Computational fluid dynamics simulation of the flow patterns and performance of conventional and dual-cone gas-particle cyclones

1. Introduction

Cyclones are devices used for the separation of droplets or particles from gas. Two-phase 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].

      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 time-consuming 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 lift-off 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 gas-particle 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 cut-off size, thereby augmenting cyclone efficiency. One-inlet channel and two-inlet 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 single-inlet 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 single-cone and dual-cone Stairmand cyclones used for the separation of calcium carbonate particles. Axial and tangential velocity distributions in nine distinct sections of the cyclones were investigated non-dimensionally. 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, single-cone and dual-cone 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 low-weight 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.

Table 1. Geometrical properties of the investigated cyclones.

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 Reynolds-averaged Navier–Stokes equation for incompressible, unsteady, and isothermal flow are as follows [25–27]:

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]

      The first term at the right-hand side of the equations above refers to turbulent diffusion, which can be expressed as follows [27]:

      The second term indicates stress production [27]:

      The term  pertains to pressure strain [27]:

The term  shows dissipation [27]:

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].

      The drag coefficient is expressed as [21, 25, 29]

      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 no-slip 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 second-order upwind scheme both for dissipation rate and for turbulent kinetic energy; also first-order upwind scheme was used for the Reynolds stress equation. Note that the first-order 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 near-wall 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]:

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]:

      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).

      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:

      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.

      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 V-shape profile in the single-cone 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 gas-particle 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 dual-cone cyclone.

      The contours of the turbulent kinetic energy of both cyclones are shown in Figure 8, which reflects a higher turbulence intensity in the dual-cone cyclone than in the typical cyclone. This difference is due to the higher tangential velocity in the separation section of the dual-cone 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.

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 dual-cone 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 dual-cone 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 gas-wall 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 non-negligible when pressure drop is taken into account. The pressure drop for one-directional 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.