Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec


and fully integrated - the equations of motions of the sailing yacht, which is considered to be a rigid body.


In the current implementation the method is used for hydrodynamic assessment of yacht hulls. Consequently the hydrodynamic forces are calculated from the RANSE solver, avoiding interpolation. To account


for the


aerodynamic forces imposed by the sails, an additional, external force is modelled which is acting on the sailing yacht as a rigid body. Since this external sailing force vector FAero is of unsteady nature, modelling of this vector implicitly requires that its calculation routine is directly coupled with the rigid body motion solver. Along with gravity force and hydrodynamic forces acting on the yacht, this sailing force vector is used to solve the equations of motion.


The sailing force vector itself is calculated using a Hazen-like empirical sail force model. As described for the conventional VPPs, the sailing force coefficients cD and cL as functions of AWA are stored in a database. The procedure is modified to take into account additional force components originating from unsteady motion and orientation of the boat, allowing calculating its influence on boat movement as a time series.


This approach wilfully keeps up the separation of aerodynamic and


paradigm of hydrodynamic


investigation for several reasons: It allows taking into account sailing force data from virtually any source and in conjunction with depowering algorithms, resembling the trimming of the sail carried out by sailors.


It


simplifies the analysis of cause and effect of changes in aerodynamic or hydrodynamic parts of a yacht. Finally it allows taking into account advanced techniques for the prediction of aerodynamic forces, e.g. fluid structure interaction methods.


In contrast to the conventional VPP approach, this procedure has no need for a database of hydrodynamic coefficients. The hydrodynamic data of the yacht is directly calculated via the RANSE solver. This has a direct impact on the number of runs necessary to predict boat velocity.


As mentioned before, the method is used for


hydrodynamic assessment of yacht performance. As thus, interpolation errors of the empirical aerodynamic force prediction are accepted, as long as the method is used for the comparison of different yacht hulls with identical sails. If the


focus of the investigation changes to


aerodynamics, the method can be inverted. Aerodynamic forces would then be calculated accurately without any interpolation


from the RANSE simulation, while


hydrodynamic properties would be predicted using empirical methods.


Results of a VPP analysis are usually displayed in a polar plot depicting boat speed for a given true wind speed over true wind angle. On average such a plot will show;


 3 – 5 true wind speeds  30° – 120° TWA Upwind  90° - 180° TWA Downwind


This gives about 60 – 100 simulation runs, which is far fewer than the numbers needed for a conventional VPP. Additionally, it is possible to investigate only the areas most interesting for a specific boat type, for example maximum VMG (Velocity made good) upwind and downwind, which further


inherently maintained.


This includes the righting moment, which takes the real deformed water surface into account.


3. 3.1


THEORETICAL METHOD FLOW SOLVER


A RANSE solver is used to calculate the flow around the fully appended hull. Descriptions of RANSE methods are widely available, see Ferziger [2] as the authors` favourite. The governing equations of RANSE methods will be sketched here only briefly.


RANSE solver use a volume based method to solve the time-averaged


Navier-Stokes equations in a


computational domain around the investigated flow body. The RANS equation evolves from time averaging mass and momentum conservation for a continuous flow. In the method used it is assumed that the Reynolds stress evolving from time averaging is modelled using the eddy viscosity hypothesis and two-equation turbulence models. Assuming incompressible flow this yields,


d ddSuuu dt 


  


   


    S





un dS  0 S


 


SS 3 T


 n


12 


T uu n b  


 dS  d (3)


The turbulence model used in the presented approach is the Shear Stress Transport (SST) model. It calculates the turbulent viscosity T from the turbulent kinetic energy k and the specific turbulent dissipation :


 


T ma 12x , ak


aF  be


 1


taken into account (4)


In the present case two different fluids (water and air) have to


in the simulation.


Therefore an additional conservation equation has to be introduced to capture the free surface interface and its deformation due to the yachts wave pattern. Since these fluids are not expected to mix, a homogenous multiphase


B-84 ©2011: The Royal Institution of Naval Architect


 p  k


 


ndS (2)


reduces the number of


necessary runs dramatically to about 24 – 40. Since any interpolation is avoided, fully accuracy of the prediction of hydrodynamic properties is


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