# Numerical Study of Internal Flow Field in a Disc Stack Centrifuge Based on Mixture-PBM Model
## 2 Physical Models and Numerical Simulation  
### Model and Meshing  
Disc stack centrifuge is a commonly used piece of equipment for separation and purification in petrochemical, biopharmaceutical, food processing, and other fields. The subject of this paper is a marine disc stack centrifuge. The physical model of the disc stack centrifuge is shown in Figure 1. The main parameters of the disc stack centrifuge are as follows: \(Q_{d}\) is the design flow rate, \(N_{d}\) is the design rotational speed, and \(D\) is the maximum radius. The maximum diameter of the disc is \(0.856D\), and the minimum diameter of the disc is \(0.266D\). The height of the disc stack centrifuge is \(3.804D\). It has a separation channel height of \(0.018D\). The diameter of the neutral pore is \(0.079D\). The flow medium in this paper is oil and water, and the specific parameters are shown in Table 1.  
Figure 1: Physical model of disc stack centrifuge. According to the solid model of the disc stack centrifuge, the fluid domain model of the bowl component of the disc stack centrifuge is established using UG NX 12.0 software, as shown in Figure 2. In this, the inlet and outlet of the fluid domain of the bowl component are extended appropriately to minimize the impact of geometrical model variations on the computational results. Combining Figures 1 and 2, the working principle of the disc stack centrifuge is as follows: the oil-water mixture enters the bowl component of the disc stack centrifuge through the inlet, passes through the distributor, a part of the liquid flows through the rectangular channel to the heavy liquid area of the bowl component, and the other part of the liquid passes through the neutral pores to the separating channel consisting of multi-layer discs. The bowl components rotate at high speed, driving the oil-water mixture to rotate. When rotating at the same speed, oil and water are subjected to different centrifugal forces due to their different densities. Under the action of centrifugal force, oil and water move in opposite directions, with oil flowing towards the oil phase outlet and water flowing towards the water phase outlet. Eventually, the separation of oil and water is completed. Considering the geometrical model and the rotational periodicity of the internal flow process, 1/12 of the fluid domain is selected as the computational domain. Numerical simulation of the oil-water two-phase flow in a single-layer separation channel is carried out using the Mixture model to verify the grid independence. Structural meshing of the computational domain was performed using ICEM CFD 2021 R1 software. The grid scheme is shown in Table 1. Under the design condition (design rotational speed: \(N_{d}\), design flow: \(Q_{d}\)), the volume fraction of the water phase at the inlet of the computational domain is set to be 5%, and the particle size of the water phase is 10 \(\upmu\)m. The flow process inside the separation channel directly affects the separation effect, so the separation efficiency \(\eta\) is used as a validation parameter, which is defined as:  
\[\eta=1-\frac{c_{1}}{c_{0}} \tag{1}\] \begin{table}
\begin{tabular}{c c c} \hline
**Material** & **Density (kg/m3)** & **Dynamic Viscosity (Pa-s)** \\ \hline Oil & 814 & 0.0031 \\ Water & 998 & 0.0010 \\ \hline \end{tabular}
\end{table} 
Table 1: Physical parameters of oil and water. Figure 2: The fluid domain of the bowl component. In the equation, \(c_{0}\) is the volume fraction of the water phase at the inlet of the computational domain, and \(c_{1}\) is the volume fraction of water at the outlet of the oil phase of the computational domain. The grid independence verification results are shown in Figure 3. It can be seen that the separation efficiency of the separation channel increases with the increase in the number of grids. When the total number of grids exceeds 60,000, the separation efficiency of the separation channel is considered to be independent of the number of grids.