Available via license: CC BY 4.0
Content may be subject to copyright.
Citation: Su, T.; Zhang, Y. Effect of
the Vortex Finder and Feed
Parameters on the Short-Circuit Flow
and Separation Performance of a
Hydrocyclone. Processes 2022,10, 771.
https://doi.org/10.3390/pr10040771
Academic Editor: Alessandro
D’Adamo
Received: 7 March 2022
Accepted: 11 April 2022
Published: 14 April 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
processes
Article
Effect of the Vortex Finder and Feed Parameters on the
Short-Circuit Flow and Separation Performance of
a Hydrocyclone
Tenglong Su 1,2 and Yifei Zhang 1,*
1Key Laboratory of Green Process and Engineering and National Engineering Laboratory for
Hydrometallurgical Cleaner Production Technology, Innovation Academy for Green Manufacture, Institute of
Process Engineering, Chinese Academy of Sciences, Beijing 100190, China; stlong07@163.com
2School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
*Correspondence: yfzhang@ipe.ac.cn
Abstract:
The short-circuit flow, which is discharged from the vortex finder without separation,
seriously affects the processing efficiency of the hydrocyclone. In this paper, the experimental test and
numerical simulation methods are used to study the effect of the vortex finder and feed parameters
on the short-circuit flow and separation performance. The Reynolds Stress method (RSM), Volume of
Fluid (VOF), and Mixture model were adopted to predict the separation process in the hydrocyclone.
The simulation results are analyzed in terms of the short-circuit flow rate, the ratio of the short-
circuit flow rate to the inlet flow rate (hereafter this paper will be abbreviated as “its ratio”) and
the separation efficiency. The results indicate that the smaller vortex finder diameter, thick-walled
vortex finder, and moderate vortex finder length are conducive to inhibiting the short-circuit flow and
decreasing the cut size (d
50
). A faster inlet velocity and higher feed concentration could increase the
short-circuit flow but reduce its ratio. The relatively faster inlet velocity and lower feed concentration
could decrease the d50 and improve the separation efficiency.
Keywords: hydrocyclone; vortex finder; feed parameter; short-circuit flow; separation efficiency
1. Introduction
Hydrocyclones are important separation equipment that uses the centrifugal effect
to classify solid particles from a liquid suspension [
1
]. It has been widely used in coal
preparation, mineral processing, medical separation, and sewage treatment [
2
]. Hydrocy-
clone has a simple structure, but many factors influence its separation performance. The
influencing factors can be divided into structural, operating, and feed parameters. Since
the first hydrocyclone was invented in 1891 [
3
], scholars have always pursued designing a
higher-performance hydrocyclone with lower energy consumption.
The fluid enters the hydrocyclone from the inlet at a certain velocity. Most of the
suspension was separated then discharged from the overflow and underflow outlets.
However, a part of the suspension flows along the cyclone’s inner wall and the vortex
finder’s outer wall then discharged through the overflow outlet. This part of the feed, which
is discharged directly without separation, is named the short-circuit flow. Short-circuit flow
is a significant feature of the flow field in hydrocyclone [
4
]. The quantitative description of
the short-circuit flow has always been the key in the study of hydrocyclone. At present,
there are two main methods to calculate the short-circuit flow rate. One is to calculate the
product of the average radial velocity and the cylinder area on the axial extension line of the
overflow pipe [
5
], the other is to calculate the downward mass flow rate around the bottom
of the overflow pipe [
6
]. Furthermore, there are two methods to study the short-circuit flow:
theoretical calculation and experimental test. Since the numerical simulation is based on
the solution of the governing equations, the simulation method is classified as theoretical
Processes 2022,10, 771. https://doi.org/10.3390/pr10040771 https://www.mdpi.com/journal/processes
Processes 2022,10, 771 2 of 16
calculation here. Bradley and Pulling [
7
] demonstrated the existence of the short-circuit
flow by using the flow field visualization method. According to the boundary layer theory,
Bloor et al. [
8
] calculated that the typical short-circuit flow accounts for about 10% of the
total inlet flow. Kelsall [
9
] measured the short-circuit flow accounting for about 15% of the
total flow by installing a ring-shaped intercepting tube at the bottom of the vortex finder.
With the rapid development of computer technology, numerical simulation has be-
come one of the most crucial hydrocyclone study methods. The flow field characteristics,
including short-circuit flow, can be extracted from simulation results. Therefore, the lo-
cation, form, and mass flow rate of the short-circuit flow can be determined. Scholars
have found that the short-circuit flow always flows along the outer wall of the vortex
finder and discharges from the bottom of the overflow pipe [
10
,
11
]. Furthermore, Zhao
et al. [
12
] found that the short-circuit flow monotonically decreases as the wall thickness
of the vortex finder increases. Huang et al. [
13
] pointed out that the inlet section angle of
cyclone separators could reduce the short-circuit flow rate markedly from the bottom of
the vortex finder. Xu [
14
] also indicated that increasing the outer diameter of the vortex
finder could significantly cut down the short-circuit flow. Tang et al. [
15
] concluded that
the effects of the short-circuit flow become increasingly significant with the increase in the
vortex finder thickness. He also pointed out that as the vortex finder thickness increased,
the separation efficiency for the coarse particles continued to decrease; the vortex finder
thickness does not significantly affect the separation efficiency of fine particles by the
overflow. The above research focuses on the vortex finder configuration, especially the wall
thickness. However, the effects of operating parameters on the flow field characteristics
and separation performance of hydrocyclone are also significant. Therefore, this paper
systematically studied the effect of the vortex finder configuration, inlet velocity, and feed
concentration on the short-circuit flow and separation efficiency. Furthermore, the relative
strength of different parameters to the short-circuit flow and separation is analyzed.
