Parametric CFD studies on hydrocyclone

Powder Technology 230 (2012) 36–47

Contents lists available at SciVerse ScienceDirect

Powder Technology journal homepage: www.elsevier.com/locate/powtec

Parametric CFD studies on hydrocyclone Y. Rama Murthy a,⁎, K. Udaya Bhaskar b a b

Research Development and Technology, Tata Steel Ltd, Jamshedpur, 831007, India ArcelorMittal Global R & D, 3001 E. Columbus Drive, East Chicago, IN 46312, USA

a r t i c l e

i n f o

Article history: Received 17 December 2011 Received in revised form 23 May 2012 Accepted 23 June 2012 Available online 9 July 2012 Keywords: Hydrocyclone CFD simulation Flyash processing

a b s t r a c t This research article encompasses development of hydrocyclone simulation methodology through validation with suitably designed experiments at a range of process conditions and further understanding on the parametric design and operating conditions. The salient features of the methodology included Eulerian primary phase flow field generation through steady state simulation using RSM turbulence modeling, and evaluation of particle distribution behavior through discrete phase modeling using particle injection technique. The results are validated with water throughput, split and cyclone cut size while classifying flyash. The results have indicated a reasonable matching between the simulated and the experimental values. The studies revealed that the cyclone cut size increases with an increase in vortex finder diameter, a decrease in the spigot diameter, decrease in the inlet velocity of the fluid, and decrease in the viscosity of the fluid. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Hydrocyclone is one of the most versatile processing units being in use applied in mineral processing industry. The cyclone as a process equipment was introduced to the industry in 1891 and the first patent on its use was granted in the United States. Driessen first reported the application of hydrocyclone to mineral industry in the year 1939. There is hardly any modern mineral processing industry without hydrocyclone as one of the unit operation. It has also wide application for classification of solids in various industries pertaining to chemical engineering, petroleum, paper and pulp industries because of its good separation efficiency, ease in operation, high throughput, less maintenance, less floor space requirement etc. A typical hydrocyclone consists of — a cylindrical section (closed with a plate from the top through which passes an axially mounted overflow pipe); a conical section — open at its apex joined to a cylindrical section; a tangential feed inlet. Fig. 1 shows the schematic of widely used hydrocyclone depicting the inner and outer spiral along with main parts. The driving force for particle separation in a cyclone separator is the strong swirling turbulent flow. The feed slurry (water laden with particles) enters the cyclone separator with a high rotational velocity through a tangential inlet which imparts a swirling motion to the pulp. Different inlet configurations like tangential, involute, scroll, axial etc., exist to provide high rotational velocity. Of these, the tangential and involute types are the most frequently used configurations in mineral industry. This swirl generates a vortex in the cyclone, with a low-pressure zone along the vertical axis. Inside the cyclone, the particles within swirling flow are subjected to two opposing forces — an outward centrifugal ⁎ Corresponding author. Tel.: +91 9204058852. E-mail address: [email protected] (Y.R. Murthy). 0032-5910/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2012.06.048

force and an inwardly acting drag. The centrifugal force developed accelerates the settling rate of the particles in the radial direction thereby separating particles according to size, shape, and specific gravity. Faster settling particles move to the wall of the cyclone, where the velocity is lowest, and migrate to the apex opening. Due to the action of the drag force, the slower-settling particles move towards the zone of low pressure along the axis and are carried upward through the vortex finder to the overflow [1]. The upward rotating flow continues along the cyclone axis forming a double vortex structure while the inner vortex leads the flow to exit through the vortex finder. The vortex finder protrudes within the cyclone body. It serves both in shielding the inner vortex from the high inlet velocity and stabilizing its swirling motion. The heavy solids are separated due to the centrifugal force and descend along the cyclone wall and further report to the underflow in the direction of gravity. An increase in inward migration occurs, closer to the cone apex and the fluid in this migratory stream reverses its vertical direction and flows upwards, to the overflow outlet. The spirals rotate in the same circular direction. Despite its simple operation, the fluid dynamics and flow structures in a cyclone separator are very complex. The hydrocyclone design and process understanding has been mostly heuristic due to the complex physical phenomenon involved in analyzing flow behavior inside the hydrocyclone system. Numerous research works have been reported on the development of empirical models for hydrocyclone process simulation. Among them widely used models include the models developed by Lynch and Rao [1] and Plitt [2]. These models found great use in regular plant controls within a well-defined range of process boundary conditions for which the model suitability is evaluated. However, understanding on the flow physics of the separation system has been a myth for several years mainly due to non-availability of experimental evidences. In this connection, the studies of Kelsall [3] on the axial, radial and tangential velocity profiles are the first of its kind,

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47

37

and geometry evaluated through the experimental and CFD simulation work is presented in Table 1. 2.1. Meshing

Fig. 1. Schematic of hydrocyclone.

The computational domain constituted of 150,000 CFD cells. Fig. 3 represents an overall view of the grid generated and zooms on different inlet and outlets of the cyclone. In order to achieve enhanced capture of the flow features, at the critical regions like near the cyclone walls, around the core, within and near the vortex finder and at the spigot opening, methods like boundary layer mesh adjacent to the outer cyclone wall, block-structured mesh at the core, and increased mesh density near the spigot region are adopted. The rest of the cyclone is meshed using unstructured hexahedral mesh, which is known to be less diffusive compared to other types of meshes like tetrahedral. A boundary layer mesh is generated adjacent to the outer wall of the cyclone. In order to capture the low-pressure central air-core, block-structured mesh is generated in that region. Additional care is taken to generate mesh near the spigot region where maximum aspect ratio is restricted to 10. This is important to capture the back flow through spigot opening. Grid independence study was carried out with five different mesh densities with mesh sizes varying from 75,000 to 200,000 for the same designs. Water distribution studies have indicated that better predictions are obtained at higher mesh densities. The computational domain is divided into 150,000 volumes based on the earlier studies of the authors [12,13] for an optimum balance between accuracy and computational time. 3. Simulation methodology

