analyzed and its properties of stability, accuracy and convergence are studied. The numerical scheme must satisfy a certain number of rules and conditions to be accepted.

Fourth step. The solution of the numerical scheme is obtained by selecting the most appropriate time integration method (see section 5.5) for time-dependent numerical formulation. Moreover, all numerical schemes finally result in an algebraic system of equations that must be solved (see section 5.6).

Fifth step. This is the post-process. In this step the calculated numerical data is manipulated to analyze and interpret the physical properties of the obtained simulation results. Powerful visualization systems are required to study, qualitatively and quanti- tatively, the obtained results. Typical examples of outputs that can be generated are: cartesian plots, color plots, visualization of streamlines and velocity vectors, local values of a quantity, animations, global values, etc.

The commercial code STAR-CCM+ allows the user to analyze the solution while the simulation is running, as well as when it is finished. The program provides the capability to generate sections, streamlines, probes, reports or plots. Furthermore, the user can generate new field functions and derived parts from the simulation. In figure 5.1 a screenshoot of the post-processing of a simulation with the STAR-CCM+ code is included. The program facilitates the joint visualization of several outputs. In the screenshoot, the geometry, the mesh, a drag plot, a pressure distribution and a report can be seen simultaneously, [93]. 57

Figure 5.1: Post process with the STAR-CCM+

The commercial code CD-Adapco’s STAR-CCM+

The numerical simulations have been performed using the computational fluid dynamic software CD-Adapco’s STAR-CCM+ [92]. The code was brought out in 2004. The CCM refers to “computational continuum mechanics”. This software delivers the entire engineering simulation process in a single integrated environment. It includes the latest physical models and solver technology. The application employs a client-server architecture, to allow users to solve problems from a lightweight computer, while the computationally expensive math is done on a remote machine [94].

This software has been used during this investigation to analyze the effect of the mast (chapter 6), the pressure distribution over the mainsail of a TP52 (chapter 7) and the aerodynamic performance of a sailing dhow (chapter 8) as well as the performance of the wing of the EU-CargoXpress vessel (chapter 9). The most relevant features than can be found in the STAR-CCM+ are listed below.

• Time: steady-state, unsteady implicit/explicit, harmonic balance

• Motion: stationary, moving reference frame, rigid body motion, mesh morphing, multiple superimposed motions 58 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

• Material: single, multiphase and multi-component fluids, non-Newtonian fluids, in- compressible, ideal gas, real gas

• MultiPhase: free surface with boiling or cavitation, Lagrangian, Eulerian and dis- crete element modeling, wave profile generation for flat, first and fifth order Stokes, irregular, superimposed waves

• Flow: segregated or coupled flow and energy

• Regime: inviscid, laminar, turbulent (RANS, LES, DES), Gamma-Re Theta and user defined transition modeling

• Dynamic Fluid Body Interaction: fluid induced motion in 6 degrees of freedom including propulsion and maneuvering, multi-body interactions including body-body linear and catenary couplings

• Moreover: multi-domain, heat transfer, combustion and chemical reaction, aeroa- coustic analysis, finite volume stress modeling and electrical field simulation.

Assumptions

As soon as in the first step, decisions must be made. The professional use of a CFD requires expertise and knowledge about not only engineering but mathematics and physics. Moreover, if sail aerodynamics is studied, it is appropriate to have experience in sailing. In order to gain skills with a commercial code plenty of time is needed. There are several models and parameters that can be manipulated to improve the simulation and make it as reliable as possible.

One of the main contributions of this investigation is the disclosure of the methodology to study sail aerodynamics with a commercial code. During this thesis, the information that is needed to perform a simulation is presented as well as the key parameters and advices for an effective simulation. The most relevant decisions that have been made at the beginning of each of the simulations are listed below.

 Three dimensional

 RANS turbulent regime and SST turbulence model

 Segregated flow model

 Implicit unsteady

 Constant density

 All wall y+ treatment

 Trimmer mesh with prism layers 5.1. NOMENCLATURE 59

Some CFD users apply the steady model although the physical phenomenon being simulated is unsteady. The STAR-CCM+ provides the ability to average results per iteration to enable these users to obtain a representative picture of the flow phenomena. But the solution will be incorrect and non-physical. Unlike a transient solution, the simulation will not be representative of the physical phenomenon at any moment in time. In the strongest terms, the practice of using the steady model for unsteady physical phenomena is not recommended [92]. The flow around a sail is the typical example of a vortex shedding problem. These simulations that are time-dependent require the unsteady model which have been chosen.

Moreover, it has been decided to use the segregated flow model instead of the coupled flow model. The segregated flow model solves the flow equations (one for each component of velocity and one for pressure) in an uncoupled manner. The linkage between the momentum and continuity equations is achieved with a predictor-corrector approach. On the other hand, the coupled flow model solves the conservation equations for mass and momentum simultaneously using a time- (or pseudo-time-) marching approach.

The coupled flow model is suitable for solving compressible flows and natural convention problems, whereas the segregated flow model is used for incompressible or mildly compressible flows. Furthermore, the segregated flow model uses less computer memory than the coupled model. It is considered that due to the low speed when sailing, the flow can be considered incompressible and therefore both the constant density and segregated flow models are activated.

Regarding the rest of the assumptions made, they will be explained during the next sections of this chapter.

5.1 Nomenclature

α Parameter (equations 5.14 and 5.22) or, scale factor (equation 5.54)

αf Limiter of Venkatakrishnan

γ Coefficient of proportionality

 Dissipation rate

κ Thermal conductivity coefficient

µ Dynamic viscosity

µt Turbulent viscosity

ν Kinematic Viscosity 60 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

ρ Density

σ¯ Internal shear stress

σk, σω Inverse turbulent Schmidt numbers τ Time-step

τ¯ Shear stress tensor

τ¯l Laminar stress tensor τ¯R Reynolds stress tensor

τ¯t Turbulent shear stress tensor τ¯V Viscous shear stress tensor

τw Wall shear stress magnitude φ, φ~ Scalar or vector quantity

ω Specific dissipation rate

Γ Diffusivity

Ω Control volume ap, an Linear coefficients

~a0, ~a1 Average of momentum coefficients

Ω ~ap Vector of central coefficients for the discretized linear system

Dω Cross-derivative term E Energy per unit of volume

~e Error

()f Referred to face fβ Vortex-stretching modification ~ fe Volume source per unit of mass ~ ¯ FC , FC Convective flux ~ ¯ FD, FD Diffusive flux

Gk, Gω Turbulent production and production of specific dissipation rate 5.1. NOMENCLATURE 61

I Turbulence intensity

I¯ Identity matrix k Turbulent kinetic energy or iteration m Mass n Time level p Pressure

Qf Parameter (equations 5.13 and 5.21) qH Heat sources ~ ¯ QS, QS Surface source ~ QV , QV Volume source r,~r Residual rf Parameter (equation 5.60)

S, S~ Control surface t Time

T Absolute temperature, time period or turbulent time scale u+ Reference velocity coefficient u∗ Reference velocity u, v, w Velocity components

~v Velocity

~vp Component of the velocity parallel to the wall w under-relaxation factor

~x Position y Normal distance from the wall to the cell centroid y+ Wall treatment parameter (equation 5.43) 62 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

5.2 Mathematical Model

This is the first step to develop a computational fluid dynamic code. A mathematical model which describes the reality that will be simulated must be chosen. The complete equations of fluid dynamics are complex and some assumptions should be made regarding the type of fluid, flow and special physics such as combustion or multi-phase mixtures, among others.

The most important feature of this first step is to realize that modeling is associated with an undefined level of error when compared to real world. The mathematical model tries to approximate the simulation to reality but there will always be a deviation.

Although the laws of fluid mechanics can be written in many different mathematical forms, CFDs use the concept of conservation law. First, the most general form of a conservation law, without specifying the conserved quantity is introduced. Then, the general conservation laws are applied to the three quantities that define uniquely the laws of fluid mechanics: mass, momentum and energy.

5.2.1 General conservation law This is the conservation law described by Hirsch [91]: The variation of the total amount of a quantity φ inside a given domain is equal to the balance between the amount of that quantity entering and leaving the considered domain, plus the contributions from eventual sources generating that quantity.

Z I Z I ∂ ~ ~ ~ ~ ~ φdΩ = − (FC + FD) · dS + QvdΩ + Qs · dS (5.1) ∂t Ω S Ω S | {z } | {z } | {z } flux term volume source surface source The right hand side of the equation is the variation per unit of time of the quantity φ within the volume Ω called control volume. This is bounded by the control surface S which is a closed surface crossed by the fluid flow.

The flux term represents the “the amount of that quantity φ entering and leaving the considered domain”. The local intensity of φ varies through the effect of fluxes which express the contribution from the surrounding points to the local value of φ and describe how the quantity φ is transported. The flux is the amount of φ crossing the unit of surface per unit of time. Therefore, the total contribution from the incoming fluxes is the sum over all surface elements of the closed surface and it is named flux term.

The fluxes are generated from two sources: a contribution due to the convective transport of the fluid and a contribution due to the molecular agitation, which can be 5.2. MATHEMATICAL MODEL 63

present even when the fluid is at rest. The first component, which is always present, is ~ the convective flux FC . It represents the amount of φ that is transported by the flow. ~ The other contribution, FD, is the diffusive flux which is defined as the contribution present in fluids, due to the effect of the molecular thermal agitation.

The volume source term represents the total contribution of the volume sources Qv, ~ whereas the surface source term represents the total contribution of the surface source Qs.

~ ¯ ¯ ¯ The conserved property can be also a vector quantity, φ. In this case, FC , FD and QS ~ become tensors and the volume source (Qv) becomes a vector.

Z I Z I ∂ ~ ¯ ¯ ~ ~ ¯ ~ φdΩ = − (FC + FD) · dS + QvdΩ + QS · dS (5.2) ∂t Ω S Ω S

As mentioned before, the dynamics of a fluid can be completely described by the conservation laws for the three basic properties: mass, momentum and energy. The only additional information needed would be the nature of the fluid (compressible, incom- pressible, perfect gas...). This set of equations are known as Navier-Stokes equations if they are applied to a viscous fluid whereas they are called Euler equations when applied to a perfect, inviscid fluid.

If the fluid is considered isothermal and incompressible, apart from the velocity field, only the pressure is calculated to characterize the flow. This is the case when studying the aerodynamic of sails. But, if the fluid is a real compressible, apart from the velocity field, both the pressure and density must be calculated to characterize the flow.

Mass conservation (continuity equation)

In this case, the conserved quantity is density, φ = ρ. This law expresses the fact that the mass cannot disappear nor be created in a fluid system.

In a single-phase fluid at rest, no diffusion of specific mass is possible since any displacement of specific mass implies a macroscopic displacement of fluid particles. Therefore, there is not diffusive flux contribution in the mass conservation equation ~ ~ (FD = 0). Although there is a convective flux FC = ρ~v. In the absence of external ~ sources (Qv = 0 and Qs = 0), the equation 5.1 becomes:

∂ Z I ρdΩ + ρ~v · dS~ = 0 (5.3) ∂t Ω S 64 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

Momentum conservation (equation of motion)

The momentum is a vector quantity defined as the product of mass and velocity, which becomes the product of density and velocity, when expressed per unit of volume: φ~ = ρ~v.

¯ The convective flux tensor is FC = ρ~v ⊗ ~v and its contribution through the surface is ¯ ~ ~ FC · dS = ρ~v(~v · dS). This convection term is nonlinear even for incompressible flows and it is the responsible for the appearance of turbulence. On the other hand, as with the mass conservation equations, it is assumed that no diffusion of momentum exists, and ¯ therefore FD = 0.

The sources that influence the variation of the momentum are the external volume forces and the internal forces defined per unit of mass. These internal forces cancel at all internal point due to the action/reaction rule and only the surface points remain for the internal force contribution. Therefore, the internal forces act as a surface source tensor ¯ ¯ ¯ which, in the case of a Newtonian fluid, is QS = −pI + τ¯. In this equation pI is the isotropic pressure component and τ¯ is the viscous shear stress tensor. The volume source ~ ~ is Qv = ρfe.

Finally, substituting the aforementioned terms in 5.2, the equation of motion is obtained:

Z I Z I I ∂ ~ ~ ¯ ~ ~ ρ~vdΩ + ρ~v(~v · dS) = ρfedΩ − pI · dS + τ¯ · dS (5.4) ∂t Ω S Ω S S

Energy conservation (first principle of thermodynamics)

In this case, the conserved quantity is φ = ρE which is the total energy per unit ~ of volume. The convective flux is FC = ρE~v and the diffusive flux can be written ~ ~ as FD = −κ∇T , where κ is thermal conductivity coefficient and T is the absolute temperature.

The sources for the variation of the total energy are the work of the forces acting on the system plus the heat transmitted to the system. The volume sources are the sum of ~ the work of the volume forces fe and the heat sources other than conduction, such as ra- ~ diation, heat released by chemical reactions, designated by qH . Therefore Qv = ρfe ·~v+qH .

The surface sources are the result of the work done on the fluid by the internal shear stresses acting on the surface of the volume considering that there are no external surface ~ heat sources: Qs = σ¯ · ~v. 5.2. MATHEMATICAL MODEL 65

Finally, substituting the aforementioned terms in 5.1, the energy conservation equation is obtained:

Z I I Z I ∂ ~ ~ ~ ~ ~ ρEdΩ + ρE~v · dS = κ∇T · dS + (ρfe · ~v + qH )dΩ + σ¯ · ~v · dS (5.5) ∂t Ω S S Ω S

When studying sail aerodynamics, the fluid (air) is considered isothermal and the density is considered constant. Therefore, the energy conservation equation is not solved.

5.2.2 Levels of approximation The most significant complexities of the Navier-Stokes equations are:

• They form a system of five fully coupled time dependent equations for the five unknowns (three velocity components, pressure and temperature).

• There is a dominant nonlinearity provided by the convection term at the momen- tum equation which is, as mentioned before, the responsible for the appearance of turbulence. This is a spontaneous instability of the flows.

As mentioned in the section Numerical Simulations (chapter 3) there are four main techniques to approximate these equations: Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), Detached Eddy Simulation (DES) and Reynolds Averaged Navier-Stokes (RANS). These are the most significant and widely used approximation levels to solve this equation system even though there are more.

Reynolds-Averaged Navier-Stokes Equations Simulations (RANS or RANSE) are the oldest approach of turbulence modeling. The approach is restricted to averaged turbulent flows which requires the RANS equations to be supplemented by models for the Reynolds stresses. This is currently the most widely applied approximation in the CFD practice and it is the most common level of approximation for studying sail aerodynamics. This approximation is the one used during this investigation.

The turbulent averaging process is introduced in order to obtain the laws of motion for the mean, time-averaged, turbulent quantities. This time averaging is defined to remove the influence of the turbulent fluctuations, while not destroying the time dependence connected with other time-dependent phenomena and time-scales distinct from those of 66 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

turbulence.

0 0 For any quantity φ it is divided in φ = φe + φ , where φ is the turbulent fluctuating part whereas φe is the time-averaged turbulent quantity obtained with equation 5.6.

1 Z T/2 φe(~x,t) = φ(~x,t + τ)dτ (5.6) T −T/2

where ~x is position, t is time, τ is the time-step and T is the period of time, which should be large compared to the turbulent time-scale.

This assumption is substituted in the Navier-Stokes equations. If it is assumed that the density is constant, the continuity equation 5.3 becomes:

∂ Z I ρdΩ + ρ~ve · dS~ = 0 (5.7) ∂t Ω S

In the other hand, the momentum equation 5.4 becomes:

∂ Z I Z I I   ~ ~ ¯ ~ ¯V ¯R ~ ρ~vde Ω + ρ~ve(~ve · dS) = ρfedΩ − peI · dS + τ¯f + τ¯ · dS (5.8) ∂t Ω S Ω S S

where τ¯fV is the averaged viscous shear stress tensor and τ¯R is the Reynolds stress tensor. The relation between the Reynolds stress tensor and the mean flow quantities is unknown. Therefore, the application of the Reynolds averaged equations to the computation of turbulent flows, requires the introduction of models for this unknown relation, based on theoretical considerations coupled to empirical information. A wide variety of models have been developed and applied with varying degrees of success: based on simple algebraic relations, transport equations for turbulent quantities or transport equations for the Reynolds stress components. In section 5.4.3 some RANS turbulence models are described. In this research the SST model has been used.

5.2.3 Boundary Conditions The equations given above govern the flow of a fluid. They are the same equations whether the flow is, for example, over an airplane or a sail. However, the flow fields are quite different for these cases, although the governing equations are the same. 5.3. SPACE DISCRETIZATION 67

The difference appears through the boundary and initial conditions, which dictate the particular solutions to be obtained from the governing equations. Therefore, once the governing flow equations are described, the real “driver” for any particular solution is the boundary conditions as stated in [95].

The no-slip condition is applied on a surface where it is assumed zero relative velocity between the surface and the fluid immediately at the surface. This is the proper physical boundary conditions for a viscous flow. On the other hand, sometimes, it is assumed that there is no friction and the slip condition is applied. Here, the veloc- ity is finite and tangent to the wall, and thus, the velocity perpendicular to the wall is zero.

Depending on the problem in study, there are various types of boundary conditions elsewhere in the flow, away from the surface boundary. At the inflow and outflow boundaries, the inlet and outlet conditions are applied respectively. Other fluids require free-stream conditions when the body in study is immerse in a fluid stream. Another common boundary condition is the symmetry plane condition.

When studying sails, the most common boundary conditions that are set at the CD-Adapco’s STAR-CCM+ are:

• Velocity Inlet. In this boundary, the inlet velocity vector is specified directly and pressure is extrapolated by the program from the adjacent cells using reconstruction gradients. • Pressure Outlet. For subsonic outflows, the boundary pressure is specified whereas the boundary face velocity is extrapolated from the interior cells using reconstruction gradients. • Wall. The object in study (sail, mast, boat...) is considered a no-slip wall where the tangential velocity is explicitly set to zero. As in the velocity inlet boundary, the pressure is extrapolated from the adjacent cell using reconstruction gradients. These walls can be smooth or on the other hand, the roughness can be set.

The remaining surfaces are considered slip walls. In this case, the face value of velocity is computed by extrapolating the parallel component of velocity in the adjacent cell using reconstruction gradients.

5.3 Space Discretization

The discretization of space is the first part of the second step when using or developing a CFD. In this part, the continuity is replaced by a finite number of points in space, which is called a grid or mesh. The accuracy of this approximation depends on the size and quality 68 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

of the mesh. It is said that the closer the points (or vertexes), the better the discretization is. Mesh is the main component in setting up a CFD simulation. It is a critical el- ement since the accuracy of the numerical results is highly dependent on the mesh quality.

The grid generation codes are difficult to develop, especially for real geometries, as they require sophisticated programming and mathematical methodologies. As mentioned in [91], the relevant software tools appeal to algebraic geometry theories, mathematical surface definitions, normals and curvature estimations, coordinate transformations, topological properties, etc.

5.3.1 Types Three dimensional grids are formed by vertexes, faces and cells. A vertex is a point in space defined by a position vector. A face comprises an ordered collection of vertexes such that they define a surface in three dimensional space. Finally, a cell is an ordered collection of faces that define a closed volume in space. Depending on the organi- zation of this elements, grids are distinguished between structured and unstructured grids.

The structured mesh is composed of families of intersecting lines, one for each space dimension. Each mesh vertex is located at the intersection of one line, and only one line, of each family. It is considered the “obvious” mesh type for flow problems since the fluid is generally aligned with the bodies and moving along streamlines, at least, theoretically. These structured meshes can be divided, according to [91] in cartesian, body-fitted and multi-block grids. The disadvantage of structured meshes is their stiffness. Every time a point is added, it implies adding lines of each family through that point, which affects the whole domain. In complex geometries, this can be unfordable.

On the hand, there are unstructured grids that refer to arbitrary distributions of mesh vertexes which are connected by polyhedrons in 3D. Unstructured grids have become the dominating approach to industrial simulations. One of the advantages of unstructured grids is the possibility to perform local refinements in a certain region, without affecting the grid point distribution outside that region. This opens the way for flexible grid adaptation by local refinement or local coarsening, based on some criteria associated either to some flow gradients or to some error estimations. Moreover, the automatic grid generation with an adequate control of grid quality is easier with unstructured grids.

The unstructured grids are made of tetrahedrons, hexahedrons or polyhedrons. There are also hybrid grids which have more than one cell type. In general, hybrid grids have been developed to deal with the boundary layer requirement of high Reynolds number flows. Next to walls, the mesh density in the perpendicular direction has to be modified to capture the boundary layer velocity profile. Hybrid grids add prisms near the wall region. 5.3. SPACE DISCRETIZATION 69

Figure 5.2: Polyhedral mesh with prism layers

It can be stated that in general, in terms of solver time, memory requirement and accuracy, structured grids are more efficiency than unstructured grids. But the generation of good quality unstructured meshes on complex geometries require less time. Nowadays, unstructured meshes for RANS solvers have gained wide acceptance.

5.3.2 STAR-CCM+ Mesh In the single integrated environment of the STAR-CCM+ code the meshing tool is also included. It can generate automatic unstructured volume grids which contain trimmed, polyhedral or tetrahedral cells. Additionally, prism layers can be automatically included next to wall boundaries and interfaces. In figure 5.2 an example of a polyhedral grid with prism layers is shown, [92].

In general, the choice of the mesh type depends on several factors. Some of these factors are: time available for building the mesh, solution accuracy and convergence rate, memory available on the computer, multi-region mesh simulations, quality of the initial surface mesh and thickness of thin geometries. In terms of general accuracy for a given number of cells, the trimmed and polyhedral cell type meshes will produce the most accurate solution when compared to a tetrahedral mesh. Mesh independent solutions 70 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

Figure 5.3: Trimmer mesh can be obtained for all three mesh types if the density is increased to the appropriate level.

During this investigation the trimmer model with prism layers is selected. In figure 5.3 the trimmer mesh of one of the simulations described in chapter 6 is plotted. The trimmer model is not directly dependent on the surface quality of the starting surface and therefore it is more likely to produce a good quality mesh for most situations. It combines a number of highly desirable meshing attributes in a single meshing scheme: predominantly hexahedral mesh with minimal cell skewness, automatic curvature and proximity refinement, surface quality independence and alignment with a user specified coordinate system.

A prism layer mesh model is included with the trimmed core mesh in order to generate orthogonal prismatic cells next to the geometry surfaces. These prisms are required to accurately simulate the turbulence. The thickness, number of layers and distribution of the prism layer mesh can be modified depending on the case in study.

5.3.3 Mesh Validity and Quality Grid generation and grid quality are essential elements of the whole discretization process. It is said that mesh generation is the critical step in the cost of running CFD simulations. Moreover, the accuracy of the calculated numerical results is dramatically dependent on mesh quality. First, a grid should be valid and then, it should have good quality.

A valid mesh permits the initialization of the simulation and this iterates so that a solution can be calculated. For example, a mesh that contains a negative volume cell would be considered invalid. Nevertheless, the determination of whether a mesh is valid or not is sometimes dependent on the underlying mesh quality. Other factors that can 5.4. DISCRETIZATION OF EQUATIONS 71

affect the validity of a mesh include: choice of solver, under-relaxation, Courant number specification or the discretization scheme used.

In spite of the fact that a mesh is valid and the solution can be successfully initialized with an appropriate model, poor mesh quality can negatively impact the solution. In general, the quality of a volume mesh may not necessarily generate problems during the simulation but a poor quality mesh will affect the accuracy and efficiency of the solution obtained.

The STAR-CCM+ provides some direct measurements of mesh quality such as cell and boundary skewness angle, face validity metrics and cell quality metrics and volume change metrics. More information regarding these parameters can be found in [92]. Other commercial codes provide similar parameters. For example, in this thesis, the “de- terminant 2x2x2” criterion, which is included in the ANSYS-CFX code, will be described.

5.4 Discretization of Equations

Once the space discretization has been concluded, the discretization of the equations is defined. This is the second part of the second step when using or developing a CFD as mentioned in the introduction of this chapter. In this part, the mathematical operators are transformed into arithmetic operations on the mesh point values, defining the numerical scheme.

The most important methods for the discretization of the space derivatives of the conservation laws, can be divided in three families which vary in degree of generality as described in [91]. The most traditional and oldest method is the Finite Difference Method, which remains the reference for all studies of numerical discretization, although it is only applicable to structured grids. The second family is the most widely applied method today in CFD and it is named Finite Volume Method. This technique discretizes directly the integral form of the conservation laws. Its popularity is due to its generality, its conceptual simplicity and the relative ease of application to both structured as well as to any kind of unstructured grids. The third method is derived from the world of structural mechanics, where the Finite Element Method is most widely, if not exclusively, applied.

The Finite Volume Method (FVM) is the name given to the technique by which the integral formulation of the conservation laws is discretized directly in the physical space. The FVM is based on cell-averaged values, which are the fundamental quantities in CFDs. This distinguishes the FVM from the finite difference and finite element methods, where the main numerical quantities are the local function values at the mesh points. Once a mesh has been generated, the FVM associates a local finite volume (named control volume) to each mesh point and applies the integral conservation law to this local volume. 72 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

The basic advantage of the FVM is connected to the concept of conservative discretization. It is important to maintain the global conservation of the basic flow quan- tities (mass, momentum and energy) at the discrete level. This concept of conservation conditions the way the discretization process of the equations is performed. The FVM has the great advantage that the conservative discretization is automatically satisfied through the direct discretization of the integral form of the conservation laws.

The finite volume method takes its full advantage on an arbitrary mesh, where a large number of options are open for the definition of the control volume on which the conservation laws are expressed. Modifying the shape and location of the control volumes associated to a given mesh point, as well as varying the rules and accuracy for the evaluation of the fluxes through the control surfaces, gives a considerable flexibility to the finite volume method.

Z I Z I ∂ ~ ~ ~ ~ ~ φdΩ = − (FC + FD) · dS + QvdΩ + Qs · dS (5.1) ∂t Ω S Ω S The previously presented integral conservation law (equation 5.1) is applied to each control volume ΩJ , associated to the mesh point J, defining hereby the discretized equations for the unknowns φJ attached to that same vertex or cell. The integral equation is replaced by its discrete form, where the volume integrals are expressed as the averaged values over the cell and where the surface integral is replaced by a sum over all the bounding faces of the considered volume ΩJ :

∂ X X (φ Ω ) = − (F~ + F~ ) · dS~ + Q Ω + Q~ · dS~ (5.9) ∂t J J C D J J s faces faces Hereafter this finite volume method will be applied to the continuity and momentum equations based on the formulation of the STAR-CCM+ code. In the next sections, how this code deals with the discretization process will be described.

5.4.1 Continuity Equation The integral form of mass conservation of the Navier-Stokes equations, assuming that there is no porosity, grid velocity, neither any volume sources, was previously presented in equation 5.3:

∂ Z I ρdΩ + ρ~v · dS~ = 0 (5.3) ∂t Ω S 5.4. DISCRETIZATION OF EQUATIONS 73

Following the Finite Volume discretization method and according to the STAR- CCM+ formulation [92], the discrete continuity equation is written:

X X ∗ 0 m˙ f = (m ˙ f +m ˙ f ) = 0 (5.10) f f

∗ where f means referred to the face,m ˙ f is the face mass flow,m ˙ f is the uncorrected 0 face flow rate andm ˙ f is the mass flow correction.

The solver algorithm is presented in section 5.4.6 but, as summary, it must be highlighted that first, the discrete momentum is solved, then, the uncorrected face mass ∗ flow ratem ˙ f . Once these values have been calculated, the pressure field is obtained and finally, the mass fluxes are corrected to verify the continuity equation.

The values concerning the continuity equation are computed differently depending on the class of the face: interior or boundary faces.

Interior faces

∗ The uncorrected mass flow rate at an interior face (m ˙ f ) may be written in terms of the cell variables as follows:

~v ∗ + ~v ∗  m˙ ∗ = ρ 0 1 · S~ − Q (p∗ − p∗ − ∇~ p∗ · ∆~x) (5.11) f 2 f 1 0 f

∗ ∗ where ~v0 and ~v1 are the cell velocities after the discrete momentum equations have ∗ ∗ ~ ∗ been solved. p1 and p0 are the cell pressures from the previous iteration. ∇pf is the volume-weighted average of the cell gradients of pressure. Moreover,

∆~x = ~x1 − ~x0 (5.12)

where ~x1 and ~x0 are the position vectors of the cell-1 and cell-0 respectively. Qf is defined as:

  Ω0 Ω1 ~ Qf = ρ + ~α · S (5.13) a¯0 a¯1

where Ω0 and Ω1 are the volumes of cell-0 and cell-1 respectively.a ¯0 anda ¯1 are the average of the momentum coefficients for all components of momentum for both cells. The paremeter ~α is: 74 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

S~ ~α = (5.14) S~ · ∆~x ∗ Once the uncorrected mass flow rate (m ˙ f ) has been calculated, the mass flow correction is presented:

m˙ ∗ m˙ 0 = Q (p0 − p0 + f p0 ) (5.15) f f 0 1 ρ upwind

0 0 0 where p0 and p1 are the unknown pressure corrections, and pupwind:

 0 ∗ 0 p0 form ˙ f > 0 pupwind = 0 ∗ (5.16) p1 form ˙ f < 0

0 0 Now, with the equations 5.10 and 5.15 the pressure corrections (p0) and (p1) can be obtained if the equations are joined and written in coefficient form as:

0 X 0 X ∗ appp + anpn = m˙ f (5.17) n f

where ap and an are linear coefficients. From this equation, the pressure corrections are obtained. Finally, the face mass flux (m ˙ f ) can be calculated with equation 5.10.

Boundary faces with specified velocity

∗ In this case the value of the uncorrected mass flow rate (m ˙ f ) is calculated directly ∗ from the known velocity ~vf on boundaries as:

∗ ~ ∗ m˙ f = ρ(S · ~vf ) (5.18) The pressure correction in this case is:

0 0 pf = p0 (5.19) When the velocity is specified on a boundary face, the mass flux corrections are zero 0 (m ˙ f = 0).

Pressure boundaries

On a specified pressure boundary, the uncorrected boundary mass flux is given by: 5.4. DISCRETIZATION OF EQUATIONS 75

∗ ~ ∗ ∗ ~ ∗ m˙ f = ρ(~vf · S) − Qf (pf − p0 − ∇p0 · ∆~x) (5.20) ∗ where ~vf is the boundary velocity, pf is the face pressure from the previous iteration, ∗ ~ ∗ p0 is the cell pressure from the previous iteration and ∇p0 is the volume-weighted average of the cell gradients of pressure. The parameter Qf is:

ρΩ0 ~ Qf = (~α · S) (5.21) a¯0

where Ω0 is the volume of cell-0 anda ¯0 is the average of the momentum coefficients for all components of momentum for cell-0. In this case, ~α is:

S~ ~α = (5.22) ~ S · (~xf − ~x0) For subsonic pressure outlet, the mass flow correction is defined as:

0 ~ 0 m˙ f = (Qf + ~vf · S)p0 (5.23) 0 where p0 is the cell-0 pressure correction.

5.4.2 Momentum Equation The integral form of the momentum conservation of the Navier Stokes equations, assuming that there is no porosity, grid velocity, neither any volumetric source, was previously presented in equation 5.4:

Z I Z I I ∂ ~ ~ ¯ ~ ~ ρ~vdΩ + ρ~v(~v · dS) = ρfedΩ − pI · dS + τ¯ · dS (5.4) ∂t Ω S Ω S S

According to the Finite Volume discretization method, the momentum equation in discrete form, assuming that there are not external forces, can be written as:

∂ X X X (ρ~vΩ) + [ρ~v(~v · S~)] = − (pI¯· S~) + τ¯ · S~ (5.24) ∂t 0 f f | {z } f f f transient | {z } | {z } convection diffusion These next paragraphs describe the basis of the finite volume discretization of the transport equation in general. The momentum equation is a particular case where the 76 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

transient, convection and diffusion terms for each velocity component is discretized in the manner as the scalar quantity φ described hereafter.

