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Hydrodynamics Analysis of Ships Side by Side in Waves using AQWA and Resistance and Diffraction Simulation over a Ship Hull using ANSYS-CFD
Hydrodynamics Analysis of Ships Side by Side in Waves using AQWA and Resistance and Diffraction Simulation over a Ship Hull using ANSYS-CFD
Franz Zdravistch, Ph.D.Technical Account ManagerFranz Zdravistch, Ph.D.Technical Account Manager
© 2008 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary
Technical Account ManagerANSYS Inc.Technical Account ManagerANSYS Inc.
OutlineOutlineOutlineOutline
• Hydrodynamic analysis of ships side by side in Hydrodynamic analysis of ships side by side in Hydrodynamic analysis of ships side by side in Hydrodynamic analysis of ships side by side in
wavewavewavewaves– Introduction to modeling ships side by side
– Theoretical background of potential flow– Numerical examples and discussion
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• Resistance and Diffraction Simulation over a Ship Resistance and Diffraction Simulation over a Ship Resistance and Diffraction Simulation over a Ship Resistance and Diffraction Simulation over a Ship
Hull using ANSYSHull using ANSYSHull using ANSYSHull using ANSYS----CFDCFDCFDCFD
– RANS CFD Solver: ANSYS-FLUENT– DTMB 5415 geometry description– Resistance Test case– Steady Resistance Test case
• ConclusionsConclusionsConclusionsConclusions
Introduction (1)
• Motivation
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Offshore LNG offloading system(M. Naciri, OMAE’ 2007)
Replenishment-at-sea
Operational condition► personnel and structural safety
● AnalysisRelative motions,mooring forces, etc
under wave, wind, current (forward speed)
Introduction (2)
●Difficulty: Standing waves between the gap
Incident wave(a = 1.0m,β = -450 )
Causes:
● Resonant fluid motion
in restricted region,
● Unrealistically enlarged
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Diffraction wavea(max)=2.2m
by ideal fluid theory.
Consequences:
● Inaccurate RAO results,
●Divergent in time domain
Introduction (3)
●Methods for suppression of standing waves
Potential theory, boundary integration approach,Fictitious lid elements on free-surface between gap
► Rigid lid (Huijsmans et al, 2001)
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► Rigid lid (Huijsmans et al, 2001)
► Flexible lid with defined modal shapes
(Newman, 2004)
► Free surface damper lid
(Chen, 2004)
used in this case
Lid elements
Theoretical background (1)
● AssumptionIdeal fluid , irrotational and incompressibleSmall wave elevation
● Governing equationsLaplace equation in fluid regionBody boundary conditionFar field radiation condition,
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Far field radiation condition,Seabed conditionFree surface condition
● Boundary integration approach
with pulsating source Green’s function,S: wetted hull surface only
dszyxGzyxs
),,;,,(41
),,( ζηξσπ
ϕ ∫∫=
Wetted surface under water
(in blue colour)
Theoretical background (2)
• Free surface damper lidConventional linear free surface condition
Absorbing beach in non -linear time domain
02
=−∂∂ φωφ
gze
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Absorbing beach in non -linear time domain
Damped free surface condition on lid
),()(21
),(
e
e
gDt
DDt
D
φφνφφηφ
νφ
−−∇⋅∇+−=
−−∇= xxx
Damping factor
Wetted hull surface with lid elements
(in blue colour)
0)( 22
=−+∂∂ φαωφ
igz
Numerical calculation and
Discussions (1) Kodan Model
3.1 Kodan ModelModel test: Conventional ship with a rectangular barge (Kodan,1 984)
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Ship: Lpp =2.085m, d R =0.131m; Barge: Lpp =3.125m, d R =0.113m; P L=1.2m
Motions and forces were measured (Fn=0.0)
Principal dimensions only were known, estimated body plans used for numerical calculation
Numerical calculation and
Discussions (2) Kodan model
• Damping factor effects on resonant response (standi ng wave) (ω=0.72rad/s, β=-450)
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► Damping lid suppresses waves► Proper damping factor needed
Amplitude of diffraction wave
without suppression,
scales to 2.5m, for 1m incident wave
α=0.01
α=0.1
Numerical calculation and
Discussions (3) Kodan model
• Damping factor effects on diffraction waves (ω=0. 45rad/s, β=-450)
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α=0.01
α=0.1
Amplitude of diffraction wave
without suppression,
Scale=1.2m, for 1m incident wave
► Damping lid suppresses waves,► Wave pattern keeps unchanged,► Amplitude changes, but not big
as at standing wave frequency
