Interaction of two in-line bubbles of equal size rising in viscous liquid

doi:10.1016/j.cjche.2019.06.003

摘要/Abstract

摘要： The interaction of bubbles is the key to understand gas-liquid bubbling flow. Two-dimensional axis-symmetry computational fluid dynamics simulations on the interactive bubbles were performed with VOF method, which was validated by experimental work. It is testified that several different bubble interactive behaviors could be acquired under different conditions. Firstly, for large bubbles (d:4, 6, 8, 10 mm), the trailing bubble rising velocity and aspect ratio have negative correlations with liquid viscosity and surface tension. The influences of viscosity and surface tension on leading bubble are negligible. Secondly, for smaller bubbles (d:1, 2 mm), the results are complicated. The two bubbles tend to move together due to the attractive force by the wake and the potential repulsive force. Especially for high viscous or high surface tension liquid, the bubble pairs undergo several times acceleration and deceleration. In addition, bubble deformation plays an important role during bubble interaction which cannot be neglected.

关键词: Bubble column reactor, Computational fluid dynamics, Bubble interaction, Bubble rise velocity, Volume-of-fluid method, Bubble aspect ratio

Abstract: The interaction of bubbles is the key to understand gas-liquid bubbling flow. Two-dimensional axis-symmetry computational fluid dynamics simulations on the interactive bubbles were performed with VOF method, which was validated by experimental work. It is testified that several different bubble interactive behaviors could be acquired under different conditions. Firstly, for large bubbles (d:4, 6, 8, 10 mm), the trailing bubble rising velocity and aspect ratio have negative correlations with liquid viscosity and surface tension. The influences of viscosity and surface tension on leading bubble are negligible. Secondly, for smaller bubbles (d:1, 2 mm), the results are complicated. The two bubbles tend to move together due to the attractive force by the wake and the potential repulsive force. Especially for high viscous or high surface tension liquid, the bubble pairs undergo several times acceleration and deceleration. In addition, bubble deformation plays an important role during bubble interaction which cannot be neglected.

Key words: Bubble column reactor, Computational fluid dynamics, Bubble interaction, Bubble rise velocity, Volume-of-fluid method, Bubble aspect ratio

Zhen Tian, Xi Li, Youwei Cheng, Lijun Wang. Interaction of two in-line bubbles of equal size rising in viscous liquid[J]. 中国化学工程学报, 2020, 28(1): 54-62.

Zhen Tian, Xi Li, Youwei Cheng, Lijun Wang. Interaction of two in-line bubbles of equal size rising in viscous liquid[J]. Chinese Journal of Chemical Engineering, 2020, 28(1): 54-62.

