Numerical study of bubble break-up in bubbly flows using a deterministic Euler-Lagrange framework

Abstract In this work we present a numerical model to predict the bubble size distribution in turbulent bubbly flows. The continuous phase is described by the volume-averaged Navier–Stokes equations, which are solved on an Eulerian grid, whereas the dispersed or bubble phase is treated in a Lagrangian manner, where each individual bubble is tracked throughout the computational domain. Collisions between bubbles are described by means of a hard-sphere model. Coalescence of bubbles is modeled via a stochastic inter-particle encounter model. A break-up model is implemented with a break-up constraint on the basis of a critical Weber value augmented with a model for the daughter size distribution. A numerical parameter study is performed of the bubble break-up model implemented in the deterministic Euler–Lagrange framework and its effect on the bubble size distribution (BSD) is reported. A square bubble column operated at a superficial gas velocity of 2 cm/s is chosen as a simulation base case to evaluate the parameters. The parameters that are varied are the values of the critical Weber number ( We crit ), the daughter size distribution (β) and the superficial gas velocity ( v sup ). Changes in the values of We crit and v sup have a significant impact on the overall BSD, while a different shaped β did not show a significant difference.

[1]  J. Kuipers,et al.  Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidised bed: A hard-sphere approach. , 1996 .

[2]  C. Peskin.  Numerical analysis of blood flow in the heart , 1977 .

[3]  Martin Sommerfeld,et al.  Euler/Lagrange Calculations of Bubbly Flows with Consideration of Bubble Coalescence , 2008 .

[4]  D. Darmana,et al.  Detailed modeling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model , 2005 .

[5]  D. Darmana,et al.  Detailed modelling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model: Chemisorption of CO2 into NaOH solution, numerical and experimental study , 2007 .

[6]  W. Howarth.  Coalescence of drops in a turbulent flow field , 1964 .

[7]  Lawrence L. Tavlarides,et al.  Description of interaction processes in agitated liquid-liquid dispersions , 1977 .

[8]  Y. Liao,et al.  A literature review on mechanisms and models for the coalescence process of fluid particles , 2010 .

[9]  H. Sovová.  Breakage and coalescence of drops in a batch stirred vessel—II comparison of model and experiments , 1981 .

[10]  H. Svendsen,et al.  Theoretical model for drop and bubble breakup in turbulent dispersions , 1996 .

[11]  E. G. Chatzi,et al.  Dynamic simulation of bimodal drop size distributions in low-coalescence batch dispersion systems , 1992 .

[12]  DarmanaD.,et al.  Parallelization of an Euler-Lagrange model using mixed domain decomposition and a mirror domain technique , 2006 .

[13]  L. Erickson,et al.  DYNAMICS OF BUBBLE SIZE DISTRIBUTION IN TURBULENT GAS-LIQUID DISPERSIONS , 1987 .

[14]  J. P. Gupta,et al.  A model for transitional breakage probability of droplets in agitated lean liquid-liquid dispersions , 1979 .

[15]  Y. Liao,et al.  A literature review of theoretical models for drop and bubble breakup in turbulent dispersions , 2009 .

[16]  Hidesada Tamai,et al.  Transverse migration of single bubbles in simple shear flows , 2002 .

[17]  V. M. Tikhomirov,et al.  On the Breakage of Drops in a Turbulent Flow , 1991 .

[18]  R. Becker,et al.  Bubble Dynamics at Boundaries at Microsecond Time Scales , 2004 .

[19]  Harvey W. Blanch,et al.  Bubble break-up in gas—liquid bioreactors: Break-up in turbulent flows , 1986 .

[20]  J.A.M. Kuipers,et al.  On the drag force of bubbles in bubble swarms at intermediate and high Reynolds numbers , 2011 .

[21]  M. J. Quinn,et al.  The coalescence of H2S and CO2 bubbles in water , 1976 .

[22]  Costas Tsouris,et al.  Breakage and coalescence models for drops in turbulent dispersions , 1994 .

[23]  Ak Allen Chesters.  The modelling of coalescence processes in fluid-liquid dispersions : a review of current understanding , 1991 .

[24]  J. Kuipers,et al.  Dynamic simulation of dispersed gas-liquid two phase flow using a discrete bubble model. , 1996 .

[25]  Nikolay Ivanov Kolev.  Multiphase Flow Dynamics 1: Fundamentals , 2004 .

[26]  T. Fukuda,et al.  A Simple Numerical Method for Solving an Incompressible Two-Fluid Model in a General Curvilinear Coordinate System , 1995 .

[27]  A. W. Vreman.  An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications , 2004 .

[28]  Joakim Majander,et al.  Simulation of the population balances for liquid–liquid systems in a nonideal stirred tank. Part 2—parameter fitting and the use of the multiblock model for dense dispersions , 2002 .

[29]  A. W. Etchells,et al.  Bubble size in horizontal pipelines , 1987 .

[30]  Jam Hans Kuipers,et al.  A three-demensional CFD model for gas-liquid bubble columns , 1999 .

[31]  A. Kitagawa,et al.  Two-way coupling of Eulerian–Lagrangian model for dispersed multiphase flows using filtering functions , 2001 .

[32]  Juan C. Lasheras,et al.  On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency , 1999, Journal of Fluid Mechanics.

[33]  Tron Solberg,et al.  Large eddy simulation of the Gas-Liquid flow in a square cross-sectioned bubble column , 2001 .

[34]  Niels G. Deen,et al.  Parallelization of an Euler-Lagrange model using mixed domain decomposition and a mirror domain technique: Application to dispersed gas-liquid two-phase flow , 2006, J. Comput. Phys..

[35]  Murray S. Klamkin,et al.  Elementary Approximations to the Area of N-Dimensional Ellipsoids , 1971 .

[36]  S. H. Park,et al.  The Splitting of Drops and Bubbles by Turbulent Fluid Flow , 1973 .

[37]  Frédéric Risso,et al.  Oscillations and breakup of a bubble immersed in a turbulent field , 1998, Journal of Fluid Mechanics.

[38]  Larry E. Erickson,et al.  BUBBLE BREAKUP AND COALESCENCE IN TURBULENT GAS-LIQUID DISPERSIONS , 1987 .

[39]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[40]  J. C. R. Hunt,et al.  The force exerted on a body in inviscid unsteady non-uniform rotational flow , 1988, Journal of Fluid Mechanics.

[41]  Jos Derksen,et al.  Euler–Lagrange modeling of a gas–liquid stirred reactor with consideration of bubble breakage and coalescence , 2012 .

[42]  D. Mewes,et al.  Bubble‐Size distributions and flow fields in bubble columns , 2002 .

[43]  K. S. Gandhi,et al.  A new model for the breakage frequency of drops in turbulent stirred dispersions , 1992 .

[44]  Costas Kiparissides,et al.  Generalized model for prediction of the steady-state drop size distributions in batch stirred vessels , 1989 .

[45]  J. Lasheras,et al.  A review of statistical models for the break-up of an immiscible fluid immersed into a fully developed turbulent flow , 2002 .

[46]  G. Batchelor,et al.  Pressure fluctuations in isotropic turbulence , 1951, Mathematical Proceedings of the Cambridge Philosophical Society.

[47]  Ng Niels Deen,et al.  Multi-scale modeling of dispersed gas-liquid two-phase flow , 2004 .

[48]  Jam Hans Kuipers,et al.  Computer simulation of the hydrodynamics of a two-dimensional gas-fluidized bed , 1993 .

[49]  H. Blanch,et al.  Bubble coalescence and break‐up in air‐sparged bubble columns , 1990 .

[50]  J. Hinze.  Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes , 1955 .