Paterson 3 Rd Open Foam Workshop

Multiphase and Free-Surface Flow Simulations

Eric PatersonApplied Research Laboratory

and Department of Mechanical EngineeringThe Pennsylvania State University

State College, PA 16803 USA

3rd OpenFOAM WorkshopPolitecnico di Milano

Milan, Italy10-11 July 2008

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3rd OpenFOAM Workshop, 10-11 July 2008

Acknowledgements

• Graduate Students: Kevin Smith, Bob Erney

• Undergrate Students: Scott Ford, Sean McIntyre

• PSU Faculty: Mario Trujillo*, Mike Kinzel

• Hrv Jasak

*current affiliation: U. Wisconsin Mech. Eng. & Engine Research Center

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Outline

• Introduction

• Related Work

• rasInterDyMFoam6DOF

• Code Verification

• Tutorial

• Solution Validation

• Conclusions

3


Introduction

• Floating Bodies in Waves

• Water-on-Deck

• Wave Impact Loads

• Seakeeping Dynamics

• Slamming

4


Introduction


• Water-on-Deck



• Slamming

4


Introduction


• Water-on-Deck



• Slamming

4


Related WorkSurface-Piercing Bodies

NACA 0024, Fr = 0.24, Re = 1x106, rasInterFoam Cylinder, Fr = 0.3, Re = 2.8x104, lesInterFoam

Mean Wave ElevationGamma on surface and centerplane

5


Related WorkVentilated Cavitation: Cavity-Jet Interactions

!"#$%&' ()*"#$%&+',&-".-$&/'''

0102'3'45'6&"'78,9):9):'

;)'<#=9">'7)"&-?#@&'

02'

A9*B'<#=9"#";-C'D#"&-#%'*>88&"->'

Gas

Water

V∞

Disk Cavitator, Re = 6.2x104, Fr = 15, CQ = 0.13

pyFoam script to vary CQ for study of cavity stability with jet velocity

2D cavitator

6


Vaporous Cavitation

Related Work

Validation DataRouse, H. and McNown, J. S., 1948, “Cavitation and Pressure Distribution, Head Forms at Zero Angle of Yaw,” Studies in Engineering Bulletin 32, State University of Iowa.

σ = 0.5

σ = 0.2

7


Related WorkJet/Free-Surface Interaction

depth = 2D depth = 1D

Q parameterCenterline Mean Velocity

M. F. Trujillo, C.-T. Hsiao, J.-K. Choi, E. G. Paterson, G. L. Chahine, L. J. Peltier, “Numerical and Experimental Study of a Horizontal Jet Below a Free Surface,” 9th International Conference on Numerical Ship Hydrodynamics, Ann Arbor, Michigan, August 5-8, 2007

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http://www.umich.edu/~icnsh/program.html





rasInterDyMFoam6DOF

• Extend interFoam family of solvers

• Hydrostatic pressure

• Forces and moments

• Dynamic mesh

• 6DOF equations of motion

• Wave boundary condition

• Air-field convective term

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Hydrostatics

• interFoam solvers are formulated to solve for the piezometric pressure

• total pressure p required for dynamic and hydrostatic forces and moments

!

f

S ·"#

1aP

$

f

(!p)f

%=

!

f

S ·#

H(U)aP

$

f

!

f

S ·"#

1aP

$

f

(!p)f

%=

!

f

S ·&

H(U)aP

'

f

H(U) = !!

N

aNUN +U0

!tH(U) = !

!

N

aNUN +U0

!t+ !K"" ! #g

Poisson equation for piezometric pressure Poisson equation for total pressure

!p = p + !K" ! #gz

!p = p + !K" ! #gz

Additional cost of additional Poisson equation justified, especially for complex free-surfaces

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6DOF EOM

• sixDOFMotion class

• ODESolver.H

• translationODE.H

• rotationODE.H

• Member functions: hullForce, hullMoment

• dynamicMeshDict

• sixDOFMotionCoeffs subDict to choose ODE options

• IOobject for translationalMotion and rotationalMotion: sets mass properties and I.C.’s

! = " =!I!1 · M

"!

