Gravity-driven separators are broadly used in various engineering applications to remove particulate matters from gaseous fluids to meet legislation demands. This study represents a detailed numerical investigation of a two-phase cyclone separator using the Eulerian–Lagrangian gas flow method. The turbulence is modelled using the Reynolds stress model (RSM). The technique has successfully predicted the typical trends and variations seen in such gas separators with an average error of approximately 5.5%. Also, the computed results show a realistic agreement with the experimental measurements.

Air pollution, equally natural and artificial pollution, is one of the conventional environmental dilemmas known to humankind. However, with the emergence of the Industrial Revolution in the 18th and 19th centuries, the phenomenon continues to deteriorate, and air pollution becomes one of the most complex environmental challenges. The health effects of air contamination are severe; for instance, air pollution due to particulate matter (PM), nitrogen dioxide, and ozone is a significant cause of severe health problems [

Cyclones are one of the widely used devices in many industries for separating substances with different densities. The selection of separators is driven by their simple construction and low operating and maintenance costs. The separation is achieved by employing the centrifugal and the gravitational forces, which generates a cyclonic vortex [

The untreated gas enters tangentially from the inlet at high velocity in vertical separators due to the centripetal forces. It continues to flow spirally to the lower part of the cyclone. To be noted is that the higher the tangential velocity, the higher the centrifugal forces. Due to the gradual reduction in the separator’s cone, the gas velocity increases, creating an additional inner central vortex at the separator’s centre—the inner vortex flows upward, carrying the clean gas [

The cyclone geometry and operational parameters have a vital influence on separation performance and collection efficiency [

Among the geometric parameters that affect the separation performance are the dimensions of the separator cylinder, cone, inlet and outlet, and vortex finder [

Furthermore, the cone dimensions impact the cyclone performance, as addressed in [

The effect of the added components inside the cyclone has also been studied experimentally and numerically [

Advanced modelling techniques are widely used in many engineering applications to design or/and optimise practical systems [

The prime objective of this study is to carry out a detailed numerical analysis using the Eulerian–Lagrangian [

In this section, the Eulerian–Lagrangian method, which is used to observe and analyse the separator’s fluid flow, is discussed briefly.

Fluid flows can be analysed mathematically, either using the Lagrangian description where the trajectories of the individual fluid particles are tracked in time [

In multiphase fluids, both descriptions are combined where the gas phase is solved in conjunction with tracking individual particles. The particles are tracked by indirectly solving transport equations using the Lagrangian particle method. The conservation of mass and momentum is represented by Eulerian conservation equations [

The equations of mass and momentum conservation are solved for the continuous phase, which is the gas phase.

The first term indicates the time variation, and the second term shows the changes due to fluid transport.

The first term on the LHS indicates the unsteady term, while the second term indicates the rate of change. On the RHS, the first term indicates the pressure gradient, where _{ij} is the viscous stress tensor and

The dominating swirl inside the separator creates an anisotropic turbulence field. When modelling the turbulence field, the Reynolds stress model (RSM) is adopted [

The RSM provides differential transport equations for each of the Reynolds stress components.

_{T,ij} represents the turbulent diffusion, _{L,ij} is the molecular diffusion, _{ij} is the stress production, _{ij} is the buoyancy production, _{ij} is the pressure strain, and _{ij} is the dissipation. These terms are a function of the mean gas-phase velocity gradients.

The Lagrangian method is based on a local force balance on each particle. The force balance considers the particle inertia with the forces acting on it and can be expressed as

The LHS represents the inertial force per unit mass, where _{p} is the particle velocity. On the RHS, the first term expresses the drag between the phases, where _{g} is the gas phase velocity. The second term represents gravity and buoyancy, respectively. _{p} and _{p} is the particle diameter, _{d} is the drag force, _{d} is the drag coefficient, and Re is the relative Reynolds number, which is defined as

One-way coupling is used in the simulations, which means that the fluid phase influences the particles via aerodynamic drag. For the drag coefficient, _{d}, the Schiller–Naumann model is used [

The computational results obtained by the CFD analysis are compared to the experimental results of Wang et al. [^{3}. A probe is used to measure the velocity and pressure of the gas field. It is placed in the flow field with five pressure transducers to obtain voltage signals. The particle distribution of the cement material can be expressed by the Rosin–Rammler equation [

A schematic of the cyclone, along with the selected axial locations, is shown in Figure

Schematic and the axial sections of the test cyclone [

Boundary conditions.

