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THEORETICAL STUDY OF MOTION OF SMALL SPHERICAL AIR BUBBLES IN A UNIFORM SHEAR FLOW OF WATER

  • MEHDI, SYED MURTUZA (Department of Mechatronics Engineering, Jeju National University) ;
  • KIM, SIN (School of Energy Systems Engineering, Chung-Ang University)
  • Received : 2014.07.24
  • Accepted : 2014.10.23
  • Published : 2015.02.25

Abstract

A simple Couette flow velocity profile with an appropriate correlation for the free terminal rise velocity of a single bubble in a quiescent liquid can produce reliable results for the trajectories of small spherical air bubbles in a low-viscosity liquid (water) provided the liquid remains under uniform shear flow. Comparison of the model adopted in this paper with published results has been accomplished. Based on this study it has also been found that the lift coefficient in water is higher than its typical value in a high-viscosity liquid and therefore a modified correlation for the lift coefficient in a uniform shear flow of water within the regime of the $E\ddot{o}tv\ddot{o}s$ number $0.305{\leq}Eo{\leq}1.22$ is also presented.

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

  1. L.S. Timkin, R.S. Gorelik, P.D. Labanov, Rise of a single bubble in ascending laminar flow: slip velocity and wall friction, Journal of Engineering Physics and Thermophysics 78 (2005) 762-768. https://doi.org/10.1007/s10891-005-0124-4
  2. A. Tomiyama, K. Isao, Z. Iztok, S. Tadashi, Drag coefficient of single bubbles under normal and micro gravity conditions, JSME International Journal Series B 41 (1998) 472-479. https://doi.org/10.1299/jsmeb.41.472
  3. S.S. Rabha, V.V. Buwa, Volume-of-fluid (VOF) simulations of rise of single/multiple bubbles in sheared liquids, Chemical Engineering Science 65 (2010) 527-537. https://doi.org/10.1016/j.ces.2009.06.061
  4. A. Tomiyama, H. Tamai, I. Zun, S. Hosokawa, Transverse migration of single bubbles in simple shear flows, Chemical Engineering Science 57 (2002) 1849-1858. https://doi.org/10.1016/S0009-2509(02)00085-4
  5. D. Bothe, M. Schmidtke, H.J. Warnecke, VOF-simulations of the rise behavior of single air bubbles in linear shear flows, Chemical Engineering and Technology 29 (2006) 1048-1053. https://doi.org/10.1002/ceat.200600168
  6. D. Rodrigue, A general correlation for the rise velocity of single gas bubbles, The Canadian Journal of Chemical Engineering 82 (2004) 382-386.
  7. G.P. Celata, F.D. Annibale, P. Di Marco, G. Memoli, A. Tomiyama, Measurements of rising velocity of a small bubble in a stagnant fluid in one-andtwo-componentsystems, Experimental Thermal and Fluid Science 31 (2007) 609-623. https://doi.org/10.1016/j.expthermflusci.2006.06.006
  8. R. Clift, J.R. Grace, M.E. Weber, Bubbles, Drops and Particles, Academic Press, New York, 1978.
  9. M. Ishii, T.C. Chawla, Local Drag Laws in Dispersed Twophase Flow, ANL-79-105, 1979.
  10. M. Jamialahmadi, C. Branch, H. Muller-Steinhagen, Terminal bubble rise velocity in liquids, Chemical Engineering Research and Design 72 (1994) 119-122.
  11. A. Tomiyama, A. Sou, Z. Iztok, N. Kanami, T. Sakaguchi, Effects of E€otv€os Number and Dimensionless Liquid Volumetric Flux on Lateral Motion of a Bubble in a Laminar Duct Flow, Advances in Multiphase Flow, 1995.
  12. N. Maeda, Behavior of a single bubble in quiescent and flowing liquid inside a cylindrical tube, Journal of Nuclear Science and Technology 12 (1975) 606-617. https://doi.org/10.1080/18811248.1975.9733161
  13. P.C. Duineveld, The rise velocity and shape of bubbles in pure water at high Reynolds number, Journal of Fluid Mechanics 292 (1995) 325-332. https://doi.org/10.1017/S0022112095001546
  14. M. Wu, M. Gharib, Experimental studies on the shape and path of small air bubbles rising in clean water, Physics of Fluids 14 (2002) L49-L52. https://doi.org/10.1063/1.1485767
  15. N.M.S. Hassan, M.M. Khan, M.G. Rasul, A study of bubble trajectory and drag co-efficient in water and non Newtonian fluids, WSEAS Transactions on Fluid Mechanics 3 (2008) 261-270.
  16. W.L. Haberman, R.K. Morton, An Experimental Investigation of Drag and Shape of Air Bubbles Rising in Different Liquids, The David W. Taylor Model Basin, Washington, 1953, 7, D.C. Report 802 NS 715-102.
  17. R.M. Wellek, A.K. Agarwal, A.H.P. Skelland, Shapes of liquid drops moving in liquid media, AIChE Journal 12 (1966) 854-862. https://doi.org/10.1002/aic.690120506
  18. W. Dijkhuizen, M. van Sint Annaland, J.A.M. Kuipers, Numerical and experimental investigation of lift force on single bubbles, Chemical Engineering Science 65 (2010) 1274-1287. https://doi.org/10.1016/j.ces.2009.09.084
  19. T. Hibiki, M. Ishii, Lift force in bubbly flow systems, Chemical Engineering Science 62 (2007) 6457-6474. https://doi.org/10.1016/j.ces.2007.07.034