Computational fluid dynamic technology (CFD) could calculate the gas-liquid-solid
system in hydrocyclone and obtain numerous information comprised of turbulent flow,
air core, and particle motion [
16
–
20
]. For turbulent flow in hydrocyclone, the Reynolds
Stress method (RSM) can adapt to the change of fluid density, the vortex bending of flow
field and the rapid change of tension, it can simulate the time-averaged value and all
the Reynolds stress of complex flow, especially suitable for the three-dimensional spiral
flow with strong curved and rotating streamline [
21
–
23
]. For the air core, the Volume of
Fluid (VOF) model can describe the free interface between the air core and the liquid with
reasonable accuracy [
24
–
27
]. As for the simulation of the separated process, the Mixture
model, which belongs to the Euler–Euler model, is proposed to predict the morphology of
particle flow accurately and can capture turbulent pulsations in all directions.
In this paper, the effects of geometric parameters (vortex finder diameter, vortex finder
wall thickness, vortex finder length) and feed parameters (inlet velocity, feed concentration)
on the short-circuit flow and separation performance in a hydrocyclone are computationally
investigated. Firstly, the numerical models and simulation methods were validated by com-
paring the velocity components and particle partition curves extracted from the measured
and numerical results. Then, the characteristics of the short-circuit flow are obtained, and
the short-circuit flow rate and its ratio are quantitatively analyzed. Likewise, the separation
efficiency under different factors was calculated and shown as partition curves. Therefore,
the influence degree of geometric and operating parameters on the short-circuit flow and
separation efficiency could be compared and analyzed.
In this paper, the parameters with great influence on the short-circuit flow of the
hydrocyclone are systematically analyzed, and the influence degree of each parameter
is compared. Different from other analyses of hydrocyclones that mostly focus on per-
formance indicators such as pressure drop and flow field velocity, this paper focuses on
the short-circuit flow rate, its ratio, and separation efficiency indicators. This study can
enrich the related research work on the short-circuit flow of hydrocyclones, and provide a
Processes 2022,10, 771 3 of 16
theoretical reference for improving the separation efficiency by inhibiting the short-circuit
flow, especially for hydrocyclones with a nominal diameter of 10 mm.
2. Mathematical Model
2.1. Geometric Parameters of a Hydrocyclone
A hydrocyclone with a nominal diameter of D= 10 mm is designed as the research
object in this paper, as shown in Figure 1a. The inlet is a rectangular structure with
dimensions of
a×b=
2.0
×
1.5. The vortex finder diameter, wall thickness, and length are
represented by d
o
,
δ
, and h
o
. Considering that the hydrocyclone is mainly used for separate
feed with low concentration suspension and fine particles, the cone angle is designed to
be
α
= 15
◦
. According to the proportional relationship between the structure parameters
and the nominal diameter in a hydrocyclone, within the design criteria [
28
], the values
of the selected influencing factors are shown in Table 1. Due to the mutual constraints
of the vortex finder structure, all values of influencing factors have been considered in
Table 1. The control variable method was adopted to study the effect of each factor on
the short-circuit flow and separation efficiency. The hydrocyclone with the vortex finder
diameter (d
o
) of 2.6 mm, the wall thickness (
δ
) of 1.5 mm, and the length (h
o
) of 6 mm at
the inlet velocity (v) of 12 m
·
s
−1
and feed volume concentration (c
v
) of 2% was determined
as the base hydrocyclone (Base_H).
Figure 1.
Geometrical parameters (
a
) and fluid domain mesh (grid number: 308,046) (
b
) of the
hydrocyclone.
Table 1. Influencing factors and values of the hydrocyclone.
Sequence Number Influencing Factors
do/mm δ/mm ho/mm v/m·s−1cv/%
1 2.0 6.0
2 2.2 0.5 2.0 8.0
3 2.4 1.0 4.0 10.0 1.0
4 (Base_H) 2.6 1.5 6.0 12.0 2.0
5 2.8 2.0 8.0 14.0 3.0
6 3.0 10.0 16.0 4.0
7 3.2 12.0 18.0 5.0
8 14.0 6.0
9 16.0
Processes 2022,10, 771 4 of 16
2.2. Model Description
The flow field characteristics and separation performance in the hydrocyclone were
obtained using the numerical simulation software Fluent 19.0. The flow field of the hy-
drocyclone is a complex gas-liquid-solid three-phases motion containing a high swirl and
strong shear flow. Therefore, the simulation procedures are divided into two steps: firstly,
the flow field containing water and air are simulated by the RSM model and VOF model;
then, the stable flow field calculated by the first step was used as the initial flow field, and
the solid particles are added to the flow field from the inlet and simulated with the Mixture
model. The above calculation methods have been verified to accurately predict the flow
field and separation performance of the hydrocyclone [12,29,30].
The transport equation and governing equation of the adopted model are as follows:
For the incompressible fluid, the governing equations of continuity and Reynolds-
Averaged Navier–Stokes can be expressed as Equations (1) and (2), respectively.
∂ρ
∂t+∂
∂xi
(ρui)=0 (1)
∂
∂t(ρui)+∂
∂xjρuiuj=−∂p
∂xi
+∂
∂xj"µ ∂ui
∂xj
+∂uj
∂xi!#+∂
∂xj−ρu0
iu0
j(2)
where the velocity components are decomposed into the mean
ui
and fluctuating
u0
i
veloci-
ties (i= 1,2,3), the relation of them is as given by
ui=ui+u0
i(3)
where
ρ
,
ui
,
u0
i
,
xi
are liquid density, velocity, velocity fluctuation, and positional length,
respectively.