∂ X X (ρφΩ) + [ρφ(~v · S~)] = − [Γ∇~ φ · S~] (5.25) ∂t 0 f f | {z } f f transient | {z } | {z } convection diffusion In this equation φ is the scalar quantity that it is transported and Γ is diffusivity.

Transient term

The transient term is only included in time-dependent calculations. As mentioned before, the Implicit Unsteady solver has been chosen and in STAR-CCM+, it offers two temporal discretization options: first-order and second-order. This transient term is related to the time integration method and therefore it is explained in section 5.5.

Convection term

The convective term at a face is discretized as follows:

~ [φρ(~v · S)]f =m ˙ f φf (5.26)

where φf andm ˙ f are the scalar value and the mass flow rate at the face, respectively. There are several schemes to compute the face value φf : first-order upwind, second-order upwind, central-differencing and blended upwind/central, among others. In this case, the second-order upwind scheme is used:

 ~ m˙ f [φ0 + (~xf − ~x0) · (∇φ)r,0] form ˙ f ≥ 0 m˙ f φf = ~ (5.27) m˙ f [φ1 + (~xf − ~x1) · (∇φ)r,1] form ˙ f < 0

where φ0 and φ1 are the scalar values at cell-0 and cell-1. ~xf , ~x0 and ~x1 are the ~ ~ position vector of the boundary face, cell-0 and cell-1, respectively. (∇φ)r,0 and (∇φ)r,1 are the limited reconstruction gradients in cell-0 and cell-1.

The advantage of this scheme over the first-order upwind scheme is that it is nominally second-order accurate. However, the fact that the reconstruction gradients are limited helps to reduce local extrema and thus introduces more dissipation than a central-differencing scheme. Clearly, the accuracy of this scheme will always be as good or better than the first-order upwind scheme. According to STAR-CCM+, the downside is that, in some situations, the reduced numerical dissipation might result in poorer convergence properties than first-order convection. 5.4. DISCRETIZATION OF EQUATIONS 77

Diffusion term (in general)

A diffusion term (Γ∇~ φ · S~) is discretized differently depending on the face class: interior or boundary face.

Interior face

To obtain an accurate second-order expression for an interior face gradient that im- plicitly involves the cell values φ1 and φ0, the following decomposition is used:

~ ~ ~ ∇φ = (φ1 − φ0)~α + ∇φ − (∇φ · ∆~x)~α (5.28) where ∆~x and ~α are calculated with 5.12 and 5.14, respectively; Moreover,

∇~ φ + ∇~ φ ∇~ φ = 0 1 (5.29) 2 The diffusion flux at an interior face may then be written:

~ ~ ~ ~ ~ ~ ~ Γf ∇φf · S = Γf [(φ1 − φ0)~α · S + ∇φ · S − (∇φ · ∆~x)~α · S] (5.30)

where Γf is an average value of the cell values.

Boundary face

A similar decomposition is used at a boundary face:

~ ~ ~ ~ ~ ~ ~ Γf ∇φf · S = Γf [(φ1 − φ0)~α · S + ∇φ0 · S − (∇φ0 · ∆~x)~α · S] (5.31)

where ∆~x = ~xf − ~x0 and ~α is obtained in 5.22.

Diffusion term (viscous fluxes)

P ¯ ~ The last term of the equation 5.24 is the viscous fluxes term ( f τ¯ · S). This term is explained separately due to its importance.

In turbulent flows, the complete stress tensor is given by:

τ¯ = τ¯l + τ¯t (5.32)

τ¯l is the laminar stress tensor and is expressed as:

 2  τ¯ = µ ∇~ ~v + ∇~ ~v T − (∇~ · ~v)I¯ (5.33) l 3 78 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

where µ is the dynamic viscosity.

The challenge of the RANS models is thus to model the Reynolds stress tensor τ¯t ¯ (or τ¯R)in terms of the mean flow quantities, and hence provide closure of the governing equations. Two basic approaches are used in STAR-CCM+: Eddy viscosity models and Reynolds stress transport models. Eddy viscosity models use the concept of turbulent viscosity (µt) to model the Reynolds stress tensor as a function of mean flow quantities. The used approximation is the following:

1  2 τ¯ = 2µ (∇~ ~v + ∇~ ~v T ) − (µ ∇~ · ~v + ρk)I¯ (5.34) t t 2 3 t where k is the turbulent kinetic energy. The eddy viscosity models solve additional transport equations for scalar quantities that enable the turbulent viscosity µt to be derived, as explained in section 5.4.3.

Interior Faces

~ To evaluate the stress tensor (τ¯), the velocity gradient tensor at a face (∇~vf ) must be written in terms of the cell velocities for purposes of linearization. The velocity gradient tensor at a face may be written according to equation 5.28 as:

~ ~ ~ ∇~vf = (~v1 − ~v0) ⊗ ~α + ∇~vf − (∇~vf · ∆~x) ⊗ ~α (5.35) where ∆~x and ~α are obtained from 5.12 and 5.14, respectively. Furthermore,

∇~ ~v + ∇~ ~v ∇~ ~v = 0 1 (5.36) f 2 Boundary Faces

For slip walls, the viscous shear force at the wall boundary face is set to zero (τ¯·S~ = 0). But, for no-slip walls in turbulent flows, it is assumed that only the component of the velocity parallel to the wall is of interest (~vp). A linear relationship between the wall t t shear force and the difference in velocity between the wall (~vf ) and the cell (~v ) is assumed:

~ t t (τ¯ · S)f = −γ(~v − ~vf ) (5.37)

∗2 Using the definitions of wall shear stress magnitude (τw = ρu ) and reference velocity + ∗ coefficient (u = |~vp|/u ) the coefficient of proportionality is: 5.4. DISCRETIZATION OF EQUATIONS 79

ρu∗ γ = |S~| (5.38) u+ The reference velocity (u∗) is computed according to the specific turbulence model. The value of (u+) is obtained, as a function of y+, from the appropriate wall law (see section 5.4.4). Finally:

ρu∗ (τ¯ · S~) = −|S~| (~v t − ~v t) (5.39) f u+ f

5.4.3 RANS Turbulence Models To obtain the Reynolds-Averaged Navier-Stokes (RANS) equations, the Navier-Stokes equations for the instantaneous velocity and pressure fields are decomposed into a mean value and a fluctuating component (see section 5.2). The resulting equations for the mean quantities are fundamentally identical to the original equations, except that an additional term now appears in the momentum transport equation. This additional term is the Reynolds Stress tensor (τ¯R), the last term of equation 5.8.

∂ Z I Z I I   ~ ~ ¯ ~ ¯V ¯R ~ ρ~vde Ω + ρ~ve(~ve · dS) = ρfedΩ − peI · dS + τ¯f + τ¯ · dS (5.8) ∂t Ω S Ω S S

The relation between this tensor and the mean flow quantities is unknown. Therefore, the challenge is to model the Reynolds Stress tensor τ¯R in terms of the mean flow quantities, and thus, provide closure of the governing equations. As mentioned before, two basic approaches are used in STAR-CCM+: Eddy Viscosity models and Reynolds Stress Transport models.

Eddy Viscosity models use the concept of a turbulent viscosity µt to model the Reynolds Stress tensor as a function of mean flow quantities. Simple models are based on on the concept of mixing length to model the turbulent viscosity in terms of mean flow quantities. The Eddy Viscosity models solve additional transport equations for scalar quantities that enable the turbulent viscosity µt to be calculated. These models include: Spalart-Allmaras, K-Epsilon and K-Omega models. On the other hand, Reynolds Stress Transport models, also known as Second-Moment Closure models, solve the transport equations for each component of the Reynolds Stress tensor.

The turbulence models included in the STAR-CCM+ are described in the following list according to the documentation provided [92]. 80 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

• Spalart-Allmaras models. They are a good choice for applications in which the boundary layers are largely attached and separation is mild, if it occurs. Typical examples would be the flow over a wing, fuselage or other aerospace external-flow applications. These models are not suited to flows that are dominated by free-shear layers, flows where complex recirculation occurs, or natural convection.

The Spalart-Allmaras turbulence models solve a single transport equation that determines the turbulent viscosity. This is in contrast to many of the early one-equation models that solve an equation for the transport of turbulent kinetic energy and required an algebraic prescription of a length scale.

• K-Epsilon models. They provide a good compromise between robustness, com- putational cost and accuracy. They are generally well suited to industrial-type applications that contain complex recirculation, with or without heat transfer.

A K-Epsilon turbulence model is a two-equation model in which transport equations are solved for the turbulent kinetic energy k and its dissipation rate . Various forms of the K-Epsilon model have been in use for several decades, and it has become the most widely used model for industrial applications.

• K-Omega models. They are similar to K-Epsilon models in that two transport equations are solved, but differ in the choice of the second transported turbulence variable. The performance differences are likely to be a result of the subtle differences in the models, rather than a higher degree of complexity in the physics being captured. These models have been mainly applied in the aerospace industry.

The K-Omega model is a two-equation model that is an alternative to the K-Epsilon model. The transport equations solved are for the turbulent kinetic energy k and a quantity called ω, which is defined as the specific dissipation rate, that is, the dissipation rate per unit turbulent kinetic energy (ω = /k).

One reported advantage of the K-Omega model over the K-Epsilon model is its improved performance for boundary layers under adverse pressure gradients. Perhaps the most significant advantage however, is that it may be applied through- out the boundary layer, including the viscous-dominated region, without further modification. Furthermore, the standard K-Omega model can be used in this mode without requiring the computation of wall distance.

• Reynolds Stress Transport (RST) models. They are the most complex and com- putationally expensive models. They are recommended for situations in which the 5.4. DISCRETIZATION OF EQUATIONS 81

turbulence is strongly anisotropic, such as the swirling flow in a cyclone separator.

By solving transport equations for all components of the specific Reynolds stress tensor (τ¯R), these models account for effects such as an anisotropy due to strong swirling motion, streamline curvature, rapid changes in strain rate and secondary flows in ducts.

The RST models carries significant computational overhead. Seven additional equations must be solved in three dimensions (as opposed to the two equations of a K-Epsilon model). Apart from the additional memory and computational time required for these equations to be solved, there is also likely to be a penalty in the total number of iterations required to obtain a converged solution due to the numerical stiffness of the RST equations.

SST K-Omega Model

This is a modification of a standard K-Omega model developed by F. Menter in 1994. “SST” refers to Shear Stress Transport. This model uses the insensitivity to free-stream conditions of the K-Epsilon model in the far-field, while retaining the advantages of the K-Omega model near walls.

The SST model has been widely used in the aerospace industry where viscous flows are generally well resolved and turbulence models are applied throughout the boundary layer. Extensive research by Collie et al. [52] into turbulence modeling for sail flow applications highlighted the benefits of the SST model. This was designed to deal with adverse pressure gradients and separated flows and thus, performs well for sail type anal- ysis [96]. As mentioned before, this is the turbulence model used during this investigation.

These are the three main equations of the Shear Stress Transport model:

∂ Z I ρkdΩ + ρk(~v · dS~) = (5.40) ∂t Ω S I Z ~ ~ (µ + σkµt)∇k · dS + (Gk − 0.09ρfβωk)dΩ S Ω

∂ Z I ρωdΩ + ρω(~v · dS~) = (5.41) ∂t Ω S I Z ~ ~ 2 (µ + σωµt)∇ω · dS + (Gω − ρ0.072fβω + Dω)dΩ S Ω 82 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

µt = ρkT (5.42) In these equations, the following variables appear among others that have already been explained:

• µt: turbulent dynamic viscosity • k: turbulent kinetic energy

• ω: specific dissipation rate

• σk and σω: inverse turbulent Schmidt numbers. They are coefficients.

• Gk and Gω: turbulent production and production of specific dissipation rate. They depend on k, ω and the velocity.

• fβ: vortex-stretching modification. It depends on the velocity and ω.

• Dω: cross-derivative term. It depends on k and ω. • T : turbulent time scale. It depends on k, ω, the velocity, the kinematic viscosity and the distance to the nearest wall.

The first two are the transport equations of “k” and “ω”, whereas the third equation determines the turbulent dynamic viscosity. These equations are solved with the finite volume discretization of the momentum equation.

Now, the diffusive term of the viscous fluxes can be solved (5.34) since the turbulent dynamic viscosity and the kinetic energy of the equations are obtained with this model. Finally, the main objective of the turbulence model has been achieved: “provide closure to the governing equations”.

5.4.4 Wall Treatment A wall treatment in STAR-CCM+ is the set of near-wall modeling assumptions for each turbulence model. Three types of wall treatment are provided: high-y+, low-y+ and all-y+ wall treatments. The parameter y+ is defined in equation 5.43.

The high-y+ wall treatment is essentially the classic wall-function approach, where wall shear stress, turbulent production and turbulent dissipation are all derived from equilibrium turbulent boundary layer theory. A wall function is the set of mathematical relations used to obtain the boundary conditions for the continuum. The main advantage of using wall functions is the significant savings in terms of near-wall mesh resolution. In this treatment it is assumed that the near-wall cell lies within the logarithmic region of 5.4. DISCRETIZATION OF EQUATIONS 83

the boundary layer.

It is suitable with models that do not explicitly damp the turbulence in the near wall region. In order to choose this treatment the wall-cell centroid should be situated in the logarithmic boundary layer (y+ > 30).

The low-y+ wall treatment assumes that the viscous sublayer is well resolved and thus wall laws are not needed. It is suitable only for low Reynolds number turbulence models. This treatment should only be used if the entire mesh is fine enough for y+ to be approximately 1 or less.

The all-y+ wall treatment is an hybrid approach that seeds to recover the behaviors of the other two wall treatments in the limit of very fine or very coarse meshes. It is a design goal that this wall treatment should give results similar to the low-y+ treatment as y+ →0 and to the high-y+ treatment for y+ > 30. It will also give reasonable results for intermediate meshes where the cell centroid falls in the buffer layer. This is the recommended wall treatment and the one used in these simulations.

The wall treatments have been specialized according to each turbulence model, since specific assumptions to that model need to be made for the wall boundary conditions for the turbulence quantities. Both the high-y+ and all-y+ wall treatments share a common need to specify profiles of the mean flow quantities in the near-wall region of turbulent boundary layers, and these profiles are termed wall laws. The all-y+ wall treatment is activated with the SST K-Omega model.

A wall law is a mathematical description of mean flow quantities, such as velocity, temperature and species concentration, in turbulent boundary layers. Two types of wall laws are use: standard walls laws and blended walls laws. The standard wall laws are slope-discontinuous between the laminar and turbulent profiles. The blended wall laws include a buffer region that smoothly blends the laminar and turbulent profiles together. When the “all-y+” is selected, the blended wall laws is activated too.

The most important non-dimensional parameters in wall treatment formulations are:

yu∗ y+ = (5.43) ν v u+ = p (5.44) u∗ where y is the normal distance from the wall to the cell centroid, u∗ is the reference velocity, ν is the kinematic viscosity and vp is the component of cell velocity parallel to the wall. The reference velocity (u∗) is derived from the turbulence model. The wall laws are set up to provide u+ as a function of y+ and other relevant quantities. 84 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

The wall laws differ only in their treatment in the buffer region since the viscous- sublayer and log-layer behaviors are identical. The velocity distribution in the viscous sublayer is modeled as:

+ + ulam = y (5.45) The velocity distribution near a smooth wall in the logarithmic layer is modeled as:

1 u+ = ln(9y+) (5.46) trb 0.42 The blended wall laws are intended to represent the buffer layer by appropriately blending the viscous sublayer and logarithmic regions. For momentum, Reichardt’s law is used and the velocity distribution is modeled as:

  +  +  + 1 + y y + u = ln(1 + 0.42y ) + 7.3 1 − exp − + − + exp(−by ) (5.47) 0.42 ym ym  +  1 0.42ym 1 b = + + (5.48) 2 7.3 ym + where ym is found by Newton iteration.

5.4.5 Gradient Computation The gradient computation process in STAR-CCM+ involves three steps. First, computing the unlimited reconstruction gradients. Once limited, these are used to evaluate the cell gradients to reconstruct face values for the flux computations. Second, limiting the reconstruction gradients. Third, computing the cell gradients from the limited reconstructions gradients.

Step 1: Reconstruction gradient

Two algorithms are used to compute reconstruction gradients: the weighted least squares method which is used for pressure and the Gauss method, which is used for all variables other than pressure.

In the Weighted Least Squares Method, the initial unlimited reconstruction gradients in cell-0 are computed using the following weighted least squares formula:

" #−1 " # u   X ∆~x ⊗ ∆~x X (φ0 − φn)∆~x ∇~ φ = (5.49) r ∆~x · ∆~x ∆~x · ∆~x f f 5.4. DISCRETIZATION OF EQUATIONS 85

where

∆~x = ~xn − ~x0 (5.50)

with ~x0 and ~xn representing the centroids of cell-0 and that of the neighbor cell addressed through face f; φ0 and φn represent the data values in cell-0 and its neighbors; The superscript u refers to unlimited gradient and the subscript r means reconstructed value.

The Gauss Method emerges from the Gauss’ divergence theorem:

Z I ∇~ φ dΩ = φ dS~ (5.51) Ω S Written in discrete form, this can be used to compute the initial (unlimited) recon- struction gradients:

u ~  1 X φ0 − φ1 ~ ∇φ = Sf (5.52) r Ω0 2 f The face value reconstructed from the cell-0 value at any face centroid is given by:

~ φf,0 = φ0 + (~xf − ~x0) · (∇φ)r,0 (5.53)

where x0 and xf are the cell and face centroids respectively.

The problem with simply reconstructing face values from the unlimited reconstruction gradients is that the reconstructed values may exceed the cell values bounding the face. For this reason, it is necessary to limit the reconstruction gradients by scaling them appropriately.

Step 2: Limiting the reconstruction   For each cell-0, a limited reconstruction gradient ∇~ φ is needed, such that when r,0 used in the above reconstruction formula, the reconstructed face value φr,0 will not exceed the maximum and minimum of the neighboring cell centroid values, including the value in cell-0. α is the scale factor that expresses the ratio of the limited and unlimited values, that is:

   u ∇~ φ = α ∇~ φ (5.54) r,0 r,0 86 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

For each cell-0, the quantities are defined:

max ~  ∇φ = max(φ0, φneig) (5.55) 0

min ~  ∇φ = min(φ0, φneig) (5.56) 0

where φneig represents the cell value in each neighbor that has a common face with cell-0. These can also be defined as:

max ∆max = φ0 − φ0 (5.57)

min ∆min = φ0 − φ0 (5.58) For each face f of cell-0, is defined:

u ~  ∆f = φf,0 − φ0 = (~xf − ~x0) · ∇φ (5.59) r,0 Now defining:

 ∆f for ∆ > 0  ∆max f rf = (5.60)  ∆f ∆min for ∆f ≤ 0 The limiter of Venkatakrishnan gives for the face:

2rf + 1 αf = (5.61) rf (2rf + 1) + 1 The cell value of α is given by:

α = min(αf ) (5.62) Step 3: Cell gradients

The reconstruction gradients obtained above are useful for computing bounded face values, and are used for convective quantities. Cell gradients are used in many other places including secondary gradients for diffusion terms, pressure gradients for pressure-velocity coupling in the segregated flow model, and strain-rate and rotation-rate calculations for turbulence models. 5.4. DISCRETIZATION OF EQUATIONS 87

The improved estimations of the face values, obtained from the reconstruction gradients, can be used to obtain better estimations of the cell gradients in turn.

Using Gauss’ divergence theorem:

1 X φf,0 + φf,1 ∇~ φ = (5.63) Ω0 2 f where, as before:

φf,0 = φ0 + (~xf − ~x0) · (∇φ)r,0 (5.64)

φf,1 = φ1 + (~xf − ~x0) · (∇φ)r,1 (5.65)

5.4.6 SIMPLE Solver Algorithm The SIMPLE algorithm is used to control the overall solution. The basic steps in the solution update are the following:

1. Set boundary conditions.

2. Compute the reconstruction gradients of velocity and pressure.

3. Compute the velocity and pressure gradients.

4. Solve the discretized momentum equation to create the intermediate velocity field ~v∗.

∗ 5. Compute the uncorrected mass fluxes at facesm ˙ f . 6. Solve the pressure correction equation to produce cell values of the pressure correc- tion p0 .

7. Update the pressure field pn+1 = pn + 0.3p0 , where 0.3 is the under-relaxation factor for pressure.

0 8. Update the boundary pressure corrections pb.

n+1 ∗ 0 9. Correct the face mass fluxes:m ˙ f =m ˙ f +m ˙ f

0 n+1 ∗ Ω∇~ p ~ 0 10. Correct the cell velocities: ~v = ~v − Ω . Where ∇p is the gradient of pressure ~ap Ω corrections, ~ap is the vector of central coefficients for the discretized linear system representing the velocity equation and Ω is the cell volume. 88 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

11. Update density due to the pressure changes.

12. Free all temporary storage.

5.5 Solution: Time Integration Method

This is the first part of the fourth step to develop or use a CFD. Here, the most appro- priate time integration method is selected for a time-dependent numerical formulation which is the case.

As mentioned before, the Segregated Flow model have been selected in this inves- tigation. The STAR-CCM+ code provides the Implicit Unsteady model with this flow model. The main function of the Implicit Unsteady model is to control the update at each physical time for the calculation as well as to control the time-step size.

Transient analysis is developed with the unsteady SIMPLE algorithm. The transient term is expressed as a source term in the momentum equation (5.25) and the regular segregated flow solver is used to perform inner iterations.

The Implicit Unsteady solver in STAR-CCM+ offers two temporal discretization options: first-order and second-order. In this case, the first-order temporal discretization, also called Euler Implicit, has been chosen. This discretizes the unsteady term using the solution at the current time level (n + 1), as well as the one from the previous time level (n) as follows:

∂ (ρφ )n+1 − (ρφ )n (ρφΩ) = 0 0 Ω (5.66) ∂t 0 ∆t 0 Finally, the discretization of the equations will result in the coefficients of a linear equation system. This system needs to be solved implicitly, in an iterative fashion. There are two methods. One is used for implicit under-relaxation, the other method is used for the delta form of the equations.

Implicit Under-Relaxation

The algebraic system for the transported variable φ at iteration k + 1 is written implicitly as:

k+1 X k+1 apφp + anφn = b (5.67) n where the summation is over all the neighbors n of cell p. The right hand side, b represents the explicit (that is, evaluated with the results from iteration k) contributions 5.6. SOLUTION: ALGEBRAIC SYSTEM OF EQUATIONS 89

to the discretized equation. The coefficients ap and an are obtained directly from the discretized terms.

An under-relaxation factor ω may be introduced implicitly as follows:

ap X ap φk+1 + a φk+1 = b + (1 − ω)φk (5.68) ω p n n ω p n where the superscript k + 1 implies the value after the solution is produced, and the source term on the right-hand side is evaluated at the previous iteration k.

Delta Form

k+1 k Sometimes, equations are transformed into “delta form” by defining ∆φp = φp − φp, the system to be solved becomes:

ap X X ∆φ + a ∆φ = b − a φk − a φk (5.69) ω p n n p p n n n n The right hand side:

k X k r = b − apφp − anφn (5.70) n It is termed the residual and represents the discretized form of the original equation 5.25 at iteration k. By definition, the residual will be zero when the discretized equation is satisfied exactly.

5.6 Solution: Algebraic System of Equations

The algebraic methods solve the discrete linear system iteratively. This is the second part of the fourth step to develop or use a CFD as described in the introduction of this chapter. The result of the discretization approach described above is a linear system (A~x = ~b) representing the algebraic equations for each computational cell. The matrix A represents the coefficients of the linear system (for example, the coefficients ap and an on equation 5.69), the vector ~x represents the unknowns (∆φ in 5.69) in each cell, and the vector ~b represents the residuals (equation 5.70) from each cell.

Typically, the matrix A will be very sparse. Direct methods such a Gauss elimination or LU decomposition on such systems are very costly, since the triangular factors of sparse matrices are not sparse, making such methods untenable for practical problems involving large grids. It is therefore preferable to use an efficient iteration method, such 90 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS

as the algebraic multigrid method in STAR-CCM+.

The Basic Iterative Methods

The general principle behind iterative methods is that, given an approximate solution, ~x k we seek a better approximation ~x k+1, and then repeat the process.

If the error at iteration k is defined as:

~e = ~x − ~x k (5.71) where ~x represents the exact solution and the residual as:

~r k = ~b − A~x k (5.72) It follows that:

A~e k = ~r k (5.73) Therefore, by continuing the iteration until the residual is driven to a small value will also caused the error to be driven to a small value.

The most basic iterative methods are Jacobi and Gauss-Seidel iteration. These methods involve visiting each cell in sequence, and updating the value of xi in each cell i using the coefficients of its n neighbor cells as follows:

! 1 X x = b − A x (5.74) i A i,n n i,i neig n The difference between Jacobi and Gauss-Seidel iteration is subtle: Jacobi uses the “old” values of xn, while Gauss-Seidel uses the available values that have been updated, resulting in better convergence.

Multigrid Methods

The primitive iteration methods described above, while relatively simple to imple- ment, exhibit relatively slow convergence characteristics. They tend to be only effective at removing high-frequency (rapidly varying) components of the error. This suggests that some of the work could be done on a coarse grid, since computations on coarse grids are much less costly and the Gauss-Seidel method converges four times faster on a grid half as fine. Multigrid algorithms do this using the following: 5.6. SOLUTION: ALGEBRAIC SYSTEM OF EQUATIONS 91

• Step 1: Agglomerate cells to form coarse grid levels.

• Step 2, Restriction: transfer the residual from a fine level to a coarser level.

• Step 3, Prolongation: transfer the correction from a coarse level back to a finer level.

Multigrid algorithms may be divided into two types: geometric and algebraic. The geometric multigrid uses the grid geometry and the discrete equation at the coarse level to arrive at the linear system to be solved on that level. The algebraic multigrid derives a coarse level system without reference to the underlying grid geometry or discrete equations. The coarse-grid equations are derived from arithmetic combinations of the fine-grid coefficients. Since it may not always be straightforward to obtain suit- able discrete equations on the coarse levels, algebraic multigrid (AMG) is clearly at an advantage. Therefore, it is used for the solution of all the linear systems in STAR-CCM+. 92 CHAPTER 5. COMPUTATIONAL FLUID DYNAMIC SIMULATIONS Chapter 6

INFLUENCE OF THE MAST

6.1 Introduction

In the research presented in this chapter, the airflow around sails is simulated using two RANS codes. The aim of this investigation is to consider the effect of the mast on sail performance.

A mast in front of the mainsail affects the aerodynamic performance of the jib-mainsail system. The mast at the luff of the mainsail changes the flow pattern on both the mainsail and the jib and it normally reduces the efficiency of the system. The resultant flow struc- ture is complex and usually with separation and recirculation bubbles appear. This is why mast design is important. It is desirable to minimize separation and thus, reduce the drag.

RANS codes are appropriate to deal with these complex separated flows where viscosity and turbulence have great importance. Furthermore, numerical methods provide not only global quantities like sail forces and moments but also flow quantities at all points around sails. CFDs are useful tools for improving mast-sail designs.

The pioneer investigations where based on experimental tests. During the 70s, J.H. Milgram [97] and C.A. Marchaj studied two-dimensional mast-sail configurations in a water tunnel and a wind tunnel respectively. In the next decade, S. Wilkinson ran an ambitious wind tunnel program to investigate the two-dimensional mast-sail interaction. Nowadays, the results obtained by Wilkinson are still in use as reference data for validation.

The first investigation where a RANS method was applied to mast-sail flows is attributed to Caponnetto and colleagues [49]. In this paper, some critical issues to the 30th America’s Cup FAST2000 Challenge are discussed. It is mentioned that a number of different mast profiles were studied using a RANS solver but results are not included due to the secrecy in the America’s Cup. In the same way, P. Jones and R. Korpus [51] mention that they also studied the mast design from section profile and rake, to

93 94 CHAPTER 6. INFLUENCE OF THE MAST

deformation under load. Again, results are not provided since the investigation was undertaken for the America’s Cup Challenge AmericaOne.

In 2005, Chapin et al. [98] studied the two-dimensional effect of design parameters such as Reynolds number, incidence angle, mast diameter and sail camber. RANS simulations were computed and comparisons with wind-tunnel experiments were con- ducted. Two years later, Paton et al. [99] investigated the effect of mast rotation on the performance of a sail using a two-dimensional RANS based CFD. In the same year, 2007, Masuyama et al. [31] presented the application of a RANS-based CFD method to evaluate the mast influence on aerodynamic forces and flow. This last paper included three-dimensional shapes.

The methodology to achieve the goal of the investigation presented in this chapter has been reproducing the full-scale measurements obtained from the previously mentioned paper [31] together with [30] and [32]. Yutaka Masuyama and Toichi Fukasawa built the sail dynamometer boat Fujin (figure 6.1) in the late 90s, as mentioned before in chapter 3. They measured flying shapes and sail performance simultaneously, as well as the corresponding sailing conditions.

Figure 6.1: Sail dynamometer boat Fujin

In the present chapter, some of the sail arrangements from these papers are simulated using the commercial packages ANSYS-CFX 10.0 [100] and CD-Adapco’s STAR-CCM+ [92]. Three arrangements are considered: the mainsail alone in two different sailing conditions and the jib+mainsail configuration in another sailing condition. The results 6.2. NOMENCLATURE 95

are compared with both experimental data and numerical computations obtained from [32].

The main contribution of the research described in this chapter is the study of the three-dimensional effect of a mast on sail performance. As far as this author’s knowledge is concerned, there are several two-dimensional studies that deal with the mast influence but there is a lack of three dimensional results. Moreover, in this investigation, two different RANS-based CFDs have been applied to a real scenario and the results have been validated with experimental data, which is the thread of this thesis.

The remainder of this chapter proceeds as follows. First, the nomenclature and main parameters are presented. Then, in section 6.3, the reference full-scale tests are described as well as the sail shapes and the results for comparison. In section 6.4, the numerical simulations carried out with ANSYS-CFX are included. In section 6.5, the simulations performed with the CD-Adapco’s STAR-CCM+ code are presented. Finally, in section 6.6 the main conclusions are summarized.

6.2 Nomenclature

µ Dynamic viscosity

ρ Air density

τ Time-step

CD Drag coefficient

CL Lift coefficient

CP Pressure coefficient P − P CP = abs (6.1) 0.5ρV 2

CX Force coefficient F CX = x (6.2) 0.5ρSV 2

CY Force coefficient F CY = y (6.3) 0.5ρSV 2

Fx Force component along “x” axis

Fy Force component along “y” axis hm Mast height 96 CHAPTER 6. INFLUENCE OF THE MAST

Lc Characteristic length (5m, approximation to jib and mainsail foot)

Mx Moments around “x” axis

Mz Moment around “z” axis. P Pressure

Pabs Absolute pressure Re Reynolds number (equation 2.2)

S Sail area

(u, v, w) Velocity components

V Wind speed

(x, y, z) Horizontal, lateral and vertical position

XCE “X” coordinate of the center of effort of sails M XCE = z (6.4) Fy y+ Wall treatment parameter (equation 5.43)

ZCE “Z” coordinate of the center of effort of sails M ZCE = x (6.5) Fy

The local reference system, fixed to the boat, is defined as follows: x-direction from bow to stern, y-direction from port to starboard and z-direction perpendicular to the previous directions and positive upwards. In the global reference system (for CFD simulations) the x-direction has the flow direction, the z-direction points upwards and y-direction is perpendicular to the previous directions and right-handed. In both reference systems, the origin of the coordinates is located at the aft face of the mast at the deck level.

6.3 Measurements of full-scale performance and sail shape

Full-scale sail tests were performed using the sail dynamometer boat Fujin [30]. The Fujin was originally built for conducting tests on sails for the Japanese America’s Cup entry in 1994. The design of the Fujin is based on the YR-10.3m class, which is an International Measurement System (IMS) ocean racer. The boat has a waterline length 6.3. MEASUREMENTS OF FULL-SCALE PERFORMANCE AND SAIL SHAPE 97

of 8.80m, 3.37m of maximum beam and a displacement of 3.86t.