which have formed the basis for further research on hydrocyclones. Measurements on flow patterns using dyes are reported by Bradley and Pulling [4]. Subsequently, laser-Doppler velocimetry (LDV) technique has been found useful for examining the velocity profiles generated through the numerical techniques (Pericleous and Rhodes [5]; Hsieh and Rajamani [6,7]). Multiphase simulations and validation using the large eddy simulation (LES) turbulence model and gamma ray tomography was reported by Narashima et al. [8]. Initial design-based studies were reported on 2D axis-symmetric simulations of different cyclone dimensions and development of particle classification curves by validating with dilute concentration of solid slurries (Monredon et al. [9]; Rajamani and Milin [10]; Devulapalli and Rajamani [11]). But the research work relevant to the effects of variables or design parameters on the cyclone performance is scanty. Present studies involves methodology development and extensive validation with the experimental data (generated on a 3 in. 20° cone angle cyclone) on water throughput, split and particle cut size (d50) achieved by treating flyash, and performance simulation at different design and operating conditions.

The flow inside a hydrocyclone is characterized by an inherently unsteady, highly anisotropic turbulent field in a confined, strongly swirling flow. Time dependent turbulence approaches such as large eddy simulation (LES) or direct numerical simulation (DNS) should be used for such flows. However, these techniques are computationally intensive and although possible, are not practical for many industrial applications. This renders most of the first order turbulence closures,

2. Geometry and meshing Fig. 2 shows the schematic of hydrocyclone and depict main parts and dimensions used for the present study. The main body of the cyclone consists of a cylindrical portion with 76 mm diameter and 85 mm height. The bottom (smaller) diameter of the frustum is variable in size with openings corresponding to 13 mm, 15 mm and 17 mm with an included angle of 20° suitably maintained by adjusting the height of the conical portion. A cylindrical vortex finder having outer diameter of 37 mm and inner diameter of 19 mm protrudes into the main cylindrical body extending over a height of 43 mm inside and 37 mm above the top closed surface. Vortex finders with different internal diameters of 19 mm, 22 mm and 25 mm are used as one of the design variable. A rectangular feed inlet opening with dimensions 23 mm× 19 mm is connected tangentially to the main cylindrical body at a height of 15 mm below the top surface. Studies were carried out under the above geometries by changing the inlet velocities of water into the cyclone body. Different hydrocyclone design details

Fig. 2. Detailed dimensions of hydrocyclone.

38

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47

Table 1 Design details of 76 mm hydrocyclone. Dimension (mm)

Cy-1

Cy-2

Cy-3

Cy-4

Cy-5

Cy-6

Cy-7

Cy-8

Cy-9

CD CyL VFOD VFID VFL FI (l × w) CA SPD

76 80 37 19 80 (37↑–43↓) 23 × 19 20 13

76 80 37 19 80 (37↑–43↓) 23 × 19 20 13

76 80 37 19 80 (37↑–43↓) 23 × 19 20 13

76 80 37 22 80 (37↑–43↓) 23 × 19 20 15

76 80 37 22 80 (37↑–43↓) 23 × 19 20 15

76 80 37 22 80 (37↑–43↓) 23 × 19 20 15

76 80 37 25 80 (37↑–43↓) 23 × 19 20 17

76 80 37 25 80 (37↑–43↓) 23 × 19 20 17

76 80 37 25 80 (37↑–43↓) 23 × 19 20 17

CD: cyclone diameter; CyL: cylindrical length; VFOD: vortex finder outer diameter; VFID: vortex finder inner diameter; VFL: vortex finder length (↑) above the cylindrical portion (↓) within the cylindrical portion; FI: feed inlet dimensions (length × width); CA: cone angle in degrees; SPD: spigot diameter.

like the popular k − ε model, unusable for reliable prediction of the flow characteristics. Several attempts were made to overcome this limitation. For turbulence calculations k − ε, k − ε RNG, Reynolds stress model (RSM) was independently used to evaluate the comparative simulation results. Turbulence models based on higher-order closure, like the Reynolds stress model (RSM) along with unsteady Reynolds averaged Navier–Stokes (RANS) formulation have shown good prediction capabilities (Slack et al. [14], Wang et al. [15]). Further, the results of previous CFD simulation work carried out by authors on hydrocyclone using RSM has proven better results. Turbulent flow inside a hydrocyclone is anisotropic in nature, hence within the framework of RANS family, Reynolds stress model (RSM) which is reported to predict turbulence behavior inside a cyclone with a better accuracy was chosen. The RSM has been proven to be an appropriate turbulence model for cyclone flow, although it is computationally more expensive. The governing equations for an incompressible fluid can thus be written as: ∂p ∂ ðρui Þ ¼ 0 þ ∂t ∂xi

ð1Þ

" !#  ∂ ∂
∂p ∂ ∂ui ∂uj 2 ∂ui ðρui Þ þ ρui uj ¼ − þ μ þ − δij ∂xj ∂xi 3 ∂xi ∂t ∂xj ∂xi ∂xi  ∂
′ ′ þ −ρu i u j : ∂xj

ð2Þ

Eqs. (1) and (2) are called Reynolds-averaged Navier–Stokes (RANS) equations. They have the same general form as the instantaneous Navier–Stokes equations, with the velocities and other solution variables representing ensemble-averaged (or time-averaged) values. Additional terms represent the effects of turbulence.
 These Reynolds stresses include turbulence closure, Rij ¼ ρu′ i u′ j must be modeled in order to close Eq. (2). In Reynolds averaging, the solution variables in the instantaneous Navier–Stokes equations are decomposed into the mean (ensemble-averaged or time-averaged) and fluctuating components. For the velocity components: ′

i þ u i ui ¼ u

ð3Þ

where ūi and u′i are the mean and fluctuating velocity components (i = 1,2,3). Likewise, for pressure and other scalar quantities:  þφ φ¼φ

′

ð4Þ

where φ denotes a scalar such as pressure, energy, or species concentration. 3.1. Turbulence model RSM The Reynolds stress model involves calculation of the individual Reynolds stresses, using differential transport equations. The individual

Predicted Throughput(kg/s)

0.70

0.60

Feed velocity 1.0 -1.2m/s

Feed velocity >1.2ms

0.50

Feed velocity >1.2m/s

0.40

Feed velocity 1.0 to 1.2m/s Feed velocity <1.0m/s

Feed velocity <1.0m/s 0.30 0.30

0.40

0.50

Ideal match

0.60

Experimental Throughput(kg/s) Fig. 3. Meshed hydrocyclone geometry.

