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| − | ==1 Title, abstract and keywords== | + | ==Abstract== |
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| − | Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.
| + | The development of efficient algorithms to understand implosion dynamics presents |
| | + | a number of challenges. The foremost challenge is to efficiently represent the coupled |
| | + | compressible fluid dynamics of internal air and surrounding water. |
| | | | |
| − | Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.
| + | Secondly, the method must allow one to accurately detect or follow the interface between the |
| | + | phases. |
| | | | |
| − | An abstract is required for every document; it should succinctly summarize the reason for the work, the main findings, and the conclusions of the study. Abstract is often presented separately from the article, so it must be able to stand alone. For this reason, references and hyperlinks should be avoided. If references are essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself.
| + | Finally, it must be capable of resolving any shock waves which may be created |
| | + | in air or water during the final stage of the collapse. |
| | | | |
| − | ==2 The main text==
| + | We present a fully Lagrangian |
| | + | compressible numerical framework for the simulation of underwater implosion. Both |
| | + | air and water are considered compressible and the equations for the Lagrangian shock |
| | + | hydrodynamics are stabilized via a variationally consistent multiscale method. |
| | | | |
| − | You can enter and format the text of this document by selecting the ‘Edit’ option in the menu at the top of this frame or next to the title of every section of the document. This will give access to the visual editor. Alternatively, you can edit the source of this document (Wiki markup format) by selecting the ‘Edit source’ option.
| + | A nodally perfect matched definition of the interface is used and then the kinetic |
| | + | variables, pressure and density, are duplicated at the interface level. An adaptive |
| | + | mesh generation procedure, which respects the interface connectivities, is applied to |
| | + | provide enough refinement at the interface level. This framework is then used to simulate |
| | + | the underwater implosion of a large cylindrical bubble, with a size in the order of |
| | + | cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm), |
| | + | and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in |
| | + | addition to the shock waves traveling in the fluid domains are among the phenomena |
| | + | that are observed in the simulation. We then extend our framework to model the |
| | + | underwater implosion of a cylindrical aluminum container considering a monolithic |
| | + | fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal |
| | + | atmospheric-pressure air from the external high-pressure water, is modeled by a three |
| | + | node rotation-free shell element. The cylinder undergoes fast transient deformations, |
| | + | large enough to produce self-contact along it. |
| | | | |
| − | Most of the documents in Scipedia are written in English (write your manuscript in American or British English, but not a mixture of these). Anyhow, specific publications in other languages can be published in Scipedia. In any case, the documents published in other languages must have an abstract written in English.
| + | A novel elastic frictionless contact model |
| | + | is used to detect contact and compute the non-penetrating forces in the discretized |
| | + | domain between the mid-planes of the shell. Two schemes are tested, implicit using |
| | + | the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler |
| | + | scheme. The results of the two simulations are compared with experimental data. |
| | | | |
| − | ===2.1 Subsections=== | + | ==Full document== |
| | + | <pdf>Media:Draft_Samper_243926140_1339_M150.pdf</pdf> |
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| − | Divide your article into clearly defined and numbered sections. Subsections should be numbered 1.1, 1.2, etc. and then 1.1.1, 1.1.2, ... Use this numbering also for internal cross-referencing: do not just refer to 'the text'. Any subsection may be given a brief heading. Capitalize the first word of the headings.
| + | ==References== |
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| − | ===2.2 General guidelines===
| + | See document |
| − | | + | |
| − | Some general guidelines that should be followed in your manuscripts are:
| + | |
| − | | + | |
| − | :* Avoid hyphenation at the end of a line.
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| − | | + | |
| − | :* Symbols denoting vectors and matrices should be indicated in bold type. Scalar variable names should normally be expressed using italics.
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| − | :* Use decimal points (not commas); use a space for thousands (10 000 and above).
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| − | :* Follow internationally accepted rules and conventions. In particular use the international system of units (SI). If other quantities are mentioned, give their equivalent in SI.