Although the hull was made using a mold of that class, the deck and interior of the boat were modified to permit the installation of the dynamometer system which is composed of a rigid aluminum frame. The frame is separated structurally from the hull and connected to it by load cells. These form a six-component dynamometer system, and their outputs can be transformed to the forces and moments about the boat axes using a calibration matrix. All rig components such as the mast, chain plates, winches and lead blocks are attached to the aluminum frame. The under-deck portion of the mast is held by the frame, and the other rig components are attached to the frame through deck holes.

The test sails were made to correspond to a typical sail plan for an IMS Class boat. Table 6.1 shows the dimensions of the sails which were made by North Sails Japan.

Mainsail Jib Peak height 13.82m 10.70m Luff length 12.50m 11.45m Foot length 4.44m 4.89m Sail area 33.20m2 26.10m2 Table 6.1: Sail dimensions

During the full-scale tests, the sail shape was recorded using pairs of CCD cameras and portable video cameras. The sail shape images were analyzed using the sail shape software SSA-2D. This software calculates the curvature of the sail section by marking several points of the sail stripe and the reference line on the PC display, and indicates the parameters such as chord length, maximum draft, maximum draft position, entry angle at the luff (leading edge) and exit angle at the leech (trailing edge).

As mentioned before, in this chapter, three cases are analyzed: the mainsail in two sailing conditions and the jib+mainsail configuration in another condition. According to the reference paper [32] these three cases are named: ID9807172F (mainsail alone), ID9807172B (mainsail alone) and ID96092335 (jib+mainsail). As it can be seen in table 6.2 the shapes of the sails were given by six points in each of the six sections in which sails were divided.

The geometry of the mast was not provided in the reference papers. The first study that is presented in this chapter is undertaken without the real mast.

During the experimental tests, the apparent wind speed and apparent wind angle were measured by an anemometer attached to the bow unit. This unit comprised a post that rotated freely to maintain its vertical attitude when the boat heeled in order to 98 CHAPTER 6. INFLUENCE OF THE MAST

ID9807172F ID9807172B ID96092335

Table 6.2: Sail shapes

measure the wind data in the horizontal plane. The wind speed and wind angle sensors were calibrated using wind tunnel tests in advance and the calibration equations were ob- tained. The three sailing upwind conditions of the studied cases are presented in table 6.3.

ID9807172F ID9807172B ID96092335 Heel angle (◦) 8.8 8.3 15.1 Apparent wind angle (◦) 30.5 29.8 30.7 Apparent wind speed (m/s) 7.3 7.2 6.9 Table 6.3: Sailing conditions

The sea trials were performed in Nanao Bay off the Noto Peninsula (Japan). There is little tidal current in that bay and the wave heights are relatively small, even though the wind can be strong. Close-hauled tests were conducted over an apparent wind angle range of 20◦-40◦ and an apparent wind speed range of 5-11m/s.

Data sampling was started when the sailing condition was considered to be in steady state. The sampling rate for the data acquisition system was set at 10 Hz. Data sampling was continued for 90s, and during this time the sail shapes were recorded using the cameras. The steady state values were obtained by averaging the data over a 30 to 60s period. The boat was steered carefully during this time. However, the measured data contained some variation due to wind fluctuation and wave reflection on the hull. If 6.4. TESTS WITH ANSYS-CFX 99

the range of deviation of the apparent wind angle exceeded ±5◦, the results were discarded.

In the reference paper [32], the measured coefficients are plotted with error bars indicating the range of deviation over the averaging period. Only the results obtained on port tack are presented in the reference papers and this is the tack reproduced in the simulations.

ID9807172F ID9807172B ID96092335 CX 0.290 0.190 0.500 CY 1.240 1.310 1.390 CD 0.380 0.450 0.280 CL 1.210 1.250 1.440 XCE (m) 1.560 1.680 0.410 ZCE (m) 5.670 5.860 4.170 Table 6.4: Measured data

Table 6.4 shows the measured data at full scale such as the driving (thrust) and side force coefficients (CX and CY ), as well as the longitudinal and vertical position of the center of effort (XCE and ZCE). The drag (CD) and lift (CL) coefficients are also included. It should be highlighted that the coordinates are given in the body-fixed axis system. Thus, when the boat heels, the side force component is not in the horizontal plane but it is normal to the mast. The aerodynamic forces acting on the mast and rigging are included in the measured sail forces.

6.4 Tests with ANSYS-CFX

The first simulations have been conducted with the commercial program ANSYS CFX-10. It is a RANS based CFD code utilized to simulate fluid flows in a variety of applications. The first version was called FLOW-3D and it was commercialized in the late 80s. Some years later, the name was changed to the current CFX.

The surface generation from the net of points has been carefully carried out with the CAD program Rhinocerosr and the grid generation process with the ICEM- CFD mesher. The reference data is full-scale so the numerical modeling has been also developed at the same scale. The sails have been treated as no-thickness rigid membranes.

Before obtaining reliable results, a grid-sensitivity study has been performed and several tests have been conducted in order to choose the best numerical parameters. In this section, only the best results are presented. It is highlighted that more than five type of meshes have been tested for each geometry, trying to find out the best parameters and 100 CHAPTER 6. INFLUENCE OF THE MAST

the optimal number of elements according to the capacity of the computer. With the suitable meshes, different parameters of the numerical scheme and boundary conditions have been established to obtain the best combination among them. Therefore, the real number of studied cases is enormous, even if in this chapter only the most satisfactory results are presented.

The simulations have been run in two independent CPU Pentium IV 3.2 GHz computer with 3GB of RAM. For a mesh size of 1,300,000 elements the typical CPU time for achieving the specified convergence has been around 11 hours.

When the simulations with the ANSYS-CFX were actually conducted, the geometry of the mast was unknown. The first results in this section have been obtained without mast and they are compared to the data provided by [32] which include the mast contribution. At the end of this section, it is presented the study conducted with different masts designed by the author from pictures of the Fujin.

The results of the research described in this section were partially disclosed by the author in [2].

6.4.1 Domain and mesh The extension of the computational domain of the mainsail-alone configurations is 100m upstream, 120m downstream, 60m upwards and 60m on each side. The extension downstream the jib+mainsail configuration is 140m. These dimensions have been proven to be sufficient for a good development of the flow without creating wall effects.

The grid is structured and concentrated next to the sails. These are generated as surfaces with no thickness, on which “no-slip” boundary condition is applied. The number of hexahedrons is around 1.3 · 106 for the mainsail-alone configuration and 2.1 · 106 for the jib+mainsail configuration.

In order to evaluate the quality of the mesh next to walls and its capability of detecting the boundary layer, the “Yplus” (y+) parameter is analyzed. This is a value that is used to check the location of the first node of the mesh away from a wall. It is the dimensionless distance from the wall and it is based on the distance from the wall to the first node and the wall shear stress, as seen in equation 5.43. The size of the elements in the direction normal to the sail is around 1-3 mm and it is adjusted to y+= 1 - 90 which is a range similar to the ones used in [10], [60], [61], [62] and to the recommended value in the CFX documentation [100]. A screen-shot of the ID96092335 mesh can be seen in figure 6.2.

The “determinant 2x2x2” criterion has been also used to verify the quality of the meshes. A determinant value of 1 would indicate a perfectly regular mesh element, 0 would indicate an element degenerated in one or more edges, and negative values would 6.4. TESTS WITH ANSYS-CFX 101

indicate inverted elements. It has been checked that the determinants are higher than 0.6 for all the hexahedrons in the meshes. These values are considered appropriate for a good quality mesh.

Figure 6.2: ID96092335 case mesh

6.4.2 Boundary conditions The most suitable boundary conditions, necessaries to reproduce the real behavior of the flow around the sail dynamometer boat Fujin, have been set.

• Inlet: The speed normal to the inlet surface is set constant and different in each case. The wind gradient is not taken into account on the numerical calculation since it was demonstrated in [32] that the gradient was not relevant. This means that the apparent wind angle and speed are assumed to be constant along the vertical direction. Turbulence intensity is set at 2% (low) and length scale of turbulence of 0.5 m (1/10Lc) according to the recommendations of the CFX documentation [100]. • Outlet: the averaged pressure over the surface is set to zero. • Walls: the condition imposed is “free-slip”. • Deck: The boundary condition is “free-slip”. Different tests have been conducted with the “no-slip” condition on the bottom. The results highlight that there is not relevant variation so it is decided to use “free-slip” because it requires less computing time. 102 CHAPTER 6. INFLUENCE OF THE MAST

• Sail: the “no-slip” condition is set.

6.4.3 Numerical scheme As usual, in order to close the RANS equations and determine the Reynolds stresses, a turbulence model is required. The SST (Shear Stress Transport) model has been chosen as previously mentioned in 5.4.3. The SST gives highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients. The SST is one of the most popular turbulence models in external aerodynamics and it is used widely in sail aerodynamic research [61], [62], [65] and [101]. As stated by Menter [96], the reason for the wide spread usage of this model in aeronautics is that it is robust; it allows an integration through the viscous sublayer without much computational effort and has advanced separation prediction capabilities.

In order to judge convergence the value of the RMS (root mean square) residual has been considered. The condition imposed has been 10−5. This target is considered to lead to a “good convergence”, [100]. A RMS target of 10−6 has been tested but the CPU time needed is unpractical and excessive for the resources available.

The Reynolds number of the simulations is around 2.3·106 with a characteristic length of 5m. The time-step (τ), with the same length, has been obtained with equation 6.6. The values obtained are 0.172s, 0.174s and 0.184s for the first, second and third case respectively.

1 L τ = c (6.6) 4 V In the third case, jib+mainsail configuration, the time-step resulted to be too small. The convergence is difficult to achieve and the periodicity of the phenomena is captured. The three cases have been studied from a steady state point of view thus, in this third case, the time-step has been increased to avoid the periodic fluctuations, and finally the time-step in this case has been set to 4s.

6.4.4 Results and comparison One of the advantages of these commercial codes is that they give a great amount of outputs. This section is focused on the values which are useful to understand the phenomena involved and the ones to compare with the data of the reference paper.

Aerodynamic coefficients and center of effort

As it can be seen in table 6.5, the drive and side force coefficients have been obtained as well as the position of the center of effort in each case. In the same table the 6.4. TESTS WITH ANSYS-CFX 103

reference data have been included in order to facilitate the comparison. It must be again emphasized that the reference values include the contribution of the mast.

ID9807172F Reference study Present study CX 0.290 0.303 CY 1.240 1.179 XCE 1.560 1.550 ZCE 5.670 4.810 ID9807172B Reference study Present study CX 0.190 0.138 CY 1.310 1.176 XCE 1.680 1.510 ZCE 5.860 5.910 ID96092335 Reference study Present study CX 0.500 0.401 CY 1.390 1.373 XCE 0.410 0.280 ZCE 4.170 4.570

Table 6.5: Comparison of results, reference vs present study

In the first case, ID9807172F, both the drive and side force coefficients are similar to the reference values. In the same way, the side force coefficient of the second case (ID9807172B) resembles the experiential value.

On the other hand, the drive force coefficient of this second case differs around the 28% from the reference value and it could be considered excessive. But the fact is that there was a big scatter of the data during the experimental tests with only the mainsail, as explained in [32]. The error bars of this CX indicate a deviation of ±80%. Since the true wind velocity was insufficient for the mainsail-alone configuration, the boat was given additional thrust using an auxiliary engine in order to obtain sufficient apparent wind speed. When the jib was hoisted, the sailing boat was steered by looking at the shape of the luff of the jib. Without this sail, it was difficult to steer adequately and the deviation in apparent wind angle became larger. This is the reason for the larger experimental error for the mainsail alone than for the mainsail+jib configurations.

Moreover, the values of drag and lift coefficients indicate that there might be a wide flow separation on the mainsail surface in this second case. The sailing conditions of the two cases of mainsail alone are similar but the performance is very different. According to 104 CHAPTER 6. INFLUENCE OF THE MAST

the experimental data, the CD of ID9807172F is 0.380 whereas the value for ID9807172B is 0.450. In the same way, according to the numerical result of this investigation the CD of the first case is 0.326 whereas the coefficient for the second case is 0.456. RANS solvers can take into account the separation but the numerical scheme and the mesh quality must be more ambitious.

The calculated value of the side force coefficient of the third case ID96092335 is similar to the experimental value. The drive force coefficient differs around a 20% which is below the error deviation of the experimental value. It is estimated that this value would be improved if the mast had been considered in the simulations.

The result of the XCE of the third case would have been better if the mast had been included. Some studies reveal that the inclusion of the mast in a jib+mainsail configuration can move the center of effort 10% aft, [32]. The values of XCE in the first two cases are similar to the experimental values.

There is a wide scatter in the experimental values of vertical position of the center of effort. According to the reference paper, this is thought to be because the measured Mx moment contains a large component from the mass of the dynamometer frame and rigging (659 kg). This moment was subtracted from the measurement, taking into account the measured heel angle. If there was a slight error in the position of center of gravity of the dynamometer frame, or in the measured heel angle, the error in the calculated moment would have been large. Despite the above, only the ZCE of the second case differs from the experimental values while the other two remain similar.

In the third configuration, ID96092335, the CFD program enables the calculation of the forces separately. The values for the mainsail are CX =0.102 and CY = 0.671, while the results for the jib are CX = 0.299 and CY = 0.703. The jib, with less area, produces more drive force and side force than mainsail does. It is thought that it occurs because the circulations of main and jib tend to oppose and cancel each other in the area between the two sails and therefore more air is forced over leeward side of the jib, [60].

Pressure coefficient distribution

In figures 6.3, 6.4 and 6.5, the pressure coefficient for each case can be seen. As mentioned before, the tests simulate port-tack sailing, therefore, the port and starboard sides correspond to the pressure (windward) and suction sides (leedward), respectively.

The images have been compared with the numerical results of Masuyama et al. [32] and they are similar. The pictures of pressure coefficient of the reference paper are not included in this document because of their bad resolution. When comparing values, the distribution of pressure coefficient is better in the first two cases than in the third. In this last case the only part that can be judged satisfactory is the leeward side of the jib. It 6.4. TESTS WITH ANSYS-CFX 105

(a) Windward (b) Leeward

Figure 6.3: Pressure distribution (ID9807172F) can be due to the detachment of the flow on that side which affects considerably the per- formance of the mainsail. In this situation the program is not able to capture the vortices on the leeward side of the mainsail. A better mesh and a transient study would be needed.

The pressure distribution cannot be validated since there are not experimental measurements. It would have been interesting to have these data since forces and moments can be obtained with different pressure distributions. In order to improve the sail design, the distribution of pressures is important especially when a mast is considered. 106 CHAPTER 6. INFLUENCE OF THE MAST

(a) Windward (b) Leeward

Figure 6.4: Pressure distribution (ID9807172B)

(a) Windward (b) Leeward

Figure 6.5: Pressure distribution (ID96092335) 6.4. TESTS WITH ANSYS-CFX 107

Flow detachment

Figure 6.6: Plane at half of the luff of mainsail (ID9807172B)

In figure 6.6 the streamlines and air velocity on the horizontal midsection of the mainsail is shown. The pink line represents the intersection of the sail with the plane. There is separation of the flow and a vortex at the trailing edge. Even if it is usually considered that when upwind there is no separation and potential methods are used, it is demonstrated that there is detachment of the flow. Because of this fact, viscous CFD codes must be used as the one in this work.

Once a complete set of streamlines are determined, it can be explained how the wind speed and pressure vary in the flow field around the sail. Where the streamlines get very close together, the air speeds up. In the other hand, where the streamlines get further apart, the air slows down.

Another relevant phenomenon can be seen in figure 6.6: upwash. As the air flows towards the sails, it changes direction before returning to its original direction some distance after the sails. The upwash flow ahead of the mainsail causes the stagnation point to be shifted around toward the windward side of the mainsail. The boat should, therefore, be pointed closer to the wind.

Generation of vortices

In figure 6.7, two vortices can be seen: one on the top of the sail and the other at the bottom. Just as it was expected the second vortex is gotten flat and in a higher height than the boom. The presence of the deck (floor) tends to tangle up the two tip vortices 108 CHAPTER 6. INFLUENCE OF THE MAST

Figure 6.7: Two vortices downstream (ID9807172B)

and affect the flow up to the middle of the mast height, usually, increasing both lift and drag.

When the performance of a sailing boat is studied as part of a fleet race, it has great importance to be able to capture the interaction between boats. If the yacht is sailing upwind and there is another yacht on windward, it is said that the first yacht is in a shadow since the upwind yacht covers the downwind yacht. There is a blanketing effect caused by the flow propagating downwind which reduces the wind speed and changes the wind direction. Therefore is very interesting to study the size and position of the vortices downstream a sailing boat.

Mast influence

Since there was no information about the geometry of the mast some test with sup- posed masts have been carried out in the first two cases. The jib+mainsail configuration have been avoided due to the complexity of the structure mesh. Three masts have been designed by the author according to the pictures of the sailing boat. One of the masts has an elliptic section and that section is constant along the height of the mast (see figure 6.8). The second has also an elliptic form but its shape decreases from bottom to top. The third mast has a circular section. The best results have been obtained with the elliptic and constant mast (see table 6.6).

In the first case, ID9807172F, the inclusion of the mast deteriorates the results, specially the CX . On the other hand, the results of the second case improve substantially. It is observed that for both cases, the mast increases the drive force coefficient as well as 6.4. TESTS WITH ANSYS-CFX 109

Figure 6.8: ID9807172F case mesh with a mast

ID9807172F Reference study With Without CX 0.290 0.379 0.303 CY 1.240 1.306 1.179 ID9807172B Reference study With Without CX 0.190 0.187 0.138 CY 1.310 1.253 1.176 Table 6.6: Comparison of results, with and without a mast the side force coefficient.

It must also be considered that the geometry of the hull was not included in the simulations neither the rigs. Although the calculus would be enormous, including the hull and the rig would make the results be closer to real values. It must be highlighted that meshing one sail is complicated and even more for a mast-mainsail configuration. The difficulty arises from the fact that the sail has no thickness but the mast does. It is very laborious to make a structured mesh next to the mast-sail configurations and control all the parameters without increasing the number of elements excessively.

These result are not conclusive and the real shape of the mast is needed. According to the investigation by Paton et al.[99] the mast profile can affect up to 40% of drag. Therefore, further studies are required. Moreover it is convenient to increase the quality of the meshes and do more research on the parameters of the numerical scheme. These conclusions lead to the research presented in the following section. 110 CHAPTER 6. INFLUENCE OF THE MAST

6.5 Tests with STAR-CCM+

The need of knowledge of the phenomena involved in the previous investigation has guided the author to the research presented in this section. More simulations are required and the inclusions of the real mast have become compulsory as a result of the conclusions of the computations with the ANSYS-CFX.

In this case, the RANs-based computational code CD-Adapcos’s STAR-CCM+ have been used. The main reason to change the software, apart from the capability to compare the two of them, is the resources available. The licenses of this software are much cheaper for the same features. During a research, not only the technical point of view is taken into account but the efficiency of the system becomes relevant. This software allows the generation of greater meshes and more processors in parallel for a lower price. Furthermore it is easier to use and all the steps are fully integrated. Moreover, it has been installed on Linux operating system.

Prof. Yutaka Masuyama, co-author of the reference papers, sent the author of this thesis, the section of the mast when the previous study was already finished. The mast section has a flat back and is often described as “bullet shaped”. This section has been modeled to obtain the three-dimensional geometry of the mast by assuming that the section is constant along its length. The real shape of the mast is similar to the elliptic mast designed by the author in the study with ANSYS-CFX. This supports the previous statement that the elliptical shaped section mast gave better results. In this research, the three cases (ID9807172F, ID9807172B and ID96092335) are simulated again without mast and then, the mast-sail configurations are computed.

Figure 6.9: Increase of the number elements vs. elapsed time per iteration (computer 1)

The calculations of this research have been run on three computers. The first computer is an Intel Core 2 Quad CPU with a Linux 2.6.31-20-generic. This computer has been used for the first studies with small meshes. Then, for larger meshes, a 8 6.5. TESTS WITH STAR-CCM+ 111

Quad-Core cluster with a Linux 2.6.27-19-5 kernel (amd64), has been used. As an example, in this second computer, for a 3.5 · 106 elements mesh, the typical CPU time to achieve the desired convergence has been around 8 hours using 7 processors of the clus- ter. The third computer is an Intelr Core i7-920 Processor with a Linux 2.6.38-12 kernel.

The increase of computational time with the increasing number of mesh elements has been analyzed. As it can be seen in figure 6.9, the relationship between the increase of number of elements and the elapsed time per iteration is linear. The values of the abscissa have been normalized with the shortest mesh which had 72493 elements. This linear tendency is also fulfilled for the other computers. This early analysis helps optimizing the computational time and planning the research more adequately.

The results of the research presented in this section were partially disclosed by the author in [3].

6.5.1 Domain and mesh As well as with the previous software, the sets of points that define the sail shapes have been introduced into Rhinocerosr 4.0, where the sail surfaces have been modeled. Unlike with the ANSYS-CFX, when simulating with STAR-CCM+, a minimum thickness of 2mm has been considered.

The computational domain is a rectangular box. The extends of the volume are set so as to permit a good development of the flow without creating wall effects. It is important to minimize the volume in order not to waste computational efforts. The extension of the computational control volume has been finally set in relation to the mast height (hm) 13.82m: hm upstream, 3hm downstream, hm leeward, hm windward, 0 below (deck level) and 2hm above (see figure 6.10). This overall domain is smaller than the box used in the preceding study with the ANSYS-CFX but it has been checked to be sufficient by simulating different boxes and evaluating the influence on the result.

The meshing procedure has been conducted with the meshing tool of the STAR- CCM+. According to the nomenclature of this software, the final mesh is surface remesher and trimmer (hexahedral) type with prism layer mesher to properly capture the phenomena involved near the sail. Other type of meshes, such as the polyhedral type, have been analyzed. The convergence of the results with the increasing number of elements have also been checked and it has been demonstrated that the trimmer mesh is the most appropriate type of grid. The number of elements of the final simulations range from 8.5 · 106 to 1.4 · 107.

In order to improve the quality of the meshes near the sail and the wake downstream, refining blocks and prism layers have been used. In the first two cases, ID9807172F and ID9807172B, 8 layers have been set whereas only 3 have been set in the third case, 112 CHAPTER 6. INFLUENCE OF THE MAST

Figure 6.10: Domain of the ID9807172B case with mast

ID96092335. This is due to the rapidly increasing number of elements with each layer.

The variable wall y+ has been studied to evaluate the quality of the mesh next to the rig and its capability of detecting the boundary layer by the numerical wall treatments. A typical target value of y+=1 has been aimed for most of the sail and mast surfaces. Moreover, the volume change ratio have been checked and it has stayed above 96%.

6.5.2 Boundary conditions The most suitable boundary conditions necessaries to reproduce the real behavior of the flow around the sail dynamometer boat Fujin have been set as in the previous investigation.

• Inlet: The speed normal to the inlet surface is set constant and different in each case. The wind gradient has not been considered as it was proved in [32] that the effect was insignificant, as mentioned before. Turbulence intensity is set to at 1% and the turbulent viscosity ratio to 10 according to the recommendation of the solver documentation [92].

• Outlet: the averaged pressure over the surface is set to zero.

• Walls: the condition imposed is “free-slip”.

• Deck: The boundary condition is “free-slip”. Again, different tests have been con- ducted with the “no-slip” condition on the bottom. The results highlight that there is not relevant variation so it is decided to use “free-slip” because it requires less computing time.

• Sail and mast: the “no-slip” condition is set. 6.5. TESTS WITH STAR-CCM+ 113

6.5.3 Numerical scheme The models utilized in these simulations are: three-dimensional, stationary, turbulent (SST K-Omega), segregated flow model, constant density, implicit unsteady and all-y+ wall treatment.

The Segregated Flow Model is suitable for constant density flows as it is supposed they are in these simulations. This model solves the flow equations (one for each component of velocity and one for pressure) in a segregated sequence. The linkage between the momentum and continuity equations is achieved with a predictor-corrector approach. Due to the fact that the time scales of the phenomena of interest are of the same order as the convection and diffusion processes, the implicit unsteady approach is recommended. In the implicit unsteady approach each physical time-step involves some number of inner iterations to converge the solution for that given instant of time. The time step has been set to 0.1s for all the simulations and the inner iterations to 5. The time step is around the 15% of the characteristic time which is the characteristic length (∼5m) divided by the apparent wind speed.

As usual, in order to close the RANS equations and determine the Reynolds stresses a turbulence model is required. The model chosen has been the SST (Shear Stress Transport) as mentioned before and described in 5.4.3.

In order to judge convergence the value of the RMS (root mean square) residual has been considered. A maximum RMS of 10−4 has been obtained for all runs but in most simulations, noticeably lower residuals have been achieved. The driving and side forces have been also monitored to ensure they have settled. The last 20% of the total physical time has been analyzed and the fluctuation of the forces in this period is below the 0.5% of the mean value.

6.5.4 Results and comparison Next, the calculated coefficients and the position of the center of effort are compared to the reference data. In the same way, the pressure coefficient distribution, the flow detachment, the upwash and the generation of vortices are presented. In appendix A the numerical values are included.

Aerodynamic coefficients and center of effort

In figure 6.11(a) it can be seen that the mast increases the drive force coefficient in the first case (ID9807172F) whereas it decreases the drive force in the third case (ID96092335). In both configurations the inclusion of the mast improves the results comparing to the reference values. It is noteworthy that in the investigation presented in the previous section it was estimated that the inclusion of the mast would improve the 114 CHAPTER 6. INFLUENCE OF THE MAST

(a) Drive force coefficient (b) Side force coefficient

Figure 6.11: Force coefficients values of the calculated drive force coefficient of the third case. Now, that assumption is verified. The drive force coefficient is increased a 14% by the presence of the mast.

On the other hand, the mast does not influence the value in the second case (ID9807172B). The difference between the calculated values and the reference datum is remarkable but still lower than the experimental error. As stated previously, during the full scale tests with the mainsail alone, the boat was given additional thrust using an auxiliary engine in order to obtain sufficient apparent wind speed besides the difficulty to steer without the jib. This is the reason for the wider error for the mainsail alone than for the mainsail+jib configurations. The error of the CX in this second case, indicate a deviation of ±80%. This error can be caused by the generation of wide flow separation on the mainsail during the tests.

In figure 6.11(b) the side force coefficient is shown. The mast increases the side force in the second and third cases, whereas it decreases the coefficient in the first case. As it occurred in the previous investigation with the elliptical section mast, the mast improves the computed value of ID9807172B, while the value of ID9807172F differs more from the reference datum. Nevertheless, the deviations of all the calculated values are within the error bars of the corresponding experimental datum. If the total force on the xy-plane is considered it is concluded that the mast improves the values of the first and third cases.

The longitudinal position of the center of effort is presented in figure 6.12(a). In the first two cases, ID9807172B and ID9807172B, the mast moves the center of effort forward. On the other hand, in the jib+maisail configuration the mast moves the center of effort aft as in the simulations of [32]. If the calculated values are compared to the reference data, it can be stated that the inclusion of the mast improves the results in the first and third cases.

In figure 6.12(b), the vertical position of the center of effort is plotted. The values obtained with the RANS solver overestimate the reference values for all the configurations with and without mast. This can be due to wide scatter in the experimental values 6.5. TESTS WITH STAR-CCM+ 115

(a) Longitudinal position (b) Vertical position

Figure 6.12: Center of effort of vertical position of the center of effort. As mentioned before, this is thought to be because the measured Mx moment contains a large component from the mass of the dynamometer frame and rigging. This moment was subtracted from the measurement, taking into account the measured heel angle. If there was a slight error in the position of center of gravity of the dynamometer frame, or in the measured heel angle, the error in the calculated moment would have been large.

It can be observed that the mast does not influence the vertical position of the center of effort for the mainsail-alone configurations. On the other hand, the mast elevates the vertical position of the center in the third situation.

It can be concluded that, in general, taking into account the mast is more realistic and it will lead to an improved prediction of the flow and the aerodynamic forces as far as the current configurations and sailing conditions are concerned.

Pressure coefficient distribution

The pressure coefficient distribution over the sail has been plotted for the ID9807172F case with (figure 6.13) and without the mast (figure 6.14). The left and right diagrams correspond to the port and starboard sides, i.e., the pressure (windward) and suction (leeward) sides, respectively.

The images have been compared with the numerical results by Masuyama et al. [32] and they are similar. The pictures of pressure coefficient of the reference paper are not included in this document because of their poor resolution. The results of the case without mast are subtly closer to the numerical results of the reference paper where the mast was not simulated either.

On the other hand, comparing current cases, it can be concluded that the general features of the pressure distribution over the windward side of mainsail alone are similar to those for the mast-sail configuration. The influence of the mast is mainly 116 CHAPTER 6. INFLUENCE OF THE MAST

(a) Windward (b) Leeward

Figure 6.13: Pressure coefficient distribution (ID9807172F with mast) focused on the leeward surface and next to the luff. The other two configurations are not included since the conclusions that are drawn are similar to the ones of the 9807172F case.

It would have been interesting to compare the computed pressures with the real values. But, as it will be explained in next chapter, the experimental measurement of pressures is very rare in sail aerodynamic research. The same aerodynamic force can be obtain with different pressure distributions and therefore, it is recommended to confirm that the computed forces are calculated for the same pressure distribution.

Flow detachment and upwash

The local flow field on the horizontal midsection of the mainsail (ID9807172F) is shown in figure 6.15 as well as the normalized velocity distribution for both configurations, with (6.15(a)) and without (6.15(b)) the mast. The colors of the flow field in the plot correspond to the dimensionless ratio of the local velocity to the apparent wind speed at the inlet.

Upwash is a remarkable feature of the flow that is presented in both cases. Upwash is the changing of the direction of the flow as it approaches the sail [99]. It is important to consider this phenomenon when designing an optimum sail performance. The configuration without the mast presents an larger angle of upwash comparing to the mast-mainsail configuration.

In these pictures it can also be seen that there is a detachment of the flow in both cases, even though it is more notorious in the mast-sail configuration, where there 6.5. TESTS WITH STAR-CCM+ 117

(a) Windward (b) Leeward

Figure 6.14: Pressure coefficient distribution (ID9807172F without mast)

(a) With (b) Without

Figure 6.15: Normalized speed and streamlines (ID9807172F) is a vortex at the trailing edge. Even if it is usually considered that when sailing upwind there is no detachment and potential methods are used, it is demonstrated that there is separation of the flow. Because of this fact, viscous CFD codes should be use.

The local flow field on the horizontal midsection of the ID96092335 case can be seen in figures 6.16(a) (with mast) and 6.16(b) (without mast). If both figures are compared, it can be observed that the mast affects mainly the leeward side of the mainsail. It also changes the area next to the leech at the windward side of the mainsail. The leeward side of the jib and most of the windward side of both sails remain unchanged regarding the presence of the mast.

The mast reduces the gap between the sails and therefore it increases the wind speed at the leeward side of the mainsail. Whereas, in the configuration without the mast, there are large areas with zero velocity which indicates detachment of the flow. 118 CHAPTER 6. INFLUENCE OF THE MAST

(a) With (b) Without

Figure 6.16: Normalized speed (ID96092335)

Midsection pressure coefficient

Figure 6.17: Pressure coefficient (ID9807172F with and without mast)

The calculated pressure coefficient on the midsection of the mainsail (ID9807172F), with and without mast, are presented in figure 6.17. In this plot the usual aerodynamic convention of reversing the vertical scales have been used: the leeward surface pressures that are negative on the top part of the curve and the windward surface pressures that are usually positive, on the bottom part of the curve. The difference in pressure between the two sides gives the aerodynamic force.