As the Reynolds-Averaged N-S equation (Equation (2)) introduces the Reynolds stress
term
−ρu0
iu0
j
. The Reynolds stress term is a new unknown term for the turbulent fluctuation
value. Therefore, in order to close the N-S equation set, it is necessary to introduce the
Reynolds stress model (RSM). The unknown values in the flow field could be obtained by
simultaneously solving the N-S equation set and RSM model.
The transport equations for the transport of the Reynolds stress
−ρu0
iu0
j
in the RSM
model can be written as
∂
∂tρu0
iu0
j+∂
∂xkρuku0
iu0
j
| {z }
Cij
=−∂
∂xkhρu0
iu0
ju0
k+p0u0
iδkj +p0u0
jδiki
| {z }
DT,j
+∂
∂xkµ∂
∂xku0
iu0
j
| {z }
DLij
−ρu0
iu’
k
∂uj
∂xk
+u0
ju0
k
∂ui
∂xk
| {z }
Pij
−ρβgiu0
jθ+gju0
iθ
| {z }
Gij
+p0 ∂u0
i
∂xj
+∂u0
j
∂xi!
| {z }
Φij
−2µ∂u0
i
∂xk
∂u0
j
∂xk
|{z }
εij
−2ρΩku0
ju0
meikm +u0
iu0
mejkm
| {z }
Fij
(4)
where
P
,
µ
,
gi
,
Ωk
are pressure, dynamic viscosity, acceleration of gravity, and rotational
velocity tensor, respectively.
The two terms on the left are the local time derivative term and the convection term,
respectively. The seven terms on the right are the turbulent diffusion term
DT,ij
, the
Processes 2022,10, 771 5 of 16
molecular diffusion term
DL,ij
, the stress production term
Pij
, the buoyancy production
term
Gij
, the pressure strain term
Φij
, the dissipation term
εij
, and the production by system
rotation term Fij.
The air core, which is one of the important features of the flow field in a hydrocyclone,
was simulated with the VOF model. The tracking of the interface between the water and the
air core is achieved by solving the following continuity equation (volume fraction equation)
∂
∂taq+∇ · aq
→
vq=0 (5)
where
aq
is the volume fraction of the qth phase and
→
vq
is the velocity vector of the qth
phase.
There is only one momentum equation that is solved in the whole domain and the
resulting velocity field is shared among the phases. The momentum equation, which is
dependent on the volume fraction of all phases through the properties
ρ
and
µ
, is given by
∂
∂tρui+∂
∂xj
ρuiuj=−∂p
∂xi
+∂
∂xj
µ ∂ui
∂xj
+∂uj
∂xi!+ρg+F(6)
where Fis the body force resulting from surface tension at the interface, and the density
ρ
,
and viscosity
µ
are derived from the values of component phases in each control cell by the
volume fraction averaged method, given by
ρ=
n
∑
k=1
akρk(7)
µ=
n
∑
k=1
akµk(8)
The separation of solid particles in the hydrocyclone was simulated by the Mixture
model. The model can be used for two-phase or multiphase flow calculation. Each phase is
treated as a continuous phase in this model and can be interpenetrating. The model solves
the dynamic equation of the mixture and describes the discrete phase by relative velocity.
Thus, the continuity equation for the mixture is
∂
∂t(ρm)+∇ · ρm
→
vm=0 (9)
where →
vmis the mass-averaged velocity
→
vm=
n
∑
k=1
akρk
→
vk
ρm(10)
and ρmis the mixture density
ρ=
n
∑
k=1
akρk(11)
akis the volume fraction of phrase k.
The momentum equation for the mixture can be obtained by summing the individual
momentum equations for all phases. It can be expressed as:
∂
∂tρm
→
vm+∇ · ρm
→
vm
→
vm=−∇p+∇ · µm∇→
vm+∇→
vT
m+ρm
→
g+
→
F−∇· n
∑
k=1
akρk
→
vdr,k
→
vdr,k!(12)
Processes 2022,10, 771 6 of 16
where nis the number of phases,
→
Fis a body force, and µmis the viscosity of the mixture:
µm=
n
∑
k=1
akµk(13)
→
vdr,kis the drift velocity for secondary phase k:
→
vdr,k=→
vk−→
vm(14)
2.3. Simulation Conditions and Boundary Condition
The grid directly affects the calculation time and accuracy of the numerical simulation.
In this study, the computational domain is discretized by the hexahedron element. In order
to capture precise flow field information, the grid was refined in the vicinity of the wall and
the vortex finder. There are six mesh models created to verify mesh independence. The grid
number of the six models is 11,7170, 163,884, 209,080, 253,356, 308,046, and 361,770. The
axial velocity and tangential velocity at z= 6 mm on the x = 0 mm plane are extracted and
compared, as shown in Figure 2. Results showed that the velocity components remained
constant when the grid number exceeded 308,046. Continuing to increase the number
of grids would not affect the simulation accuracy. Considering both the accuracy of the
numerical results and computational resources, the number of discrete grids is determined
to be about 300,000, as shown in Figure 1b.
Figure 2. The axial velocity (a) and tangential velocity (b) under different grids number.
Water with a density of 998.2 kg
·
m
−3
and a viscosity of 0.001003 pa
·
s is the liquid phase.
The solid phase is quartz powder with a density of 2600 kg
·
m
−3
. The size distribution
of the particles is shown in Table 2. The size interval “
−
60 + 40” means that the particle
diameter is bigger than 40
µ
m and smaller than 60
µ
m. The particles are divided into
fifteen fractions, and each fraction represents by its mean diameter in the simulation. The
boundary condition of the inlet is set as “velocity-inlet”, and both the water and particles
have the same velocity in the same condition. The overflow and underflow outlets are set
as “pressure outlet”, and the relative pressure is 0 atm. Furthermore, the backflow volume
fraction of the gas phase is set as 1, which means that air is allowed to return from the two
outlets into the separating domain again. The wall is set as the stationary wall, and the
near-wall treatment is set as standard wall functions.
