This document summarizes a fluid-structure interaction (FSI) analysis of a composite bow foil. The analysis compared a quasi-static structural analysis, dynamic structural analysis with rigid CFD, and a full FSI analysis with two-way fluid-structure coupling. The FSI analysis found a 40-50% reduction in bending moment and vertical force compared to the quasi-static analysis. Compressible air effects provided a minor 10% difference from an incompressible analysis. The hydroelasticity parameter indicated structural dynamics were important given the short load duration. Overall, the FSI and dynamic analyses provided a lighter and more optimized structural design compared to a traditional quasi-static approach.

1. Fluid-Structure Interaction
Analysis of Composite Bow Foil
MARINE || COMPOSITES || RENEWABLES || SUBSEA

2. CDYNAMICS COMPANY INTRO
• Located in Kristiansand, Norway
• Founded in 2015 as a supplier of analysis
services to marine industry
• 5 co-workers
• Expertise in composites and fluid dynamics
• Applicable skills in CFD and FEA to any
engineering problem
http://cdynamics.no/

3. Wavefoil
• Retractable bow foil that dampens heave
and pitch motion
• Decreases fuel consumption in head-on
waves.
Eirik Bøckmann, Phd thesis 2015
wavefoil.com

4. Project objectives
• Structural dimensioning of Wavefoil against
slamming loads
• Find importance of hydroelasticity by
comparing three approaches:
1. Quasi-static: Quasi-static structural analysis
using pressure from rigid structure CFD
2. Dynamic (One-way coupling): Dynamic
structural analysis using pressure from rigid
structure CFD
3. FSI (two-way coupling): Dynamic analysis
where structural deformation affects the
fluid pressure.

5. • Free body drop: Vertical DOF is free.
• Large mass of ship -> nearly constant
velocity impact at 6 m/s
• Flat water surface
• 10 deg deadrise angle
FSI model setup – CFD model

6. Property Value
Software StarCCM+
Timestep 2.5e-5 - 1e-4 s
Cell size at foil 10 mm
Mesh size 500000 cells
Viscous regime Laminar
Co-simulation Implicit
Mesh motion Overset+morphing
Equation of state Compressible (both
air and water)
FSI model setup – CFD model

7. Time step convergence
0
0.2
0.4
0.6
0.8
1
1.2
0.00E+00 2.00E-05 4.00E-05 6.00E-05 8.00E-05 1.00E-04 1.20E-04
Verticalforce/CFL
Timestep [s]
Vertical force CFL
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
0.035 0.037 0.039 0.041 0.043 0.045 0.047
Verticalforce[MN]
Time [s]
dt=1e-4 dt=2.5e-5 dt=1e-5
• CFL < 1 gives sufficient accuracy on forces (average of pressure)

8. Property Value
Software Abaqus
Element size ~20 mm
No. of elements 23000
Element type Linear quadrilateral
Non-linear geometry No
Timestep 1e-4 s
Boundary condition: vertical
direction is free.
Other DOFs are fixed -> conservative
FSI model setup – FEA model

9. Foil structure
E-glass=22.9 mm
E-glass=30.4 mm
E-glass=37.8 mm
3m

10. Validation of FSI model
• FSI setup with StarCCM+ and
Abaqus in co-simulation is
validated against drop tests of
cantilever plates by Panciroli et
al. 2012.
Experimental setup from Panciroli et al. 2012

11. Validation of FSI model
• FSI setup with StarCCM+ and
Abaqus in co-simulation is
validated against drop tests of
cantilever plates by Panciroli et
al. 2012.

12. Validation of FSI model
Experimental data from Panciroli et al. 2012
-0.002
-0.0015
-0.001
-0.0005
0
0.0005
0.001
0.0015
0.002
0.0025
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Strain[%]
Time[s]
FSI (CFD)
Experiment (Panciroli)
• FSI setup with StarCCM+ and
Abaqus in co-simulation is
validated against drop tests of
cantilever plates by Panciroli et
al. 2012.

