Figure 1.
Longitudinal balance of forces on a NACRA 17 foiling catamaran.
Figure 1.
Longitudinal balance of forces on a NACRA 17 foiling catamaran.
Figure 2.
Example of large rudder deflection during sailing load of the Team USA high-performance catamaran from the F50 fleet in a SailGP event.
Figure 2.
Example of large rudder deflection during sailing load of the Team USA high-performance catamaran from the F50 fleet in a SailGP event.
Figure 3.
Reference systems for the investigated forces, leeway and rake angles, and measured deflections. The arrows point toward the positive directions.
Figure 3.
Reference systems for the investigated forces, leeway and rake angles, and measured deflections. The arrows point toward the positive directions.
Figure 4.
NACRA 17 schematics of side force generation from the leeward and windward Z-foils.
Figure 4.
NACRA 17 schematics of side force generation from the leeward and windward Z-foils.
Figure 5.
Main dimensions of the hydrofoil. Cross section taken from the elbow of the hydrofoil.
Figure 5.
Main dimensions of the hydrofoil. Cross section taken from the elbow of the hydrofoil.
Figure 6.
Planes used for extraction of normal span-wise cross sections along the foil to create the geometry for the numerical simulations.
Figure 6.
Planes used for extraction of normal span-wise cross sections along the foil to create the geometry for the numerical simulations.
Figure 7.
Cloud to mesh (C2M) of the NACRA 17 Z-Foil geometry as designed with cross-section planes and lofting compared to 3D-scan with differences presented in mm.
Figure 7.
Cloud to mesh (C2M) of the NACRA 17 Z-Foil geometry as designed with cross-section planes and lofting compared to 3D-scan with differences presented in mm.
Figure 8.
Estimation of the internal stiffener.
Figure 8.
Estimation of the internal stiffener.
Figure 9.
SSPA’s cavitation tunnel test section with the NACRA 17 foil with speckle pattern applied to it. Two high powered LED lights are used as white light imaging from the oval side window. Two Phantom VEO 710L high-speed cameras are recording the foil displacement through prisms from the circular side windows.
Figure 9.
SSPA’s cavitation tunnel test section with the NACRA 17 foil with speckle pattern applied to it. Two high powered LED lights are used as white light imaging from the oval side window. Two Phantom VEO 710L high-speed cameras are recording the foil displacement through prisms from the circular side windows.
Figure 10.
Calibration of the DIC system with view of the calibration plate from the two cameras and the final calibrated image with the coordinate system overlaid.
Figure 10.
Calibration of the DIC system with view of the calibration plate from the two cameras and the final calibrated image with the coordinate system overlaid.
Figure 11.
Average static error in the DIC system.
Figure 11.
Average static error in the DIC system.
Figure 12.
NACRA 17 Z-Foil tip section deflection as measured from the stereo-DIC configuration. The rainbow color-map specifies the displacement magnitude. The gray-scale color-map specifies the intensity counts of the randomized speckles applied with paint on the surface of the Z-Foil as seen from the DIC cameras.
Figure 12.
NACRA 17 Z-Foil tip section deflection as measured from the stereo-DIC configuration. The rainbow color-map specifies the displacement magnitude. The gray-scale color-map specifies the intensity counts of the randomized speckles applied with paint on the surface of the Z-Foil as seen from the DIC cameras.
Figure 13.
Fluid-Structure Interaction coupling routine where the dynamics of the flow is described using Computational Fluid Dynamic (CFD) and the Solid is characterized using Finite Element Analysis (FEA).
Figure 13.
Fluid-Structure Interaction coupling routine where the dynamics of the flow is described using Computational Fluid Dynamic (CFD) and the Solid is characterized using Finite Element Analysis (FEA).
Figure 14.
Placement of weights during static load test inside the cavitation tunnel test section.
Figure 14.
Placement of weights during static load test inside the cavitation tunnel test section.
Figure 15.
Boundary conditions at the root and 500 mm below the root and example location of applied and forces. In red the location of the probed line from which the displacement and stresses are extracted.
