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

1. CFD Applications for Marine Foil ConfigurationsVolker 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 thickness 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 Transverse plate 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 Transverse 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 Superfast XII Increase maximum rudder angle to 45º

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

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 distributionat 2.6m above rudder base 25º 35º 45º

28. Reverse flow also simulated Velocity distributionat 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 V „micro-bubble“ R0 liquidVl 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. First test: 2-D NACA 0015 Vapor volume fraction Cv for one period

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

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

41. 2-D NACA 16-206 Vapor volume fraction Cv for one period

42. 2-D NACA 16-206 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. 3-D NACA 16-206 pressure distribution Cpand vapor volume fraction Cv

46. 3-D NACA 16-206 Cv= 0.005 Cv= 0.5 Correlation between visual type of cavitation and vapor volume fraction Cv ?

47. 3-D NACA 16-206 Pressure distribution with and without calculation of cavitation

48. 3-D NACA 16-206 Exp. Minimal and maximal cavitation extent with vapor volume fraction Cv=0.05

49. 3-D NACA 16-206: VRML model

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