Modeling of Bubbly Flow using a Combined Volume of Fluid and Discrete Bubble Model: Investigation on Interphase Forces

Document Type : Regular Article

Authors

National-Provincial Joint Engineering Laboratory for Fluid Transmission System Technology, Zhejiang Sci-Tech University, Hangzhou, Zhejiang, 310018, China

Abstract

The gas-liquid two-phase flow with interfacial behaviors and bubble-liquid interactions is widely encountered in industrial processes such as that in gas-liquid reactors. The complicated phase structure makes it difficult to be modeled. The present work proposes a multi-scale mathematical model to simulate the bubbly flow in a square column. The volume of fluid (VOF) method is applied to treat the separated interface, and the discrete bubble model (DBM) is incorporated to handle the dynamics of dispersed bubbles. The hybrid model is validated against the benchmark experimental data to study the accuracy and suitability of the modeling framework for bubbly flows. And the influence of interphase forces on bubbly flow patterns and velocity profiles is investigated. It is found that the employment of both pressure gradient force and Ishii-Zuber drag model provides fairly good agreements with experimental data for velocity profiles. 

Keywords


Bokkers, G. A., J. A. Laverman and M. V. S Annaland (2006). Modelling of large-scale dense gas–solid bubbling fluidised beds using a novel discrete bubble model. Chemical Engineering Science 61(17), 5290-5302.##
Brackbill, J. U., D. B. Kothe and C. Zemach (1992). A continuum method for modeling surface tension. Journal of Computational Physics 100(2), 335–354.##
Chahed, J., V. Roig and L. Masbernat (2003). Eulerian–Eulerian two-fluid model for turbulent gas–liquid bubbly flows. International Journal of Multipahse Flow 29, 23-49.##
Clift, G. and W. Bubbles (1978). Drops, and Particles. Technical Report. Academic Press.##
Cloete, S. W. P., J. J. Eksteen and S. M. Bradshaw (2013). A numerical modelling investigation into design variables influencing mixing efficiency in full scale gas stirred ladles. Minerals Engineering 46-47, 16-24.##
Darmana, D., N. G. Deen and J. A. M. Kuipers (2006). Parallelization of an Euler–Lagrange model using mixed domain decomposition and a mirror domain technique: Application to dispersed gas–liquid two-phase flow. Journal of Computational Physics 220 (1), 216–248.##
Deen, N.G., B. H. Hjertager and T. Solberg (2000). Comparison of PIV and LDA Measurement Methods Applied to the Gas-Liquid Flow in a Bubble Column. Proc. 10th Intl Symp. on Appl. of Laser Techniques to Fluid Mech, Lisbon, Portugal.##
Deen, N. G., T. Solberg and B. H. Hjertager (2001). Large Eddy simulation of the gas–liquid flow in a square cross-sectioned bubble column. Chemical Engineering Science 56, 6341–6349.##
Delnoij, E., F. A. Lammers, J. A. M. Kuipers and W. P. M. V. Swaaij (1997). Dynamic simulation of dispersed gas-liquid two-phase flow using a discrete bubble model. Chemical Engineering Science 52(9), 1429-1458.##
Gosman, A. D. and E. Ioannides (1983). Aspects of computer simulation of liquid-fuelled combustors. Journal of Energy Chemistry 7(6), 482–490. ##
Hirt, C. W. and B. D. Nichols (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physic 39, 201-225.##
Hoomans, B. P. B., J. A. M. Kuipers, W. J. Briels and W. P. M. V. Swaaij (1996). Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: A hard-sphere approach. Chemical Engineering Science 51, 99.##
Ishii, M. and N. Zuber (1979). Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulate Flows. AIChE Journal 25, 843-855.## 
Jain, D., J. A. M. Kuipers and N. G. Deen (2014). Numerical study of coalescence and breakup in a bubble column using a hybrid volume of fluid and discrete bubble model approach. Chemical Engineering Science 119, 134-146.##