Fig. 4. Comparison of actual and simulated water throughput.

0.70

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47

Reynolds stresses are then used to obtain closure of the Reynoldsaveraged momentum equation (Eq. (2)). The exact form of the Reynolds stress transport equations may be derived by taking moments of the exact momentum equation. This is a process wherein the exact momentum equations are multiplied by a fluctuating property, the product then being Reynolds averaged. Since several of the terms in the exact equation are unknown and modeling assumptions are required in order to close the equations. The Reynolds stress transport equations are presented together with the modeling assumptions required to attain closure. This method of simulation implicitly has generated the low-pressure core around the cyclone axis without any additional definitions for
air core. Transport equations of the Reynolds stresses terms Rij ¼ ρu′ i u′ j , are written as:

∂t

þ C ij ¼ P ij þ Dij −ε ij þ φij þ Gij :

ð5Þ

Where Cij, Pij,Dij, εij, φij, Gij are respectively: the convective transport term, the stress production term, the diffusion term, the dissipation term, the pressure strain term and the buoyancy production term. The RSM model requires the following empirical constants: Cμ = 0.09, Cε1 = 1.44, Cε2 = 1.92, σε = 1.3, σk =1.0. 3.1.1. Discrete phase modeling (DPM) The motion of a particle is described by the stochastic Lagrangian multiphase flow model. Its trajectory is obtained by integrating the force balance on particle. There are many forces that act on a particle in cyclone as centrifugal force, drag force and gravitational force. Thus, the particle motion equation can be written in the following form:

 g x ρp −ρ dup ¼ F D u−up þ þ Fx: dt ρp

ð6Þ

Fx is a source term which expresses the presence of additional acceleration (force/unit particle mass). u — fluid phase velocity; up — particle velocity; ρ — fluid density ; ρp — particle density. FD(u − up) — drag force per unit particle mass and FD is given by FD ¼

18μ C D Re ρp d2p 24

ð7Þ

where,
 Re ¼ ρf uf −up dp =μ f :

field. PRESTO (pressure staggered option), a pressure interpolation scheme which was reported to be useful for predicting highly swirling flow characteristics prevailing inside the cyclone body was adopted [17]. To obtain the pressure field inside the system, SIMPLE (semi-implicit pressure linked equations) algorithm scheme, which uses a combination of continuity and momentum equations to derive an equation for pressure was used. Interpolation of field variables from cell centers to faces of the control volumes was opted with higher-order quadratic upwind interpolation (QUICK) spatial discretization scheme as it was reported to be useful for swirling flows. No slip boundary condition was used for wall boundary, and near-wall treatment was standard wall function. A velocity inlet condition is used to prescribe water inflow through the rectangular cyclone feed inlet. The overflow and underflow outlets were designated as pressure outlets. The primary water phase (density=998.2 kg/m 3 and viscosity = 1.003 ∗ 10−6 kg/m s) enters the cyclone through the feed inlet. Radial pressure distribution from the cyclone axis to the edges is opted at both the pressure outlets. Backflow direction was specified as normal to the boundary zones and backflow turbulence intensity was assigned a value of 10%. The vortex finder outlet diameter of the hydrocyclone was varied at 19 mm, 22 mm and 25 mm. Similarly, the spigot diameter was varied at 13 mm, 15 mm and 17 mm. For each of the above conditions, water flow behavior was simulated at different feed inlet velocities and further particle distribution characteristics were carried out using particle injection from the inlet surface. Inert solid spherical particles of different sizes varying from 1 μm to 100 μm were injected through the feed inlet. The fly ash particles below 100 μm are completely spherical and hence no factors for shape correction were considered. The particles leaving from any of the pressure outlet zones were assigned to escape from the vessel. Before particle tracking, simulation was conducted with single phase (water) to determine the velocity distribution of water inside the cyclone. The outlet stream in which the each particle reported was noted and the separation characteristics of the cyclone were determined. Sample group of 1000 particles of defined sizes within a selected range were injected into the cyclone body through the feed inlet. The density of the material is maintained constant at 2300 kg/m3 which corresponds to the density of flyash. Each time 10 sample runs were carried out and the report of particles into the overflow and underflow outlet streams were averaged. These data were then used to generate the partition curve of the cyclone and to predict the cut size (d50). The model predictions were compared with the experimental results obtained for similar conditions.

ð8Þ

CD, ρf, ρp, μf, dp are the drag coefficient, the density of the fluid, the density of the particle, the molecular viscosity of the fluid and the particle diameter respectively. It was assumed that the trajectories of particles do not influence the primary phase flow behavior. The discrete phase formulation used in fluent contains the assumption that the second phase is sufficiently diluted that particle–particle interactions and the effects of the particle volume fraction on the primary phase are negligible. In slurries with dilute concentrations of solids (particle concentration below 10% by weight) (Stovin and Saul [16]), particle distribution behavior can be simulated using Lagrangian particle tracking approach. Thus in the present study particle tracking is carried out using the above methodology. 3.2. Boundary conditions

100

90

Predicted water split (%)

∂Rij

39

80

70

60 Feed velocity >1.2m/s Feed velocity 1.0 to 1.2m/s

50

Feed velocity <1.0m/s Ideal match

Flow simulation was carried out using a 3-D segregated, steady state, double precision implicit solver. Initially, the properties of the water were used along with the pressure and face mass fluxes for calculating the momentum equations and further update the velocity

40 40

50

60

70

80

90

100

Experimental water split (%) Fig. 5. Relation between the experimental and simulated water split results.