The transient pressure-based solver was used for the solution of the model with
implicit double precision solver formulation. The SIMPLE algorithm was selected for
pressure-velocity coupling. Based on the current mesh and inlet velocity, the time step was
set at 1 ×10−5s. The total time of numerical simulation is 5 s.
Processes 2022,10, 771 7 of 16
Table 2. Particle size distribution of quartz in the feed.
Size Interval/µm Mean Size/µm Yield/%
−60 + 40 52.5 4.26
−40 + 35 37.5 3.14
−35 + 30 32.5 4.72
−30 + 25 27.5 6.9
−25 + 20 22.5 9.77
−20 + 18 19 4.85
−18 + 16 17 5.42
−16 + 14 15 5.99
−14 + 12 13 6.52
−12 + 10 11 6.98
−10 + 8 9 7.37
−8 + 6 7 7.77
−6 + 4 5 8.58
−4 + 2 3 11
−2 1 6.73
Total 100%
2.4. Model Validation
To verify the accuracy of the adopted models is vital before it applies for further
comprehensive study. In this study, the RSM model and VOF model were verified by
comparing the experimental and numerical results of axial velocity in the base hydrocyclone.
Furthermore, the Mixture model was verified by comparing the separation efficiency.
The experimental measurement apparatus for the flow field characteristic and separation
performance is shown in Figure 3. The PIV (Particle Image Velocimetry) system consists
of PIV equipment manufactured by DANTEC Dynamics A/S and Dynamics Studio V3.0
image processing system. Among them, the laser is an Nd: YAG dual-pulse laser, the
output laser wavelength is 532 nm, the repetition rate is 1~15 Hz, and the pulse width is
6~8 ns. The CCD camera with 2048
×
2048 pixels is used to capture the picture, and the
frame rate can reach 20 fps. In order to reduce the test deviation caused by laser scattering,
a transparent plexiglass tank is installed on the outside of the hydrocyclone. The feed is
pumped into the hydrocyclone, and an adjustable valve controls the inlet velocity. An
appropriate amount of polystyrene particles with densities approaching water are added as
the tracer into the stirring tank. The location of tracer particles at the measured plane was
marked by the laser beam and recorded as pictures by the charge-coupled device camera
(CCD camera). Then, the pictures that included detailed information of the flow field are
processed by a high-performance computer.
Figure 3.
Scheme of experimental apparatus: 1-mixing tank; 2-valve; 3-pump; 4-rotor flow meter;
5-piezometer; 6-hydrocyclone; 7-plexiglass tank; 8-high-speed camera; 9-laser generator; 10-high-
performance computer.
Processes 2022,10, 771 8 of 16
The axial velocities at z= 2 mm and z= 10 mm extracted from measured and simulated
results are shown in Figure 4. Due to the influence of the hydrocyclone structure and the
air core, only half of the flow field can be measured precisely. It is obvious that the velocity
distributions and trends obtained by experiment and simulation are in good agreement. The
axial velocity shows that the fluid flows down at the wall and upward at the center. After
uncertainty analysis, the maximum error of the numerical simulation on the calculation
results of the flow field is 3.17%, which is acceptable.
Figure 4. Comparison of the distribution of axial velocity at z=2mm(a) and z= 10 mm (b).
Quartz particles with a density of 2600 kg
·
m
−3
and a feed solids concentration of
2% by volume are added into the storage tank and stirred evenly. The inlet velocity is
controlled by a valve and adjusted to 12 m
·
s
−1
. Then, the suspensions were collected
synchronously from the inlet and underflow when the flow field was stable. The samples
are analyzed by Mastersizer 2000 laser particle characterization system, and then the particle
size distribution is obtained. The separation efficiency of the measured and simulated
methods is shown in Figure 5. On the whole, the separation efficiencies obtained by the two
methods are in good agreement. The prediction accuracy of the relatively coarse particles
is higher than that of fine particles. However, when the particle size exceeds 5
µ
m, the
maximum error of the Mixture model on the separation efficiency is only 4.87%, which is
acceptable. Therefore, the Mixture model could describe the separation performance of
hydrocyclone accurately.
Figure 5. Comparison of the simulated and measured partition curves.
According to the above analyses, it can be concluded that the RSM model, VOF model,
and Mixture model in this paper can give reasonable and reliable predictions of the flow
field characterization and separation performance.
Processes 2022,10, 771 9 of 16
3. Characteristics of Short-Circuit Flow
3.1. Structural Form of Short-Circuit Flow
The detailed description of the short-circuit flow by the experimental method is limited.
However, the numerical method can carry out a comprehensive and accurate prediction of
the flow field in a hydrocyclone, which is very meaningful for studying the short-circuit
flow. The premise of the quantitative description of the short-circuit flow is to determine its
location accurately. Figure 6a shows the structural characteristics of the short-circuit flow,
including the axial velocity cloud diagram at x= 0 mm plane, a partially enlarged view,
and an axial velocity cloud diagram at z= 14 mm plane. It can be seen from the region
marked by an ellipse that part of the feed flows down along the overflow pipe. Due to
the combined effect of the radial velocity and the air core, this part of the feed would flow
to the overflow pipe and be discharged from the vortex finder directly. This part of the
feed is named the short-circuit flow, which can be observed clearly in the red rectangle
in the partially enlarged view. As shown in the axial section velocity cloud diagram, the
structure of the short-circuit flow is not strictly a circular ring shape but a semi-ring or
similar circular ring shape. It might be caused by the asymmetric inlet configuration that
only one inlet is adopted in this hydrocyclone.
