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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Nakoryakov, V. E., Pokusaev, B. G., and Shreiber, I. R., 1993, Wave Propagation in Gas–Liquid Media, 2nd ed., BCRC Press, New Brighton, PA.
Kolev, N. I., 2011, Multiphase Flow Dynamics, Vol. 3, 4th ed., Springer-Verlag, Heidelberg, Germany.
Plesset, M. S., and Zwick, S., 1954, “The Growth of Bubbles in Superheated Liquids,” J. Appl. Phys., 25(4), pp. 493–500. [CrossRef]
Florschuetz, L. W., and Chao, B. T., 1965, “On the Mechanics of Vapor Bubble Collapse,” ASME J. Heat Transfer Ser. C, 87(2), pp. 209–220. [CrossRef]
Winters, W. S., Jr., and Merte, H., Jr., 1979, “Experiments and Nonequilibrium Analysis of Pipe Blowdown,” Nucl. Eng. Des., 69(3), pp. 411–429.
Dergarabedian, P., 1960, “Observations on Bubble Growths in Various Superheated Liquids,” J. Fluid Mech., 9(1), pp. 39–48. [CrossRef]
Carslaw, H. S., and Jager, J. S., 1959, Conduction of Heat in Solids, Oxford University Press, Oxford, UK.
Reynolds, A. B., and Berthoud, G., 1981, “Analysis of EXCOBULLE Two-Phase Expansion Tests,” Nucl. Eng. Des., 67(1), pp. 83–100. [CrossRef]
Scriven, L. E., 1959, “On the Dynamics of Phase Growth,” Chem. Eng. Sci., 10(1–2), pp. 1–13. [CrossRef]
Prosperetti, A., and Crum, L. A., 1988, “Nonlinear Bubble Dynamics,” J. Acoust. Soc. Am., 82(2), pp. 502–514. [CrossRef]
Kamath, V., and Prosperetti, A., 1989, “Numerical Integration Methods in Gas-Bubble Dynamics,” J. Acoust. Soc. Am., 85(4), pp. 1538–1548. [CrossRef]
Hao, Y., and Prosperetti, A., 2000, “The Collapse of Vapor Bubbles in a Spatially Non-Uniform Flow,” Int. J. Heat Mass Trans., 43(19), pp. 3539–3550. [CrossRef]
Matber, D. J., 1977, “HUBBLE-BUBBLE I: A Computer Program for the Analysis of Non-Equilibrium Flows of Water,” UK Atomic Energy Authority, Report.
Sharipov, V., 2011, “Temperature Dynamics of Liquid Outside a Spherical Bubble,” Proceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, Rio-de-Janeiro, May 8–12.
Sharipov, V., 2013, “Two-Pressure Model of One-Dimensional Bubbly Flow,” Proceedings of the International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Pisa, May 12–17.
Nugmatilin, R., 1990, “Heat and Mass Transfer in Wave Dynamics of Gas–Liquid Systems,” Proceedings of the 9th International Heat Transfer Conference, Jerusalem, pp. 223–235.
Hasanein, H. A., Kazimi, M. S., and Golay, M. W., 1996, “Forced Convection In-Tube Steam Condensation in the Presence of Non-Condensable Gases,” Int. J. Heat Mass Transfer, 39(13), pp. 2625–2639. [CrossRef]
Coddington, E. A., and Levinson, N., 1955, Theory of Ordinary Differential Equations, McGraw-Hill, New York.
Drell, I. L., and Belles, F. E., 1958, “Survey of Hydrogen Combustion Properties,” NACA Report No. 1383.


Grahic Jump Location
Fig. 1

Schematic representation of a spherical bubble

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In