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A Review on Size, Shape and Velocity of a Bubble Rising in Liquid

총설: 액체 중에서 상승하는 기포의 크기, 형상 및 속도

  • Park, Sung Hoon (Department of Environmental Engineering, Sunchon National University)
  • 박성훈 (순천대학교 환경공학과)
  • Received : 2017.03.06
  • Accepted : 2017.03.15
  • Published : 2017.03.31

Abstract

Accurate prediction of size, shape and velocity of a bubble rising through a liquid pool is very important for predicting the particulate removal efficiency in pool scrubbing, for designing engineering safety features to prepare for severe accidents in nuclear power plants, and for predicting the emission of fission products from MCCI (molten core-concrete interaction) process during severe accidents. In this review article, previous studies on the determination of the size, shape and rising velocity of a bubble in liquid are reviewed. Various theoretical and parameterization formulas calculating the bubble size, shape and velocity from physical properties of liquid and gas flowrate are compared. Recent studies tend to suggest simple parameterizations that can easily determine the bubble shape and rising velocity without iteration, whereas iteration has to be performed to determine the bubble shape and velocity in old theories. The recent parameterizations show good agreement with measured data obtained from experiments conducted using different liquid materials with very diverse physical properties, proving themselves to be very useful tools for researchers in related fields.

본 총설에서는 액체층을 통과하는 기포의 크기, 형상, 상승속도를 결정하기 위한 이론들을 살펴보았다. 액체의 물리적 특성과 기포의 유량으로부터 기포의 크기, 형상, 상승속도를 체계적으로 계산하는 여러 가지 이론식 및 모수식들을 살펴보고, 각각의 장단점을 정리하였다. 이 분야에서 발표된 초기 저작들에서는 주로 반복계산을 통해 기포의 형상과 상승속도를 결정하는 기법들이 사용되었으나, 최근에 발표된 논문들에서는 간단한 모수식을 통해 기포의 형상과 상승속도를 반복계산 없이 쉽게 구하는 기법들이 제시되고 있다. 이러한 기법들은 매우 다양한 물리적 특성을 가지는 실험결과들과의 비교에서도 우수성을 보여주고 있어, 관련 분야의 연구에 매우 유용한 도구로 사용할 수 있을 것으로 보인다.

