DOI QR코드

DOI QR Code

A Simple Parameterization for the Rising Velocity of Bubbles in a Liquid Pool

  • Received : 2016.07.28
  • Accepted : 2016.12.13
  • Published : 2017.08.25

Abstract

The determination of the shape and rising velocity of gas bubbles in a liquid pool is of great importance in analyzing the radioactive aerosol emissions from nuclear power plant accidents in terms of the fission product release rate and the pool scrubbing efficiency of radioactive aerosols. This article suggests a simple parameterization for the gas bubble rising velocity as a function of the volume-equivalent bubble diameter; this parameterization does not require prior knowledge of bubble shape. This is more convenient than previously suggested parameterizations because it is given as a single explicit formula. It is also shown that a bubble shape diagram, which is very similar to the Grace's diagram, can be easily generated using the parameterization suggested in this article. Furthermore, the boundaries among the three bubble shape regimes in the $E_o-R_e$ plane and the condition for the bypass of the spheroidal regime can be delineated directly from the parameterization formula. Therefore, the parameterization suggested in this article appears to be useful not only in easily determining the bubble rising velocity (e.g., in postulated severe accident analysis codes) but also in understanding the trend of bubble shape change due to bubble growth.

Keywords

References

  1. A.T. Wassel, A.F. Mills, D.C. Bugby, R.N. Oehlberg, Analysis of radionuclide retention in water pools, Nucl. Eng. Des. 90 (1985) 87-104. https://doi.org/10.1016/0029-5493(85)90033-0
  2. S.M. Ghiaasiaan, G.F. Yao, A theoretical model for deposition of aerosols in rising spherical bubbles due to diffusion, convection, and inertia, Aerosol Sci. Technol. 26 (1997) 141-153. https://doi.org/10.1080/02786829708965420
  3. C. Gabillet, C. Colin, J. Fabre, Experimental study of bubble injection in a turbulent boundary layer, Int. J. Multiphase Flow 28 (2002) 553-578. https://doi.org/10.1016/S0301-9322(01)00075-1
  4. T.S. Laker, S.M. Ghiaasiaan, Monte-Carlo simulation of aerosol transport in rising spherical bubbles with internal circulation, J. Aerosol Sci. 35 (2004) 473-488. https://doi.org/10.1016/j.jaerosci.2003.10.007
  5. H. Allelein, A. Auvinen, J. Ball, S. Guentay, L.E. Herranz, A. Hidaka, A.V. Jones, M. Kissane, D. Powers, G. Weber, State-of-the-art report on nuclear aerosols, 2009, p. 5. OECD/NEA/CSNI; 2009. Report nr NEA/CSNI/R.
  6. J.S. Hadamard, Mouvement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux, Comp. Rend. Acad. Sci. 152 (1911) 1735-1738 [in French].
  7. H.D. Mendelson, The prediction of bubble terminal velocities from wave theory, AIChE J. 13 (1967) 250-253. https://doi.org/10.1002/aic.690130213
  8. R.M. Davies, G. Taylor, The mechanics of large bubbles rising through extended liquids and through liquids in tubes, Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 200 (1950) 375-390. https://doi.org/10.1098/rspa.1950.0023
  9. J.R. Grace, Shapes and velocities of bubbles rising in infinite liquids, Trans. Inst. Chem. Eng. 51 (1973) 116-120.
  10. T. Tadaki, S. Maeda, On the shape and velocity of single air bubbles rising in various liquids, Kagaku Kogaku 25 (1961) 254-264 [in Japanese]. https://doi.org/10.1252/kakoronbunshu1953.25.254
  11. M. Ishii, N. Zuber, Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE J. 25 (1979) 843-855. https://doi.org/10.1002/aic.690250513
  12. G. Bozzano, M. Dente, Shape and terminal velocity of single bubble motion: a novel approach, Comput. Chem. Eng. 25 (2001) 571-576. https://doi.org/10.1016/S0098-1354(01)00636-6
  13. A. Frumkin, V.G. Levich, On surfactants and interfacial motion, Zh. Fiz. Khim. 21 (1947) 1183-1204.
  14. G.B. Wallis, The terminal speed of single drops or bubbles in an infinite medium, Int. J. Multiphase Flow 1 (1974) 491-511. https://doi.org/10.1016/0301-9322(74)90003-2
  15. M. Jamialahmadi, C. Branch, H. Muller-Steinhagen, Terminal bubble rise velocity in liquids, Chem. Eng. Res. Des. 72 (1994) 119-122.
  16. J.R. Grace, T. Wairegi, T.H. Nguyen, Shapes and velocities of single drops and bubbles moving freely through immiscible liquids, Trans. Inst. Chem. Eng. 54 (1976) 167-173.
  17. R. Clift, J.R. Grace, M.E. Weber, Bubbles, Drops, and Particles, Academic Press, New York (NY), 1978.
  18. W. Rybczynski, On the translatory motion of a fluid sphere in a viscous medium, Bull. Int. Acad. Pol. Sci. Lett. Cl. Sci. Math. Nat., Ser. A (1911) 40-46.
  19. R.L. Datta, D.H. Napier, D.M. Newitt, The properties and behaviour of gas bubbles formed at circular orifices, Trans. Inst. Chem. Eng. 28 (1950) 14-26.
  20. W.L. Haberman, R.K. Morton, An experimental investigation of the drag and shape of air bubbles rising in various liquids, David Taylor Model Basin, Washington (WA), 1953. Report nr DTMB-802.
  21. B. Rosenberg, The drag and shape of air bubbles moving in liquids, David W. Taylor Model Basin, 1950. Report nr 727.
  22. T. Bryn, Speed of rise of air bubbles in liquids, David Taylor Model Basin, 1949. Report nr 132.
  23. N.M. Aybers, A. Tapucu, Studies on the drag and shape of gas bubbles rising through a stagnant liquid, Warme Stoffubertragung 2 (1969) 171-177. https://doi.org/10.1007/BF00751164
  24. G. Houghton, P.D. Ritchie, J.A. Thomson, Velocity of rise of air bubbles in sea-water, and their types of motion, Chem. Eng. Sci. 7 (1957) 111-112. https://doi.org/10.1016/0009-2509(57)80026-8
  25. A. Gorodetskaya, The rate of rise of bubbles in water and aqueous solutions at great Reynolds numbers, Russ. J. Phys. Chem. A 23 (1949) 71-78.
  26. F.N. Peebles, H.J. Garber, Studies on the motion of gas bubbles in liquids, Chem. Eng. Prog. 49 (1953) 88-97.
  27. P.H. Calderbank, D.S.L. Johnson, J. Loudon, Mechanics and mass transfer of single bubbles in free rise through some Newtonian and non-Newtonian liquids, Chem. Eng. Sci. 25 (1970) 235-256. https://doi.org/10.1016/0009-2509(70)80018-5
  28. B. Sumner, F.K. Moore, Boundary layer separation on a liquid sphere, National Aeronautics and Space Administration, Washington, D.C, 1970. Report nr NASA CR-1669.
  29. V.G. Levich, S. Technica, Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, N.J., 1962.
  30. W.N. Bond, D.A. Newton, Bubbles, drops and stokes law, Philos. Mag 5 (1928) 794-800. https://doi.org/10.1080/14786440408564523
  31. P. Savic, Circulation and distortion of liquid drops falling through a viscous medium, National Research Council of Canada, Ottawa, Ontario, Canada, 1953. Report nr MT-22.
  32. R.E. Davis, A. Acrivos, The influence of surfactants on the creeping motion of bubbles, Chem. Eng. Sci. 21 (1966) 681-685. https://doi.org/10.1016/0009-2509(66)80017-9
  33. R.M. Griffith, The effect of surfactants on the terminal velocity of drops and bubbles, Chem. Eng. Sci. 17 (1962) 1057-1070. https://doi.org/10.1016/0009-2509(62)80084-0
  34. T.D. Taylor, A. Acrivos, On the deformation and drag of a falling viscous drop at low Reynolds number, J. Fluid Mech. 18 (1964) 466-476. https://doi.org/10.1017/S0022112064000349

