Simulation of Flocculation in Stirred Vessels Lagrangian Versus Eulerian

Abstract A study has been performed to evaluate Lagrangian and Eulerian approaches for simulating flocculation in stirred vessels. The prediction of the transient floc size evolution was performed using the quadrature method of moments (QMOM) while flow field characteristics within the turbulent stirred vessel were obtained using computational fluid dynamics (CFD). The Eulerian and Lagrangian CFD/QMOM models were applied to a 28 l square tank using either a Rushton turbine or a fluid foil impeller. Simulations were performed with an initial concentration of 100 mg L −1 of 1 μm nominal clay particles for several average characteristic velocity gradients (40-, 70-, 90-, 150-s −1 ). For the Lagrangian approach, the results showed that the average floc size transient evolution curve does not predict a peak followed by a lower steady-state size as observed for higher shear rates with the Eulerian approach. However, the overall good agreement between the Eulerian and Lagrangian CFD/QMOM models, indicates that a Lagrangian approach combined with a QMOM model would be an efficient method to quantify the impact of non-fluid flow experimental conditions on the flocculation process. In addition, the Lagrangian CFD/QMOM approach may be a useful tool to study the dynamics of flocculation and determine appropriate coalescence/breakup kernels when performing an inverse problem technique.

[1]  A. Cockx,et al.  Experimental Analysis of Floc Size Distribution and Hydrodynamics in a Jar-Test , 2001 .

[2]  J. Ducoste A two-scale PBM for modeling turbulent flocculation in water treatment processes , 2002 .

[3]  Norihito Tambo,et al.  Physical characteristics of flocs—I. The floc density function and aluminium floc , 1979 .

[4]  P. Gaskell,et al.  Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm , 1988 .

[5]  M. Clark,et al.  The influence of tank size and impeller geometry on turbulent flocculation : I. Experimental , 1998 .

[6]  Jyeshtharaj B. Joshi,et al.  Simulation of Flow in Stirred Vessels with Axial Flow Impellers: Effects of Various Numerical Schemes and Turbulence Model Parameters , 1995 .

[7]  Daniele Marchisio,et al.  Implementation of the Quadrature Method of Moments in CFD codes for aggregation-breakage problems , 2003 .

[8]  Costas Kiparissides,et al.  Prediction of particle size distribution in suspension polymerization reactors: effect of turbulence nonhomogeneity , 2000 .

[9]  Mark M. Clark,et al.  Turbulence in flocculators: Effects of tank size and impeller type , 1997 .

[10]  C. Selomulya,et al.  Evidence of Shear Rate Dependence on Restructuring and Breakup of Latex Aggregates. , 2001, Journal of colloid and interface science.

[11]  Mark M. Clark,et al.  Turbulence in Flocculators: Comparison of Measurements and CFD Simulations , 1999 .

[12]  Patrick T. Spicer,et al.  Coagulation and fragmentation: Universal steady‐state particle‐size distribution , 1996 .

[13]  Jesse T. Pikturna,et al.  Quadrature method of moments for population‐balance equations , 2003 .

[14]  S. Pratsinis,et al.  Shear-induced flocculation: The evolution of floc structure and the shape of the size distribution at steady state , 1996 .

[15]  William H. Press,et al.  Orthogonal Polynomials and Gaussian Quadrature with Nonclassical Weight Functions , 1990 .

[16]  D Dirk Thoenes,et al.  Aggregation kinetics of small particles in agitated vessels , 1997 .

[17]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[18]  Milorad P. Dudukovic,et al.  A Lagrangian description of flows in stirred tanks via computer-automated radioactive particle tracking (CARPT) , 2001 .

[19]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[20]  J. Ducoste,et al.  Modeling spatial distribution of floc size in turbulent processes using the quadrature method of moment and computational fluid dynamics , 2006 .

[21]  William H. Press,et al.  Book-Review - Numerical Recipes in Pascal - the Art of Scientific Computing , 1989 .

[22]  P. Saffman,et al.  On the collision of drops in turbulent clouds , 1956, Journal of Fluid Mechanics.

[23]  Y. Watanabe,et al.  Physical aspect of flocculation process—III: Flocculation process in a continuous flow flocculator with a back-mix flow , 1984 .

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

[25]  Fernando J. Muzzio,et al.  Experimental and computational investigation of the laminar flow structure in a stirred tank , 1999 .

[26]  Carlos F.M. Coimbra,et al.  Fundamental aspects of modeling turbulent particle dispersion in dilute flows , 1996 .

[27]  F. White Viscous Fluid Flow , 1974 .

[28]  Derek M. Causon,et al.  A cartesian cut cell method for compressible flows Part A: static body problems , 1997, The Aeronautical Journal (1968).

[29]  Michael Yianneskis,et al.  Assessment of Sliding Mesh CFD Predictions and LDA Measurements of the Flow in a Tank Stirred by a Rushton Impeller , 1998 .

[30]  P. Adler Heterocoagulation in shear flow , 1981 .

[31]  Richard A. Williams,et al.  In situ measurement of particle aggregation and breakage kinetics in a concentrated suspension , 1992 .

[32]  C. Crowe,et al.  The Particle-Source-In Cell (PSI-CELL) Model for Gas-Droplet Flows , 1977 .

[33]  Keller,et al.  The Effect of Impeller Type on Floc Size and Structure during Shear-Induced Flocculation , 1996, Journal of Colloid and Interface Science.

[34]  V. Oles Shear-induced aggregation and breakup of polystyrene latex particles , 1992 .

[35]  Kendra V. Sharp,et al.  Dissipation Estimation Around a Rushton Turbine Using Particle Image Velocimetry , 2000 .

[36]  Modelling shear-flocculation by population balances , 1987 .

[37]  D. C. Hopkins,et al.  Characterizing flocculation under heterogeneous turbulence. , 2003, Journal of colloid and interface science.

[38]  D. Wilcox Turbulence modeling for CFD , 1993 .

[39]  D. E. Rosner,et al.  Bivariate Extension of the Quadrature Method of Moments for Modeling Simultaneous Coagulation and Sintering of Particle Populations. , 2001, Journal of colloid and interface science.

[40]  Karel Antonius Kusters,et al.  The influence of turbulence on aggregation of small particles in agitated vessels , 1991 .

[41]  R. A. Sack,et al.  An algorithm for Gaussian quadrature given modified moments , 1971 .

[42]  R. D. Vigil,et al.  Quadrature method of moments for aggregation-breakage processes. , 2003, Journal of colloid and interface science.

[43]  Simon Judd,et al.  Flocculation modelling : A review , 1999 .

[44]  David Jenkins,et al.  Floc Breakup in Turbulent Flocculation Processes , 1972 .

[45]  N. Tambo Physical aspect of flocculation process—I: Fundamental treatise , 1979 .

[46]  Robert McGraw,et al.  Chemically resolved aerosol dynamics for internal mixtures by the quadrature method of moments , 2003 .