On the windward surface the flow appears to have similar trends although there are variations in values at the leading edge. On the other hand, the pressure distribution is much higher (more negative) when the mast is not considered. The sail develops more lift when it is operating in a flow field created without the mast. For both cases, the trailing edge of the mainsail is in high speed region of flow created on the leeward side of 6.5. TESTS WITH STAR-CCM+ 119

the mainsail.

Figure 6.18: Pressure coefficient (ID96092335 with and without mast)

The calculated pressure coefficient on the midsection of the jib+mainsail configuration (ID96092335), with and without mast, are presented in Figure 6.18. As stated before, the mast affects the leeward side of the mainsail. The curve of the configuration without the mast shows a large zone of detachment on the leeward side of the mainsail. On the other hand, the presence of the mast produces a reattachment of the flow.

Generation of vortices

As mentioned before, it is important to study the generation of vortices in order to understand the blanketing effect caused by the upwind yacht’s sails and its effect on the flow propagating downwind which reduces its magnitude and alters its direction.

Figures 6.19(a) and 6.19(b) show the streamlines in the flow field to identify the influence of the mast by comparison of the two cases. The configurations without the mast has smooth streamlines, whereas at the mast-sail configuration, two main vortices are generated: one at the top of the mast and the other at the end of the foot of the mainsail. As it can be seen in the present results, the influence of the mast on flow is particularly significant although some effect can be due to the meshing resolution. Near the sail, the meshes are similar, but in the far field, the mesh of the without-mast configuration is slightly coarser than the mast-sail case. The mesh of the case without the mast can be dissipating the vortices.

Figure 6.20 displays the development of the maximal vorticity downstream of the mainsail (ID9807172F case). The vorticity is the curl of the velocity field (see equation 6.7). This is a very common concept used in fluid dynamics. The vorticity is related to the amount of local angular rate of rotation in a fluid. 120 CHAPTER 6. INFLUENCE OF THE MAST

(a) Without (b) With

Figure 6.19: Generation of vortices (ID9807172F)

∂w ∂v ∂u ∂w ∂v ∂u V orticity = − , − , − (6.7) ∂y ∂z ∂z ∂x ∂x ∂y

Figure 6.20: Maximum vorticity (ID9807172F)

It can be observed that the vorticity values have different starting values and decrease exponential. The steep decrease in vortex strength continues up to the value of 2-3 foot lengths downstream and decelerates afterwards. It is noteworthy the increase of the vorticity values due to the inclusion of the mast although, again, part of the effect can be due to the meshing resolution.

Two specific simulations have been conducted in the case of ID9807172F. The configurations with and without the mast have been again computed but a refinement of the mesh downstream have been built. Figure 6.21 shows the development of the 6.5. TESTS WITH STAR-CCM+ 121

maximum vorticity with two identical refined meshes. It is clear that coarse meshes dissipate the vorticity. Moreover, for this size of mesh, the difference of vorticity with and without the mast is negligible. It is concluded that there is a great dependency of the vorticity with the mesh size.

Figure 6.21: Maximum vorticity downstream, (ID9807172F, identical downstream mesh) 122 CHAPTER 6. INFLUENCE OF THE MAST

6.6 Conclusions

The work presented in this chapter has been focused on developing a methodology for studying racing yacht sails in upwind conditions by combining full scale measurements with three-dimensional RANS simulations. The aim of this investigation has been to analyze the effect of the mast on sail performance.

These RANS viscous solvers have now reached a mature stage and can be used as top-quality design tools to study sail flow and to perform optimization of modern rigs. Not only full scale force predictions can be achieved, but the whole flow field around the sails can be studied for a better understanding of the main flow features. For example, the detachment of the flow in upwind condition that has been showed in this chapter suggests that viscous CFD codes must be used and not potential codes as it is usually done.

The methodology to achieve the goal of this investigation has been reproducing the full-scale tests described in [30], [31] and [32]. Three sail arrangements have been simulated specifically with the commercial packages ANSYS-CFX and CD-Adapco’s STAR-CCM+. The results have been compared with both experimental data and numerical computations obtained from the reference papers.

A positive agreement of the present numerical study with the reference one is considered, both in terms of qualitative aspect and in terms of numerical values. The inclusion of the mast in the numerical simulations improves the results mainly of the driving force coefficient and the horizontal position of the center of effort. Moreover it has been observed that the influence of the mast is focused on the leeward side where detachment is presented. In general, this research points out the significant influence of the mast on sail performance which shows the necessity of the inclusion of the mast in this type of three-dimensional numerical calculations.

A CFD code is a cost-effective tool for the performance prediction of a sailing yacht. If experimental results can be accurately reproduced using the same methodology for a fair number of cases, the latter can be afterwards trusted for providing reliable results for new cases, for which no experimental data are available [61]. The study shows that CFD codes can be used with remarkable accuracy to estimate aerodynamic forces but there is still a lack of pressure distribution validation. Chapter 7

PRESSURE DISTRIBUTION ON A TP52 MAINSAIL

7.1 Introduction

The general problem presented in this chapter is related to the better understanding of the pressure distribution over a sail. As stated by R.G.J. Flay [102], there are four main reasons why one would carry out pressure measurements on sails. Firstly, if the pressure measurements are integrated over the sail surface, the forces and moments obtained from a balance can be checked. Secondly, pressure measurements can be used to validate estimated pressures obtained from CFD codes. Usually total forces are utilized to validate codes, but they cannot provide the same amount of detail as pressure measurements. In fact, the pressure distribution on sails might be computed incorrectly even when the computed resultant aerodynamic forces agreed with the measured force. This is because different pressure distributions can lead to the same global aerodynamic force. Thirdly, pressure measurements can be used to understand the phenomena involved near the sail such as the flow detachment. Fourthly, in the near future, they will by used directly by sailors in real-time to adjust the sails optimally.

The core motivation of the author to start this research was the lack of publications regarding this topic despite its importance. Moreover, the conclusions of the previous research, where the importance of pressure measurements to validate CFD was high- lighted, encouraged the author to begin this investigation.

In the 20s, pressure distributions on full-scale sails were measured by E.P. Warner and S. Ober [103]. In the 60s, the pressures on a model-scale mainsail were measured with manometers by C.A. Marchaj [104]. In the 70s and 80s, A. Gentry [105] [38] investigated pressure distributions with an Analogue Field Plotter on a 2D model. At the same time, S.L. Wilkinson also studied pressure distributions on 2D model-scale sections.

Between 2006-2008, instigations regarding full-scale measurements were published.

123 124 CHAPTER 7. PRESSURE DISTRIBUTION ON A TP52 MAINSAIL

It was highlighted the importance of the new lightweight small devices. In [102], there were reviewed some of the lessons learned by the Yacht Research Unit of the University of Auckland in measuring pressures on the sails of a Farr 1020 Class yacht. In [106], the pressure measurements on the mainsail of a Tornado Class catamaran were presented. In [107], they measured the pressures on the mainsail of a IACC Class yacht. Moreover, during this period, some pressure measurements were carried out at model scale to gain further understanding of downwind sails and validate numerical codes such as in [108].

In 2009 the research presented in this section began. At that time, pressure distributions on three-dimensional upwind model-scale sails had never been published. This encouraged the author to carry out this investigation. However, in recent years, the Yacht Research Unit (YRU) of the University of Auckland has developed a project aimed at comparing full-scale tests, wind tunnel tests and numerical analysis predictions. They have carried out wind tunnel tests in upwind condition ([109], [28], [110]) as well as full-scale measurements ([111], [112], [36]). They have also studied downwind conditions in the wind tunnel ([113], [114]) and in full-scale [37]. In [39] a summary of the project can be found.

The aim of this research is to measure the pressure distribution on a model-scale sail in a wind tunnel and then, validate the results obtained with a numerical code. The comparison between experimental data and numerical estimations permits an increase of the confidence in CFDs and helps the researcher to gain knowledge of the phenomena involved near the sail.

The method to achieve the objectives of this investigation is the development of specific wind tunnel tests to measure the pressure distribution on the mainsail of a Transpac 52 Class yacht in upwind condition. The pressure distribution has been measured on 18 horizontal sections of a rigid pressure-tapped sail in the Atmospheric Boundary Layer Wind Tunnel at the CEAMA (Universidad de Granada, Spain). The experimental technique that has been used is widely spread in civil wind engineering but it is innovative in sail aerodynamics. Then, the experimental conditions have been reproduced in the RANS code CD-Adapco’s STAR-CCM+ and the pressure distribution has been calculated.

The remainder of this chapter proceeds as follows. First, the nomenclature and main parameters are presented. Then, in section 7.3, the Transpac 52 Class is described. In section 7.4, the experimental test are included whereas, in section 7.5, the numerical simulations are presented as well as the comparison of results. Finally, in section 7.6, the main conclusions are summarized. 7.2. NOMENCLATURE 125

7.2 Nomenclature

ρ Air density

φair Air relative humidity

Cp Pressure coefficient (equation 7.1) hh Height of the mainsail head

P0 Static pressure

Pd Dynamic pressure

Pi Pressure at the sensor

Pt Total pressure or stagnation pressure

Tair Air temperature

V Air speed (equation 7.2)

Vrot Rotor speed

7.3 Transpac 52 Class

In the introduction of the TP52 Rule it can be read: The Transpac 52 Rule (TP52 Rule) is intended to produce a class of fast, monohull keel boats for high quality level racing. Development is allowed in such factors as hull shape, foil shape, construction, interior, deck layout and rigging. However, speed producing factors such as length, displacement, draft and sail area are strictly controlled. Boats in this Class shall sail without time allowance. Any developments which are contrary to this purpose may give rise to rule changes. In figure 7.1, an example of one of these sailing boats is included.

The TP52 Class Association was started in 2001 by owners who wanted a sailing boat for racing on real/true time. The first boat across the finish line wins. The original thought behind the TP52 Rule and Class was beating the one-off racing yachts for handicap rules such as IMS and IRC.

The TP52 Rule is a Box-rule, the boats built under this rule have to literally fit a box of the dimensions. Nevertheless, there are quite some rules underneath the box, like the rules on construction (ABS or ISO from 2010), the rules on safety (OSR) and the ISAF racing and equipment rules (RRS and ERS).

By setting a fairly tight “Box”, TP52’s have very similar performance characteristics, although the owner has some room to customize for local conditions. Every member 126 CHAPTER 7. PRESSURE DISTRIBUTION ON A TP52 MAINSAIL

Figure 7.1: TP52 Class yacht Balearia (2005) of the TP52 Class has a vote and the box rule will only be changed if 2/3ds of the owners agree. Stability of the TP52 Box Rule has been a key ingredient to the Class’s growth worldwide. No rule making body has the authority to change the TP52 Box Rule, except the owners themselves. The rule gets updated at every Annual Meeting.

The 2012 TP52 Rule has 34 limitations under the “box” which include the length limitation, maximum beam, hollows permitted, center of gravity of the mast, maximum sail areas, among others. In table 7.1 some relevant restrictions included in the TP52 Rule are presented.

• Maximum length 15.85m • Maximum beam 4.42m • Maximum draft 3.35m • Minimum displacement 7300kg • Maximum mainsail area 93.50m2 • Maximum headsail area 65.00m2 • Maximum spinnaker area 260.00m2

Table 7.1: Main dimension limits

The TP52 Class permits sponsors to take advantage of advertising their names and products on what has become perhaps one of the greatest media sailing platform. Sponsors and the general public have instant results when a TP52 crosses the finish line. Moreover, unlike the America’s Cup or Volvo Ocean Race boats which only race once every 4 years, the TP52’s schedule is year round on a global scale providing the owners, sailors and sponsors a lot of value for their time and money. Approximately 70% of the 7.3. TRANSPAC 52 CLASS 127

races on the TP52 schedule are allocated for traditional buoy racing with the remaining races being coastal, point to point and/or offshore.

7.3.1 Brief History The TP52 Class Association was started in 2001 by owners who wanted a sailing boat for racing on real time. TP52 Class members decided not to use water ballast, canting keels, running back stays...They preferred to keep it “simple, safe & reliable”.

Since 2001, the TP52 Class grew steadily over the next 4 years. In the summer of 2004, the King of Spain, H.M. Juan Carlos decided to join the TP52 Class. As a consequence of his association, 27 of these boats raced all over the globe in 2005 repre- senting 13 countries. A year later, in 2006, King Harald of Norway joined the TP52 Class.

In 2007, the members of the association decided that the Rule needed to be updated and therefore, they voted in favor of a of a revamped TP52 Bylaws and TP52 Rule at the 2007 Annual Meeting.

During this year, the TP52 racing moved solidly to the Mediterranean Sea and the MedCup took place with as many as 21 boats. Moreover, the Class received the ISAF (International Sailing Federation) recognized status and since then, their main event carries the title of World Championship.

In 2008, there were six MedCup events and the World Championship in Spain. With more than 50 TP52’s built worldwide, the Class saw two developments: first, the TP52’s racing under the TP52 Rule in the Med and second, TP52’s being optimized for handicap racing under IRC elsewhere. Research was done on how the interests of both options could be best served and how the TP52 could be made most suitable for both options without compromising the original concept of the TP52 Class.

The TP52 Class did not escape the economic recession and the fully sponsored team disappeared. In 2009, the number of members was reduced to 12. During this year, the TP52 Class members decided to put a complete new TP52 Rule in place for 2011.

In 2010, when many of the high profile America’s Cup teams choose to join the Class, the level of racing was improved noticeably.

The 2011 TP52 Rule led to a faster, lighter, modern racing yacht. The new rule in wording and set-up streamlined to ISAF requirements for class rules and it attempted to use terms that follow the Equipment Rules of Sailing. Six new boats were build to the 2011 TP52 Rule and raced in the Audi MedCup 2011, together with two boats of the 2009 generation. 128 CHAPTER 7. PRESSURE DISTRIBUTION ON A TP52 MAINSAIL

The aim of the members for 2012 is to add 4 to 6 new boats to the fleet for a total of 10 competitors in the events. On the other hand, in the USA and Australia, the fleet of TP52’s racing under IRC handicap is growing rapidly.

NOTE: The information presented in this section is a summary of the information disclosed in [115], where more details can be found concerning the TP52 Class.

7.4 Experimental tests

7.4.1 Wind tunnel description The experimental tests have been conducted in an open-circuit close-section atmospheric boundary layer wind tunnel (figure 7.2). This is the main facility of the CEAMA (Centro Andaluz de Medio Ambiente), a research center associated with the Universidad de Granada, Spain (http://www.ceama.es/en).

The tunnel has a length of 26m and a closed test section of 2.15m x 1.8m. The air is sucked by a fan which is connected to a 160kW synchronous motor. This can rotate from 0 to 750rpm and generate a maximum wind speed of 150km/h approximately.

(a) Side view (b) The fan

Figure 7.2: Atmospheric boundary layer wind tunnel at CEAMA

This wind tunnel is utilized to study urban development and architectural plans, diffusion and concentration of pollutants/sediments, wind on structures (buildings, bridges...), solid bulks, ports and port facilities (cranes). Lately, sails are studied too. 7.4. EXPERIMENTAL TESTS 129

7.4.2 The model The model is a scale version of a real TP52 mainsail provided by UK Sailmakers. The sail has a luff length of 22.4m, a leech length of 23.5m, a foot length of 7.2m and a high luff (head) length of 0.25m. The rough frontal sail is 83.44m2.

Since the tunnel section has an area of 3.87m2, the scale chosen has been 1:20. This means that the sail area is approximately the 5.4% of the wind tunnel section, which prevents it from blockage effects. Finally, the luff, leech and foot lengths are 1120mm, 1175mm and 360mm, respectively. In figure 7.3(a) the windward side of the model can be observed.

(a) Windward side (b) Leeward side

Figure 7.3: The model

The three-dimensional shape of the sail was provided by the sailmaker and scaled on the computer. Instead of assuming a flying shape it was decided to use the original designing shape. Since the condition that has been reproduced in the wind tunnel is close-hauled, it is considered that the assumption is not far from reality.

The model has been built by the author. First, a positive mold of foam has been built, then, a negative mold of fiberglass and finally, the model of carbon fiber. An epoxi laminating system (resin and slow hardener) has been used with a 0/90◦ woven carbon fiber reinforcement fabric. All the components of the process have been cured in an oven designed and built by the author. The final thickness of the model has been 1.37mm, as a mean value of 13 measurements. The sail has been joined to a steel mast of 8mm in diameter.

The advantage of rigid sails over cloth sails is that the shape is fixed and known. Rigid models facilitate the validation process of numerical tools through comparison with 130 CHAPTER 7. PRESSURE DISTRIBUTION ON A TP52 MAINSAIL

wind tunnel tests. Moreover, it would be complicated to included the pressure transducer or taps, if the sail were flexible. The main disadvantage is that the sail cannot be trimmed.

In order to measure pressure distributions on sails, small pressure transducers can be placed directly onto the sail. On the other hand, pressure taps can also be used. In this case a tube would be needed between the pressure tap and the sensor. The pressure tap must be small enough that it does not influence the pressure significantly and the tube must convey the pressure to the sensor without distorting the pressure substantially. This is the techniques used in this investigation (see figure 7.3(b)).

The aim of this research is to compare physical measurements to predictions from CFD. For this comparison it is desirable to determine the pressure distribution separately on both sides of the sail. The pressure distribution on the windward side has been measured.

62 holes (pressure taps) have been made along 18 horizontal sections to enable the pressure to be measured at those locations. In table 7.2 the position of the holes is included. The “distance” is referred to the luff and measured along the section. The name of each pressure tap is presented in brackets. In figure 7.4, a diagram of the position of the pressure taps can be found.

Section Height (mm) Distance (mm) [name] 90% 1008 35 [101] 85% 952 26 [102] 58 [103] 80% 896 27 [104] 80 [105] 75% 840 29 [106] 56 [107] 48 [108] 70% 784 30 [109] 56 [110] 68 [111] 65% 728 30 [112] 62 [113] 82 [114] 60% 672 31 [115] 82 [116] 81 [115] 55% 616 31 [118] 82 [119] 98 [120] 50% 560 30 [121] 57 [122] 75 [123] 64 [124] 45% 504 31 [125] 57 [126] 75 [127] 80 [128] 40% 448 30 [129] 82 [130] 75 [131] 71 [132] 35% 392 30 [201] 107 [202] 75 [203] 60 [204] 30% 336 29 [205] 57 [206] 75 [207] 75 [208] 49 [209] 25% 280 28 [210] 82 [211] 100 [212] 75 [213] 20% 224 27 [214] 82 [215] 125 [216] 75 [301] 15% 168 26 [302] 82 [303] 125 [304] 87 [305] 10% 112 56 [306] 76 [307] 75 [308] 101 [309] 5% 56 23 [310] 57 [311] 100 [312] 100 [313] 60 [314]

Table 7.2: Pressure tap location 7.4. EXPERIMENTAL TESTS 131

The pressures are transmitted from these holes to the sail foot through circular core tubes. Then, the tubes are connected to the scanners. The length of the polyurethane tubes is 2.15m, the external diameter is 1.67mm and the internal diameter is 0.86mm. The tubing system is important since it influences the measurements of the pressure peaks. Long tubes can attenuate the peaks but, if mean values are considered, the effect of the tubing is neglectful. This is because the attenuation of the maximum and minimum peaks tend to be similar and therefore, they cancel each other.

For sail studies there is the added difficulty since the tube itself provides interference to the flow, unless a special double-sided sail is manufactured, which is not the case. It is assumed that there is flow disturbance at the bottom of the leeward side of the sail, near the luff, due to the accumulation of tubes (see figure 7.3(b)).

Figure 7.4: Sections and sensors 132 CHAPTER 7. PRESSURE DISTRIBUTION ON A TP52 MAINSAIL

7.4.3 Experimental set-up and test description The pressures have been measured with the System 8400. This can measure 2048 ports simultaneously with a frequency of 200000 samples per second. This is a powerful device to determine the forces generated by the wind on different structures and pressure distributions. The system is connected to the tubes through the scanners. These transform the pressure acquired on the pressure taps to a digital signal. Three scanners have been used simultaneously: two of 16 ports and one of 32 ports.

Pressures have been acquired at 167Hz for 120 seconds. The frequency is considered adequate since, due to the long tubes, the high frequency signals are damped. Higher frequencies would have led to an excessive amount of stored data. The measurements have been recorded and averaged on the sampling period to obtain the mean pressure on each hole (Pi).

It is a common practice to measure differential values of pressure instead of absolute values. In the case of tests, the differential values between the two faces can be measured. But if the pressure distribution on the windward (or leeward) side of the sail needs to be measured individually, a reference pressure is necessary. In particular, to relate the pressures with the test conditions, the undisturbed far field conditions are usually chosen, like the reference static (P0) and dynamic pressure (Pd). The reference pressure is provided by the static tap of a Pitot-static tube, which is located roughly 2m upstream of the model. The total-pressure (Pt) tap of the same Pitot-static tube is used to measure the reference dynamic pressure (Pd = Pt − P0). Finally, in order to relate the pressures with the test conditions, the pressure coefficient is calculated, Cp (see equation 7.1).

Pi − P0 Pi − P0 Cp = = (7.1) Pd Pt − P0 The test condition has been defined by the sailmaker: 28◦ of apparent wind angle, 7.4◦ of heel angle and 0.5◦ of mast rake. The foot height above the tunnel floor has been set to 85mm.

Two set of tests have been conducted. In the first set, the wind has been sped up to increase the Reynolds number. In figure 7.5(a) a picture of one of the tests is included. In table 7.3 the test conditions are described: name of the tests, air temperature (Tair), air relative humidity (φair) and rotor speed (Vrot). With these data and the values of the Pitot tube, the wind speed is calculated with equation 7.2 assuming that 1 2 Pt = P0 + Pd = P0 + 2 ρV . For example, the wind speed at TP52 04 is 4.7m/s. In this test, the Reynolds number based on the average chord length of 0.36m is 1.1 · 105.

s 2(P − P ) V = t 0 (7.2) ρ 7.4. EXPERIMENTAL TESTS 133

(a) Windward side (b) Fishing line

Figure 7.5: The model in the wind tunnel

During the test TP52 03 one of the tubes was accidentally disconnected from the scanner. Therefore, the test was repeated and named TP52 04.

In the second set of tests the sails are supported by tensioned thin nylon fishing lines, which are almost transparent to the wind. In figure 7.5(b) a picture of the clew is included. In table 7.3, the test conditions of this second set of tests are also presented.

7.4.4 Results The results are illustrated in figure 7.6. All the pressures are negative or positive regardless of the wind speed, except from the 213 pressure tap. This is near the leech but not so close to the trailing edge of the section comparing to others. This can indicate that it is located in a transition zone between positive and negative pressures.

The area next to the leech is a negative pressure zone according to the results and except from the value on the pressure tap 309. This is also near the leech but again, not so close comparing to the others. On the other hand, next to the head, there is a positive pressure zone as it can be concluded from the results of the pressure coefficients on the pressure taps 101 to 105.

It can be observed that at each section, the maximum pressure occurs next to the luff. Approximately, the maximum pressure area of the sail is between the pressures taps 104 and 214.

In each of the three tests (60rpm, 90rpm, 120rpm), the pressure coefficient deviate 134 CHAPTER 7. PRESSURE DISTRIBUTION ON A TP52 MAINSAIL

First set ◦ Test Tair ( C) φair (%) Vrot (rpm) TP52 01 29.6 34 60 TP52 02 29.9 34 90 TP52 03 29.6 35 120 TP52 04 29.9 35 120 Second set ◦ Test Tair ( C) φair (%) Vrot (rpm) TP52 05 30.1 35 60 TP52 06 30.0 35 90 TP52 07 30.0 35 120 TP52 08 30.0 35 150

Table 7.3: The tests from the mean value ±22%, ±9% and ±23% respectively. In general, at 60rpm the pressures are larger when positive and they are smaller when negative.

The results obtained for the second set of test indicate the tensioned fishing lines modify the frequency of vibration of the model. The acquisition frequency and the sam- pling period are not adequate. Further experimental tests would be needed to analyze the influence of the lines on the pressure distribution. The results are included in appendix B. 7.4. EXPERIMENTAL TESTS 135

Figure 7.6: Pressure coefficients, first set of tests 136 CHAPTER 7. PRESSURE DISTRIBUTION ON A TP52 MAINSAIL

7.5 Numerical simulations

The calculations of this research have been conducted with the RANS solver CD-Adapco’s STAR-CCM+. The simulations have been run on an Intelr Core i7-920 Processor with a Linux 2.6.38-12 kernel in amd64. For a 5.7·106 elements mesh, the typical CPU time to achieve the desired convergence has been around 21 hours using 7 processors.

7.5.1 Domain and mesh

The three-dimensional shape that defines the model have been introduced into Rhinocerosr 4.0, where the sail surface has been modeled as well as the mast. A sail thickness of 1.37mm has been considered. The geometry of the sail has been placed according to the experimental test conditions: 28◦ of apparent wind angle, 7.4◦ of heel angle and 0.5◦ of mast rake.

The computational domain is a rectangular box. The extends of the volume are set so as to permit a good development of the flow without creating wall effects and reproduce the dimensions of the wind tunnel. The extension of the computational control volume has been set in relation to the height of the head (hh) 1.197m and the size of the wind tunnel: hh upstream, 5hh downstream, 1.075m leeward, 1.075m windward, 0 below (floor) and 1.8m in height.

The meshing procedure has been conducted with the meshing tool of the STAR- CCM+. According to the nomenclature of this software, the final mesh is surface remesher and trimmer (hexahedral) type with prism layer mesher to properly capture the phenomena involved near the sail.

Before obtaining reliable results, a grid-sensitivity study has been performed and several tests have been conducted in order to choose the best numerical parameters. With the suitable meshes, different parameters of the numerical scheme and boundary conditions have been established to obtain the best combination among them. In this section, only the best result is presented. The number of elements of the final simulation is 5,665,965. In figure 7.7, two screenshots of the mesh are included.

In order to improve the quality of the mesh near the sail and the wake downstream, refining blocks and prism layers have been used. Three prism layers have been set with a stretching factor of 1.5 and a thickness of 5mm. The variable wall y+ has been studied to evaluate the quality of the mesh next to the rig and its capability to detect the boundary layer by the numerical wall treatments. A typical target value of y+=1 has been aimed for most of the sail and mast surfaces. The maximum y+ of the final simulation has been 21 which is within the optimum range. Moreover, the volume change ratio have been checked. 7.5. NUMERICAL SIMULATIONS 137

(a) Midsection (b) Detail

Figure 7.7: Midsection plane mesh

7.5.2 Boundary conditions The most suitable boundary conditions have been set in order to reproduce the real behavior of the flow around the TP52 mainsail in the wind tunnel.

• Inlet: The speed normal to the inlet surface is set constant (5m/s) which is similar to the velocity of the TP52 04 test. Turbulence intensity is set to 1% and the turbulent viscosity ratio to 10, according to the recommendations in the solver’s documentation [92]. • Outlet: the averaged pressure over the surface is set to zero. • Walls: the condition imposed is “free-slip”. • Floor: The boundary condition is “no-slip”. • Sail and mast: the “no-slip” condition is set.

7.5.3 Numerical scheme The models utilized in these simulations are: three-dimensional, stationary, turbulent (SST K-Omega), segregated flow model, constant density, implicit unsteady, 2nd order temporal discretization and all-y+ wall treatment.

The time step has been set to 0.01s and the inner iterations to 5. The time step is around the 20% of the characteristic time which is the characteristic length (0.36m) divided by the wind speed (5m/s).

The pressure on each step has been monitored to ensure they have settled. The last 20% of the total physical time has been analyzed and the fluctuation of the pressures in this period is below the 0.05% of the mean value. There is an exception on the fluctuation of the pressure of the 103 which is under 1%. It can be concluded that the pressures are settled. 138 CHAPTER 7. PRESSURE DISTRIBUTION ON A TP52 MAINSAIL

7.5.4 Comparison between simulations and experiments According to figure 7.8, some of the statements described in the experimental results section are verified in the numerical simulation. The area next to the leech is a negative pressure zone whereas the head of the sail is mainly a positive pressure zone. It can be also observed that there is a maximum pressure line between the pressure taps 125 and 302. This is approximately the same line obtained from the experimental results. In figure 7.9 the experimental and numerical values are included together for comparison.

Figure 7.8: Computed pressure coefficient distribution (windward)

A qualitative view shows that, except from the pressures on 103 and 105, the results are both positive (or negative) in the experiments and the simulations. It is also observed that the trend for each section is kept. The pressure coefficient is high near the luff and then, it decreases along the section until it reaches a negative value near the leech.

A quantitatively analysis highlights that the worst values appear near the leech. Even if the negative sign is capture, the value is worse. It can be clearly seen in the figure in the middle, where the results of the pressure taps 121 to 209 are presented. The negative values differ 50% while the positive values only differ 5%. This can be due to the flow disturbance produced by the tubing on the leeward side, which affects more the values near the leech.

It is also observed that on the positive pressure area at the upper part of the sail the CFD estimates less pressure than in the wind tunnel. On the other hand, at the lower part of the sail, the numerical calculation provides more pressure than in the experiments. It should be emphasized that the accumulation of the tubing on the leeward side is nonuniform. The 62 tubes converge to the lower corner of the sail, i.e., the tack. Therefore it is clear that the influence of the tubing is different at the upper part of the 7.5. NUMERICAL SIMULATIONS 139

sail comparing to the lower part.

Further studies would be interesting to develop an uncertainty analysis, to evaluate the effect of the noise in the measurements, to study the bond of the mast-sail and the influence of the sailing conditions. Nevertheless, the results are promising and highlight the capability of the software to capture the pressure distribution over the sail. 140 CHAPTER 7. PRESSURE DISTRIBUTION ON A TP52 MAINSAIL

Figure 7.9: Wind tunnel data vs CFD results 7.6. CONCLUSIONS 141

7.6 Conclusions

In this section, the pressure distribution on a Transpac 52 Class mainsail has been studied. Firstly, the pressure distribution has been measured on a model-scale sail in a wind tunnel in upwind condition. The experiments have been conducted at the Atmo- spheric Boundary Layer Wind Tunnel at the CEAMA (Universidad de Granada, Spain). The pressure distribution has been measured on 62 points of a rigid pressure-tapped model-scale sail.

The experimental technique that has been used is widely spread in civil wind engineering but it is innovative in sail aerodynamics. Two set of experimental tests have been carried out. In the first set, the wind speed has been varied. In the second tests, apart from the varying speed, tensioned fishing lines have been added to stiffen the model up. The results obtained for the second set of tests indicate that the tensioned fishing lines modify the frequency of vibration of the model. The acquisition frequency and the sampling period are not adequate.

Secondly, one of the tests of the first set of experiments has been simulated with the commercial RANS code CD-Adapco’s STAR-CCM+. The numerical results have been validated with the experimental data. The results show a reasonable good agreement between them, both quantitatively and qualitatively. The comparison has permitted an increase of the confidence in numerical codes and has helped the researcher to gain knowledge of the phenomena involved near the sail. Nonetheless, further analyses would be needed to complement this research. 142 CHAPTER 7. PRESSURE DISTRIBUTION ON A TP52 MAINSAIL Chapter 8

AERODYNAMICS OF SAILING DHOWS

8.1 Introduction

This chapter describes the first investigation carried out to understand the aerodynamics of sailing Dhows. Due to the lack of information, a wide program has been conducted at the Twisted Flow Wind Tunnel of the Yacht Research Unit (University of Auckland) to study the performance of sailing dhows.

This research comes up from the interest shown by different sailmakers and the Yacht Research Unit (YRU) on the performance of sailing dhows. As far as it is known, there haven’t been conducted any aerodynamic nor hydrodynamic tests of these boats. It has been impossible to find any technical article or report which describes dhows. The only written references that have been found are focused on a descriptive and historical analysis.

Due to the lack of background, the main aim of this project has been the char- acterization of the main parameters that affect the sail performance of dhows. This understanding will facilitate future works to optimize these sails and improve their performance. The second objective of this research is the use a numerical code to improve the knowledge of the flow around sailing dhows.

