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Research Article

Multi-fluid modelling of bubbly channel flows with an adaptive multi- group population balance method

D. Papoulias1( )A. Vichansky2M. Tandon3
Siemens Industries Software Computational Dynamics Ltd., 200 Shepherds Bush Road, London, W6 7NL, UK
Siemens Industries Software Computational Dynamics Ltd., Basil Hill Road, Didcot, OX11 7HJ, UK
Siemens Industries Software (India) Pvt.Ltd., Global Business Park Mehrauli-Gurgaon Road, Gurgaon, 122002, India
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An erratum to this article is available online at:

Abstract

Mass, momentum, and energy transfer in bubbly flows strongly depends on the bubble’s size distribution, which determines the contact area between the interacting phases. Characterization of bubble sizes in polydisperse flows requires empirical modelling of sub-grid physical mechanisms such as break-up and coalescence. In the present work an adaptive multiple size-group (A-MuSiG) method is incorporated into the Eulerian multiphase solver available in Simcenter STAR-CCM+ in order to model polydisperse bubbly flows in horizontal and vertical channels. The disperse phase- space is discretized into multiple size-groups each represented by its own size, number-density, and velocity field. The diameter of the bubbles in each of the size-groups varies in time and space, dynamically adapting to the local flow conditions. The interphase momentum transfer between the continuous phase and polydisperse bubbles is modelled through drag, virtual mass, turbulent dispersion, and lift forces. For modelling sub-grid bubble break-up and coalescence processes, different phenomenological kernels are evaluated. The empirical parameters of the adopted kernels are calibrated in two steps. The initial stage of the analysis considers experimental channel flows at low Reynolds number and zero-gravity conditions, under which the bubble size distribution is solely dependent on coalescence. As part of the second phase of the evaluation, additional parametric simulations in turbulent channel flows are performed in order to calibrate the break-up models, assuming the coalescence scaling constants derived in the previous step. The obtained results demonstrate that in flows with high turbulent mixing the ensuing bubble dynamics are strongly coupled to the internal properties of the population, which in turn influence the developing multiphase interactions in a transient manner.

References

 
T. R. Auton,, J. C. R. Hunt,, M. Prud'Homme, 1988. The force exerted on a body in inviscid unsteady non-uniform rotational flow. J Fluid Mech, 197: 241-257.
 
C. Bartsch,, V. Wiedmeyer,, Z. Lakdawala,, R. I. A. Patterson,, A. Voigt,, K. Sundmacher,, V. John, 2019. Stochastic-deterministic population balance modeling and simulation of a fluidized bed crystallizer experiment. Chem Eng Sci, 208: 115102.
 
G. K. Batchelor, 1970. An Introduction to Fluid Dynamics. Cambridge University Press.
 
M. R. Bhole,, J. B. Joshi,, D. Ramkrishna, 2008. CFD simulation of bubble columns incorporating population balance modeling. Chem Eng Sci, 63: 2267-2282.
 
G. A. Bird, 1976. Molecular Gas Dynamic. Oxford University Press.
 
A. K. Chesters, 1991. The modelling of coalescence processes in fluid-liquid dispersions: a review of current understanding. Chem Eng Res Des, 69: 259-270.
 
P. A. Durbin, 1993. A Reynolds stress model for near-wall turbulence. J Fluid Mech, 249: 465-498.
 
R. O. Fox, 2003. Computational Models for Turbulent Reacting Flows. Cambridge University Press.
 
T. Frank,, H. M. Prasser,, M. Beyer,, S. Al. Issa, 2007. Gas-liquid flow around an obstacle in a vertical pipe - CFD simulation & comparison to experimental data. In: Proceedings of the International Conference on Multiphase Flow, 6: 1-14.
 
M. Frenklach, 2002. Method of moments with interpolative closure. Chem Eng Sci, 57: 2229-2239.
 
M. M. Gibson,, B. E. Launder, 1978. Ground effects on pressure fluctuations in the atmospheric boundary layer. J Fluid Mech, 86: 491-511.
 