!I!1 · # " (I · #)

"a = x =

Fm

+ g

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Wave B.C.Equations for 2nd-order Stokes wave in shallow water

u =gAk

!

cosh k(y + H)cosh kh

cos(kx! !t)

v =gAk

!

sinh k(y + H)cosh kh

sin(kx! !t)

!(x, t) = A cos(kx! "t) +12kA2 cos 2(kx! "t)

!p

!x! 0

!p

!x= gAk

cosh k(y + H)cosh hH

sin(kx! "t)

!!

gAk

"

"2 k

cosh2 kHsin(kx! "t) cos(kx! "t)

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Wave B.C.

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Air-side convective-term treatment

• Water waves create vortices on the air-side of the free surface

• These vortices have high velocity, impact the Courant number, push the time step to be smaller, and increase the simulation costs

• For many problems, stresses generated on air side are negligible.

• Solution: ignore convective term on air-side fvVectorMatrix UEqn ( fvm::ddt(rho, U) + gamma*fvm::div(rhoPhi, U) - fvm::laplacian(muf, U, "laplacian(mut,U)") - (fvc::grad(U) & fvc::grad(muf)) );

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Results: Code VerificationHydrostatic Equilibrium of a Floating Cylinder (D = 1cm)

Case Mass (kg)

Depth of CG (mm)Theoretical

Depth of CG (mm)CFD

0 3.89E-05 0.0 0.0

1 4.91E-05 1.0 1.0

2 5.87E-05 2.0 2.0

3 6.74E-05 3.0 3.0

4 7.45E-05 4.0 4.0

5 7.85E-05 5.0 5.0

Gamma field contours, Case 5

Velocity field contours, Case 5

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Tutorial: rectBargeFreeDecay

[1] Jung, K.H., Chang, K.A., Jo, H.J., Viscous Effect on the Roll Motion of a Rectangular Structure, J. of Engineering Mechanics, 2006

0.3 m

0.1 m

allowed to rotate about

fixed center axis,

Regular waves

Moment of inertia given Iz = 0.236 kg m^2

0.9 m Wave

generator x

y

z

Free-Roll Decay of a Box Barge

Experiment: Texas A&M Ocean Engineering Wave Tank [1]• 0.9 m deep, 35 m long, 0.9 m wide• Barge positioned 20 m from wave generator• Free roll• Wave-excited roll• Motion restricted to 1DOF rotation

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Tutorial: Mesh

• Structured mesh with 62,858 cells• Corners of barge have a small bilge radius

0.625 % of beam• Near-wall spacing = 2.7x10-3

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Tutorial: IC & BC

U: pressureInletOutletVelocity

P: totalPressure

U: fixedValue, value (0 0 0)

P: zeroGradient

U: movingWallVelocity, value(0 0 0)

P: zeroGradient

Close up view

• Body rotated to 15 deg using moveDynamicMesh utility• Initialized gamma field using setFields• k-ε turbulence model

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Tutorial: Results

Natural frequency (Fourier Analysis)• CFD: 6.9 rad/s

• Experiment: 6.8 rad/s

Damping ratio (Curve of Extinction)• CFD: 0.133

• Experiment: 0.106

Free Roll Decay of 2D Barge

Time (s)

Ang

le o

f Inc

linat

ions

(de

g)

Curve of Extinction

Mean Amplitude

Loss

of a

mpl

itude

per

sw

ing

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0-15

-10

-5

0

5

10

15

0 5.0 10 15-5

0

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Results: Solution ValidationWave-Induced Roll Motions of a Box Barge

U: pressureInletOutletVelocity

P: totalPressure

U: fixedValue, value (0 0 0)

P: zeroGradient

U: movingWallVelocity, value(0 0 0)

P: zeroGradient

Wave boundary condition

U: zeroGradient

P: zeroGradient

• Structured mesh with 78,000 cells• Finer mesh refinement upstream to

capture waves

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Results: Solution ValidationWave-Induced Roll Motions of a Box Barge

λ = 1.56 m, H = 0.044 mMagnification factors for roll motion of 2D Box Barge

ω/ωn

ϕ/(

kA)

0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.60

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

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Conclusions

• interFoam class of solvers have been extended for 6DOF motions of floating bodies

• Code has been verified for hydrodynamic equilibrium test case

• Simulations have been validated for free- and wave-induced roll test cases

• Solver and tutorial: provide to community

• Future work

• application to ship hulls

• create overFoam library with hooks to DiRTlib and SUGGAR for overset (Chimera) grid capability

• utilize quarternion 6DOF solver in $(FOAM_LIBBIN)/libODE

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Paterson 3 Rd Open Foam Workshop

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