Figure 6.
(
a
) Location and structural form of the short-circuit flow, (
b
) axial velocity distribution at
z= 14 mm on the y= 0 mm section.
3.2. Calculation Method of the Short-Circuit Flow
Quantitative calculation of the short-circuit flow is of great significance to analyze the
internal flow field characteristics and separation efficiency of the hydrocyclone. The axial
velocity distribution at z= 14 mm on the x= 0 mm section is shown in Figure 6b, and the
shaded rectangular is the overflow pipe. On the whole, the axial velocity is symmetrically
distributed about the centerline of the hydrocyclone, and the velocity near the vortex finder
is large. The short-circuit flow rate could be determined by integrating the axial velocity
from r
1
to r
2
, where the axial velocity is zero. Therefore, the short-circuit flow rate can be
obtained by CFD-post software, and the calculation equations could be written as follows:
Qs=Zr2
r1
2πrvzdr =xsvzds (15)
where sis the short-circuit flow axial cross-section and v
z
is the corresponding axial velocity.
Processes 2022,10, 771 10 of 16
4. Effects of the Geometric and Operating Parameters on the Short-Circuit Flow and
Separation Efficiency
The short-circuit flow and its ratio can directly reflect the hydrocyclone’s effective pro-
cessing capacity. The separation efficiency could reveal the separate sharpness and ability
of the hydrocyclone. Therefore, the short-circuit flow rate and separation performance
under different structural and operating parameters were calculated and compared.
4.1. Effects of the Geometric Parameters on the Short-Circuit Flow and Separation Efficiency
4.1.1. Vortex Finder Diameter
The vortex finder diameter is closely related to the shape of the air column and the
overflow flow rate. The overlarge diameter would generate a large air core, which is
larger than the underflow diameter, then the separation performance would deteriorate
rapidly [
11
,
31
]. The effect of seven kinds of vortex finder diameters (2.0 mm, 2.2 mm,
2.4 mm, 2.6 mm, 2.8 mm, 3.0 mm) on the short-circuit flow and separation efficiency are
shown in Figure 7. When the vortex finder diameter is 3.2 mm, the short-circuit flow
interfering with the axial downward flow makes extracting the short-circuit flow rate
difficult. Therefore, the value of the short-circuit flow when d
o
= 3.2 mm is not shown in
Figure 7a. The total inlet flow rate Q
i
at the inlet velocity of 12 m
·
s
−1
is 3.594
×
10
−2
kg
·
s
−1
.
In Figure 7a, the mass flow rate of the short-circuit flow and its ratio increase with the vortex
finder diameter increases. That is due to the increasing vortex finder diameter shortening
the flow distance of short-circuit flow. Therefore, the larger vortex finder diameter increases
the tendency of the feed into the overflow pipe. When 2.2 < d
o
< 2.6, the increasing rate of
the short-circuit flow is relatively slow. That might be that the separating space under this
vortex finder diameter is suitable for generating the circulation flow. The circulation flow
located at the cricoid region between the vortex finder’s outer wall and the cyclone’s inner
wall facilitates the separation of the surrounding fluid. Furthermore, studies have found
that the increased vortex finder diameter can increase the circulation flow rate to some
extent [
32
]. In addition, the ratio of the short-circuit flow to the inlet flow has the same
trend as that of the short-circuit mass flow rate because the total inlet flow rate is constant.
Figure 7.
Effect of the vortex finder diameter on the short-circuit flow rate and the ratio (
a
) and
separation performance (b).
Figure 7b shows the effect of vortex finder diameter on the separation efficiency. The
separation efficiency, also called the partition curve, could be obtained by calculating the
recovery rate of different diameter particles in the underflow. The vortex finder diameter
has a greater impact on the particles the diameter is smaller than the cut size (d
50
). The
smaller diameter vortex finder decreases the particle cut size, and it is conducive to the
enrichment of the coarse particles in the underflow. However, the bigger diameter vortex
finder is beneficial to the enrichment of the fine particles in the overflow. This is because
the increased vortex finder diameter causes an increase in the short-circuit flow ratio,
which increases the content of fine particles in the overflow. Therefore, A smaller vortex
Processes 2022,10, 771 11 of 16
finder diameter is beneficial to decrease the short-circuit flow and the d
50
. Appropriately
increasing the diameter of the vortex finder can improve the classification of fine particles.
4.1.2. Vortex Finder Wall Thickness
The vortex finder wall thickness affects the pre-separation space of the hydrocyclone.
A thick-walled vortex finder would compress the separating region. The effect of four wall
thicknesses on the short-circuit flow and separation efficiency was studied, as shown in
Figure 8. The short-circuit flow rate and its ratio monotonically decrease with the increased
wall thickness of the vortex finder, as shown in Figure 8a. Compared with the
δ
= 0.5 mm,
the short-circuit flow rate has the smallest ratio of 9.78% at
δ
= 2.0 mm, and a reduction of
42.91%. The result that the thick-walled vortex finder can effectively inhibit the short-circuit
flow is consistent with Xu [
14
] and Zhao [
12
]. The thick-walled vortex finder increases the
distance of inlet feed directly flows into the vortex finder. Therefore, part of the short-circuit
flow could reenter the separation region under the influence of the flow field.
Figure 8.
Effect of the vortex finder thickness on the short-circuit flow rate and the ratio (
a
) and
separation performance (b).
In Figure 8b, the vortex finder wall thickness has a greater effect on the particles
around the cut size. With the increase of the vortex finder wall thickness, the cut size (d
50
)
decreases. Due to the increasing vortex finder wall thickness increases the flow distance
that the inlet fluid directly flows into the vortex finder. Part of the short-circuit flow would
be influenced by the circulation flow and then return to the separating space. The changing
trend of the cut size along with the wall thickness is consistent with that of Zhao [
12
].