40

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47

a

4. Results and discussions

2.66e+04 2.51e+04 2.56e+04 2.20e+04 2.05e+04 1.90e+04 1.75e+04 1.60e+04 1.45e+04 1.30e+04 1.14e+04 9.92e+03 8.41e+03 6.89e+03 5.38e+03 3.87e+03 2.35e+03 8.36e+02 -6.79e+02 -2.19e+03 -3.71e+03

The results obtained in the present work are discussed in three sections i.e., validation studies, general flow behavior and the parametric studies as follows: 4.1. Validation

4.2. Flow features 4.2.1. Static pressure The simulated static pressure contours in central vertical plane are presented in Fig. 7a. Higher values of static pressures were observed

Simulated cut size (microns)

25

20

15

10

5

5

10

15

20

25

Experimental cut size (microns) Fig. 6. Relation between the experimental and simulated cyclone cut size values.

b

8000 Spigot Interface Votex finder

6000

Static pressure (Pascal)

Validation is brought between the experimental and simulation results for cyclone throughput (water entering the cyclone), water-split into overflow product and with the cyclone classification cut size. The experimental and simulated mass flow rate achieved using different hydrocyclone design and operating conditions is presented in Fig. 4. Here the mass flow rates obtained at different inlet velocities are presented in three groups. The first group comprises the mass flow at velocities corresponding to b 1.0 m/s. The second group represents the mass flow rates at velocities between 1.0 and 1.2 m/s and the third group having velocities >1.2 m/s. It is observed from Fig. 4 that the actual and predicted values of mass flow rates have a close match. The actual and predicted water splits in the outlets for various inlet water velocities is presented in Fig. 5. It is observed that the simulated values are slightly higher than the actual values at all the normal range of splits between 55% and 90%. However, lower predictions are made where splits above 95% (at a combination of smallest spigot opening and maximum vortex finder diameter) are obtained. Higher values of error in the mass splits are observed at lower velocity inlet groups corresponding to wider spigot opening especially when the mass splits are below 55%. The experimental results on the particle classification cut size which is generated through distribution points of different size particles in the feed to report into either of the products is presented against the simulated cut size results (Fig. 6) at different design and operating conditions. It is observed that the data is matching with ideal line of actual and predicted values over the entire range of cut sizes between 8 μm and 20 μm achieved at different process conditions. The maximum error value observed is at an experimental value of 16.5 μm where the simulated value is 20 μm indicating a deviation of 3.5 μm and in terms of percent error is about 21%. Though the error at 8.1 μm cut size is 23%, the absolute deviation is only by 1.9 μm.

4000

2000

0 -0.015

-0.01

-0.005

0

0.005

0.01

0.015

-2000

Radial position in m Fig. 7. (a). Contours of static pressure axial and radial planes. (b). Radial distribution of static pressure values.

at the cyclone walls and at radial distances away from the cyclone axis whereas lower values were observed near the spigot outlet. To analyze the static pressure values generated around the core region, static pressure values were captured at three different heights (Fig. 7b) corresponding to the spigot opening, interface of the vortex finder and upper cylindrical portion and at the vortex finder. The figure indicates that the steep region is the boundary region for the air core and the water where, large amount of shear is expected between air and water due to pressure differential. The total pressure increases in the radial direction from the center to the wall of the cyclone. Flow reversal in a cyclone is due to the low pressure center.

4.2.2. Axial velocity The axial velocity contour obtained on central vertical plane along with positive and negative flow in the vertical plane is presented in Fig. 8a, b and c respectively. It is observed that the axial velocity is positive indicating a vertically upward flow throughout the axial height, for a characteristic radial distance around the cyclone axis. Beyond this radial distance, the axial velocity shows a negative value indicating a downward flow. In between these regions exists the region of zero vertical velocity. In general, concentric cylinders of constant axial velocities can be observed along the radial planes. However considerable anisotropy in the flow behavior can be observed at heights approaching the spigot opening.

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47

(a) Axial velocity contour at central vertical 2.52e+00 2.27e+00 2.03e+00 1.79e+00 1.55e+00 1.31e+00 1.07e+00 8.28e-01 5.87e-01 3.46e-01 1.05e-01 -1.36e-01 -3.78e-01 -6.19e-01 -8.60e-01 -1.10e+00 -1.34e+00 -1.58e+00 -1.82e+00 -2.07e+00 -2.31e+00

(b) Zone of positive axial velocity 2.52e+00 2.39e+00 2.26e+00 2.14e+00 2.01e+00 1.89e+00 1.76e+00 1.64e+00 1.51e+00 1.38e+00 1.26e+00 1.13e+00 1.01e+00 8.80e-01 7.55e-01 6.29e-01 5.03e-01 3.77e-01 2.52e-01 1.26e-01 0.00e+00

41

(c) Zone of negative axial velocity 0.00e+00 -1.15e-01 -2.31e-01 -3.46e-01 -4.61e-01 -5.77e-01 -6.29e-01 -8.01e-01 -9.23e-01 -1.04e+00 -1.15e+00 -1.27e+00 -1.38e+00 -1.50e+00 -1.61e+00 -1.73e+00 -1.85e+00 -1.96e+00 -2.08e+00 -2.19e+00 -2.31e+00

Fig. 8. (a) Axial velocity contours at central vertical plane; (b) zone of positive axial velocity; (c) zone of negative axial velocity.

