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


First, the apparent wind vector AW is calculated as a function of true wind conditions, current boat speed and current heel angle. The values for current boat speed and current heel angle are obtained from the current state of the transient flow and rigid body motion simulation.


AW  TWS TWA u us  0


 





sin cos  


cos


xx  yy





Figure 3: Rigid Body motion Coordinate System Since the whole computational


grid is


Here, the vector us has been added in the equation to account for changes in AW due to rotating motions of the boat, namely pitch and roll. Thus, us is defined as the angular velocity of the boat B times the vertical centre of effort of the sails, zceAero, see (16).


kept very rigidly


attached to the floating body, the resulting displacements and rotations of the body are resolved by moving the complete grid. In the daily work of the authors, this single-grid strategy has showed to be


robust


compared to mesh deformation techniques, with the only additional effort needed to keep the RANSE solution valid being the correction of flow variables for


grid


movement 3.3 AERODYNAMIC FORCES


The aerodynamic model is responsible for the calculation of aerodynamic forces. It is implemented as a direct two- way coupling with the flow solver and coded in JAVA. Sail forces from the aerodynamic model are to the flow solver as an aerodynamic force vector acting on the rigid body yacht.


The calculation of the unsteady aerodynamic force vector is based on a Hazen-like sail force model [7]. Since Hazen’s model is for quasi-steady forces, the sail force model used in this work has been modified to give unsteady sail forces which depend on boat motion.


As an initial input before the beginning of the calculation procedure, the user


has to provide tables with


permutations of True Wind Angle (TWA) and True Wind Speed (TWS) as well as data about the sail plan of the yacht and aerodynamic data of the individual sails in form of lift and drag coefficients as functions of the Apparent Wind Angle (AWA).


During the unsteady RANS simulation, the flow code is called by the sail force calculation routine at the beginning of every time step, thus whenever the solution advances in time. The calculation routine receives the yacht’s current linear and angular velocity components as well as its orientation in space as input data. From these the sail force vector FAero is calculated at every time step of the simulation in the following manner:


tan us  Bω zceAero (16)


The changes of apparent wind speed and angle due to the angular velocity of the boat may thus be interpreted as an equivalent damping due to sails. Using AW as calculated above, one can easily derive AWA (17) and AWS (18) by applying basic vector calculus.


AWA a AW 


AW x


y x


AWS AW AW y 22 (17) (18)


RVPP uses a modification of the sail force calculation method that has been implemented in the IMS velocity prediction program [4]. It is based on individual sail force coefficients for mainsails, jibs and spinnakers, derived from wind tunnel tests. Whilst the individual sail force data for RVPP may come from any source, the procedure has been adapted because of its versatile usable approach.


From the individual sail coefficients aggregate lift and drag coefficients cLtotal and cDtotal for a sail set are calculated from:


c DTotal Dc reef CE cL flat reef 2* 2 cLTotal  flat reef cL 2 2 2 (19) (20)


Here cD and cL are weighted sums of the drag and lift coefficient of all sails in the sail set while CE* is an efficiency coefficient, taking into account the quadratic parasite profile drag and the effective span of the sail set. reef and flat are trimming parameters for the sail to obtain maximum boat velocity via depowering the sail or reducing sail area. flat is a linear reduction of lift and a squared reduction of induced and parasitic drag at constant span, corresponding to a sail chord or traveller angle trimming action of the sailors. reef is a factor


B-86 ©2011: The Royal Institution of Naval Architect TWS TWA u us  (15)


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