Density of air | 1.205 kg/m^{3} |

Density of particles | 3320 kg/m^{3} |

The volume fraction of the discrete phase | 3% |

Pressure | 1 bar (atmospheric) |

Temperature | 300 K |

Inlet velocity | 5–35 m/s |

Particle diameter | 1–5 |

The computational tool used in this study is commercial software STAR-CCM+. The tool solves the steady Favre-averaged transport equations (

The Reynolds stress turbulence model (RSM) is used because of the intense swirl inside the separator. Since the volume fraction of the particles is low, a point-particle injector is used to add particles. To be noted is that the computational model selected for the two-phase simulation captures physics and the typical behaviour of such separators reasonably. Hence, the chosen computational model is independent of the chosen boundary conditions shown in [

The physical grid is refined near the centre line near the outlet and inlet streams to capture the details with a reasonable computational cost. The sensitivity of the computed solution to the cell size and type is examined by using two different types of cells (hexahedrons and polyhedrons). It has been observed that the polyhedron cells produce a more realistic solution. The polyhedral mesh is less sensitive to stretching since the gradients can be accurately approximated as each of the individual cells has sufficient neighbouring cells.

The flow is set to be implicit unsteady, with a time step of 0.01 seconds. The turbulence intensity is set to 0.01. The solution has converged in approximately 6000 iterations. Hence, the solution presented in Section

Grid sensitivity test.

Cell type | Cells | Pressure |
---|---|---|

Poly | 39266 | 1417 |

Poly | 99436 | 1433,1 |

Poly | 19887 | 1538,7 |

Hexa | 187558 | 1005,9 |

Residual function plot.

The pressure drop is a vital parameter in industrial separators. For a higher pressure drop, greater power is required to move the fluid across the separator. Figure

The computed pressure drops compared to the experimental measurements at different inlet velocities.

From the design and efficiency point of views, the tangential velocity is critical; it aids to determine the centrifugal forces inside the separator. Accordingly, the tangential velocity is computed and compared to the experimental measurements at different axial locations inside the separator. As observed in Figure

Tangential velocity profiles at different axial locations and inlet velocities.

The contours of the tangential velocity are shown in Figure

Tangential velocity contours at different inlet velocities.

The axial force is vital to the separation efficiency; it affects the downstream discharge and residence time. To be noted is that the higher residence time leads to more efficient separation. The axial force pushes the particles against the wall of the separator, which increases the centripetal accelerations. With the aid of gravitational force, high forces are exerted on the particles, driving them to spin around along the walls of the separator. Figure

Axial velocity profiles for different cross sections at different inlet velocities.

Furthermore, it is noted that there are some variations in the rotational characteristic of the flow when the velocity exceeds 30 m/s, as shown in the axial velocity contours in Figure

Axial velocity contours with different inlet velocities.

The reason for this deviation is that when the axial velocity increases, the bottom exit is incapable of handling the increased flow, which results in an overflow. The overflow leads to an accumulation of upward flow, thus changing the radial location of the zero axial velocity interface, which is observed by the “fluctuations” in the bottom of the separator.

One of the most significant parameters of the cyclone separators is efficiency, which is greatly influenced by both the size of the particles and the inlet velocity. Figure

Particle separation efficiency as a function of particle diameter.

Figure

Particle separation efficiency as a function of inlet velocity compared with calculated results and previous simulations.

This study represents a detailed two-phase numerical simulation of a cyclone separator using a multiphase Eulerian–Lagrangian gas flow method. The computational results obtained are compared to the experimental results of Wang et al. [

The computed pressure drop was in good agreement with experimental measurements at different inlet velocities. It has been noted that the computed pressure drops increase with an increase in the inlet velocities, which reduces the separation efficiency and makes the separation operation costly. The model was also able to mimic the two distinctive symmetric vortexes inside the separator. The tangential velocity was also computed and compared to the experimental measurements at different axial locations inside the separator. It was observed that the tangential velocity has an M-shaped profile at axial locations S1, S2, and S3 while V-shaped at axial location S4.

Even though there were some minor discrepancies between the measured and computed solution, the Eulerian–Lagrangian gas flow method has successfully mimicked the experimental measurement at different axial locations inside the separator, and the general agreement was reasonably acceptable.

Readers can access the experimental data used in this study from [

The authors declare no conflicts of interest.