4.3. Parametric studies The effect of parameters such as vortex finder diameter, spigot diameter, velocity inlet and viscosity on the flow characteristic variables is discussed as follows. 4.3.1. Effect of vortex finder diameter The vortex finder diameter has visible effect on flow characteristics like static pressure, tangential velocity, and axial velocity. 4.3.1.1. On static pressure. The effect of vortex finder diameter on the static pressure along the radial distances, and at different axial heights is presented in Fig. 9. Each set of curves represents effect of vortex finder diameter on static pressure values at different radial positions. For instance, a decrease in the vortex finder diameter from 25 mm to 19 mm, at an axial position of 75 mm below the cylindrical top surface has decreased the maximum value of static pressure from 18.7 kPa to 14.6 kPa at a radial distance of 38 mm from the cyclone axis. It can be observed from the figure that the values of negative static pressure are higher at wider vortex finder diameter. For instance, an increase in the vortex finder diameter from 19 mm to 25 mm, at an axial position of 175 mm below the cylindrical top surface has increased the negative value of static pressure from −0.5 kPa to −4.2 kPa. A negative pressure zone appears in the forced vortex region (central region) due to high swirling velocity. The pressure gradient is largest along the radial direction, while the gradient in axial direction is very limited. 4.3.1.2. On axial velocity. Empirical models based on the double vortex structure postulate radially constant values for the downward flow in the outer vortex and upward flow in the inner vortex. Both these values are zero at the axial position where the vortex ends. In reality, the profiles are not flat but exhibit maxima and minima. Typically the downward flow shows a maximum near the walls, while the upward flow shows either a maximum or a minimum at the symmetry axis. The effect of vortex finder diameter on the axial velocity is presented in Fig. 10. The result is an inverted V, or an inverted W shaped profile for the inner vortex. The V pattern forms an axial velocity maximum at the vortex core of the cyclone while the W pattern forms an axial velocity maximum at the vortex finder radius with a minimum at the vortex core (Harasek et al. [18]). An observation of the data at different axial heights

indicates that the high values of positive vertical velocity in case of smaller vortex finder diameter hydrocyclone is confined to cylindrical portion of the cyclone and to a small height in the conical portion. At wider vortex finder diameter, it can be observed that the vertical velocities in the core region are extended to larger heights in the conical portion. Similarly the magnitude of negative axial velocities indicating a downward vertical flow is high at smallest vortex finder opening. For instance, in the cyclone with 19 mm vortex finder opening at 75 mm axial height the maximum positive axial velocity is 1.05 m/s while at 125 mm it is 0.22 m/s. In case of cyclone with 25 mm diameter vortex finder the maximum positive axial velocity at 75 mm axial height is 0.90 m/s, is more or less similar at 125 mm axial height and 1.20 m/s at 175 mm axial height. The observation indicates that at wider vortex finder diameter increased water splits into overflow products are achieved due to classification at extended heights in the conical portion. 4.3.1.3. On tangential velocity. The tangential velocity component is the dominant component of fluid flow in cyclones which results in centrifugal force for particle separation. Fig. 11 shows tangential velocity profiles at five different radial positions for the cyclone from simulations performed with different vortex finder inner diameters. The figure shows an increase in the vortex finder diameter which decreases the maximum value of tangential velocity at all the axial heights. For instance, an increase in vortex finder diameter from 19 mm, 22 mm and 25 mm has resulted in decrease in maximum value of tangential velocity (corresponding to an axial height of 75 mm from the cyclone top and at a radial distance of 10 mm from the cyclone axis) from 3.55 m/s, 3.35 m/s and 3.25 m/s respectively. The tangential velocity values at 125 mm axial height are 3.53 m/s, 3.48 m/s and 3.22 m/s for vortex finder diameter of 19 m, 22 mm and 25 mm respectively. The observations indicate that at smaller diameter vortex finder, the tangential velocity and hence the centrifugal force generated is higher at the boundary layer of free and forced vortex zones. It diminishes at relatively higher rate compared to a wider opening vortex finder in the free vortex zone. Due to lower values of centrifugal forces generated inside the cyclone at wider vortex finder diameter, while classification with solids, relatively coarser particles which are uninfluenced at lower centrifugal forces cannot penetrate towards higher radial distances to reach the cyclone walls and thus are influenced by the vertical drag to report into the overflow product.

42

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47 25mm 22mm 19mm

20000

Axial heights

15000

25mm

10000 VFD 19mm VFD 22mm VFD 25mm

5000 0 -5000 20000 15000

75mm

10000 5000 0 -5000 20000 15000

125mm

10000 5000 0 -5000 20000

15000 10000

175mm

5000 0 -5000 20000 15000 10000 5000

-0.04

-0.03

-0.02

0 -0.01 0 -5000

225mm 0.01

0.02

0.03

0.04

Radial Position (m) Fig. 10. Effect of vortex finder diameter on axial velocity (m/s). Fig. 9. Effect of vortex finder diameter on static pressure (Pascal).