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| − | | + | |
| − | ===2.3 Tables, figures, lists and equations===
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| − | | + | |
| − | Please insert tables as editable text and not as images. Tables should be placed next to the relevant text in the article. Number tables consecutively in accordance with their appearance in the text (<span id='cite-_Ref382560620'></span>[[#_Ref382560620|table 1]], table 2, etc.) and place any table notes below the table body. Be sparing in the use of tables and ensure that the data presented in them do not duplicate results described elsewhere in the article.
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| − | | + | |
| − | <span id='_Ref382560620'></span>
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| − | {| style="margin: 1em auto 1em auto;border: 1pt solid black;border-collapse: collapse;"
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| − | |-
| + | |
| − | | style="text-align: center;"|Thickness
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| − | | style="text-align: center;"|3.175 mm
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| − | |-
| + | |
| − | | style="text-align: center;"|Young Modulus
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| − | | style="text-align: center;"|12.74 MPa
| + | |
| − | |-
| + | |
| − | | style="text-align: center;"|Poisson coefficient
| + | |
| − | | style="text-align: center;"|0.25
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| − | |-
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| − | | style="text-align: center;"|Density
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| − | | style="text-align: center;"|1107 kg/m<sup>3</sup>
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| − | |}
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | <span style="text-align: center; font-size: 75%;">Table 1: Material properties</span></div>
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| − | Graphics may be inserted directly in the document and positioned as they should appear in the final manuscript.
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| − | <span id='_Ref448852946'></span>
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | [[Image:Scipedia.gif|center|480px]]
| + | |
| − | </div>
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| − | <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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| − | <span style="text-align: center; font-size: 75%;">Figure 1. Scipedia logo.</span></div>
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| − | Number the figures according to their sequence in the text (<span id='cite-_Ref448852946'></span>[[#_Ref448852946|figure 1]], figure 2, etc.). Ensure that each illustration has a caption. A caption should comprise a brief title. Keep text in the illustrations themselves to a minimum but explain all symbols and abbreviations used. Try to keep the resolution of the figures to a minimum of 300 dpi. If a finer resolution is required, the figure can be inserted as supplementary material
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| − | For tabular summations that do not deserve to be presented as a table, lists are often used. Lists may be either numbered or bulleted. Below you see examples of both.
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| − | 1. The first entry in this list
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| − | 2. The second entry
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| − | 2.1. A subentry
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| − | 3. The last entry
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| − | | + | |
| − | * A bulleted list item
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| − | | + | |
| − | * Another one
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| − | You may choose to number equations for easy referencing. In that case they must be numbered consecutively with Arabic numerals in parentheses on the right hand side of the page. Below is an example of formulae that should be referenced as eq. <span id='cite-_Ref424030152'></span>[[#_Ref424030152|(1)]].
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| − | | + | |
| − | {| style="width: 100%;"
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| − | |-
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| − | | style="vertical-align: top;"| <math>{\nabla }^{2}\phi =0</math>
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| − | | style="text-align: right;"|<span id='_Ref424030152'></span>
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| − | (1)
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| − | |}
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| − | | + | |
| − | ===2.4 Supplementary material===
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| − | | + | |
| − | Supplementary material can be inserted to support and enhance your article. This includes video material, animation sequences, background datasets, computational models, sound clips and more. In order to ensure that your material is directly usable, please provide the files with a preferred maximum size of 50 MB. Please supply a concise and descriptive caption for each file.
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| − | | + | |
| − | ==3 Bibliography==
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| − | <span id='_Ref449344604'></span>
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| − | Citations in text will follow a citation-sequence system (i.e. sources are numbered by order of reference so that the first reference cited in the document is [<span id='cite-1'></span>[[#1|1]]], the second [<span id='cite-2'></span>[[#2|2]]], and so on) with the number of the reference in square brackets. Once a source has been cited, the same number is used in all subsequent references. If the numbers are not in a continuous sequence, use commas (with no spaces) between numbers. If you have more than two numbers in a continuous sequence, use the first and last number of the sequence joined by a hyphen (e.g. [<span id='cite-1'></span>[[#1|1]], <span id='cite-3'></span>[[#3|3]]] or [<span id='cite-2'></span>[[#2|2]]-<span id='cite-2'></span>[[#4|4]]]).