Jiang, X., N. Yang and B. Yang (2016). Computational fluid dynamics simulation of hydrodynamics in the riser of an external loop airlift reactor. Particuology 27, 95–101.##
Li, A. and G. Ahmadi (1992). Dispersion and Deposition of Spherical Particles from Point Sources in a Turbulent Channel Flow. Aerosol Science and Technology 16, 209-226.##
Li, L. and B. Li (2018). Implementation and validation of a volume-of-fluid and discrete-element-method combined solver in OpenFOAM. Particuology 39, 109-115.##
Li, L., B. Li and Z. Liu (2017). Modeling of Gas-Steel-Slag Three-Phase Flow in Ladle Metallurgy: Part II. Multi-scale Mathematical Model. ISIJ International 57(11), 1980-1989.##
Li, L., X. Li, Z. Zhu and B. Li (2020). Numerical modeling of multiphase flow in gas stirred ladles: From a multiscale point of view. Powder Technology 373, 14-25.##
Liu, J., C. Zhu, T. Fu and Y. Ma (2014). Systematic Study on the Coalescence and Breakup Behaviors of Multiple Parallel Bubbles Rising in Power-law Fluid. Industrial & Engineering Chemistry Research 53, 4850–4860.##
Liu, M. and Z. Hu (2004). Studies on the hydrodynamics of chaotic bubbling in a gas–liquid bubble column with a single nozzle. Chemical Engineering & Technology 27, 537–547.##
Ma, D., M. Liu, Y. Zu and C. Tang (2012). Two-dimensional volume of fluid simulation studies onsingle bubble formation and dynamics in bubble columns. Chemical Engineering Science 72, 61–77.##
Matiazzo, T., R. K. Decker, J. C. S. C. Bastos, M. K. Silva and H. F. Meier (2020). Investigation of Breakup and Coalescence Models for Churn-Turbulent Gas-Liquid Bubble Columns. Journal of Applied Fluid Mechanics 13, 737-751.##
Menter, F. R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications. Aiaa Journal 32(8), 1598-1605.##
Morsi, S. A. and A. J. Alexander (1972). An Investigation of Particle Trajectories in Two-Phase Flow Systems. Journal of Fluid Mechanics 55(2), 193–208.##
Olsen, J. E. and P. Skjetne (2016). Modelling of underwater bubble plumes and gas dissolution with an Eulerian-Lagrangian CFD model. Applied Ocean Research 59, 193-200.##
O'Rourke, P. J (1981). Collective Drop Effects on Vaporizing Liquid Sprays, Ph.D. Thesis, Mechanical and Aerospace Engineering, Princeton University, USA.##
Passalacqua, A. and R. O. Fox (2011). Implementation of an iterative solution procedure for multi-fluid gas–particle flow models on unstructured grids. Powder Technology 213, 174-187.##
Pfleger, D., S. Gomes, N. Gilbert and H. G. Wagner (1999). Hydrodynamic simulations of laboratory scale bubble columns fundamental studies of the Eulerian–Eulerian modelling approach. Chemical Engineering Science 54, 5091-5099.##
Saffman, P. G. (1965). The Lift on a Small Sphere in a Slow Shear Flow. Journal of Fluid Mechanics 22, 385–400.##
Bourloutski E. and Sommerfeld M. (2004). Euler/Lagrange Calculations of Gas-Liquid-Solid-Flows in Bubble Columns with Phase Interaction. In: Sommerfeld M. (eds) Bubbly Flows. Heat and Mass Transfer. Springer, Berlin, Heidelberg.##
van den Hengel, E. I. V., N. G. Deen and J. A. M. Kuipers (2005). Application of Coalescence and Breakup Models in a Discrete Bubble Model for Bubble Columns. Industrial & Engineering Chemistry Research 44(14), 5233-5245.##
Wang, T. and J. Wang (2007). Numerical simulations of gas-liquid mass transfer in bubble columns with a CFD-PBM coupled model. Chemical Engineering Science 62, 7107–7118.##
Xu, Y., M. Liu and C. Tang (2013). Three-dimensional CFD-VOF-DPM simulations of effects of low-holdup particles on single-nozzle bubbling behavior in gas-liquid-solid systems. Chemical Engineering Journal 222, 292–306.##
Zhang, Y., M. Liu, Y. Xu and C. Tang (2012). Three-dimensional volume of fluid simulations on bubble formation and dynamics in bubble columns. Chemical Engineering Science 73, 55–78.##
Zhou, L. (2010). Advances in studies on two-phase turbulence in dispersed multiphase flows. International Journal of Multipahse Flow 36, 100-108. ##