Ninth International Conference on CFD in the Minerals and Process Industries
CSIRO, Melbourne, Australia
10-12 December 2012
Copyright © 2012 CSIRO Australia 1
MODELLING THREE-PHASE FLOW IN METALLURGICAL PROCESSES
Christoph GONIVA
1,2*
, Gijsbert WIERINK
4
, Kari HEISKANEN
4
, Stefan PIRKER
2,3
and Christoph KLOSS
1,2
1
DCS Computing GmbH, Linz, AUSTRIA
2
Christian-Doppler Laboratory on Particulate Flow Modelling, Johannes Kepler University, Linz, AUSTRIA
3
Institute of Fluid Mechanics and Heat Transfer, Johannes Kepler University, Linz, AUSTRIA
4
Mechanical Process Technology and Recycling, Aalto University, Espoo, FINLAND
*Corresponding author, E-mail address: christoph.goniva@jku.at
ABSTRACT
The interaction between gasses, liquids, and solids plays a
critical role in many processes, such as coating,
granulation and the blast furnace process. In this paper we
present a comprehensive numerical model for three phase
flow including droplets, particles and gas. By means of a
coupled Computational Fluid Dynamics (CFD) - Discrete
Element Method (DEM) approach the physical core
phenomena are pictured at a detailed level. Sub-models for
droplet deformation, breakup and coalescence as well as
droplet-particle and wet particle-particle interaction are
applied. The feasibility of this model approach is
demonstrated by its application to a rotating drum coater.
The described numerical model is implemented
completely in an open source framework developed and
provided by the authors.
NOMENCLATURE
Greek symbols
volume fraction (-)
p
Poisson ratio (-)
f
bulk viscosity (kg/(m s))
c
Coulomb friction coefficient (-)
f
gas phase shear viscosity (kg/(m s))
friction coefficient (-),dynamic viscosity (kg/(m s))
density (kg/m
3
)
σ surface tension (N/m)
τ
stress tensor (Pa)
ω
angular velocity (1/s)
Latin symbols
c damping coefficient (kg/s)
C
d
drag coefficient (-)
d diameter (m)
e coefficient of restitution (-)
F force exerted on a single particle (N)
g gravity vector (m/s
2
)
I identity matrix (-)
K momentum exchange coefficient (kg/(m
3
s))
k spring stiffness (N/m)
m mass (kg)
N number (cells, particles) (-)
p pressure (Pa)
r radius (m)
R momentum source term (N/m
3
)
R
μ
rolling friction model parameter (-)
Re Reynolds number (-)
T torque (Nm)
t time (step) (s)
u velocity (m/s)
u
p
relative particle velocity at contact point (m/s)
V volume (m
3
)
x position (m)
x, y, z Cartesian-coordinates (-)
x particle overlap at contact point (m)
Y Young’s modulus (Pa)
Sub/superscripts
c contact
f fluid
n normal to contact point
p particle
t tangential to contact point
rel relative
INTRODUCTION
The interaction between gasses, liquids, and solids plays a
critical role in many processes, such as coating,
granulation and the blast furnace process to name a few.
Control and manipulation of the interaction between
phases is of key interest in engineering practise. Typically,
industrial applications are of such a scale that detailed
modelling is generally not feasible, while governing
processes are characterised by length and time scales that
are many orders of magnitudes smaller than those of the
unit process. In this light the understanding and modelling
of governing phenomena on an intermediate temporal and
spatial scale can deepen understanding of the unit process
at an industrial scale.
During the last years several models for three phase flow
mostly applied to granulation or coating can be found.
Most of them used a DEM approach in combination with a
residence time within a spray region to capture the effect
of droplet-particle liquid transfer (Fries et al. 2011; Dubey
et al. 2011; Sahni et al. 2011), an assumption which
strictly holds only if the spray is not influenced by the
fluid flow. The coating and granulation process in
fluidized bed reactors modelled by coupled CFD-DEM