# Numerical Study of Internal Flow Field in a Disc Stack Centrifuge Based on Mixture-PBM Model
## 1 Introduction
[24] used a coupled CFD-PBM model to study the coalescence and breakup process of oil droplets in a disc stack centrifuge equipped with five-layer discs, focusing on the analysis of the particle size distribution of oil droplets in the flow field, but did not pay attention to the pressure and velocity distributions of the flow field considering the phenomena of coalescence and breakup of the dispersed phase. The above studies have shown that most of the researchers have used the Mixture model for numerical simulation of oil-water two-phase flow within the bowl components of a disc stack centrifuge. The Mixture model is suitable for multiphase flows in which the two phases are moving at different velocities, for simulating strongly coupled isotropic multiphase flows as well as multiphase flows in which the two phases are moving at the same velocity, and for multiphase flows in which there are coalescence and breakup phenomena in the flow. Inside the bowl of the disc stack centrifuge, the oil and water phases move at the same speed, the particle diameters of the dispersed phase water droplets have a wide range, and the inter-phase drag force law is unknown, so it is suitable for the selection of the Mixture model. Therefore, the Mixture model is chosen as the multiphase flow model in this paper. To consider the phenomena of coalescence and breakup of water droplets during the flow process, and concerning the experience of previous researchers, a PBM model is used in this paper to describe the changes in water droplets [24]. Some of these numerical simulation studies simplify the model to two-dimensional or the number of disc layers is too small, some of them do not match the setting of the boundary conditions with the actual working process, and some of them do not take into account the coalescence and breakup phenomena of the water droplets in the process of flow, which probably leads to the discrepancy between the simulation results and the actual process. In addition, they do not analyze the details of the flow field in sufficient depth. Therefore, in this paper, the bowl component of a disc stack centrifuge containing multilayer discs is taken as a model, uses the oil-water mixture with inlet particle size distribution measured experimentally as a boundary condition, considers the coalescence and breakup phenomena in the flow process, and carries out the numerical simulation of the internal flow field of the bowl of the disc stack centrifuge based on the Mixture-PBM coupling model. We investigate the flow processes in the internal flow field in a disc stack centrifuge, the distribution of the treatment capacity in each layer of the separation channel, and the process of coalescence and breakup in the disc stack centrifuge. The research in this paper provides effective and reliable technical means for the development of a large-flow and high-speed disc stack centrifuge, which has important engineering significance. The paper is structured as follows: In Section 2, the geometry and working principle of the bowl component of a disc stack centrifuge are introduced, and a reasonable numerical simulation methodology is determined, including the establishment of the computational domain model, mesh division, and boundary conditions. In Section 3, the error be-tween the numerical simulation results and the experimental results is first discussed to verify the reliability of the numerical simulation results. Then, the effect of ribs on the numerical simulation results is discussed by analyzing the pressure and velocity fields in the separation channel. Then, the flow process of the liquid inside the bowl component of the disc stack centrifuge is analyzed, and the changing law of the processing capacity of each layer of the separation channel, as well as the changing law of the separation efficiency, are discussed. Finally, the coalescence and breakup processes of dispersed-phase droplets are analyzed. In Section 4, the conclusions of this study are summarized.