Development and implementation of a polydispersed multiphase flow model in OpenFOAM

Abstract The two-phase flow solver implemented in the open-source OpenFOAM code was extended to a multiphase flow formulation ( n dispersed and one continuous phases) and then coupled to the population balance equation (PBE) solution by the Direct Quadrature Method of Moments (DQMOM), originating a polydispersed multiphase flow solver. Although each dispersed phase has its own velocity field, the present implementation considers only the interfacial momentum exchange between the continuous and the dispersed phases. The multiphase flow formulation was described and the details of the PBE–CFD coupling algorithms in OpenFOAM were provided. The implementation of the multiphase flow code was verified and evaluated against the original OpenFOAM two-phase flow solver for flow through a 2D backward facing step, using simplified breakage and aggregation kernels. The computational cost of both codes were compared for serial and parallel simulations.

[1]  Daniele Marchisio,et al.  Solution of population balance equations using the direct quadrature method of moments , 2005 .

[2]  Milorad P. Dudukovic,et al.  CFD modeling of bubble columns flows: implementation of population balance , 2004 .

[3]  Stefano Bove Computional Fluid Dynamics of Gas-Liquid Flows including Bubble Population Balances , 2005 .

[4]  Hrvoje Jasak,et al.  A tensorial approach to computational continuum mechanics using object-oriented techniques , 1998 .

[5]  Doraiswami Ramkrishna,et al.  A puristic analysis of population balance—II. , 1973 .

[6]  Doraiswami Ramkrishna,et al.  Simulation of particulate systems using the concept of the interval of quiescence , 1977 .

[7]  H. Rusche Computational fluid dynamics of dispersed two-phase flows at high phase fractions , 2003 .

[8]  Hrvoje Jasak,et al.  Error analysis and estimation for the finite volume method with applications to fluid flows , 1996 .

[9]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[10]  Rodney O. Fox,et al.  Bivariate direct quadrature method of moments for coagulation and sintering of particle populations , 2006 .

[11]  M. Ishii Thermo-fluid dynamic theory of two-phase flow , 1975 .

[12]  Luiz Fernando L. R. Silva,et al.  Implementation and analysis of numerical solution of the population balance equation in CFD packages , 2008, Comput. Chem. Eng..

[13]  E. Loth Numerical approaches for motion of dispersed particles, droplets and bubbles , 2000 .

[14]  D. Marchisio,et al.  Bubble size distribution modeling in stirred gas–liquid reactors with QMOM augmented by a new correction algorithm , 2010 .

[15]  A. Gosman,et al.  High resolution NVD differencing scheme for arbitrarily unstructured meshes , 1999 .

[16]  R. I. Issa,et al.  Numerical aspects of an algorithm for the Eulerian simulation of two‐phase flows , 2003 .

[17]  Roy G. Gordon,et al.  Error Bounds in Equilibrium Statistical Mechanics , 1968 .

[18]  Robert McGraw,et al.  Description of Aerosol Dynamics by the Quadrature Method of Moments , 1997 .

[19]  R. Fox,et al.  Application of the direct quadrature method of moments to polydisperse gas–solid fluidized beds , 2004 .

[20]  Stefan Heinrich,et al.  Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique , 2006 .

[21]  Marc Massot,et al.  Numerical simulation of spray coalescence in an Eulerian framework: Direct quadrature method of moments and multi-fluid method , 2007, J. Comput. Phys..

[22]  M. Hounslow,et al.  A discretized population balance for nucleation, growth, and aggregation , 1988 .

[23]  D. Ramkrishna,et al.  On the solution of population balance equations by discretization—II. A moving pivot technique , 1996 .

[24]  A. M. Al Taweel,et al.  CFD simulation of gas-liquid contacting in tubular reactors , 2007 .

[25]  A. Gosman,et al.  Solution of the implicitly discretised reacting flow equations by operator-splitting , 1986 .

[26]  Doraiswami Ramkrishna,et al.  Population Balances: Theory and Applications to Particulate Systems in Engineering , 2000 .

[27]  D. Drew,et al.  Theory of Multicomponent Fluids , 1998 .

[28]  L. Schiller Uber die Grundlegenden Berechnungen bei der Schwerkraftaufbereitung , 1933 .

[29]  Benjamin J. McCoy,et al.  Analytical solution for a population balance equation with aggregation and fragmentation , 2003 .