Document Type : Full Lenght Research Article
Authors
Faculty of Mechanical Engineering, Semnan University, Semnan, Iran
Abstract
Keywords
Main Subjects
1. Introduction
Cyclones are devices used for the separation of droplets or particles from gas. Twophase flow is directed toward a cyclone, where particles are collected at its bottom as gas exits from its upper outlet [1]. This separation happens because of centrifugal and gravitational acceleration forces [2]. Nowadays, these industrial devices are extensively used in food and petroleum industries. The use of cyclones rapidly increased because of their simplicity, low operational costs, and ease of installation. In the past, gravitational separators were utilized to separate oil or water droplets and particles from gas. The problem with these separators is that they involve high industrial costs; by contrast, cyclones improve separation at reduced expenses [1].
In a Stairmand cyclone, two vortex flows are generated. The outer vortex is a descending vortex that tends toward the cyclone wall and assumes a conical shape, whereas the inner vortex is an ascending vortex that exits the cyclone through the device’s vortex finder. These vortexes, which depend on geometrical parameters, affect cyclone efficiency. Cyclone efficiency is defined as the ratio of the outlet mass to the inlet mass of particles. A deep understanding of flow behavior and the effects of geometrical parameters is needed to accurately estimate cyclone performance [2]. Many researchers have predicted the efficiency of cyclones using different mathematical models and then compared the findings to experimental results [1, 2]. Several researchers, however, neglected surface friction in their analysis of cyclone hydrodynamics [3–5]. Surface friction is due to surface roughness, which can originate from the erosion, collision, and rebounding of particles above the surface of a cyclone. Surface roughness can therefore remarkably influence cyclone performance. This issue was first presented by Barth [6], who calculated the tangential velocity of the gas phase inside vortex flow. He computed pressure drop and cyclone efficiency via the tangential velocity of a Rankine vortex flow. Barth’s model was extended by Muschelknautz and Krambrock [7] by modifying the friction coefficient and probing into the effects of friction increase on a cyclone wall. The authors also calculated pressure drop by using the friction coefficient and tangential velocity formula. Their model more accurately predicts cyclone efficiency than does Barth’s model.Meissner and Loffler [8] derived an empirical expression of tangential velocity, with consideration for wall friction. The model established by the authors includes two additional friction factors. Karagoz and Avci [9] also proposed a model for predicting pressure drop and cyclone efficiency. In the model, the wall friction coefficient is a function of Reynolds number and surface roughness.
Accurate measurement instruments and modern experimental techniques are necessary to explore complicated flows. Recent advances in computational fluid dynamics (CFD) have generated impressive alternatives to current analytical models and reliable tools for preventing expensive and timeconsuming experiments. Numerical techniques such as CFD are widely used to approximate the efficiency and pressure drop in cyclones and the effects of geometrical factors on cyclone performance [10, 11]. Kaya et al. [12] used CFD to study the flow field and efficiency of cyclones with one inlet and two inlet channels. Their results satisfactorily corresponded with experimental data. Wang et al. [13] investigated the effects of particles size and gas velocity on the internal flow field and efficiency of a Lapple cyclone and discovered that cyclone performance is improved by increasing particle size and volumetric flow rate. A comparative study of numerical results and experimental data in literature was conducted by Shi