Response of Cylindrical Floating Structure Subjected to an Underwater Explosion

Response of Cylindrical Floating Structure Subjected to an

Underwater Explosion

Akihiko Imakita*, Akihiro Yasudc,*

ABSTRACT

This paper describes numerical simulations and experimental results of the dynamic response ola cylindrical floating

structure subjected to an underwater explosion. An explosion was generated under the center

of

structure s bottom plate

by wire explosion method. The responses

of

the structure were recorded in the experiments with three different offset

conditions. Nonlinear explicit /ìnite element method and fìnite volume method were used for the structural analysis and

the fluid analysis, respectively. The compress ibilitv o/fluid and fluid-structure interaction were taken into account in the

numerical simulation. Explosion bubble shapes were observed with a high speed camera and were compared with the

numerical simulation results. Time histories of pressures on the bottoni surface and displacement

of

the bottoni plate

measured during the experiments were also compared with the numerical simulation results. As a result of this

comparison, it was found thai numerical simulations

of

the dynamic response of the cylinder corresponded well with

experimental results. Finally, discus,sions are given to boundamy effects on the behavior of the explosion bubble and

offset distance efjècts on the responses o/the structure.

1.

INTRODUCTION

Number of terrorist incidents using explosives has increased

in recent years, and interest as to the effects of explosions on

maritime structures

is growing. Research on the effects of

explosions on structures

both underwater and above the

waterline has mainly focused on naval vessels.1> 2> However, some studies on underwater explosions have been carried out in

Japan as part of industrial research conducted on bridge

foundations.3>

When an explosive is detonated in water, pressure waves and

an explosion bubble are generated, and structures respond to changes in the surrounding fluid. Pressure waves consist of

shock waves (incident shock wave) generated during the

explosion and bubble pulses generated when a bubble reaches its smallest diameter and expands again (rebound). Underwater explosions may be divided into three categories - long distance explosions, close explosions, and contact explosions. In a long distance explosion, the explosion occurs far from the structure

and pressure waves are the primary factors affecting the

structure. In a close explosion, the explosion occurs

comparatively close to the structure, and the effects of both

pressure waves and an explosion bubble on the structure have

to be taken under consideration. In a contact explosion, the explosion occurs on the surface of the structure, and both the high temperatures and high pressure gas generated during the explosion as well as pressure waves and the explosion bubble

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need to be taken into consideration.

Previously, research using a simplified method has been

conducted on two-node whipping of hull structures 4) arising from explosion bubbles assumed to be of spherical shape. A study on structural responses to explosion bubbles

accompanying large deformation in potential flows has also

been conducted. Due to advances in computer technology,

explosions and the response of structures in their vicinity have

become the objects of studies

via large-scale numerical analyses. However, practically no study has been carried out on

the response of structures to close explosion, especially

considering expansion and contraction of an explosion bubble in addition to shock wave due to fluid compressibility.

This paper discusses both numerical analysis and experiments carried out to study the effects of close explosions on structures.

When a bubble contracts near a structure, a deformation is

created on the bubble surface on the opposite side of the

structure and evolves rapidly. Finally, a high speed water flow

(jet) develops in the direction of the structure penetrating the

bubble. This phenomenon is also studied in

the field of

cavitation, and is

considered to be one of the causes of

propeller damage in ships and other fluid machinaries.6 For this reason, it is important to consider the effects of pressure

due to the jet and the bubble pulse (in this report, the combined

pressure due to both of these components is called "bubble collapse pressure") when studying the response of structures

subjected to a close explosion.

During an underwater close explosion, resonance phenomena

occur when the period of bubble oscillation is close to the

whipping period of the hull girder, and this resonance may lead to total collapse of the hull. On the other hand, structures close

to the explosion may be damaged due to the incident shock

wave and bubble collapse pressure. When such damage occurs,

longitudinal bending strength is reduced. In such cases, it is important to consider not only the distribution of external

forces in space, but also the relationship between bubble

dynamic behavior and structural response. Therefore, the series of phenomenon must be analyzed considering a fluid-structure

interaction in order to understand the effects of underwater explosions, including the effects of the jet on the structures.

