Browse > Article
http://dx.doi.org/10.1016/j.net.2016.12.006

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

Park, Sung Hoon (Department of Environmental Engineering, Sunchon National University)
Park, Changhwan (FNC Technology, Co., Ltd.)
Lee, JinYong (FNC Technology, Co., Ltd.)
Lee, Byungchul (FNC Technology, Co., Ltd.)
Publication Information
Nuclear Engineering and Technology / v.49, no.4, 2017 , pp. 692-699 More about this Journal
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
Bubble Rising Velocity; Bubble Shape; $E_o-R_e$ Plane; Pool Scrubbing; Radioactive Aerosol Emissions;
Citations & Related Records
연도 인용수 순위
  • Reference
1 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.   DOI
2 C. Gabillet, C. Colin, J. Fabre, Experimental study of bubble injection in a turbulent boundary layer, Int. J. Multiphase Flow 28 (2002) 553-578.   DOI
3 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.   DOI
4 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.
5 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].
6 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.
7 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.   DOI
8 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.
9 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.   DOI
10 F.N. Peebles, H.J. Garber, Studies on the motion of gas bubbles in liquids, Chem. Eng. Prog. 49 (1953) 88-97.
11 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.
12 V.G. Levich, S. Technica, Physicochemical Hydrodynamics, Prentice-Hall, Englewood Cliffs, N.J., 1962.
13 W.N. Bond, D.A. Newton, Bubbles, drops and stokes law, Philos. Mag 5 (1928) 794-800.   DOI
14 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.   DOI
15 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.
16 R.E. Davis, A. Acrivos, The influence of surfactants on the creeping motion of bubbles, Chem. Eng. Sci. 21 (1966) 681-685.   DOI
17 R.M. Griffith, The effect of surfactants on the terminal velocity of drops and bubbles, Chem. Eng. Sci. 17 (1962) 1057-1070.   DOI
18 T. Bryn, Speed of rise of air bubbles in liquids, David Taylor Model Basin, 1949. Report nr 132.
19 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.   DOI
20 H.D. Mendelson, The prediction of bubble terminal velocities from wave theory, AIChE J. 13 (1967) 250-253.   DOI
21 A. Frumkin, V.G. Levich, On surfactants and interfacial motion, Zh. Fiz. Khim. 21 (1947) 1183-1204.
22 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.   DOI
23 J.R. Grace, Shapes and velocities of bubbles rising in infinite liquids, Trans. Inst. Chem. Eng. 51 (1973) 116-120.
24 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].   DOI
25 M. Ishii, N. Zuber, Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE J. 25 (1979) 843-855.   DOI
26 G. Bozzano, M. Dente, Shape and terminal velocity of single bubble motion: a novel approach, Comput. Chem. Eng. 25 (2001) 571-576.   DOI
27 G.B. Wallis, The terminal speed of single drops or bubbles in an infinite medium, Int. J. Multiphase Flow 1 (1974) 491-511.   DOI
28 M. Jamialahmadi, C. Branch, H. Muller-Steinhagen, Terminal bubble rise velocity in liquids, Chem. Eng. Res. Des. 72 (1994) 119-122.
29 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.
30 R. Clift, J.R. Grace, M.E. Weber, Bubbles, Drops, and Particles, Academic Press, New York (NY), 1978.
31 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.
32 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.
33 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.   DOI
34 B. Rosenberg, The drag and shape of air bubbles moving in liquids, David W. Taylor Model Basin, 1950. Report nr 727.