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Computation and Validation of Springing and Whipping Analyses for Modern Containerships
Jung-Hyun Kim and Yonghwan Kim
Seoul National University
2013.12.20~21 SOE in Osaka University
Research Background
• Hydroelastic responses?
– Wave-induced vibration with natural frequency
– Springing: resonant vibration excited by periodic force
– Whipping: transient vibration excited by impulsive force
• Why is it important?
– Larger ships -> low natural frequency -> springing
– Faster ships -> high encounter frequency -> springing and whipping
– Increased number of cyclic stress
– Increased amplitude of cyclic stress
Accident ex.) MSC NAPOLI structural failure - Date: 2007. 1. 18 - Ship: 4419 TEU containership - Operation condition: 11 knots, wave height 9 m - Large compressive load due to whipping - Source from: http://officerofthewatch.com
Methodology
• Fluid-structure interaction • Fluid: 2-D/3-D potential theory, CFD
• Structure: 1-D/3-D FEM with direct integration/modal superposition
• Coupling: weak coupling (staggered), strong coupling
• Nonlinearity • Nonlinear radiation/diffraction: SOST, CFD, weak scatterer
• Nonlinear Froude-Krylov and restoring: CFD, weakly nonlinear approach
• Water entry slamming: CFD, MLM, GWM, momentum conservation
• Nonlinear components in irregular waves: sum and difference freq. components, multi-directional waves
• Nonlinear incident wave: high order Stokes wave
Objectives
• Validation of numerical analysis for springing and slamming-whipping – 3-D Rankine panel method + 2-D GWM + 1-D/3-D FEM
– Model test of 10,000 TEU and 18,000 TEU containership
– Springing responses to regular waves
– Slamming-whipping responses to regular and irregular waves
Hydroelastic Analysis Procedure
Initializing
Solve Global B.V.P. (3-D Rankine Panel
Method)
Calculate Slamming (Wedge or GWM)
Calculate Motion of Structure (FEM)
Advance Time
Motion Force
Implicit time integration method requires iterative calculation.
Panel model for Global B.V.P. 2-D strips for slamming
1-D or 3-D FEM
Fluid domain
3-D Rankine panel method in time domain Linear potential flow Linearized boundary condition on mean position Weakly nonlinear approach Froude-Krylov and restoring pressure on instantaneously wetted surface
2 0 in the fluid domain
2
2( ) ( ) on the free surfaced d
d d IU Ut z z
1( ) ( ) on the free surface
2
dd d IU g U U
t t
( )( ) (( ) ) on the body surfaced IU U n nn t n
( , ) ( ) ( , ) ( , )I dx t x x t x t
( , ) ( , ) ( , )I dx t x t x t
Coordinate system and notations
2-D Slamming Models
Wedge Approximation
- Approximated with a wedge shape
- Change rates of infinite frequency
added mass
2
Momentum conservation
1 Infinity-frequency added mass2 2 2
aa a
a
dMdF M v M a v
dt dt
bM
y
x
h(t)
H(t)
c(t)
f(t)
Generalized Wagner Model (GWM)
- Exact body shape
- Free surface elevation
- Pressure distribution
- Conformal mapping (by Prof. Korobkin)
2 0 Governing equation
0 ( ( )) Dynamic Free Surface B.C
( , ) ( , ( ), ) ( ( )) Kinematic Free Surface B.C
( ) ( ) ( ( ) ( ), ( )) Body
y
y x
y H t
S x t x H t t x c t
f x h t y f x h t x c t
2 2
Surface B.C
0 ( ) Radiation Condition
( ) ( ( )) ( ) Wave Elevation
( ,0) 0, (0) 0 Initial Condition
x y
H t f c t h t
S x c
Coordinate system and notations
b
Structural Domain
U1
V1
W1
U2
V2
W2
Q’2x
z y
x l
Q2x
Q2z
Q2y
Q’1x
Q1x
Q1z
Q1y
Node 1 Node 2
14-DOFs beam element for Vlasov beam theory
1-D Timoshenko/Vlasov beam (WISH-FLEX BEAM) + 2-D analysis (WISH-BSD) Timoshenko-Vlasov beam theory - Non-uniform torsion (warping) - Coupling of HB and torsion - 14 DOFs for each beam element
2-D analysis - Warping function analysis - Shearflow analysis for effective shear factor
Warping distortion by 3D FE model Warping distortion by 2D analysis
Structural Domain
3-D FEM + Approximation by lower modes (WISH-FLEX 2.5D) 3-D FEM - Sophisticated modelling - High accuracy for non-uniform torsion - Direct stress assessment
Approximation by lower modes - Approximately 10 modes in motion analysis - Lower mode: dynamic response - Higher mode: quasi-static response - Minimized computational burden - Adequate for springing and whipping analysis
2-node vertical bending
3-node vertical bending
4-node vertical bending
Segmented Model Test
Item 10,000 TEU 18,000 TEU
Model Scale 1/60 1/60
No. of segment 6 units 7 units
LBP 321.0 m 382.0 m
Breadth 48.4 m 58.0 m
Depth 27.2 m 30.2 m
Draft 15.0 m 14.4 m
Total Weight 143,741 tons 224,009 tons
Natural Freq. of 2-node VB 0.43 Hz 0.37 Hz
Natural Freq. of 2-node Tor 0.29 Hz Not measured
Test model of 10,000 TEU containership (MOERI, WILS 2/3 JIP)
Test model of 18,000 TEU containership (SHI, NICOP Project)
Nonlinear Springing of Torsion
10,000 TEU containership ( WILS 2 JIP, 2011 )
2nd harmonic springing (150 degree, 17.5 knots, T=6.3 s, H=5.0 m)
3rd harmonic springing (150 degree, 18.0 knots, T=14.1 s, H=5.0 m)
T im e (s )
Mx
(Nm
)
2 0 2 5 3 0 3 5 4 0-5 .0 E + 0 8
0 .0 E + 0 0
5 .0 E + 0 8
W IS H -F L E X B E A M W IS H -F L E X 2 .5 D E x p .