The authors conducted experiments and numerical analyses, and studied the effects of underwater explosions on structures with consideration of fluid-structure interaction. In this paper,

the authors report the results of studies on the behavior of a cylindrical floating structure subjected to underwater close

explosions.

2.

Experimental method and results

Experiments on underwater explosions were carried out using a wire explosion apparatus. A schematic of the wire explosion

circuit of the apparatus is shown in Fig. I. In this apparatus. electrodes fitted with copper wire are immersed in water and an explosion is generated by instantaneously discharging electric energy stored in the capacitor. This type of apparatus offers a number of advantages, including explosions that can be safely

tested in the laboratory, easy experimental set up, and the

ability to perform multiple experiments consecutively in a short amount of time: and to easily adjust the scale of the explosion.

A schematic of the apparatus is shown in Fig. 2. Fig. 3 shows the wire explosion setup. The water tank had a length of 3.0 m, idth of2.0 m and depth of2.0 m. Acrylic windows were fitted

on the side walls of the water tank and the explosion was

visually recorded (1000 frames per second) using a high speed

camera through these windows. The water depth during the

experiment was 1.6 m.

As shown in Fig. 4, a cylindrically-shaped structure was tested. The material was mild steel, and the dimensions of the structure

were as follows: outside diameter: 0.4064 m, depth: 0.35 m,

bottom plate thickness: 18 mm, and side panel thickness: 8 mm.

A pressure gauge (Kyowa PS-300KSA32) was fitted at the center of the bottom plate of the cylindrical structure. The

displacement of the center of the bottom plate was measured using a laser displacement sensor (Keyence LB-300). The laser displacement sensor was installed on a beam fixed to the wall

2

of the water tank. The cylinder was made to float at the center

of the water tank and the draft was 0.285 m. A Tourmaline gauge (PCB138AIO) was installed at a position 0.3 m away from the center of the explosion at the same depth as the

explosion depth. Pressures were measured on the bottom plate of the cylinder and in the fluid. Measurement sampling was I

tsec for pressure gauge and 900 Hz for the displacement

sensor. Charging equipment Switch i Resistance Switch 2 Condenser

Figure 1 Wire explosion circuit

Pressure Gage Explosive Point

Pote Wire

Figure 2 Schematic view of test apparatus

Figure 3 Wire explosion setup

Video Camera

Figure 4 Test structure

Table I shows the test conditions. In CASE 1, the explosion

was initiated in water with no cylindrical floating structure, and

the pressure and bubble behavior were observed. In CASE 2.

the cylinder was fixed in position using a jig, and the pressure

on the bottom plate was measured. In CASES 3, 4. and 5, the

cylindrical floating structure was not constrained. The distance

from the center of the explosion to the bottom plate of the cylindrical floating structure (offset) was set at 0.1 m, 0.12 m

and 0.14 m, respectively. The effect of the offset on the

response of the cylindrical floating structure was observed. The charged energy in the wire explosion was 2.5 ki for all cases.

Fig. 5 shows the pressure time history (0.3 m distance from

the explosion). Fig. 6 is a high-speed photograph showing the bubble behavior. The photos on the left of the figure show the experimental results, while those on the right are the numerical analysis results. The results of numerical analyses shown in the

figure are discussed later. Fig. 7 shows the time history of the bubble radius. This radius is obtained from the high-speed

photograph. The pressure peak at 18.7 msec in Fig. 5 is the one due to the bubble collapse pressure.

From these figures, the first period from the expansion to the contraction of the bubble is obtained by subtracting the arrival

time of the incident shock wave (0.22 msec) from the time of

bubble collapse peak pressure

(18.7

msec). which gives

18.5 msec. The time from the generation of the incident shock wave to the first bubble collapse peak pressure is herein called

the first bubble period, while the time from the first bubble

collapse peak pressure to

the next bubble collapse peak

pressure is called the second bubble period. As found from

high-speed photographs, the maximum bubble radius was

0.115m.