Therefore, increasing the vortex finder wall thickness helps inhibit the short-circuit flow
and improves the separation efficiency. A thick-walled vortex finder should be considered
and used in the design of the hydrocyclone.
4.1.3. Vortex Finder Length
The vortex finder length affects the separating space of the cylindrical section of the
hydrocyclone and the separated time of the particles discharged from the overflow pipe.
Furthermore, the longer vortex finder length might increase the flow distance of the short-
circuit flow. According to the design manual [
28
], the optional range of vortex finder length
is 0 to 2D, and D is the nominal diameter of the hydrocyclone. The effect of eight vortex
finder lengths on the short-circuit flow and separation efficiency is shown in Figure 9. In
Figure 9a, the short-circuit flow rate and its ratio are higher when the length is shorter
than 6 mm and longer than 12 mm. When
h≤
6 mm, the bottom of the vortex finder is
closer to the inlet. So, it is easy for the inlet fluid flows into the vortex finder through such
a shorter distance. When
h≥
12 mm, the vortex finder’s bottom is closed to the juncture
of the cylinder and cone of hydrocyclone. Due to the effect of the surrounding flow field,
the axial downward velocity along the outer wall of the vortex finder increases. However,
the short-circuit flow rate and its ratio is smaller when 6
≤h≤
12. Based on the above
Processes 2022,10, 771 12 of 16
analysis, the reason is that the vortex finder length appropriately increases the flow distance
of the short-circuit flow and has avoided the influence of the juncture region. Therefore,
the moderate vortex finder length is conducive to inhibiting the short-circuit flow.
Figure 9.
Effect of the vortex finder length on the short-circuit flow rate and the ratio (
a
) and
separation performance (b).
Figure 9b shows the effect of the vortex finder length on the separation efficiency. The
vortex finder length affects the particles of a diameter larger than 10
µ
m. With the increase of
the vortex finder length, the separation efficiency decreases, and the cut size (d
50
) increases
slightly. The longer vortex finder length decreases the residence time of particles and leads
to an inadequate separation for coarse particles. Therefore, the unseparated coarse particles
would flow into the vortex finder and deteriorate the separation efficiency, especially
when the vortex finder length is longer than 12 mm. Comprehensively considering the
influence of the vortex finder length on the short-circuit flow and separation efficiency, a
medium vortex finder length, such as 6~12 mm, is suitable for inhibiting the short-circuit
and improving separation efficiency.
4.2. Effects of the Operating Parameters on the Short-Circuit Flow and Separation Efficiency
4.2.1. Inlet Velocity
Inlet velocity directly affects the tangential velocity of the flow field and the particle’s
residence time. An appropriate inlet velocity could make the hydrocyclone achieve better
separation efficiency with a larger processing capacity. The effect of the inlet velocity on
the short-circuit flow rate, its ratio, and separation efficiency is shown in Figure 10. With
the increase of the inlet velocity, the short-circuit flow rate gradually increased, and its
ratio decreased slowly. The increasing inlet velocity increases the velocity of the flow
field, including the axial downward velocity of the short-circuit flow. Furthermore, the
shear action of the larger inlet velocity could weaken the layer of the short-circuit flow.
Therefore, the short-circuit flow’s changing trend with the increasing inlet velocity is shown
in Figure 10a. In addition, the inlet velocity has a slight influence on the ratio, and the
maximum difference of the ratio is only 0.67%. In Figure 10b, the larger inlet velocity could
effectively improve the separation efficiency and decrease the cut size (d
50
), especially when
v
≤
12 m
·
s
−1
. When the inlet velocity exceeds 12 m
·
s
−1
, the separation efficiency increases
slowly. It means it is not feasible to improve the separation performance by unlimited
increasing inlet velocity. In addition, the excessive inlet velocity might deteriorate the flow
field, accompanied by higher energy consumption. Therefore, when determining the feed
rate of the cyclone separator, it is necessary to comprehensively consider the short-circuit
flow rate, power consumption, and separation performance. A moderate inlet velocity
would be reasonable to inhibit the short-circuit flow and improve separation performance.
Processes 2022,10, 771 13 of 16
Figure 10.
Effect of the inlet velocity on the short-circuit flow rate and the ratio (
a
) and separation
performance (b).
4.2.2. Feed Concentration
Feed concentration determines the particle number of the flow field in the hydrocy-
clone. The effect of the feed concentration on the short-circuit flow and separation efficiency
is shown in Figure 11. Due to the increasing feed concentration, the fluid would entrain
more particles into the vortex finder. So, the short-circuit flow rate increases with the feed
concentration increases, as shown in Figure 11a. However, its ratio slightly decreases while
the feed concentration increases, the maximum difference in the ratio is 0.17%. Therefore,
the feed concentration could increase the short-circuit flow but slightly affect its ratio. In
Figure 11b, the partition curves decrease as the feed concentration increases. The separation
efficiency indicates that the recovery rate of both the fine particles and coarse particles to un-
derflow is reduced. Meanwhile, the particle cut size (d
50
) increases as the feed concentration
increases. This might be because the higher feed concentration increases particles’ collision,
leading to the displacement of particles. Therefore, the lower the feed concentration is
conducive to the classification of the fine particles.
Figure 11.
Effect of the feed concentration on the short-circuit flow rate and the ratio (
a
) and separation
performance (b).
4.3. Comparison and Analysis
In order to compare the influence degree of five parameters on the short-circuit flow
and separation efficiency, the max/min value of short-circuit mass flow rate and particle
cut size affected by vortex finder configuration and operating parameters are shown
in Figure 12. In Figure 12a, the abscissa is the influencing factor, and the y-coordinate
is the short-circuit flow rate. The black line connects the values of each factor of the
base hydrocyclone. The short-circuit mass flow rate of the Base_H is 5.34
×
10
−3
kg
·
s
−1
.
