XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 2109
coarse and fines inflections are observed. The lighter par-
ticle displacement in the presence of heavier component is
further supported by the locus of maximum volume frac-
tion and equilibrium position from the numerical analy-
sis.” The slurry relative viscosity is a key parameter when
the solids concentration or the proportion of the magnetite
changes in the bi-component mixture (Padhi et al., 2019)
[5]. Hence, utilising the proposed viscosity model as addi-
tional function of solids volume fraction to improve the
prediction of the slurry property and hence the classifica-
tion behaviour inside hydrocyclone.
MATHEMATICAL MODEL
The non-dimensional form of single/mono density par-
ticle hydrocyclone performance characteristics model is
presented in literature [1,28]. The hydrocyclone specifica-
tions from the geometry and characteristics of the particles,
slurry, and operating conditions are the key parameters
considered for describing the classification performance of
the device. Narasimha et al. (2012) [29] proposed a con-
cept for hydrocyclone classification model accounting for
the multi-density particles but didn’t have sufficient data
to fully develop the model. The multi-component model
developed in this work is based on the non-dimensional
parametric approach that was successfully used in the
formulation for the single average density classification
performance of hydrocyclone [1,30] .The dimensionless
flow parameters incorporated in the single average density
model for hydrocyclones are leveraged in the description
of multi-component hydrocyclone model, presented in this
work. These terms include the G-forces as the ratio of cen-
trifugal forces to the gravitational force, relative viscosity
of the suspension, and turbulent diffusion coefficient. This
model is further extended to the multi-density particle sys-
tem, using the criteria that Plitt and Finch (1980) [8] used
which involve adding a modified density ratio to accommo-
date each density particle of the material in the feed. The
components cut size and the alpha equations resemble the
single-average density particle system shown in equation 9
and 10, respectively.
Equation 9 presents model for the prediction of the
average density cut size (d50ci).
tan
d
D k D
Do
D
Du fvh2
D
D
D
L
i
10
1
2
.*
.187
c
d1
c c
fv
c
i
c
c
f
si f
50ci
1.093
1 82
0 #Re
#`cos`
i
t
t t
=
-
-
-1.00 -0.703
-0.436
-0.936 -0.1988
-1.034
-1.37
c
c
c
d
c
d
^1
b
jj
m
m
m
m
n
n
l (9)
Equation 10 presents model for the prediction of the sharp-
ness of separation (αci).
Figure 5. (a) Validation of CFD model for 50:50 (Silica: magnetite) proportion (b) Comparison of CFD predicted LZVV for
different proportions of magnetite: silica, at 10 wt.% feed solids concentration in 3-inch hydrocyclone
coarse and fines inflections are observed. The lighter par-
ticle displacement in the presence of heavier component is
further supported by the locus of maximum volume frac-
tion and equilibrium position from the numerical analy-
sis.” The slurry relative viscosity is a key parameter when
the solids concentration or the proportion of the magnetite
changes in the bi-component mixture (Padhi et al., 2019)
[5]. Hence, utilising the proposed viscosity model as addi-
tional function of solids volume fraction to improve the
prediction of the slurry property and hence the classifica-
tion behaviour inside hydrocyclone.
MATHEMATICAL MODEL
The non-dimensional form of single/mono density par-
ticle hydrocyclone performance characteristics model is
presented in literature [1,28]. The hydrocyclone specifica-
tions from the geometry and characteristics of the particles,
slurry, and operating conditions are the key parameters
considered for describing the classification performance of
the device. Narasimha et al. (2012) [29] proposed a con-
cept for hydrocyclone classification model accounting for
the multi-density particles but didn’t have sufficient data
to fully develop the model. The multi-component model
developed in this work is based on the non-dimensional
parametric approach that was successfully used in the
formulation for the single average density classification
performance of hydrocyclone [1,30] .The dimensionless
flow parameters incorporated in the single average density
model for hydrocyclones are leveraged in the description
of multi-component hydrocyclone model, presented in this
work. These terms include the G-forces as the ratio of cen-
trifugal forces to the gravitational force, relative viscosity
of the suspension, and turbulent diffusion coefficient. This
model is further extended to the multi-density particle sys-
tem, using the criteria that Plitt and Finch (1980) [8] used
which involve adding a modified density ratio to accommo-
date each density particle of the material in the feed. The
components cut size and the alpha equations resemble the
single-average density particle system shown in equation 9
and 10, respectively.
Equation 9 presents model for the prediction of the
average density cut size (d50ci).
tan
d
D k D
Do
D
Du fvh2
D
D
D
L
i
10
1
2
.*
.187
c
d1
c c
fv
c
i
c
c
f
si f
50ci
1.093
1 82
0 #Re
#`cos`
i
t
t t
=
-
-
-1.00 -0.703
-0.436
-0.936 -0.1988
-1.034
-1.37
c
c
c
d
c
d
^1
b
jj
m
m
m
m
n
n
l (9)
Equation 10 presents model for the prediction of the sharp-
ness of separation (αci).
Figure 5. (a) Validation of CFD model for 50:50 (Silica: magnetite) proportion (b) Comparison of CFD predicted LZVV for
different proportions of magnetite: silica, at 10 wt.% feed solids concentration in 3-inch hydrocyclone