4.3.2. Effect of spigot diameter 4.3.2.1. On static pressure. The effect of spigot diameter on static pressure at different axial heights is presented in Fig. 12. The observation of change in the value of positive static pressure with spigot opening is found reducing with decreasing axial height. The maximum negative static pressure values observed near the cyclone axis at 17 mm and 13 mm spigot opening are 0.9 kPa and 1.2 kPa respectively. The observations on increase in the positive static pressure on the walls and decrease in the negative static pressure at the cyclone core indicate increased radial pressure differential at constricted spigot opening. 4.3.2.2. On tangential velocity. The effect of spigot diameter on the tangential velocity is presented in Fig. 13. It can be observed from the figure that an increase in the spigot diameter increases the maximum value of tangential velocity in the transition region of free and forced

vortex at all the axial heights. The figure also indicates that in both the free vortex and forced vortex regions, the slope of the data points corresponding to 19 mm diameter vortex finder is higher. This steeper decrease in tangential velocity values cause the relatively coarser particles remain in smaller radial distances from the cyclone axis and hence report to overflow which results in higher cyclone cut size. 4.3.2.3. On axial velocity. The effect of spigot diameter on the axial velocity indicated that an increase in the spigot diameter decreases the positive vertical velocity (upward flow) around the core region and increases the negative vertical velocity (downward flow). The observation which shows the increase in the positive vertical velocity is prominent at the heights corresponding to higher axial positions from the cyclone top. Similarly, the increase in the downward axial velocity corresponds to the axial heights nearing to the spigot position. For instance an increase in the spigot diameter from 13 mm to 17 mm at an axial height of 75 mm has decreased the upward axial velocity from

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47

4.0

VFD 19mm VFD 22mm VFD 25mm

3.0

43

20000

Axial heights

15000

25mm

10000

2.0

SPD 13mm SPD 15mm SPD 17mm

5000

1.0

Axial heights 25mm

0.0 4.0

0 -5000 20000

75mm

15000

3.0

10000 5000

2.0

0

1.0 -5000 20000

75mm

0.0 4.0

125mm

15000 10000

3.0

5000

2.0 0

1.0

-5000 20000

125mm

0.0 4.0

15000

175mm 10000

3.0 5000

2.0

0

1.0

-5000 20000

175mm

0.0 4.0

10000

3.0

225mm

5000 0

2.0

-0.04 -0.03 -0.02 -0.01 0 -5000

1.0

0.01

0.02

0.03

0.04

Radial Position (m)

0.0

-0.04 -0.03 -0.02 -0.01

15000

0

0.01

0.02

0.03

0.04

225mm

Fig. 12. Effect of spigot diameter on static pressure (Pascal).

Radial Position (m) Fig. 11. Effect of vortex finder diameter on tangential velocity (m/s).

cut-size. The studies revealed that with decrease in spigot diameter the cyclone sharpness of separation improves. 4.3.3. Effect of feed velocity inlet

1.03 m/s to 0.55 m/s. Similarly, for an increase in the spigot diameter from13mm to 17 mm, at 225 mm axial position, the negative axial velocity is 0.94 m/s to 0.97 m/s. The observations indicate increased water split to overflow and hence results in higher cut size. From the predictions, it is observed that when the spigot diameter increases, the efficiency drops for both coarse and fine particles. The drop in efficiency for fine particles is due to the increase in the water underflow split ratio. When spigot diameter is enlarged a greater portion of the inflow fluid reports to the underflow, which carries with it more particles in each class. In addition to the fluid split effect, the crowding effect plays a role in the classification of coarse particles. Crowding effect refers to the crowding of particles between the air core and conical wall near the spigot region. The bulk volume of solids in the spigot region becomes greater than the solids capacity of the spigot opening, hence a portion of the coarse particle is carried upward to the overflow. The saturation in the spigot region is responsible for the decrease in the efficiency and corresponding decrease in the

4.3.3.1. On static pressure. The effect of feed inlet velocity (at vortex finder diameter 22 mm and 13 mm spigot opening) on the radial distribution of static pressure at different axial heights is presented in Fig. 14. It is observed that for any given radial distance, the positive value of static pressure increases for an increase in feed inlet velocity. It can also be observed that negative values of static pressure around the core region are decreased with increase in the feed inlet velocity. The observations indicate an increase in differential pressure at increased feed inlet velocity, which causes more radial transfer of water to core region and hence higher water mass splits to overflow. 4.3.3.2. On tangential velocity. The effect of feed inlet velocity on the tangential velocity at different radial distances and at different axial heights is presented in Fig. 15. It can be observed from the figure that an increase in the feed inlet velocity increases the values of tangential velocity at both free and forced vortex regions at all the axial heights.

44

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47 SPD 13mm SPD 15mm SPD 17mm

4.0

30000

3.0

20000

2.0

10000

1.0

Axial heights 25mm

0.0 4.0

25mm VI 0.88 m/s VI 1.10 m/s VI 1.39 m/s

0 -10000 30000

3.0

20000 2.0

10000

75mm

1.0

0 0.0 4.0

75mm -10000 30000

3.0

20000 2.0

10000

125mm

1.0

125mm

0.0 4.0

0 -10000 30000

3.0 2.0

20000

1.0

10000

175mm

0.0 4.0

175mm

0 -10000

3.0

30000 2.0

20000 1.0 0.0

-0.04 -0.03 -0.02 -0.01

0

0.01

0.02

0.03

0.04

225mm

Radial Position (m) Fig. 13. Effect of spigot diameter on tangential velocity (m/s).

10000

225mm

0

-0.04 -0.03 -0.02 -0.01 0 -10000

0.01

0.02

0.03

0.04

Radial distance (m) Fig. 14. Effect of velocity inlet on pressure (Pascal).

Within the forced vortex region the slope of increase in data points with increase in the radial distance is high at higher velocity inlet. Similarly, the slope of the data points in the free vortex region decreases with decrease in the feed inlet velocity. For instance, an increase in feed inlet velocity from 0.91 m/s to 1.52 m/s has increased the maximum value of tangential velocity (corresponding to at an axial height of 75 mm from the cyclone top) from 2.57 m/s to 4.28 m/s. The observations indicate that at higher feed inlet velocity, the tangential velocity and hence the centrifugal force is higher at all the radial distances. An increase in the centrifugal field centrifuges relatively finer particles to reach the cyclone wall and further into the underflow product and hence reduces the cut size of the cyclone.