In order to achieve the goals of this research both experimental and numerical tests have been conducted. The two most important dhow classes (43ft and 60ft) have been tested in the wind tunnel with one hull and the respective rigs. A broad range of variables have been studied such as heel angle, apparent wind angle, different yards and tension levels. It has been analyzed the effect of yard stiffness, heel and apparent wind angles, the influence of bending, the optimization of the trimming and the performance of the 60ft mainsail alone without the mizzen.

143 144 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

Figure 8.1: A 43ft dhow racing

Moreover, one of the experimental tests of the 43ft model has been reproduced with a RANS code. The flying shape of the sail has been acquired by means of the V-SPAR system. Forces, moments and the pressure distribution over the sail have been calculated among other parameters. The results have been validated with the experimental data.

As mentioned before, this project comes up from the interest shown by different sailmakers on the performance of sailing dhows. The most important feature of this investigation is that it raises from the industry, with the industry and for the industry. During the whole research Calibre Sailsmakers Lt. have supervised the tests. Presently, they have already incorporate some of the results in their actual designs. This investiga- tion is relevant not only for sailmakers and designers but also for sailors. Some of the conclusions drawn by this research can help sailors to improve the performance of their boats during a race.

It should be highlighted that the main contribution of this research it to be the first that has scientifically studied sailing dhows. These tests lay the grounds of future investigations. The results of the experimental tests have been partially disclosed by the author of this thesis in [4].

The structure of the reminder of this chapter is the following. In the second section, 8.2. NOMENCLATURE 145

the nomenclature and abbreviations are listed. In the third section, a description and the history of dhows are presented. In the fourth section, the experimental tests are described. In the fifth section, the numerical simulations are included. In the last section, there is a summary of the main conclusions drawn by this research.

8.2 Nomenclature

β Velocity scale

γ Length scale

AWA Apparent wind angle

AWS Apparent wind speed

CD Drag coefficient

CF Aerodynamic force coefficient CL Lift coefficient

CMX Heeling moment coefficient

CX Drive force coefficient

CY Side force coefficient

D Diameter

De External diameter

Di Internal diameter

E Young modulus

F Load

FX Drive force

FY Side force

()FS Referred to full scale HA Heel angle

I Inertia

L Yard length 146 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

Lm Mast length

()mod Referred to model scale MX Heeling moment

Pd Dynamic pressure Re Reynolds number

S Sail area, different for each model w Distributed load y Deflection

Abbreviations BEN Bending Test

BT Basic Test

BYT Bent Yard Test

OPT Optimum trimming test

TFWT Twisted Flow Wind Tunnel

YST Yard Stiffness Test

8.3 The Dhow

8.3.1 History of the Dhow For many centuries, boats that sailed on the Indian Ocean were called dhows. Despite their historical attachment to Arab traders, dhows were basically an Indian boat because much of the wood for their construction came from the forests of India. The origin of the word “dhow” remains ambiguous [116]. Some suggest it’s derived from the Persian dawh and other etymologists argue that it could be from the Swahili word for boat daw.

Dhows were categorized according to the shape of their hulls, unlike European boats, which were classified according to their rigging. For example, dhows with double-ended hulls were named buum, zaaruuq or badan, while dhows with square sterns were called gaghalah, ganja, sanbuuq or jihaazi. This square stern dhows had a European influenced stern which had its origins in the 16th century when the Portuguese and some other boats visited the Arabian gulf. 8.3. THE DHOW 147

The current knowledge of early dhows comes from three sources: first, the records of early Roman and Greek historians; second, shipwrecks and third, modern dhows. The construction of dhows have always been considered an art and it has been passed down from fathers to sons, preserving the basic design and use. Two distinctive features made the dhow so popular: on one hand, the stitched construction and on the other hand, the lateen sail.

In the West, the wooden hull planks overlapped, while the planks of dhows laid edge to edge. The planks were stitched together using coir, which was passed through holes drilled in the planks. The light sewn hull of the dhow worked well in the shallow sandy waters of much of the Arabian Gulf. It could withstand groundings and its broad flat bottom allowed it to easily be beached for maintenance or storage.

Apart from the construction, the other distinctive feature of dhows was the lateen sail. These lateen sails were not completely triangular. The forward angle was cut off to form a leading edge. This luff added a much greater area of sail to be hoisted than a completely triangular design would have. The lateen had an enormous advantage over the mul- tiple square sails used in the West. It allowed the dhow to sail well, even against the wind.

Different types of sail were made according to the requirements: a sail wanted for reaching was made less flat and with a fuller luff than a sail wanted for close hauling. Moreover, two main sails were carried: one for night and bad weather and the other, for day and fair weather, since sails on a dhow could not be reefed. The long strips of the cloth were sewn together, parallel to luff and leech. It is thought that originally sails were woven from coconut of palm leaves, and that eventually Indian cotton cloth became the favorite for merchants on long voyages.

Dhows could be single-, double- or triple-masted. In early times, masts were made of coconut wood and teak and they were mounted to a large piece of wood block fastened to the keel. Masts were secured in place with ropes which acted as shrouds but they were not fixed and could be tied up to different points depending on the tack of the boat. Traditionally, the ropes were made of Indian coconut fibers.

The upper edge of the lateen sail was tied up to a leaning yard, which was in turn attached high on the mast by a strong rope called parrel. The yard was very long in comparison with the mast, and sometimes it was made of more than one piece of timber. Yards were also made of coconut wood and teak.

8.3.2 The Dhow nowadays At the end of the eighties, in order to emphasize the historic connection to the sea and to revive the skills of local seamen, the Dubai’s deputy ruler initiated a dhow sailing competition. The Dubai International Marine Club was requested to organize the race. 148 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

Figure 8.2: A 60ft dhow sailing in Dubai

On the 23rd of May of 1991 the first al Gaffal (journey back home) race took place, in order to remember the journeys undertaken in the past by the traditional Arabian pearl boats.

The fleet of the first race was comprised of 53 dhows in various lengths and designs. After the race, it was requested that within two years all the boats entering the race had to be built with a standard design, keeping the rules of original dhows and all 60ft in length (see picture 8.2). The race was included in the racing calendar and every year since 1991 it has been carrying on with the same al Gaffal route. At present, the race attracts up to 100 60ft dhows and the international interest is surprisingly increasing. These boats weight only 1-3 tons and the speed can easily exceed 20 knots, which makes them attractive.

Apart from this annual event, a race calendar for the 60ft class has been drawn up. Moreover, the 43ft class has been included (see picture 8.1) as well as the new 22ft class. A decade ago, this new class was introduced as a training boat for the youth so that they could learn to sail on this class and then join family members and friends on the 43ft or 60ft classes. In a 43ft dhow, the crew number is between 8 and 15 sailors, whereas a 60ft dhow can usually carry between 15 and 35 men.

Formal dhow class rules have not been issued yet but there are some implicit features that must be fulfilled when building and designing these boats. For example, the hull must be teakwood, which may be varnished but not painted. Traditionally, the hull was treated with lime below the waterline to prevent from fouling, but the remaining timber was uncoated. The mast and bowsprit must also be wooden, but the strong yard that supports the sail may be made of aluminum or carbon fiber. Similarly, sails that originally would have been cotton may now be made of modern cloths. Furthermore, 8.4. EXPERIMENTAL TESTS 149

motorized winches are not allowed: just blocks, tackle and muscle-power. There are no speed logs, wind gauges, depth sounders, weather computers or satellite positioning systems, [117].

Comparing to modern yachts, large dhows are very unstable because they are built without a weighted keel. In the past, when dhows were used for the transportation of goods, the cargo was stored below the deck, which kept the dhow balanced. Nowadays, around 50 bags filled with sand are used to perform the same task [116]. When the wind changes, crewmen must shift the sandbags about to keep the boat correctly trimmed. The sailors can also shift their own weight to balance the boat. And, if the wind vanishes, the crew just throws the sandbags overboard.

Tacking a dhow is also something that makes the boat special. Unlike modern racing yachts, the dhow cannot easily turn across the wind. Each maneuver requires oscillating the mainsail to the other side of the mast. This means that the heavy yard must be freed from the mast and lowered slightly. In addition, the spar’s front end must be lowered almost to vertical and swung around the base of the mast to the other side. At the same time, the shrouds as well as the rope to the parrel must be moved to the other side. Tacking can take 10 to 15 minutes in large dhows.

This maneuvering complexity makes the dhow races have only one or two legs, which are usually cross wind, unlike the modern triangle races or beating/running races. There are mainly two types of races: the al khayour course, a route that features a turn and the al-yoush or al yoush al wahed course, which is a straight course, [116]. For example, a 43ft dhow needs around two hours to complete the 13-15 miles one leg race with 10-15 knots of averaged wind. Another curiosity of dhows is that they are towed upwind to the starting area and they keep the sails furled. Sailors care little about pre-start tactics. Unlike most racing boats, dhows wait for a signal before hoisting the yards that hold the sails. Their vessels sit quietly, sails dropped, until the smoke appears, [117]. This is the reason why the speed and aerodynamic optimization have such importance. In some way, the fastest wins the race regardless the taking and tactics.

Despite all the characteristics mentioned above, the striking feature of modern racing dhows, that remains unchangeable from the past, it is the familiar atmosphere. Dhows belong to the family and each sailor’s father sailed before him, as well as his father before him. The only difference is that nowadays the priorities have changed and the sport has become more competitive and everyone is more driven to win [116]. 150 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

Figure 8.3: The Twisted Flow Wind Tunnel at the University of Auckland

8.4 Experimental Tests

8.4.1 Wind tunnel description The tests have been conducted at the Twisted Flow Wind Tunnel (TFWT) which is owned and operated by the Yacht Research Unit, University of Auckland (see picture 8.3). The current tunnel is an open-circuit design with two fans at one end and an open test section at the other. The tunnel is used for both research projects within the University and commercial testing with, among others, Volvo Ocean Race and America’s Cup teams.

The concept of the TFWT was originally developed by Flay et al.[21] for the New Zealand America’s Cup Challenge in 1995. Since then, the concept has remained the same but improvements are constantly being made. In 2000, the wind tunnel was relocated and the design was changed.

The tunnel was used by Team New Zealand in the preparation for the defenses of the America’s Cup in 2000 and 2003. Moreover, the TFWT was used by Emirates Team New Zealand and several other syndicates in preparation for the America’s Cup 2007 and was also used by most teams of the last three editions of the Volvo Ocean Race, Open 60 projects, Maxi yacht designers and record breakers like MariCha III and IV.

The TFWT is unique in that it was developed specifically for the testing of yacht sails. It was the first wind tunnel that could simulate the change in wind direction with height experienced by sails. More recently other wind tunnels have incorporated the flow twisting concept, including the Politecnico di Milano and the University Applied Science Kiel in Germany. 8.4. EXPERIMENTAL TESTS 151

In figure 8.4 there is a sketch of the wind tunnel with the sections that are described hereafter.

• Fans and motors. The flow is sucked into the tunnel by two 3m diameter 4-blade fans. Each fan is housed in a steel ring which incorporates stator blades. Both fans are situated at the upstream end of the tunnel in order to have free access to the boundary layer development duct and test zone, and so that the boundary layer has enough space to develop.

The fans are powered by two 45kW electric motors which are driven by a variable frequency speed control. The fans and motors have been designed to reach a flow top speed of about 8m/s at a 720 rpm motor rotation.

• Transition zone. Inside the wind tunnel, just after the fans, there is a transition zone to convert the round section of the propellers to the rectangular wooden section of the rest of the tunnel (3.5m x 7m). The transition zone is made of a combination of plywood and sail-cloth.

• Flow stabilizing zone. There are two wire screens and a honeycomb downstream the transition zone. Here, the flow is straightened and conditioned. The inconve- nience of having upstream fans is that they generate a swirl in the airflow before entering the test section, resulting in a non uniform flow in the test region. This is the reason why the screens and the honeycomb are main parts of this type of tunnels.

The screens are wire meshes with gaps of 1mm and are placed one before, and the other one after the honeycomb. This honeycomb is built of corrugated metal roofing sheets of 1 meter long and approximately, a hydraulic diameter of 100 mm, giving an aspect ratio of 10:1. The total pressure drop coefficient, taking into account the screens and the honeycomb, is about 5.

• Boundary layer development duct. After this pressure drop zone, the flow travels into the boundary layer development zone. By using a suitable combination of different types of roughness elements (blocks, planks or corrugated metal), the desired velocity and turbulence profiles can be created. If required, the end part of the boundary layer development duct can be turned into a contraction allowing to increase the wind speed in the test section. The contraction lessens the width of the duct to 3.5 m while the height is kept the same, 3.5m. At the end of the boundary layer development duct, the twist controlling vanes are placed. 152 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

Figure 8.4: Plan of the wind tunnel

• Twisting vanes. The 20 vertical vanes to alter the angle of the flow with height are placed at the end of the enclosed section, upwind the opened test section. Each vane has a steel profile at the leading edge which is spaced 350mm from the others and fixed in its positions. Attached to this profile and downwind, there is a flexible plastic sheet, which has a chord length of 600mm. Close to the trailing edge, the sheets are connected together with 8 horizontal wires. These wires are used to create the twist. Digital outputs on the electric winches which control the wires, enable the settings to be calculated in advance and repeated accurately.

Since the tunnel can also be used for other purposes than sail testing, the twist controlling vanes can be easily moved out by retracting them to one side. And the dimensions of the development duct can be reduced in order to increase the wind speed. This setup has been used, for example, for testing yacht keels or buildings.

• Test section. Just downwind the vanes, the test section is situated. This section has ceiling and floor but has open sides and open downstream. The use of this open configuration eliminates the need of using blockage corrections.

A six-component force balance is located under the wind tunnel floor, in the test section, [118]. The balance consists of an aluminum frame, which is connected to a steel frame through six force transducers. This steel frame can rotate on an axial bearing to accommodate tests at different wind angles. The TFWT is set up for the model yacht to be tested on port tack. 8.4. EXPERIMENTAL TESTS 153

The six Linear Voltage Displacement Transducers (LVDTs) measure the voltage due to their displacement in one direction and a calibration matrix relates the six voltages to three forces and three moments. The six transducers are divided in: three for z-axis, two for y-axis and one for x-axis. Therefore the least accurate values are measured in the z-axis and the most accurate ones in x-axis. From the calibration measurements a mean error in the x-axis of ±0.09N is obtained, ±0.11N in the y-axis and ±0.27N in the z-axis. It has been calculated that an accuracy of ±1% in the x and y-axis and ±5% in z-axis are achieved for typical measurements. The force balance is primarily designed to measure static loads and the measurements are usually averaged over sampling periods between 30 and 120 seconds.

Three brackets of the balance protrude through the tunnel floor to hold the model. As it has been mentioned before, the force balance can be turned together with the floor above (turntable) to change the apparent wind angle. The turntable has a trough to allow the waterline of the hull to coincide with the wind tunnel floor. This recess is filled with water to prevent the air from flowing under the hull.

8.4.2 The model

Figure 8.5: The model fitted with the 43ft rigging and winches

A complete the 3D model has been designed on the computer. Since there are no records of shape plans, the hull has been designed from pictures and overall dimensions. Only one hull has been built and used for both rigs, which leads to two scales of the rigging. In table 8.1 the main dimensions of the model are included. 154 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

Lenght (mm) 1524 Beam(mm) 412 Depth (mm) 145 Draught (mm) 41

Table 8.1: Model-scale hull dimensions

The hull has been built of medium-density 9mm fiberboards. First, the waterlines have been obtained from the 3D model. Second, they have been drawn on the fiberboards and cut. After this, they have been sticked together forming a block which has been sanded until the shape of the hull has been smoothed. Then, three layers of sealer and three layers of acrylic paint have been coated. Finally, the hull has been fitted with eyebolts, pulleys and remotely controlled electric winches to allow instantaneous sail trimming. In picture 8.5 the hull with part of the rigging and fitting can be observed.

43ft Dhow model (1/8.6th scale) Length (mm) Diameter (mm) Area (m2) Mast 1189 22 Original yard 1949 18 Bowsprit 1032 18 Sail 2.231 Medium yard* 1949 16 Soft yard* 1949 12 60ft Dhow model (1/12th scale) Length (mm) Diameter (mm) Area (m2) Main mast 1024 18 Main yard 1657 16 Bowsprit 950 16 Main sail 1.609 Mizzen mast 866 16 Mizzen yard 1397 12 Mizzen sail 1.146

Table 8.2: The rigging dimensions

In table 8.2, the spars that have been built are presented. In order to reproduce the real behavior of the masts and bowsprits, they have been designed to be stiff enough to avoid deflection. But in the case of the yards, it has been reproduced and scaled the stiffness of full-scale yards. In Appendix C the procedure to scale the stiffness is described. The only difference between the calculated and the finally build yard is the diameter of the mizzen yard of the 60ft model since a 13mm dowel is not manufactured. 8.4. EXPERIMENTAL TESTS 155

In this case, it has been decided to use a 12mm dowel instead. Masts, bowsprits and yards are built in pine.

The hull and the rigging have been fully designed and build by the author of this thesis. On the other hand, the sails have been designed and provided by Calibre Sailmakers Lt. The main property of the sail cloth is lightness with minimal stretch since the elastic scaling is not considered. The sails have been fitted with cotton tufts to facilitate the trimming and visualize the flow.

(*)These two yards have been built for the Yard Stiffness Test that is described in the next section.

8.4.3 Experimental set-up and test description

This is the first time that the sails of dhows are tested in a wind tunnel. This is the reason why it has been tried to reduce the sources of uncertainty. Due to the low aspect ratio of the sails, it has been considered that the disadvantages of reproducing the wind profile and twist, exceeded the advantages of having an accurate flow. Therefore, in this study, the onset flow is uniform. All tests have been carried out at the dynamic pressure of approximately 10Pa resulting from a wind speed of about 4m/s. This gives sufficient large forces for accurate measurements with the appropriate model rig deflection.

During the tests, the three moments and forces have been acquired for 50s and 200Hz, but only the drive force, side force and heeling moment are analyzed. The force in the x-direction (FX) is called the driving force since it acts along the centerline of the boat and propels the boat forward (if a zero leeway angle is assumed). Similarly, FY is the horizontal side force, and it acts perpendicular to the centerline of the yacht. The moment about the x-axis (MX) is the heeling moments since it tries to rotate the yacht around its centerline.

A significant buoyancy force is generated when the model is heeled as it is not heave and the center of gravity changes. It is therefore necessary to subtract tare forces from the model forces as a result of the changing heel angle. At the beginning of the tests, the differences of the heeled tare forces from the upright tare forces are measured over a range of heel angles and a polynomial curve is fitted. At each subsequent measurement reading, this polynomial is interpolated such that the heeled tare component is subtracted, as explained in [119].

From now on, both forces and the heeling moment are expressed in a non-dimensional coefficient form to facilitate the comparison (see equations 8.1, 8.2 and 8.3), where Pd is the dynamic pressure and S is the sail area (2.231m2 for the 43ft model and 2.755m2 for the 60ft model). As well as the forces and moments, other magnitudes have been recorded 156 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

during each test such as air temperature, dynamic pressure, atmospheric pressure, etc.

FX CX = (8.1) Pd · S

FY CY = (8.2) Pd · S

MX CMX = 3/2 (8.3) Pd · S

Drag and lift have been also calculated. Drag is defined as the force in line with the onset flow and lift as being perpendicular to it. They can be obtained from CX and CY by rotating the coordinate system appropriately. In the Appendix D and Appendix E, the tables with all the tests that have been conducted are detailed. Moreover in the Appendix F and Appendix G the figures with the results have been included for the most relevant parameters (CX, CMX, CX/CMX, CD and CL).

43ft Dhow Model

Hereafter the different tests that have been conducted with the 43ft dhow model are explained. In table 8.4 there is a summary of these tests.

• Basic Test, BT. A range of apparent wind angles between 20◦ and 100◦, in steps of 10, has been tested. For each AWA, four heel angles have been tested: 0◦, 5◦, 10◦ and 15◦. For each AWA, the trimming is optimized to give the maxi- mum drive force when the model upright (HA=0◦) and it is kept constant for the rest heel angles. The results of this test are the basis for comparison with other tests.

• Bent Yard Test, BYT. Both the AWA range and HA range are the same as the ones in the previous test. The difference is that in this test, the yard has been bent by means of two stiffeners, as it can be seen in figure 8.6. The trimming has been also optimized to obtain the maximum drive force on the upright condition and then, it remains fastened. This test has been conducted to study the influence of a forced bending on the performance of the sail.

• Optimum Trimming Test, OPT. Three AWA have been selected (40◦, 60◦ and 80◦) considering that they are in the range of normal apparent wind angles in which a dhow would sail. For each AWA, the previous four heel angles have been tested 8.4. EXPERIMENTAL TESTS 157

Figure 8.6: 43ft dhow model during a test with stiffeners

in four different situations: a) Optimizing the trimming for HA=0◦ and keep it constant for the rest of HA (as in BT); b) Optimizing each heel angle; c) The first situation (a), with the stiffeners bending the yard; d) The second situation (b), with the stiffeners bending the yard.

• Bending Test, BEN. In this test there have been also selected the apparent wind angles 40◦, 60◦ and 80◦. Each angle has been tested at 5◦ of heel angle with three different bending situations, named: small bending, medium bending and large bending. In each case, the trimming has been optimized to obtain the maximum drive force.

• Yard Stiffness Test, YST. In the aforementioned tests, the yard has been bent by means of stiffeners which provoke a forced and artificial bending. In order to compare different yard stiffness without the inclusion of external devices, two new yards have been built. Their dimensions are presented in table 8.3. The yards have less diameter than the standard yard (stiff yard) to reduce the stiffness with the same material. The inertia of the medium yard is the 62% of the original, whereas the inertia of the soft yard is the 20% of the original.

It has been tested a range of apparent wind angles between 40◦ and 80◦, in steps of 10. For each AWA, the same four heel angles have been tested: 0◦, 5◦, 10◦ and 15◦. Here, the trimming has been also optimized to obtain the maximum drive force when upright. 158 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

Length (mm) Diameter (mm) Stiff yard (original) 1949 18 Medium yard 1949 16 Soft yard 1949 12

Table 8.3: The yards dimension

60ft Dhow model

Now, the 60ft dhow model tests are described and in table 8.4 a summary is included.

• Basic Test. As in the BT case, a range of apparent wind angles between 20◦ and 100◦, in steps of 10, has been tested. For each AWA, the same four heel angles are tested: 0◦, 5◦, 10◦ and 15◦. For each AWA, the trimming is optimized to give the maximum drive force when the model is upright (HA=0◦) and it is kept constant for the rest heel angles.

• Optimum Trimming Test. Three AWA have been selected (40◦, 60◦ and 80◦) and the same four HA have been tested for each AWA. In this test, the trimming has been optimized not only for the upright condition but for each HA.

• Basic Test without mizzen. In order to study the influence of the mizzen on the mainsail performance, this test has been conducted. Again, a range of apparent wind angles between 20◦ and 100◦, in steps of 10, has been tested. For each AWA, the same four heel angles are tested: 0◦, 5◦, 10◦ and 15◦. For each AWA, the trimming is optimized to give the maximum drive force when the model is upright (HA=0◦) and it is kept constant for the rest heel angles.

8.4.4 Results 8.4.4.1 43ft Dhow Model Basic Test vs Bent Yard Test

In figure 8.7 the drive force coefficient(CX) is presented against the apparent wind angle for the Basic Test (left) and Bent Yard Test (right). As it can be observed the trend is similar in both plots. There is an increase of CX with the increasing AWA. For low angles the slope is large but then, it decreases with the apparent wind angle. For low apparent wind angles, the Basic Test provides slightly higher values of the coefficient comparing to the BYT. In the other hand, for high AWA the Bent Yard Test is better 8.4. EXPERIMENTAL TESTS 159

43ft Dhow model AWA HA Basic Test 20◦ - 100◦ 0◦ - 15◦ Bent Yard Test (small, medium, large) 20◦ - 100◦ 0◦ - 15◦ Optimum Trimming Test 40◦, 60◦, 80◦ 0◦ - 15◦ Bending Test 40◦, 60◦, 80◦ 5◦ Yard Stiffness Test (stiff, medium, soft) 40◦ - 80◦ 0◦ - 15◦ 60ft Dhow model AWA HA Basic Test 20◦ - 100◦ 0◦ - 15◦ Optimum Trimming Test 40◦, 60◦, 80◦ 0◦ - 15◦ Basic Test without mizzen 20◦ - 100◦ 0◦ - 15◦

Table 8.4: Summary of the conducted tests since the values are larger.

(a) Basic Test (b) Bent Yard Test

Figure 8.7: 43ft model, CX

The effect of the heel angle is not significant since the curves are plotted together except from one range in each figure: 40◦-70◦ in the BT and 60◦-90◦ in the BYT. In these ranges, the curves separate and indicate that the heeling decreases the drive force. This effect can be due to the large draft of the sails that at certain apparent wind angles performs worse.

In the Basic Test plot it can be seen that 0◦ heel angle is slightly above the other curves until 70◦ of AWA whereas in the BYT figure, the upright position is always better. In both tests, the worst heel angle is 15◦. Here, it should be highlighted again that in these two tests, the trimming is optimum (maximum possible drive force) only for the upright position. 160 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

The heeling moment is another important magnitude because it takes into account not only the side force, but the vertical force and the center of effort too. Moreover, the heeling moment must balance the righting moment of the hull and crew. In this type of sailing boats, the heeling moment is usually limited by a value that it is related to the capacity of the crew to create a moment. The righting moment of the hull is very small because dhows are designed without a weighted keel.

(a) Basic Test (b) Bent Yard Test

Figure 8.8: 43ft model, CMX

In figure 8.8 the heeling moment coefficient (CMX) against the apparent wind angle is illustrated. In both plots the trend is similar. First, the coefficient increases and then, a decline. For the whole range of AWA, the BT provides greater values than BYT. Unlike the drive force coefficient, it is usually preferred a low value of the heeling moment coefficient. There are two main reasons to prefer low moments: a) the capacity of the crew to create a righting moment is limited and b) the hull hydrodynamics is usually optimized for low heel angles.

Unlike in the CX plots, here, the curves are displayed separately. This means that the heel angle has a great influence in the righting moment. The trend is similar in both BT and BYT: the 0◦ HA gives more righting moment which decreases with an increasing HA. There is an exception in the BYT at high apparent wind angles where the contribution of the heel angle becomes almost negligible.

Therefore, the best situation would be sailing with a high drive force and a low right- ing moment. In order to consider the two magnitudes and compare similar situations, the CX/CMX ratio can be plotted against apparent wind angles as illustrated in figure 8.9.

In the BT figure it can be seen a linear trend and then, the slope of the curve increases. This means that the efficiency improves from 80◦ on. In the BYT plot, it is not so obvious. In the BT, the heel angle has a small effect on the ratio whereas in 8.4. EXPERIMENTAL TESTS 161

the Bent Yard Test it can be observed that there is an unevenly trend of the ratio for different heel angles. The curve of 0◦ heel angle is very stable but the other three curves change with the apparent wind angle.

(a) Basic Test (b) Bent Yard Test

Figure 8.9: 43ft model, CX/CMX

The Basic Test figure suggest that the 15◦ of HA is more efficient because it gives more drive force for the same moment. This is mainly because the big drop of the heeling moment with the heel angle. It is a very interesting result since the trimming is not optimized for this angle. As it will be discussed next, optimizing the trimming for different heel angles gives even higher values of this ratio, because the drive force can be increased and the righting moment, decreased. In the BYT is not so clear which heel angle would be better.

If the same curve (for example HA=0◦) is compared in both plots, it can be observed that after 70◦ of AWA the BYT is better. This means that for high apparent wind angles is desirable to have a forced bending of the yard. This result was expected since for high apparent wind angles, the sail behaves like a downwind sail and needs more curvature whereas for low angles, the sail behaves like a jib and needs a stiff leech.

In order to see more easily the influence of the heel angle, the drive force and heel- ing moment coefficients can be plotted against the heel angle as displayed in 8.10 and 8.11.

The trend is similar for both coefficients. In general, the effect of the heel angle is negligible (constant slope) or reduces the coefficients (decreasing slope). As mentioned before, this was expected since the trimming remains constant for 5◦, 10◦ and 15◦.

In the drive force coefficient figures, two curves must be highlighted: the 60◦ AWA of the Basic Test and the 70◦ of the Bent Yard Test, because they have a big drop of the drive force coefficient which should be taken into account. The reader should remember 162 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

(a) Basic Test (b) Bent Yard Test

Figure 8.10: 43ft model, CX vs HA

(a) Basic Test (b) Bent Yard Test

Figure 8.11: 43ft model, CMX vs HA the way these boats race. Usually, there race is only one leg with a very steady wind intensity and direction. This means that is very common to fasten the main sheet in the beginning and adjust the sails very little during the race. This means that the influence of the heel angle must be taken into account, especially if the main-sheet is not going to be trimmed.

Optimum Trimming Test

In this test, the trimming has been optimized to obtain the maximum drive force for each heel angle. Three apparent wind angles (40◦, 60◦ and 80◦) have been tested and the same four heel angles (0◦, 5◦, 10◦ and 15◦). As it has been observed in the previous section, sail performance gets worse when increasing the heel angle if there is not trimming. This test has been conducted to evaluate if it is possible to keep the performance for any heel angle. 8.4. EXPERIMENTAL TESTS 163

Here, only the results of the 60◦ of AWA are presented since the other two angles (40◦ and 80◦) provide similar results (see appendix F).

(a) Drive Force Coefficient (b) Heeling Moment Coefficient

Figure 8.12: 43ft model, Optimum Trimming Test, CX and CMX (AWA=60◦)

As it was expected, and according to figure 8.12, optimizing the trimming increases enormously the sail performance. It can not only keep the performance of the upright position but increase it, as it can be seen comparing the slope of the curves in figure 8.13.

It can be also seen that the BYT results are better than the BT results. The optimized BYT has more drive force and less moment than the values of the Basic Test.

Figure 8.13: 43ft model, Optimum Trimming Test, CX/CMX (AWA=60◦)

Bending Test 164 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

During this test, three different bending situations have been tested for three apparent wind angles (40◦, 60◦ and 80◦) and only one heel angle (5◦). In the BYT a tension on the stiffeners has been applied as explained before. Now, the aim of this test is to compare the effect that three different tensions provoke on the performance. In order to facilitate the comparison, the figures of this section include the results of the three bending cases and the optimized Basic Test at 5◦ of heel angle.

(a) Drive Force Coefficient (b) Heeling Moment Coefficient

Figure 8.14: 43ft model, Bending Test, CX and CMX

In figure 8.14(a) the drive force coefficient for the three apparent wind angles is plotted. As it can be observed, for 40◦ AWA, the CX increases with the small bending and decreases with both the medium and large bending. In the results of the 60◦ and 80◦, the drive force increases for the three bending situations. In this figure it can also be seen the change of the drive force among apparent wind angles. There is a big change between 40◦ and 60◦ comparing to the one between 60◦ and 80◦. This is in agreement with figure 8.7 where the drive force coefficient increases rapidly for low apparent wind angles and then the slope of the curves decays.

As illustrated in figure 8.14(b), the heeling moment coefficient decreases with the addition of the stiffeners whatever the tension is.

Therefore, due to the drive force increase and heeling moment decrease, it can be concluded that the stiffeners improve the sail performance as plotted in figure 8.15. The improvement is notorious especially for 80◦ of apparent wind angle and a large tension. But even for the small apparent wind angles and tension, the stiffeners improve the performance.

Yard Stiffness Test

In the previous tests, the bending was forced by means of stiffeners. This new Yard 8.4. EXPERIMENTAL TESTS 165

Figure 8.15: 43ft model, Bending Test, CX/CMX

Stiffness Test has been conducted to study the effect of the natural bending without exter- nal devices. The stiffeners provoke a forced bending but also a tension to windward. The stiffeners prevent the yard from bending to leeward which would be its natural behavior. In this test, three yards with different stiffnesses (stiff, medium and soft) have been tested.