Keywords

References

  1. Allelein, H.-J., Auvinen, A., Ball, J., Guentay, S., Herranz, L.E., Hidaka, A., Jones, A.V., Kissane, M., Powers, D., and Weber., G. (2009). State-of-the- Art Report on Nuclear Aerosols, OECD/NEA/CSNI.
  2. Aybers, N.M., and Tapucu. A. (1969). Studies on the drag and shape of gas bubbles rising through a stagnant liquid, Warme-Und Stoffubertragung, 2, 171-177. https://doi.org/10.1007/BF00751164
  3. Bozzano, G., and Dente, M. (2001). Shape and terminal velocity of single bubble motion: a novel approach, Computers and Chemical Engineering, 25, 571-576. https://doi.org/10.1016/S0098-1354(01)00636-6
  4. Bryn, T. (1949). Speed of rise of air bubbles in liquids, David Taylor Model Basin.
  5. Calderbank, P.H., Johnson, D.S.L., and Loudon., J. (1970). Mechanics and mass transfer of single bubbles in free rise through some Newtonian and non-Newtonian liquids, Chemical Engineering Science, 25, 235-256. https://doi.org/10.1016/0009-2509(70)80018-5
  6. Clift, R., Grace, J.R., and Weber, M.E. (1978). Bubbles, drops, and particles, New York, Academic Press.
  7. Datta, R.L., Napier, D.H., and Newitt, D.M. (1950). The properties and behaviour of gas bubbles formed at circular orifices, Transactions of the Institution of Chemical Engineers, 28, 14-26.
  8. Davidson, J.F., and Schuler, B.O.G. (1960a). Bubble formation at an orifice in a viscous liquid, Transactions of the Institution of Chemical Engineers, 38, S105-S115.
  9. Davidson, J.F., and Schuler, B.O.G. (1960b). Bubble formation at an orifice in an inviscid liquid, Transactions of the Institution of Chemical Engineers, 38, 335-342.
  10. Davies, R.M. and Taylor, G. (1950). The mechanics of large bubbles rising through extended liquids and through liquids in tubes, Proceedings of the Royal Society of London.Series A. Mathematical and Physical Sciences, 200, 375-390. https://doi.org/10.1098/rspa.1950.0023
  11. Fritz, W. (1935). Berechnung des Maximalen Volumens von Dampfblasen, Physik, 36, 379-384.
  12. Frumkin, A., and Levich, V.G. (1947). On surfactants and interfacial motion, Russian Journal of Physical Chemistry A, 21, 1183-1204.
  13. Fuchs, N.A. (1964). The mechanics of aerosols, New York, Pergamon.
  14. Gabillet, C., Colin, C., and Fabre, J. (2002). Experimental study of bubble injection in a turbulent boundary layer, International Journal of Multiphase Flow, 28, 553-578. https://doi.org/10.1016/S0301-9322(01)00075-1
  15. Ghiaasiaan, S.M., and Yao, G.F. (1997). A theoretical model for deposition of aerosols in rising spherical bubbles due to diffusion, convection, and inertia, Aerosol Science and Technology, 26, 141-153. https://doi.org/10.1080/02786829708965420
  16. Gorodetskaya, A. (1949). The rate of rise of bubbles in water and aqueous solutions at great Reynolds numbers, Russian Journal of Physical Chemistry A, 23, 71-78.
  17. Grace, J.R. (1973). Shapes and velocities of bubbles rising in infinite liquids, Transactions of the Institution of Chemical Engineers, 51, 116-120.
  18. Grace, J.R., Wairegi, T., and Nguyen, T.H. (1976). Shapes and velocities of single drops and bubbles moving freely through immiscible liquids, Transactions of the Institution of Chemical Engineer, 54, 167-173.
  19. Haberman, W.L. and Morton, R.K. (1953). An experimental investigation of the drag and shape of air bubbles rising in various liquids. Washington, D.C., David Taylor Model Basin.
  20. Hadamard, J.S. (1911). Mouvement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux, Comptes Rendus De L'Academie Des Sciences, 152, 1735-1738.
  21. Herranz, L.E., Peyres, V. Polo, J., Escudero, M.J., Espigares, M.M., and Lopez-Jimenez, J. (1997). Experimental and analytical study on pool scrubbing under jet injection regime, Nuclear Technology, 120, 95-109. https://doi.org/10.13182/NT97-A35419
  22. Houghton, G., Ritchie, P.D., and Thomson, J.A. (1957). Velocity of rise of air bubbles in sea-water, and their types of motion, Chemical Engineering Science, 7, 111-112. https://doi.org/10.1016/0009-2509(57)80026-8
  23. Ishii, M., and Zuber, N. (1979). Drag coefficient and relative velocity in bubbly, droplet or particulate flows." AIChE Journal, 25, 843-855. https://doi.org/10.1002/aic.690250513
  24. Jamialahmadi, M., Branch, C., and Müller-Steinhagen, H. (1994). Terminal bubble rise velocity in liquids, Chemical Engineering Research and Design, 72, 119-122.
  25. Kim, H.-S., and Park, S.H. (2008). Experimental study on particulate removal in a pool scrubber, Journal of Korean Society of Environmental Technology, 9, 20-25.
  26. Kim, J. (1999). A basic study on developing an electrocharged scrubber, Journal of Korean Society for Atmospheric Environment, 15, 33-39.
  27. Kim, M.Y., and Park, S.H. (2014). Characteristics of radioactive aerosol particles in nuclear power plant containments, Particle and Aerosol Research, 10, 137-154. https://doi.org/10.11629/jpaar.2014.10.4.137
  28. Laker, T.S., and Ghiaasiaan, S.M. (2004). Monte-Carlo simulation of aerosol transport in rising spherical bubbles with internal circulation, Journal of Aerosol Science, 35, 473-488. https://doi.org/10.1016/j.jaerosci.2003.10.007
  29. Levich, V.G., and Technica, S. (1962). Physicochemical hydrodynamics, Vol. 689, Englewood Cliffs, N.J., Prentice-Hall.
  30. Mendelson, H.D. (1967). The prediction of bubble terminal velocities from wave theory, AIChE Journal, 13, 250-253. https://doi.org/10.1002/aic.690130213
  31. Park, S.H., and Lee, B.-K. (2009). Development and application of a novel swirl cyclone scrubber: (2) Theoretical, Journal of Hazardous Materials, 164, 315-321. https://doi.org/10.1016/j.jhazmat.2008.08.023
  32. Park, S.H., Park, C., Lee, J., and Lee, B. (2017). A simple parameterization for the rising velocity of bubbles in a liquid pool, Nuclear Engineering and Technology, 49, http://dx.doi.org/10.1016/j.net.2016.12.006.
  33. Peebles, F.N., and Garber, H.J. (1953). Studies on the motion of gas bubbles in liquids, Chemical Engineering Progress, 49, 88-97.
  34. Pohorecki, R., Moniuk, W., Bielski, P., Sobieszuk, P., and Dąbrowiecki, G. (2005). Bubble diameter correlation via numerical experiment, Chemical Engineering Journal, 113, 35-39. https://doi.org/10.1016/j.cej.2005.08.007
  35. Powers, D.A., Brockmann, J.E., and Shiver, A.W. (1986). VANESA: a mechanistic model of radionuclide release and aerosol generation during core debris interactions with concrete. Albuquerque, N.M., Sandia National Labs.
  36. Ramsdale, S.A., Bamford, G.J., Fishwick, S., and Starkie, H.C. (1992). Status of research and modelling of water-pool scrubbing, Commission of the European Communities.
  37. Rosenberg, B. (1950). The drag and shape of air bubbles moving in liquids, David W. Taylor Model Basin.
  38. Rybczynski, W. (1911). On the translatory motion of a fluid sphere in a viscous medium, Bulletin international de l'Academie des sciences de Cracovie Series A, 40-46.
  39. Shin, S., Huyen, T.T., and Song, J. (2008). Removal of inorganic odorous compounds by scrubbing techniques using silver nano-particles, Journal of Korean Society for Atmospheric Environment, 24, 674-681. https://doi.org/10.5572/KOSAE.2008.24.6.674
  40. Sumner, B., and Moore, F.K. (1970). Boundary layer separation on a liquid sphere. Washington, D.C., National Aeronautics and Space Administration.
  41. Tadaki, T. and Maeda, S. (1961). On the shape and velocity of single air bubbles rising in various liquids, Kagaku Kogaku, 25, 254-264. https://doi.org/10.1252/kakoronbunshu1953.25.254
  42. Wallis, G.B. (1974). The terminal speed of single drops or bubbles in an infinite medium, International Journal of Multiphase Flow, 1, 491-511. https://doi.org/10.1016/0301-9322(74)90003-2
  43. Wassel, A.T., Mills, A.F., Bugby, D.C., and Oehlberg, R.N. (1985). Analysis of radionuclide retention in water pools, Nuclear Engineering and Design, 90, 87-104. https://doi.org/10.1016/0029-5493(85)90033-0