A summary of numerical studies of t

A summary of numerical studies of the flow within
hydrocyclones is given in Table 1 for the period from
1982 onwards. This provides a compilation of many of
the major contributions to the study of hydrocyclone
fluid dynamics, although it may not be wholly comprehensive.
The major milestones and approaches are evident
in the papers cited. For example, it is evident from
the table that the application of full three-dimensional
modelling to the hydrocyclone is a recent advance of
only the last 5 years with early attempts being made by
Concha et al. (1998) and Slack and Boysan (1998).
Authors such as He et al. (1999) demonstrated that full
three-dimensional modelling is essential in order to
accurately model the hydrocyclone flow-field, as a result
of its inherent axial asymmetry. Clearly, the twodimensional
approach cannot capture axial flow-field
asymmetries, although progress was made with turbulence
and multiphase modelling as well as accounting for
the air-core interface for the two-dimensional approach.
Comparison of two-dimensional predictions as a function
of the turbulence model indicates a significant increase
in prediction accuracy as the turbulence model
order was increased, evident from predicted pressure
drops and axial and radial velocity profiles. It is clear
from predictions that the differential-stress turbulence
model (DSM) represents a lower bound of turbulence
modelling, appropriate for the hydrocyclone flow-field.
The two-dimensional multi-continuum approach of
Pericleous and Rhodes (1986, 1987) was well advanced
for its time and represents to some degree the direction
that modern day multiphase hydrocyclone modelling
could take. Computational resources limited the scope
of their modelling. Other authors have considered
Lagrangian particle tracking superimposed upon Eulerian
simulation, which has validity for very dilute flows
(maximum solids volume fraction 5%). Improvement
of this approach was made by Hsieh and Rajamani
(1991) adopting a coupled iterative approach, whereby
the continuous viscosity was updated and the continuous
prediction recalculated. This approach was developed
further by Devulapalli and Rajamani (1996) who
treated the Lagrangian particle tracks as representing
spreading Gaussian clouds.
Predictions of the air-core diameter have been provided
through: application of Bernoulli’s equation applied
with a minimisation procedure (Davidson, 1988);
through the use of an effective air-core interface viscosity
(Dyakowski and Williams, 1995); as well as
through application of Young–Laplace’s relation
(Concha et al., 1998). Notably, the later two approaches
offer the potential to account for an asymmetric air-core
geometry.
To address some of the severe limitations that were
cited earlier as barriers to practical and comprehensive
computational fluid dynamics (CFD) modelling, the
present authors have endeavoured to compute hydrocyclone
performance using their own finite element code
and the commercial computational fluid dynamics
package Fluent. Some aspects of the numerical algorithm
development have previously been described in
detail in Nowakowski and Dyakowski (2003). In order
to study numerically, the influence of the hydrocyclone
entrance region, an accurate representation of the
computational domain was based upon unstructured
grids. The primary purpose of the research has been
focused on providing an alternative numerical approach
for simulation of the flow in hydrocyclones, which
should be flexible enough to be used for multi-objective
design purposes. The created software enables investigation
of the influence of the hydrocyclone geometry
upon flow character.
The numerical simulations were able to reproduce the
swirling character of the flow and confirmed the existence
of asymmetry as observed in laboratory experiments (Fig. 1). Fig. 1 shows a sequence of instantaneous
trajectories constructed by integrating the velocity field.
The images reveal the characteristic outer downward
helical flow surrounding an inner upward flow. At the
outlets, the mathematical description of the problem
enables imposition of natural boundary conditions in
terms of forces, provided that the necessary data can be
determined experimentally. In the simulations performed,
zero stress boundary conditions were prescribed
at the outlets of the hydrocyclone. The choice, neutral in
character, does not restrict the profile of velocity field. It
is dictated by the need to truncate computational domain.
Such an imposition of boundary conditions
avoids any a priori assumptions concerning the velocity
field at the outlets and in particular, does not define the
mass split-ratio. The postulated descriptions of outflow
boundary conditions enable simulation of a characteristic
spray profile velocity field at the spigot. The hydrocyclone
considered in simulations was assumed to be
operating without an air-core. This circumstance occurs
when the hydrocyclone forms part of a piping network,
or in a liquid–liquid separation system, where the aircore
is actively suppressed. Numerical simulations,
where the air-core is considered, require interfacial
boundary conditions. Natural boundary conditions
relating forces could be advantageous for such situations.