and Bayless [14]. They used three different boundary conditions of bottom trap, cone and bottom trap, and tangential liftoff for calculating cyclone efficiency. The third boundary condition shows more accurate predictions, however, it is more complex and needs more care. Raoufi et al. [15] and Kepa [16] investigated the gas flow field inside a cyclone separator at different vortex finder geometries. Their results revealed that different geometries account for significant effects on the performance of gasparticle cyclones. Four vortex finders with different cylindrical shapes and six vortex finders of various conical shapes were used by Raoufi et al. [15]. They found that the shape of a vortex finder exerts a major effect on the flow pattern and separation efficiency of a cyclone. Elsayed and Lacor [17] numerically studied the effects of inlet channel dimensions on the performance of five different cyclones. They concluded that maximum tangential velocity and pressure drop decrease with increasing inlet dimensions. Increasing inlet dimensions also reduces cutoff size, thereby augmenting cyclone efficiency. Oneinlet channel and twoinlet channel configurations of a Stairmand cyclone were explored by Zhao et al. [18], who demonstrated that the installation of two inlet channels in a cyclone generates a more symmetrical flow pattern and improves efficiency to levels higher than that exhibited by a cyclone with a singleinlet channel. Chuah et al. [19] and Xiang et al. [20] analyzed the effects of changes in the conical dimensions of an aerocyclone. They showed that a decrease in cone tip diameter increases the maximum tangential and axial velocities and pressure drop in the cyclone. Kaya and Karagoz [21] and Qian et al. [22] delved into the effects of a prolonged vertical tube on the particle collection of a cyclone, and Yoshida et al. [23] examined various shapes of cone apices located at the entrance of a dustbin. The researchers determined that low apex cone angles increase the efficiency of a cyclone. They also mounted an apex cone at the bottom of the conical collector and found improvements in cyclone performance at low tangential velocities.
The current research was a numerical study intended to evaluate the effects of inlet velocity and particle diameter on the efficiency levels and flow patterns of singlecone and dualcone Stairmand cyclones used for the separation of calcium carbonate particles. Axial and tangential velocity distributions in nine distinct sections of the cyclones were investigated nondimensionally. A Reynolds stress model was employed to simulate turbulent flow, and the Eulerian–Lagrangian statistical approach was used to track particles and predict cyclone performance.
2. Conceptual model
A Stairmand cyclone consists of four parts, namely, an inlet channel, a central cylinder, a vortex finder, and a conical section (Figure 1). The dimensions of the cyclone are listed in Table 1. As previously stated, singlecone and dualcone configurations were simulated. A mixture of fluid and suspended calcium carbonate particles (Table 2) was blown tangentially through the inlet channel toward the cyclones.
Tangential velocity declines as flow moves downward along the central cylinder until the particles accelerate in the conical section, which prevents the decreasing trend of tangential velocity. Because of the formation of a second vortex in the conical section, which plays an important role in the separation of particles, tangential velocity can cause lowweight particles to rebound toward flow in the cyclone core. The secondary vortex, created mostly in the conical section, guides particles to the vortex finder tube.
Fig. 1. Schematic of the two models. 
Table 1. Geometrical properties of the investigated cyclones.
Parameters 
Dimensional values (m) 
Nondimensional values 
Table 2. Physical properties of air and calcium carbonate particles [24, 25].
Materials 
Density [kgm^{–3}] 
Dynamic viscosity [Pa.s] 
Air 

