Aerodynamic and Hydrodynamic Modelling of Sailing Yachts for Course-keeping Investigations

Abstract

In this thesis is described the development of an integrated mathematical model for the study of sailing yacht dynamic behaviour in wind and waves. An aerodynamics sub-model, referring to the calculation of the forces acting on the sails, and a hydrodynamics one, for the forces on the hull, are combined within a modular vessel-kinematic structure. Depending on the nature of the individual forces, potential or viscous flow computational procedures are adopted. The model is intended for systematic time-domain investigations of course-keeping capability. The motivation is to fill a gap in the field since the literature on the manoeuvring and course-keeping qualities of sailing yachts is rather scarce. The adopted modelling approach is as much as possible physics-based, without impairing nonetheless the primary objective, which is, to make available an integrated model that can be effectively utilized for large scale time-domain, or similar, investigations. As a matter of fact, effective computational procedures enabling fast processing were sought. Verification of the developed calculation schemes was carried out; whilst the validation effort targeted the individual modules by comparison of the numerical predictions against available experimental data. Sail modelling approaches are diversified according to the intended type of sailing. For motion towards the wind (upwind sailing) the assumption of continually attached flow on the sails could be reasonably made, allowing the implementation of the transient flow lifting surface theory through the vortex lattice method. The calculated, at each time step, aerodynamic pressures feed a shell finite element structural solver which is set up in order to determine the instantaneous deformation of the sails. Hence, the aerodynamic and the structural solver operate within a coupled scheme during the simulation. For sailing away from the wind (downwind sailing) where separations effects are domi- nant, the aerodynamic responses for a family of two-dimensional sail camber surfaces (curves) and various operating conditions were pre-calculated using well-known software implementing the numer- ical solution of the Reynolds Averaged Navier-Stokes (RANS) equations. The respective pressures were used as input into a finite element solver for flexures in order to retrieve the deformed shapes. The converged driving coefficients, for each operational combination, populated a large interpolation table, using the apparent wind and heel angles as input. It is remarked that prior to the use of the RANS software, the author made two attempts to model the two-dimensional downwind sails using Eulerian and Lagrangian representations of vorticity. In general, the RANS approach was employed only when it did not seem to have available any faster method that could be reasonably trusted. The modules comprising the hydrodynamic part are categorized as hydrodynamic reaction (ma- noeuvring part), hydrostatic and wave excitation. Discretisation of the hull surface geometry was carried out through flat triangular panels and transverse two-dimensional sections. The calculation of the hydrostatic and incident wave loads was obtained by numerical integration of the related pres- sure components on the hull panels. The radiation and diffraction loads for the hull sections were pre-calculated for a wide range of evaluated frequencies and several drafts and were incorporated into the model along with appropriate memory effects for the transition from the frequency to the time domain. The resistance of the yacht was calculated using combined empirical and pre-design stage methods. The potential flow part of the manoeuvring hydrodynamic derivatives and their variation due to the instant sea surface were extended with the calculation of the local sway added mass in the limit of zero frequency. The manoeuvring lift contribution on the hull and the appendages, taking into account the influence of the incident wave orbital velocities, was obtained by employing, again, the lifting surface theory for transient flows, additionally accounting for the thickness effects of the appendages. The cross-flow drag of the hull sections in manoeuvring motion was retrieved using drag coefficients obtained from the literature and based on similar two-dimensional shapes. The potential of the developed model to serve as a tool for investigating of the course-keeping capability of sailing yachts was evaluated by performing a vast family of upwind and downwind sailing simulations for regular waves. Environmental parameters, namely the wind speed, the wave length and wave steepness, as also ship control parameters (mainly the ordered heading of the yacht) were systematically varied. In particular, in the upwind simulations were investigated: a) the capability of performing the so-called tacking manoeuvres; and b) scenarios of fixed course-keeping with minimum rudder action. In the downwind simulations, the interest was on whether the ordered heading could be adequately maintained. However, critical types of behaviour, including surf-riding and also vessel failures due to broaching-to course instability and/or capsize, were observed in several cases. Through post-processing of the results of the simulations, stability diagrams were created, where, for combi- nations of wind speed, wave length and ordered heading, was presented the critical wave steepness beyond which the yacht would either fail to perform the commanded manoeuvre, be trapped in a surf-riding incident or suffer a major failure event (broaching-to/capsize). Thus the developed model has succeeded in providing means of identification of environmental excitations that define the safe operation envelope of a sailing yacht.