1. CFD Applications for Marine Foil Configurations Volker Bertram, Ould M
CFD Applications for Marine Foil Configurations Volker Bertram, Ould M. El Moctar

2. COMET employed to perform computations
RANSE solver:
Conservation of mass 1
momentum 3
volume concentration 1
In addition: k- RNG turbulence model 2
In addition: cavitation model (optional) 1
HRIC scheme for free-surface flow
Finite Volume Method:
arbitrary polyhedral volumes, here hexahedral volumes
unstructured grids possible, here block-structured grids
non-matching boundaries possible, here matching boundaries

3. Diverse Applications to Hydrofoils
Surface-piercing strut
Rudder at extreme angle
Cavitation foil

4. Motivation: Struts for towed aircraft ill-designed
Wing profile bad choice in this case

5. Similar flow conditions for submarine masts

6. Similar flow conditions for hydrofoil boats

7. Grid designed for problem
Flow highly unsteady: port+starboard modelled
1.7 million cells, most clustered near CWL
8 L
4 L
10 L to each side
10 L
10 L
Starboard half of grid (schematic)

8. Cells clustered near free surface

9. Flow at strut highly unsteady
Circular section strut, Fn=2.03, Rn=3.35·106

10. Wave height increases with thickness of profile
almost
doubled
Thickness “60” Thickness “100”
circular section strut, Fn=2.03, Re=3.35·106

11. Wave characteristic changed from strut to cylinder
parabolic strut cylinder
Fn=2.03, Re=3.35·106

12. Transverse plate reduces waves
attached
Parabolic strut, Fn=2.03, Re=3.35·106

13. Transverse plate reduces waves
Parabolic strut, Fn=2.03, Rn=3.35·106
Transverse
plate
attached

14. Transverse plate less effective for cylinder
plate (ring)
attached
cylinder, Fn=2.03, Re=3.35·106

15. Problems in convergence solved
Large initial time steps
overshooting leading-edge wave for usual number of outer iterations
convergence destroyed
Use more outer iterations initially
leading-edge wave reduced
convergence good

16. Remember: High Froude numbers require unsteady computations
Comet capable of capturing free-surface details
Realistic results for high Froude numbers
Qualitative agreement with observed flows good
Response time sufficient for commercial applications
Some “tricks” needed in applying code

17. Diverse Applications to Hydrofoils
Surface-piercing strut
Rudder at extreme angle
Cavitation foil

18. Concave profiles offer alternatives
Rudder profiles employed
in practice

19. Concave profiles: higher lift gradients and max lift than NACA profiles of same maximum thickness
IfS-profiles: highest lift gradients and maximum lift due to the max thickness close to leading edge and thick trailing edge
NACA-profiles feature the lowest drag

20. Validation Case (Whicker and Fehlner DTMB)
Stall Conditions

21. Superfast XII Ferry used HSVA profiles
Increase maximum rudder angle to 45º

22. RANSE grid with 1.8 million cells, details
Fine RANSE grid used
RANSE grid with 1.8 million cells, details
10 c ahead
10 c abaft
10 c aside
6 h below

23. Grid generation allows easy rotation of rudder

24. Body forces model propeller action
Radial Force Distribution
Root
Tip
Source Terms

25. Pressure distribution / Tip vortex
Rudder angle 25°

26. Maximum before 35º Superfast XII, rudder forces in forward speed lift
drag
shaft
moment

27. Separation increases with angle
Velocity distribution at 2.6m above rudder base
25º 35º 45º

28. Reverse flow also simulated
Velocity distribution at top for 35°
forward reverse
no separation massive separation

29. Stall appears earlier in reverse flow

30. Remember: RANSE solver useful for rudder design
higher angles than standard useful

31. Diverse Applications to Hydrofoils
Surface-piercing strut
Rudder at extreme angle
Cavitation foil

32. Cavitation model: Seed distribution
different seed types &
spectral seed distribution
„micro-bubble“ &
homogenous seed distribution
average seed radius R0
average number of seeds n0

33. Cavitation model: Vapor volume fraction
„micro-bubble“ R0
liquid Vl
vapor bubble R
Vapor volume fraction:

34. Cavitation model: Effective fluid
The mixture of liquid and vapor is treated as an effective fluid:
Density:
Viscosity:

35. Cavitation model: Convection of vapor bubbles
Lagrangian observation
of a cloud of bubbles
&
Equation describing the transport of the vapor fraction Cv:
convective transport bubble growth or collapse
Task: model the rate of the bubble growth

36. Cavitation model: Vapor bubble growth
Conventional bubble dynamic =
observation of a single bubble in infinite stagnant liquid
„Extended Rayleigh-Plasset equation“:
Inertia controlled growth model by Rayleigh:

37. Application to typical hydrofoil
Stabilizing fin rudder

38. Vapor volume fraction Cv for one period
First test: 2-D NACA 0015
Vapor volume fraction Cv for one period

39. Comparison of vapor volume fraction Cv for two periods
First test: 2-D NACA 0015
Comparison of vapor volume fraction Cv for two periods

40. Periodic cavitation patterns
3-D NACA 0015
Periodic cavitation patterns
on 3-D foil

41. Vapor volume fraction Cv
2-D NACA
Vapor volume fraction Cv
for one period

42. Pressure coefficient Cp
2-D NACA
Pressure coefficient Cp
for one period

43. 2-D NACA 16-206 Comparison of vapor volume fraction Cv with
pressure coefficient Cp
for one time step

44. 3-D NACA 16-206: Validation with Experiment
Experiment by Ukon (1986)
Cv= 0.05

45. pressure distribution Cp and vapor volume fraction Cv
3-D NACA
pressure distribution Cp and vapor volume fraction Cv

46. visual type of cavitation vapor volume fraction Cv ?
3-D NACA
Cv= 0.5
Cv= 0.005
Correlation between
visual type of cavitation
and
vapor volume fraction Cv ?

47. Pressure distribution calculation of cavitation
3-D NACA
Pressure distribution
with and without
calculation of cavitation

48. cavitation extent with vapor volume fraction Cv= 0.05
3-D NACA
Exp.
Minimal and maximal
cavitation extent with
vapor volume fraction Cv= 0.05

49. 3-D NACA : VRML model

50. Remember cavitation model reproduces essential characteristics
of real cavitation
reasonable good agreement with experiments
threshold technology