Above and below the line are the maximum and minimum values of the short-circuit flow,
respectively. The vortex finder diameter and feed concentration have little effect on the
Processes 2022,10, 771 14 of 16
short-circuit flow, while the vortex finder wall thickness, length, and inlet velocity have a
greater influence. Especially for the vortex finder wall thickness, the 1.5 mm increase in
the wall thickness could decrease the short-circuit flow 2.65
×
10
−3
kg
·
s
−1
, accounting for
7.37% of the total inlet flow rate. Therefore, the thick-walled vortex finder can effectively
inhibit the short-circuit flow compared with the other parameters.
Figure 12.
Comparison of the effect of influencing factors on the short-circuit flow (
a
) and cut size (
b
).
Figure 12b shows the particle cut size (d
50
) under different influencing factors. In
sequence, the influencing factors are the d
o
,
δ
,h,v, and c
v
. The sequence number represents
the value of each parameter, as shown in Table. 1. Sequence number 4. represents the base
hydrocyclone (Base_H), and its cut size is 8.17
µ
m. It can be seen that the cut size increases
with the vortex finder diameter and length, and feed concentration increases. However, the
cut size decreases with the vortex finder wall thickness, and inlet velocity increases. The
inlet velocity has a greater effect on the cut size, and a relatively higher inlet velocity is
conducive to reducing cut size. Compared with the geometric parameters, the operating
geometric has a greater influence on the cut size. Therefore, smaller vortex finder diameter,
thick-walled vortex finder, longer vortex finder length, higher inlet velocity, and lower feed
concentration are conducive to the application of the hydrocyclone to the classification of
fine particles.
5. Conclusions
(1) The influence of the structural parameters of the vortex finder on the short-circuit flow
and separation efficiency was clarified. It is effective by reducing the vortex finder
diameter, increasing the vortex finder wall thickness, and adopting the moderate
vortex finder length to inhibit the short-circuit flow and decrease the particle cut size.
(2)
The effects of inlet velocity and feed concentration on the short-circuit flow and sepa-
ration efficiency were obtained. The faster inlet velocity and higher feed concentration
can improve the processing efficiency of the hydrocyclone. Furthermore, the relatively
faster inlet velocity and lower feed concentration could decrease the particle cut size
and improve the separation efficiency.
(3)
The comparison of the influence degree of each parameter shows that the vortex
finder wall thickness, vortex finder length, and inlet velocity have a greater influence
on the short-circuit flow. Especially for the vortex finder wall thickness, the 1.5 mm
increase in the wall thickness could decrease the short-circuit flow 2.65
×
10
−3
kg
·
s
−1
,
accounting for 7.37% of the inlet flow.
(4)
Compared with the structural parameters, the higher inlet velocity can effectively
improve the separation performance. Furthermore, it is not feasible to improve the
separation performance by unlimited increasing inlet velocity.
Processes 2022,10, 771 15 of 16
Author Contributions:
Conceptualization, T.S. and Y.Z.; methodology, Y.Z.; software, T.S.; validation, T.S.
and Y.Z.; formal analysis, T.S.; investigation, T.S.; resources, Y.Z.; data curation, T.S.; writing—original
draft preparation, T.S.; writing—review and editing, Y.Z.; visualization, T.S.; supervision, Y.Z.; project
administration, Y.Z.; funding acquisition, Y.Z. All authors have read and agreed to the published
version of the manuscript.
Funding:
This work was supported by the National Natural Science Foundation of China (21276258).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement:
Informed consent was obtained from all subjects involved in this study.
Data Availability Statement:
The data presented in this study are available on request from the
corresponding author. The data are not publicly available due to continuous research.
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
Sakin, A.; Karagoz, I.; Avci, A. Effects of separation space diameter on the performance of a novel reverse flow cyclone. Sep. Sci.
Technol. 2019,54, 2450–2460. [CrossRef]
2.
Yu, J.; Fu, J. Separation performance of an 8 mm mini-hydrocyclone and its application to the treatment of rice starch wastewater.
Sep. Sci. Technol. 2020,55, 313–320. [CrossRef]
3. Bretney, E. Water Purifier. US Patent 453105, 26 May 1891.
4. Yuan, H.; Chen, G.; Yu, J. Study on short circuit flow under hydraulic cyclone cover. Fluid Mach. 2000,28, 10–12.
5.
Fu, X.; Sun, G.; Liu, J.; Shi, M. Discuss on estimation difficulties and numerical computation methods for short circuit flow in
cyclone separators. J. Chem. Ind. Eng. 2011,62, 2535–2540.
6.
Li, F.; Liu, P.; Yang, X.; Zhang, Y.; Jiang, L.; Wang, H. Numerical analysis of the effect of solid rod on the flow field and separation
performance of thick-walled overflow pipe hydrocyclone. Powder Technol. 2021,388, 261–273. [CrossRef]
7.
Bradley, D.; Pulling, D.J. Flow patterns in the hydraulic cyclone and their interpretation in terms of performance. Trans. Inst.
Chem. Eng. 1959,37, 34–45.
8. Bloor, M.I.G.; Ingham, D.B. Theoretical investigation of flow in a conical hydrocyclone. Trans. Inst. Chem. Eng. 1973,51, 36–41.
9. Kelsall, D.F. A further study of the hydraulic cyclone. Chem. Eng. Sci. 1953,2, 254–272. [CrossRef]
10.
Wang, B.; Chu, K.W.; Yu, A.B. Numerical study of particle-fluid flow in a hydrocyclone. Ind. Eng. Chem. Res.