Fig. 8 shows the pressure time history at the center of the bottom plate in CASE 2. The bubble behavior in this case is shown in Fig. 9. The noise before and after the arrival time of the incident shock wave was large, and the peak pressure of

incident shock wave could not be measured from the pressure time history.

o

Figure 5 Experimental results of pressure time history (0.3 m from explosion center, CASE I)

Figure 6 Bubble shape (CASE I)

(Left side : experiment, Right side : numerical simulation) (i): I msec,(ii):5 msec,(iii): 10 msec,(iv): 15 msec.(v):20 msec

By assuming a speed of sound 1500 mIs in water, the shock

wave is considered to have arrived at 0.07 msec, and since the

first peak of the bubble collapse pressure is at 21.3 msec. the bubble first period is estimated as 21.2 msec. This is longer

than 18.5 msec in CASE I, suggesting that structure affects the behavior of the bubble and the period of the bubble oscillation.

0.14

Experunnt

-//

0 2 4 6 8 10 12 14 16 18 20

Tütze (mzec)

Figure 7 Time history of bubble radius (CASE 1)

Cond. No.

Offset distance (m)

Cylinder CASE I depth 0.3 none

CASE 2 0.1 fixed

CASE 3 0.1 free

CASE4 0.12 free

(ASE 5 0.14 free

Table I Test condition 0.12

o 10 15 20 25 30 Tizne (rnse) 0.1 0.08 0 0.06 Cylinder 0.64 Offset 0.02 O

o o

k.

5 10 LS 20 Time (msec) 25 30 35

Figure 8 Experimental results of pressure time history at the bottom plate center (CASE 2)

Figure 9 Bubble shape (CASE 2)

(Left side : experiment, Right side : numerica! simulation) (i):l msec,(ii):5 msec,(iii):l0 msec,(iv):15 msec,(v):21 msec

The displacement time histories at the center of the bottom

plate for CASE 3 to CASE 5 are shown in Figs. 10 to 12,

respectively. The displacement in the upward direction is

positive.

As shown in Fig. IO. the displacement of the bottom plate of the cylindrical floating structure (offset 0.1 ni) shows a period that coincides with the first bubble period, but effects of local ibration also exist. Excluding the effects of local vibration, the

maximum displacements for CASE 3, CASE 4, and CASE 5

were approximately 0.0079

ni. 0.0070 ni and 0.0064 ni,

respectively. In actual measurement data, very large

displacement was recorded in the initial stage of the explosion,

but this was electrical noise and it has not been shown in the

figures. This noise was a temporary phenomenon, and its effect probably disappeared in the initial stage of the explosion.

No residual deformation was observed in the bottom plate of

the cylindrical floating structure after the experiment; so it is regarded that the material did not reach the plasticity range

during the experiment. 4

0,01 0.008

-0,002

Figure 10 Experimental results of displacement time history (CASE 3) 0.01 0.008 f 0.006 o 0.004 0002 -0.002 5.01 0.006 o -0.002 lime mmc) Time (msec)

Figure 12 Experimental results of displacement time history (CASE 5)

3.

Numerical anah'sis model

Numerical analysis was performed considering the following conditions:

I) Compressible and inviscid fluid

Explosion bubble is a non-condensable gas; air is an ideal

gas

Gravity effects

Fluid-structure interaction

Large deflection of structure (geometrical non-linearity)

The relation between the density, energy and pressure of the

fluid was expressed as an equation of state, and modeled using

Euler elements. The following equation was used as the

equation of state of the waler:

ClassNK TECHNICAL BULLETIN 2009

o o 0.004

0.002

5 10 15 20 25 30

Time (moco)

FigLlrc li Experimental results of displacement time history (CASE 4) 10 15 20 25 30 0.004 0.006 o o 0.002 S lO 15 20 23 30 18 16 14 12 10 4 2

11=

(1)

P is the pressure (Pa), p is the density of water (kg/rn3). .()

is the initial density (1000 kg! m3), a, is the bulk modulus (=

2.1 x l0 Pa). y form was used in the equation of state of air.

P = (y - l)p, Eaj,.