R. G. Gordon, 1968. Error bounds in equilibrium statistical mechanics. J Math Phys, 9: 655-663.
 
A. D. Gosman,, C. Lekakou,, S. Politis,, R. I. Issa,, M. K. Looney, 1992. Multidimensional modeling of turbulent two-phase flows in stirred vessels. AIChE J, 38: 1946-1956.
 
U. Hampel, 2019. Measurement techniques and experimental investigations for multiphase flows. In: Proceedings of the 17th Multiphase Flow Workshop - Conference and Short Course.
 
R. P. Hesketh,, T. W. Fraser Russell,, A. W. Etchells, 1987. Bubble size in horizontal pipelines. AIChE J, 33: 663-667.
 
J. O. Hinze, 1955. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J, 1: 289-295.
 
J. O. Hinze, 1959. Turbulence. Mc Graw-Hill Inc, USA.
 
X. Hao,, H. Zhao,, Z. Xu,, C. Zheng, 2013. Population balance-Monte Carlo simulation for gas-particle synthesis of nanoparticles. Aerosol Sci Tech, 47: 1125-1133.
 
A. M. Kamp,, A. K. Chesters,, C. Colin,, J. Fabre, 2001. Bubble coalescence in turbulent flows: A mechanistic model for turbulence-induced coalescence applied to microgravity bubbly pipe flow. Int J Multiphase Flow, 27: 1363-1396.
 
Y. P. Kim,, J. H. Seinfeld, 1990. Simulation of multicomponent aerosol condensation by the moving sectional method. J Colloid Interf Sci, 135: 185-199.
 
G. Kocamustafaogullari,, M. Ishii, 1995. Foundation of the interfacial area transport equation and its closure relations. Int J Heat Mass Tran, 38: 481-493.
 
G. Kocamustafaogullari,, Z. Wang, 1991. An experimental study on local interfacial parameters in a horizontal bubbly two-phase flow. Int J Multiphase Flow, 17: 553-572.
 
E. Krepper,, M. Beyer,, T. Frank,, D. Lucas,, H. M. Prasser, 2009. CFD modelling of polydispersed bubbly two-phase flow around an obstacle. Nucl Eng Des, 239: 2372-2381.
 
S. Kumar,, D. Ramkrishna, 1996a. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chem Eng Sci, 51: 1311-1332.
 
S. Kumar,, D. Ramkrishna, 1996b. On the solution of population balance equations by discretization—II. A moving pivot technique. Chem Eng Sci, 51: 1333-1342.
 
B. Launder,, N. Sandham, 2002. Closure Strategies for Turbulent and Transitional Flows. Cambridge University Press.
 
K. W. Lee,, J. Chen,, J. A. Gieseke, 1984. Log-normally preserving size distribution for Brownian coagulation in the free-molecule regime. Aerosol Sci Tech, 3: 53-62.
 
V. G. Levich, 1962. Physichemical Hydrodynamics. New Jersey: Prentice Hall, Engewood Cliffs.
 
Y. Liao,, D. Lucas, 2010. A literature review on mechanisms and models for the coalescence process of fluid particles. Chem Eng Sci, 65: 2851-2864.
 
S. Lo,, D. Zhang, 2009. Modelling of break-up and coalescence in bubbly two-phase flows. J Comput Multiphase Flows, 1: 23-38.
 
H. Luo, 1993. Coalescence, breakup and liquid circulation in bubble column reactors. Ph.D. Thesis. Norges Tekniske Hoegskole, Trondheim.
 
M. Ma,, J. Lu,, G. Tryggvason, 2015. Using statistical learning to close two-fluid multiphase flow equations for a simple bubbly system. Phys Fluids, 27: 092101.
 
R. Manceau,, K. Hanjalic, 2000. A new form of the elliptic relaxation equation to account for wall effects in RANS modeling. Phys Fluids, 12: 2345-2351.
 
D. L. Marchisio,, R. O. Fox, 2005. Solution of population balance equations using the direct quadrature method of moments. J Aerosol Sci, 36: 43-73.
 
