This report describes the MFIX (Multiphase Flow with Interphase exchanges) computer 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 information 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 design process. The MFIX 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 arbitrary number 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 semi-permeable internal surfaces; user-friendly input data file; multiple, single-precision, binary, direct-access, output files that minimize disk storage and accelerate data retrieval; and extensive error reporting. This report, which is Volume 1 of the code documentation, describes the hydrodynamic theory used in the model: the conservation equations,more » constitutive relations, and the initial and boundary conditions. The literature on the hydrodynamic theory is briefly surveyed, and the bases for the different parts of the model are highlighted.« less

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MFIX documentation theory guide

The multiphase particle-in-cell (MP-PIC) method for dense particulate flows

Eulerian two-phase flow theory applied to fluidization

[1] This paper presents a new, generalized two-phase debris flow model that includes many essential physical phenomena. The model employs the Mohr-Coulomb plasticity for the solid stress, and the fluid stress is modeled as a solid-volume-fraction-gradient-enhanced non-Newtonian viscous stress. The generalized interfacial momentum transfer includes viscous drag, buoyancy, and virtual mass. A new, generalized drag force is proposed that covers both solid-like and fluid-like contributions, and can be applied to drag ranging from linear to quadratic. Strong coupling between the solid- and the fluid-momentum transfer leads to simultaneous deformation, mixing, and separation of the phases. Inclusion of the non-Newtonian viscous stresses is important in several aspects. The evolution, advection, and diffusion of the solid-volume fraction plays an important role. The model, which includes three innovative, fundamentally new, and dominant physical aspects (enhanced viscous stress, virtual mass, generalized drag) constitutes the most generalized two-phase flow model to date, and can reproduce results from most previous simple models that consider single- and two-phase avalanches and debris flows as special cases. Numerical results indicate that the model can adequately describe the complex dynamics of subaerial two-phase debris flows, particle-laden and dispersive flows, sediment transport, and submarine debris flows and associated phenomena.

/pdf/a-general-two-phase-debris-flow-model-3sijccpo55.pdf

A general two-phase debris flow model

The influence of interfacial pressure forces on the character of two-phase flow model equations

Equation systems describing one-dimensional, transient, two-phase flow with separate continuity, momentum, and energy equations for each phase are classified by use of the method of characteristics. Little attempt is made to justify the physics of these equations. Many of the equation systems possess complex-valued characteristics and hence, according to well-known mathematical theorems, are not well-posed as initial-value problems (IVPs). Real-valued characteristics are necessary but not sufficient to insure well-posedness. In the absence of lower order source or sink terms (potential type flows), which can affect the well-posedness of IVPs, the complex characteristics associated with these two-phase flow equations imply unbounded exponential growth for disturbances of all wavelengths. Analytical and numerical examples show that the ill-posedness of IVPs for the two-phase flow partial differential equations which possess complex characteristics produce unstable numerical schemes. These unstable numerical schemes can produce apparently stable and even accurate results if the growth rate resulting from the complex characteristics remains small throughout the time span of the numerical experiment or if sufficient numerical damping is present for the increment size used. Other examples show that clearly nonphysical numerical instabilities resulting from the complex characteristics can be produced. These latter types of numerical instabilities are shown to be removed by the addition of physically motivated differential terms which eliminate the complex characteristics. (auth)

/pdf/characteristics-and-stability-analyses-of-transient-one-13rgn4uey1.pdf

Characteristics and stability analyses of transient one-dimensional two- phase flow equations and their finite difference approximations

Safety consideration and economic advantage of a new underground nuclear power plant design

Pharmaceutical processing includes several processes that are based on a multiphase system, particularly, gas/solid flow and fluidization. These processes are devoted to making particles, modifying their properties, and then turning them into structured products and may include crystallization, mixing, granulation, pulverization, drying, and tableting. Drying is one of the major unit operations in the manufacturing of solid pharmaceuticals. Optimum design of the drying process will significantly enhance the rate and reliability of the production and, in turn, decrease the cost of the pharmaceutical products. The focus of this chapter is on the computational fluid dynamics (CFD) approach for design, scale-up, and performance optimization of a pharmaceutical bubbling fluidized bed dryer. Gas/solid flow patterns, mixing, and drying of pharmaceutical particles in bubbling fluidized bed dryers of three different scales are simulated.

Application of Multiphase Flow Simulation in Pharmaceutical Processes

The governing equations describing the flow of an unequal phase velocity, equal phase temperature (UVET) seriated two-phase continuum as derived by Solbrig and Hughes (1978) are solved in this article, in one space dimension. A simple implicit iterative solution procedure is developed to numerically evaluate the five non-linear coupled field equations. Analytical solutions are developed, against which the computer code results are compared. The prototype UVET code results are compared to the equivalent equal phase velocity, equal phase temperature (EVET) code results for the same problem. Major phenomena such as phase flow reversal, counter-current flow and flooding-like behavior are predicted.

Calculation of the governing equations for a seriated unequal velocity, equal temperature two‐phase continuum

Comment on the Drift-Flux Approximation in Transient Two-Phase Flows

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