As illustrated in figure 8.16, the forced bending with stiffeners is better than any of the natural bending cases, except for high AWA and high HA, where a medium stiffness yard would give better results. What it is clear is that the soft stiffness yard provides the worst results. The results for the stiff and medium yards are similar. The curves are displayed together until high apparent wind angles when the medium stiffness yards gives better results.

It can be concluded that in general, it is better to include stiffeners to bend the mast rather than let the yard bend itself.

8.4.4.2 60ft Dhow Model Basic Test with and without Mizzen

In figure 8.17(a) the drive force coefficient against apparent wind angles is plotted, for the 60ft model with (solid lines) and without mizzen (dashed lines). As it is observed, the trend is the same in both sets of curves. The influence of the mizzen for low AWA is negligible, then it increases until 50◦ and then it remains constant. It can also be concluded that the heel angle is not affecting the values of the drive force since the curves are displayed together. 166 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

(a) 0◦ Heel Angle (b) 5◦ Heel Angle

(c) 10◦ Heel Angle (d) 15◦ Heel Angle

Figure 8.16: 43ft model, Yard Stiffness Test, CX/CMX

In the figure 8.17(b) the heeling moment coefficient against AWA is included. It can be observed that the trend is similar with and without mizzen. The effect of the mizzen is insignificant for low and high AWA, while it is greater for the middle range of AWA, especially for 50◦.

For these tests, the ratio between the drive force and heeling moment has also been plotted (see figure 8.17(c)). There is a linear trend of the ratio until 90◦ of AWA and then, the slope changes. The behavior of the curves with and without mizzen is similar but the performance of the mainsail by itself is more “efficient” since it would give more drive force for the same righting moment.

In order to analyze the effect of heel angle on the performance, the drive force and heeling moment coefficients have been plotted against heel angles, as seen in figure 8.18. Only the case with mizzen has been included since the case without mizzen shows the same behavior. 8.4. EXPERIMENTAL TESTS 167

(a) Drive Force Coefficient (b) Heeling Moment Coefficient

(c) CX/CMX

Figure 8.17: 60ft model, Basic Test, CX, CMX and CX/CMX

As in the case of the 43ft model, except from the 70◦ of AWA curve, all the curves are linear with a constant or decreasing slope. Again, this result was expected since the trimming has been optimized for the upright condition and kept constant for the rest of heel angles.

Optimum Trimming Test

In this test, the trimming has been optimized for each heel angle and, as it can be seen in figure 8.19, the sail performance can slightly been improved. For all the apparent wind angles tested, the trend is similar. Even though there is an improvement, it is not as notorious as in the 43ft model case (see figure 8.13). 168 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

(a) CX vs HA (b) CMX vs HA

Figure 8.18: 60ft model, Basic Test with mizzen, CX and CMX

(a) Drive Force Coefficient (b) Heeling Moment Coefficient

(c) CX/CMX

Figure 8.19: 60ft model, Optimum Trimming Test, CX, CMX and CX/CMX 8.5. NUMERICAL SIMULATIONS 169

8.5 Numerical simulations

Here, as in chapters 6 and 7, the experimental tests have been reproduced with a RANS solver. The first set of numerical tests have been conducted with the geometry obtained from the wind tunnel tests. Different parameters have been studied such as the type of meshes, time-step, inner iterations, stopping criteria, temporal discretization method and turbulence model. For each test, the residuals, the convergence of forces, time of calculation and the wall-y+ have been checked. Once the appropriate combination of parameters has been obtained, the final tests have been carried out with a customized geometry which looks more like the real shape.

The calculations of this research have been conducted with the RANS solver CD-Adapco’s STAR-CCM+. The simulations have been run on an Intelr Core i7-920 Processor with a Linux 2.6.38-12 kernel in amd64 and an AMD Phenom II X6 1090T with 8GB of RAM. For a 5.3·106 elements mesh, the typical CPU time to achieve the desired convergence has been around 39 hours using five processors of the second computer.

8.5.1 Geometry In order to simulate an experimental test, the flying shape of the flexible sail must be acquire. It has been decided to simulate the combination of 60◦ of apparent wind angle and 0◦ of heel angle from the Basic Test of the 43ft model. This situation has been repeated several times and the flying shape has been measured with the V-SPAR system [90] (http://www.vspars.com). Hereafter, this geometry is named “original”. In fig- ures 8.20(b), 8.20(e) and 8.20(h), the bow, head and stern views are included, respectively.

The V-SPAR system determines the global location in Cartesian coordinates of specific targets on the sails and rig. The system uses deck mounted cameras to look up at stripes marked on the sails. It has the ability to correct for large perspective effects and stripes with very high curvature. In addition, the rig deflection is measured from the dis- placement of target points and it is combined with the sail shapes to give a global position of the sails and rig above the deck. The accuracy of the system is dependent on the type of sail being flown. It has been measured a deviation of <2% stripe length on downwind sails.

The TP52 World Champion 2011 Quantum Racing used VSPARS RealTime through- out the last campaign. Moreover, the system has helped every one of the 7 teams entered in the 2011-2012 Volvo Ocean Race to design the best sail shapes in order to optimized their performance. This confirms that it is a leading system among the flying shape acquisition softwares.

Nevertheless, the version of the system that has been utilized on the experimental tests had never been used before with this kind of sails. If the pictures of the test and the original geometry are compared in figure 8.20, it can be concluded that the shape is 170 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

not perfectly acquire. Therefore a “customized” geometry has been designed from the pictures taken during the tests. In figures 8.20(c), 8.20(f) and 8.20(i), the bow head and stern views of the customized geometry are included, respectively. As mentioned before, the first numerical tests have been conducted with the original geometry and then, the parameters have been applied to the final customized geometry.

The three-dimensional shape has been introduced into Rhinocerosr 4.0, where the sail surface has been modeled as well as the mast, yard, bowsprit, hull and deck. A sail thickness of 2mm has been considered.

The geometry of the 43ft model has been placed as in the wind tunnel: 60◦ of apparent wind angle and 0◦ of heel angle. The origin of the coordinate system is placed in the intersection of the bow with the waterline (floor of the wind tunnel), whereas the center for the calculation of the moments is situated in the same place as the cen- ter of the force balance. This is -0.468m downwind, 0.810m to port and 0m from the floor.

8.5.2 Domain and mesh The computational domain is a rectangular box. The extends of the volume are set so as to permit a good development of the flow without creating wall effects and reproduce the dimensions of the wind tunnel. The extension of the computational control volume has been set in relation to the length of the 43ft model mast (Lm) 1.189m and the size of the wind tunnel: 2Lm upstream, 5Lm downstream, 7m of width and 3.5m in height.

The meshing procedure has been conducted with the meshing tool of the STAR- CCM+. According to the nomenclature of this software, the final mesh is surface remesher and trimmer (hexahedral) type with prism layer mesher to properly capture the phenomena involved near the sail.

Before obtaining reliable results, a grid-sensitivity study has been performed and several tests have been conducted with the original geometry. More than ten meshes have been simulated varying the base size, refining blocks and prism layers.

The final number of elements of the customized geometry mesh is 5.3·106. In this last mesh, five prism layers have been set with a stretching factor of 1.5 and a thickness of 4mm on the sail, 10mm on the deck and 5mm on the hull.

The variable wall y+ has been studied to evaluate the quality of the mesh next to the rig and its capability to detect the boundary layer by the numerical wall treatments. A typical target value of y+=1 has been aimed for most of the sail, spars and hull surfaces. The maximum y+ of the final simulation has been 17 which is within the optimum range. Moreover, the volume change ratio have been checked and it is confirmed to be between 8.5. NUMERICAL SIMULATIONS 171

(a) Bow view (b) Original (c) Customized

(d) Head view (e) Original (f) Customized

(g) Stern view (h) Original (i) Customized

Figure 8.20: Flying shapes: experimental, original and customized

0.1 and 1 for the 98% of the cells.

8.5.3 Boundary conditions The most suitable boundary conditions have been set in order to reproduce the real behavior of the flow around the 43ft model mainsail in the wind tunnel.

• Inlet: the speed normal to the inlet surface is set constant (4m/s) which is similar to the wind speed in the wind tunnel. Turbulence intensity is set to 1% and the turbulent viscosity ratio to 10. • Outlet: the averaged pressure over the surface is set to zero. • Walls: the condition imposed is “free-slip”. 172 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

• Sea (floor of the wind tunnel): the boundary condition is “no-slip”.

• Deck, hull and rigging: the “no-slip” condition is set.

8.5.4 Numerical scheme The models utilized in these simulations are: three-dimensional, stationary, segregated flow model, constant density, implicit unsteady and all-y+ wall treatment.

Two different turbulence methods have been used: the SST K-Omega and the K-Epsilon models. It is concluded that the first of them is better as far as these simulations are concerned. In the same way, two temporal discretization methods have been used: the Euler’s method (1st order) and Newmark’s method (2nd order). It is concluded that the 1st order method is better.

Four time-steps have been studied (1, 0.1, 0.01 and 0.001s) with different meshes. The inner iterations and the stopping criteria have been also analyzed. Based on the results obtained with the original geometry, in the final test, the time-step has been set to 0.1s, inner iterations to 3 and a stooping criteria to 6000 iterations (which is 200s of physical time).

The force coefficients on each step have been monitored to ensure they have settled. The last 20% of the total physical time has been analyzed and the fluctuation of the coefficients in this period is below the 0.4% of the mean value.

8.5.5 Results

CX CY CMX Experimental 0.544 -0.924 0.339 Numerical (customized) 0.525 -0.703 0.252 Numerical (original) 0.420 -0.672 0.246 Table 8.5: Comparison of results

Both the force and moment coefficients have been calculated similarly to the coef- ficients presented in the previous section. In this case, the dynamic pressure has been 2 substituted by Pd = 0.5ρV in equations 8.1, 8.2 and 8.3.

In table 8.5 the drive force, side force and heeling moment coefficients are included. The values related to the experimental tests are the mean values obtained from several repetitions of the same combination. In order to compare the difference between the two geometries, the results of a similar numerical test have been included. The mesh of 8.5. NUMERICAL SIMULATIONS 173

the simulation of the original geometry has 3.9·106 cells and the same numerical scheme parameters.

It can be seen that the simulation of the customized geometry provides a drive force coefficient similar to the experimental value. But, on the other hand, the values of the side force coefficient and heeling moments coefficient differ substantially. If both simulations are compared (original and customized geometries), it is observed that the results of the original geometry are even less accurate. Clearly, the geometry affects the results and it can be estimated that most of the error in the results is based on the flying shape acquisition.

(a) Windward (b) Leeward

Figure 8.21: Pressure coefficient distribution

Although the real conditions of the experimental test have not been reproduced, other parameters are analyzed such as the pressure coefficient distribution over the sails and the vortex shedding. The aim of this study is to demonstrate that numerical tools can not only provide forces and moments, but calculate other outputs that can help the sailmakers to design sails more efficiently.

In figure 8.21 the pressure coefficient distribution on windward and leeward sides is plotted. On the middle of the windward side, a high pressure zone can be observed. On the leeward side, a negative pressure is presented near the yard and then, a detachment of the flow can be seen due to the uniformity of the color.

The pressure coefficient has been studied in detail (figure 8.22(b)) at three different sections (z= 0.25m, 0.75m and 1.25m) plotted in figure 8.22(a). The lowest cut shows an increase of the pressure on windward at the second half of the section and a flow reattachment on leeward. Both z=0.75m and z=1.25m show the same behavior, a constant pressure on windward whereas on the leeward side, there is an attached flow next to the yard and then, the flow separates. 174 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

(a) Profiles (b) Pressure coefficient

Figure 8.22: Pressure coefficient

Figure 8.23: Normalized speed at the midsection

In figure 8.23 the normalized speed is plotted at the midsection plane. This is, the actual speed has been divided by the inflow speed (4m/s). A vortex shedding can be observed. The simulations have been conducted with an unsteady model which permits the solution to show these vortices. An specific test could measure them in a wind tun- nel and then the numerical results could be validated. This is not a very common practice.

The vortices that are shed can be seen in figure 8.24. There are two main vortices. One of them, the largest one, comes out from the highest part of the yard and it is very intensive. The other one, the smallest vortex, comes out from the bowsprit. It can be also observed that there is an area behind the hull in which there is turbulent flow.

These considerations are important in a fleet race. It should be reminded how these sailing boats race. It is normal that once the race has started the boat keeps the same course during the whole race. This means that the behavior of the boat depends on the flow from the boat upwind. Therefore, it is very important to know the performance of your sail but it is also important to know what the boat upwind provokes on your flow. 8.6. CONCLUSIONS 175

Figure 8.24: Vortices downstream

8.6 Conclusions

This chapter has detailed the research carried out by the author to understand the aerodynamics of sailing dhows. This is the first investigation that has scientifically studied sailing dhows. The main parameters that affect the sail performance have been quantify. This facilitates future investigations to optimize these sails and improve their performance. A CFD analysis has been also conducted to improve the knowledge of the flow around sailing dhows.

The two most important dhow classes (43ft and 60ft) have been tested in the Twisted Flow Wind Tunnel of the YRU where a broad range of parameters have been studied. It has been analyzed the effect of yard stiffness, heel and apparent wind angles, the influence of bending, the optimization of the trimming and the performance of the 60ft mainsail alone without the mizzen. Moreover, one of the experimental tests of the 43ft model has been reproduced with the CD-Adapco’s STAR-CCM+. The flying shape of the sail has been acquired by means of the V-SPAR system. The results have been validated with the experimental data.

The main conclusions drawn by the experimental tests are: 1. Forced bending of the yard improves the performance of the sail for high apparent wind angles. 2. Trimming for each heel angle improves the sail performance enormously, which is more significant for the 43ft model than for the 60ft model. 3. For the apparent wind angles tested (40◦, 60◦ and 80◦), the sail performance im- proves with a medium to large tension on the yard. 176 CHAPTER 8. AERODYNAMICS OF SAILING DHOWS

4. Generally, it is better to include stiffeners to bend the mast than let the yard bend naturally due to its stiffness.

5. In the 60ft model, the mainsail is more effective when sailing without the mizzen.

6. After these several tests, the effect of the heel angle and the apparent wind angle on the sail performance of dhows has been described thoroughly.

The results of the numerical study are not fully satisfactory. The validation of the force and moment coefficients highlight the importance of an adequate flying shape acquisition. Nevertheless, the flow analysis can help both the designers and sailors to improve the performance of their sailboats during a race.

These experimental and numerical tests lay the grounds for future investigations. Different shapes will be tested in the wind tunnel and the twisting vanes will be included to take into account the real inflow. Again, it must be emphasized that this research has been conducted together with the industry and the results are used on a daily basis. Chapter 9

EU-CARGOXPRESS PROJECT

9.1 Introduction

Nowadays the 90% of all the global trade is transported by sea and the shipping industry highly depends on fuel. Since there is a finite amount of fuel, the cost is continuously increasing and it is not likely to change in the future. Furthermore, the problem is not only the fuel cost but the environmental concern. Everyday the governmental air and water quality regulations become stricter. This leads the shipping industry to make vessels cleaner and more economical by optimizing their engines and hulls. The objective is reducing fuel consumption, or reducing emissions, which is normally simultaneous. But, the potential to enhance the existing propulsion systems is almost exhausted.

Consequently, new technologies are needed, especially using renewable energies. In the past, global trade was powered by wind but after the arrival of steam power and diesel engines, sailing cargo vessels were relegated to the history books. Nowadays, due to the price of fuel and pollution, there is a new revival of wind power. The shipping industry has high requirements on propulsion technologies using offshore wind which is an endless energy source, free of charge, powerful at seas and renewable.

Since the 80s, there has been a new attempt to bring back commercial sailing vessel. But there are some drawbacks that have not yet been totally overcome such as: the cost of the equipment, the inability to schedule wind power, the structural reinforcement or the size of the rigging. Various methods have been developed to fulfill the requirements but, unfortunately, no system has been able to come up to the expectations on a global scale yet. Anyway, it is clear that the wind power is intermittent and commercial vessels cannot exclusively depend on it since there are routes and schedules to keep. Therefore, there will be always a conventional propulsion system in parallel with the sailing equipment.

The objective of EU-CargoXpress Project is to develop a new generation of competi- tive cargo vessels for accelerated maritime and fluvial shipping, using innovative concepts

177 178 CHAPTER 9. EU-CARGOXPRESS PROJECT

and technologies in order to support the greening of surface transport and prepare for fast and efficient modal shift in ports. One of the considerations of this project is to include sustainable energies and to reduce fuel consumption for some transport scenarios. The updated concept consists of hoisting the superstructure and using it as a sail together with the conventional propulsion.

The aim of this contribution, under the scope of this thesis, is to study the viability of the structural wing-sail. First, three different geometries have been studied with a RANS code and their aerodynamic performance has been compared. Then, the most efficient shape has been built and tested in a wind tunnel to validate the numerical results. Finally, a feasibility study has been developed for that geometry, in six different navigation routes.

In this chapter, the contribution of the author to the EU-CargoXpress project is presented. The results of this investigation have been partially disclosed by the author in [5] and [6]. Moreover, the paper “EU-CargoXpress: Wind Propulsion Concept”[7], presented at the Transport Research Arena Europe 2012 won the Best Paper Award. This highlights the relevance of this project and in particular, the innovative contribution of this author to the concern of the shipping industry.

The structure of the reminder of this chapter is the following. In the second section, the nomenclature and abbreviations are listed. In the third section, the existing technologies are indicated. In the fourth section, the EU-CargoXpress project is briefly summarize. In the fifth section, the numerical simulations are included. In the sixth section, the experimental tests are presented. In the seventh section, the feasibility study is described. In the last section, there is a summary of the main conclusions that have been drawn.

9.2 Nomenclature

ρ Air density

AWA Apparent wind angle

AWS Apparent wind speed

Cp Pressure coefficient (equation 9.1)

Pi − P0 Pi − P0 Cp = 2 = (9.1) 0.5 · ρ · S · AW S Pd

CX Drive force coefficient (equation 9.2) FX FX CX = 2 = (9.2) 0.5 · ρ · S · AW S Pd · S 9.2. NOMENCLATURE 179

CY Side force coefficient (equation 9.3)

FY FY CY = 2 = (9.3) 0.5 · ρ · S · AW S Pd · S

CZ Vertical force coefficient

EHP Effective Power

FX Longitudinal force (centerline), drive force

FY Side force

FZ Vertical force

P0 Static pressure

Pd Dynamic pressure

Pi Pressure at the pressure tap

Pt Total pressure or stagnation pressure

Psail average power, during a year, at a certain route

Psaved Power saved with a speed and an angle of wind

P rsail Total probability of using the sail

P rwind Probability of having a speed and an angle of wind

S Sail surface

TWA True wind angle

TWS True wind speed

Abreviaturas

CFD Computational Fluid Dynamics

WT Wind tunnel 180 CHAPTER 9. EU-CARGOXPRESS PROJECT

9.3 Existing technologies

In this section the existing technologies which use the wind as a source of power are presented. Not only the technology is described but projects in which they have been applied are included. Moreover, the advantages and disadvantages are explained.

Sails on masts

Sails on masts include both traditional sails and wings, which are airfoil-like structures that are similar to airplane wings. In the late 1970s, the high oil price stimulated the involvement in wind power for merchant vessels. Some interesting vessels were built or converted like the “Shin Aitoku Maru” tanker and the “Usuki Pioneer” bulk carrier. It was calculated an average fuel reduction of 30%-40% but due to the falling oil prices at that time, the projects were canceled [120]. In Denmark, the “Windship” bulk carrier was designed with six masts with fixed sails. Energy savings of up to 27% were estimated, but the system was never tested because there were many disadvantages.

The cruise vessel “Eoseas” has been designed at the Yards STX [http://www.stxeurope.com]. On its 305 meters of length there are six sails with a total surface of 12440m2. It is calculated that the new technologies applied in this vessel will allow reducing the 50% of the energetic consumptions. The designers estimate that the Eoseas would cost around 30% more than a conventional cruise vessel but its developers are confident that the investment will be amortized by the reduction of fuel consumption. This boat is still in a project stage.

The Solar Sailor Company has patented SolarSails which harness renewable solar and wind energy. These sails have been installed at the “Solar Albatross” (see figure 9.1). This is the first commercial hybrid vessel propelled by fossil fuel, stored electricity, wind power and solar power, in which this technology has been tested. This vessel is a 24m long, 100 passenger carrying catamaran ferry, with stowable SolarSails. According to the company, in early trials when sailing at 15 knots of true wind intensity and 45 degrees of true wind angle from the bow, the boat speed increased almost 2 knots for the same engine power.

The E/S Orcelle is a pentamaran vessel designed by Wallenius Wilhelmsen Logistics [http://www.2wglobal.com]. She is 250m long and has a 13,000t of deadweight. The design includes six rigid sails of 1400 m2 each. The conceptual designing began in 2004 and it is expected to be launched in 2025.

The Emax Deliverance is a 426m tanker desinged by Sauter Carbon Offset Design [http://www.sautercarbonoffsetdesign.com]. The project assumes a combined propulsion system with twenty sails on the deck. The total sail area is 500,000m2 which, according to the estimations, will reduce the fuel consumption a 25%. 9.3. EXISTING TECHNOLOGIES 181

Figure 9.1: Solar Albatros

The use of sails on masts can reduce the fuel consumption and therefore, reduce the emissions too, but there are certain potential disadvantages:

• The rig takes up valuable loading space and there can be restrictions during load- ing/unloading since the cranes must work around the rigging.

• Mast creates drag in unfavorable winds. Furthermore, safety risk exists for the crew due to the inflexibility of the system with regard to changing wind conditions. Especially in squalls, masts and sails can cause ships to heel dangerously.

• When navigating with sails, the vessel tends to heel. It would be unfeasible for container and bulk cargo vessels to operate under the typical inclined position of sailing ships. In order to avoid this situation excessive ballast is needed which is uneconomical.

Flettner rotor

The Flettner Rotor uses the Magnus force to propel a vessel. This rotor is a cylinder rotating around its own axis and exposed to an airflow moving at right angles to that axis. The cylinder experiences a lateral force that acts at right angles to the airflow and the axis of rotation. The effectiveness of the Flettner Rotor was first demonstrated in 1928.

In 1924, Anton Flettner rebuilt the sailing ship “Buckau” (see figure 9.2). It was equipped with two cylinders, each 18.3 meters high and 2.8 meters in diameter, to propel the ship. The two cylinders were put in rotation by individual motors. The rebuilt ship could sail into the wind at 20-30 degrees, while the vessel with its original sail rig 182 CHAPTER 9. EU-CARGOXPRESS PROJECT

Figure 9.2: Buckau could not tack closer than 45 degrees to the wind. However, the rotor system was less efficient than conventional engines. The gain in wind power was not enough to compen- sate for the energy needed to drive the rotors and therefore, the cylinders were dismantled.

Flettner’s invention did not succeed in his lifetime but nowadays the Flettner rotor is again being tested as a parallel propulsion system. Currently, Enercon Company has built a 130 meters long vessel with four Flettner rotors for its transport of wind turbine equipment [http://www.enercon.de]. The vessel called E-Ship 1 uses wind energy to reduce fuel costs and emissions. E-Ship 1 uses four giant 25 meter high, 4 meter in diameter, rotating, vertical Flettner rotors positioned two fore and two aft to harness wind energy. It was estimated that the vessel could reduce fuel cost by 30% but since the vessel was launched, no further results have been published.

Turbosails

In the 80s Capitain Jacques Cousteau, Professor Lucien Malavard and Dr. Bertrand Charrier, developed another wind traction system. They designed and prototyped the first wind-propulsion cylinder based on the Savonius principle, the Turbosail System. In 1986, they patented the idea named “Apparatus for producing a force when in a moving fluid”, patent number US 4630997(A).

A turbosail is a fixed, hollow, rotating metal cylinder that works like an airplane wing. The cylinder is perforated with thousand of little holes to allow the air to enter and escape. Fans, moved by engines, are placed at the top of the turbosail to accelerate the flow around the wing-masts and increase the lift, producing the driving force forward.

A ship called Alcyone was build and equipped with two 10m high turbosails (see figure 9.3). Two diesel engines provided the necessary power to complement the wind. It was concluded that the energy obtained from the device did not compensate the installation. 9.3. EXISTING TECHNOLOGIES 183

Figure 9.3: Alcyone

The design of the turbosails on-board has some drawbacks such as: the large loading space it takes, it is still not efficient enough and it still expensive comparing to other technologies.

Kites

At least two firms have developed kite-assisted systems for application to commercial cargo ships: the German company SkySails [http://www.skysails.info] and the American KiteShip [http://www.kiteship.com].

The kites fly at 100-300 meters above the free surface of the sea which permits the kites generate 25 times the amount of energy of conventional sails due to the high speed winds at that height. Comparing to other wind traction devices, kites do not require a mast and can be easily stowed. This means that they need little space on board and do not disturb the loading/unloading operations. Moreover, these devices incorporate an automatic control system resulting in easy handling and high reliability. Unlike conventional wind propulsion systems, kites cause small heel angles and therefore, there is no need for ballast.

They could be fitted to almost any existing cargo vessels. Furthermore, it has low investment costs comparing to other systems but higher efficiency of energy savings.

In 2006, it was announced that Beluga Shipping had purchased a SkySails kite system to be installed on the newly built 140m heavy cargo freighter MS Beluga SkySails. The vessel was launched the 17th of December 2007 (see figure 9.4).

In February 2011, Cargill Company signed an agreement with SkySails to install a 320m2 kite on a vessel of 30,000 deadweight tonnes, making it the largest vessel propelled by a kite in the world. Cargill and SkySails aim to have the system fully operational in 2012. 184 CHAPTER 9. EU-CARGOXPRESS PROJECT

Figure 9.4: Beluga-SkySails

As well as the previous systems, kites have also potential disadvantages. Kite cannot be operated on courses against the wind. That is because the force is created by the wind being captured in the sail area and pulling the ship; for this reason, the system cannot be used when the apparent wind is forward of the beam.

The greatest drawback of kites is that they cannot be operated at low winds. Some studies reveal that the potential hazard of the kite falling in the water, particularly in the ship’s path, outweighs any financial benefits obtained from this system. Moreover, the kite should not be operated in areas with dense ship traffic for safety reasons. In these areas the vessel might need to rapidly change her course, or stop, and it is difficult to do so when the kite is flying.

Even though there are some modern examples in which this technology has been applied, the disadvantages provoke that its use hasn’t become massive.

Structural wing

This innovative concept has been developed in the EU-CargoXpress project [http://cargoxpress.eu] which is the core issue of this chapter.

9.4 The project

9.4.1 Description This is a collaborative Project of the Seventh Framework Program called “Greening of surface transport through an innovative and competitive CARGO-VESSEL Concept connecting marine and fluvial intermodal ports” or the acronym “EU-CargoXpress”. The conclusions of the project were drawn in April 2012. A picture of the EU-CargoXpress 9.4. THE PROJECT 185

Figure 9.5: EU-CargoXpress Project

cargo-vessel is illustrated in figure 9.5.

The partners that participated in the project were: Acciona-Transmediterr´anea (Spain), Autoridad Portuaria de Gij´on (Spain), Ship Design & Consult GmbH (Denmark), MARINTEK-Norwegian Marine Technology Institute A/S (Norway), Universidad Polit´ecnicade Madrid (Spain), Innovacion Log´ıstica SL (Spain), Center of Marine Technologies e.V. (Denmark), Swedish Institute for Composite Materials (Sweden), Kockums AB (Sweden), Fjellstrand AS Shipyards (Norway), Royal Institute of Technology Stockholm (Sweden) and National Technical University of Athens (Greece).

The project concentrated on those subjects which have the mayor impact on future sustainable and green marine transport, investigating: alternative energy forms, usage and conversion; best low resistance hull forms; materials to lower the lightweight of the vessel; and, innovative cargo loading and port accessing devices. These solutions make this concept very competitive to the ever growing road transport. The planned competitive cargo-vessel included highly innovative features not yet used by the marine community. In table 9.1, the main specifications of the cargo-vessel are presented. These are the values obtained at the end of the project after a thorough investigation.

The concept of a structural wing is one of the pillars of the EU-CargoXpress project. 186 CHAPTER 9. EU-CARGOXPRESS PROJECT

Type Multi purpose cargo-vessel (catamaran) Classification IMO HSC 2000 & DNV HSLC Class sign 1A2 R1 LC Cargo A Gas Fuelled 200 TEU Main dimensions Length = 84m, beam = 21m, draught = 4.1m Displacement 3000mt Capacity 200 TEU Deadweight 2000 t Service speed 12kn

Table 9.1: Main characteristics

It is an innovative concept to use part of the superstructure as a sail/wing. The project has studied the possibility of designing the cover of the holds as a sail. Moreover, the cover/superstructure could also be the crane for loading and unloading containers. That is, if the wind is appropriate, the wing is hoisted and used to propel the vessel. If there is no wind or it is not adequate, the wing is lowered to cover the hatches. If the vessel is in-port, the wing becomes the crane.

9.4.2 Conclusions of the EU-CargoXpress Project Next, a summary of the advantages of this innovative concept is presented.

• The optimized hull form shows very low resistance in tank testing comparing to conventional vessels.

• The on-board Ship to Shore crane allows for shorter port stays and reduced traveling speed between ports, still arriving at the same time as the current vessels. Conven- tional vessels perform 20-25 moves per hour whereas the CargoXpress cargo-vessel performs 8-15, thanks to the onboard crane which is more efficient.

• The large battery set allows for port accessing and maneuvering without main ma- chinery and serves as auxiliary back-up. This permits no contamination in ports due to the electric power.

• A conventional vessel consumes 1855t/year of diesel fuel while the CargoXpress con- sumes 735t/year of LNG fuel. It has been calculated that there is a CO2 reduction of 3270t/year and 66.8t/year of NOx.

• Since the vessel is a catamaran, there is no need for ballast water which means less fuel and less bio contamination.

• In the CargoXpress vessel the 100% of the cargo is protected when the wing is down, whereas only the 35% is protected in conventional vessels. 9.5. NUMERICAL SIMULATIONS 187

• Comparing to other vessels, this concept has lower maintenance costs because the containerized equipment.

• It has been calculated that the structural wing-sail adds 700kW in 46% of the studied routes, reducing fuel consumption and emissions. This conclusion has been drawn from the investigation that is presented in this chapter.

In appendix H, two energy balances are presented, one of the EU-CargoXpress vessel and the other one of a conventional vessel. These were included in the last report of the project. They highlight the importance of using the sail as a propulsion system combined with other sources such as electric power or fuel engines.

9.4.3 Contribution In this chapter, the study conducted by the author of this thesis at the Universidad Polit´ecnicade Madrid is presented. This investigation is focused on the aerodynamic contribution of the structural sail. First, different geometries of the sail have been compared with numerical simulations. Then, the most efficient shape has been built and tested in a wind tunnel to validate the numerical results. Finally, a feasibility study has been conducted in six real scenarios.

9.5 Numerical simulations

The numerical analysis has been carried out using the computational fluid dynamic software CD-Adapco’s STAR-CCM+ [121], which is a Reynolds Averaged Navier Stokes Equations based solver. The aerodynamic performance of three geometries has been simulated and compared.

The calculations of this study have been run at an Intelr CoreTM i7-920 Processor with a Linux 2.6.32-27 kernel. A typical simulation has required around 50 hours for a 4.5 million element mesh.

9.5.1 Geometries The three geometries of the structural sail that have been simulated are illustrated in figure 9.6. In table 9.2, the main dimensions of the geometries are included. The shapes were provided by one of the partners of the project.

The first geometry has a rounded shape and curved edges. It has been simulated with 80◦ of opening since this is the maximum angle for this geometry. This arrangement places the highest point of the sail 62 m above the hinge. The lower part of the geometry 188 CHAPTER 9. EU-CARGOXPRESS PROJECT

(a) Perspective view (b) Side view

Figure 9.6: First (red), second (blue) and third geometry (green) has been designed considering the bridge, even though, in this case, it has not been simulated with the sail.