Cited by

  1. 총설: 액체 중에서 상승하는 기포의 크기, 형상 및 속도 vol.13, pp.1, 2017, https://doi.org/10.11629/jpaar.2017.3.31.001
  2. Semiempirical model for wet scrubbing of bubble rising in liquid pool of sodium-cooled fast reactor vol.50, pp.6, 2017, https://doi.org/10.1016/j.net.2018.04.003
  3. Using Noble Gases to Compare Parameterizations of Air‐Water Gas Exchange and to Constrain Oxygen Losses by Ebullition in a Shallow Aquatic Environment vol.123, pp.9, 2018, https://doi.org/10.1029/2018jg004441
  4. A numerical study on bubble dynamics in sinusoidal channels vol.31, pp.5, 2017, https://doi.org/10.1063/1.5092870
  5. NUMERICAL AND EXPERIMENTAL INVESTIGATION OF AIR-WATER SYSTEM TO SIMULATE BUBBLE DYNAMICS IN LIQUID SODIUM POOL vol.36, pp.4, 2017, https://doi.org/10.1590/0104-6632.20190364s20190268
  6. Tunable and precise miniature lithium heater for point-of-care applications vol.117, pp.9, 2017, https://doi.org/10.1073/pnas.1916562117
  7. Broadband Acoustic Inversion for Gas Flux Quantification-Application to a Methane Plume at Scanner Pockmark, Central North Sea vol.125, pp.9, 2020, https://doi.org/10.1029/2020jc016360
  8. Preliminary analyses on decontamination factors during pool scrubbing with bubble size distributions obtained from EPRI experiments vol.53, pp.2, 2017, https://doi.org/10.1016/j.net.2020.08.013
  9. Adsorption Kinetics of Various Frothers on Rising Bubbles of Different Sizes under Flotation Conditions vol.11, pp.3, 2017, https://doi.org/10.3390/min11030304
  10. The effect of nonlinear drag on the rise velocity of bubbles in turbulence vol.924, pp.None, 2017, https://doi.org/10.1017/jfm.2021.556
  11. Shapes and Rise Velocities of Single Bubbles in a Confined Annular Channel: Experiments and Numerical Simulations vol.6, pp.12, 2017, https://doi.org/10.3390/fluids6120437