4.3.4. Effect of fluid viscosity In process industries where hydrocyclones are used for classification, the concentration of fine particles in slurries varies between dilute concentrations like 2% by weight to high as 40%. The concentration of solid particles especially in the sub micron size range, increase the slurry viscosity values to a considerable extent. It is reported that a clay concentration around 2% by weight has increased the viscosity to 4.5 cP and at a fine size flyash solid concentration of 40% the viscosity of the slurry is reported to be 47.7 cP. Thus, in order to understand the effect of viscosity, the primary phase viscosity has been studied at three different levels i.e., 0.001 cP, 0.005 cP and 0.01 cP. The results obtained on the flow characteristics are discussed as follows.

4.3.3.3. On axial velocity. The effect of spigot diameter on the axial velocity indicated that an increase in the velocity inlet has in general, increased the positive (upward flow through the vortex finder) and negative (downward flow through the spigot outlet) axial velocities. The observation of increase in the positive axial velocity is prominent at the heights corresponding to cylindrical region.

4.3.4.1. On static pressure. The effect of fluid viscosity on the radial distribution of static pressure at different axial heights is presented in Fig. 16. The figure indicates that fluid viscosity has a major influence on the static pressure distribution. It can be observed from the figure that for an increase in liquid viscosity the positive values of static pressure decrease. It can also be observed that for an increase in the

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47

6.0

30000

VI 0.88 m/s VI 1.10 m/s VI 1.39 m/s

5.0

45

25000 20000

4.0

Axial heights

15000

3.0

25mm

10000

2.0

5000

1.0

0

25mm

0.0 6.0

Viscosity-0.01 Viscosity-0.005 Viscosity-0.001

-5000 30000 25000

5.0

20000

4.0

15000

3.0

10000

75mm

5000

2.0

0

1.0

75mm

0.0 6.0

-5000 30000 25000 20000

5.0

15000

4.0

10000

3.0

125mm

5000

2.0

0

1.0

-5000 30000

125mm

0.0 6.0

25000 20000

5.0

15000

4.0

10000

3.0

5000

2.0

0

1.0

-5000 30000

175mm

0.0 6.0

25000 20000

5.0

15000

4.0

10000

3.0

5000

2.0

0 -0.04 -0.03 -0.02 -0.01 -5000 0

1.0 0.0 -0.04 -0.03 -0.02 -0.01 0

175mm

225mm 0.01

0.02

0.03

0.04

Radial Position (m)

225mm

0.01

0.02

0.03

0.04

Radial position (m) Fig. 16. Effect of viscosity on static pressure (Pascal).

Fig. 15. Effect of velocity inlet on tangential velocity (m/s).

viscosity from 0.001 cP to 0.005 cP, the decrease in the static pressure is high compared to the decrease from 0.005 to 0.01 cP. For instance, an increase in the fluid viscosity from 0.001 to 0.01 cP, at an axial position of 75 mm below the cylindrical top surface, has decreased the maximum value of static pressure from 29.1 kPa to 11.0 kPa. Further, in the core region around the cyclone axis, the negative values of static pressure decrease marginal with increase in the fluid viscosity. The observations indicate a decrease in differential pressure at increased fluid viscosity which causes reduced radial water flows to the core region and hence lower mass splits to overflow. 4.3.4.2. On tangential velocity. The effect of viscosity on the tangential velocity at different radial distances and at different axial heights is

presented in Fig. 17. It can be observed from the figure that an increase in the viscosity decreases the values of tangential velocity at both free and forced vortex regions at all the axial heights. Within the forced vortex region the slope of increase in tangential velocity data points with increase in the radial distance is higher at lower liquid viscosity indicating rapid increase in the tangential velocity values. For instance at a viscosity of 0.001 cP, the increase in the tangential velocity from the cyclone axis to a radial distance of 10 mm is 0.08 m/s to 4.6 m/s. Likewise, at 0.01 cP liquid viscosity, the increase in the tangential velocity from the cyclone axis to a radial distance of 10 mm is 0.02 m/s to 2.82 m/s. Similar observations can be made at all the axial heights. The observation made could be explained due to the dominating effect of viscosity of the fluid on the shear between individual layers that there is a gradual tangential velocity distribution at higher viscosity

46

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47

5.0

Viscosity-0.01 Viscosity-0.005 Viscosity-0.001

4.0 3.0 2.0 1.0

Axial heights 25mm

0.0 5.0 4.0 3.0 2.0

5. Conclusions

1.0

75mm

0.0 5.0 4.0 3.0 2.0 1.0

125mm

0.0 5.0 4.0 3.0 2.0 1.0

175mm

0.0 5.0 4.0 3.0 2.0 1.0

225mm

0.0

-0.04 -0.03 -0.02 -0.01

flow caused due to the axial pressure differential. Similarly, the viscous shear forces are dominant at the lower conical portion of the cyclone body where relatively higher vertical velocities are observed with higher viscosity fluid. Thus, the conditions like low viscosity in the cylindrical and upper conical region and high viscosity in the lower conical section helps in improved separation efficiency in the actual practice during solids classification. This condition can be achieved by having high solid concentration gradient between these regions. In general, higher vortex finder diameter and smaller spigot diameter generates overflow and underflow products with high difference in the solids concentration when classifying fine particles. This results in viscosity differential from top to bottom of the cyclone body which is a condition for higher cut size and sharper classification.