The second shape is flat with two ailerons, one on each side. In this case, the geometry encompasses both the sail and the bridge. Even though the bridge has been simulated, only the sail has been taken into account when measuring forces and moments. It has been difficult to reproduce the lower part of the geometry since it has been necessary to capture the joints between the sail and the bridge. Moreover, due to the bridge cover, there is a gap which has also been modeled.

The third geometry is even flatter than the previous shape and it has smooth rounded edges. This geometry has the most slender shape among the three of them. It has an 85◦ opening. Also in this case, the geometry encompasses both the sail and the bridge. Again, although the bridge has been simulated, only the sail has been taken into account when measuring the forces.

First Second Third Span (m) 65 61 65 Height (m) 8 11 6 Width (m) 21 21 20 Total area (m2) 3572 3733 3018

Table 9.2: Main dimensions of the three geometries 9.5. NUMERICAL SIMULATIONS 189

Figure 9.7: The third geometry in the numerical domain

9.5.2 Domain and mesh

The computational domain is a rectangular box for the first geometry and in the last two, the inlet wall has been curved to half a cylinder (see figure 9.7). The dimensions of the volume have been set so as to permit a good development of the flow without creating wall effects. The main dimensions of the domain are: length (x-axis)= 403m, breadth (y-axis)= 248m and height (z-axis)= 186m. As an example, for the last geometry the blockage effect is less than a 3%.

The x-axis is the centerline (positive to the bow), the z-axis is the vertical direction (positive upwards) and the y-axis is the transversal direction (positive to port). The origin of the reference system is the center of the axis around which the sail is hoisted. The moments of the results are referred to this point.

The reference system is fixed to the sail and the wind is introduced with different angles. In order to obtain the thrust and the power provided by the sail the appropriate geometrical transformations are conducted. In the simulations, the apparent wind enters from starboard and it is assumed that the system is symmetrical and therefore, only one side winds are modeled.

The meshing procedure has been conducted in the STAR-CCM+ code with its own meshing tool. First, a convergence study has been conducted to obtain the main characteristics of the final mesh. According to the nomenclature of this software, the final mesh is surface remesher and trimmer (hexahedral) type with prism layer mesher to properly capture the phenomena involved near the sail. 190 CHAPTER 9. EU-CARGOXPRESS PROJECT

9.5.3 Numerical scheme and boundary conditions The physical models utilized in these simulations are: three dimensional, stationary, gas (air), constant density, turbulent, SST K-Omega, segregated flow model, implicit unsteady and all y+ wall treatment.

The most suitable boundary conditions, necessaries to reproduce the real behavior of the sail have been set:

• Outlet: the averaged pressure over the surface is set to zero.

• Walls: the condition imposed is “free-slip”.

• Deck (floor): the boundary condition is “free-slip”.

• Sail and bridge: the “no-slip” condition is set.

• Inlet: the apparent wind is specified. It has been assumed that the sail will be hoisted with wave heights lower than 4 meters which correspond to true wind speeds of 30 knots. Taken into account the studied operation areas (see section 9.7.2), this sea condition occurs the 90% of the time. These true wind speeds lead to apparent wind speeds (AWS) which range from 1 knot to 40 knots approximately. It has been decided to simulate the geometries with 30knots of apparent wind speed.

The sail is fixed in the domain, and the apparent wind angle varies from 0◦ (from the stern) to 80◦ (starboard). In real sailing, when the apparent wind angle (AWA) is greater than 80◦, the sail rotates until the relative apparent wind angle becomes 80◦ again. Therefore, the sail performance is studied only up to 80◦. According to the cargo-vessel specifications, the sail rotates 60◦ to each side which means that the maximum AWA is 140◦. If the AWA is greater than this value, the sail is lowered down.

9.5.4 Results Forces are calculated at different apparent wind angles (AWA). Since the dimensions of the shapes are different, in order to compare the sail performance, it is a com- mon practice to calculate dimensionless coefficients. For example, the longitudinal and side force coefficients are obtained with equations 9.2 and 9.3, respectively. In figure 9.8, these force coefficients are plotted. From 0◦ to 80◦ the results presented are obtained directly from the forces of the CFD. From 80◦ to 140◦, the value at 80◦ 9.5. NUMERICAL SIMULATIONS 191

(a) Longitudinal force coefficient (b) Side force coefficient

Figure 9.8: Force coefficients is transformed geometrically assuming that the sail rotates up to 60◦, as mentioned before.

The most important contribution to the thrust comes from the positive longitudinal force. Therefore a high positive value of CX is desirable. On the other hand, the side force contributes negatively to thrust and moreover it decreases the stability. Consequently, small and negative values of CY are better. The figure of CZ is not included since the values are small and constant regardless of the apparent wind angles, as it was expected.

As it can be seen in figure 9.8(a), the curve of the first geometry has a great decreasing slope. Moreover, after 90◦ of apparent wind angle, the sails contribute negatively and generate resistance instead of thrust. The third geometry also decays but in a less pronounced way and its longitudinal force coefficient curve is the highest one which indicates that this shape is the most efficient one.

In figure 9.8(b) the side force coefficient is plotted. The first geometry produces the vessel sail down leeward in the whole range whereas the second and the third, permits the vessel sail up windward for low apparent wind angles. Approximately, from 80◦ on, these sails also generate a force down leeward. At low apparent wind angles, the third geometry is very efficient whereas at high apparent wind angles, the second geometry is slightly better. According to the figures 9.8(a) and 9.8(b), the second and third geometries are the most effective ones.

Now, the power that could be saved at a constant vessel speed is calculated for the last two shapes. The value of forces is obtained from the CFD, then, the thrust is calculated. If a constant vessel speed is assumed, the power (Psaved) is obtained by simply multiplying the thrust and this speed. Throughout the study it has been assumed that the vessel speed is constant regardless the wind contribution. The goal of using the sail is the reduction of fuel consumption and not increasing the vessel speed. 192 CHAPTER 9. EU-CARGOXPRESS PROJECT

Figure 9.9: Saved power at 15knots of vessel speed (second and third geometries)

In figure 9.9, the values of Psaved are presented for the second and third geometries at different true wind speeds (TWS) and true wind angles (TWA). In this case, a constant vessel speed of 15 knots has been assumed. The plot shows that the third geometry provides more thrust in most of the range. Only, at low true wind angles, the second geometry is slightly better. Consequently, a model of the third geometry has been built and tested in the wind tunnel to validate the numerical results.

Furthermore, with the information in figure 9.9, it can be easily evaluate the potential of the sails in different scenarios. For example, with the third geometry, if the mean true wind is 20 knots at a certain operation area it can be expected a thrust between 200kW and 1400kW depending on the wind direction and the sailing course. For strong winds and the appropriate combination of sailing course/wind direction, the sail could provide almost 3000kW.

9.6 Experimental Tests

According to the discussion of the previous section a model of the third geometry has been built and tested in a wind tunnel. The aim of this study is the determination of the aerodynamic performance of the sail and the validation of the numerical results. These tests have been conducted at the Instituto Universitario de Microgravedad “Ignacio Da Riva” (IDR) at the Universidad Polit´ecnica de Madrid (Spain). This is an institute for R&D activities in the field of space science, microgravity and civil engineering.

Two tests have been carried out. In the first test, the global aerodynamic forces and 9.6. EXPERIMENTAL TESTS 193

Figure 9.10: A9 IDR/UPM wind tunnel

moments have been measured for different apparent wind angles. Then, in the second test, the pressure distribution over the sail has been measured for the same range of angles. Two different models have been built, one for each test.

The experimental tests have been conducted by the staff of the IDR with the collaboration and supervision of the author of this thesis. The information presented in this section has been partially disclosed in [122].

9.6.1 Wind tunnel description The A9 wind tunnel has been used. It is an open-circuit closed-section wind tunnel. As illustrated in figure 9.10, the facility is divided in different parts:

• Inlet contraction (1). The contraction is bi-dimensional, that is, the airflow is only contracted in one of the symmetry planes of the tunnel. The ceiling and the floor remain parallel while the vertical walls of this area provoke the adaptation of the inlet to the test section. The inlet section of the contraction has a width of 4.8m and a height of 1.8m. It has a length of 5.25m.

• Test section (2). It has a length of 3m, a width of 1.5m and a height of 1.8m. On the upper part of the test section the lighting system, the Pitot-tubes and the video camera are located. The staff in charge of the test work at the control room where the computers and monitors are situated.

• Adaptation diffuser (3). This adapts the test section to the location of the fans. This diffuser has a length of 6m. 194 CHAPTER 9. EU-CARGOXPRESS PROJECT

Figure 9.11: Pressure model

• Fans (4). There are nine SODECA-HTC-90 fans. Each of them has eight blades, a nominal power of 10kW and an inner diameter of 0.9m. They have an adjustable speed and they are placed in a 3x3 matrix. The air is blown directly to the room. The maximum wind speed at the test section can exceed 30m/s.

9.6.2 The model As mentioned before, two models have been built: one of them to measure global forces and moments, and the other one, to measure pressure distributions.

The first model have been milled on a CNC 5-axis machining center. The model has been made from a block of NECURONr-1150 which is a synthetic and isotropic material. The scale is 1:70. This value has been chosen in order to reach a high Reynolds number and a low blockage effect.

The bridge has been also built with the same technique but in this case, from a NECURONr-480 block. This piece is placed under both sail-models to capture its influence on the wind but the measurements are concentrated on the sail-models. It has been carefully designed not to alter the measurements on the load cell or the pressure tubes. In figure 9.13, the bridge can be seen (light brown rounded piece under the sails).

In order to measure the pressure distribution over the sail, an specific 1:70 scaled model has been built. This model has been manufactured by a steroeolithography technique. This is a fast process to built models thanks to the stratification by levels of a complex digital model. The CAD geometry is exported to STL format and then, the machine reproduces the model with a melted ABS type solid resin by levels of 0.254mm.

The model has been fitted with ninety eight pressure taps. Each sensor is formed 9.6. EXPERIMENTAL TESTS 195

Figure 9.12: Sensor distribution, leeward(left) and windward(right) (Dimensioning in mm)

by a brass tube of 25mm in length and an inner diameter of 1mm. One of the ends of the brass tube is smoothed down with the outer skin of the sail at the point where the pressure is going to be measured. The other end of the brass tube is connected to a flexible plastic long tube. This transmits the pressure to the systems that is placed outside the test section. A picture where the inner arrangement of the tubes is presented in figure 9.11. In figure 9.12, there is a sketch of the distribution of the pressure taps on leeward (bow side) and windward (stern side). The enumeration is also included. In appendix I the position of the pressure taps are included.

9.6.3 Experimental set-up and test description Force test

The force model has been mounted in the test section of the A9 wind tunnel. The sail has been linked to the six component load cell ATI’s Gamma SI 130-10 which is inside the bridge. Again, even thought the bridge is included, the forces and moments are only measured on the sail.

All the components are held on a Newport’s turntable which is located under the 196 CHAPTER 9. EU-CARGOXPRESS PROJECT

(a) Force model (b) Pressure model

Figure 9.13: Models of the third geometry wind tunnel and permits the system control the angle of attack. Unlike in the numerical simulations, in this case, the sail is rotated whereas the wind direction is kept constant. Anyway, the relative angle is the same and is equivalent to the real apparent wind angle.

In figure 9.13(a), the force model can be seen ready to be tested. Apart from the load cell, it is also needed: a Pitot tube (Airflow model 3.3.311), an A/D converter, a computer and finally, the acquisition and control software. The Pitot tube measures the total pressure (or stagnation pressure), Pt, and the reference static pressure, P0. The 2 dynamic pressure, Pd, is obtained as Pd = Pt − P0 = 0.5 · ρ · AW S , where ρ the air density and AW S is the wind speed.

A constant and uniform airflow of 8m/s is set. The turbulence intensity is approxi- mately 2.5%. The measurements have been acquire for a range of angles from 0◦ to 100◦, every 10◦. For each angle, the forces have been measured for 20 seconds with a sampling period of 100Hz. The results are the average data of the 2000 values.

Thanks to the dynamic pressure (Pd) measured with the Pitot tube, the dimensionless force coefficients have been obtained. These coefficients have been calculated with the second part of equations 9.2 and 9.3.

Pressure test

This model is placed in the A9 wind tunnel on a lateral turntable as shown in figure 9.13(b). The pressure tubes are connected to the transducer (Scanivalve, model ZOC 33/64PxX2). This device can measure up to 256 values simultaneously. Moreover, the systems has a A/D converter, a computer, the acquisition-control software and a Pitot tube (Airflow, model 3.3.311). 9.6. EXPERIMENTAL TESTS 197

(a) Longitudinal force coefficient (b) Side force coefficient

Figure 9.14: Force coefficients

The dimensionless pressure coefficients have been calculated with the second part of equation 9.1, the pressure measurements on each sensor and the dynamic pressure obtained from the Pitot tube.

In the same way as in the previous test, a constant and uniform airflow of 8m/s is set. The turbulence intensity is approximately 2.5%. The measurements have been acquire for a range of angles from 0◦ to 100◦, every 10◦. For each angle, pressures have been measured for 30 seconds with a sampling period of 100Hz. The results are the average data of the 3000 values.

9.6.4 Results Force test

In figure 9.14 the longitudinal force and side force coefficients obtained from the wind tunnel test are plotted together with the CFD data. As it can be seen, the results are promising. The most important coefficient is the CX since it represents the largest force value. The worst difference between the CFD and wind tunnel data occurs at 60◦ of apparent wind angle and it is under 20%.

It is clear that the CFD curves capture the tendency even the peak at 70◦. In the side force coefficient case the curves differ. Since the contribution of the side force to the thrust is considerable less than the longitudinal force, the fact of being slightly different do not imply considerable variations when comparing the power provided as it is demonstrated in next section.

Pressure test

In figure 9.15 the pressure coefficients are plotted. The values of the wind tunnel test 198 CHAPTER 9. EU-CARGOXPRESS PROJECT

are included in appendix I, whereas the CFD results are in appendix J. The numerical values have been obtained from the pressures on the position of the sensors in each of the simulations. Then, the pressure coefficients have been calculated with the first part of equation 9.1.

The pressure taps are organized in seven sections (the 1st is the highest and the 7th is the lowest) as shown in figure 9.12. In each section, there are seven pressure taps on leeward (L) and another seven on windward (W). Each of the figures of 9.15 represents the pressure coefficient at different angles of attack (apparent wind angle). As mentioned before, 0◦ means wind coming from the stern when the sail is hoisted and kept in place.

In figures 9.15(d) and 9.15(e), some lines have been included to better understand the trend of the coefficient on each section. In these plots the conventional agreement of reversing the vertical scales has been used: the leeward surface pressures that are negative on the top part of the figure and the windward surface pressures that are usually positive, on the bottom part of the figures. The difference in pressure between the two sides gives the aerodynamic force.

In figure 9.15(a) the results at 0◦ of angle of attack are included. It can be seen that the numerical results capture the trend of the experimental values. The CFD over-predicts the positive data (windward) while it under-predicts the negative values (leeward). The force would be similar since both sides compensate each other.

Figure 9.15(b) shows the results for an angle of attack of 20◦. In the same way as in the previous plot, the numerical code over-predicts the positive values (windward) whereas it under-predicts the negative data (leeward). The trend is captured on windward. On the other side, the trend in leeward is also captured except from the 1st and the 7th sections which are located at both ends of the sails. This can be explained by the three-dimensional effect of the flow near the tip and the influence of the bridge on the bottom.

In figure 9.15(c) the pressure coefficients at 40◦ of angle of attack are plotted. Here, the data on windward are closer together and have the same trend. On the other hand, the numerical values under-predict the experimental data and moreover, the trend is not capture on the 3rd, 4th and 5th sections.

Figure 9.15(d) illustrates the values obtained for an angle of attack of 60◦. Similarly to the previous plot, the results on windward are substantially accurate. On leeward, although the tren is capture, the numerical values are still below the experimental data.

Finally, in figure 9.15(e) the results at 80◦ are included. In this plot, it should be highlighted that both the unevenly trend and the values have successfully been captured. These results could be expected since this is the lowest relative angle of attack. This 9.6. EXPERIMENTAL TESTS 199

value (80◦) would represent a 10◦ of an angle of attack with the conventional direction agreement. Therefore, this situation represents a typical close-hauled condition.

In general, it can be concluded that the results of the comparison are promising both quantitatively and qualitatively.

(a) Apparent wind angle = 0◦ (b) Apparent wind angle = 20◦

(c) Apparent wind angle = 40◦ (d) Apparent wind angle = 60◦

(e) Apparent wind angle = 80◦

Figure 9.15: Pressure coefficient, experimental vs numerical results 200 CHAPTER 9. EU-CARGOXPRESS PROJECT

9.7 Feasibility study

It has been proven that the structural sail can provide a large value of power at a certain combination of wind intensity and angle. But now, a real scenario must be introduced in which the most common wind intensities and their probability of occurrence are taken into account. Six routes have been chosen along which, this cargo-vessel could navigate. The routes have been provided by the partner of the project in charge of the operational issues.

In order to study the viability of using a sail combined with a conventional propulsion system, three main steps must be analyzed.

• Step 1: Wind study. First, the wind intensity, direction and probability of occur- rence should be studied. The wind is the source of this power and it should be guaranteed, at least, in a certain level.

• Step 2: Sail performance. Once the wind at the navigation area is considered appropriate, the sail performance is studied. The forces and moments which are provided by the sail are studied in this step. In this case, the aerodynamic performance of the geometry in study has been calculated in the previous sections both numerically and experimentally.

• Step 3: Power savings. In the last step, the combination of the wind in the navigation area and the sail performance is carried out. Here, the course of the vessel is taken into account, as well as the constant vessel speed.

9.7.1 Routes The routes in which all the calculations have been made come from some possible operation routes provided by a partner of the project. Six significant routes have been considered (see table 9.3). All the calculations made in this section when referred to routes, imply round-trip routes.

9.7.2 Wind characteristics The wind is an endless energy source but, in this first step, it must be studied if the intensity, direction and probability of occurrence is appropriate for the purpose of the investigation. The wind at this step is the “true wind” compared to the “apparent wind” concept (see section 2.5).

There are several databases which provide information regarding the wind charac- teristics. The data come from meteorological stations or the information recorded by 9.7. FEASIBILITY STUDY 201

Route Area Kiel (Germany) - R¨ıga(Latvia) 5 Aberdeen (United Kingdom) - Dunkerque (France) 11 A Coru˜na(Spain) - Bourdeaux (France) 17 Marseille (France) - Cartagena (Spain) 26 Alexandria (Egypt) - Tripoli (Libya) 27 Lobito (Angola) - Banana (Democratic Republic of Congo) 68

Table 9.3: Routes and areas

Wave Height (m) Wind Speed (knots) 0-1 0-13 1-2 13-19 2-3 19-24 3-4 24-30

Table 9.4: Relationship between waves and wind speed

vessels. Nowadays, there are different numerical prediction programs which estimate the wind characteristics in a specific area.

A very well known data source used in the maritime field is the Global Wave Statistics (GWS) [123]. The information given is related to waves but there is a correlation between those wave heights and the wind speed at 10 meters above sea level (see table 9.4). In this reference, seas and oceans are divided in different areas. Each of the routes in study lies inside only one area. This means that it has been assumed a uniform wind/wave height pattern along each route. In table 9.3, the area of each route is included in the second column of the table.

Each area is divided into 8 directions of wind and into 4 seasons in a year. The GWS provides the probability in each area, in each season, and in each direction of having a certain wind intensity (P rwind in equation 9.4). In tables 9.5 and 9.6 the annual probabilities for different wave heights and for different wind directions are shown.

Using this simple study as a starting point, there are some improvements than can be done. One of the first assumptions is that the wind intensity is constant in height but as mentioned in Chapter 2, there is a wind gradient within the atmospheric boundary layer. Reference [88] explains how this profile can affect sail performance. Another improvement is the inclusion of gusts. Moreover, a detailed description of the wind at small areas should be carried out for further investigations. The wind is completely different inside a port, near the cost or at open seas. 202 CHAPTER 9. EU-CARGOXPRESS PROJECT

Wave height (m) Route 0-1 1-2 2-3 3-4 Kiel - Riga 34.5 39.0 18.5 6.2 Aberdeen - Dunkerque 25.3 32.3 21.0 11.2 A Coru˜na- Bourdeaux 12.1 28.5 25.2 16.0 Marseille - Cartagena 34.5 35.7 17.8 7.3 Alexandria - Tripoli 34.9 37.3 17.1 6.5 Lobito - Banana 7.1 40.5 35.6 12.9

Table 9.5: Annual probabilities for different wave heights

Direction Route S SE E NE N NW W SW Kiel - Riga 12.8 9.9 10.1 9.8 10.1 10.6 16.9 17.4 Aberdeen - Dunkerque 13.8 9.9 9.0 8.3 11.1 12.5 13.8 15.8 A Coru˜na- Bourdeaux 13.0 7.1 9.9 11.4 8.1 12.5 16.8 15.7 Marseille - Cartagena 10.7 7.9 15.3 11.1 7.7 14.0 19.2 11.5 Alexandria - Tripoli 9.1 7.0 7.5 8.3 11.3 21.9 23.3 9.1 Lobito - Banana 24.9 57.1 11.2 0.9 0.2 0.2 0.6 3.2

Table 9.6: Annual probabilities for different wind directions for wave height less than 4m

9.7.3 Energy saving

The author of this thesis has developed a program than can study the viability of using a sail as an auxiliary propulsion system combined with a conventional system. The program executes this third step. It reads the data from a CFD (or wind tunnel) and the Global Wave Statistics information, and calculates the power that can be obtained as well as the probability of using the sail.

A specific power by itself does not provide complete information about how the system works in an environment as changeable as the open sea. Due to this reason, the data must be related to the routes and the probability of finding different winds. The third step is the answer to “during a year, which is the average power that it is expected to be obtained at a certain route?” (Psail).

First, the navigation route is set to obtain the course, the wind intensity (TWS), direction (TWA) and probability (P rwind). Then, a constant vessel speed is assumed. Third, the sail performance is analyzed with a CFD, or wind tunnel tests, to obtain the aerodynamic forces (FX, FY, FZ). After the appropriate geometrical transformation the thrust is obtained. Then, the saved power (Psaved) is calculated with the thrust and the vessel speed. Finally, Psail is calculated with equation 9.4. 9.7. FEASIBILITY STUDY 203

Psaved · P rwind Psail = (9.4) P rsail

P rsail is the total probability of using the sail which depends not only on the intensity (limit of 30knots of true wind speed) but on the apparent wind angle (values over 140◦ are not affordable since the sail only rotates 60◦). Therefore, this probability is calculated depending on the case and the restrictions of the system.

Vessel speed (knots)→ 15 13 10 5 Route ↓ Psail P rsail Psail P rsail Psail P rsail Psail P rsail Kiel - Riga 750 42 658 45 511 52 260 61 Aberdeen - Dunkerque 897 41 787 44 622 49 319 57 A Coru˜na- Bourdeaux 974 42 872 46 697 48 381 52 Marseille - Cartagena 761 40 655 42 511 46 285 51 Alexandria - Tripoli 722 39 635 42 612 47 268 60 Lobito - Banana 1025 50 902 50 723 51 404 52

Table 9.7: Third geometry, sail power obtained with CFD data

In table 9.7, the values of the annual average expected power and the probability of using the sail, calculated with CFD data, are presented. As it was expected, the higher the vessel speed, the lower the probability of using the sail and the higher the obtained power. The results indicate that in average, half of the time during a year the sail could be hoisted. It is also concluded that the route at which the sail is more interesting is the Lobito-Banana route. In average, the contribution of the wind to the EU-CargoXpress, sailing at 13 knots, can go up to 752 kW using the sail the 45% of the time.

Route Psail(kW), CFD Psail(kW), WT Kiel - Riga 658 603 Aberdeen - Dunkerque 787 721 A Coru˜na- Bourdeaux 872 802 Marseille - Cartagena 655 599 Alexandria - Tripoli 635 583 Lobito - Banana 902 824

Table 9.8: Third geometry, comparison between numerical (CFD) and experimental (WT) results (13 knots of vessel speed)

In table 9.8, the results obtained with wind tunnel data and CFD data are compared at 13 knots of vessel speed. It can be seen that the CFD results overestimate the 204 CHAPTER 9. EU-CARGOXPRESS PROJECT

Figure 9.16: Effective power (EHP) compare to the expected power (Psail)

expected power. At this vessel speed, the difference between the two sources is below 10%. As mentioned before, the longitudinal force has been simulated correctly and this is the force component which contributes the most.

The goal of the study presented in this chapter is the demonstration of the reduction of fuel consumption by using the superstructure as a sail. It has been already measured the capability of the sail to provide a certain amount of power. Now, this power must be compared to the power necessary to compensate the hydrodynamic resistance at a certain constant speed. This is the effective power (EHP).

In figure 9.16 the effective power and the expected power (Psail) are plotted. The values of the expected aerodynamic power are the average of the six routes at each vessel speed. The effective power curve has been obtained from the towing tank tests conducted by the National Technical University of Athens (Greece). Throughout the project different hull forms have been developed in order to minimize the hydrodynamic resistance. These values are referred to the last tested model.

It is observed that at 13 knots, the 40% of the power required to propel the vessel could be obtained from the sail. The average probability of using the sail at that speed is 45%. This is, the 45% of the time during a year, instead of consuming fossil fuel to generate 1187kW of effective power, only 435kW would be required to keep 13 knots of constant speed. At vessel speeds below 10 knots, the vessel could be propelled by the sail. 9.8. CONCLUSIONS 205

9.8 Conclusions

Through the analysis of the results and the comments indicated in the previous para- graphs, the following conclusions can be drawn:

• The aerodynamic performance of a structural sail has been simulated with the com- putational fluid dynamic software CD-Adapco’s STAR-CCM+.

• The results obtained with the computational software have been validated with wind tunnel tests. The comparison of the results is promising.

• The power that can be obtained from the sail has been calculated taken into account the probability of wind occurrence at six different navigation routes.

• The expected power obtained from the sail has been compared to the effective power required to compensate the hydrodynamic resistance. It is concluded that there is a real chance to reduce the fossil fuel consumption by using the sail.

• The contribution of the wind to the EU-CargoXpress, sailing at 13 knots, can go up to 752 kW using the sail the 45% of the time. This represents the 40% of the effective power needed to propel the vessel at that speed. 206 CHAPTER 9. EU-CARGOXPRESS PROJECT Chapter 10

CONCLUSIONS

The core of this thesis is the combination of experimental tests and numerical simulations in four different scenarios (IMS Class, Transpac 52 Class, Dhows and structural wings) to understand the sail performance. The principal objective of this thesis is to establish a procedure to study the sail aerodynamics by combining the use of both tools and take advantage of the best features of each.

The three-dimensional effect of the mast on the sail performance of an IMS Class rigging has been evaluated. Racing yacht sails in upwind conditions have been studied by combining three-dimensional RANS simulations and full scale measurements described in the reference papers.

Three sail arrangements have been simulated with the commercial packages ANSYS- CFX and CD-Adapco’s STAR-CCM+. The results have been compared with both experimental data and numerical computations obtained from the reference papers. A positive agreement of the present numerical study with the reference one is considered, both in terms of qualitative aspects and in terms of numerical values. The inclusion of the mast in the numerical simulations improves the results. Moreover, it has been observed the substantial influence of the mast on the leeward side where detachment is presented.

The pressure distribution on a Transpac 52 Class mainsail has been also determined. First, the pressure distributions have been measured on a model-scale sail in a wind tunnel, in upwind condition. The experiments have been conducted at the Atmospheric Boundary Layer Wind Tunnel at the CEAMA (Universidad de Granada, Spain). The pressure distribution has been measured on 62 points of a rigid pressure-tapped model-scale sail.

One of the experimental tests of the mainsail model has been simulated with the commercial RANS code CD-Adapco’s STAR-CCM+. The numerical results have been validated with the experimental data. The results show very good agreement between experimental data and numerical calculations, both quantitatively and qualitatively.

207 208 CHAPTER 10. CONCLUSIONS

The comparison has permitted an increase of the confidence in numerical codes and has helped the researcher to gain knowledge of the phenomena involved near the sail such as the flow detachment or the pressure distribution, among others.

On the other hand, the main parameters that affect the sail performance of the two most important Dhow classes (43ft and 60ft) have been characterized. The experimental tests have been conducted at the Twisted Flow Wind Tunnel at the YRU (University of Auckland, New Zealand) where a broad range of parameters have been studied. It has been analyzed the effect of yard stiffness, heel and apparent wind angles, the influence of bending, the optimization of the trimming and the performance of the 60ft mainsail alone without the mizzen. Moreover, one of the experimental tests of the 43ft model has been reproduced with the CD-Adapco’s STAR-CCM+ through the acquisition of the flying shape by means of the V-SPAR system. The results have been validated with the experimental data.

This is the first investigation that has scientifically studied sailing dhows. These experimental and numerical tests lay the grounds of future investigations. It must be emphasized that this research have been conducted together with the industry and the results are already used in daily work.

Finally, it has been studied the viability of using a structural wing to reduce the fuel consumption and emissions on the EU-CargoXpress Project. The aerodynamic perfor- mance of three different structural wings have been simulated with the Computational Fluid Dynamic software CD-Adapco’s STAR-CCM+. Then, the results obtained with the computational software have been validated with wind tunnel tests at the A9 Wind Tunnel (Universidad Polit´ecnicade Madrid, Spain). The comparison of the results is promising.

The power that can be obtained from the sail has been calculated taken into account the probability of wind occurrence at six different navigation routes. The expected power obtained from the sail has been compared to the effective power required to compensate the hydrodynamic resistance. The contribution of the wind to the EU-CargoXpress, sailing at the design speed, represents the 40% of the effective power needed to propel the vessel at that speed, the 45% of the time.

To sum up, the main achievements of this thesis are listed next:

• The significant influence of the mast on sail performance shows the necessity of the inclusion of the mast in this type of three-dimensional numerical calculations.

• The experimental technique that has been used to measure the pressure distribution on a TP52 model-scale mainsail is widely spread in civil wind engineering but it is innovative in sail aerodynamics. 209

• There is a real chance to reduce the fossil fuel consumption and gas emissions by using a sail in maritime transport.

• The advantages of using CFDs to determine sail performance have been presented as well as the validation in four different scenarios (IMS Class, Transpac 52 Class, Dhows and structural wings).

• Experimental benchmark data have been generated to validate numerical codes.

It can be concluded that CFD codes are a cost-effective tool for the performance prediction of a sailing yacht. Although this study shows that numerical codes can be used with remarkable accuracy to estimate aerodynamic forces, there is still the need to combine simulations with experimental tests to have a better idea of the phenomena involved.

Different lines of investigation emerge from the possible improvements of this thesis which would need further research. A proposal for future developments which would enhance the achievements of this thesis are presented below.

• Wind tunnel tests are required to study the influence of the mast, where pressure distributions would be measured. Regarding the numerical analysis, a thorough grid sensitivity study is needed to ensure identical meshes with and without the mast.

• Simultaneous measurement of the pressure distribution on windward and leeward sides of model scale sails are indispensable.

• Different shapes of the sails of dhows can be designed and tested in the wind tunnel to improve the aerodynamic performance based on the current results. Moreover, the twisting vanes should be included to take into account the real inflow. On the other hand, the V-SPAR system needs to be calibrated with this type of sails.