C. Martinez-Bazan,, J. Rodriguez-Rodriguez,, G. B. Deane,, J. L. Montañes,, J. C. Lasheras, 2010. Considerations on bubble fragmentation models. J Fluid Mech, 661: 159-177.
 
R. McGraw, 1997. Description of aerosol dynamics by the quadrature method of moments. Aerosol Sci Tech, 27: 255-265.
 
A. J. Mohs,, F. M. Bowman, 2011. Eliminating numerical artifacts when presenting moving center sectional aerosol size distributions. Aerosol Air Qual Res, 11: 21-30.
 
D. Papoulias,, A. Spalwski,, A. Vikhansky,, S. Lo, 2016. Eulerian multiphase predictions of turbulent bubbly flow in a step-channel expansion. Int Conference Mult Flow, Firenze, Italy.
 
D. Ramkrishna, 2000. Population Balances Theory and Applications to Particulate Systems in Engineering. Academic Press.
 
D. Ramkrishna,, M. R. Singh, 2014. Population balance modeling: Current status and future prospects. Annu Rev Chem Biomol Eng, 5: 123-146.
 
A. D. Randolph, 1964. A population balance for countable entities. Can J Chem Eng, 42: 280-281.
 
A. D. Randolph,, M. A. Larson, 1971. Theory of Particulate Processes: Analysis and Techniques of Continuous Crystallization. New York: Academic.
 
B. Sajjadi,, A. A. A. Raman,, S. Ibrahim,, R. Shah, 2012. Review on gas-liquid mixing analysis in multiscale stirred vessel using CFD. Rev Chem Eng, 28: 171-189.
 
C. C. Shu,, A. Chatterjee,, W. S. Hu,, D. Ramkrishna, 2012. Modeling of gene regulatory processes by population-mediated signaling: New applications of population balances. Chem Eng Sci, 70: 188-199.
 
A. Tomiyama,, H. Tamai,, I. Zun,, S. Hosokawa, 2002. Transverse migration of single bubbles in simple shear flows. Chem Eng Sci, 57: 1849-1858.
 
C. Tsouris,, L. L. Tavlarides, 1994. Breakage and coalescence models for drops in turbulent dispersions. AIChE J, 40: 395-406.
 
A. Vikhansky, 2013. Direct quadrature spanning tree method for solution of the population balance equations. J Aerosol Sci, 55: 78-88.
 
A. Vikhansky, 2017. Combined Multifluid-Population Balance Method for Polydisperse Multiphase Flows. Progress in App CFD, Trondheim, Norway: 281-284.
 
A. Vikhansky,, A. Splawski, 2015. Adaptive multiply size group method for CFD-population balance modelling of polydisperse flows. Can J Chem Eng, 93: 1327-1334.
 
K. Wang,, S. Yu,, W. Peng, 2019. Extended log-normal method of moments for solving the population balance equation for Brownian coagulation. Aerosol Sci Tech, 53: 332-343.
 
J. Young,, A. Leeming, 1997. A theory of particle deposition in turbulent pipe flow. J Fluid Mech, 340: 129-159.
 
L. I. Zaichik,, O. Simonin,, V. M. Alipchenkov, 2010. Turbulent collision rates of arbitrary-density particles. Int J Heat Mass Tran, 53: 1613-1620.
 
H. Zhao,, A. Maisels,, T. Matsoukas,, C. Zheng, 2007. Analysis of four Monte Carlo methods for the solution of population balances in dispersed systems. Powder Technol, 173: 38-50.
Experimental and Computational Multiphase Flow
Pages 171-185
Cite this article:
Papoulias D, Vichansky A, Tandon M. Multi-fluid modelling of bubbly channel flows with an adaptive multi- group population balance method. Experimental and Computational Multiphase Flow, 2021, 3(3): 171-185. https://doi.org/10.1007/s42757-020-0084-5

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Received: 30 March 2020
Revised: 23 June 2020
Accepted: 19 August 2020
Published: 21 October 2020
© Tsinghua University Press 2020
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