(2)

y is the specific heat ratio (= 1.4), while Ea,r is the internal

energy (i/kg). The Jones-Wilkins-Lee (JWL) form was used in the equation of state of the gas in the explosion bubble.

i \ -R1

/

\ -R,

(O17

P=A 1-

e

+B 1---

e

\

R,1

(3) Coefficients used were: A= 3.712 x 10" Pa, B=0.32l x 10''

Pa, R,=4. 15, R,=0.95, (0=0.3. q =p _{'Pg.o, Pguu.0l630 kg/rn3,}

E,,4.29 x iø' J/kg. 7)

To apply The JWL form, which is the equation of state of the explosive gas, to the wire explosion, the equivalent mass of the explosive must be determined. The equation obtained from Ref. (8) was used to determine the equivalent mass.

/3

Rrn,1. =12.67 ,, (4)

(D+33)

-The unit system for Rmax: Maximum bubble radius in feet, W is the mass of the explosive in lb, and D is the depth of water in

feet.

The coefficient in Eq. (4) is derived from the conventional explosive, TNT. The TNT mass for the maximum radius of 0.115 ni was determined from Eq. (4), based on the results of

the experiment in CASE I with no cylindrical floating structure.

as 4.05 x 10 kg. This equivalent mass was used as the initial condition in the analysis.

Fig. 13 shows the finite element mesh distribution of fluid and structure. The fluid model had a volume which is an extension of a sector with a 15-degree angle. The radius of the sector was

I m, which is half the width of the water tank. The upper part

of the model element is the air layer, and its initial condition is

1 atmosphere (0.10 13 MPa). The boundary condition of the

upper surface of the air layer was a constant pressure of

I

atmosphere: rigid boundary conditions were assumed for other boundaries. The bottom plate of the structure was a 15-degree

sector, same as the fluid model, with side walls attached

vertically on the bottoni plate. Shell elements were used for the

structure. The elastic modulus was 2.1 x 10'' Pa. and the

Poissons ratio was 0.3.

The numerical analysis code used was MSC-DYTRAN 9) In

MSC-DYTRAN, the fluid is analyzed using the finite volume

method, and the structure is analyzed using the finite element method in the code. In this analysis. the General Coupling

function was used for the fluid-structure

interaction. This function judges the volume occupied by the inner sides of the structure in the fluid element, and calculates the pressure acting on the boundary of the structure.

Using the model mentioned above, time domain numerical

analysis was carried out on the dynamic response of the

cylindrical structure to an explosion and on explosion bubble

behavior under the free surface.

Side Shell

Bottom Plate

Firnd

Figure 13 Simulation model

Water

4.

Comparison of experimental and

numerical results and discussion

Figs. 14 and IS show the pressure time histories at a position

0.3 m from the center of the explosion in CASE I. Fig. 14

shows the incident shock wave, while Fig. 15 shows the bubble collapse pressure. The peak pressure is smaller in the numerical

analysis compared to experimental results. High frequency pressure can be observed in the numerical analysis results in

Fig. 14. This is attributed to the slightly larger element size 0.3

ni away from the center. However, if the duration of incident

shock waves is smaller than the response period of the structure. pressure impulse (time integration of pressure) becomes more

important than the pressure peak of the shock wave in

structural The duration of both the incident shock

wave and the bubble collapse pressure is extremely short

compared to the structural response. Impulse is, therefore, an important factor for studying the effects on the structure. The

impulse of the incident shock wave was 178.8 Pas in the

experiments and 167.6 Pas in the numerical analysis, while

the bubble collapse pressure was 229.1 Pa-s in the experiments

and 201.2 Pa-s in the analysis. The difference is 6.3% for

incident shock wave and 12.2% for bubble collapse pressure.

From the above, it can be observed that the peak value of pressure by numerical analysis is lower than that from the

experiments; however, the integration of pressure with respect

to time (impulse) is in close agreement: and thus numerical

analysis captures the characteristics of pressure variation very well. The first bubble period is 18.5 rnsec in the experiment and

lo 8 0 -2 o 20 18 16 14 12 10 4 2 o 20 E,'perimnit Simulation 0.2 0.4 0.6 Time (mseC)

Figure 14 Pressure time history at 0.3 m (CASE 1)

Experiment Simulenon

A

jI'ÄVL

JI

18.7 msec in the analysis: the difference between the two

results is 1.1%.