13. Results - compressible air effects
• FSI versus quasi-static yields
reduction of bending moment of
50%
• Dynamic vs quasi-static yields
reduction of bending moment of
50%
-0.9
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065
Verticalforce[MN]
Time [s]
Quasi-static Quasi-static (incompressible air)
• Compressible air effects are
relevant
• Part of Hull adjacent to foil
needs to be included in CFD
model

14. • FSI approach renders vertical
force about 40% of quasi-static
• Dynamic approach gives spurious
oscillations because of no
damping
-0.9
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065Verticalforce[MN]
Time [s]
Quasi-static FSI Dynamic
Results – vertical force

15. • FSI bending moment about 40% of
quasi-static
• Dynamic bending moment about
60% of quasi-static
• Incompressible air effects yields
only 10% difference to FSI bending
moment
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06 0.065
Bendingmoment[MNm]
Time [s]
Quasi-static FSI (two-way coupling) Dynamic (One-way coupling) FSI (incompressible)
Results – bending moment

16. Results

17. Tsai-Wu utilization for FSI approach Tsai-Wu utilization for Quasi-static approach
Results – Tsai-Wu

18. The role of hydroelasticity
Hydroelasticity parameter:
R =
𝑙𝑜𝑎𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 (𝑟𝑖𝑔𝑖𝑑 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒)
𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 1𝑠𝑡 𝑑𝑟𝑦/𝑤𝑒𝑡 𝑚𝑜𝑑𝑒
R < 1-2: hydroelastic effects are relevant
(Faltinsen 1999, Bereznitski 2001)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Normalizedresponse
R
Theoretical dynamic response (DAF) Quasi-static
Faltinsen 1999 Panciroli 2001

19. The role of hydroelasticity
Dry mode 1: 34Hz
Hydroelasticity parameter:
R =
𝑙𝑜𝑎𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 (𝑟𝑖𝑔𝑖𝑑 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒)
𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 1𝑠𝑡 𝑑𝑟𝑦/𝑤𝑒𝑡 𝑚𝑜𝑑𝑒
R < 1-2: hydroelastic effects are relevant
(Faltinsen 1999, Bereznitski 2001)

20. The role of hydroelasticity
-0.9
-0.7
-0.5
-0.3
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
0.02 0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04 0.042 0.044 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06 0.062 0.064
Verticalforce[MN]
Time [s]
Quasi-static
Duration=5-10 ms
R=0.2-0.3
Hydroelasticity parameter:
R =
𝑙𝑜𝑎𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 (𝑟𝑖𝑔𝑖𝑑 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒)
𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 1𝑠𝑡 𝑑𝑟𝑦/𝑤𝑒𝑡 𝑚𝑜𝑑𝑒
R < 1-2: hydroelastic effects are relevant
(Faltinsen 1999, Bereznitski 2001)

21. The role of hydroelasticity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Normalizedresponse
R
Theoretical dynamic response Quasi-static
Faltinsen 1999 Panciroli 2001
FSI (bending moment) Dynamic (bending moment)
Dynamic (tip deformation)
Hydroelasticity parameter:
R =
𝑙𝑜𝑎𝑑 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 (𝑟𝑖𝑔𝑖𝑑 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒)
𝑝𝑒𝑟𝑖𝑜𝑑 𝑜𝑓 1𝑠𝑡 𝑑𝑟𝑦/𝑤𝑒𝑡 𝑚𝑜𝑑𝑒
R < 1-2: hydroelastic effects are relevant
(Faltinsen 1999, Bereznitski 2001)

22. Conclusions
• FSI and dynamic analysis of Wavefoil yield considerable
reduction in laminate utilization compared to quasi-static
analysis ->
– Lighter structure
– Easier production
• Compressible air effects are only minor in FSI approach
• Dynamic approach can be a good trade-off between CPU
time/cost and accuracy

23. THANK YOU FOR YOUR TIME
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