Figure 15.
Boundary conditions at the root and 500 mm below the root and example location of applied and forces. In red the location of the probed line from which the displacement and stresses are extracted.
Figure 16.
Convergence for displacement.
Figure 16.
Convergence for displacement.
Figure 17.
Convergence of first principle stress.
Figure 17.
Convergence of first principle stress.
Figure 18.
Difference between the measured and simulated numerical deflections for the static load case in millimeter.
Figure 18.
Difference between the measured and simulated numerical deflections for the static load case in millimeter.
Figure 19.
The structure of the mesh for the whole cavitation tunnel domain illustrating the refinement zones near the foil.
Figure 19.
The structure of the mesh for the whole cavitation tunnel domain illustrating the refinement zones near the foil.
Figure 20.
The structure of the mesh at a the foil region.
Figure 20.
The structure of the mesh at a the foil region.
Figure 21.
The structure of the mesh around the Z-foil showing a plane intersecting the span where the refinement regions at the leading and trailing edges are shown, as well as the boundary layer mesh.
Figure 21.
The structure of the mesh around the Z-foil showing a plane intersecting the span where the refinement regions at the leading and trailing edges are shown, as well as the boundary layer mesh.
Figure 22.
Convergence of the lift-coefficients.
Figure 22.
Convergence of the lift-coefficients.
Figure 23.
Convergence of the drag-coefficients.
Figure 23.
Convergence of the drag-coefficients.
Figure 24.
Change in z-deflection for a range of rake angles at a leeway of zero degrees at flow speed of 9 m/s.
Figure 24.
Change in z-deflection for a range of rake angles at a leeway of zero degrees at flow speed of 9 m/s.
Figure 25.
Change in z-deflection for a range of rake angles at a leeway of -1 degrees at flow speed of 7 m/s.
Figure 25.
Change in z-deflection for a range of rake angles at a leeway of -1 degrees at flow speed of 7 m/s.
Figure 26.
Averaged z-displacement for the investigated ranges of leeway and rake angles at flow speeds of 7 and 9 m/s.
Figure 26.
Averaged z-displacement for the investigated ranges of leeway and rake angles at flow speeds of 7 and 9 m/s.
Figure 27.
Lift and drag for the investigated range of leeway and rake angles and flow speed of 5 m/s.
Figure 27.
Lift and drag for the investigated range of leeway and rake angles and flow speed of 5 m/s.
Figure 28.
Lift and drag for the investigated range of leeway and rake angles and flow speed of 7 m/s.
Figure 28.
Lift and drag for the investigated range of leeway and rake angles and flow speed of 7 m/s.
Figure 29.
Lift and drag for the investigated range of leeway and rake angles and flow speed of 9 m/s.
Figure 29.
Lift and drag for the investigated range of leeway and rake angles and flow speed of 9 m/s.
Figure 30.
Drag coefficient over lift coefficient for the range of operating leeway angles at flow speed of 5 m/s.
Figure 30.
Drag coefficient over lift coefficient for the range of operating leeway angles at flow speed of 5 m/s.
Figure 31.
Computed lift force at 9 m/s, dimensions are in [N].
Figure 31.
Computed lift force at 9 m/s, dimensions are in [N].
Figure 32.
Computed drag force at 9 m/s, dimensions are in [N].
Figure 32.
Computed drag force at 9 m/s, dimensions are in [N].
Figure 33.
Difference between the computed and the measured lift force at 9 m/s, dimensions are in %.
Figure 33.
Difference between the computed and the measured lift force at 9 m/s, dimensions are in %.
Figure 34.
Difference between the computed and the measured drag force at 9 m/s, dimensions are in %.
Figure 34.
Difference between the computed and the measured drag force at 9 m/s, dimensions are in %.
Figure 35.
Surface representation and deflection difference as measured by DIC and simulated numerically for the case where rake and leeway angles are set to zero (T0R0).
Figure 35.
