A multi-temperature multiphase flow model

VTT PUBLICATIONS, 1996

Numerical flow simulation utilising a full multiphase model is impractical for a suspension possessing wide distributions in the particle size or density. Various approximations are usually made to simplify the computational task. In the simplest approach, the suspension is represented by a homogeneous single-phase system and the influence of the particles is taken into account in the values of the physical properties. The multiphase nature of the flow cannot, however, be avoided when the concentration gradients are large and the dispersed phases alter the hydrodynamic behaviour of the mixture or when the distributions of the particles are studied. In many practical applications of multiphase flow, the mixture model is a sufficiently accurate approximation, with only a moderate increase in the computational effort compared to a single-phase simulation. The interest of applying computational fluid dynamics in industrial multiphase processes has increased during the last few years. Fluidised beds, polymerisation processes, settling tanks, chemical reactors, gas dispersion in liquids and air-lift reactors are typical examples in process industry. Modelling of multiphase flows is, however, very complicated. Full multiphase modelling requires a large computing power, especially if several secondary phases need to be considered. In this study, we investigate the mixture model, which is a simplification of the full models. This approach is a considerable alternative in simulating dilute suspensions of solid particles or small bubbles in liquids.

International journal of multiphase flow, 1990

Almtraet--Turbulent flows of dispersed multiphase solid-fluid mixtures are considered. From the global equations of balance for each phase and via a special ensemble-averaging technique, the local conservation laws for the mean motions are developed. Particular attentions are given to the averaged form of the Clausius-Duhem inequality and the fluctuation energies of the fluid phase and the particulate constituents. The thermodynamics of the mixture in the turbulent state is studied. The concept of coldness of turbulence for each phase is introduced, the free energy function is discussed and several thermodynamical relationships are established. Based on the averaged entropy inequality, constitutive equations for the stresses, energy and heat fluxes of various species are developed. It is shown that the model contains the recently developed turbulence models for dilute two-phase flows and dense granular flows as special limiting cases.

ESAIM: Proceedings, 2013

We give in this paper a short review of some recent achievements within the framework of multiphase flow modeling. We focus first on a class of compressible two-phase flow models, detailing closure laws and their main properties. Next we briefly summarize some attempts to model two-phase flows in a porous region, and also a class of compressible three-phase flow models. Some of the main difficulties arising in the numerical simulation of solutions of these complex and highly non-linear systems of PDEs are then discussed, and we eventually show some numerical results when tackling twophase flows with mass transfer.

International Journal of Engineering Science, 2006

A general thermodynamic theory for chemically active multiphase solid-fluid mixtures in turbulent state of motion is formulated. The global equations of balance for each phase are ensemble averaged and the local conservation laws for the mean motions are derived. As a classical treatment, the averaged form of the Clausius-Duhem inequality is used and the thermodynamics of the chemically active mixtures in turbulent state of motion is studied. Particular attention is given to the species concentration of the miscible fluid constituents and chemical reaction effects, in addition to the transport of the phasic fluctuation energies between phases. Based on the averaged entropy inequality, constitutive equations for the stresses, energy, heat and mass fluxes of various species are developed. Explicit governing equations of motion, along with the equation of the dissipation rate of the turbulent kinetic energy are also derived and discussed. A particular emphasis is on the thermodynamically consistent formulation of different solid-fluid interaction terms in these equations.

2009

The purpose of this work is to review the present status of both theoretical and numerical research of multiphase flow dynamics and to make the results of that fundamental research more readily available for students and for those working with practical problems involving multiphase flow. Flows that appear in many of the common industrial processes are intrinsically multiphase flows – e.g. flows of gas-particle suspensions, liquid-particle suspensions, and liquid-fiber suspensions, as well as bubbly flows, liquid-liquid flows, and the flow through porous medium. In the first part of this publication we give a comprehensive review of the theory of multiphase flows accounting for several alternative approaches. The second part is devoted to numerical methods for solving multiphase flow equations.

An Introduction to Reservoir Simulation Using MATLAB/GNU Octave

We will return to models having three phases and more than one component per phase in Chapter 11. For now, however, we assume that our system consists of two immiscible phases.

Mechanics Research Communications, 2011

In the present paper, attention is focused to clarify how temperature level may affect parallel mixing of two gas streams initially separated by a splitter plate. This is achieved by computing distinct cases with different inlet temperatures and comparing the corresponding results. A recently proposed kinetic model is utilized for the simulation of the flow field. The model provides a separate equation set for one component species of the system and an equation set for average quantities of the mixture. Thereby, it can automatically describe diffusion processes without the use of any coefficients for ordinary, pressure, and thermal diffusion which are generally required during Navier-Stokes computations of gas mixtures.

Multiscale Modeling & Simulation, 2003

We present a numerical model of two fluid mixing based on hyperbolic equations having complete state variables (velocity, pressure, temperature) for each fluid. The model is designed for the study of acceleration driven mixing layers in a chunk mix regime dominated by large scale coherent mixing structures. The numerical solution of the model is validated by comparison to the incompressible limit. For the purpose of this comparison, we present a newly obtained analytic solution of the pressure equation for this model and an analytic constraint derived from the asymptotic limit of the compressible pressures, which determines uniquely the incompressible pressure solution. The numerical solution is also validated by a mesh convergence study.

The flow problems considered in previous chapters are concerned with homogeneous fluids, either single phases or suspensions of fine particles whose settling velocities are sufficiently low for the solids to be completely suspended in the fluid. Consideration is now given to the far more complex problem of the flow of multiphase systems in which the composition of the mixture may vary over the cross-section of the pipe or channel; furthermore, the components may be moving at different velocities to give rise to the phenomenon of "slip" between the phases. Multiphase flow is important in many areas of chemical and process engineering and the behaviour of the material will depend on the properties of the components, the flowrates and the geometry of the system. In general, the complexity of the flow is so great that design methods depend very much on an analysis of the behaviour of such systems in practice and, only to a limited extent, on theoretical predictions. Some of the more important systems to be considered are: Mixtures of liquids with gas or vapour. Liquids mixed with solid particles ("hydraulic transport"). Gases carrying solid particles wholly or partly in suspension ("pneumatic transport"). Multiphase systems containing solids, liquids and gases. Mixed materials may be transported horizontally, vertically, or at an inclination to the horizontal in pipes and, in the case of liquid-solid mixtures, in open channels. Although there is some degree of common behaviour between the various systems, the range of physical properties is so great that each different type of system must be considered separately. Liquids may have densities up to three orders of magnitude greater than gases but they do not exhibit any significant compressibility. Liquids themselves can range from simple Newtonian liquids such as water, to non-Newtonian fluids with very high apparent viscosities. These very large variations in density and viscosity are responsible for the large differences in behaviour of solid-gas and solid-liquid mixtures which must, in practice, be considered separately. For, all multiphase flow systems, however, it is important to understand the nature of the interactions between the phases and how these influence the flow patterns — the ways in which the phases are distributed over the cross-section of the pipe or duct. In design it is necessary to be able to predict pressure drop which, usually, depends not only on the flow pattern, but also on the relative velocity of the phases; this slip velocity will influence the holdup , the fraction of the pipe volume which is occupied by a particular phase. It is important to note that, in the flow of a