CFD calculation of symmetrical planing of windsurf board in water without chop and without waves
As a resumption of the theme " implementation of negative rocker area with step between foot straps " this year it was simply applied
to 73 cm wide 2006 board . The purpose was to keep planing in lulls in very small wind range 10-14knots in almost flat water conditions .
in target velocity span - 33-45 kmh .
Some ideas regarding comparison of usual flat bottom hull and concave stepped hull can be driven from thin wing profile planing theory by Sedov L.I , VLM methods and CFD simulation at ideal flat water .
Symmetrical case withot fin is considered firstly , which needs half of full mesh and is less consuming Cpu time.
The only one value of velocity V=10 m/s( 36 kmh) is considered here as an example . Desired Lift range is 1069-1080N ( around 110 kg load) . center of pressure along X direction is to be 0.67-0.7 cm from tail .
Variant of planing without step
Below is a simple CFD simulation of common windsurf flat hull Length 235cm ( No Vee used zero deadrise angle, flat rocker is till 70cm from tail , tail rocker is 0 cm ,nose rocker is 23cm. max width -73 cm ) in stationary movement without side drift( symmetry case) , and absolutely flat water :)) ( no chop) . RRD Spitfire 2006 235 cm which was modified by author is a rough prototype of CFD model .
Velocity is set to V=10 m/s ( 36 kmh) . Trim angle ( considered between flat rear part of the board and X axis) is chosen 3.2 degrees to be in most efficient range for such Aspect ratio wetted forms of flat planing hulls /
All the settings of mesh , physics models, and especially tuning of the solvers( Hric, VOF , time steps .. etc) are omitted here as it is very specialized area to achieve good convergence and reliable results for validation .And often it looks like as a successful "recipe" of CFD setup
Below is the mesh in virtual towing tank . Trim cells mesher with special fine mesh at free surface , around the board and especially in spray formation area at predicted location of stagnation line by more simple methods is used with 1.52 million cells
Below is the free surface scene with some data after some work of solvers : Lift 1071 N , Drag 116.7N , Center of Loads 67 cm from tail,
depth of submersion of tail is 3.4 cm efficinecy of planing 9.2
In the combined picture below Cp ( pressure coefficient) plot in parrallel XY sections along the bottom( X=0..-2.3m) is in red dots., And appropriate 3D Cp distribution on the bottom is added in the left side .
All surface from the tail is wetted and has water friction approximately till mean value X=-0.78 cm of stagnation line zone . While the main contribution to Lift force makes this area of stagnation line where water meets the board region . So it would be interesting not to have wetted this back area which makes very small contribution to Lift and at same time has friction drag. Higher Aspect ratio of wetted surface( for example tail cut-outs) can reduce this effect
For this purpose we 'll try to modify the origin bottom to stepped hull.
Modified variant with redan
Only small step( pink) as stuck cambered wedge is added to the same board , used above .It can be noticed that there is rather easy way to make such small modification with use of polyester putty ( 240-340g additional weight). Step position from tail , height , camber% and length is specially choosen from previous years estimations , obtained from 2D linearised free surface solutions of planing thin profile ,2D and 3D VLM wing analogy linearised methods and Epstein L.A works . The step must be suitable to achieve good ventilation of after body and at the same time solution must result in roughly given Lift and center of pressure from tail. The chosen height is much less than usually recommended 5% of width here for classical rectangular step. Dynaplane E. Clement project and experiments with cambered Johnson step height 1% to beam show that due to camber it may have much smaller %height to achieve sufficient ventilation of aft body.
Almost the same mesh with added super fine mesh in step area is used for simulation with 1.47 million cells
Speed is the same V=10 m/s Trim angle is 1.5 degree to be in efficient range for such cambered profile ,sinkage of lower edge of step only 0.52 cm . This set produces almost the same Lift Force (1080N) and almost the same center of pressure ( X = 67.5 cm from tail ) at given speed .
Below is the free surface scene of cfd solvers with some data Lift , Drag , Center of pressure . also it can be noticed that to produce the same lift
appropriate stern submerge is 1.2 cm so the board with step sits 2 см higher in the water than without
In the combined picture below Cp ( pressure coefficient) plot in parrallel XY sections along the bottom( X=0..-2.3m) is in red dots., And appropriate 3D Cp distribution on the bottom is added in the left side .
In spite of not too high step the after body part ( X= -0.49.. 0) is well ventilated with almost no water friction here. It can be seen that due to camber Pressure diagram is more filled along wetted surface , The wetted surface is much smaller than of flat bottom in previous no step case . Trim angle is small - 1.5 degrees ,calculated efficiency K ( Lift/Drag) is rather high = 14.4
Max width of wetted surface B ( X= -0.49 .... -0.79) is around 0.62m( slightly less) ,Sinkage of lower trailing edge of the step is only 5.2mm. The main purpose of concave is to use much smaller wetted surface at not high trim angle to produce almost the same Lift with Center of Loads to be located not far bottom of no step case value.
Although it is not vast and deep CFD investigation .Meshes used are rather coarse.
But it can be noticed that it is possible to achieve higher efficiency Lift/Drag = 14.4 with the special step with concave camber compared to 9.18 without it.
Additional lift is produced due to concavity and as a result less wetted area is sufficient to achieve the same Lift at less trim angle with almost the same wetted width . As a result 1) aspect ratio of wetted surface is higher , 2) trim angel is smaller , which together results in less full Drag .
Further investigation
3. At the next nonsymmetrical case stage of CFD Simulation we'll add fin 42 cm 9% profile and drift ( 2.9-4 degrees) to compensate side Force around 370N .
4. It is known that in displacement mode of motion of the board rectangular bottom step increases drag and partly decrease Lift because of vorticity zone after step location which may result in deminishing abilty in getting in ti the plane , So the CFD will be used to estimate same hull without step and with such small step at small velocity V=3m/s
... coming soon
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