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

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

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

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

Similar flow conditions for submarine masts

Similar flow conditions for hydrofoil boats

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)

Cells clustered near free surface

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

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

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

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

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

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

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

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

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

Concave profiles offer alternatives Rudder profiles employed in practice

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

Validation Case (Whicker and Fehlner DTMB) Stall Conditions

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

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

Grid generation allows easy rotation of rudder

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

Pressure distribution / Tip vortex Rudder angle 25°

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

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

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

Stall appears earlier in reverse flow

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

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

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

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

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

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

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:

Application to typical hydrofoil Stabilizing fin rudder

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

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

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

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

Pressure coefficient Cp 2-D NACA 16-206 Pressure coefficient Cp for one period

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

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

pressure distribution Cp and vapor volume fraction Cv 3-D NACA 16-206 pressure distribution Cp and vapor volume fraction Cv

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

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

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

3-D NACA 16-206: VRML model

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