Calcium carbonate 
 
3. Governing equations
3.1 Continuum phase equations
The maximum fluid velocity in the cyclone inlet is 19.5 ms^{–1}.Thus, the Mach number is equal to 0.06, and flow can be considered incompressible. The continuity equation and Reynoldsaveraged Navier–Stokes equation for incompressible, unsteady, and isothermal flow are as follows [25–27]:
(1) 

(2) 
where , , , and ( ) are the density, velocity, kinematic viscosity, and Reynolds stress tensor, respectively.
3.2 Turbulence modeling
A Reynolds Stress Model (RSM) was employed because of the high curvature streamline of the swirling flow inside the cyclones. The RSM equation can be written as [27]
(3) 
The first term at the righthand side of the equations above refers to turbulent diffusion, which can be expressed as follows [27]:
(4) 
The second term indicates stress production [27]:
(5) 
The term pertains to pressure strain [27]:
(6) 
The term shows dissipation [27]:
(7) 
3.3 Discrete phase
The governing equation for particle motion is expressed as Eq. (8). In this study, the interaction between particles was disregarded because of the dilute flow in the cyclones. Given the absence of diffusion, the motion equation describes each particle’s motion by considering hydrodynamic drag force [28].
(8) 
The drag coefficient is expressed as [21, 25, 29]
(9) 
The equation above is used for spherical particles, for which constants are calculated on the basis of different relations at different ranges of Reynolds numbers [21].
3.4 Boundary conditions
As shown in Figure 1, the computational domain boundaries were divided into four conditions. The first was assigned to the inlet, where air is blown into the cyclone through the inlet channel at a constant velocity of 19.5 ms^{–1}. The second boundary condition was assigned to the cyclone outlet, where flow exits the cyclones through the vortex finders located at the top of the cyclones. To examine cyclone performance, the bottom of the cyclones was regarded as a trap. The noslip boundary condition, forth boundary condition, was assigned to the walls.
4. Solver settings
The simulations described here were run using ANSYS Fluent 16 (Fluent, Inc.). An efficient and robust algorithm was employed to capture steep pressure gradients, strong swirling flow, and high anisotropy. The SIMPLE^{[1]} algorithm was for pressure–velocity coupling. For the discretization of momentum equations, the QUICK^{[2]} scheme was employed. The solver settings for the CFD modeling were set to secondorder upwind scheme both for dissipation rate and for turbulent kinetic energy; also firstorder upwind scheme was used for the Reynolds stress equation. Note that the firstorder scheme was chosen because it enables improved convergence and avoids numerical instabilities. The convergence criteria for all the equations was set to 10^{–4}. A standard wall function was used to model fluid flow in the nearwall region. The aforementioned settings have been widely used by many researchers, who reported very encouraging results [30]. Particles were tracked by setting 900,000 integral steps with a length scale of 0.005 m To take turbulent dispersion and the characteristic lifetime of an eddy into account, the discrete random walk model and a random eddy lifetime model were adopted, respectively [30, 31].
In accordance with the literature, turbulence intensity and turbulence characteristic length were set at 5% and 0.07 times the inlet width, respectively [30, 31]. Normal components of Reynolds stress tensors were defined by , where the kinetic energy was defined as , and the shear stress components were all set to zero [32]. Calcium carbonate was the working powder used in the discrete phase modeling (DPM). Dust loading was considered as powder per unit volume of air, with the mean powder diameter equaling and the geometric standard deviation being 2.08. For an exponential relationship between the particle diameter and the mass fraction of particles with diameters greater than , was assumed in the Rosin–Rammler distribution function [29, 32]:
(10) 
where and n reflect the characteristic diameter and distribution parameter, respectively. Particle sizes were in the range 0.3 to 6.8 µm. Solid particles were injected using the face normal condition, with velocity equaling that of flowing fluid at the cyclone inlet. At the cyclone bottom, DPM settings were defined as a trap. The particles that reach the cyclone walls collide with the walls and rebound. For the low dust loading condition, a reasonable assumption is that the collision of discrete phase particles with cyclone walls is perfectly elastic; hence, the coefficients of restitution in the tangential and wall normal directions were taken as unity [29, 32].
At the core regions of the cyclones, flow is non stationary and swirls over time. This swirling motion continues until it reaches the steady state. This period of time is known as residence time, given as follows [25, 31]:
(11) 
Residence time depends on cyclone dimensions and gas volumetric flow rate. Increasing the volumetric flow rate and decreasing the dimensions of a cyclone decreases and increases resident time, respectively. The time step for the simulations was 0.0001 s [22, 25].
5. Grid independence test and validation
Hexagonal cells produced via Gambit are presented in Figure 2. To evaluate the independence of the numerical solution from grid structure, the number of cells was increased until the difference between the evaluated indicators became negligible. Total pressure drop and static pressure drop were employed to evaluate mesh independence. Details regarding the grid independence test are provided in Table 3, and the results on tangential velocity at different mesh sizes are illustrated in Figure 3.
After the mesh independence test, the problem was validated. The validation of the continuum phase and the tangential velocity profile was compared with the experimental data of Hoekstra [24] (Figure 4).
Fig. 2. Schematic of generated grids.


Table 3. Results of grid independence test on the conventional cyclone configuration. 

