CFD model of a Hydrocyclone

Transcription

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 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. * mpev6@nus.edu.sg, Tel

2 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. 2

3 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 semiempirical 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 3

4 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 4

5 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 5

6 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] R erosion N ( ) m ( ) ( ) b v pc d p f α v = & (1) A p= 1 where C( d p ) 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 piecelinear profile [20-21] 2 o f ( α) = sin(2 α) 3sin ( α) for α (2a) 2 o f ( α) = cos ( α) / 3 for α > (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 6

7 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 ). 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/m 3 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. 7

8 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. 8

9 Axial Velocity (m/s) (a) Experiment RNG k-ε QPS RSM SLM LES RNG LES Radius (m) Tangential Velocity (m/s) Experiment RNG k-ε QPS RSM SLM LES RNG LES (b) Radius (m) Axial Velocity (m/s) (c) Experiment RNG k-ε QPS RSM SLM LES RNG LES Radius (m) Tangential Velocity (m/s) Experiment RNG k-ε QPS RSM SLM LES RNG LES (d) Radius (m) Axial Velocity (m/s) (e) Experiment RNG k-ε QPS RSM SLM LES RNG LES Radius (m) Tangential Velocity (m/s) Experiment RNG k-ε QPS RSM SLM LES RNG LES Radius (m) (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. 9

10 Table 1. General mass balance for four different turbulent models Experiment RNG QPS SLM RNG k-ε RSM LES LES Feed flow rate (kg/s) Overflow flow rate (kg/s) Underflow flow rate (kg/s) Split ratio (%) Pressure drop (kpa) Air core diameter (mm) 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 10

11 integral erosion rates are 3.72E-4 and 1.87E-6 kg/(m 2 s), 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/(m 2 s), 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/(m 2 s) and the average value is 2.91E-8 kg/(m 2 s) while for the elliptical involute inlet, the maximum and integral erosion rates are 4.37E-7 and 3.90E-8 kg/(m 2 s), 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. 11

12 Table 2. Computed Erosion rate for four inlet duct designs Inlet Pressure Maximum Erosion Face average erosion drop (kpa) rate ( kg/(m 2 s)) rate ( kg/(m 2 s)) Standard tangential inlet E E-6 Modified tangential inlet E E-8 Circular involute inlet E E-8 Elliptical involute inlet E E-8 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. 12

13 Acknowledgements This work was supported by M3TC at NUS, partial support of the National Natural Science Foundation of China through grant number , as well as the Foundation for Study Abroad of Education of Ministry of China is also acknowledged. Reference [1] Svarovsky, L. Hydrocyclones; Holt: Rinehart and Winston, [2] Dai, G.Q.; Chen, W.M.; Li, J.M.; Chu, L.Y. Experimental study of solid-liquid twophase flow in a hydrocyclone. Chemical Engineering Journal 1999, 74, [3] Boysan, F.; Ayers, W.H.; Swithenbank, J. Fundamental mathematical-modelling approach to cyclone design. Chemical Engineering Research and Design 1982, 60, [4] Fraser, S.M.; Rasek, A.M.; Abdel; Abdullah, M.Z. Computational and experimental investigations in a cyclone dust separator. Journal of Process Mechanical Engineering 1997, 211, [5] He, P.; Salcudean, M.; Gartshore, I.S. A numerical simulation of hydrocyclones. Chemical Engineering Research and Design 1999, 77, [6] Ma, L.; Ingham, D.B.; Wen, X. Numerical modelling of the fluid and particle penetration through small sampling cyclones. Journal of Aerosol Science 2000, 31, [7] Cullivan, J.C.; Williams, R.A.; Cross, C.R. Understanding the hydrocyclone separator through computational fluid dynamics. Chemical Engineering Research and Design 2003, 81, [8] Schuetz, S.; Mayer, G.; Bierdel, M.; Piesche, M. Investigations on the flow and separation behaviour of hydrocyclones using computational fluid dynamics. International Journal of Mineral Processing 2004, 73, [9] Cullivan, J.C.; Williams, R.A.; Dyakowski, T.; Cross, C.R. New understanding of a hydrocyclone flow field and separation mechanism from computational fluid dynamics. Minerals Engineering 2004, 17, [10] Nowakowski, A.F.; Cullivan, J.C.; Williams, R.A.; Dyakowski, T. Application of CFD to modeling of the flow in hydrocyclones. Is this a realizable option or still a research challenge? Minerals Engineering 2004, 17, [11] Narasimha, M.; Sripriya, R.; Banerjee, P.K. CFD modelling of hydrocyclone-- prediction of cut-size. International Journal of Mineral Processing 2005, 71, [12] Delgadillo, J.A.; Rajamani, R.K. A comparative study of three turbulence-closure models for the hydrocyclone problem. International Journal of Mineral Processing 2005, 77,

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