CFD Applications for Marine Foil Configurations

Volker Bertram, Ould M. El Moctar

2

COMET employed to perform computations

RANSE solver:

Conservation of mass 1momentum 3volume concentration 1

In addition: k- RNG turbulence model 2In 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 modelled1.7 million cells, most clustered near CWL

10 L to each side

8 L

4 L

10 L 10 LStarboard 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

circular section strut, Fn=2.03, Re=3.35·106

Thickness “60” Thickness “100”

11

Wave characteristic changed from strut to cylinder

parabolic strut cylinderFn=2.03, Re=3.35·106

12

Transverse plate reduces waves

Transverseplate

attached

Parabolic strut, Fn=2.03, Re=3.35·106

13

Transverse plate reduces waves

Transverseplate

attached

Parabolic strut, Fn=2.03, Rn=3.35·106

14

Transverse plate less effective for cylinder

Transverseplate (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

Body forces model propeller action

Radial Force Distribution

RootTip

Source Terms

25

Pressure distribution / Tip vortex

Rudder angle 25°

26

Maximum before 35º

Superfast XII, rudder forces in forward speed

lift

shaft moment

drag

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

average seed radius R0average number of seeds n0

different seed types &spectral seed distribution

„micro-bubble“ &homogenous seed distribution

33

Cavitation model: Vapor volume fractionV

liquid Vl

„micro-bubble“ R0

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

Task: model the rate of the bubble growth

convective transport bubble growth or collapse

Lagrangian observation of a cloud of bubbles

Equation describing the transport of the vapor fraction Cv:

&

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 patternson 3-D foil

41

2-D NACA 16-206

Vapor volume fraction Cvfor one period

42

2-D NACA 16-206

Pressure coefficient Cp for one period

43

2-D NACA 16-206

Comparison ofvapor 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 Cp and vapor volume fraction Cv

46

3-D NACA 16-206

Cv= 0.005 Cv= 0.5

Correlation between visual type of cavitation

andvapor volume fraction Cv ?

47

3-D NACA 16-206Pressure distribution

with and without calculation of cavitation

48

3-D NACA 16-206

Minimal and maximalcavitation extent with

vapor volume fraction Cv= 0.05

Exp.

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

51