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 OJFD  Vol.7 No.3 , September 2017
Simulating Spiraling Bubble Movement in the EL Approach
Abstract: Simulating the detailed movement of a rising bubble can be challenging, especially when it comes to bubble path instabilities. A solution based on the Euler Lagrange (EL) approach is presented, where the bubbles show oscillating shape and/or instable paths while computational cost are at a far lower level than in DNS. The model calculates direction, shape and rotation of the bubbles. A lateral force based on rotation and direction is modeled to finally create typical instable path lines. This is embedded in an EL simulation, which can resolve bubble size distribution, mass transfer and chemical reactions. A parameter study was used to choose appropriate model constants for a mean bubble size of 3 mm. To ensure realistic solution, validation against experimental data of single rising bubbles and bubble swarms are presented. References with 2D and also 3D analysis are taken into account to compare simulative data in terms of typical geometrical parameters and average field values.
Cite this paper: Weber, A. , Bart, H. and Klar, A. (2017) Simulating Spiraling Bubble Movement in the EL Approach. Open Journal of Fluid Dynamics, 7, 288-309. doi: 10.4236/ojfd.2017.73019.
References

[1]   Aybers, N.M. and Tapucu, A. (1969) The Motion of Gas Bubbles Rising through Stagnant Liquid. Wärme-und Stoffübertragung, 2, 118-128.
https://doi.org/10.1007/BF01089056

[2]   Shew, W.L. and Pinton, J.-F. (2006) Viscoelastic Effects on the Dynamics of a Rising Bubble. Journal of Statistical Mechanics: Theory and Experiment, 01, P01009-P01009.
https://doi.org/10.1088/1742-5468/2006/01/P01009

[3]   Mougin, G. and Magnaudet, J. (2006) Wake-Induced Forces and Torques on a Zigzagging/Spralling Bubble. Journal of Fluid Mechanics, 567, 185-194.
https://doi.org/10.1017/S0022112006002266

[4]   Mason, L.R., Stevens, G.W. and Harvie, D.J.E. (2012) Multi-Scale Volume of Fluid Modelling of Droplet Coalescence. The 9th International Conference on CFD in the Minerals and Process Industries, Melbourne, 10-12 December 2012, 1-6.

[5]   Gruber, M.C., Radl, S. and Khinast, J.G. (2015) Rigorous Modeling of CO2 Absorption and Chemisorption. The Influence of Bubble Coalescence and Breakage. Chemical Engineering Science, 137, 188-204.
https://doi.org/10.1016/j.ces.2015.06.008

[6]   Launder, B.E. and Spalding, D.B. (1972) Lectures in Mathematical Models of Turbulence. Academic Press (London), London, New York.

[7]   Rzehak, R. and Krepper, E. (2013) Bubble-Induced Turbulence: Comparison of CFD Models. Nuclear Engineering and Design, 258, 57-65.
https://doi.org/10.1016/j.nucengdes.2013.02.008

[8]   Tomiyama, A. (2004) Drag, Lift and Virtual Mass Force Acting on a Single Bubble. 3rd International Symposium on Two-Phase Flow Modelling and Experimentation, Pisa, 22-25 September 2004, 22-24.

[9]   Delnoij, E., Lammers, F., Kuipers, J.A. and van Swaaij, W. (1997) Dynamic Simulation of Dispersed Gas-Liquid Two-Phase Flow Using a Discrete Bubble Model. Chemical Engineering Science, 52, 1429-1458.
https://doi.org/10.1016/S0009-2509(96)00515-5

[10]   Lahey, R.T., Lopez de Bertodano, M. and Jones, O.C. (1993) Phase Distribution in Complex Geometry Conduits. Nuclear Engineering and Design, 141, 177-201.
https://doi.org/10.1016/0029-5493(93)90101-E

[11]   Smith, B.L. and Milelli, M. (1998) An Investigation of Confined Bubble Plumes. International Conference on Multiphase Flow, 98, 8-12.

[12]   O’Rourke, P.J. (1981) Collective Drop Effects on Vaporizing Liquid Sprays. Los Alamos National Lab., NM (USA), No. LA-9069-T.

[13]   Moore, D.W. (1965) The Velocity of Rise of Distorted Gas Bubbles in a Liquid of Small Viscosity. Journal of Fluid Mechanics, 23, 749.
https://doi.org/10.1017/S0022112065001660

[14]   Shew, W.L. and Pinton, J.-F. (2006) Dynamical Model of Bubble Path Instability. Physical Review Letters, 97, Article ID: 144508.
https://doi.org/10.1103/PhysRevLett.97.144508

[15]   Taylor, G.I. (1923) The Motion of Ellipsoidal Particles in a Viscous Fluid. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 103, 58-61.
https://doi.org/10.1098/rspa.1923.0040

[16]   Junk, M. and Illner, R. (2007) A New Derivation of Jeffery’s Equation. Journal of Mathematical Fluid Mechanics, 9, 455-488.
https://doi.org/10.1007/s00021-005-0208-0

[17]   Kováts, P., Thévenin, D. and Zähringer, K. (2017) Investigation of Mass Transfer and Hydrodynamics in a Model Bubble Column. Chemical Engineering & Technology, 8, 1434-1444.
https://doi.org/10.1002/ceat.201600679

[18]   Rzehak, R., Krauβ, M., Kováts, P. and Zähringer, K. (2017) Fluid Dynamics in a Bubble Column: New Experiments and Simulations. International Journal of Multiphase Flow, 89, 299-312.
https://doi.org/10.1016/j.ijmultiphaseflow.2016.09.024

[19]   Kováts, P., Thévenin, D. and Zähringer, K. (2017) Characterizing Fluid Dynamics in a Bubble Column Aimed for the Determination of Reactive Mass Transfer. Heat and Mass Transfer, Submitted.
https://doi.org/10.1007/s00231-017-2142-0

[20]   Liao, Y., Rzehak, R., Lucas, D. and Krepper, E. (2015) Baseline Closure Model for Dispersed Bubbly Flow. Bubble Coalescence and Breakup. Chemical Engineering Science, 122, 336-349.
https://doi.org/10.1016/j.ces.2014.09.042

[21]   Sommerfeld, M. and Bröder, D. (2009) Analysis of Hydrodynamics and Microstructure in a Bubble Column by Planar Shadow Image Velocimetry. Industrial & Engineering Chemistry Research, 48, 330-340.
https://doi.org/10.1021/ie800838u

[22]   Ellingsen, K. and Risso, F. (2001) On the Rise of an Ellipsoidal Bubble in Water. Oscillatory Paths and Liquid-Induced Velocity. Journal of Fluid Mechanics, 440, 235-268.
https://doi.org/10.1017/S0022112001004761

[23]   Mercier, J., Lyrio, A. and Forslund, R. (1973) Three-Dimensional Study of the Nonrectilinear Trajectory of Air Bubbles Rising in Water. Journal of Applied Mechanics, 3, 650-654.
https://doi.org/10.1115/1.3423065

[24]   Ern, P., Risso, F., Fabre, D. and Magnaudet, J. (2012) Wake-Induced Oscillatory Paths of Bodies Freely Rising or Falling in Fluids. Annual Review of Fluid Mechanics, 1, 97-121.
https://doi.org/10.1146/annurev-fluid-120710-101250

 
 
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