A three-dimensional simulation of a hydrocyclone for the sludge separation in water purifying plants and comparison with experimental data

doi:10.1016/j.mineng.2003.12.010

Minerals Engineering

Volume 17, Issue 5, May 2004, Pages 637-641

https://doi.org/10.1016/j.mineng.2003.12.010 Get rights and content

Abstract

A three-dimensional simulation was performed to predict the flow field and the separation efficiency for particles in a hydrocyclone to be used for the sludge separation in water purifying plants. The Reynolds averaged Navier–Stokes and Reynolds averaged continuity equations employing renormalization group k–ε model were solved to calculate the turbulent flow field in a hydrocyclone. The particle trajectories were computed by integrating the force balance equations on particles based on the predicted flow field. The separation efficiency defined as the fraction of particles recovered to underflow was obtained by using the calculated particle trajectories. The separation efficiency of a hydrocyclone for the sludge separation in water purifying plants was measured experimentally as a function of particle size. Simulation results agreed favorably with experimental data.

Introduction

Hydrocyclone is a device which is used for the separation of materials contained in the liquid fed to it. These materials are normally in the form of solid particles, but they may also be the gas bubbles, oil, or others. The suspended particles are separated from the liquid due to the centrifugal force induced inside the hydrocyclone. Unlike centrifuges that use the same separation principle, hydrocyclones have no moving parts and the necessary vortex motion is performed by the liquid itself. Hydrocyclone geometry and operating parameters can be calculated based on the empirical or semi-empirical equations as reviewed by Svarovsky (1984) and Chen et al. (2000). These equations can be used to predict the performance of hydrocyclones and make the proper selections. These equations may often have their limitations due to the specific system on which the correlation development was based.

Therefore, it is important to understand the fluid flow and its effect on particle separation in order to improve the performance of hydrocyclone. With the advance in computational fluid dynamics, many numerical works on the flow patterns inside hydrocyclones emerged (Hsieh and Rajamani, 1991; Monrendon et al., 1992; Dyakowski and Williams, 1993; Dyakowski et al., 1994; Malhotra et al., 1994; Dyakowski and Williams, 1996). Although previous authors assumed that the flow was axisymmetric and the relevant two-dimensional equations were solved, the inlet conditions are clearly not axisymmetric for commercial hydrocyclones. Three-dimensional computational works to simulate the flows in hydrocyclones were reported in recent years (He et al., 1999; Dai et al., 1999; Nowakowski et al., 2000; Petty and Parks, 2001; Statie et al., 2001).

It is the purpose of the present work to study the feasibility of hydrocyclone process for the thickening of sludge in water purifying plants, since the classical process adopted for sludge thickening in water purifying plants may require more space and longer processing time to produce high sludge concentration than hydrocyclone process. In order to attain the purpose, a three-dimensional simulation was performed to predict the flow field and the separation efficiency for particles in a hydrocyclone based on Reynolds averaged Navier–Stokes and Reynolds averaged continuity equations employing renormalization group k–ε model. To test the validity of the simulation, the calculated separation efficiency of a hydrocyclone as a function of particle size was compared with the experimentally measured data.

Section snippets

Mathematical model

To model a highly turbulent fluid flow in a hydrocyclone, Reynolds averaged continuity and Reynolds averaged Navier–Stokes equations were solved. They can be written in Cartesian component form as follows $∂ u_{i} ∂ x_{i} =0$ $ρ ∂ u_{i} ∂ t +u_{j} ∂ u_{i} ∂ x_{j} =− ∂ P ∂ x_{i} + ∂ ∂ x_{j} μ ∂ u_{i} ∂ x_{j} + ∂ u_{j} ∂ x_{i} −ρ u^{′}_{i} u^{′}_{j} +ρg_{i}$ where u_i is the fluid velocity component, x_i is the Cartesian coordinate component, ρ is the fluid density, t is the time, P is the pressure, μ is the fluid viscosity, and g_i is the component of gravitational acceleration vector. The

Experimental

The experiment was conducted in a recirculation system, of which the schematic diagram is shown in Fig. 1. The liquid phase was water. Solid particles were taken out of the sludge from the field site of Seong–Hwan water purifying plant. The sludge was composed of various minerals such as quartz, muscovite, kaolinite, and albite. The average density of the solid particles was 2.1 g/cm³ and the particle size was distributed broadly from sub-micron to 100 μm. The solid concentration of feed was

Results and discussion

The flow field in a hydrocyclone was obtained by using a commercial computational fluid dynamics code FLUENT 6.0, which employs the finite volume method (FLUENT, 1998). The finite volume mesh used for the calculation is shown in Fig. 3. A total of 47,488 cells having 51,152 nodes were used for the mesh. Calculations were performed on Pentium IV 1.6A PC. The computation time required for a converged solution was 1.5 h. The calculated vector plot of the axial and radial components of the velocity

Conclusions

A three-dimensional simulation was performed to study the flow field in a hydrocyclone to be used for the sludge separation in water purifying plants. The particle trajectories were calculated to predict the separation efficiency of the hydrocyclone. In addition, the experiments were carried out to measure the separation efficiency as a function of particle size for the sludge taken from the field site of a water purifying plant. The calculated separation efficiency agreed favorably with the

Acknowledgements

This work was supported by the ministry of construction and transportation of Republic of Korea under the industry-university cooperative research program. One of the authors (C. B. Shin) is grateful to the Korea Science and Engineering Foundation (KOSEF R01-2003-000-10103-0) for financial support.

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A three-dimensional simulation of a hydrocyclone for the sludge separation in water purifying plants and comparison with experimental data

Abstract

Introduction

Section snippets

Mathematical model

Experimental

Results and discussion

Conclusions

Acknowledgements

Chemical Engineering Journal

Chemical Engineering Journal

Chemical Engineering Science

Powder Technology

Transactions of The Institution of Chemical Engineers

Chemical Engineering Journal

Filtration & Separation

Filtration & Separation