Comparison of bubble shapes between experiment and

numerical analysis

result shown in

Fig.

6 shows good

agreement. As for the time history of the bubble radius shown

in Fig. 7, although the maximum radius is slightly smaller in the results

of

numerical analysis compared with the experimental results, the overall trend shows satisfactory

agreement.

Fig. 16 shows a comparison between the experimental and analysis results of pressure time histories at the center of the

bottom plate in CASE 2. This figure shows the time history of

bubble collapse pressure. The experimental results show two

peaks: however, the two pressure peaks are not obiously

found in the numerical analysis results. The reason that two peaks are seen in the experimental results is because of the difference between the time when a bubble rebounds arid the time when the jet penetrates the bubble. On the other hand, to

obtain more accurate pressure peak in the analysis, the shape of

the bubble at the

smallest diameter must be calculated

accurately in the analysis, and for this, a finer finite element mesh is necessary. However, calculation of impulse values

from 20 msec to 25 msec shows that the impulses are 5306 Pa

s and 5205 Pa s

in the experiments and in the analysis.

respectively, indicating a difference of 2%. The impulse values of bubble collapse pressure show satisfactory agreement. The numerical analysis is thus considered to have adequate

accuracy for simulating structural response.

The numerical analysis results of the flow velocity vector distribution of the fluid at 21 msec are shown in Fig. 17. This

figure shows half of the transverse section. It is shown that the

bubble becomes donut shaped (toroidal), because of the

penetration of the jet, which is also striking the bottom plate of the structure. The maximum flow velocity at 21 msec is 90 rn/s.

pp

r1'.

!-

_,

ii.uuui

1'.1

'1

I UkiUUUUI.,..

.

!t

uuuuai. .isi ! (s) ills) . u

i . III

zI

z ¡.

u...

liii

iiii.iuu

BiiI:ible

i...

ii

iiuuuuuu_

_im

iiaaaiisuuuuuu

auusuuuuuuuuuuuuuuu

_{uuuuuuuuuuuuuuu}

umsuuuuuuuuauuuuuu

Figure 17 Numerical result of velocity vector distribution at 21 msec (CASE 2)

()

_{ClassNK TECHNICAL BULLETIN 2009}

o

15 16 17 18 19 20 21 22 23 24 25 Töne (msec)

Figure 15 Pressure time history at 0.3 m (CASE 1)

21 22 23 24 25

Tinte Imsec)

Figure 16 Pressure time history at bottom plate center (CASE 2)

0.8

i

lo I I I I

Expenment - Simulalion

According to analysis results, the first bubble period was 21.4

msec. The fact that the first bubble period is strongly affected by the structure in CASE i is seen in the analysis results as well.

Comparison of the bubble shapes in Fig. 9 shows that the bubble contracts and translates toward the bottom plate of the structure. This shows different behavior from that of CASE I

under the free surface. The results of numerical analysis

correspond very well with the results of experiments.

Figs. 6 and 9 show that when there is no structure above the

explosion, the bubble remains at the center of the explosion and

expands and contracts; however, when a structure exists, the

bubble approaches the structure during contraction. Generally,

the bubble in fluid rises due to the effects of gravity, but if a free surface exists, it may descend depending on the distance

between the free surface and the bubble» The explosion depth in CASE I was 0.3 ru: however, since the bubble has remained

at the position of explosion. it has probably been affected by

the free surface.

Figs.

18 to 20 show the displacement time history by

numerical analysis at the center of the bottom plate of the

structure. For all eases, the experimental results and analysis results show good agreement. The features of the dynamic response of the cylindrical floating structure to the incident

shock waves, expansion and contraction of bubble and bubble

collapse pressure, have all been satisfactorily captured by

numerical analysis. Fig.

18 shows the displacement time

history of the ends of the bottom plate by numerical analysis.

The displacement at the ends of the bottom plate coincides with the displacement at the center of the bottom plate except local vibration, suggesting that the entire cylindrical floating structure moves as a rigid body in the vertical direction. Modal

analysis of the cylinder in water was carried out using the

singular point distribution method. The results indicate that the

natural period for the heaving motion of the cylinder is 1.45 s (0.690 Hz). and the natural period of local vibration of the bottom panel as 1.66 msec (604.2 Hz). The high frequency

vibration observed in the displacement time history (Figs. 18 to 20) is regarded local vibration of the bottom panel.

