# Simulation Analysis of Cyclone Separator for Separation of Cenospheres
## 2 Methods
### Numerical Modeling and Boundary Conditions  
Based on the above theory, the energy equation (Energy) was applied and the turbulence model was modeled using the re-normalization group (RNG) k-epsilon model, which is a modified k-epsilon model that better handles highly rotating and curved flows, to simulate the flow and particle motion in the cyclone separator. In the computational fluid dynamics (CFD) software Fluent, the discrete phase model (DPM) is a model used to simulate the motion and interactions of particles in a fluid. The DPM model uses a Lagrangian approach to track the trajectories of particles, while the Eulerian approach describes the flow in the continuous phase. This approach allows researchers to analyze in detail how particles are affected by a variety of forces such as fluid forces, gravity, Brownian forces, etc., and predict the behavior of particles in a flow field. The DPM model was used to track the particles, which is essential for predicting the separation efficiency of the particles in the cyclone separator. In this study, the DPM model was used to track the particles. In this study, particles were tracked using a DPM model set up with two different particles, one for fly ash particles and one for cenospheres particles. The minimum diameter of the fly ash particles was 0.001 mm, the maximum diameter was 0.1 mm, and the average diameter was 0.01 mm; the minimum diameter of the cenospheres was 0.005 mm, the maximum diameter was 0.5 mm, and the average diameter was 0.01 mm. Fly ash particles and cenospheres particles escaping from the upper discharge port were collected and compared with the total number of particles of fly ash and the total number of particles  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Number of Grids**} & **Separation Efficiency** & **Fly Ash Separation** & **Newton’s Efficiency** \\  & **of Cenospheres** & **Efficiency** & \(\gamma_{\text{B}}\) **(\%)** & \(\eta_{\text{N}}\) \\ \hline
24,786 & 92.86 & 47.02 & 0.457 \\
29,120 & 93.33 & 46.11 & 0.472 \\
42,456 & 95.76 & 47.64 & 0.4812 \\
52,089 & 95.71 & 47.37 & 0.4834 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Grid independence study table.  
Figure 2: Cyclone separator meshing diagram.  
of nanospheres, respectively, to derive the separation efficiency of fly ash and the separation efficiency of cenospheres.  
The turbulent viscosity ratio was 0.0845, the turbulent dissipation rate C\({}_{1}\) was 1.42, the turbulent dissipation rate C\({}_{2}\) was 1.68, the vortex coefficient was 0.07 s\({}^{-1}\), the wall Prandtl number was 0.85, the turbulent viscosity was 1 m\({}^{2}\)/s, and the outflow boundary condition was set to a free outlet in order to allow the fluid to flow out of the separator without any restriction. The pressure-velocity coupling method \"SIMPLEC\" was used for the pressure-velocity coupling problem in fluid flow. In order to improve the accuracy of the numerical solution, a second-order windward format was chosen, which captures the gradient changes in the flow field more accurately. The residual accuracy was set to 0.001.  
As shown in Figure 3, a cyclone separator was modeled for this study, which was cylindrical in shape and divided into four upper and lower sections. After entering from the air inlet, the fly ash moves downward along the wall spiral of the cyclone separator. When the particles touch the sloping surface, their trajectory is affected and subjected to centripetal force. The particles with smaller density move upward with the inner spiral, while the particles with larger density move in the bottom spiral, thus realizing the separation of particles.