1

CFD model of a Hydrocyclone

Peng Xu

∗ and Arun S Mujumdar

Minerals, Metals and Materials Technology Centre (M3TC), Faculty of Engineering,

National University of Singapore, Singapore 117576

Abstract

The hydrocyclone is an industrial apparatus used commonly to separate by centrifugal

action dispersed solid particles from a liquid suspension. It is widely used in the mineral

and chemical processing industries because of its simplicity in design and operation, high

capacity, low maintenance and operating costs as well as its small physical size. The

computational fluid dynamic (CFD) technique is used for design and optimization as it

provides a good means of predicting equipment performance of the hydrocyclone under a

wide range of geometric and operating conditions with lower cost. The objective of this

study is to numerically investigate the properties of hydrocyclone and explore several

innovative designs which offer high separation efficiency at low energy cost as well as

reduced erosion-induced wear.

In this study several turbulence models are tested and compared with experimental

results. Also, the effect of the hydrocyclone geometry e.g. inlet duct shape on the erosion

rate within the hydrocyclone is calculated and the hot spots of wear are indicated.

Additionally, several new designs are presented and studied numerically for their erosion

characteristics, pumping power requirements and collection efficiency.

* Email: mpev6@nus.edu.sg, Tel. +65-65168870.

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1. Introduction

The hydrocyclone is a mechanical separation device to separate dispersed solid

particles from a liquid suspension fed to it by centrifugal action, it is broadly used in

industry because of its simplicity in design and operation, high capacity, low maintenance

and operating costs as well as its small physical size [1]. Experimental investigation using

the LDA technique [2] is a relatively difficult technique and very expensive as well while

empirical models can be used only within the limits of the experimental data from which

the empirical parameters are determined. In view of these shortcomings, mathematical

models based on the basic fluid mechanics are highly desirable to intensify innovation.

The computational fluid dynamic (CFD) technique is gaining popularity in process

design and optimization, it provides a good means of predicting equipment performance

of the hydrocyclone under a wide range of geometric and operating conditions, and also

offers an effective way to design and optimize the hydrocyclones [3-17].

Erosion of parts of the internal wall of the hydrocyclone is a critical issue in mineral

processing both from both safety and economic considerations. The injected solid

particles, such as sand and ore particles, impinge at high vellocity on the inside surfaces

of the components of the hydrocyclone, causing mechanical wear and eventual failure of

the devices. Therefore, the erosion-induced wear should be taken into account together

with separation efficiency and energy cost for optimizing and designing hydrocyclones.

As testing for erosion of industrial devices generally requires special equipment and

methodology, further modeling effort is needed for advancing our capability in predicting

wear of hydrocyclones.

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This work presents results of a CFD model of a hydrocyclone based on Fluent version

6.3. First, results using different turbulence models viz. k-ε, RSM and LES, are compared

with published experimental results for a 75mm standard hydrocyclone [18]. The air core

formation and geometry will be predicted with CFD model. Then, in order to study the

effect of the fed inlet on erosion rate, four designs of a 75mm hydrocyclone fitted with

different inlets are compared.

2. Model description

2.1 Turbulence Model

The turbulence model is the key component in the description of the fluid dynamics of

the hydrocyclone. The free surface, air core and presence of solid particles make the

swirling turbulent flow highly anisotropic, which adds to the difficulty for modeling

hydrocyclones using CFD. Three kinds of turbulence models, k-ε model, RSM and LES,

are often adopted for modeling the turbulent flow in hydrocyclones.

In mineral processing, the fluid suspensions processed are generally dilute (<10%), thus

the incompressible Navier-Stokes equations supplemented by a suitable turbulence model

are appropriate for modeling the flow in hydrocyclones. The k-ε model is a semi-

empirical model with the assumption that the flow in fully turbulent and the effects of

molecular viscosity are negligible. Comparing with standard k-ε model, the RNG k-ε

model is more responsive to the effects of rapid strain and streamline curvature and

presents superior performance for the highly swirling flow in a hydrocyclone. While, the

Reynolds stress model (RSM) closes the Reynolds-averaged Navier-Stokes equations

(RANS) by solving transport equations for the individual Reynolds stresses without

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isotropic eddy-viscosity hypothesis and together with an equation for the dissipation rate.