Total pressure drop 
Static pressure drop 
Number of cells 

1139.28 
1355.44 

1159.77 
1398.9 

1188.48 
1458.32 

4.1% 
7.05% 
Deviation 

31 
Fig. 3. Results for three mesh sizes. 
The relationship between inlet velocity and pressure drop is depicted in Figure 5, on whose basis the simulation results of the current work and the experimental findings of Hoekstra were analyzed. The results on the dispersed phase were then compared with the experimental data derived by Zhao [26] (Figure 6).
6. Results
6.1. Tangential velocity
One of the main parameters of the cyclone models is tangential velocity, which consists of two regions, namely, the forced and free vortex regions (Figure 7). These regions create a Rankine vortex. All elements of a fluid revolve at a velocity of Ω as rigid bodies in the forced vortex region. Such flow is described in the following equation:
(12) 
For the free vortex region, the following correlation can be used to describe tangential velocity:
Fig. 4. Comparison of (a) tangential velocity and (b) axial velocity profiles in the current numerical simulation and the work of Hoekstra [24] on section Z=0.75 D.
Fig. 5. Comparison of pressure drop in the current numerical simulation and the work of Hoekstra [24]. 



Fig. 6. Comparison of current numerical simulation and the work of Zhao [26] on the dispersed phase. 
(13) 
Regarding the previous studies, the tangential velocity profile examined in the entire Rankine vortex region [3, 4, 6, 12, 22]. The radial distribution of tangential velocity was investigated in nine sections (Table 4) of the cyclone models. Figure 9 indicates that the tangential velocity has a Vshape profile in the singlecone cyclone. It reaches its maximum far from the core region of the cyclone at the vortex finder boundary, after which it decreases as it moves toward the wall because of increased dissipation. Adding another cone to the gasparticle cyclone generates a maximum tangential velocity that is 1.5 times greater than that of a conventional cyclone. The Rankine vortex region is also limited by the smaller separation space of the dualcone cyclone.
The contours of the turbulent kinetic energy of both cyclones are shown in Figure 8, which reflects a higher turbulence intensity in the dualcone cyclone than in the typical cyclone. This difference is due to the higher tangential velocity in the separation section of the dualcone cyclone. Therefore, the maximum turbulent kinetic energy can be seen at the vortex finder. Conversely, turbulent kinetic energy is lower at the bottom of the cyclone.
Fig. 7. Two regions of tangential velocity, which create the Rankine vortex [33]. 
a 


Turbulent kinetic energy [j/kg] 



b 


Turbulent kinetic energy [j/kg] 



Fig. 8. Turbulent kinetic energy contour plots for the (a) conventional cyclone and (b) dualcone cyclone. 
6.2 Axial velocity
Axial velocity causes axial flow, which dips in the middle of the vortex finder. Although swirl decreases in the conical section, this core flow dominates all over the separation components. This central flow also reduces swirl in the conical part of the cyclone. The axial velocity profile is unchanged inside the cyclone core region beneath the vortex finder. In the radial direction, when the core region peak is created, two extra peaks are generated, and axial velocity declines tending toward the wall. Note that negative values of axial velocity correspond to downstream flow, whereas positive values are related to upstream flow. The axial velocity profiles, as shown in Figure 10, are inverted W profiles in all the nine sections.
Figure 10 likewise shows that adding an extra conical section causes no recognizable difference in axial velocity in the upstream region of the dualcone cyclone in comparison with the axial velocity in the conventional cyclone. When the separation region space decreases because of the addition of a second cone, however, the axial velocity in the dualcone cyclone is higher than that in the conventional one. This higher velocity plays an important role in the separation and collection of particles.
6.3 Pressure drop
Cyclone pressure drop is essentially a consequence of the vortex energy, solid loading, and gaswall friction at the inlet, outlet, and walls of a cyclone. The walls provide the highest contribution to pressure drop, which cannot be reduced because doing so may affect separation efficiency.
Decreasing pressure drop is inadvisable because it imposes a negative effect on cyclone performance. This challenge prompted researchers to illuminate geometrical optimization for pressure drop reduction. Figure 11 shows that a higher gas inlet velocity increases pressure drop. Incorporating a second cone into the cyclone thus produces a smaller separation section, thereby reducing axial flow and increasing pressure drop. Vortex movement and its radial pressure gradient are nonnegligible when pressure drop is taken into account. The pressure drop for onedirectional flow over a smooth and clean wall of a cyclone is the result of three losses, namely, inlet losses, losses due to the fluid friction of two vortexes inside the separation space, and outlet tube losses. Among these, inlet losses provide minor contributions to pressure drop, whereas outlet tube losses provide major contributions. Overall, cyclone pressure drop increases with rising friction coefficient, cyclone length, and solid particle concentration.
Figure 12 shows that the highest pressure drop occurs in the separation section and near the walls; the lowest pressure drop takes place at the bottom of the second cone.


