A Computational Fluid Dynamic Investigation Of
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ACOMPUTATIONAL FLUID DYNAMIC INVESTIGATION OF ROWING OAR BLADES by ANNA LOUISE COPPEL A thesis submitted to The University of Birmingham for the degree of DOCTOR OF PHILOSOPHY School of Sport and Exercise Sciences The University of Birmingham May 2010 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. Abstract This thesis describes the application of computational fluid dynamics (CFD) to model the flow regime around rowing oar blades. The two phase flow that was present at the surface between the water and the air was also incorporated into the CFD model. Firstly, a quasi–static method was applied, whereby the blade was held at a discrete number of angles of attack to the oncom- ing flow. The performance of the model was assessed by applying it to four scaled oar blade designs and validating results against an experimental data set. The results were encouraging with lift and drag coefficients acting on the blades being well predicted throughout. The scope was extended to include full size oar blades of designs typically found in competition rowing. A second approach to investigating the flow around oar blades was also adopted, where instead of being held stationary, the blades moved in the fluid domain. The unsteady effects induced by this rotational motion were found to be substantial, with a 72% and 67% increase in the lift and drag coefficients respectively. Finally, through coupling the CFD predictions of oar blade force coefficients with a mathematical model of rowing, it was possible to determine the influence of oar blade design on rowing performance, and also use the mathematical model to further vali- date the CFD predictions against on–water data. The results provided an accurate assessment of boat performance during the rowing stroke. Publications arising from this thesis Journal Papers 1. Simulating the fluid dynamic behaviour of oar blades in competition rowing. Proceedings of the Institution of Mechanical Engineers, Part P, Journal of Sports Engineering and Technology, vol. 224, 2010. 2. A review of propulsive mechanisms in rowing. Proceedings of the Institution of Mechan- ical Engineers, Part P, Journal of Sports Engineering and Technology, vol. 224, 2010. Conference Proceedings 1. Oar blade force coefficients and a mathematical model of rowing. In: International Soci- ety of Biomechanics in Sport Proceedings. Limerick, August 2009. 2. Computational fluid dynamics and oar blade design. In: BEAR Conference. The Univer- sity of Birmingham, June 2008. 3. Numerical modelling of the flow around rowing oar blades. In: The Engineering of Sport 7. (Eds. M. Estivalet and P. Brisson), 353–361, Springer–Verlag, Paris, June 2008 4. Numerical modelling and validation using Fluent for the flow around three-dimensional quasi–static oar blades. In: ANSYS UK Regional Conference, October, 2007. Acknowledgements First of all I would like to thank my supervisors Dr Trevor Gardner and Dr Nick Caplan, for their expert advice and guidance throughout my PhD. You have both been great mentors over past three years. To my family; I have been fortunate that you have always been so happy to listen and give me your total support during the past seven years. A big thank you to all of my friends for keeping me motivated throughout as well. I would also like to express my gratitude to the staff at the Birmingham Environment for Aca- demic Research (BEAR), without whose expertise and facilities this PhD would not be possible. Finally, I would like to acknowledge, Dr David Hargreaves of The University of Nottingham for his indispensable insight into the complexities of CFD, without which I would be truly lost; thank you. ‘Ideas, like large rivers, never have just one source. Just as the water of a river near its mouth, in its final form, is composed largely of many tributaries, so an idea, in its final form, is composed largely of later additions.’ Ley, W. (Rockets, Missiles and Space Travel, 1951) Contents 1 Literature Review 1 1.1 Introduction . 1 1.2 Mechanics of the rowing stroke . 3 1.3 Oar blade fluid dynamics . 7 1.4 Oar blade design . 