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==1 Title, abstract and keywords==
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==Resumen==
  
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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.
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El objetivo de este trabajo es formular y evaluar una metodología para la resolución de las ecuaciones de Navier-Stokes para los fluidos viscoplásticos de Bingham y de Herschel-Bulkley mediante el método de los elementos finitos mixtos estabilizados velocidad/presión. Se desarrolla una formulación teórica, se realiza la implementación computacional y se presentan y evalúan soluciones numéricas para estos fluidos viscoplásticos.
  
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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.
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Los fluidos viscoplásticos se caracterizan por presentar una tensión de corte mínima, denominada tensión de fluencia. Por encima de esta tensión de corte mínima el fluido comienza a moverse. En caso de no superarse esta tensión de fluencia, el fluido se comporta como un cuerpo rígido o quasi-rígido, con velocidad de deformación nula.
  
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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.
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Se presentan inicialmente las ecuaciones de Navier-Stokes para un fluido y dos fluidos incompresibles e inmiscibles considerando superficie libre. Se presenta una revisión de los modelos reológicos Newtonianos y los modelos no-Newtonianos. Se hace una descripción detallada de los modelos viscoplásticos. Se describen los modelos viscoplásticos regularizados de Papanastasiou. Se proponen modelos regualarizados de doble viscosidad como alternativa a los comúnmente usados.
  
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==2 The main text==
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Se deducen las soluciones analítica en flujos paralelos para el fluido Newtoniano, el fluido de Bingham, de Herschel-Bulkley, el fluido pseudoplástico y dilatante.
  
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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.
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Se desarrolla el modelo discreto, así como la formulación estabilizada con los métodos de subescalas algebraica (Algebraic subgrid scale, ASGS), de subescalas ortogonales (Orthogonal subgrid scale, OSS) y de subescalas ortogonales con la presión y el termino convectivo desacoplados, split-OSS. En el caso del fluido con superficie libre se presenta el método euleriano simplificado, el cual usa el método de superficie de nivel level set para resolver el movimiento de esta superficie libre.
  
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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.
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Se presenta un estudio de convergencia con los métodos de estabilización OSS y ASGS en los flujos paralelos de Bingham y de Herschel-Bulkley. Los modelos regularizados se doble viscosidad muestran menor error de convergencia que los usados regularmente.
  
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===2.1 Subsections===
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Se presentan las soluciones numéricas desarrolladas en este trabajo para un amplio conjunto de problemas benchmark. Pueden dividirse en tres grupos: flujos de Bingham, flujos de Herschel-Bulkley y flujos con superficie libre. Las soluciones obtenidas validan la metodología propuesta en este trabajo de investigación comparándose muy bien con las soluciones analíticas, numéricas, con resultados experimentales y datos de campo.
  
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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.
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La metodología propuesta en este trabajo proporciona una herramienta computacional para estudiar flujos viscoplásticos confinados, muy comunes en la industria, y los flujos detríticos viscoplásticos con superficie libre.  
  
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===2.2 General guidelines===
 
  
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<pdf>Media:Draft_Samper_187723667_2095_M142.pdf</pdf>
  
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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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==References==
  
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:*  Use decimal points (not commas); use a space for thousands (10 000 and above).
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ABDALI, S. & MITSOULIS, E. 1992. "Entry and exit flows of Bingham fluids". J. Rheology, 36(2).
  
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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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AHMED, A. & ALEXANDROU, A. 1994. "Processing of semi-solid materials using a shearthickening Bingham fluid model". J. Non-Newtonian Fluid Mechanics, ASME publication No. FED-179, 83-89.
  
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===2.3 Tables, figures, lists and equations===
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ALEXANDER, J. 1961. "On complete solution for frictionless extrusion in plane strain". Q. J. Applied Mathematic, 19, 31-40.
  
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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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ALEXANDROU, A., MCGILVREAY, T. & BURGOS, G. 2001. "Steady Herschel–Bulkley fluid flow in three-dimensional expansions". J. Non-Newtonian Fluid Mechanics, 100, 77-96.
  
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ALLEBORN, K., NANDAKUMAR, K., RASZILLIER, H. & DURST, F. 1997. "Further contributions on the two-dimensional flow in a sudden expansion". J. Fluid Mechanical, 330, 169-188.
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| style="text-align: center;"|12.74 MPa
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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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ANDRES, V. 1960. "Equilibrium and motion of a sphere in a viscoplastic fluid". Dokl. Akad. Nauk SSSR, 133, 777-780.
  