T im e (s )
Mx
(Nm
)
2 0 3 0 4 0 5 0 6 0-2 .0 E + 0 8
0 .0 E + 0 0
2 .0 E + 0 8 W IS H -F L E X B E A M W IS H -F L E X 2 .5 D E x p .
Nonlinear Springing of Vertical Bending
2nd harmonic springing (180 degree, 19.0 knots, T=8.2 s, H=5.0 m)
3rd harmonic springing (180 degree, 18.5 knots, T=10.9 s, H=5.0 m)
10,000 TEU containership ( WILS 2 JIP, 2011 )
T im e (s )
My
(Nm
)
2 0 2 5 3 0 3 5 4 0
0 .0 E + 0 0
5 .0 E + 0 9 W IS H -F L E X B E A M W IS H -F L E X 2 .5 D E x p .
T im e (s )
My
(Nm
)
2 0 3 0 4 0 5 0 6 0-2 .0 E + 0 9
0 .0 E + 0 0
2 .0 E + 0 9
4 .0 E + 0 9 W IS H -F L E X B E A M W IS H -F L E X 2 .5 D E x p .
Nonlinear Springing of Vertical Bending
18,000 TEU containership ( NICOP Project, 2013 )
2nd harmonic springing (180 degree, 20.0 knots, T=9.0 s, H=5.0 m)
3rd harmonic springing (180 degree, 20.0 knots, T=12.0 s, H=5.35 m)
Time
No
rma
lize
dV
BM
40 50 60 70
-1
0
1
2
EXP
WISH-FLEX BEAM
WISH-FLEX 2.5D
Time
No
rma
lize
dV
BM
40 50 60 70
-1
0
1
2
EXP
WISH-FLEX BEAM
WISH-FLEX 2.5D
Whipping in Regular Waves
(Case ID 104: 18 knots forward speed, head sea, H=12.0 m, Tp=14.3 s)
Time [sec]
VB
M[k
Nm
]
40 60 80 100
-1E+07
0
1E+07
WISH-FLEX BEAM GWM
Exp.
Time [sec]
VB
M[k
Nm
]
40 60 80 100
-1E+07
0
1E+07WISH-FLEX BEAM GWM
Exp.
(Case ID 103: 18 knots forward speed, head sea, H=9.0 m, T=14.3 s)
Bow flare slamming dominant case 10,000 TEU Containership ( WILS 3 JIP, 2013 )
Whipping in Regular Waves
Time [sec]
VB
M[k
Nm
]
20 40 60 80-1E+07
-5E+06
0
5E+06
1E+07 WISH-FLEX BEAM GWM
Exp.
Time [sec]
VB
M[k
Nm
]
20 40 60 80
-5E+06
0
5E+06
1E+07 WISH-FLEX BEAM GWM
Exp.
(Case ID 503: 0 knots forward speed, following sea, H=9.0 m, T=14.3 s)
(Case ID 502: 0 knots forward speed, following sea, H=9.0 m, T=13.6 s)
Stern slamming dominant case 10,000 TEU Containership ( WILS 3 JIP, 2013 )
Springing and Whipping in Irregular Waves
(Hs=11.5 m, Tp=16.9 s, Speed=10.0 knots)
time
Inc
ide
nt
Wa
ve
(m)
1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200
-5
0
5
10Experiment
WISH-FLEX BEAM GWM
time
No
rma
lize
dV
BM
1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200-1.0E+00
.0E+00
1.0E+00
Experiment
WISH-FLEX BEAM GWM
18,000 TEU containership ( NICOP Project, 2013 )
Springing and Whipping in Irregular Waves
Band-pass filtered VBM
time
No
rma
lize
dV
BM
1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200
-0.5
0
0.5 Springing (WISH-FLEX)
Whipping (WISH-FLEX)
time
No
rma
lize
dV
BM
1000 1020 1040 1060 1080 1100 1120 1140 1160 1180 1200
-0.5
0
0.5 Springing+Whipping (EXP)
Conclusion
• The computation results show similar 2nd and 3rd harmonic springing responses to
regular waves compared with the model test result.
• The coupled method of 3-D Rankine panel method + 2-D slamming model + 1-D/3-D
FEM gives similar whipping responses with those of the model test in both bow flare
slamming dominant case and stern slamming dominant case.
• GWM and wedge approximation show almost same performances in simulation of
whipping even though the latter method is very simple.
• In the irregular wave condition, the numerical method tends to overestimate
whipping and underestimate springing.