Trans RINA, Vol 153, Part B2, Intl J Small Craft Tech, 2011 Jul-Dec
However, the most accurate comparison is probably the comparison with experimental and numerical towing tank data based VPP results as mentioned above. This is currently in the works and will be a major part of future publication on this topic.
7.1 DOWNWIND RESULTS
Figure 10 shows a number of partial polar curves for downwind courses to demonstrate the capability of RVPP to calculate VMG from a very limited number of simulations. Whilst the results for TWS of 3, 4, 6 and 7 m/s have been only calculated at certain TWAs, the information on boat performance gained is sufficient to allow deriving the maximum Velocity Made Good, VMG, as a measurement of the boat speed in terms of making way to windward or leeward.
0 1
Boat Speed [m/s] 2
3 4 5 90 Figure 11: Resolution of free surface at larger heel angles TWS 3m/s TWS 4m/s TWS 5m/s 120
TWS 6m/s TWS 7m/s
A visual analysis of the present simulation results showed that RVPP currently suffers from a problem regarding the smooth resolution of the free surface for heel angles greater than 15°. A typical example of this problem is shown in Figure 11. Here one can clearly see the wave pattern of the free surface on starboard side is crossed by stripes. The resolution on port side on the contrary is quite satisfactory.
150 180 TWA
RVPP VMG Conventional VPP RVPP
Figure 10: Downwind Velocity Polar plot
The points of maximum VMG for the respective TWSs are marked on the velocity polar plot as circles on the dotted line which intersects the downwind polar curves. In many investigations of yacht designs, getting this information is the final goal of a VPP calculation. Since conventional testing procedures only return forces for a possible boat state, one would have to calculate or test the points of complete test matrix as mentioned in section 2.1.
Contrary to this, the approach presented in this paper calculates the actual performance of the boat for a given wind condition. Under the assumption that polar curves are smooth and can be represented by cubic splines one is now able to calculate VMG results from a greatly reduced number of simulations. For instance, to acquire downwind VMG for five true wind speeds as depicted in Figure 10, only 20 computational runs are necessary.
Figure 12: Free surface intersection of grid cells
The problem seems to be grounded in the use of a single grid strategy with a moving computational domain. This strategy results in the need to produce a grid which is sufficient to resolve the free surface for heel angles of +/- 30° around the boat’s DWL.
Figure 12 shows an x-normal plane of the grid with the free water surface included. One can see that the grid pattern on the port side almost follows the free surface contour, while on starboard side the grid cells are intersected in an inappropriate angle.
From this picture one can conclude that the difficulties encountered with the free surface resolution are related to grid resolution and are most likely interpolation errors.
7.2 KNOWN PROBLEMS
Whilst the results presented above are quite satisfactory for the first
development phase, there a currently some unsolved problems present.
results of a method being in an early
B-92
©2011: The Royal Institution of Naval Architect
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