• Some of the assumptions made on the feasibility study of the EU-CargoXpress project can be improved. One of the first assumptions is that the wind intensity is constant in height and therefore, it would be recommended to include the wind profile and twist. Wind gusts could be considered too. Moreover, a detailed de- scription of the wind at small areas should be carried out such as in-port or next to the coast. 210 CHAPTER 10. CONCLUSIONS Appendix A

Mast effect data with STAR-CCM+

ID 9807172F ID 9807172B ID 96092335 With Without With Without With Without CX 0.277 0.310 0.136 0.136 0.470 0.411 CY 1.096 1.274 1.245 1.194 1.600 1.502 XCE (m) 1.791 1.951 1.482 1.562 0.371 0.311 ZCE (m) 6.309 6.320 6.566 6.547 4.979 4.742 CD 0.308 0.368 0.494 0.464 0.371 0.374 CL 1.068 1.234 1.133 1.090 1.588 1.476

Table A.1: Results of the simulations with and without the mast

211 212 APPENDIX A. MAST EFFECT DATA WITH STAR-CCM+ Appendix B

Second set of tests: results

Figure B.1: Pressure coefficient, second set of tests

213 214 APPENDIX B. SECOND SET OF TESTS: RESULTS Appendix C

Yard Stiffness Scale

In order to scale the stiffness of the yard, the expression C.1 must be verified.

 y   y  = (C.1) L mod L FS where y is the deflection and L is the yard length. To obtain the deflection, it is assumed that a yard behaves like a cantilever beam with a uniformly distributed load:

wL4 y = (C.2) 8EI where w is the distributed load, E is the Young modulus and I is the inertia. For a sailing yard:

F C 1 ρSAW S2 w = = F 2 (C.3) L L where F is the load, CF is the aerodynamic force coefficient, ρ is the air density, S is the sail area and AW S is the apparent wind speed. If C.2 and C.3 are replaced in equation C.1 and moreover, find the value of the inertia in model scale, it is deduced that:

   2  2   Smod Vmod Lmod EFS Imod = IFS (C.4) SFS VFS LFS Emod

Additionally, the length, surface and velocity scales are known: LFS = γLmod, 2 SFS = γ Smod and AW AFS = βAW Amod. Therefore, if they are replaced in equation C.4 it would be obtained C.5:

 4  2   1 1 EFS Imod = IFS (C.5) γ β Emod

215 216 APPENDIX C. YARD STIFFNESS SCALE

Since the yards of the model are solid cylinders, their inertia is:

πD4 I = (C.6) mod 64 where D is the diameter. On the other hand, the full scale yard is a hollow cylinder and its inertia is:

π(D4 − D4 ) I = eF S iF S (C.7) FS 64

where De is the external diameter and Di is the internal diameter. Now, replacing C.6 and C.7 in C.5 and finding the value of the diameter of the yard at model scale, it is finally obtained:

s  4  2    4 4  4 64 1 1 EFS π(DeF S − DiF S) Dmod = (C.8) π γ β Emod 64 In table C.1 all the data required to calculate the diameter of the yards are included. In full scale the yards are build of carbon fiber and the yards of the model are built in pine.

60ft Dhow 43ft Dhow Main Mizzen Length Scale (γ) 12 12 8.6 Velocity Scale (β) 2.57 2.57 2.57 2 10 10 10 EFS(N/m ) [Carbon fiber] 8.5 · 10 8.5 · 10 8.5 · 10 DeF S(m) 0,201 0,170 0,170 DiF S(m) 0,171 0,145 0,145 2 9 9 9 Emod(N/m ) [Pine] 8 · 10 8 · 10 8 · 10

Dmod(mm) 16 13 18 Table C.1: Yard data Appendix D

43ft Dhow Model Tests

Table D.1: 43ft model: Basic Test(BT)

Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending BT 20 0 18 X × BT 20 5 18 × × BT 20 10 18 × × BT 20 15 18 × × BT 30 0 18 X × BT 30 5 18 × × BT 30 10 18 × × BT 30 15 18 × × BT 40 0 18 X × BT 40 5 18 × × BT 40 10 18 × × BT 40 15 18 × × BT 50 0 18 X × BT 50 5 18 × × BT 50 10 18 × × BT 50 15 18 × × BT 60 0 18 X × BT 60 5 18 × × BT 60 10 18 × × BT 60 15 18 × × BT 70 0 18 X × BT 70 5 18 × × BT 70 10 18 × × BT 70 15 18 × × BT 80 0 18 X × Continued on next page. . .

217 218 APPENDIX D. 43FT DHOW MODEL TESTS

Table D.1 – Continued Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending BT 80 5 18 × × BT 80 10 18 × × BT 80 15 18 × × BT 90 0 18 X × BT 90 5 18 × × BT 90 10 18 × × BT 90 15 18 × × BT 100 0 18 X × BT 100 5 18 × × BT 100 10 18 × × BT 100 15 18 × ×

Table D.2: 43ft model: Bent Yard Test(BYT)

Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending BYT 20 0 18 X X BYT 20 5 18 × X BYT 20 10 18 × X BYT 20 15 18 × X BYT 30 0 18 X X BYT 30 5 18 × X BYT 30 10 18 × X BYT 30 15 18 × X BYT 40 0 18 X X BYT 40 5 18 × X BYT 40 10 18 × X BYT 40 15 18 × X BYT 50 0 18 X X BYT 50 5 18 × X BYT 50 10 18 × X BYT 50 15 18 × X BYT 60 0 18 X X BYT 60 5 18 × X BYT 60 10 18 × X BYT 60 15 18 × X BYT 70 0 18 X X BYT 70 5 18 × X BYT 70 10 18 × X Continued on next page. . . 219

Table D.2 – Continued Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending BYT 70 15 18 × X BYT 80 0 18 X X BYT 80 5 18 × X BYT 80 10 18 × X BYT 80 15 18 × X BYT 90 0 18 X X BYT 90 5 18 × X BYT 90 10 18 × X BYT 90 15 18 × X BYT 100 0 18 X X BYT 100 5 18 × X BYT 100 10 18 × X BYT 100 15 18 × X

Table D.3: 43ft model: Optimum Trimming Test(OPT)

Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending OPT 40 0 18 X × OPT 40 5 18 × × OPT 40 10 18 × × OPT 40 15 18 × × OPT 40 5 18 X × OPT 40 10 18 X × OPT 40 15 18 X × OPT 40 0 18 X X OPT 40 5 18 × X OPT 40 10 18 × X OPT 40 15 18 × X OPT 40 5 18 X X OPT 40 10 18 X X OPT 40 15 18 X X OPT 60 0 18 X × OPT 60 5 18 × × OPT 60 10 18 × × OPT 60 15 18 × × OPT 60 5 18 X × OPT 60 10 18 X × OPT 60 15 18 X × Continued on next page. . . 220 APPENDIX D. 43FT DHOW MODEL TESTS

Table D.3 – Continued Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending OPT 60 0 18 X X OPT 60 5 18 × X OPT 60 10 18 × X OPT 60 15 18 × X OPT 60 5 18 X X OPT 60 10 18 X X OPT 60 15 18 X X OPT 80 0 18 X × OPT 80 5 18 × × OPT 80 10 18 × × OPT 80 15 18 × × OPT 80 5 18 X × OPT 80 10 18 X × OPT 80 15 18 X × OPT 80 0 18 X X OPT 80 5 18 × X OPT 80 10 18 × X OPT 80 15 18 × X OPT 80 5 18 X X OPT 80 10 18 X X OPT 80 15 18 X X

Table D.4: 43ft model: Yard Stiffness Test (YST)

Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending YST 40 0 18 X × YST 40 5 18 × × YST 40 10 18 × × YST 40 15 18 × × YST 50 0 18 X × YST 50 5 18 × × YST 50 10 18 × × YST 50 15 18 × × YST 60 0 18 X × YST 60 5 18 × × YST 60 10 18 × × YST 60 15 18 × × YST 70 0 18 X × Continued on next page. . . 221

Table D.4 – Continued Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending YST 70 5 18 × × YST 70 10 18 × × YST 70 15 18 × × YST 80 0 18 X × YST 80 5 18 × × YST 80 10 18 × × YST 80 15 18 × × YST 40 0 16 X × YST 40 5 16 × × YST 40 10 16 × × YST 40 15 16 × × YST 50 0 16 X × YST 50 5 16 × × YST 50 10 16 × × YST 50 15 16 × × YST 60 0 16 X × YST 60 5 16 × × YST 60 10 16 × × YST 60 15 16 × × YST 70 0 16 X × YST 70 5 16 × × YST 70 10 16 × × YST 70 15 16 × × YST 80 0 16 X × YST 80 5 16 × × YST 80 10 16 × × YST 80 15 16 × × YST 40 0 12 X × YST 40 5 12 × × YST 40 10 12 × × YST 40 15 12 × × YST 50 0 12 X × YST 50 5 12 × × YST 50 10 12 × × YST 50 15 12 × × YST 60 0 12 X × YST 60 5 12 × × YST 60 10 12 × × Continued on next page. . . 222 APPENDIX D. 43FT DHOW MODEL TESTS

Table D.4 – Continued Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending YST 60 15 12 × × YST 70 0 12 X × YST 70 5 12 × × YST 70 10 12 × × YST 70 15 12 × × YST 80 0 12 X × YST 80 5 12 × × YST 80 10 12 × × YST 80 15 12 × ×

Table D.5: 43ft model: Bending Test (BEN)

Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending BEN 40 5 18 X Small BEN 40 5 18 X Medium BEN 40 5 18 X Large BEN 60 5 18 X Small BEN 60 5 18 X Medium BEN 60 5 18 X Large BEN 80 5 18 X Small BEN 80 5 18 X Medium BEN 80 5 18 X Large Appendix E

60ft Dhow Model Tests

Table E.1: 60ft model: Basic Test(BT) with and without mizzen

Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending BT 20 0 18 X × BT 20 5 18 × × BT 20 10 18 × × BT 20 15 18 × × BT 30 0 18 X × BT 30 5 18 × × BT 30 10 18 × × BT 30 15 18 × × BT 40 0 18 X × BT 40 5 18 × × BT 40 10 18 × × BT 40 15 18 × × BT 50 0 18 X × BT 50 5 18 × × BT 50 10 18 × × BT 50 15 18 × × BT 60 0 18 X × BT 60 5 18 × × BT 60 10 18 × × BT 60 15 18 × × BT 70 0 18 X × BT 70 5 18 × × BT 70 10 18 × × BT 70 15 18 × × Continued on next page. . .

223 224 APPENDIX E. 60FT DHOW MODEL TESTS

Table E.1 – Continued Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending BT 80 0 18 X × BT 80 5 18 × × BT 80 10 18 × × BT 80 15 18 × × BT 90 0 18 X × BT 90 5 18 × × BT 90 10 18 × × BT 90 15 18 × × BT 100 0 18 X × BT 100 5 18 × × BT 100 10 18 × × BT 100 15 18 × ×

Table E.2: 60ft model: Optimum Trimming Test(OPT)

Test AWA(◦) HA(◦) Yard, D(mm) Opt. Trimming Bending OPT 40 0 18 X × OPT 40 5 18 × × OPT 40 10 18 × × OPT 40 15 18 × × OPT 40 5 18 X × OPT 40 10 18 X × OPT 40 15 18 X × OPT 60 0 18 X × OPT 60 5 18 × × OPT 60 10 18 × × OPT 60 15 18 × × OPT 60 5 18 X × OPT 60 10 18 X × OPT 60 15 18 X × OPT 80 0 18 X × OPT 80 5 18 × × OPT 80 10 18 × × OPT 80 15 18 × × OPT 80 5 18 X × OPT 80 10 18 X × OPT 80 15 18 X × Appendix F

43ft Dhow Model Results

Figure F.1: 43ft model, Basic Test: CX vs AWA.

Figure F.2: 43ft model, Basic Test: CMX vs AWA.

225 226 APPENDIX F. 43FT DHOW MODEL RESULTS

Figure F.3: 43ft model, Basic Test: CX/CMX vs AWA.

Figure F.4: 43ft model, Basic Test: CD vs AWA.

Figure F.5: 43ft model, Basic Test: CL vs AWA. 227

Figure F.6: 43ft model, Basic Test: CX vs HA.

Figure F.7: 43ft model, Basic Test: CMX vs HA.

Figure F.8: 43ft model, Bent Yard Test: CX vs AWA. 228 APPENDIX F. 43FT DHOW MODEL RESULTS

Figure F.9: 43ft model, Bent Yard Test: CMX vs AWA.

Figure F.10: 43ft model, Bent Yard Test: CX/CMX vs AWA.

Figure F.11: 43ft model, Bent Yard Test: CD vs AWA. 229

Figure F.12: 43ft model, Bent Yard Test: CL vs AWA.

Figure F.13: 43ft model, Bent Yard Test: CX vs HA.

Figure F.14: 43ft model, Bent Yard Test: CMX vs HA. 230 APPENDIX F. 43FT DHOW MODEL RESULTS

Figure F.15: 43ft model, Optimum Trimming Test: CX vs HA (AWA=40◦)

Figure F.16: 43ft model, Optimum Trimming Test: CMX vs HA (AWA=40◦)

Figure F.17: 43ft model, Optimum Trimming Test: CX/CMX vs HA (AWA=40◦) 231

Figure F.18: 43ft model, Optimum Trimming Test: CX vs HA (AWA=60◦)

Figure F.19: 43ft model, Optimum Trimming Test: CMX vs HA (AWA=60◦)

Figure F.20: 43ft model, Optimum Trimming Test: CX/CMX vs HA (AWA=60◦) 232 APPENDIX F. 43FT DHOW MODEL RESULTS

Figure F.21: 43ft model, Optimum Trimming Test: CX vs HA (AWA=80◦)

Figure F.22: 43ft model, Optimum Trimming Test: CMX vs HA (AWA=80◦)

Figure F.23: 43ft model, Optimum Trimming Test: CX/CMX vs HA (AWA=80◦) 233

Figure F.24: 43ft model, Bending Test: CX vs AWA.

Figure F.25: 43ft model, Bending Test: CMX vs AWA.

Figure F.26: 43ft model, Bending Test: CX/CMX vs AWA. 234 APPENDIX F. 43FT DHOW MODEL RESULTS

Figure F.27: 43ft model, Yard Stiffness Test: CX vs AWA (HA=0◦)

Figure F.28: 43ft model, Yard Stiffness Test: CMX vs AWA (HA=0◦)

Figure F.29: 43ft model, Yard Stiffness Test: CX/CMX vs AWA (HA=0◦) 235

Figure F.30: 43ft model, Yard Stiffness Test: CD vs AWA (HA=0◦)

Figure F.31: 43ft model, Yard Stiffness Test: CL vs AWA (HA=0◦)

Figure F.32: 43ft model, Yard Stiffness Test: CX vs AWA (HA=5◦) 236 APPENDIX F. 43FT DHOW MODEL RESULTS

Figure F.33: 43ft model, Yard Stiffness Test: CMX vs AWA (HA=5◦)

Figure F.34: 43ft model, Yard Stiffness Test: CX/CMX vs AWA (HA=5◦)

Figure F.35: 43ft model, Yard Stiffness Test: CD vs AWA (HA=5◦) 237

Figure F.36: 43ft model, Yard Stiffness Test: CL vs AWA (HA=5◦)

Figure F.37: 43ft model, Yard Stiffness Test: CX vs AWA (HA=10◦)

Figure F.38: 43ft model, Yard Stiffness Test: CMX vs AWA (HA=10◦) 238 APPENDIX F. 43FT DHOW MODEL RESULTS

Figure F.39: 43ft model, Yard Stiffness Test: CX/CMX vs AWA (HA=10◦)

Figure F.40: 43ft model, Yard Stiffness Test: CD vs AWA (HA=10◦)

Figure F.41: 43ft model, Yard Stiffness Test: CL vs AWA (HA=10◦) 239

Figure F.42: 43ft model, Yard Stiffness Test: CX vs AWA (HA=15◦)

Figure F.43: 43ft model, Yard Stiffness Test: CMX vs AWA (HA=15◦)

Figure F.44: 43ft model, Yard Stiffness Test: CX/CMX vs AWA (HA=15◦) 240 APPENDIX F. 43FT DHOW MODEL RESULTS

Figure F.45: 43ft model, Yard Stiffness Test: CD vs AWA (HA=15◦)

Figure F.46: 43ft model, Yard Stiffness Test: CL vs AWA (HA=15◦) Appendix G

60ft Dhow Model Results

Figure G.1: 60ft model, Basic Test: CX vs AWA (with and without mizzen)

Figure G.2: 60ft model, Basic Test: CMX vs AWA (with and without mizzen)

241 242 APPENDIX G. 60FT DHOW MODEL RESULTS

Figure G.3: 60ft model, Basic Test: CX/CMX vs AWA (with and without mizzen)

Figure G.4: 60ft model, Basic Test: CD vs AWA (with and without mizzen)

Figure G.5: 60ft model, Basic Test: CL vs AWA (with and without mizzen) 243

Figure G.6: 60ft model, Basic Test: CX vs HA

Figure G.7: 60ft model, Basic Test: CMX vs HA

Figure G.8: 60ft model, Basic Test: CX vs HA (without mizzen) 244 APPENDIX G. 60FT DHOW MODEL RESULTS

Figure G.9: 60ft model, Basic Test: CMX vs HA (without mizzen)

Figure G.10: 60ft model, Optimum Trimming Test: CX vs HA

Figure G.11: 60ft model, Optimum Trimming Test: CMX vs HA 245

Figure G.12: 60ft model, Optimum Trimming Test: CX/CMX vs HA

Figure G.13: 60ft model, Optimum Trimming Test: CD vs HA

Figure G.14: 60ft model, Optimum Trimming Test: CL vs HA 246 APPENDIX G. 60FT DHOW MODEL RESULTS Appendix H

Energy Scenarios

247 248 APPENDIX H. ENERGY SCENARIOS

(a) EU-CargoXpress vessel

(b) Conventional vessel

Figure H.1: Energy balance Appendix I

Wind tunnel results

Table I.1: Pressure tap position and pressure coefficient

Press. tap Location Angle of attack Name X(mm) Y(mm) Z(mm) 0◦ 20◦ 40◦ 60◦ 80◦ 1 63 110 870 -1.387 -1.299 -1.287 -3.380 -1.778 2 56 73 870 -1.399 -1.322 -1.323 -2.240 -1.232 3 55 37 870 -1.404 -1.340 -1.342 -2.244 -1.077 4 55 0 870 -1.402 -1.351 -1.364 -2.405 -1.060 5 55 -37 870 -1.399 -1.368 -1.393 -2.323 -1.212 6 56 -73 870 -1.397 -1.386 -1.422 -2.528 -1.993 7 63 -110 870 -1.378 -1.381 -1.432 -1.990 -3.104 50 72 -110 870 0.537 0.419 0.326 0.303 0.300 51 69 -73 870 0.485 0.352 0.198 0.102 0.078 52 69 -37 870 0.463 0.355 0.183 0.011 -0.013 53 69 0 870 0.462 0.391 0.233 0.009 0.018 54 69 37 870 0.462 0.456 0.348 0.114 0.222 55 69 73 870 0.478 0.530 0.491 0.301 0.309 56 72 110 870 0.500 0.580 0.620 0.487 -0.826 8 47 110 744 -1.492 -1.399 -1.339 -3.842 -2.540 9 38 73 744 -1.482 -1.398 -1.331 -1.821 -1.741 10 37 37 744 -1.503 -1.427 -1.370 -1.557 -1.338 11 37 0 744 -1.506 -1.443 -1.391 -1.499 -1.160 12 37 -37 744 -1.510 -1.463 -1.419 -1.460 -1.242 13 38 -73 744 -1.504 -1.474 -1.440 -1.464 -1.585 14 47 -110 744 -1.483 -1.462 -1.432 -1.409 -1.385 57 57 -110 744 0.926 0.830 0.733 0.709 0.632 58 54 -73 744 0.942 0.815 0.664 0.581 0.484 59 53 -37 744 0.969 0.856 0.681 0.559 0.415 60 53 0 744 0.977 0.910 0.751 0.613 0.450 Continued on next page. . .

249 250 APPENDIX I. WIND TUNNEL RESULTS

Table I.1 – Continued Press. tap Location Angle of attack Name X(mm) Y(mm) Z(mm) 0◦ 20◦ 40◦ 60◦ 80◦ 61 53 37 744 0.965 0.951 0.834 0.706 0.561 62 54 73 744 0.938 0.973 0.920 0.828 0.271 63 57 110 744 0.925 0.963 0.966 0.922 -0.129 15 32 110 618 -1.502 -1.424 -1.360 -2.935 -2.708 16 21 73 618 -1.514 -1.441 -1.372 -1.687 -2.327 17 18 37 618 -1.492 -1.431 -1.358 -1.559 -1.504 18 19 0 618 -1.501 -1.446 -1.377 -1.476 -1.261 19 18 -37 618 -1.506 -1.458 -1.394 -1.448 -1.404 20 21 -73 618 -1.503 -1.459 -1.399 -1.425 -1.695 21 32 -110 618 -1.507 -1.465 -1.389 -1.429 -1.134 64 42 -110 618 0.977 0.901 0.829 0.804 0.719 65 38 -73 618 0.989 0.887 0.770 0.694 0.598 66 37 -37 618 1.013 0.919 0.777 0.665 0.534 67 37 0 618 1.022 0.964 0.834 0.704 0.565 68 37 37 618 1.011 0.998 0.907 0.789 0.631 69 38 73 618 0.984 1.012 0.972 0.887 0.191 70 42 110 618 0.977 1.005 1.006 0.985 0.043 22 16 110 493 -1.443 -1.380 -1.439 -2.389 -2.726 23 3 73 493 -1.416 -1.371 -1.332 -1.355 -2.623 24 0 37 493 -1.422 -1.380 -1.311 -1.305 -1.688 25 0 0 493 -1.436 -1.400 -1.326 -1.346 -1.382 26 0 -37 493 -1.434 -1.398 -1.333 -1.350 -1.484 27 3 -73 493 -1.440 -1.407 -1.337 -1.385 -1.794 28 16 -110 493 -1.426 -1.390 -1.301 -1.312 -0.916 71 26 -110 493 0.998 0.931 0.881 0.858 0.778 72 22 -73 493 1.000 0.906 0.813 0.744 0.654 73 21 -37 493 1.021 0.929 0.813 0.703 0.580 74 22 0 493 1.029 0.969 0.858 0.724 0.601 75 21 37 493 1.016 1.002 0.921 0.801 0.641 76 22 73 493 0.995 1.011 0.963 0.903 0.151 77 26 110 493 1.001 1.012 0.966 0.979 0.084 29 -1 110 367 -1.326 -1.287 -1.216 -2.296 -2.770 30 -15 73 367 -1.334 -1.304 -1.234 -1.268 -2.840 31 -18 37 367 -1.315 -1.289 -1.228 -1.262 -1.798 32 -18 0 367 -1.313 -1.283 -1.232 -1.274 -1.343 33 -18 -37 367 -1.319 -1.288 -1.250 -1.301 -1.485 34 -15 -73 367 -1.325 -1.292 -1.248 -1.332 -1.658 35 -1 -110 367 -1.333 -1.300 -1.226 -1.272 -0.818 Continued on next page. . . 251

Table I.1 – Continued Press. tap Location Angle of attack Name X(mm) Y(mm) Z(mm) 0◦ 20◦ 40◦ 60◦ 80◦ 78 11 -110 367 1.006 0.950 0.908 0.890 0.797 79 6 -73 367 1.007 0.930 0.849 0.790 0.692 80 6 -37 367 1.022 0.945 0.842 0.746 0.631 81 6 0 367 1.031 0.979 0.871 0.758 0.619 82 6 37 367 1.018 1.001 0.925 0.840 0.343 83 6 73 367 1.005 1.013 0.972 0.928 -0.002 84 11 110 367 1.004 1.010 1.009 0.994 0.054 36 -17 110 241 -1.261 -1.212 -1.158 -3.366 -2.401 37 -33 73 241 -1.239 -1.220 -1.176 -1.752 -2.558 38 -36 37 241 -1.223 -1.214 -1.179 -1.152 -1.469 39 -36 0 241 -1.224 -1.204 -1.182 -1.191 -1.190 40 -36 -37 241 -1.221 -1.193 -1.182 -1.219 -1.273 41 -33 -73 241 -1.252 -1.206 -1.170 -1.277 -1.510 42 -17 -110 241 -1.251 -1.198 -1.114 -1.226 -1.066 85 -5 -110 241 1.014 0.975 0.936 0.916 0.673 86 -9 -73 241 1.012 0.955 0.880 0.829 0.526 87 -10 -37 241 1.025 0.966 0.865 0.781 0.396 88 -10 0 241 1.030 0.992 0.886 0.784 0.183 89 -10 37 241 1.024 1.017 0.944 0.860 0.055 90 -9 73 241 1.011 1.025 0.992 0.936 0.057 91 -5 110 241 1.010 1.021 1.019 0.997 0.099 43 -34 110 115 -1.271 -1.209 -1.171 -3.034 -1.585 44 -51 73 115 -1.260 -1.220 -1.177 -1.835 -1.767 45 -54 37 115 -1.217 -1.181 -1.159 -1.200 -1.176 46 -54 0 115 -1.210 -1.170 -1.160 -1.057 -1.094 47 -54 -37 115 -1.216 -1.167 -1.162 -1.013 -1.053 48 -51 -73 115 -1.240 -1.172 -1.128 -0.979 -0.931 49 -34 -110 115 -1.258 -1.205 -1.079 -0.934 -0.895 92 -20 -110 115 1.018 0.988 0.950 0.912 0.403 93 -25 -73 115 1.017 0.967 0.891 0.838 0.305 94 -26 -37 115 1.031 0.978 0.867 0.775 0.203 95 -26 0 115 1.033 1.000 0.891 0.777 0.148 96 -26 37 115 1.030 1.032 0.959 0.859 0.138 97 -25 73 115 1.013 1.031 1.004 0.935 0.136 98 -20 110 115 1.016 1.030 1.030 0.968 0.147 252 APPENDIX I. WIND TUNNEL RESULTS Appendix J

Numerical results

Table J.1: Pressure coefficient

Press. tap Angle of attack Name 0◦ 20◦ 40◦ 60◦ 80◦ 1 -0.637 -0.589 -0.908 -2.383 -1.177 2 -0.670 -0.642 -0.937 -1.774 -0.810 3 -0.681 -0.693 -0.950 -1.845 -0.705 4 -0.688 -0.760 -0.972 -1.757 -0.784 5 -0.692 -0.826 -0.999 -1.584 -1.001 6 -0.689 -0.881 -1.025 -1.587 -1.598 7 -0.665 -0.909 -1.031 -1.888 -2.826 50 0.778 0.650 0.492 0.434 0.339 51 0.746 0.595 0.381 0.271 0.186 52 0.751 0.630 0.410 0.252 0.161 53 0.757 0.689 0.495 0.307 0.226 54 0.753 0.737 0.578 0.368 0.309 55 0.749 0.775 0.672 0.475 0.368 56 0.780 0.833 0.771 0.697 -0.164 8 -0.804 -0.805 -0.906 -3.432 -1.773 9 -0.809 -0.837 -0.901 -1.889 -1.336 10 -0.818 -0.861 -0.928 -1.172 -0.962 11 -0.826 -0.882 -0.966 -1.064 -1.104 12 -0.825 -0.890 -0.993 -0.853 -0.930 13 -0.820 -0.887 -1.019 -0.904 -1.224 14 -0.818 -0.880 -0.975 -0.837 -1.348 57 1.108 1.015 0.861 0.804 0.714 58 1.125 1.007 0.800 0.688 0.585 59 1.149 1.052 0.834 0.681 0.530 60 1.154 1.103 0.913 0.750 0.566 Continued on next page. . .

253 254 APPENDIX J. NUMERICAL RESULTS

Table J.1 – Continued Press. Tap Angle of attack Name 0◦ 20◦ 40◦ 60◦ 80◦ 61 1.145 1.132 0.967 0.791 0.575 62 1.121 1.142 1.037 0.888 0.664 63 1.103 1.133 1.084 0.998 0.286 15 -0.818 -0.838 -0.837 -3.338 -1.928 16 -0.812 -0.841 -0.846 -1.748 -1.690 17 -0.812 -0.840 -0.849 -0.760 -1.203 18 -0.813 -0.831 -0.890 -0.739 -1.222 19 -0.815 -0.816 -0.900 -0.746 -1.085 20 -0.815 -0.796 -0.896 -0.742 -1.347 21 -0.824 -0.790 -0.818 -0.772 -1.014 64 1.152 1.088 0.944 0.872 0.773 65 1.165 1.075 0.889 0.771 0.664 66 1.191 1.113 0.911 0.759 0.615 67 1.201 1.159 0.973 0.815 0.635 68 1.191 1.183 1.022 0.864 0.660 69 1.167 1.180 1.074 0.947 0.556 70 1.155 1.168 1.110 1.024 0.239 22 -0.771 -0.803 -0.660 -2.836 -1.923 23 -0.760 -0.797 -0.740 -0.956 -1.983 24 -0.756 -0.788 -0.780 -0.620 -1.332 25 -0.755 -0.776 -0.787 -0.647 -1.105 26 -0.756 -0.762 -0.773 -0.676 -1.182 27 -0.761 -0.749 -0.750 -0.716 -1.494 28 -0.775 -0.749 -0.738 -0.691 -0.644 71 1.187 1.135 1.005 0.927 0.817 72 1.191 1.115 0.948 0.831 0.705 73 1.212 1.141 0.956 0.806 0.662 74 1.221 1.177 0.998 0.834 0.673 75 1.212 1.198 1.049 0.897 0.701 76 1.191 1.199 1.093 0.973 0.429 77 1.187 1.192 1.119 1.038 0.287 29 -0.668 -0.770 -0.906 -2.916 -1.806 30 -0.658 -0.748 -0.880 -1.607 -2.130 31 -0.649 -0.736 -0.757 -0.592 -1.338 32 -0.647 -0.732 -0.722 -0.604 -0.909 33 -0.647 -0.730 -0.708 -0.605 -1.185 34 -0.657 -0.729 -0.682 -0.626 -1.593 35 -0.675 -0.733 -0.659 -0.561 -0.447 Continued on next page. . . 255

Table J.1 – Continued Press. Tap Angle of attack Name 0◦ 20◦ 40◦ 60◦ 80◦ 78 1.211 1.159 1.045 0.960 0.767 79 1.210 1.137 0.990 0.878 0.712 80 1.225 1.152 0.987 0.842 0.667 81 1.233 1.178 1.011 0.842 0.642 82 1.225 1.201 1.067 0.918 0.575 83 1.210 1.203 1.104 0.986 0.341 84 1.210 1.201 1.125 1.042 0.157 36 -0.510 -0.544 -0.555 -2.955 -1.563 37 -0.496 -0.563 -0.614 -2.273 -2.001 38 -0.481 -0.581 -0.600 -0.868 -1.129 39 -0.476 -0.600 -0.595 -0.556 -0.649 40 -0.474 -0.615 -0.602 -0.583 -0.942 41 -0.491 -0.625 -0.595 -0.609 -1.301 42 -0.513 -0.637 -0.586 -0.582 -0.730 85 1.223 1.175 1.077 0.982 0.640 86 1.220 1.152 1.022 0.906 0.598 87 1.230 1.161 1.013 0.864 0.549 88 1.236 1.181 1.026 0.849 0.477 89 1.230 1.205 1.083 0.930 0.330 90 1.220 1.209 1.117 0.997 0.253 91 1.222 1.207 1.137 1.048 0.304 43 -0.363 -0.360 -0.345 -2.108 -1.077 44 -0.318 -0.343 -0.386 -1.101 -1.292 45 -0.286 -0.322 -0.398 -0.737 -0.568 46 -0.275 -0.328 -0.407 -0.617 -0.428 47 -0.270 -0.339 -0.418 -0.586 -0.456 48 -0.303 -0.343 -0.387 -0.574 -0.475 49 -0.360 -0.390 -0.345 -0.598 -0.482 92 1.224 1.187 1.091 0.993 0.555 93 1.221 1.163 1.037 0.921 0.502 94 1.229 1.169 1.022 0.873 0.421 95 1.234 1.190 1.038 0.857 0.345 96 1.229 1.214 1.091 0.925 0.301 97 1.221 1.220 1.126 0.992 0.297 98 1.224 1.218 1.143 1.038 0.302 256 APPENDIX J. NUMERICAL RESULTS Bibliography

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