By comparing Figs. IO and 18 and observing the maximum displacement of the cylindrical floating structure seen in the

second bubble period, it

is found that the results of the

numerical analysis give slightly larger values of the

displacement than the experimental results. Table 2 shows the results of the comparison of the maximum displacement at the

mean values, excluding local vibrations. The difference in

maximum displacement in the first bubble period is 6.0%, and in the second bubble period is 20%. The reason the difference

g E 0.004 2- 0.002 0.008 0.006 0.004 0.000 0.010 0.008 0.000 .0002 0.010 E' 0.002 0.000 -0.002 BotIomplate edge

WA__

va__

7

Maximum dis'slacement (ru) Ist period 2nd period Experiment 0.0079 0.003 7

Simulation 0.0084 0.0046 0.010

o 10 15 20 25 30

Time (msee)

Figure 19 Numerical results of displacement time history (offset 0.12 m, CASE 4)

0 5 10 15 20 25 30

Time (UISCC)

Figure 18 Numerical results of displacement time history (offset 0.1 ru, CASE 3)

o 10 15 20 2.5 30

TIme (msec)

Figure 20 Numerical results of displacement time history (offset 0.14 m, CASE 5)

in the second bubble period is larger,

is that if the JWL

equation of state is used for the explosion gas, then the effects of the composition and temperature of the gas in the bubble are

somewhat different from the explosion gas of the wire

explosion. Attention must be paid in studies of structural

response up to the second bubble period, but, the numerical analysis up to the bubble second period may be considered to

correspond well to the experimental results.

Table 2 Maximum displacement (CASE 3) 0.008 E 0.006 E 0.004 0.002

Next, the effects of offset were studied by numerical analysis. The time history of displacement when the offset was taken as 0.06 m, is shown in Fig. 21 together with the results for offsets of0.l m, 0.12 m and 0.14 m. As seen from the figure, the offset that gives the maximum displacement in the bubble first period

is 0.06 ni, and the offset that gives the maximum displacement in the bubble second period is 0.1 m. Estimating the response of the cylindrical floating structure in the bubble second period

from the response of the cylindrical floating structure in the bubble first period is difficult because the bubble behavior, such as the jet, affects the motion of the cylindrical floating

structures. 0.012 0.010 0.008 0.006 0.004 0.002 0.000 -0.002 6000 5000 4000 3000 ¡ 2000 1000 offset m 0.06 0.1 0.12 0,14 -- 0.12 -i'- 0.14 -- 0.06 -- 0.08 -e- 0.1 -e- 0.12 -- (4.14

Figs. 22 and 23 show the distribution of impulse values in the

radial direction of the bottom plate of the structure obtained

from numerical analysis. Fig. 22 shows the impulse due tcl the

incident shock wave, while Fig. 23 shows the impulse due to bubble collapse pressure. Comparison of these figures shows

that the impulse duc to bubble collapse pressure is larger than the impulse due to the incident shock wave.

The impulse due to the bubble collapse pressure when the

offset was 0.1 m. was 10.5 times larger than the impulse due to the incident shock wave.

Fig. 23 shows the tendency of the distribution of' impulse

values at the bottoni plate of the structure to concentrate at the center

of the

bottom plate when the offset becomes

approximately the same as the maximum bubble radius. lt is

found from the displacement time history of the bottom plate,

that the amplitude of the local vibration in the second bubble period increases as the offset decreases. The features of the pressure distribution due to bubble collapse are considered to

be related to the bubble position at the time of its collapse. Fig. 24 shows the shape of bubble at the time of collapse in the case

of a 0.14 m offset. lt can be observed from this figure that the bubble is far from the surface of the structure. On the other

hand, in the case of a 0. 1 m offset, the bubble is in contact with

the surface of the structure (see Figs. 9 and 17), and the

position of bubble collapse is near the surface of the structure.

