CFD calculation of flat and stepped cambered windsurf board
As a continuation of part 1 with estimations of Lift and Efficiency of planing board with wedge cambered step and usual flat bottom in the second stage below nonsymmetrical movement with drift is considered , fin is added
Non Symmetrical case needs more cell in mesh and Cpu time.
The same velocity V=10 m/s( 36 kmh) and absolutely flat surface ( calm water) is considered first as an example . Desired Lift range is 1069-1079N , center of pressure in X direction is to be at 0.66-0.68cm from tail .The same board as in the part 1 , but the fin is added ( 42 cm symmetrical 9% profile Naca009 area 355cm2) nonzero drift angle to compensate side force around 370 N .Such side force value is taken for example from Drake's physics of windsurfing 2005 paper.
Variant without step usual bottom
. Trim angle( considered between flat rear part of the board and X axis) is choosen 3.2 degrees to represent efficient range for such Aspect ratio wetted form of flat planing hulls ,
All the settings of mesh , physics models, and especially tuning of the solvers 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 .( Hric, VOF solver , internal, vof dynamic sub steps, time step for Courant number, Y+, AMR .. etc) .
The mesh is around 2.51 million cells with refinements at zones of incoming free surface and around the fin
Below is the free surface scene of cfd solvers with some data Lift (Fy) , shoulders of resultant force in XY plane L Mz 66.2 cm , in XZ plane L My -0.18cm . In this case Drift angle 2.9 deg is needed to achieve 369 N Force Z Some oscillations ( +/-1 %) were observed in values of Y forces and fraction of water on the bottom after some time of solution which can be attributed to forward spray foundation and water surface disturbance by drops in front of stagnation line . The edficiency of the fin is rather high =13.8 , the efficiency of the board 8.96
The total Fy/Fx efficiency of board +fin = 7.3 . Total Drag Fx fin+ Fx board 145.6 H
In the combined picture below Cp ( pressure coefficient) plot in parallel XY sections along the bottom( X=0..-2.3m) is presented , And appropriate 3D Cp distribution on the bottom is added in the left side .The difference of pressure distribution compared with part1 symmetrical planning without fin and wothout drift is the area of pressure disturbance around place of fin fitting -0.1..-0.21
m from tail , which is caused by fin work as a wing ( higher pressure on windward and lower pressure on leeward sides which is seen on the board bottom )
The picture below shows that all surface from tail is wetted and has friction approximately till mean value X=-76 cm of stagnation line area while the main contribution to Lift force makes the region where water meets the board around stagnation line .
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. It is known that higher Aspect ratio AR of wetted surface can reduce this effect ( for example tail cut-outs rises AR ) .For this purpose we 'll try to modify the origin bottom to stepped hull.
Modified variant with step and camber
The same modificaction as in part 1 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 (only 240-340g additional weight). Step position, height , camber% and length is specially chosen 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 position of center of pressure from tail. The chosen step height is much less than usually recommended 5% of width here for classical rectangular step. Dynaplane E. Clement project and experiments with 1% cambered step showed that due to camber it may have much smaller %height/width to achieve sufficient ventilation of aft body.
Almost the same mesh with added super refinement in step area and around fin is used for simulation with 3.42 million cells
Speed of the board is the same V=10 m/s Trim angle is 1.5 degree to be most efficient for such cambered profile ,sinkage of lower edge of step - 0.52 cm ( 1.2 cm of stern).
Below is the free surface scene of cfd solvers with some data , the stern sinkage is 1.2 cm , lowest stern edge of boards stays 2cm higher in vertical Y position compared to no step case above.This set produces by simulation almost the same Lift Force (1071N) and almost the same center of pressure ( X = 67.2 cm from tail ) at given speed . To achive the same Force Z 371 N needs 4 degrees of drift . It can be notice that efiiciency of the fin is less than in the case of a borad without step. It can be explained by presence of free surface around fin fitting and less effective work of upper sections of the fin here.
Total Drag (Fx fin+ Fx board) 107.8 H
In the combined picture below Cp ( pressure coefficient) the plot in parrallel XY sections along the bottom( X=0..-2.3m) is presented in red dots., And appropriate Cp distribution on the bottom with XY sections is added in the left side .
The simulation gives that due to camber Pressure diagram is more filled along wetted surface ,
In spite of not too high step the after body part ( X= -0.49.. 0) is well ventilated with almost no water friction here.The skin friction
coefficient distribution is shown in picture below:
The wetted surface is much smaller than of flat bottom in previous no step case . Trim angle is small - 1.5 degrees which is due to additional lift by concave profile in wetted area from stagnation line to step , As a result total efficiency K ( Lift/Drag) of board +Fin is = 9.9
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 from that of flat bottom of no step case value. It can be added that concave of wetted profile in XY plane may be achieved by more simple straight line triangle wedge of definite height and length to form the necessary step .
Although it is not deep CFD investigation .Meshes used are not super fine, simulation is in ideak calm water , only one velocity 10 m/s and the question of stability is not considered here .
But it can be noticed that it is possible to achieve in calm water higher efficiency Lift/Drag including fin = 9.9 with the special step with concave camber compared to value 7.3 without it.
Additional lift is produced by longitudial concavity of wetted surface 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 less , which together results is less full Drag. But at the same time the efficiency of fin drops slightly because of presence of free surface at fitting region .
In the picture below is the view of manualy added Concave Wedge ( parabolic) in RRD Spitfire 149l 235cm*73cm board , adjacent to forebody , located in the bottom area between forward and rear footstraps:
... coming soon
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 , 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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