2007
,46, 4695–4705.
[CrossRef]
11. Wang, B.; Chu, K.W.; Yu, A.B.; Vince, A. Modeling the Multiphase Flow in a Dense Medium Cyclone. Ind. Eng. Chem. Res. 2009,
48, 3628–3639. [CrossRef]
12.
Zhao, Q.; Cui, B.Y.; Wei, D.Z.; Song, T.; Feng, Y.Q. Numerical analysis of the flow field and separation performance in hydrocy-
clones with different vortex finder wall thickness. Powder Technol. 2019,345, 478–491. [CrossRef]
13.
Huang, X.; Qian, F. Effect of the improvement of inlet geometry of cyclone separators on shortcut flow rate. J. Filtr. Sep.
2008
,
11–13.
14.
Xu, J.R.; Luo, Q.; Qiu, J.C. Research on the preseparation space in hydrocyclones. Int. J. Miner. Process.
1991
,31, 1–10. [CrossRef]
15.
Tang, B.; Xu, Y.X.; Song, X.F.; Sun, Z.; Yu, J.G. Numerical study on the relationship between high sharpness and configurations of
the vortex finder of a hydrocyclone by central composite design. Chem. Eng. J. 2015,278, 504–516. [CrossRef]
16.
Vakamalla, T.R.; Koruprolu, V.B.R.; Arugonda, R.; Mangadoddy, N. Development of novel hydrocyclone designs for improved
fines classification using multiphase CFD model. Sep. Purif. Technol. 2017,175, 481–497. [CrossRef]
17.
Zhu, G.F.; Liow, J.L.; Neely, A. Computational study of the flow characteristics and separation efficiency in a mini-hydrocyclone.
Chem. Eng. Res. Des. 2012,90, 2135–2147. [CrossRef]
18.
Murphy, S.; Delfos, R.; Pourquie, M.; Olujic, Z.; Jansens, P.J.; Nieuwstadt, F.T.M. Prediction of strongly swirling flow within an
axial hydrocyclone using two commercial CFD codes. Chem. Eng. Sci. 2007,62, 1619–1635. [CrossRef]
19.
Lee, H.; Park, J.; Lee, J.C.; Ko, K.; Seo, Y. Development of a hydrocyclone for ultra-low flow rates. Chem. Eng. Res. Des.
2020
,156,
100–107. [CrossRef]
20.
Lu, Y.J.; Zhou, L.X. Numerical simulation of fluid flow and oil-water separation in hydrocyclones. Chin. J. Chem. Eng.
2003
,11,
97–101.
21.
Wang, B.; Pei, B.B.; Liu, H.; Jiang, Y.C.; Xu, D.L.; Chen, Y.X. Function and effect of the inner vortex on the performance of cyclone
separators. AlChE J. 2017,63, 4508–4518. [CrossRef]
22.
Lim, E.W.C.; Chen, Y.R.; Wang, C.H.; Wu, R.M. Experimental and computational studies of multiphase hydrodynamics in a
hydrocyclone separator system. Chem. Eng. Sci. 2010,65, 6415–6424. [CrossRef]
23.
Liu, M.L.; Chen, J.Q.; Cai, X.L.; Han, Y.H.; Xiong, S. Oil-water pre-separation with a novel axial hydrocyclone. Chin. J. Chem. Eng.
2018,26, 60–66. [CrossRef]
24.
Mokni, I.; Dhaouad, H.; Bournot, P.; Mhiri, H. Numerical investigation of the effect of the cylindrical height on separation
performances of uniflow hydrocyclone. Chem. Eng. Sci. 2015,122, 500–513. [CrossRef]
Processes 2022,10, 771 16 of 16
25.
Evans, W.K.; Suksangpanomrung, A.; Nowakowski, A.F. The simulation of the flow within a hydrocyclone operating with an air
core and with an inserted metal rod. Chem. Eng. J. 2008,143, 51–61. [CrossRef]
26.
Xu, Y.X.; Song, X.F.; Sun, Z.; Tang, B.; Li, P.; Yu, J.G. Numerical Investigation of the Effect of the Ratio of the Vortex-Finder
Diameter to the Spigot Diameter on the Steady State of the Air Core in a Hydrocyclone. Ind. Eng. Chem. Res.
2013
,52, 5470–5478.
[CrossRef]
27.
Cui, B.Y.; Wei, D.Z.; Gao, S.L.; Liu, W.G.; Feng, Y.Q. Numerical and experimental studies of flow field in hydrocyclone with air
core. T. Nonferr. Metal. Soc. 2014,24, 2642–2649. [CrossRef]
28. Pang, X. Technical Calculation of Hydrocyclone; China Petrochemical Press: Beijing, China, 1997.
29.
Zhang, C.; Wei, D.Z.; Cui, B.Y.; Li, T.S.; Luo, N. Effects of curvature radius on separation behaviors of the hydrocyclone with a
tangent-circle inlet. Powder Technol. 2017,305, 156–165. [CrossRef]
30.
Cui, B.Y.; Zhang, C.E.; Zhao, Q.; Hou, D.X.; Wei, D.Z.; Song, T.; Feng, Y.Q. Study on interaction effects between the hydrocyclone
feed flow rate and the feed size distribution. Powder Technol. 2020,366, 617–628. [CrossRef]
31.
Wang, B.; Yu, A.B. Numerical study of the gas-liquid-solid flow in hydrocyclones with different configuration of vortex finder.
Chem. Eng. J. 2008,135, 33–42. [CrossRef]
32.
Liu, Y.; Yang, Q.; Qian, P.; Wang, H.L. Experimental study of circulation flow in a light dispersion hydrocyclone. Sep. Purif.
Technol. 2014,137, 66–73. [CrossRef]