Numerical calculation and
Discussions (4) Kodan model
• Damping factor effects on wave exciting forces
0.2
0.3
0.4
ζζ ζζAW
R
hydro-int non-inter vlid=0.01vlid=0.02 vlid=0.1 test(Kodan, 1984)
0.6
0.9
1.2
gζζ ζζA
WR
hydro-int non-inter vlid=0.01vlid=0.02 vlid=0.1 test(Kodan, 1984)
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► Hydrodynamic interaction is evident <=> standing wave is due to this interaction► α=0.01 gives closer results► α=0.1 over-damped the wave exciting forces at sta nding wave frequency
0.0
0.1
0.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
(ωωωω **2/g)dR
F2
/ ρρ ρρg ζζ ζζ
0.0
0.3
0.6
0 0.2 0.4 0.6 0.8 1 1.2 1.4
(ωωωω**2/g)dR
F3
/ ρρ ρρg
Numerical calculation and
Discussions (5) Kodan model
• Damping factor effects on ship motions
0.4
0.6
0.8
1
Sw
ay /
ζζ ζζ
hydro-int non-inter plid=0.01
plid=0.02 plid=0.1 test(Kodan, 1984)
0.6
0.9
1.2
Hea
ve /
ζζ ζζ
hydro-int non-inter vlid=0.01
vlid=0.02 vlid=0.1 test(Kodan, 1984)
© 2008 ANSYS, Inc. All rights reserved. 12 ANSYS, Inc. Proprietary
► Hydrodynamic interaction is evident► α increases, RAOs at standing wave frequency decrease► Hull viscous damping not included => α=0.1 is closer because force over-damped
0
0.2
0.4
0 0.2 0.4 0.6 0.8 1 1.2 1.4
(ωωωω**2/g)dR
Sw
ay /
0
0.3
0 0.2 0.4 0.6 0.8 1 1.2 1.4
(ωωωω**2/g)dRH
eave
/
Resistance and Diffraction Simulation over
a Ship Hull: Mathematical Description
• Governing equations:
( ) 0vt
=⋅∇+∂∂ rρρ
( ) ( ) ( )τρρ ⋅∇+−∇=⋅∇+∂∂
pvvvt
rrr
vr
( )
⋅∇−∇+∇≡ Ivvv T rrr 2µτ
: velocity vector in the Cartesian coordinate system
The stress tensor is given by
Mass conservation:
Momentum conservation:
p: static pressure
where µµµµ is molecular viscosity
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( ) ⋅∇−∇+∇≡ Ivvv
3µτThe stress tensor is given by where µµµµ is molecular viscosity
• After Reynolds averaging the above equations can be written as
( ) 0uxt i
i
=∂∂+
∂∂ ρρ
( ) ( )jij
i uux
ut
ρρ∂∂+
∂∂
∂∂
−∂∂
+∂∂
∂∂+
∂∂−=
l
lij
i
j
j
i
ji x
u
x
u
x
u
xx
p δµ3
2 ( )jij
uux
′′−∂∂+ ρ
the Reynolds stresses iji
it
i
j
j
itji x
uk
x
u
x
uuu δµρµρ
∂∂
+−
∂∂
+∂∂
=−3
2''
• Interface tracking between the phases is achieved by solving a continuity equation for the volume fraction of each one of the phases (VOF method)
RANS CFD solver: ANSYS-FLUENT
• Works based on cell centered finite volume discretization schemes
• Works with structured and unstructured (tetrahedral, prism, polyhedral) and hybrid mesh topologies
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prism, polyhedral) and hybrid mesh topologies
• General purpose CFD solver with many physical models and turbulence models
DTMB 5415
• DTMB 5415 : Geometry description– Conceived as a preliminary design for a Navy Surface combatant– The hull geometry includes a sonar dome and transom stern– There is a large EFD database for Model 5415 due to a current
international collaborative study on EFD/CFD and uncertainty
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assessment
• Reference– http://www.nmri.go.jp/cfd/cfdws05/index.html
Resistance: Computational Grid
Outlet
Inlet
• Hexahedral mesh with 1.8 Million cells
• Half domain modeled to exploit
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symmetry
• The ship is fixed i.e. all the 6 degrees of freedom are off
• Average wall Y+ is 36.5
Resistance: Problem description
• Ship Length, Lpp = 5.72 m
• Ship speed = 2.1 m/s (Froude Number = 0.28)
• Fixed attitude
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• Ship moving in calm water
Resistance: Simulation setup
• Turbulence models– Realizable k-e – SST k-omega
• Open channel flow
• Boundary Conditions
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• Boundary Conditions– Inlet boundary: Pressure-inlet– outlet boundary: pressure-outlet– Side, center, top and bottom: symmetry
• Discretization schemes– Modified HRIC for VOF– Second order upwind for momentum and turbulence– SIMPLE pressure-velocity coupling in FLUENT
Resistance: Wave Elevation Contours
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Kelvin wave pattern predicted by ANSYS-FLUENT simulation (filled contours)
Resistance: Wave Elevation Contours
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Kelvin wave pattern predicted by FLUENT simulation (contour lines)
Resistance: Wave Profile and Forces
-0.005
0
0.005
0.01
Z /
Lpp
EXP SST RKE
-0.005
0
0.005
0.01
0.015
0.02
Z /
Lpp
EXP SST RKE
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-0.01
-0.5 0.0 0.5 1.0 1.5
X / Lpp
-0.01-0.5 -0.25 0 0.25 0.5
X / Lpp
Expt. SST RKE
[N] [N] % diff. [N] % diff.
