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Added mass of rising bubble approaching to solid wall – numerical studies

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The numerical approach for determination of influence of deformation of the gas bubble (radius 0.74 mm) on added mass coefficient in (i) steady-state conditions and (ii) during approach to the horizontal wall, is proposed. It is shown that the bubble deformation can be tuned numerically (within the range 1.06 - 1.88) via proper variations of the Laplace pressure, without changing the bubble radius. Influence of the bubble deformation on its motion parameters is discussed and compared to theoretical predictions regarding the bubble drag coefficient and Reynolds number. Moreover, the approach allowing determination of the added mass of rising bubble, on the basis of variations in fluid kinetic energy, is described. It is shown that calculated added mass variations strongly depends on the interplay between (i) the bubble deformation ratio and (ii) its rising velocity. This effect is especially important for added mass of a gas bubble approaching a solid wall, because it can affect the kinetics of drainage of the separating liquid film formed under dynamic conditions, when Re >> 1.
Rocznik
Strony
41--50
Opis fizyczny
Bibliogr. 26 poz., rys., tab., wykr., wz.
Twórcy
autor
  • Jerzy Haber Institute of Catalysis and Surface Chemistry Polish Academy of Sciences, ul. Niezapominajek 8, 30-239 Krakow, Poland
Bibliografia
  • BIRD, R., STEWART, W., LIGHTFOOT, E., 2007. Transport Phenomena, (2nd ed.). John Wiley and Sons, Inc., New York.
  • BRENNEN, C., 1982. A review of added mass and fluid inertial forces. CR 82.010 Report, Naval Civil Engineering Laboratory, Port Hueneme, 1-50.
  • CESCHIA M., NABERGOJ, R., 1978. On the motion of a nearly spherical bubble in a viscous liquid. Phys. Fluids 21, 140-142.
  • CLIFT, R., GRACE, J., WEBER, M., 1978. Bubbles, Drops and Particles. Academic Press, New York, San Francisco, London.
  • SANGANI, A., ZHANG, D., PROSPERETTI, A., 1991. The added mass, basset, and viscous drag coefficients in nondilute bubble liquids undergoing small-amplitude oscillatory motion. Phys. Fluids 3, 2955-2970.
  • FUSTER, D., AGBAGLAH, G., JOSSERAND, C., POPINET, S., ZALESKI, S., 2009. Numerical simulation of droplets, bubbles and waves: state of the art. Fluid Dyn. Res. 41, 065001.
  • HARPER, J., 2001. Growing bubbles rising in line. J. Appl. Math. Dec. Sci. 5, 65-73.
  • KLASEBOER, E., CHEVAILLER, J., MATE, A., MASBERNAT, O., GOURDON, C., 2011. Model and experiments of a drop impinging on a immersed wall. Phys. Fluids 13, 45–57.
  • KLASEBOER, E., MANICA, R., CHAN, D., KHOO, B., 2011. BEM simulations of potential flow with viscous effects as applied to a rising bubble. Eng. Analysis Boundary Elements 35, 489-494.
  • KLASEBOER, E., MANICA, R., HENDRIX, X., OHL, X., CJAN, D., 2014. A force balance model of the motion, impact and bounce of bubble. Phys. Fluids 26, 092101.
  • KOSIOR, D., ZAWALA, J., MALYSA, K., 2011. When and how a-terpineol and n-octanol can inhibit the bubble attachment to hydrophobic surfaces. Physicochem. Probl. Miner. Process, 47, 169-182.
  • KRISHNA, R., URSCANU, M., VAN BATEN, J., ELLENBERGER, J., 1999. Wall effect on the rise of single gas bubbles in liquids. Int. Comm. Heat Mass Transfer 26, 781-790.
  • KULKARNI, A., JOSHI, J., 2005. Bubble formation and bubble rise velocity in gas-liquid systems: a review. Ind. Eng. Chem. Res. 44, 5873-5931.
  • LEGENRE, D., ZENIT, R., VELEZ-CORDERO, R., 2012. On the deformation of gas bubbles in liquids. Phys. Fluids 24 043303.
  • LEVICH, V., 1962. Physicochemical Hydrodynamics. Prentice Hall, Inc., Englewood Cliffs, NJ.
  • MALYSA, K., 1992. Wet foams: Formation, properties and mechanism of stability. Adv. Colloid Interface Sci., 40, 37-83.
  • MILNE-THOMSON, L., 1968. Theoretical Hydrodynamics, (5th ed.). Macmillan and Co., LTD, London.
  • MOORE, D., 1965. The velocity of rise of distorted gas bubbles in a liquid of small viscosity,” J. Fluid Mech. 23, 749-766 (1965).
  • MUKUNDAKRISHNAN, K., QUAN, S., ECKMANN, D., AYYASWAMY, P., 2007. Numerical study of wall effects on buoyant gas-bubble rise in a liquid-filled finite cylinder. Physical Review E 76, 036308.
  • POPINET, S., 2003. Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190, 572-600.
  • POPINET, S., 2009. An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838-5866.
  • RASTELLO, M., MARIE, J.-L., LANCE, M., 2011. Drag and lift forces on clean spherical and ellipsoidal bubbles in a solid body rotating flow. J. Fluid Mech., 682, 434-459.
  • SIMCIK, M., RUZICKA, M., 2013. Added mass of dispersed particles by cfd: Further results. Chem. Eng. Sci. 97, 366-375.
  • TSAO, H.-K., KOCH, D., 1997. Observations of high reynolds number bubble interacting with rigid wall. Phys. Fluids 9, 44-56.
  • ZAWALA J., DABROS, T., 2013, Analysis of energy balance during collision of an air bubble with a solid wall. Phys. Fluids 25, 123101.
  • ZAWALA, J., 2016. Energy balance in viscous liquid containing a bubble: rise due to buoyancy. Can. J. Chem. Eng., 94, 586-595.
Uwagi
This research was supported by the statutory research founds of the ICSC PAS.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-9256e520-44e3-4d01-91c5-1c3f8781c3d4
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