15 1.5 Mathematical modelling in rowing . 18 1.6 Summary and thesis overview . 22 1.6.1 Aims . 22 1.6.2 Structure . 23 2 Numerical Modelling 25 2.1 Introduction . 25 2.2 Governing equations for fluid flow . 25 2.2.1 Discretization methods . 27 2.3 Turbulence modelling . 37 2.3.1 The k − ε model . 41 2.3.2 The k − ω model . 44 2.3.3 Boundary conditions . 45 2.4 Free surface flow . 50 2.4.1 Governing equations . 52 2.5 Moving mesh theory . 59 2.6 Computational considerations . 62 2.7 Summary . 63 3 Quasi–Static Investigation 65 3.1 Introduction . 65 3.2 Experimental overview . 66 3.3 CFD methodology . 68 3.3.1 Geometry . 68 3.3.2 Mesh . 69 3.3.3 Boundary conditions . 72 3.3.4 Modelling procedure . 76 3.4 Results and discussion . 78 3.4.1 Flat rectangular oar blade . 81 3.4.2 Flat Big Blade . 84 3.4.3 Big Blade . 87 3.4.4 Macon . 87 3.4.5 Comparison of blade designs . 89 3.5 Extension to full size . 93 3.5.1 Methods . 93 3.5.2 Results and discussion . 97 3.6 Free surface flow . 101 3.6.1 Methods . 102 3.6.2 Results and discussion . 107 3.7 Summary . 112 4 Dynamic Investigation 114 4.1 Introduction . 114 4.2 CFD methodology . 119 4.2.1 Geometry . 119 4.2.2 Mesh . 125 4.2.3 Boundary conditions . 128 4.2.4 Modelling procedure . 130 4.3 Results and discussion . 132 4.3.1 Flat rectangular oar . 134 4.3.2 Big Blade . 140 4.4 Summary . 145 5 Simulations using Mathematical Model of Rowing 147 5.1 Introduction . 147 5.2 Model derivation . 148 5.3 Methodology . 151 5.4 Quasi–static input . 152 5.4.1 Validation using rowing model . 153 5.4.2 Oar blade performance . 156 5.4.3 Comparing full size and quarter scale predictions . 162 5.5 Dynamic input . 165 5.5.1 Comparison against on water data . 165 5.5.2 Comparing quasi–static and dynamic predictions . 167 5.6 Summary . 169 6 Conclusions and Future Work 171 List of References 174 A User Defined Function (UDF) to specify variable inlet velocity 184 2.9 Subdivisions of the near wall region: the inner region contains the viscous sub– layer (a linear relationship between v+ and y+ is found), the buffer region (ed- dies are damped and the turbulent shear stress reduces to be comparable to vis- cous stresses) and the log–law layer (the fluid’s average velocity is proportional to the logarithm of the distance from the wall). In the outer region, the size of the eddies is constant and proportional to the depth of the boundary layer. 48 2.10 Turbulent boundary layer structure: velocity profile as a function of distance normal to the wall. 49 2.11 Drag coefficient of surface-piercing flat plates. 51 2.12 Percentage resistance increase in shallow water. 52 2.13 A description of boundary conditions at the free surface. 54 2.14 Volume fractions on a discrete mesh. 57 2.15 Sliding mesh across a two–dimensional grid interface. 61 3.1 View of the blade orientation. 67 3.2 Dimensions of the computational domain in millimetres. 69 3.3 Development of velocity magnitude along the length of the flume (x–axis). In- let, a location downstream of the blade and outlet are plotted. Velocity magni- tude reduces downstream of the blade, but it is shown to recover by outlet. 70 3.4 The inner mesh (medium) generated around the Big Blade oar using inflation layers and size functions. 73 3.5 Inflation layer growth from surface of Big Blade for the medium mesh. 73 3.6 Surface mesh of (a) Big Blade oar (b) flat rectangular oar of same projected area as the Big Blade. 74 3.7 The outer mesh generated for the Big Blade. The inner and outer meshes are united through a non–conformal interface. 75 3.8 Boundary conditions of computational domain. 76 3.9 Convergence of residuals. 77 3.10 Contours of (a) velocity magnitude (b) pressure coefficient at 20◦, 45◦, 70◦ and 90◦. ........................................ 80 3.11 Path lines released upstream of a Big Blade held at (a) 45◦ (b) 90◦ to the free stream flow. Separation is induced over the upper and lower surfaces of the blade in (a) and (b). Stall is seen in (b). 80 3.12 Effect of turbulence model on the variation of lift coefficient with angle of attack for a flat rectangular oar. 81 3.13 Effect of turbulence model on the variation of drag coefficient with angle of attack for a flat rectangular oar. ..