The quadratic pressure strain (QPS) model in RSM has been demonstrated to give

superior performance in a range of basic shear flow comparing with standard linear

pressure strain (LPS) model [7]. Large eddy simulation (LES) provides an alternative

approach in which large eddies are explicitly resolved in a time-dependent simulation

using the filtered Navier-Stokes equations. Both of Smagorinsky-Lilly subgrid-scale

model (SLM) [13,14] and renormalization group (RNG) subgrid-scale model [15] have

ever been adopted for simulation of hydrocyclone with better performance. It should be

pointed out that LES model requires highly accurate spatial and temporal discretization,

finer mesh than a comparable RANS simulation, and more compute resources.

Therefore, four turbulence models, RNG k-ε, QPS RSM, and SLM and RNG LES will

be performed in 75mm standard hydrocyclone. And the numerical results will be

compared with each other and that of experiment.

2.2 Multiphase model

Another striking feature of the flow field is the presence of an air core in the

hydrocyclone. The centrifugal force generated by the tangential acceleration pushes the

fluid to the wall and creates a low pressure in the central axis, which gives the right

conditions to suck air into the device and form an air core.

The VOF model can simulate two or more immiscible fluid phases, in which the

position of the interface between the fluids is of interest. In VOF method, the variable

density equations of motion are solved for the mixture, and an additional transport

equation for the volume fraction of each phase is solved, which can track the interface

between the air core and the liquid in hydrocyclone. The single momentum equation is

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solved throughout the domain, and the resulting velocity field is shared among the

phases. Thus, the VOF model can be adopted for modeling the air core in hydrocyclone.

However, for the dense slurry, the more sophisticated Eulerian multiphase model will be

more suitable.

2.3 Particle Tracking

In most mineral processing operations, the solid phase is sufficiently dilute (<10%).

Hence discrete phase model (DPM) can be employed, the fundamental assumption of

which is that the dispersed second phase occupies a low volume fraction can be used to

track solid particle movement. The Lagrangian DPM follows the Euler-Lagrange

approach. The fluid phase is treated as a continuum by solving the time-averaged Navier-

Stokes equations, while the dispersed phase is solved by tracking a large number of

particles through the calculated flow field. The dispersed phase can exchange

momentum, mass, and energy with the fluid phase.

The dispersion of particles can be accounted for with a stochastic tracking model, in

which the turbulent dispersion of particles is predicted by integrating the trajectory

equations for individual particles and using the instantaneous fluid velocity. Also,

unsteady tracking is used, where at the end of each time step the trajectory is updated

with the instantaneous velocity. As for the slurry feed concentrations in excess of 10% by

volume, the DPM is not suitable and Eulerian multiphase model is more appropriate for

tracking particles in hydrocyclone.

2.4 Erosion Model

The impingement of solid particles with hydrocyclone walls can cause considerable

wear, which is an issue of great industrial concern, both from safety and economic

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considerations. The damage induced by the erosion can cause equipment failure. Hence,

estimation of potential erosion of the hydrocyclone wall is important to predict the

lifetime of the equipment; it is useful to know how it is affected by geometry and

different operating conditions. Because of experimental difficulties, CFD analysis is an

effective tool to investigate the erosion rate of hydrocyclone.

Particle erosion and accretion rates can be computed at wall boundaries using the

following model equations. The erosion rate is defined as [19]

( )

1

( ) ( ) b vNp p

erosion

p

m C d f vR

A

α

=

=∑&

(1)

where ( )pC d is a function of particle diameter, α is the impact angle of the particle path

with the wall face, ( )f α is a function of impact angle, v is the relative velocity, ( )b v is

a function of relative particle velocity, and A is the area of the cell face at the wall. The

three functions C, f and b can be defined as boundary conditions at the wall; however the

default values are not updated to reflect the material being used. Therefore, these

parameters have to be updated for different materials. It is known that one of the main

parameters which influence the erosion rate is the particles impingement angle. The

impingement angle function can be used as the following model and defined by a piece-

linear profile [20-21]

2( ) sin(2 ) 3sin ( )f α α α= − for o18.43α ≤ (2a)

2( ) cos ( ) / 3f α α= for o18.43α > (2b)

To calculate the erosion rate from Eq. (1), the diameter function and velocity exponent

function are adopted as 1.8E-09 and 1.73.[19,22] The CFD model records the number,

velocity, mass and the impact angle of the various particles for each of the grids that form

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the internal geometry of the hydrocyclone. Then, the erosion rate of the hydrocyclone

walls is determined using Eqs. (1) and (2).