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ANSLEY, R. & SMITH, T. 1967. "Motion of spherical particules in a Bingham plastic". J. A I Ch E, 13, 1193-1196.
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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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ATAPATTU, D., CHHABRA, R. & UHLHERR, P. 1990. "Wall effect for spheres falling at small reynolds number in a viscoplastic medium". J. Non-Newtonian Fluid Mechanics, 38, 31-42.
  
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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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ATAPATTU, D., CHHABRA, R. & UHLHERR, P. 1995. "Creeping sphere motion in Herschel-Bulkley fluids: flow field and drag". J. Non-Newtonian Fluid Mechanics, 59, 245-265.
  
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AZOUZ, U., SHIRAZI, S. & AZAR, J. 1993. "Numerical simulation of laminar flows of yiel-power law fluids in conduits of arbitrary cross-section". J. Fluid Engineering, 115, 710-716.
  
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BADÍA, S. & CODINA, R. 2009. "Unified satbilized finite elemnt formulation for the Stokes and Darcy problems". SIAM J. Numerical analysis, 47, 1971-2000.
  
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2.1. A subentry
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BAGNOL, R. 1954. "Experiment on a gravity free dispersión of large solid spheres in a newtonian fluid under shear". Proceeding of the Royal Society of London., A 225, 49-63.
  
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3. The last entry
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BARNES, H. ‘‘The yield stress myth? Revisited’’. In: MOLDENAERS & KEUNINGS, P. A., eds. Proc. XIth Int. Congr. Rheology, 1992 Brussels, Belgium. Elsevier, Amsterdam, 576-578.
  
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* A bulleted list item
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BARNES, H. 1997. "Thixotropy-a review". J. Non-Newtonian Fluid Mech., 70, 1.
  
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BARNES, H. & WALTERS, K. 1985. ‘‘The yield stress myth?’’. Rheology Acta 24.
  
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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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BATCHELOR, J. & HORSFALL, F. 1973. "Die swell in elastic and viscous fluids". Research Report No. 189. Rubber and Plastic Research Assoc. of Grain Britain.
  
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BEAULNE, M. & MITSOULIS, E. 1997. "Creeping motion of a sphere in tubes filled with Herschel–Bulkley fluids". J. Non-Newtonian fluid mechanics, 72, 55-71.
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===2.4 Supplementary material===
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BERCOVIER, M. & ENGELMAN, M. 1980. "A finite-element method for incompressible non-Newtonian flows". J. Computational Physics, 36, 313-326.
  
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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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BERIS, A. N., TSAMOPOULOS, J. A., ARMSTRONG, R. C. & BROWN, R. A. 1985. "Creeping motions of sphere through a Bingham Plastic". J. Fluid Mechanical, 158, 219-244.
  
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==3 Bibliography==
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BHARTI, R., CHHABRA, R. & ESWARAN, V. 2006. "Steady flow of power law fluids across a circular cylinder". The Canadian Journal of Chemical Engineering, 84, 406-421.
  
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<span id='_Ref449344604'></span>
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BINGHAM, E. 1922. "Fluidity and plasticity", New York, McGraw-Hill.
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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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BIRD, R., ARMSTRONG, R. & HASSAGER, O. 1987. "Dynamics of polymeric liquids", Wiley.
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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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BIRD, R., DAI, G. & YARUSSO, B. 1983. "Rheology and flow of viscoplastic materials". Reviews Chemical Enginnering, 1, 1-70.
  
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Acknowledgments should be inserted at the end of the document, before the references section.
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BLACKERY, J. & MITSOULIS, E. 1997. "Creeping motion of a sphere in tubes filled with a Bingham plastic material". J. Non-Newtonian Fluid Mechanics, 70, 59-77.
  
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==5 References==
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BOTELLA, O. & PEYRET, R. (eds.) 1998. "Benchmark spectral results on the lid_driven cavity flow", Great Britain: Elseiver.
  