参考文献

[1] H.A.N. Wang, Z.Y. Zhang, Y.M. Yang, H.S. Zhang, Numerical investigation of the interaction mechanism of two bubbles, Int. J. Mod. Phys. C 21(01) (2010) 33-49.
[2] A.A. Kulkarni, J.B. Joshi, Bubble formation and bubble rise velocity in gas-liquid systems:a review, Ind. Eng. Chem. Res. 44(16) (2005) 5873-5931.
[3] J.F. Harper, The motion of bubbles and drops through liquids, Adv. Appl. Mech, Elsevier 12(1972) 59-129.
[4] B. Bunner, G. Tryggvason, An examination of the flow induced by the motion of many buoyant bubbles, J. Visual 2(2) (1999) 153-158.
[5] X. Chai, X. Liu, J. Xiong, X. Cheng, Numerical investigation of bubble wake properties in the moving liquid with LES model, J. Nucl. Sci. Technol. 53(11) (2016) 1870-1880.
[6] J.B. Joshi, K. Nandakumar, G.M. Evans, V.K. Pareek, M.M. Gumulya, M.J. Sathe, M.A. Khanwale, Bubble generated turbulence and direct numerical simulations, Chem. Eng. Sci. 157(2017) 26-75.
[7] H.A. Jakobsen, H. Lindborg, C.A. Dorao, Modeling of bubble column reactors:progress and limitations, Ind. Eng. Chem. Res. 44(14) (2005) 5107-5151.
[8] J. Crabtree, J. Bridgwater, Bubble coalescence in viscous liquids, Chem. Eng. Sci. 26(6) (1971) 839-851.
[9] D. Bhaga, M. Weber, In-line interaction of a pair of bubbles in a viscous liquid, Chem. Eng. Sci. 35(12) (1980) 2467-2674.
[10] I. Komasawa, T. Otake, M. Kamojima, Wake behavior and its effect on interaction between spherical-cap bubbles, J. Chem. Eng. Jpn 13(2) (1980) 103-109.
[11] S. Narayanan, L.H.J. Goossens, N.W.F. Kossen, Coalescence of two bubbles rising in line at low Reynolds numbers, Chem. Eng. Sci. 29(10) (1974) 2071-2082.
[12] J. Katz, C. Meneveau, Wake-induced relative motion of bubbles rising in line, Int. J. Multiphase Flow 22(2) (1996) 239-258.
[13] J.F. Harper, On bubbles rising in line at large Reynolds numbers, J. Fluid Mech. 41(04) (1970) 751-758.
[14] H. Yuan, A. Prosperetti, On the in-line motion of two spherical bubbles in a viscous fluid, J. Fluid Mech. 278(1994) 325-349.
[15] M. Watanabe, T. Sanada, In-line motion of a pair of bubbles in a viscous liquid, Jsme. Int. J. B-Fluid. T 49(2) (2006) 410-418.
[16] J. Zhang, L.S. Fan, On the rise velocity of an interactive bubble in liquids, Chem. Eng. J. 92(1-3) (2003) 169-176.
[17] J.R. Muñoz, A. Soria, E. Salinas-Rodríguez, On the relative motion of two spherical bubbles rising in line and interacting by a laminar wake, AIChE Annual Meeting, Conference Proceedings 2005, pp. 689-693.
[18] J. Ramírez-Muñoz, A. Soria, E. Salinas-Rodríguez, Hydrodynamic force on interactive spherical particles due to the wake effect, Int. J. Multiphase Flow 33(7) (2007) 802-807.
[19] J. Ramírez-Muñoz, A. Gama-Goicochea, E. Salinas-Rodríguez, Drag force on interacting spherical bubbles rising in-line at large Reynolds number, Int. J. Multiphase Flow 37(8) (2011) 983-986.
[20] J. Ramírez-Muñoz, E. Salinas-Rodríguez, A. Soria, A. Gama-Goicochea, Hydrodynamic interaction on large-Reynolds-number aligned bubbles:drag effects, Nucl. Eng. Des. 241(7) (2011) 2371-2377.
[21] S.A. Baz-Rodríguez, J. Ramírez-Muñoz, A. Soria, In-line interaction between two spherical particles due to a laminar wake effect, Int. J. Multiphase Flow 39(2012) 240-244.
[22] J. Ramírez-Muñoz, S. Baz-Rodríguez, E. Salinas-Rodríguez, E. Castellanos-Sahagún, H. Puebla, Forces on aligned rising spherical bubbles at low-to-moderate Reynolds number, Phys. Fluids 25(9) (2013), 093303.
[23] S.A. Baz-Rodríguez, J. Ramírez-Muñoz, A. Soria, J.C. Sacramento-Rivero, Hydrodynamic interaction of two spherical bubbles rising in-line:a semi-analytical approach, Chem. Eng. Commun. 201(5) (2014) 674-687.
[24] M. Gumulya, R.P. Utikar, G.M. Evans, J.B. Joshi, V. Pareek, Interaction of bubbles rising inline in quiescent liquid, Chem. Eng. Sci. 166(2017) 1-10.
[25] J. Feng, X. Li, Y. Bao, Z. Cai, Z. Gao, Coalescence and conjunction of two in-line bubbles at low Reynolds numbers, Chem. Eng. Sci. 141(2016) 261-270.
[26] N. Hasan, Z.b. Zakaria, Computational approach for a pair of bubble coalescence process, Int. J. Heat Fluid Flow 32(3) (2011) 755-761.
[27] M. Cheng, J. Hua, J. Lou, Simulation of bubble-bubble interaction using a lattice Boltzmann method, Comput. Fluids 39(2) (2010) 260-270.
[28] E. Delnoij, J.A.M. Kuipers, W.P.M. van Swaaij, Computational fluid dynamics applied to gas-liquid contactors, Chem. Eng. Sci. 52(21) (1997) 3623-3638.
[29] C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys. 39(1) (1981) 201-225.
[30] D. Ma, M. Liu, Y. Zu, C. Tang, Two-dimensional volume of fluid simulation studies on single bubble formation and dynamics in bubble columns, Chem. Eng. Sci. 72(2012) 61-77.
[31] J. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension, J. Comput. Phys. 100(2) (1992) 335-354.
[32] D.L. Youngs, Time-dependent multi-material flow with large fluid distortion, Numerical Methods for Fluid Dynamics, 1982.
[33] R. Moissis, P. Griffith, Entrance effects in a two-phase slug flow, J. Heat Transf. 84(1) (1962) 29-38.
[34] A.M.F.R. Pinto, M.N. Coelho Pinheiro, J.B.L.M. Campos, Coalescence of two gas slugs rising in a co-current flowing liquid in vertical tubes, Chem. Eng. Sci. 53(16) (1998) 2973-2983.
[35] D. Bhaga, M.E. Weber, Bubbles in viscous liquids:shapes, wakes and velocities, J. Fluid Mech. 105(1981) 61-85.
[36] R. Turton, O. Levenspiel, A short note on the drag correlation for spheres, Powder Technol. 47(1) (1986) 83-86.
[37] Z. Yu, H. Yang, L.-S. Fan, Numerical simulation of bubble interactions using an adaptive lattice Boltzmann method, Chem. Eng. Sci. 66(14) (2011) 3441-3451.
[38] M. Manga, H.A. Stone, Collective hydrodynamics of deformable drops and bubbles in dilute low Reynolds number suspensions, J. Fluid Mech. 300(1995) 231-263.