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

CFD Applications for Marine Foil Configurations

Volker Bertram, Ould M. El Moctar

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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

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Diverse Applications to Hydrofoils

Surface-piercing strut

Rudder at extreme angle

Cavitation foil

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Motivation: Struts for towed aircraft ill-designed

Wing profile bad choice in this case

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Similar flow conditions for submarine masts

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Similar flow conditions for hydrofoil boats

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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)

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Cells clustered near free surface

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Flow at strut highly unsteady

Circular section strut, Fn=2.03, Rn=3.35·106

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Wave height increases with thickness of profile

thickness almost

doubled

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

Thickness “60” Thickness “100”

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Wave characteristic changed from strut to cylinder

parabolic strut cylinderFn=2.03, Re=3.35·106

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Transverse plate reduces waves

Transverseplate

attached

Parabolic strut, Fn=2.03, Re=3.35·106

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Transverse plate reduces waves

Transverseplate

attached

Parabolic strut, Fn=2.03, Rn=3.35·106

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Transverse plate less effective for cylinder

Transverseplate (ring)attached

cylinder, Fn=2.03, Re=3.35·106

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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

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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

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Diverse Applications to Hydrofoils

Surface-piercing strut

Rudder at extreme angle

Cavitation foil

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Concave profiles offer alternatives

Rudder profiles employed in practice

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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

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Validation Case (Whicker and Fehlner DTMB)

Stall Conditions

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Superfast XII Ferry used HSVA profiles

Superfast XII

Increase maximum rudder angle to 45º

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Fine RANSE grid used

RANSE grid with 1.8 million cells, details

• 10 c ahead• 10 c abaft• 10 c aside• 6 h below

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Grid generation allows easy rotation of rudder

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Body forces model propeller action

Radial Force Distribution

RootTip

Source Terms

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Pressure distribution / Tip vortex

Rudder angle 25°

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Maximum before 35º

Superfast XII, rudder forces in forward speed

lift

shaft moment

drag

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Separation increases with angle

Velocity distribution at 2.6m above rudder base

25º 35º 45º

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Reverse flow also simulated

Velocity distribution at top for 35°

forward reverse no separation massive separation

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Stall appears earlier in reverse flow

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Remember:

• RANSE solver useful for rudder design• higher angles than standard useful

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Diverse Applications to Hydrofoils

Surface-piercing strut

Rudder at extreme angle

Cavitation foil

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Cavitation model: Seed distribution

average seed radius R0average number of seeds n0

different seed types &spectral seed distribution

„micro-bubble“ &homogenous seed distribution

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Cavitation model: Vapor volume fractionV

liquid Vl

„micro-bubble“ R0

vapor bubble R

Vapor volume fraction:

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Cavitation model: Effective fluid

The mixture of liquid and vapor is treated as an effective fluid:

Density:

Viscosity:

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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:

&

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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:

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Application to typical hydrofoil

Stabilizing fin rudder

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First test: 2-D NACA 0015

Vapor volume fraction Cv for one period

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First test: 2-D NACA 0015

Comparison of vapor volume fraction Cv for two periods

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3-D NACA 0015

Periodic cavitation patternson 3-D foil

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2-D NACA 16-206

Vapor volume fraction Cvfor one period

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2-D NACA 16-206

Pressure coefficient Cp for one period

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2-D NACA 16-206

Comparison ofvapor volume fraction Cv

with

pressure coefficient Cp for one time step

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3-D NACA 16-206: Validation with Experiment

Experiment by Ukon (1986) Cv= 0.05

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3-D NACA 16-206

pressure distribution Cp and vapor volume fraction Cv

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3-D NACA 16-206

Cv= 0.005 Cv= 0.5

Correlation between visual type of cavitation

andvapor volume fraction Cv ?

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3-D NACA 16-206Pressure distribution

with and without calculation of cavitation

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3-D NACA 16-206

Minimal and maximalcavitation extent with

vapor volume fraction Cv= 0.05

Exp.

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3-D NACA 16-206: VRML model

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Remember

• cavitation model reproduces essential characteristics

of real cavitation• reasonable good agreement with experiments • threshold technology

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