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Numerical simulation of surface ship hull beam whipping response due to submitted underwater explosion Presenter / Ssu-Chieh Tsai

Supervisor / Pr. Hervé Le Sourne 1 March 2017, Rostock

1 NUMERICAL SIMULATION OF SURFACE SHIP HULL BEAM WHIPPING RESPONSE DUE TO SUBMITTED TO UNDERWATER EXPLOSION

Motivation

UNDEX Plume Above-Surface Effects


Background

3

• Complete bubble migration process

• First shock wave (Mauricio,2015) o Exponential decay o Empirical approach o Very short time duration (ms)

• Bubble oscillation phase o Non-linear o Longer time duration o Motion of bubble migration o Radius and vertical displacement

NUMERICAL SIMULATION OF SURFACE SHIP HULL BEAM WHIPPING RESPONSE DUE TO SUBMITTED TO UNDERWATER EXPLOSION


Methodology – 3 models

4

• Waveless model

- Consider as an ideal fluid - Without damping effect and the effect of gas bubble pressure inside bubble

• DAA model (Doubly Asymptotic Approximation)

- Considering the interaction between the liquid and gas bubble

- Including damping effect in the liquid

• Empirical model

- Peak approximation method

- Restricted to experienced coefficients, specific material cases


Development of Matlab programs • Developed code in Matlab

• Empirical and analytical models

• Calculate motion of bubble

• Pressure loads

• Test program by 3 charge cases

5


Comparison on 3 different UNDEX cases • The 3 models are tested on:

Case 1: Barras Guillaume’s Case

Case 2: Hunter & Geers’ Case

Case 3: Keith G, Webster’s Case

Case 1 Description mc TNT charge mass, mc= 500 kg

Distance from charge to free surface, = 50 m r Distance from charge to standoff point, r = 50 m

Density of charge, = 1600 kg/m3

Case 2 Description mc TNT charge mass, mc= 0.3 kg

Distance from charge to free surface, = 92 m Density of charge, = 1500 kg/m3

Case 3 Description mc TNT charge mass, mc= 1.45 kg

Distance from charge to free surface, = 178 m Density of charge , = 1500 kg/m3 Radial distance from charge,

6


• Comparison with experience (Case 1) Experience: Barras Guillaume, Numerical simulation of underwater explosions using an ALE method. The pulsating bubble phenomena. (2012)

7

Case 1 / Pressure Case 1 / Radius: a

DAA model is close to Experience model !


• Comparison 3 models for Case 2 & Case 3

8

↓ With damping

↓ With damping

Case 2 / Radius: a

Case 3 / Radius: a

↓Without damping

↓Without damping Case 3 / Pressure

Case 2 / Pressure

← not realistic

← not realistic

Conclusions

Analytical models can be used for various charge materials, mass and water depth

DAA model is more representative of the reality than waveless model



Example 1 : Clamped plate model

Clamped B.C. ( Tx, Ty, Tz, Rx, Ry, Rz) Symmetrical B.C. (Tx, Ry, Rz)

Girder Girder

Frame

Frame Symmetrical B.C. (Ty, Rx, Rz)

4.9 m

8.4 m

10

[30 mm]


• Case1: mc= 500 kg , 𝑑𝑑𝑖𝑖 = 50 m, 𝜌𝜌𝑐𝑐= 1600 kg/m3

Results of clamped plate

11

The deformation seems to be realistic !


• Charge Case 1: mc= 500 kg , 𝑑𝑑𝑖𝑖 = 50 m, 𝜌𝜌𝑐𝑐= 1600 kg/m3

• Length: 150 m, Breadth: 20m, Draft: 8 m

Example 2 : Semi-cylinder model

12

[10 mm]

[20 mm]

[80 mm]

½ L ¼ L

B1

B2

B3

D1 D2

D3

S1

S2

S3

50 m


Pressure loads for semi-cylinder

13

• Charge Case 1: mc= 500 kg , 𝑑𝑑𝑖𝑖 = 50 m, 𝜌𝜌𝑐𝑐= 1600 kg/m3

B1 B2

B3 S1

S2

S3

14

• Results of semi-cylinder model

0.0E+00

1.0E+07

2.0E+07

3.0E+07

4.0E+07

5.0E+07

6.0E+07

7.0E+07

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Ener

gy (J

)

Time (s)

Energies in LS-DYNA

Kinetic Energy Internal Energy Total Energy

Hourglass Energy External Work

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Z-D

ispl

acem

ent (

m)

Time (s)

Z-displacement on Bottom (LS-DYNA)

B1_Elm_9906 B2_Elm_10020 B3_Elm_9681

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 0.2 0.4 0.6 0.8 1 1.2Nod

al D

ispl

acee

nt (m

) Time (s)

Difference of Z-Displacement at Bottom of Cylinder (LS-DYNA)

UZ (B1-B3)

↓High energy ↓High energy


The deflection is realistic.

Analysis process for ANSYS

Model Preparation

• Transient solution • Calculate for all model • Time consumption

Pressure Calculation Direct Integration Method

Modal Superposition

Constraint DOF to all nodes on hull

Static analysis for reaction force

Modal analysis

Transient solution

Create modal basis

Export hull model

Reaction force calculation to nodes

Fluid field mesh

Structural model

OR


• Objective: Convert code from MATLAB to ANSYS language

Example 2: Semi-cylinder model


Pressure load calculation is validated in ANSYS program !


Results of semi-cylinder model

17

• Static analysis

• Transient solution by model superposition

o Displacement is should be zero at time 0

o Too high deflection > 14m !!!

B1 B2 B3

• Modal analysis

Deflection is not realistic !

Example 3 : Frigate ship model


Charge location Charge location

64.7

5 m

40

m

Case Description SF Shock factor = 0.6 mc TNT charge mass, mc= 1296 kg

Distance from charge to free surface, = 64.75 m r Distance from charge to standoff point, r = 60 m

Density of charge, = 1600 kg/m3

• Length of all: 95.0 m • Breadth: 14.0 m • Draught: 4.75 m

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0 0.2 0.4 0.6 0.8 1 1.2

Nod

al D

ispl

acee

nt (m

)

Time (s)

Difference of Z-displacement at Bottom (Frigate ship)

UZ(B1-B3)


Results of Example 3

19

• Transient solution by modal superposition

Deflection seems to be more realistic

Displacement should be zero at time 0


Conclusion

20

• DAA analytical model, representative of the reality, has been chosen

• Secondary bubble oscillation phase has significant influence on structure

• Model superposition method leads to unrealistic results

This method is suitable only for small displacements (it is not the case here)

• Direct integration method


Future work

21

• Perform shock response analysis for one or several embarked materials using

Dynamic Design Analysis Method (DDAM)

• Examples : Shaft line or / and pipes line

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