The Interaction of an Underwater Explosion Bubble and an Elastic-plastic Structure

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Transcript of The Interaction of an Underwater Explosion Bubble and an Elastic-plastic Structure

  • 7/30/2019 The Interaction of an Underwater Explosion Bubble and an Elastic-plastic Structure

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    Applied Ocean Research 30 (2008) 159171

    Contents lists available at ScienceDirect

    Applied Ocean Research

    journal homepage: www.elsevier.com/locate/apor

    Review

    The interaction of an underwater explosion bubble and an elasticplasticstructure

    A.M. Zhang , X.L. Yao, J. LiCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China

    a r t i c l e i n f o

    Article history:

    Received 27 February 2008Received in revised form

    22 October 2008

    Accepted 9 November 2008

    Available online 20 December 2008

    Keywords:

    Underwater explosion

    Bubble

    Ring

    Jet

    Elastic-plasticity

    Structure

    Surface ship

    a b s t r a c t

    Based on the potential flow theory, the boundary element method (BEM) is applied to calculate the

    dynamics of an underwater explosion bubblenear boundaries, and in conjunction with thefinite elementmethod (FEM) it is employed to compute the interaction between a bubble and an elasticplasticstructure. A complete 3D underwater explosion bubble dynamics code is developed;the simulatedresultscompare well with an underwater explosion experiment. With this code, the interactions between an

    underwater explosion bubble andelasticplasticstructuressuch as a flatplate, a cylinder andother simplestructures arecalculated andanalyzed. Besides, the damages caused by theafter flow, pulsating pressure,

    and jetting load on thestructures arealso calculated, with or without a free surface. From thetime historyof the pressure and stress of the structure, it can be observed that the stress reaches its maximum value

    when the bubble collapses, which proves that the pressure and jet impact induced by the collapse ofthe bubble can result in severe damage to the structure. In particular, the 3D analysis code is applied to

    some engineering problems, for example it is used on a surface ship to study the interaction between abubble and a complex elasticplastic structure. Under the bubble load, the low-order eigenfrequency of

    the ship is aroused usually, leading to the so-called whipping effect, because the pulsating frequency ofthe bubble matches the low-order eigenfrequency of the ship. The ship moves up and down with the

    expansion and collapse of the bubble respectively. Meanwhile, the power of the bubble generated by anear-field underwater explosion in short range is discussed, and some important conclusions which canbe applied to project application field are drawn.

    2008 Elsevier Ltd. All rights reserved.

    Contents

    1. Introduction........................................................................................................................................................................................................................1602. Theory and numerical model ............................................................................................................................................................................................160

    2.1. Introduction ...........................................................................................................................................................................................................1602.2. Boundary-element method (BEM) for the fluid part...........................................................................................................................................160

    2.3. Toroidal bubble model ..........................................................................................................................................................................................1612.4. Time-step size control and numerical procedures ..............................................................................................................................................162

    2.5. Finite-element method (FEM) solver for the structural part and coupling with fluid part ..............................................................................1623. Results and discussions .....................................................................................................................................................................................................163

    3.1. Circular plate model ..............................................................................................................................................................................................1643.2. Cylinder model.......................................................................................................................................................................................................165

    3.2.1. Comparison of the simulated results and experimental data..............................................................................................................165

    3.2.2. The case with a free surface ...................................................................................................................................................................1653.2.3. The case with bubble under cylinder ....................................................................................................................................................166

    3.3. The interaction between a bubble and a complex elasticplastic structure (e.g. a surface ship) ....................................................................1673.3.1. Explosion in middle and far field...........................................................................................................................................................167

    3.3.2. Explosion in near field............................................................................................................................................................................1694. Conclusions.........................................................................................................................................................................................................................169

    Acknowledgments .............................................................................................................................................................................................................170References...........................................................................................................................................................................................................................170

    Corresponding author. Fax: +86 0451 82518296.E-mail address: amanzhang@gmail.com(A.M. Zhang).

    0141-1187/$ see front matter 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.apor.2008.11.003

    http://www.elsevier.com/locate/aporhttp://www.elsevier.com/locate/apormailto:amanzhang@gmail.comhttp://dx.doi.org/10.1016/j.apor.2008.11.003http://dx.doi.org/10.1016/j.apor.2008.11.003mailto:amanzhang@gmail.comhttp://www.elsevier.com/locate/aporhttp://www.elsevier.com/locate/apor
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    160 A.M. Zhang et al. / Applied Ocean Research 30 (2008) 159171

    1. Introduction

    During an underwater explosion, there will be an initial shockwave propagating radially outwards to be followed by a high-pressure bubble containing hot gaseous products of the explosion.Under the effects of hydrostatic pressure, gravity and inertia, theso-called after flow, jet and pulsating pressure are developedowing to the motion of the bubble. Not only the shock wave butalso the bubble load can have great damages on the underwaterstructures. For instance, the pulsating pressure and after flow cancause global damage on the structure (e.g. a surface ship), whilethe high-speed re-entrant water jet will cause local damage tothe structure. Nowadays, researches are mainly focused on theinteraction between a bubble and a rigid wall (e.g. [17]), butfewer published literatures are about the interaction betweenan underwater explosion bubble and an elasticplastic structure.Kalumuck andChahine et al.[8] calculated the interaction betweena bubble and an elasticplastic structure with the combinationof the finite element method (FEM) and boundary elementmethod (BEM), and also developed the 2DYNAFS, 3DYNAFS andother codes. Klaseboerk [9] studied the underwater explosionbubble dynamics and the interaction between a bubble and a

    simple flat plate numerically and experimentally. Based on theirachievements, this paper discusses the interaction between abubble and a complex elasticplastic structure (e.g. a surfaceship), taking the free surface into account simultaneously. Thedamages caused by the after flow, pulsating pressure, jetting loadare investigated, aiming at revealing the power of the bubble load.

    2. Theory and numerical model

    2.1. Introduction

    The numerical calculations can be split into two parts: the fluidpart and the structural part. The fluid part is carried out usingthe boundary integral method. Special care must be taken after

    the jet impact induced by the collapse of the bubble, since thefluid domain then becomes doubly connected; a vortex ring isplaced inside the bubble to account for this phenomenon. Thestructural part is solved using the finite-element solver ABAQUS. Afull coupling between the two codes has been made; informationconcerning displacements of the structure is passed on from thestructural code to the fluid code and forces (deduced from thepressure loading on thestructure) arepassed on from thefluidcodeto the structural code. A controlling interface code decides whichcode has to be called to do the