Turbulence models for prediction of very high swirl
flow contain empirical constants and are still being
developed. The computational cost of such simulations
is also very high. Therefore, predictions of laminar flows
have been explored to greater extent for this research.
Such an analysis can give a reliable insight into the
behaviour of high viscosity slurry flow.
In parallel with the above work, a commercial CFD
package Fluent, with its finite volume platform, has
been used to investigate the capability of different turbulence
models for hydrocyclone simulation, Cullivan
et al. (2003). It has been highlighted that modelling of
hydrocyclone flow-field requires comprehensive modelling
of turbulence to account for significant anisotropy
and turbulence generation mechanisms. The full differential
stress model (DSM) with high-order treatment of
the pressure–strain term has been shown to be a good
compromise between accuracy and computational cost.
The DSM does not represent an entirely accurate
description of the turbulence, in particular sub-grid scale
modelling and equilibrium turbulence is assumed. The
equilibrium assumption presumes that the rate of
transfer of turbulence energy down through the energy
containing length-scales is constant, which is not expected
to hold for the rapidly developing and short
residence time hydrocyclone flow-field. Even so, the
DSM turbulence model offers practicality in terms of
computational resource
Alternatives such as large-eddy simulation (LES) and
proper-orthogonal decomposition are still subject to
active research and these require considerable additional
computational cost. For example, Slack et al. (2000)
have demonstrated the DSM to perform remarkably
well in comparison to LES without such prohibitively
high computational costs. It seems however, that the
computationally more expensive LES provides the best
solution for capture of time dependent vortex oscillations
and non-equilibrium turbulence, which will
potentially impact upon the separation efficiency.
Challenging tasks associated with LES including the
implementation of a sub-grid scale model accounting for
the effects of particles, correlation of different time scales
related to collisions and aggregation of particles. Hence
the application of LES to flows with particles is an active
research area (see e.g. Yamamoto et al., 2001).

Results (English) 3:

A summary of numerical studies of the flow within
hydrocyclones is given in Table 1 for the period from
1982 onwards. This. Provides a compilation of many of
the major contributions to the study of hydrocyclone
fluid dynamics although it, may not. Be wholly comprehensive.
The major milestones and approaches are evident
in the papers cited. For example it is, evident. From
.The table that the application of full three-dimensional
modelling to the hydrocyclone is a recent advance of
only the. Last 5 years with early attempts being made by
Concha et al. (1998) and Slack and Boysan (1998).
Authors such as He et, al. (1999) demonstrated that full
three-dimensional modelling is essential in order to
accurately model the, hydrocyclone flow-field. As a result
.Of its inherent axial asymmetry. Clearly the, twodimensional
approach cannot capture axial flow - field
asymmetries although,, Progress was made with turbulence
and multiphase modelling as well as accounting for
the air-core interface for the two-dimensional. Approach.
Comparison of two-dimensional predictions as a function
of the turbulence model indicates a significant increase
.In prediction accuracy as the turbulence model
order, was increased evident from predicted pressure
drops and axial and. Radial velocity profiles. It is clear
from predictions that the differential-stress turbulence
model (DSM) represents a. Lower bound of turbulence
modelling appropriate for, the hydrocyclone flow-field.
The two-dimensional MULTI-CONTINUUM approach. Of
Pericleous and, Rhodes (19861987) was well advanced
for its time and represents to some degree the direction
that modern day multiphase hydrocyclone. Modelling
could take. Computational resources limited the scope
of their modelling. Other authors have considered
Lagrangian. Particle tracking superimposed upon Eulerian
simulation which has, validity for very dilute flows
(maximum solids volume. Fraction  5%). Improvement
.Of this approach was made by Hsieh and Rajamani
(1991) adopting a coupled, iterative approach whereby
the continuous viscosity. Was updated and the continuous
prediction recalculated. This approach was developed
further by Devulapalli and Rajamani. (1996) who
treated the Lagrangian particle tracks as representing
spreading Gaussian clouds.
Predictions of the air-core. Diameter have been provided
.Through: application of Bernoulli 's equation applied
with a minimisation, procedure (Davidson 1988);
through the use of. An effective air-core interface viscosity
(Dyakowski, and Williams 1995); as well as
through application of Young - Laplace s. ' Relation
(Concha et al, 1998). Notably the later, two approaches
offer the potential to account for an asymmetric geometry air-core
.
