Research Papers: Two-Phase Flow and Heat Transfer

High Order Bubble Dynamics in Incompressible Liquid

[+] Author and Article Information
Vasilii Sharipov

Siemens AG,
Siemensallee 84,
Karlsruhe 76187, Germany
e-mail: vasilii.sharipov@siemens.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 12, 2013; final manuscript received December 15, 2014; published online January 21, 2015. Assoc. Editor: Cila Herman.

J. Heat Transfer 137(4), 042901 (Apr 01, 2015) (6 pages) Paper No: HT-13-1442; doi: 10.1115/1.4029457 History: Received August 12, 2013; Revised December 15, 2014; Online January 21, 2015

A semi-analytical approximation to the solution of the radial Fourier equation describing liquid temperature dynamics in the vicinity of a spherical bubble is presented. This approximation opens a possibility to construct a computationally efficient bubble model that is flexible enough to simulate different bubble dynamics behavior like bubble growth, collapse, and oscillations. In turn, it allows development of two-pressure computer codes aiming at simulation of processes in liquid with bubbles that are important for industrial applications. The model is based on the system of ordinary differential equations (ODEs) and is presented together with results of simulations and comparison with some available experimental data. Additionally, scenarios like strong bubble parameter oscillations in largely subcooled water and abrupt liquid pressure change are considered. As respective simulations show, the latter may lead to subsequent hydrogen explosion if hydrogen–oxygen mixture is presented in the bubble. This may be important for boiling water reactor piping safety analysis.

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Fig. 1

Schematic representation of a spherical bubble

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Fig. 2

Bubble radius as a function of time in case of bubble collapse in subcooled water

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Fig. 3

Bubble radius as a function of time in case of bubble growth in superheated water

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Fig. 4

Bubble radius as a function of time in case of bubble collapse in largely subcooled water for different temperature change speed

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Fig. 5

Gas temperature as a function of time in case of bubble collapse in largely subcooled water for different temperature change speed

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Fig. 6

Gas temperature as a function of time of the bubble experiencing abrupt pressure wave for different mass concentrations of noncondensable gases



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