MFIX documentation theory guide

Abstract

This report describes the MFIX (Multiphase Flow with Interphase eXchanges) compurer model. MFIX is a general-purpose hydrodynamic model that describes chemical reactions and heat transfer in dense or dilute fluid-solids flows, flows typically occurring in energy conversion and chemical processing reactors. MFIX calculations give detailed infor-" marion on pressure, temperature, composition, and velocity distributions in the reactors. With such information, the engineer can visualize the conditions in the reactor, conduct parametric • studies and what-if experiments, and, thereby, assist in the dessgn process. The MHX model, developed at the Morgantown Energy Technology Center (METC), has the following capabilities: mass and momentum balance equations for gas and multiple solids phases; a gas phase and two solids phase energy equations; an arbitrarynumber of species balance equations for each of the phases; granular stress equations based on kinetic theory and frictional flow theory; a user-defined chemistry subroutine; three-dimensional Cartesian or cylindrical coordinate systems; nonuniform mesh size; impermeable and semipermeable internal surfaces; user-_endly input data file; multiple, single-precision, binary, direct-access, output f'desthat minimize disk storage and accelerate data retrieval; and extensive error reporting. This report, which is Volume I of the code documentation, describes the hydrodynamic theory used in the model: the conservation equations, constitutive relations, and the initial and boundary conditions. The literatureon the hydrodynamic theory is briefly surveyed, and the bases for the different parts of the model are highlighted.

Eulerian–Eulerian simulation of dense solid–gas cylindrical fluidized beds: Impact of wall boundary condition and drag model on fluidization

“…The computation of the stress tensor is based on the solid phase pressure and viscosity which are both dependent on the granular temperature Θ [42]. The granular temperature is a measure of the specific kinetic energy of the random fluctuating component of the particle velocity and is computed using the transport equation given by 3 2…”

“…On the other hand, the Syamlal-O'Brien drag model evaluates the drag based on the single-sphere drag function and the terminal velocity correlation for the solid phase [42]:…”

“…where parameters A and B are dependent on the local void fraction and empirical coefficients c 1 and d 1 tuned to recover the experimentally observed minimum fluidization velocity U mf [42].…”

“…While choosing an inappropriate gas-solids drag model is likely to weaken the validation study, the mechanism and dependency of fluidization metrics on φ and any qualitative discussion presented in Section 5 remain unaltered with the choice of the drag model. A more elaborate justification is presented in Section 5.6 while more details regarding the governing equations and the constitutive relations may be found in [42,47].…”

“…The Gidaspow drag model combines the pressure drops from the Ergun equation and the Wen and Yu model [14] to derive the drag coefficient in the dense and dilute pockets of the bed, respectively, while the Syamlal-O'Brien model [42] converts the terminal velocity correlations to drag correlations adjusted to match the experimentally measured minimum fluidization velocity. Thus, the Gidaspow model is more applicable to homogeneous bubbling fluidization [54,55] while the adjusted Syamlal-O'Brien model is more suited at higher velocities [46].…”