Surface representation and deflection difference as measured by DIC and simulated numerically for the case where rake and leeway angles are set to zero (T0R0).
Figure 36.
Impact on average displacement with respect to the Young’s modulus.
Figure 36.
Impact on average displacement with respect to the Young’s modulus.
Table 1.
NACRA 17 particulars.
Table 1.
NACRA 17 particulars.
Particular | Dimension | Unit |
---|
Length Overall (LOA) | 5.25 | m |
Waterline Length (LWL) | 5.15 | m |
Overall beam | 2.59 | m |
Hull beam | 0.40 | m |
Boat weight (dry condition—minimum) | 163 | kg |
Crew weight | 131–148 | kg |
Mainsail area | 16.1 | m |
Jib area | 4.0 | m |
Gennaker area | 17.9 | m |
Z-Foil span | 1.9 | m |
Z-Foil chord | 0.238 | m |
Z-Foil t/c | 0.16 | - |
Table 2.
Cavitation tunnel balance specifications.
Table 2.
Cavitation tunnel balance specifications.
Component | Range | Uncertainty |
---|
Fx | 1000 N | 4 N |
Fy | 4000 N | 15 N |
Fz | 4000 N | 15 N |
Mx | 2000 Nm | 4 Nm |
My | 200 Nm | 2 Nm |
Mz | 500 Nm | 5 Nm |
Ry | 360 | 0.5 |
Rz | 15 | 0.5 |
Table 3.
DIC performance table showing the equipment and the setting used.
Table 3.
DIC performance table showing the equipment and the setting used.
Equipment | Set-Up |
---|
Camera | 2 high-speed Phantom VEO 710L |
Sensor size: 25.6 × 16 mm |
Pixel size: 20 m |
Resolution (max): 1080 × 800 pixels |
Exposure time: 2000 s |
Frame rate: 0.5–2 kHz |
Lens | Nikon: Nikkor 50 mm f/1.8D |
Aperture: f-8 |
Depth of field: 302 mm |
Speckle pattern | Speckle size: approx. 6 pixels |
Dimensions: 500 × 180 mm |
Angles | Prism angle: |
Stereo angle: approx. |
Effective stereo angle: approx. |
DIC Processing | Subset size: 29 pixel |
Step size: 9 pixel |
Table 4.
Test matrix for static test load test.
Table 4.
Test matrix for static test load test.
Position | Loads [kg] |
---|
165 mm behind trailing edge | 5 | 10 | 15 | 20 | - | - |
Centered | 5 | 10 | 15 | 20 | 25 | 30 |
195 mm in front of leading edge | 5 | 10 | 15 | 20 | - | - |
Table 5.
Numerical settings.
Table 5.
Numerical settings.
Property | Mesh |
---|
Cell type | Trimmed cell |
| 30–50 everywhere |
CL number | <10 |
Physics | Wall function |
Surface refinement | Around the foil |
Around the fluid domain |
Around the extruder at the top of the tunnel |
Around the foil part inside the extruder |
Volumetric refinement | Around the foil |
Around the fluid domain |
Behind the foil tip |
Number of elements | 7.1 million cells |
Boundary conditions | Inlet: = 3.26 m/s, defined from |
A = A to reach |
a fully developed flow at the |
the foil Position of 9 m/s |
Outlet: pressure outlet |
Top, bottom, Side, Wall: wall with |
no-slip conditions |
Table 6.
Test matrix used in the experiments, the complete set shown in red and black, and in the numerical simulations, highlighted in black, at 9 m/s.
Table 6.
Test matrix used in the experiments, the complete set shown in red and black, and in the numerical simulations, highlighted in black, at 9 m/s.
Leeway Angle (T) | Rake Angle (R) |
---|
| 0, 0.3, , |
| 0, 1, , |
0 | 0, 1, 1.5, , |
0.5 | 0, 1, 2, , |
1 | 0, 1, 2, 2.5, , |
2.5 | 0, 1, 2, 3, 3.75, , |
3.5 | 0, 1, 2, 3, 4, 4.75, , |