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

/pdf/mfix-documentation-theory-guide-3zhuwh0yn7.pdf

MFIX documentation theory guide

Evaporation and combustion of sprays

Two-fluid model and hydrodynamic constitutive relations

The ascent and emplacement of basaltic magma on the earth and moon is modeled by the application of geological and physical observations and constraints. Relatively simple mathematical models of the motion of gas/liquid mixtures are shown to be adequate in the treatment of basaltic eruptions, provided that allowance is made for the coalescence of gas bubbles and that realistic geological and petrochemical constraints are applied to the numerical values of variables. Because gas exsolution from magmas on the earth and moon commonly occur at depths of less than 2 km, it is generally convenient to consider separately the rise of bubble-free magmatic liquid at depth in a planetary crust and the more complex motions occurring near the surface with gas exsolution.

http://www.planetary.brown.edu/pdfs/262.pdf

Ascent and eruption of basaltic magma on the earth and moon

Summary
Plinian air-fall deposits and ignimbrites are the principal products of explosive eruptions of high viscosity magma. In this paper, the flow of gas/pyroclast dispersions and high viscosity magma through various magma chamber/conduit/vent geometries is considered. It is argued that after the first few minutes of an eruption magma fragmentation occurs at a shallow depth within the conduit system. Gas pressures at the fragmentation level are related to exsolved gas contents by consideration of the exsolution mechanism.

The sizes of blocks found near vents imply that gas velocities of 200 to 600 m s−1 commonly occur. These velocities are greater than the effective speed of sound in an erupting mixture (90-200 m s−1) and the transition from subsonic to supersonic flow is identified as occurring at the depth at which the conduit has its minimum diameter. The range of values of this minimum diameter (∼ 5 to ∼ 100 m) is estimated from observed and theoretically deduced mass-eruption rates.

The energy and continuity equations are solved, taking account of friction effects, for numerous geometries during the evolution, by wall erosion, of a conduit. Conduit erosion ceases, near the surface, when an exit pressure of one atmosphere is reached. Eruption velocities are found to depend strongly on exsolved magma gas content and weakly on radius of conduit and friction effects. Assuming water as the main volatile phase, velocities of 400-600 m s−1 for plinian events imply magma water contents of 3-6 per cent by weight.

Three scenarios are presented of eruptions in which: (1) conduit radius increases but gas content remains constant; (2) conduit radius increases and gas content decreases with time; and (3) conduit radius remains fixed and gas content decreases. These models demonstrate that the reverse grading commonly observed in plinian air-fall deposits is primarily a consequence of conduit erosion, which always results in increasing eruption intensity and eruption column height with time. The models also show that a decrease in gas content as deeper levels in a magma chamber are tapped or an increasing vent radius as conduit walls are eroded leads to the prediction of a progression from air-fall activity through ignimbrite formation to cessation of eruption and caldera collapse.

/pdf/explosive-volcanic-eruptions-iv-the-control-of-magma-2krlwvzkox.pdf

Explosive volcanic eruptions — IV. The control of magma properties and conduit geometry on eruption column behaviour

Fluid dynamics of multiphase systems

This study shows that fully developed pipe flow of a particulate suspension is defined by four dimensionless parameters of particle-fluid interactions in addition to the Reynolds number Effects accounted for include the Magnus effect due to fluid shear, electrostatic repulsion due to electric charges on the particles, and Brownian or turbulent diffusion In the case of a laminar liquid-solid suspension, electrostatic effect is negligible but shear effect is prominent Solution of the basic equations gives the density distribution of particles with a peak at the center (Einstein, Jeffery) or at other radii between the center and the pipe wall (Segre et al) depending on the magnitudes of the various flow parameters In the case of a turbulent gas-solid suspension, the Magnus effect is significant only within the thickness of the laminar sublayer However, charges induced on the particles by the impact of particles at the wall produce a higher density at the wall than at the center of the pipe The velocity distribution of particles is characterized by a slip velocity at the wall and a lag in velocity in the core from the fluid phase These results are verified by earlier measurements

Pipe flow of suspensions

The general case of a fully developed pipe flow of a suspension in a turbulent fluid with electrically charged particles or with significant gravity effect, or both, and for any inclination of the pipe with the direction of gravity, is formulated. Parameters defining the state of motion are: pipe flow Reynolds number, Froude number, electro diffusion number, diffusion response number, momentum transfer number and particle Knudsen number. Comparison with experimental results is made for both gas-solid and liquid-solid suspensions. It is shown that the gravity effect becomes significant in the case of large pipe diameters and large particle concentrations.

S. L. Soo

Papers

Fluid dynamics of multiphase systems

Pipe flow of suspensions

Pipe flow of suspensions in turbulent fluid

Turbulent flow of a suspension into a channel

Comparisons of formulations of multiphase flow