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Hydrodynamic Modelling and Granular
Dynamics
Peter Dybdahl Hede
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Hydrodynamic Modelling and Granular Dynamics
Contents
Contents
Introduction to hydrodynamic modelling and granular dynamics
1.
1.1
1.2
1.2.1
1.2.2
1.2.3
1.3
1.3.1
1.3.2
Hydrodynamic modelling and granular dynamics in respect
to fluid bed processing
Eulerian models
Lagrangian models – Discrete Element Methods
Hard-particle models
Soft-particle models
Summing up on Lagrangian modelling
Other granular dynamic modelling principles
Monte Carlo techniques
Finite Element scheme
3
4
5
6
8
11
14
14
14
15
16
20
26
Summary
Table of symbols
Literature
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Hydrodynamic Modelling and Granular Dynamics
Introduction to hydrodynamic modelling and granular dynamics
Introduction to hydrodynamic modelling and
granular dynamics
The present text introduces hydrodynamic modelling principles in the context of batch wet
granulation and coating systems and it reviews the latest achievements and proposals in the
scientific literature in this field. The text concerns primarily the Eulerian and the Lagrangian
modelling technique. In accordance with some of the latest published Ph.d. thesis in the field of
hydrodynamics modelling, the Lagrangian technique is divided into a soft-particle and a hard-
sphere approach. The text further presents some of the latest trends and results from the growing
field of applying Computational Fluid Dynamics and Discrete Element Modelling in the field of
modelling fluid bed granulation processes. Further, a number of other granule dynamic modelling
principles including the Finite Element and Monte Carlo techniques are introduced.
The text is aimed at undergraduate university or engineering-school students working in the field
of mathematical or chemical and biochemical engineering. Newly graduated as well as
experienced engineers may also find relevant new information as emphasis is put on the newest
scientific discoveries and proposals presented in recent years of scientific publications. It is the
hope that the present introductory text will be helpful to the reader – particularly in the early
stages of the process of working with hydrodynamics in a granulation context. The
comprehensive literature list may also hopefully be an inspiration for further reading.
I alone am responsible for any misprints or errors and I will be grateful to receive any critics
and/or suggestions for further improvements.
Copenhagen, September 2006
Peter Dybdahl Hede
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Hydrodynamic Modelling and Granular Dynamics
Hydrodynamic modelling and granular dynamics
in respect to fluid bed processing
1. Hydrodynamic modelling and granular
dynamics in respect to fluid bed processing
As it has been emphasised elsewhere (e.g. Hede, 2006b), a lot of research in fluid bed processing
has focussed on modelling and understanding of the separate growth mechanisms associated with
agglomeration. Much of this understanding of these separate mechanisms has been integrated into
population balance models as it was presented in Hede (2006c). The available population balance
models almost never take into account the hydrodynamic properties and influence on the fluid
bed process, although the nature and detailed knowledge of fluidisation must be regarded as a
prerequisite for precise modelling – especially when it comes to scaling of fluid bed processes.
Hydrodynamic modelling of fluid bed systems seeks to include the effect of fluidisation although
this approach is somewhat different from the population balance approach
1
. A hydrodynamic
approach to fluid bed systems is a fairly new discipline that has developed in the last five to ten
years due to the enormous increase in computer processing power and algorithm development. It
is nevertheless a difficult but promising discipline being a prerequisite for discrete element
modelling and computational fluid dynamic modelling which are both subjects to be presented in
the present chapter.
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Hydrodynamic Modelling and Granular Dynamics
Hydrodynamic modelling and granular dynamics
in respect to fluid bed processing
Hydrodynamics is fluid dynamics applied to liquids, and as the bed load is fluidised in the fluid
bed vessel during processing,
hydrodynamics
is often used as a term rather than the more general
term
fluid dynamics
ii
. As with other typical fluid dynamic problems, a fluid bed hydrodynamic
problem often involves the calculation of various properties for the fluidised particles such as
velocity, pressure, density and temperature as function of space and time. The system consisting
of the fluidised solid particles and the fluidising gas is often treated as a two-phase gas-solid flow
system (Goldschmidt, 2001 and Goldschmidt et al., 2003). Modern approaches by Goldschmidt
(2001) reduce this simplification by treating the fluid bed system as a multiphase system, which
allows a detailed hydrodynamic modelling of the fluid phase of top-spray fluid beds. The
description of such systems seeks in any case to account for the inherent complexity of dense gas-
particle flows, which in its turn can be related to particle-particle and particle-wall interactions as
well as gas-particle interactions (Goldschmidt, 2001). Hydrodynamic modelling is rarely
combined with mass transfer or chemical/physical reactions and mechanisms as first attempts by
Samuelsberg & Hjertager (1996) strongly indicate the prior need for valid and well-proven
hydrodynamic models.
On an overall scale, there are basically two types of hydrodynamic models being the Eulerian
models
iii
and the Lagrangian models of which the first is commonly known as Computational
Fluid Dynamic models (CFD) and the latter is commonly referred to as Discrete Element Models
(DEM)
iv
. Both types consider the gas phase as a continuum but there are quite a few differences
in the modelling approaches and assumptions. The following sections will briefly introduce the
basic principles and differences. An in-depth treatment of fluidised bed hydrodynamics and
granular dynamics of two-phase flows should be found in Hoomans (1999) and Goldschmidt
(2001).
1.1 Eulerian models
In Eulerian models the gas and the solid phases are treated as interpenetrating phases, and the
theory behind such models is basically an extension of the classical kinetic theory that takes non-
ideal particle-article collisions and gas-particle drag into account (Goldschmidt, 2001). In this
scheme, collections of particles are modelled using continuous medium mechanics. The solid
particles are generally considered to be identical having a representative diameter and density,
meaning that the particle phase is volume averaged (Taghipour et al., 2005 and Depypere, 2005).
The general idea in formulating such a multi-fluid model is to treat each phase as an
interpenetrating continuum and therefore to construct integral balances of continuity, momentum
and energy for both phases with appropriate boundary conditions and jump conditions for the
phase interfaces. Since such a resulting continuum approximation for the solid phase has no
equation of state and obviously lacks variables such as viscosity and normal stress, certain
averaging techniques and assumptions are required to obtain a momentum balance for the solid
phase (Pain et al., 2001).
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