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BOZKUS, Z. & KASAP, A. 1998. "Comparison of physical and numerical dam-break simulations". Tr. J. Engineering and Environmental Science, 22, 429 -443.
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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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BREZZI, F. & FORTIN, M. 1991. "Mixed and Hibrid Finite Element Methods", Springer Verlag.
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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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BREZZI, F. & PITKÄRANTA, J. 1984. "On the stabilization of finite element approximations of Stokes equations". In: HACKBUSH, W. (ed.) Efficient Solution of Elliptic Systems. Vieweg, Braunschweig.
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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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BROOKS, A., HUGHES, T. & RUSSO, A. 1982. "Streamlines Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompresible Navier-Stokes Equation". J. Computer Methods in Applied Mechanics and Engineering, 32, 199-259.
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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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BURGOS, G. & ALEXANDROU, A. 1999. "Flow development of Herschel-Bulkley fluis in a sudden three-dimensional square expansion". J. Rheology.
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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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CASSON, N. 1959. "Rhelogy of disperse system", New York, Ed. C. C. Mill, Pergamon Press.
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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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CERVERA, M. & CHIUMENTI, M. 2009. "Size effect and localization in J2 plasticity". Int. J. Solids and Structures, 46(17), 3301-3312.
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CERVERA, M., CHIUMENTI, M. & CODINA, R. 2010a. "Mixed stabilied finite element methods in nonlinear solid mechanics. Part I: Formulation". J. Computer Methods in Applied Mechanics and Engineering, 46 (17), 3301-3312.
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CERVERA, M., CHIUMENTI, M. & CODINA, R. 2010b. "Mixed stabilied finite element methods in nonlinear solid mechanics. Part II: Strain localization". J. Computer Methods in Applied Mechanics and Engineering, 199 (37-40), 2571-2589.
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CERVERA, M., CHIUMENTI, M. & CODINA, R. 2011. "Mesh objetive modeling of cracks using continuos linear strain and displacement interpolations". Int. J. Numerical Methods in Enginnering, 87 (10), 962-987.
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CERVERA, M., CHIUMENTI, M. & DE SARACIBAR, A. 2004a. "Shear band localization via local J2 continuum damage mechanics". J. Computer Methods in Applied Mechanics and Engineering, 193, 849-880.
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CERVERA, M., CHIUMENTI, M. & DE SARACIBAR, A. 2004b. "Softening, localization and stabilization: capture of discontinuous solutions in J2 plasticity". Int. J. for Numerical and Analytical Methods in Geomechanics, 28, 373-393.
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CERVERA, M., CHIUMENTI, M. & DI CAPUA, D. 2012. "Benchmarking on bifurcación and localization in J2 plasticity for plane strain conditions". J. Computer Methods in Applied Mechanics and Engineering, 241-244, 206-224.
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CERVERA, M., CHIUMENTI, M., VALVERDE, Q. & DE SARACIBAR, A. 2003. "A mixed linear/linear simplicial elements for incompressible elasticity and plasticity". J. Computer Methods in Applied Mechanics and Engineering, 192 (49-50), 5253-5264.
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CODINA, R. 2000a. "On stabilized finite element methods for linear systems of convection–diffusion-reaction equations". J. Computer Methods in Applied Mechanics and Engineering, 188, 61-82.
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CODINA, R. 2000b. "Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods". J. Computer Methods in Applied Mechanics and Engineering, 190, 1579-1599.
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CODINA, R. 2000c. "Stabilized finite element approximation of transient incompresible flows using orthogonal subscale". CIMNE.
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CODINA , R. 2001. "A stabilized finite element method for generalized stationary incompressible flows". J. Compu. Methods in Applied Mechanics and Engineering, 190, 2681-2706.
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CODINA, R. 2002. "Stabilized finite element approximation of transient incompressible flows using orthogonal scale". J. Computer Methods in Applied Mechanics and Engineering, 191, 4295-4321.
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CODINA, R. & BLASCO, J. 1997. "A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation". J. Computer Methods in Applied Mechanics and Engineering, 143, 373-391.
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DALL´ONDER DOS SANTOS, D., FREY, S., NACCACHE, M. & MENDES, P. R. D. S. 2011. "Numerical approximations for flow of viscoplastic fluid in a lid-driven cavity". J. Non-Newtonian Fluid Mech., 166, 667-679.
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DE ALMEIDA, B. & FRANCO, B. 1994. "Modeling of dam-break flow", computer modeling of free-surface and pressurized flows".
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DE SARACIBAR, A., CHIUMENTI, M., VALVERDE, Q. & CERVERA, M. 2006. "On thorthogonal subgrid scale pressure stabilization of finite deformation J2 plasticity". J. Computer Methods in Applied Mechanics and Engineering, 195 (9-12), 1224-1251.
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DE WAELE, A. 1923. "Viscometry and plastometry". J. Oil Color Chemists’ Assoc., 6 (38), 33-88.
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DEGLO, D. B., MAGNIN, B. & JAY, P. 2003. "Viscoplastic flow around a cylinder in an infinite medium". J. Non-Newtonian Fluid Mechanics, 115, 27-49.
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DIEZ, M. & GODOY, L. 1991. "Flujo viscoplástico incompresible de materiales con fricción y cohesión. Aplicación a problemas bidimensionales". Revista Internacional de Métodos Numéricos para Cálculo en Ingeniería".
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ELLINGWOOD, B., COROTIS, R., BOLAND, J. & JONES, N. 1993. "Assessing cost of dam failure". J. Water Resources Planning and Management, ASCE, Vol. 119, No.1.
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ELLWOOD, K., GEORGIOU, G., PAPANASTASIOU, T. & WILKES, J. 1990. "Laminar jets of Bingham-Plastic liquids". J. Rheology, 34, 6.
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FAURE, J. & NAHAS, N. 1961. "Etude numérique et expérimentale díntumescences à forte courbure du front". J. La Houille Blanche, No. 5, 576-586.
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FAXÉN, O. 1946. "Forces excerted on a rigid cylinder in a viscous fluid between two parallel fixed planes". Proceeding of the Royal Swedish academy of Engineering and Science, 187, 1-13.
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FORTIN, M. 1972. "Calcul numérique des écoulements des fluides de Bingham et des fluides newtoniens incompressibles par la méthodes des éléments finis". Tese de Doutorado, l´Unibersité de Paris VI.
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FREY, S., FILIPE, S. & ZINANI, F. 2010. "Stabilized mixed approximations for inertial viscoplastic fluid flows". J. Mechanical Research Comunications, 37, 145-152.
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Latest revision as of 11:06, 11 June 2019