2.5 Simulation results

In this work, the simulations are conducted using Fluent CFD software package

(version 6.3.26). The geometry of the 75mm standard hydrocyclone is the same as

Hsieh's experiment [18] (figure 1(a)). In the simulation, the velocity inlet boundary

condition and pressure outlet boundary conditions for vortex finder and spigot are

applied. And the inlet flow rate is kept as 1.12 kg/s and the pressure at the two outlets is

1atm. The physical constants of the liquid phase were set to those of water. The solid

particle density is 2700 kg/m3 and its wt fraction is 4.8%, which is injected at the inlet.

The flow problem is simulated with three-dimensional unstructured mesh of hexahedral

cells (figure 1(b)). Trial numerical results indicated that the solution is independent of the

characteristics of the mesh size.

(a) (b)

Figure. 1. (a) Schematic dimensions of the standard hydrocyclone with stream lines, (b)

Grid representation used in simulation.

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3. Model Validation

The simulated flow field, air core and separation results are compared with

experimental results to validate the model. In order to explore the inner flow field in

hydrocyclone, three different horizontal planes situated 60, 120 and 170mm from the top

wall of 75mm standard hydrocyclone are selected to give a general description of

velocity field. On each plane, the axial and tangential velocity profiles are compared with

those of the experimental results. The comparison results show that the predicted axial

and tangential velocities of the RNG k-ε turbulence model are far from the experimental

results while the performances of QPS RSM, SML LES and RNG LES models can

capture the velocity profiles. Comparison between the latter three turbulence models

indicates that the although the QPS RSM and SML LES models perform better near the

center, the RNG LES model can track the turbulent velocities near the wall better.

Furthermore, the absolute error is little for the axial velocity and nearly zero for

tangential velocity near wall. Another point should be noted that the QRS RSM

turbulence model combing with VOF multiphase model can lead to numerical stability,

while the LES model consumes significantly more computing resources and times.

The ability to predict well the development of the air core in the hydrocyclone is a test

of the CFD model. The predicted air core and general mass balances are calculated and

compared with experiments as listed in Table 1. For RNG k-ε turbulence model, there is

no obvious air core after reaching steady state, while the predicted air core diameters with

QPS RSM, SLM LES and RNG LES are 10.6mm, 11.5mm and 10.45mm respectively,

which are all close to the experimental value 10mm. In all, QPS RSM, SLM LES and

RNG LES can be used for modeling a hydrocyclone.

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-0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Axial Velocity (m/s)

Radius (m)

Experiment

RNG k-εεεε

QPS RSM

SLM LES

RNG LES

(a)

-0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04

0

1

2

3

4

5

6

7

Radius (m)

Tangential Velocity (m/s)

SLM LES

RNG LES

Experiment

RNG k-εεεε

QPS RSM

(b)

-0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Radius (m)

Axial Velocity (m/s)

Experiment

RNG k-εεεε

QPS RSM

SLM LES

RNG LES

(c)

-0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04

0

1

2

3

4

5

6

7

SLM LES

RNG LES

Radius (m)

Tangential Velocity (m/s)

Experiment

RNG k-εεεε

QPS RSM

(d)

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Radius (m)

Axial Velocity (m/s)

Experiment

RNG k-εεεε

QPS RSM

SLM LES

RNG LES

(e)

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

0

1

2

3

4

5

6

7

SLM LES

RNG LES

Radius (m)

Tangential Velocity (m/s)

Experiment

RNG k-εεεε

QPS RSM

(f)

FIG. 2. Axial and tangential velocity profile- comparison with experimental results at (a)-

(b) 60mm, (c)-(d) 120mm, and (e)-(f) 170mm from the top wall of 75mm standard

hydrocyclone.

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Table 1. General mass balance for four different turbulent models