.To address some of the severe limitations that were
cited earlier as barriers to practical and comprehensive
computational. Fluid dynamics (CFD), modelling the
present authors have endeavoured to compute hydrocyclone
performance using their own. Finite element code
and the commercial computational fluid dynamics
package Fluent. Some aspects of the numerical algorithm
.Development have previously been described in
detail in Nowakowski and Dyakowski (2003). In order
to, study numerically. The influence of the hydrocyclone
entrance region an accurate, representation of the
computational domain was based upon. Unstructured
grids. The primary purpose of the research has been
focused on providing an alternative numerical approach
.For simulation of the flow, in hydrocyclones which
should be flexible enough to be used for multi-objective
design, purposes. The created software enables investigation
of the influence of the hydrocyclone geometry
upon flow character.
The numerical. Simulations were able to reproduce the
swirling character of the flow and confirmed the existence
.Of asymmetry as observed in laboratory experiments (Fig. 1). Fig. 1 shows a sequence of instantaneous
trajectories constructed. By integrating the velocity field.
The images reveal the characteristic outer downward
helical flow surrounding an inner. Upward flow. At the
outlets the mathematical, description of the problem
enables imposition of natural boundary conditions. In
terms, of forcesProvided that the necessary data can be
determined experimentally. In the simulations performed
zero, stress boundary. Conditions were prescribed
at the outlets of the hydrocyclone. The, choice neutral in
character does not, restrict the profile. Of velocity field. It
is dictated by the need to truncate computational domain.
Such an imposition of boundary conditions
.Avoids any a priori assumptions concerning the velocity
field at the outlets and in particular does not, define the
mass. Split-ratio. The postulated descriptions of outflow
boundary conditions enable simulation of a characteristic
spray profile. Velocity field at the spigot. The hydrocyclone
considered in simulations was assumed to be
operating without an, air-core. This circumstance occurs
.When the hydrocyclone forms part of a piping network
or, in a liquid - liquid, separation system where the aircore
is actively. Suppressed. Numerical simulations
where, the air-core, is considered require interfacial
boundary conditions. Natural boundary. Conditions
relating forces could be advantageous for such situations.
Turbulence models for prediction of very high swirl
.Flow contain empirical constants and are still being
developed. The computational cost of such simulations
is also very. High. Therefore predictions of, laminar flows
have been explored to greater extent for this research.
Such an analysis can. Give a reliable insight into the
behaviour of high viscosity slurry flow.
In parallel with the above work a commercial,, CFD
package, FluentWith its finite, volume platform has
been used to investigate the capability of different turbulence
models for hydrocyclone. Simulation Cullivan
et, al. (2003). It has been highlighted that modelling of
hydrocyclone flow-field requires comprehensive. Modelling
of turbulence to account for significant anisotropy
and turbulence generation mechanisms. The full differential
.Stress model (DSM) with high-order treatment of
the pressure - strain term has been shown to be a good
compromise between. Accuracy and computational cost.
The DSM does not represent an entirely accurate
description of the turbulence in particular,, Sub-grid scale
modelling and equilibrium turbulence is assumed. The
equilibrium assumption presumes that the rate of
.Transfer of turbulence energy down through the energy
containing length-scales, is constant which is not expected
to hold. For the rapidly developing and short
residence time hydrocyclone flow-field. Even, so the
DSM turbulence model offers practicality. In terms of

computational resource Alternatives such as large-eddy simulation (LES) and
proper-orthogonal decomposition. Are still subject to
.Active research and these require considerable additional
computational cost. For example Slack et, al. (2000)
have demonstrated. The DSM to perform remarkably
well in comparison to LES without such prohibitively
high computational costs. It, seems however. That the
computationally more expensive LES provides the best
solution for capture of time dependent vortex oscillations
.And, non-equilibrium turbulence which will
potentially impact upon the separation efficiency.
Challenging tasks associated. With LES including the
implementation of a sub-grid scale model accounting for
the effects of particles correlation of,, Different time scales
related to collisions and aggregation of particles. Hence
the application of LES to flows with particles. Is an active
.Research area (see e.g. Yamamoto et al, 2001).