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.

Thank you for your attention!

Q & A