Eulerian simulation of bubble formation at a jet in a two-dimensional fluidized bed

A promising method to describe the fluid dynamics of highly loaded particle flows is the Eulerian representation. In this approach, the solid phase is treated as a continuum, although physically it consists of individual particles. This is possible by using physical models derived from the kinetic theory of granular flow. Central to these models is the so-called granular temperature, representing the specific fluctuating kinetic energy of the particles. In this paper, several forms proposed for these models are summarized and different descriptions of granular temperature are investigated. Furthermore, an alternative approach derived from soil mechanics is tested. Measurements of a two-dimensional bubbling bed found in literature are finally used to verify the results.

[1]  D. Geldart.  Types of gas fluidization , 1973 .

[2]  R. Jackson,et al.  Frictional–collisional constitutive relations for granular materials, with application to plane shearing , 1987, Journal of Fluid Mechanics.

[3]  V. V. Sokolovskii,et al.  Statics of Granular Media , 1965 .

[4]  J. M. Ekmann,et al.  Remarks on the modeling of fluidized systems , 1992 .

[5]  D. Gidaspow.  Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions , 1994 .

[6]  R. Jackson,et al.  Some Mathematical and Physical Aspects of Continuum Models for the Motion of Granular Materials , 1983 .

[7]  B. Alder,et al.  Studies in Molecular Dynamics. II. Behavior of a Small Number of Elastic Spheres , 1960 .

[8]  K. Morgan,et al.  Recent advances in numerical methods in fluids , 1980 .

[9]  R. D. Felice,et al.  The voidage function for fluid-particle interaction systems , 1994 .

[10]  G. Ahmadi,et al.  A thermodynamical formulation for dispersed multiphase turbulent flows—1 , 1990 .

[11]  Dimitri Gidaspow,et al.  Three-dimensional hydrodynamic modeling of a bubbling fluidized bed , 1995 .

[12]  J. L. Moseley,et al.  A model for agglomeration in a fluidized bed , 1993 .

[13]  J. X. Bouillard,et al.  Porosity distributions in a fluidized bed with an immersed obstacle , 1989 .

[14]  S. Savage,et al.  The effects of an impact velocity dependent coefficient of restitution on stresses developed by sheared granular materials , 1986 .

[15]  J. F. Richardson,et al.  Sedimentation and fluidisation: Part I , 1997 .

[16]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases , 1939 .

[17]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[18]  J. Grace,et al.  Permanent jet formation in beds of particulate solids , 1987 .

[19]  D. Jeffrey,et al.  Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield , 1984, Journal of Fluid Mechanics.

[20]  David J. Jeffrey,et al.  The stress tensor in a granular flow at high shear rates , 1981, Journal of Fluid Mechanics.

[21]  Sankaran Sundaresan,et al.  Gas‐solid flow in vertical tubes , 1991 .

[22]  C. S. Campbell,et al.  Particle pressures in gas-fluidized beds , 1991 .

[23]  J. Jenkins,et al.  A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles , 1983, Journal of Fluid Mechanics.

[24]  Todd Pugsley,et al.  The hydrodynamics of circulating fluidized beds , 1995 .

[25]  D. Gidaspow,et al.  Hydrodynamics of circulating fluidized beds: Kinetic theory approach , 1991 .

[26]  D. Gidaspow,et al.  A bubbling fluidization model using kinetic theory of granular flow , 1990 .

[27]  D. Brian Spalding,et al.  Numerical computation of multi-phase fluid flow and heat transfer , 1980 .

[28]  W. C. Mih.  An empirical shear stress equation for general solid-fluid mixture flows , 1993 .

[29]  K. E. Starling,et al.  Equation of State for Nonattracting Rigid Spheres , 1969 .