Fig. 9. Radial distribution of tangential velocity profiles in sections S1–S9 in the (a) conventional cyclone and (b) dualcone cyclone. 

Fig. 10. Radial distribution of axial velocity profiles in sections S1–S9 in the (a) conventional cyclone and (b) dualcone cyclone. 
6.4 Efficiency
One of the principal parameters that remarkably distinguishes cyclones from one another is efficiency. This parameter is defined as the ratio of the mass flow rate of captured particles to the total inlet mass flow rate.
(14) 
The total efficiency levels of the conventional and dualcone cyclones at different velocities are presented in Figure 13. An increase in inlet velocity increases the total efficiency of both cyclones. Given that tangential velocity increases because of rising inlet velocity, efficiency also improves. Each cyclone efficiency level corresponds to a different particle size (Figure 14). The efficiency of the dualcone cyclone is greater than that of the typical cyclone. The larger the particles, the higher the efficiency in the two cyclones. The higher efficiency of the dualcone cyclone is attributed to its higher tangential velocity, which produces stronger centrifugal force and causes large particles to rebound opposite the wall. Axial velocity, which moves the particles in cyclones downward, is also higher in the dualcone cyclone. Hence, more particles are separated at the bottom of the cyclone, thereby increasing efficiency.
The paths of calcium carbonate particles are plotted in Figures 15 and 16. In the dualcone cyclone, large particles travel over a short path, indicating a more rapid exit from the cyclone through the vortex finder. Such exit decreases separation time. Overall, decreasing conical space enables the accumulation of numerous particles inside the computational domain. In a conventional cyclone, particles are more dispersed.
Fig. 11. Comparison of pressure drop in the conventional and dualcone cyclones at three inlet velocities. 
a 
Static pressure [Pa]


b 
Static pressure [Pa]


Fig. 12. Contour plots for pressure drop in the (a) conventional and (b) dualcone cyclones. 
Fig. 13. Comparison of total efficiency of the conventional and dualcone cyclones at different inlet velocities. 
35 
Fig. 14. Comparison of collection efficiency of the conventional and dualcone cyclones at different particle sizes.
The radial pressure gradient drives the natural instability of vortex flow. Consequently, separation efficiency can be disrupted if nearwall flow deviates from ideal surfaces, such as weld seams, measurement probes, riveted unions, and the like. These features present considerable difficulties in the prediction of cyclone performance via complicated calculations. The key feature for explaining cyclone performance is the fact that the instability of a double vortex structure affects the flow parameters of a cyclone.




a 

b 

c 

d 

Fig. 15. Particle tracking in the dualcone cyclone at particle diameters of (a) , (b) , (c) , and (d) . 
a 

b 

c 

d 

Fig. 16. Particle tracking in the singlecone cyclone at particle diameters of (a) , (b) , (c) , and (d) . 
37 
Conclusion
This research probed into industrial gasparticle cyclones of different shapes. A Reynolds stress model was employed to simulate turbulent flow in the continuum phase, and the Eulerian–Lagrangian approach was applied for particle tracking and cyclone performance investigation. The numerical results are summarized as follows:
Nomenclature 


Drag coefficient 

Cyclone diameter 

Friction factor 

Gravitational acceleration 

Turbulent kinetic energy 

Mean pressure 

Stress generation 

Volumetric flow rate 

Reynolds stress tensor 

Section of study 

Particle residence time 

xcomponent of velocity 

Fluctuating component of velocity 




Mean velocity 

ycomponent of velocity 

Cyclone volume 

zcomponent of velocity 

Location 

Greek Symbols 


Kinematic viscosity 

Turbulent viscosity 

Density 

Turbulent dissipation 

Dynamic viscosity 

Subscripts 


Particle 

Turbulence 