From this result, it can be concluded that the high impulse values concentrates at the center of the bottom plate because

the bubble collapse is close to the bottoni plate.

Fig. 25 shows the relationship between offset and impulse due

to bubble collapse pressure at the center of the bottom plate.

From this figure, it can be concluded that for close explosions.

the impulse becomes maximum when the offset is

approximately equal to the maximum radius of the bubble.

CIassNK TECHNICAL BuLLETIN 2009

6000 5000 4000 8 3000 2000 1000 0.06 --- 0.08 -e- 0.1

Distance (m) _{Figure 24 Numerical result of bubble shape at 19 msec}

Figure 23 Offset effect on distribution of impulse due to bubble (offset 0.12 m, CASE 4) collapse (numerical result)

0 5 10 15 20 25 30

Time (msec)

Figure 21 Offset effect on displacement (numerical result)

o

o 0.05 0.1 0.15 0.2 0.25 Oistnce (m)

Figure 22 Offset effect on distribution of impulse due to incident shock wave (numerical result)

6000

1000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Offset (m)

Figure 25 Offset effect on impulse due to bubble collapse (numerical result)

From the above, it can be understood that not only the scale of the explosion with a parameter of explosive mass but also the

offset are important parameters in considering the effects of

underwater close explosions on structures.

5.

CONCLUSIONS

The response of a cylindrical floating structure subjected to underwater close explosion was studied by experiments and numerical analysis. The fluid-structure interaction and the

compressibility of fluid were considered in the numerical

analysis, and the gas in the explosion bubble was modeled using

the JWL equation.

In the experiments, underwater

explosions were initiated directly under the cylindrical floating

structure using a wire explosion apparatus, and experiments

were conducted under three different offset conditions.

Moreover, analysis using different offset conditions from the

experimental conditions was carried out to study the effects of

offsets on structural response. The conclusions, based on the results of comparison with experimental results and analysis

results, were summarized as follows:

Although there were differences between experimental and analysis results regarding peak pressure, numerical analysis using the JWL equation of state and equivalent mass of explosive gave fairly good results with regard to pressure impulses which are important parameters in structural response.

The period of vertical movement of the structure coincided with the bubble period. Its amplitude was affected by the position of explosion under the condition keeping the constant explosive mass.

The structural response in second bubble period can not be estimated by the one in the first bubble period. In order to obtain it, it is necessary to carry out the numerical analysis taking incident shock wave, bubble behavior, bubble collapse pressure, and structural response into account.

The impulse given by the bubble collapse pressure on the bottom plate is larger than the one given by the incident shock wave. The distribution of impulse concentrates around the center of the bottom plate when the offset is smaller than maximum bubble radius. Maximum collapse pressure impulse is obtained when the offset is roughly equal to maximum bubble radius.

Acknowledgements

are grateful to Prof. Arai of Yokohama National University for his invaluable assistance to the authors in the

writing of this report.

REFERENCES

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1996, pp. 167-174

Umemoto, K., "Structural response of a submerged cylindrical shell subjected to shock pressure loads" (in Japanese), doctoral thesis, Osaka University, 2000 "Underwater blasting" (in Japanese). Research Institute for Safety Engineering. 1985, Sankaido

Hicks, A. N., "Explosion Induced Hull Whipping". Advances in Marine Structure, 1986, p.390

Hung. K. C. et al.. "Modeling and Simulation of Bubble Dynamics and Its Effects on submerged Structure". Proceedings of 74th Shock and Vibration Symposium.

2003

"Cavitation - Fundamentals and Latest Advances - New Edition" (in Japanese). edited by Kato, Y., Maki Shoten,

1999

Shin. Y. S. and Chisum. J. E.. "Modeling and Simulation of Underwater Shock Problems Using a Coupled

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Cole, R. H., "Underwater Explosion", Princeton University Press. 1948

"DYTRAN Theory Manual", MSC Software, 2007 Shibue, T., Itoh, N., Nakayama, E., "Structural response analysis of cylindrical shell subjected to surface impact" (in Japanese), Journal of the Society of Naval Architecture of Japan, No. 1 74, 1993, pp. 479-484 9 5000 4000 3000 2000