Experiment RNG

k-ε

QPS

RSM

SLM

LES

RNG

LES

Feed flow rate (kg/s) 1.117 1.12 1.12 1.12 1.12

Overflow flow rate (kg/s) 1.062 0.882 1.072 1.071 1.03

Underflow flow rate (kg/s) 0.055 0.238 0.058 0.053 0.09

Split ratio (%) 95.1 78.75 95.7 95.6 92.0

Pressure drop (kPa) 46.7 38.3 41.13 40.2 38.4

Air core diameter (mm) 10.0 0.2 10.6 11.5 10.45

4. Erosion Rate

There are many parameters affecting the erosion rate, such as flow rate, design of the

inlet, geometry and dimensions of the hydrocyclone and slurry properties etc. can affect

the erosion rate, among which the inlet has a very important effect on the wear

characteristics of hydrocyclone. Thus, as a preliminary work, we will calculate erosion

rate for hydrocyclone with four different inlets and discuss the influence of the design of

inlet ducting on wear characteristics of hydrocyclone. . In order to compare the effect of

the inlet geometry on the erosion rate, the same fluid and particle velocity 2.25m/s are

adopted for each case, the flow rate of solid particles is set as 0.05kg/s, particle diameter

is 11.5µm. In calculation of the erosion rate of hydrocyclone, the interactions of the solid

particles and the continuous phase need to be taken into account.

Fig. 3 shows the erosion rate of the inner wall of the simulated hydrocyclones fitted

with different inlets. Table 2 lists the maximum and average erosion rates and computed

pressure drop for each case. Although the standard hydrocyclone with tangential inlet

(fig. 3(a)) has been widely used in mineral processes, the erosion rate for it is the highest

compared with the other three designs. Also, obvious wear hot spot can be found at the

bottom of the cone section, where the erosion rate is very high. The maximum and

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integral erosion rates are 3.72E-4 and 1.87E-6 kg/(m2s), respectively. However, the

pressure drop is the lowest, 32.8 kPa. For the modified tangential inlet (fig. 3(b)), there is

no obvious wear hot spot, but the erosion rate is still high compared with the involute

inlet. The maximum and average erosion rates are 7.61E-7 and 4.72E-8 kg/(m2s),

respectively, and the pressure drop is very high (81.7kPa). For the involute inlet which

can provide a smooth transition from pressure energy to rotational momentum, the

distribution of erosion rate is relatively uniform and the value is low. For the circular

involute inlet, the maximum computed erosion rate is only 4.32E-7 kg/(m2s) and the

average value is 2.91E-8 kg/(m2s) while for the elliptical involute inlet, the maximum and

integral erosion rates are 4.37E-7 and 3.90E-8 kg/(m2s), respectively. Moreover, the

pressure drop of circular involute inlet (45.7kPa) is much smaller than that of elliptical

involute inlet (72.3kPa). It can be seen from fig. 4 that the erosion rate at the inlet is

nearly zero, while the erosion rate for conical section and spigot is much higher than that

of cylindrical section and vortex finder.

(a) (b) (c) (d)

Figure.3. Computed local erosion rates of the inner wall of tested hydrocyclone fitted

with different inlets: (a) standard tangential inlet, (b) modified tangential inlet, (c)

circular involute inlet and (d) elliptical involute inlet.

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Table 2. Computed Erosion rate for four inlet duct designs

5. Conclusions

Four turbulence models, RNG k-ε, QPS RSM, SLM LES and RNG LES, were used to

predict the aerodynamic performance of a 75mm standard hydrocyclone. The comparison

of numerical and experimental results indicates that the RNG k-ε turbulence model is not

suitable for modeling the highly swirling flows in hydrocyclones, while QPS RSM, SML

LES and RNG LES models can capture well the velocity profiles and predict the

formation of air core. With a VOF multiphase model, the air core formation was analyzed

in detail and the diameter of steady air core was successfully predicted. The effects of

inlet on the erosion rate were investigated with the RNG LES model. The involute inlet

can eliminate the wear hot spot and lower the level of concentrated wear. This is only a

preliminary study of the design and optimization process concerning erosion rate of a

hydrocyclone. In our future study, other parameters and conditions such as inlet flow

rate, particle characteristics etc. which can affect erosion rate will be investigated as all of

the performance parameters should be taken into account for good design and operation

of the hydrocyclone and to increase its service life.

Inlet Pressure

drop (kPa)

Maximum Erosion

rate ( kg/(m2s))

Face average erosion

rate ( kg/(m2s))

Standard tangential inlet 32.8 3.72E-4 1.84E-6

Modified tangential inlet 81.7 7.62E-7 4.72E-8

Circular involute inlet 45.7 4.32E-7 2.91E-8

Elliptical involute inlet 72.3 4.37E-7 3.90E-8

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Acknowledgements

This work was supported by M3TC at NUS, partial support of the National Natural

Science Foundation of China through grant number 10572052, as well as the Foundation

for Study Abroad of Education of Ministry of China is also acknowledged.

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