AVELOCITY PREDICTION PROCEDURE FOR SAILING YACHTS WITH A HYDRODYNAMIC MODEL BASED ON INTEGRATED FULLY COUPLED RANSE-FREE-SURFACE SIMULATIONS Christoph BÖHM AVELOCITY PREDICTION PROCEDURE FOR SAILING YACHTS WITH A HYDRODYNAMIC MODEL BASED ON INTEGRATED FULLY COUPLED RANSE-FREE-SURFACE SIMULATIONS Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties, in het openbaar te verdedigen op woensdag 8 oktober 2014 om 10:00 uur door Christoph BÖHM Diplom-Ingenieur (Fachhochschule) Schiffbau geboren te Essen, Duitsland. Dit proefschrift is goedgekeurd door de promotor: Prof. dr. ir. R.H.M. Huijsmans Copromotor: Dr. ir. M. Gerritsma, Samenstelling promotiecommissie: Rector Magnificus, voorzitter Prof. dr. ir. R. H. M. Huijsmans, Technische Universiteit Delft, promoter Dr. ir. M. I. Gerritsma, Technische Universiteit Delft, copromotor Prof. dr. F.Fossati, Politecnico di Milano Prof. dr. K. Graf, University of Applied Sciences Kiel Dr. ir. J. A. Keuning, Technische Universiteit Delft Prof. dr. ir. T. J. C. van Terwisga, Technische Universiteit Delft Prof. dr. P.A. Wilson, University of Southampton Prof. dr. ir. J. J. Hopman, Technische Universiteit Delft, reservelid Copyright © 2014 by Christoph Böhm An electronic version of this dissertation is available at http://repository.tudelft.nl/. To my whole family for their support and patience, especially to my wife Bettina and my sons Maximilian and Felix Alexander. TABLEOF SYMBOLS LATIN LETTERS (1 k) Form factor [ ] Å £ ¡2¤ AS ail s Sail area m AR Wing aspect ratio [ ] ¡ AW S Apparent wind speed [m/s] B Bias component of uncertainty U [ ] ¡ C Drag coefficient [ ] D ¡ C Drag coefficient at zero lift [ ] D0 ¡ C Induced drag coefficient [ ] Di ¡ C Separation drag coefficient [ ] Ds ¡ C Force coefficient [ ] F ¡ C Correction factor [ ] k ¡ C Lift coefficient [ ] L ¡ C Moment coefficient [ ] M ¡ C Total resistance coefficient [ ] T ¡ CFL Courant number [ ] ¡ CV Control volume of a grid cell £m3¤ e,CE Efficiency coefficient [ ] ¡ E Comparison error [ ] ¡ fH Heeling force coefficient [ ] f ¡ @ H Heeling force gradient [ ] @¯ ¡ f Heeling force coefficient at zero leeway [ ] H0 ¡ FS Sail force vector [N] FH Heeling force perpendicular on flow direction and span [N] F n Froude number [ ] ¡ I Unit tensor [ ] ¡ I Tensor of the moment of inertia w.r.t to center of gravity £kg m2¤ G ¢ KPP Quadratic parasite drag coefficient [ ] ¡ LCE Longitudinal center of effort [m] LCG Longitudinal center of gravity [m] LOA Length over all [m] LW L Length of waterline [m] m Mass £kg¤ M Heeling moment around boat x-axis [N m] x ¢ vii viiiT ABLEOF SYMBOLS M Righting moment around boat x-axis [N m] xR ¢ M Pitch moment around boat y-axis [N m] y ¢ M Pitch moment around boat y-axis [N m] y ¢ M Yaw moment around boat z-axis [N m] z ¢ n Surface normal vector [ ] ¡ p Pressure £N/m2¤ P Precision component of uncertainty U [ ] ¡ P Order of accuracy [ ] k ¡ q Dynamic pressure £N/m2¤ r Refinement ratio of parameter k [ ] k ¡ R Convergence ratio [ ] k ¡ Rn Reynolds number [ ] ¡ RH Added resistance due to heel [N] RI Induced resistance [N] RPP Parasitic profile drag [N] RU Upright resistance [N] Rtot Total hydrodynamic resistance [N] s Wing span [m] S Simulation result [ ] ¡ SC Simulation result corrected [ ] £ ¡2¤ Sf Cell surface vector m SF Side force, component of the heeling force parallel to the water sur- [N] face T Truth [ ] ¡ T Draft [m] T Transformation matrix, viscous stress tensor [ ,Pa s] ¡ ¢ TCG Transverse center of gravity [m] TE Effective draft [m] TWA True wind angle [±,rad] uB Boat velocity vector [m/s] UB Boat velocity [m/s] U Parameter uncertainty (e.g. iteration number I grid size G and time [ ] P ¡ step T ) U Corrected numerical uncertainty [ ] SC N ¡ U Numerical uncertainty [ ] SN ¡ U Validation uncertainty [ ] V ¡ v Velocity vector [m/s] vA Apparent wind vector [m/s] vb Grid velocity vector [m/s] vf Velocity vector at cell face [m/s] TABLEOF SYMBOLS ix vG Linear velocity of center of mass [m/s] £ 2¤ v˙G Linear acceleration of center of mass m/s vT True wind vector [m/s] VA,AW A Apparent wind angle [±,rad] VCG Vertical center of gravity [m] VCE Hydrodynamic vertical center of effort [m] £ 3¤ Vf Cell volume associated with cell face m VMG Velocity made good, velocity component directly into the wind, re- [m/s] spective away from the wind VT ,TWS True wind speed [m/s] xG Position of center of gravity [m] yÅ Dimensionless wallscale [ ] ¡ zre f True wind reference height [m] z0 Equivalent grain roughness [m] ZCE Aerodynamic vertical center of effort [m] GREEK LETTERS ® Flow angle of incidence [±] ® Volume fraction of VOF model [ ] i ¡ ¯ Leeway or drift angle [±,rad] ¯A Apparent wind angle [±,rad] ¯T True wind angle [±,rad] ± Rudder angle [±,rad] ±? Error estimate with sign and magnitude of kth parameter [ ] k ¡ ± Parameter error (e.g. iteration number I grid size G and time step T ) [ ] P ¡ ± Simulation error [ ] S ¡ ± Simulation error corrected [ ] SC ¡ ± Simulation modeling error [ ] SM ¡ ± Simulation numerical error [ ] SN ¡ ² Solution change [ ] i jk ¡ ² Change between two solutions [ ] ¡ ¸ Scale factor [ ] ¡ ¹ Dynamic viscosity [Pa s] ¢ ¹ Turbulent viscosity [Pa s] T ¢ ¹ Effective dynamic viscosity [Pa s] e f f ¢ !G Angular velocity around center of mass [rad/s] Á Heeling angle, rotation around yacht’s x-axis or distance function [±,rad] Á Central node value of the NVD [ ] C ¡ Á˜ Normalized face value of the NVD [ ] f ¡ à Yaw angle, rotation around yacht’s z-axis [±,rad] ½ Density £kg/m3¤ xT ABLEOF SYMBOLS £ 2 ¤ ¿ Shear stress, tab angle N/m ,± θ Free surface interface angle or pitch angle, rotation around yacht’s y- [±,rad] axis ³ Wave height [m] ¢TA Time allowance delta, time difference between two boats when sail- [s] ing one nautical mile at a specific true wind angle ¢x Increment in kth input parameter (e.g. iteration number I grid size G [ ] k ¡ and time step T ) SUBSCRIPTS f Cell face C Corrected error or uncertainty BS Body-fixed coordinate system GS Global, space fixed newtonian coordinate system ACRONYMS ABL Atmospheric boundary layer ACCV5 America’s Cup class version 5 CBC Convection boundness criterion CFD Computational fluid dynamics CSYS Coordinate system DSKS Delft systematic keel series DSYHS Delft systematic yacht hull series EFD Experimental fluid data ESG Equilibrium state guess for conventional VPP FSBC Free surface boundary condition FSI Fluid-structure-interaction FVM Finite volume method HRIC High resolution interface capturing scheme IMS International measurement system ITTC International towing tank conference MPI Message passing interface NVD Normalized value diagram ORC Offshore racing congress PVM Parallel virtual machine RANSE Reynolds-averaged-Navier-Stokes-equations SIMPLE Semi-implicit method for pressure linked equations TG Turbulence generator TWFT Twisted flow wind tunnel UD Upwind differencing scheme VOF Volume-of-fluid TABLEOF SYMBOLS xi VPP Velocity prediction program CONTENTS Table of Symbols vii 1 Introduction1 1.1 Problem definition and objectives.....................1 1.2 Overview of this thesis...........................1 2 Background of Velocity Prediction for Sailing Yachts3 2.1 Preface...................................3 2.2 History of VPP................................4 2.3 Investigation methods for Aerodynamics of Sails..............5 2.4 Investigation methods for Hydrodynamics of Yacht Hull and Appendages.9 2.5 Current Contributions to VPP........................ 12 2.5.1 Approach using Conventional VPPs................. 12 2.5.2 Approach using dynamic VPP.................... 13 2.6 Objective of the Research.......................... 15 3 Basic Decisions on the Formulation of the RANSE-VPP 19 3.1 Overview of present methods in Hydrodynamics.............. 19 3.1.1 Yacht Flow Problems......................... 20 3.1.2 Classification of free surface models................. 22 3.1.3 Free Surface Modeling Methods................... 23 3.1.4 Overview of existing codes...................... 35 3.1.5 Conclusions............................. 37 3.2 Overview of present methods in Aerodynamics............... 39 3.2.1 Aerodynamics of Sails........................ 39 3.2.2 Structure of the Apparent Wind................... 44 3.2.3 Aerodynamic Force Models..................... 49 3.2.4 Kerwin / Hazen / IMS model..................... 51 4 Mathematical Model 55 4.1 Standard Mathematical Models for Conventional VPPs........... 55 4.1.1 Coordinate System.......................... 55 4.1.2 Hydrodynamic Model........................ 56 4.1.3 Derivation of Hydrodynamic Coefficients from Towing Tank Test Results................................ 58 4.1.4 Aerodynamic Model......................... 63 4.1.5 Solution Algorithm.......................... 64 xiii xiv CONTENTS 4.2 Mathematical Model for RANSE coupled VPP................ 64 4.2.1 Coupling of RANSE simulation and VPP............... 66 4.2.2 Formulation of Aerodynamic Forces................. 66 4.2.3 Optimization of Boat Speed..................... 70 4.2.4 Integration of Rudder Forces..................... 71 4.2.5 Convergence criterion........................ 72 4.2.6 Summary.............................. 72 5 Numerical Method 75 5.1 Outline of the RANSE solver......................... 75 5.1.1 Governing Equations......................... 75 5.1.2 Discretization............................ 77 5.1.3 Solution procedure......................... 77 5.2 Rigid Body Dynamics............................ 78 5.2.1 Frames