Resumen

El objetivo de este trabajo es formular y evaluar una metodología para la resolución de las ecuaciones de Navier-Stokes para los fluidos viscoplásticos de Bingham y de Herschel-Bulkley mediante el método de los elementos finitos mixtos estabilizados velocidad/presión. Se desarrolla una formulación teórica, se realiza la implementación computacional y se presentan y evalúan soluciones numéricas para estos fluidos viscoplásticos.

Los fluidos viscoplásticos se caracterizan por presentar una tensión de corte mínima, denominada tensión de fluencia. Por encima de esta tensión de corte mínima el fluido comienza a moverse. En caso de no superarse esta tensión de fluencia, el fluido se comporta como un cuerpo rígido o quasi-rígido, con velocidad de deformación nula.

Se presentan inicialmente las ecuaciones de Navier-Stokes para un fluido y dos fluidos incompresibles e inmiscibles considerando superficie libre. Se presenta una revisión de los modelos reológicos Newtonianos y los modelos no-Newtonianos. Se hace una descripción detallada de los modelos viscoplásticos. Se describen los modelos viscoplásticos regularizados de Papanastasiou. Se proponen modelos regualarizados de doble viscosidad como alternativa a los comúnmente usados.

Se deducen las soluciones analítica en flujos paralelos para el fluido Newtoniano, el fluido de Bingham, de Herschel-Bulkley, el fluido pseudoplástico y dilatante.

Se desarrolla el modelo discreto, así como la formulación estabilizada con los métodos de subescalas algebraica (Algebraic subgrid scale, ASGS), de subescalas ortogonales (Orthogonal subgrid scale, OSS) y de subescalas ortogonales con la presión y el termino convectivo desacoplados, split-OSS. En el caso del fluido con superficie libre se presenta el método euleriano simplificado, el cual usa el método de superficie de nivel level set para resolver el movimiento de esta superficie libre.

Se presenta un estudio de convergencia con los métodos de estabilización OSS y ASGS en los flujos paralelos de Bingham y de Herschel-Bulkley. Los modelos regularizados se doble viscosidad muestran menor error de convergencia que los usados regularmente.

Se presentan las soluciones numéricas desarrolladas en este trabajo para un amplio conjunto de problemas benchmark. Pueden dividirse en tres grupos: flujos de Bingham, flujos de Herschel-Bulkley y flujos con superficie libre. Las soluciones obtenidas validan la metodología propuesta en este trabajo de investigación comparándose muy bien con las soluciones analíticas, numéricas, con resultados experimentales y datos de campo.

La metodología propuesta en este trabajo proporciona una herramienta computacional para estudiar flujos viscoplásticos confinados, muy comunes en la industria, y los flujos detríticos viscoplásticos con superficie libre.


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