Total Drag 45.08 43.90 2.6 42.45 5.8
Viscous Drag 30.69 30.99 0.9 29.90 2.5
Wave profile along y/Lpp = 0.172 plane Wave profile along the hull
Diffraction: Computational Grid
• Hexahedral mesh with 3 Million cells
• Half domain modeled to exploit symmetry
• Damping zone to apply numerical beach condition
OutletDamping zone
Inlet
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beach condition
• Constant mesh size in the flow direction from inlet to the bow, to preserve the incoming wave form
• The ship is fixed all the 6 degrees of freedom are off
Inlet
Diffraction: Problem description
• Ship Length, Lpp = 3.048 m
• Ship speed = 1.53 m/s (Froude Number = 0.28)
• Fixed attitude, moving into incoming head sea waves
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• Wave length = 4.572 m
• Wave height = 0.018 m
• Resulting encounter period, Te = 1.088 sec
• Resulting encounter velocity, Ve = 4.2 m/s
Diffraction: Boundary Conditions
( )[ ]( ) ( )nnnynx
n n
nnn tykxk
hk
hzkA
v
uεω
θθ
ω −−+×
+=
∑
∞
=
cossin
cos
cosh
cosh
1
( )[ ]( ) ( )nnnynx
nnn tykxk
hk
hzkAw εωω −−++=∑
∞
sincosh
sinh
• Incoming wave boundary condition
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( ) nnnynxn
nn
n hk∑= cosh1
θcoskkx = θsinkk y =where the wave numbers in x-y directions are:
h: calm water tank depthA: wave amplitudeθ : wave headingω: wave frequency
Reference: Kim, M.H., Niedzwecki, J.M., Roesset, J.M., Park, J.C., Hong, S.Y., and Tavassoli, A., Fully Nonlinear Multidirectional Waves by a 3-D Viscous Numerical Wave Tank, ASME J. Offshore Mecahnics and Arctic Eng., Vol. 123, August 2001
Diffraction: Simulation Setup
• SST k-omega turbulence model• Open channel flow• Boundary Conditions
– Inlet boundary: Pressure-inlet – outlet boundary: pressure-outlet– Side, center, top and bottom: symmetry
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– Side, center, top and bottom: symmetry– Wave bc: through user defined function (udf)– Numerical beach condition at the outlet: through udf
• Discretization schemes– Modified HRIC for VOF– Second order upwind for momentum and turbulence– First order time accuracy– SIMPLE pressure-velocity coupling in FLUENT
Diffraction: Wave Elevation Contours
Incoming waves Waves dampened due to numerical beach conditionShip hull
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Wave elevation contours coloured by wave height, seen from top view
Diffraction: Wave elevation contours
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Wave elevation contours coloured by wave height, diffracted waves
Diffraction: Wave elevation contours
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Wave pattern along the ship hull, with transparent free-surface
Diffraction: Wave elevation contours
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Experiment ANSYS-FLUENT
Diffraction: Forces & moment
0
0.002
0.004
0.006
0.008
0.01
0.012
Cd
EXP CFD
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
Ch
EXP CFD
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-0.002
0 0.5 1 1.5 2 2.5 3
t / Te
Drag Force coefficient (Cd) Heave Force coefficient (Ch)
Moment coefficient (Cm)
-0.1
0 0.5 1 1.5 2 2.5 3
t / Te
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0 0.5 1 1.5 2 2.5 3
t / Te
Cm
EXP CFD
Conclusions (1)
Side-by-side ships floating in waves• Standing wave (resonant response of fluid in restri ct region)
exists;
• Its amplitude needs to be damped if using potential theory
• Free surface damping lid method is an applicable/re liable
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• Free surface damping lid method is an applicable/re liable approach;
• Damping factor on lid is about 0.01, but more exper imental data needed.
Conclusions (2)
• The RANS CFD solver ANSYS-FLUENT is used to validat e resistance and diffraction tests
• The resistance simulation was performed using SST k -w and Realizable k-e turbulence models and the SST model found to give b etter results
• The resistance drag predictions were of the order o f 0.9% to 5.8% error
© 2008 ANSYS, Inc. All rights reserved. 32 ANSYS, Inc. Proprietary
• The diffraction simulation results show good qualit ative comparison in terms of the wave elevation contours
• The diffraction force predictions show phase differ ence and error in the peak force predictions, one of the reasons for the discrepancy could be first order time accuracy
• Overall results show good comparison with the exper imental data for a real life application
Conclusions (3)
• Both AQWA and ANSYS-CFD provide useful and complementary design information – AQWA simulations much faster than CFD. Allows for p reliminary
evaluation of larger number of design options– CFD simulations provide more detailed physics, incl uding viscous
effects
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• Currently working on integrating AQWA-Suite and ANSYS-CFD:
– Couple potential flow and viscous effects (where ne eded) for increased accuracy and efficiency
– Use a unified environment (Workbench) for case set up, execution and post-processing