0

0.01

0.02

0.03

0.04

Radial position (m) Fig. 17. Effect of viscosity on tangential velocity (m/s).

compared to lower viscosity level. Similarly, due to lesser frictional forces between individual layers at lower viscosity, the tangential velocity values achieved are higher at all the radial distances. A higher tangential velocity values observed at lower viscosity result in higher centrifugal forces on particles to report towards the cyclone walls and reduce the particle size reporting to overflow which in turn reduce the cyclone cut size. 4.3.4.3. On axial velocity. Increase in the viscosity decreases the maximum value of positive vertical velocity in the cylindrical and upper conical portions of the cyclone body as observed at heights 75 mm (1.43 m/ s) and 125 mm(0.99 m/s). However, at the heights corresponding to 175 mm (1.40 m/s) and 225 mm (1.10 m/s) it can be observed that the maximum value of positive axial velocity is observed at high viscosity conditions. High values of positive vertical velocity in the upper cyclone body at lower fluid viscosity could be explained due to lower values of friction between individual water layers which are influenced by vertical

A CFD simulation methodology for hydrocyclone process characteristics has been developed. Validation of the simulated results with the experimental results indicated a good match over a range of cyclone water throughput, water split ranging between 55% and 90% and cut sizes between 8 μm and 20 μm during flyash classification. The methodology included primary water phase simulation in an Euler approach using RSM turbulence modeling for turbulence followed by Lagrangian particle tracking approach using discrete phase tracking of solid particles. An increase in the vortex finder diameter decreases the static pressure differential within the cyclone body, reduces the value of maximum tangential velocity at the interface of forced and free vortex regions and increases the positive axial velocity in the cylindrical portion. Under these conditions higher cyclone cut sizes are achieved. An increase in the spigot diameter, though to a lesser extent, decreases the static pressure differential inside the cyclone, decreases the maximum tangential velocities and hence reduces the cyclone cut size. An increase in the velocity of the fluid at the feed inlet has increased to a major extent the radial pressure differential, tangential and axial velocities. The increase in radial pressure differential results in higher water split to overflow and increased tangential velocity results in decrease in the cyclone cut size. An increase in the viscosity of the fluid has significantly reduced the differential pressure and tangential velocities. Higher axial velocities are observed at cylindrical and upper conical regions at lower viscosity and in the lower conical regions, higher axial velocities are observed at higher viscosity. An increase in feed flow rate will improve efficiency by increasing the centrifugal force on particles, and d50 is decreasing. It has been observed that when the spigot diameter increased, the efficiency drops for both coarse and fine particles. Acknowledgments The authors would like to thank Tata Steel Management and Director, and Advanced Materials and Processes Research Institute (AMPRI), CSIR, Bhopal for their support and permission to publish this research work. References [1] B.A. Wills, T. Napier-Munn, Mineral processing technology, An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery, Seventh ed. Elsevier Science & Technology Books, October 2006. Chapter 9—Classification. [2] A.J. Lynch, T.C. Rao, Modelling and scale up of hydrocyclone classifiers, In: 11th International Mineral Processing Congress, Cagliari, 1975, pp. 245–269. [3] L.R. Plitt, A mathematical model of hydrocyclone classifier, CIM Bulletin (1976) 114; D.F. Kelsall, A study of the motion of solid particles in a hydraulic cyclone, Transactions of the Institute of Chemical Engineers 30 (1952) 87–108. [4] D. Bradley, D.J. Pulling, Flow patterns in the hydraulic cyclone and their interpretation in terms of performance, Transactions of the Institute of Chemical Engineers 37 (1959) 34–45. [5] K.A. Pericleous, N. Rhodes, The hydrocyclone classifier—a numerical approach, International Journal of Mineral Processing 17 (1–2) (1986) 23–43. [6] K.T. Hsieh, R.K. Rajamani, Phenomenological model of the hydrocyclone: model development and verification for single-phase flow, International Journal of Mineral Processing 22 (1–4) (1988) 223–237.

Y.R. Murthy, K.U. Bhaskar / Powder Technology 230 (2012) 36–47 [7] K.T. Hsieh, R.K. Rajamani, A mathematical model of the hydrocyclone based on physics of fluid flow, AICHE Journal 37 (1991) 735–746. [8] M. Narasimha, M.S. Brennan, P.S. Holtham, T.J. Napier-Munn, A comprehensive CFD model of dense medium cyclone performance, Minerals Engineering 20 (2007) 414–426. [9] T.C. Monredon, K.T. Hsieh, R.K. Rajamani, Fluid flow model of the hydrocyclone: an investigation of device dimensions, International Journal of Mineral Processing 35 (1–2) (1992) 65–83. [10] R.K. Rajamani, L. Milin, Fluid flow model of the hydrocyclone for concentrated slurry classification, In: Hydrocyclones: Analysis and Application: 4th Intentional Conference, 12, 1992, pp. 95–108. [11] B. Devulapalli, R.K. Rajamani, A comprehensive CFD model for particle‐size classification in industrial cyclones, In: Hydrocyclones '96, Mechanical Engineering Publications, Ltd., London, U.K., 1996, pp. 83–104. [12] K. Udaya Bhaskar, Y. Rama Murthy, M. Ravi Raju, Sumit Tiwari, J.K. Srivastava, N. Ramakrishnan, CFD simulation and experimental validation studies on hydrocyclone, Minerals Engineering 20 (2007) 60–71.

47

[13] K. Udaya Bhaskar, Y. Rama Murthy, N. Ramakrishnan, J.K. Srivastava, Supriya Sarkar, Vimal Kumar, CFD validation for flyash particle classification in hydrocyclones, Minerals Engineering 20 (2007) 290–302. [14] M.D. Slack, S. Del Porte, M.S. Engelman, Designing automated computational fluid dynamics modeling tools for hydrocyclone design, Minerals Engineering 17 (2003) 705–711. [15] B. Wang, K.W. Chu, A.B. Yu, A. Vince, G.D. Barnett, P.J. Barnett, Computational study of the multiphase flow and performance of dense medium cyclones: effect of body dimensions, Minerals Engineering 24 (2011) 19–34. [16] V.R. Stovin, A.J. Saul, A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction, Water Science and Technology 37 (1) (1998) 285–293. [17] Fluent 6.2, “documentation”, User's Guide Fluent Inc., 2006. [18] M. Harasek, A. Horvath, C. Jordan, Influence of vortex finder diameter on axial gas flow in simple cyclone, Chemical Product and Process Modeling 3 (1) (2008) Article 5.