Development of an implicit framework for the two-fluid model on unstructured grids
File(s)
Author(s)
Bartholomew, Paul Thomas
Type
Thesis or dissertation
Abstract
The two-fluid model is an efficient method for simulating multiphase flows, based on an averaged
description of the phases as interpenetrating and interacting continua. It is particularly attractive
for the simulation of dispersed gas-solid flows in which the large number of particles in practical
devices can impose an insurmountable computational burden for particle tracking methods,
given currently available computing resources. Whilst the two-fluid model is more efficient than
particle tracking methods, it results in large, strongly coupled and highly non-linear systems of
equations, placing a premium on efficient solution algorithms. Additionally, the constitutive
models used to describe the solid phase introduce stiff source terms, requiring a robust solution
algorithm to handle them.
In this thesis a fully-coupled algorithm is developed for the two-fluid model, based on a
Newton linearisation of the underlying equation system, resulting in an algorithm treating all
inter-equation couplings implicitly. For comparison, a semi-coupled algorithm, based on a Picard
linearisation of the two-fluid model is also implemented, yielding a smaller implicitly coupled
pressure-velocity system and a segregated system for the transport of phase concentrations.
Motivating this work is the highly non-linear nature of the two-fluid model and the stiff source
terms arising in the models of the dispersed phase, these are treated explicitly in the semi-coupled
algorithm and may impose stability limits on the algorithm. By treating these terms implicitly,
it is expected that the fully-coupled solution algorithm will be more robust.
The algorithms are compared by application to test cases ranging from academic problems
to problems representative of industrial applications of the two-fluid model. These comparisons
show that with increasing problem complexity, the robustness of the fully-coupled algorithm
leads to an overall more efficient solution than the semi-coupled algorithm.
description of the phases as interpenetrating and interacting continua. It is particularly attractive
for the simulation of dispersed gas-solid flows in which the large number of particles in practical
devices can impose an insurmountable computational burden for particle tracking methods,
given currently available computing resources. Whilst the two-fluid model is more efficient than
particle tracking methods, it results in large, strongly coupled and highly non-linear systems of
equations, placing a premium on efficient solution algorithms. Additionally, the constitutive
models used to describe the solid phase introduce stiff source terms, requiring a robust solution
algorithm to handle them.
In this thesis a fully-coupled algorithm is developed for the two-fluid model, based on a
Newton linearisation of the underlying equation system, resulting in an algorithm treating all
inter-equation couplings implicitly. For comparison, a semi-coupled algorithm, based on a Picard
linearisation of the two-fluid model is also implemented, yielding a smaller implicitly coupled
pressure-velocity system and a segregated system for the transport of phase concentrations.
Motivating this work is the highly non-linear nature of the two-fluid model and the stiff source
terms arising in the models of the dispersed phase, these are treated explicitly in the semi-coupled
algorithm and may impose stability limits on the algorithm. By treating these terms implicitly,
it is expected that the fully-coupled solution algorithm will be more robust.
The algorithms are compared by application to test cases ranging from academic problems
to problems representative of industrial applications of the two-fluid model. These comparisons
show that with increasing problem complexity, the robustness of the fully-coupled algorithm
leads to an overall more efficient solution than the semi-coupled algorithm.
Version
Open Access
Date Issued
2017-09
Online Publication Date
2019-02-28T07:00:31Z
2019-04-04T16:07:13Z
Date Awarded
2018-09
Advisor
van Wachem, Berend
Marquis, Andrew
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
1381452
Publisher Department
Mechanical Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)