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Analysis of the behavior of a bubble in a viscous incompressible liquid by finite element method

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Summary

The finite element method is used for the analysis of the behavior of a nonspherical bubble in a viscous incompressible liquid under axial conditions. The finite element approximations of the Navier Stokes equations are formulated by taking velocity and pressure as unknown variables. The flow field is discretized by triangular elements, and the bubble surface is represented by isoparametric elements with curved sides. This numerical technique is applied to the simulation of an initially spherical vapor bubble collapsing near a plane solid wall. It is made clear that a jet formed on the bubble is decelerated by the effect of liquid viscosity.

Übersicht

Mit dem Verfahren der Finiten Elemente wird das Verhalten einer nichtkugelförmigen Blase in einer zähen inkompressiblen Flüssigkeit bei rotationssymmetrischen Bedingungen untersucht. Die Navier-Stokesschen Gleichungen werden mit der Methode der Finiten Elemente näherungsweise gelöst. Das Strömungsfeld um die Blase wird in kleine dreieckige Elemente zerlegt, wobei die Oberfläche der Blase durch isoparametrische Elemente mit gekrümmten Seiten ersetzt wird. Die numerischen Rechnungen werden für den Zusammenbruch einer Blase, die anfangs kugelförmig war, in der Nähe einer ebenen festen Wand durchgeführt. Das Ergebnis zeigt, daß sich die Geschwindigkeit des in der Blase entstehenden Flüssigkeitsstrahls wegen des Einflusses der Zähigkeit vermindert.

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Authors and Affiliations

  1. Institute of High Speed Mechanics, Tōhoku University, Sendai, Japan

    K. Nakajima &  A. Shima

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  1. K. Nakajima
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  2. A. Shima
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Nakajima, K., Shima, A. Analysis of the behavior of a bubble in a viscous incompressible liquid by finite element method. Ing. arch 46, 21–34 (1977). https://doi.org/10.1007/BF00534957

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  • DOI: https://doi.org/10.1007/BF00534957

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