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| − | | + | |
| − | <span id='_Ref449084254'></span>
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| − | You should ensure that all references are cited in the text and that the reference list. References should preferably refer to documents published in Scipedia. Unpublished results should not be included in the reference list, but can be mentioned in the text. The reference data must be updated once publication is ready. Complete bibliographic information for all cited references must be given following the standards in the field (IEEE and ISO 690 standards are recommended). If possible, a hyperlink to the referenced publication should be given. See examples for Scipedia’s articles [<span id='cite-1'></span>[[#1|1]]], other publication articles [<span id='cite-2'></span>[[#2|2]]], books [<span id='cite-3'></span>[[#3|3]]], book chapter [<span id='cite-4'></span>[[#4|4]]], conference proceedings [<span id='cite-5'></span>[[#5|5]]], and online documents [<span id='cite-6'></span>[[#6|6]]], shown in references section below.
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| − | ==4 Acknowledgments==
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| − | Acknowledgments should be inserted at the end of the document, before the references section.
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| − | ==5 References==
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| − | <span id='_Ref449083719'></span>
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| − | <div id="1"></div>
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| − | [[#cite-1|[1]]] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Article code. Available: [http://www.scipedia.com/ucode. http://www.scipedia.com/ucode.]
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| − | <div id="2"></div>
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| − | [[#cite-2|[2]]] Author, A. and Author, B. (Year) Title of the article. Title of the Publication. Volume number, first page-last page.
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| − | <div id="3"></div>
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| − | [[#cite-3|[3]]] Author, C. (Year). Title of work: Subtitle (edition.). Volume(s). Place of publication: Publisher.
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| − | <div id="4"></div>
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| − | [[#cite-4|[4]]] Author of Part, D. (Year). Title of chapter or part. In A. Editor & B. Editor (Eds.), Title: Subtitle of book (edition, inclusive page numbers). Place of publication: Publisher.
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| − | <div id="5"></div>
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| − | [[#cite-5|[5]]] Author, E. (Year, Month date). Title of the article. In A. Editor, B. Editor, and C. Editor. Title of published proceedings. Paper presented at title of conference, Volume number, first page-last page. Place of publication.
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| − | <div id="6"></div>
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| − | [[#cite-6|[6]]] Institution or author. Title of the document. Year. [Online] (Date consulted: day, month and year). Available: [http://www.scipedia.com/document.pdf http://www.scipedia.com/document.pdf]. [Accessed day, month and year].
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The development of efficient algorithms to understand implosion dynamics presents
a number of challenges. The foremost challenge is to efficiently represent the coupled
compressible fluid dynamics of internal air and surrounding water.
Secondly, the method must allow one to accurately detect or follow the interface between the
phases.
Finally, it must be capable of resolving any shock waves which may be created
in air or water during the final stage of the collapse.
We present a fully Lagrangian
compressible numerical framework for the simulation of underwater implosion. Both
air and water are considered compressible and the equations for the Lagrangian shock
hydrodynamics are stabilized via a variationally consistent multiscale method.
A nodally perfect matched definition of the interface is used and then the kinetic
variables, pressure and density, are duplicated at the interface level. An adaptive
mesh generation procedure, which respects the interface connectivities, is applied to
provide enough refinement at the interface level. This framework is then used to simulate
the underwater implosion of a large cylindrical bubble, with a size in the order of
cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm),
and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in
addition to the shock waves traveling in the fluid domains are among the phenomena
that are observed in the simulation. We then extend our framework to model the
underwater implosion of a cylindrical aluminum container considering a monolithic
fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal
atmospheric-pressure air from the external high-pressure water, is modeled by a three
node rotation-free shell element. The cylinder undergoes fast transient deformations,
large enough to produce self-contact along it.
A novel elastic frictionless contact model
is used to detect contact and compute the non-penetrating forces in the discretized
domain between the mid-planes of the shell. Two schemes are tested, implicit using
the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler
scheme. The results of the two simulations are compared with experimental data.
