4
h
Kqta v v
2pg 27gpe
2t
in
c
a in
2
2
2
=e o (8)
Thus, using the above set of equations and adjusting
them for a hydrocyclone operation, the base design of a
hydrocyclone can be obtained and optimized through fine
tuning of the critical parameters.
RESULTS AND DISCUSSION
This pressure difference is essentially symbolized by the
energy loss when the fluid rotates under the action of high
turbulence force field. Since the inner vortex, mainly occu-
pied by the air core, behaves like a solid body, the transport
of water and slurry through the overflow stream is mainly
controlled by the induced shear created by the inner vor-
tex. In connection to the above theoretical interpretation
on the Rankine vortex flow, one can appreciate a radial
pressure drop essentially takes place both in the cylindrical
section and the conical section, as well due to the prevail-
ing swirling flow. Figure 4 represents the radial distribution
of static pressure obtained through the theoretical analysis.
With increasing inlet pressure (or flow rate), the separation
efficiency increases, which is possibly due to the increase in
centrifugal force that causes an inflation of static pressure
drop. Figure 5 presents the radial distribution of the tan-
gential velocity profile inside the hydrocyclone. Specifically,
near the central region (the region close to r =0), a high
magnitude of uθ signifies the presence of a strong forced
vortex zone. Subsequently, the magnitude of uθ reduces to
very low value towards the wall. This feature is similar to a
free vortex zone.
The magnitude of centrifugal intensity, Γ (defined as
u2⁄Rg) is very sensitive to the pressure drop between the free
and forced vortex regions. It is imperative to note that the
increase in Γc results in an increase in the magnitude of
Γmax (defined as u2⁄Rmg). The magnitude of Γmax decides
whether a particle will move towards the wall or not and
thereby creates a graded distribution of particles inside the
hydrocyclone. The variation of the cut size and split factor
with Γmax is depicted in Figure 6 which shows an inverse
power relationship between the Γmax and the cut size and
the split ratio. Figure 6(a) explains the enhancement in
Γmax leads to a finer cut size. Thus, to achieve a finer cut
size for a given diameter hydrocyclone we have to select
the design or operating parameters, which can increase the
magnitude of Γmax. The variation of centrifugal intensity
has a strong influence on the swirl flow transition from the
forced to the free vortex zones, which causes an induced
drag to drive the slurry through the periphery of the inner
vortex to the overflow outlet. Increase in the magnitude of
Γmax is, therefore, increasing the overflow slurry flowrate
and thereby causing a decrease in the split ratio (defined as
underflow slurry flowrate with respect to feed flowrate) as
shown in Figure 6(b).
Figure 4: Calculated pressure profile in the hydrocyclone
h
Kqta v v
2pg 27gpe
2t
in
c
a in
2
2
2
=e o (8)
Thus, using the above set of equations and adjusting
them for a hydrocyclone operation, the base design of a
hydrocyclone can be obtained and optimized through fine
tuning of the critical parameters.
RESULTS AND DISCUSSION
This pressure difference is essentially symbolized by the
energy loss when the fluid rotates under the action of high
turbulence force field. Since the inner vortex, mainly occu-
pied by the air core, behaves like a solid body, the transport
of water and slurry through the overflow stream is mainly
controlled by the induced shear created by the inner vor-
tex. In connection to the above theoretical interpretation
on the Rankine vortex flow, one can appreciate a radial
pressure drop essentially takes place both in the cylindrical
section and the conical section, as well due to the prevail-
ing swirling flow. Figure 4 represents the radial distribution
of static pressure obtained through the theoretical analysis.
With increasing inlet pressure (or flow rate), the separation
efficiency increases, which is possibly due to the increase in
centrifugal force that causes an inflation of static pressure
drop. Figure 5 presents the radial distribution of the tan-
gential velocity profile inside the hydrocyclone. Specifically,
near the central region (the region close to r =0), a high
magnitude of uθ signifies the presence of a strong forced
vortex zone. Subsequently, the magnitude of uθ reduces to
very low value towards the wall. This feature is similar to a
free vortex zone.
The magnitude of centrifugal intensity, Γ (defined as
u2⁄Rg) is very sensitive to the pressure drop between the free
and forced vortex regions. It is imperative to note that the
increase in Γc results in an increase in the magnitude of
Γmax (defined as u2⁄Rmg). The magnitude of Γmax decides
whether a particle will move towards the wall or not and
thereby creates a graded distribution of particles inside the
hydrocyclone. The variation of the cut size and split factor
with Γmax is depicted in Figure 6 which shows an inverse
power relationship between the Γmax and the cut size and
the split ratio. Figure 6(a) explains the enhancement in
Γmax leads to a finer cut size. Thus, to achieve a finer cut
size for a given diameter hydrocyclone we have to select
the design or operating parameters, which can increase the
magnitude of Γmax. The variation of centrifugal intensity
has a strong influence on the swirl flow transition from the
forced to the free vortex zones, which causes an induced
drag to drive the slurry through the periphery of the inner
vortex to the overflow outlet. Increase in the magnitude of
Γmax is, therefore, increasing the overflow slurry flowrate
and thereby causing a decrease in the split ratio (defined as
underflow slurry flowrate with respect to feed flowrate) as
shown in Figure 6(b).
Figure 4: Calculated pressure profile in the hydrocyclone