Towards a unified approach for modelling uniform and non‐uniform bubbly flows

An important ingredient of closure relations for the Euler-Euler two-fluid model is the description of turbulent fluctuations. Models proposed in the literature disagree concerning the treatment of such on all scales. The large scale fluctuation structures as well as the bubble induced turbulence might be neglected or resolved and/or modeled respectively in different ways. Each treatment has been demonstrated to work for a certain application but a unifying perspective is lacking so far. To this end a set of closure relations for the fluid dynamics of bubbly flow has been collected that represents the best available knowledge and may serve as a baseline for further improvements and extensions. This model comprises a set of bubble forces as well as a turbulence model including turbulence modification due to the bubbles and has been successfully validated for bubbly flows in pipes and bubble columns. Here it is applied to two sets of data representing non-uniform and uniform flows in bubble columns which are dominated by large scale fluctuations and bubble induced turbulence respectively. This article is protected by copyright. All rights reserved

[1]  Akio Tomiyama,et al.  On the role of the lateral lift force in poly-dispersed bubbly flows , 2011 .

[2]  A. Tomiyama.  SINGLE BUBBLES IN STAGNANT LIQUIDS AND IN LINEAR SHEAR FLOWS , 2002 .

[3]  L. Hernández,et al.  Hydrodynamic characterization of a needle sparger rectangular bubble column: Homogeneous flow, static bubble plume and oscillating bubble plume , 2007 .

[4]  Annalisa Manera,et al.  Influence of the lift force on the stability of a bubble column , 2005 .

[5]  Michel Lance,et al.  Homogeneous Turbulence in Bubbly Flows , 1991 .

[6]  J. Converti,et al.  A model for turbulent polydisperse two-phase flow in vertical channels , 2003 .

[7]  Dirk Lucas,et al.  Transient simulation for large scale flow in bubble columns , 2015 .

[8]  T. Frank,et al.  The Favre Averaged Drag Model for Turbulent Dispersion in Eulerian Multi-Phase Flows , 2004 .

[9]  A. K. Agrawal,et al.  Shape of liquid drops moving in liquid media , 1966 .

[10]  Ng Niels Deen,et al.  Scale-adaptive simulation of a square cross-sectional bubble column , 2015 .

[11]  Eckhard Krepper,et al.  Baseline Model for the Simulation of Bubbly Flows , 2015 .

[12]  Roland Rzehak,et al.  Multiphase CFD-simulation of bubbly pipe flow: A code comparison , 2015 .

[13]  W. Jones,et al.  The prediction of laminarization with a two-equation model of turbulence , 1972 .

[14]  J. Magnaudet,et al.  The generalized Kirchhoff equations and their application to the interaction between a rigid body and an arbitrary time-dependent viscous flow , 2002 .

[15]  Dieter Bothe,et al.  VOF‐Simulation of the Lift Force for Single Bubbles in a Simple Shear Flow , 2006 .

[16]  Isao Kataoka,et al.  Turbulence suppression in bubbly two-phase flow , 1990 .

[17]  Frédéric Risso,et al.  Experimental characterization of the agitation generated by bubbles rising at high Reynolds number , 2009, Journal of Fluid Mechanics.

[18]  Akio Tomiyama,et al.  BUBBLE TRACKING SIMULATION OF BUBBLE-INDUCED PSEUDOTURBULENCE , 2012 .

[19]  F. Menter.  Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[20]  S. J. Lee,et al.  The Prediction of Two-Phase Turbulence and Phase Distribution Phenomena Using a Reynolds Stress Model , 1990 .

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

[22]  G. Riboux,et al.  Wake attenuation in large Reynolds number dispersed two-phase flows , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[23]  I. Zun,et al.  Effects of Eötvös Number and Dimensionless Liquid Volumetric Flux on Lateral Motion of a Bubble in a Laminar Duct Flow , 1995 .

[24]  Gerhart Eigenberger,et al.  Gas—liquid flow in bubble columns and loop reactors: Part I. Detailed modelling and numerical simulation , 1994 .

[25]  Eckhard Krepper,et al.  Bubbly flows with fixed polydispersity: Validation of a baseline closure model , 2015 .

[26]  N. Zuber,et al.  Drag coefficient and relative velocity in bubbly, droplet or particulate flows , 1979 .

[27]  Akio Tomiyama,et al.  Lateral Migration of Single Bubbles Due to the Presence of Wall , 2002 .

[28]  B. Niceno,et al.  CFD MODELING OF ADIABATIC BUBBLY FLOW , 2011 .

[29]  Eckhard Krepper,et al.  Baseline closure model for dispersed bubbly flow: Bubble coalescence and breakup , 2015 .

[30]  Eckhard Krepper,et al.  On the modelling of bubbly flow in vertical pipes , 2005 .

[31]  I. Zun,et al.  The transverse migration of bubbles influenced by walls in vertical bubbly flow , 1980 .

[32]  Tiefeng Wang,et al.  Numerical simulations of gas–liquid mass transfer in bubble columns with a CFD–PBM coupled model , 2007 .

[33]  G. Eigenberger,et al.  Simulation of Buoyancy Driven Bubbly Flow: Established Simplifications and Open Questions (Journal Review) , 2004 .

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

[35]  R. F. Mudde,et al.  Uniform Flow in Bubble Columns , 2009 .

[36]  Michio Sadatomi,et al.  Momentum and heat transfer in two-phase bubble flow—I. Theory , 1981 .

[37]  P. Spalart.  Strategies for turbulence modelling and simulations , 2000 .

[38]  A. Tomiyama,et al.  Distributions of void fraction and liquid velocity in air–water bubble column , 2014 .

[39]  M. Ishii,et al.  Thermo-Fluid Dynamics of Two-Phase Flow , 2007 .

[40]  Eckhard Krepper,et al.  Closure models for turbulent bubbly flows: A CFD study , 2013 .

[41]  Miguel A. Galán,et al.  Influence of the lift force closures on the numerical simulation of bubble plumes in a rectangular bubble column , 2009 .

[42]  Eckhard Krepper,et al.  CFD modeling of bubble-induced turbulence , 2013 .

[43]  C. Lifante,et al.  Comparative study of wall-force models for the simulation of bubbly flows , 2012 .

[44]  C. Rauh,et al.  CFD simulation of bubble column flows: An explicit algebraic Reynolds stress model approach , 2014 .

[45]  Eckhard Krepper,et al.  Closure relations for CFD simulation of bubble columns , 2014 .

[46]  Tadashi Sakaguchi,et al.  Drag Coefficients of Single Bubbles under Normal and Micro Gravity Conditions , 1998 .

[47]  H. Wagner,et al.  Hydrodynamic simulations of laboratory scale bubble columns fundamental studies of the Eulerian–Eulerian modelling approach , 1999 .

[48]  Mandar Tabib,et al.  CFD simulation of bubble column—An analysis of interphase forces and turbulence models , 2008 .

[49]  Yassin A. Hassan,et al.  A two-equation turbulence model of turbulent bubbly flows , 2001 .

[50]  Gerhart Eigenberger,et al.  Gas—liquid flow in bubble columns and loop reactors: Part II. Comparison of detailed experiments and flow simulations , 1994 .

[51]  Eckhard Krepper,et al.  Numerical Simulation of Polydispersed Flow in Bubble Columns with the Inhomogeneous Multi‐Size‐Group Model , 2013 .

[52]  Carlos A. Dorao,et al.  Modeling of Bubble Column Reactors: Progress and Limitations , 2005 .