# Numerical Study of Internal Flow Field in a Disc Stack Centrifuge Based on Mixture-PBM Model
## 4 Conclusions  
In this paper, based on the Mixture-PBM coupling model, a numerical simulation study was carried out on a real-size disc stack centrifuge, and the results of the study showed that:  
1. The error between the numerical simulation results and the separation efficiency of the test results is less than 1%. When \(N_{d}=\) 1-1.06, the separation efficiency of the disc stack centrifuge increases with the increase in rotational speed. When \(N_{d}=\) 1.06, the separation efficiency \(\eta=\) 99.99%. 2. Considering the ribs of the disc, the hysteresis phenomenon of the liquid flow in the disc stack centrifuge is significantly reduced, and the results of numerical simulation (parameter distribution of the flow field) can reach 98% of the theoretical results, which verifies the reliability of the numerical simulation results. The ribs of the disc have an indispensable role. 3. A total of 90% of the water droplets in the oil-water mixture complete coalescence and precipitation in the distributor and do not pass through the rising channel but enter the heavy liquid area of the bowl through the rectangular channel and are discharged to the disc stack centrifuge through the water-phase outlet. The coalescence phenomenon of the water droplets entering the separation channel is greater than the breakup phenomenon. 4. The water content in the rising channel gradually decreases, and 95% of the water enters the bottom separation channel of the bowl component. The processing capacity of each layer of the separation channel gradually increases, showing the law of having a small bottom layer, large top layer, and uniform middle layer. 5. After the oil-water mixture enters the separation channel from the neutral pore, under the action of Coriolis force, the motion trajectory is not parallel to the generatrix of the disc but forms a vortex near the neutral pore, and the area of the vortex is small at the bottom and large at the top. The coalescence phenomenon and the water content of the water droplets affect the vortex scale, which is different from the classical two-dimensional simplified model with obvious three-dimensional characteristics. With the increase in \(\lambda\), the motion trajectory of the liquid is more and more deviating from the generatrix direction of the disc. In addition, the circumferential and radial velocities in the separation channel show a law of being large in the middle and small near the wall. Figure 21: Changes in water content at the small end of the separation channel. **Author Contributions:** Writing--original draft preparation, H.D. and S.L. ([PERSON]); Methodology, S.L. ([PERSON]), L.C. and S.L. ([PERSON]); Validation, C.H. and X.S. ; Writing--review and editing, S.L. ([PERSON]); Visualization, R.W. ; Funding acquisition, S.L. ([PERSON]). All authors have read and agreed to the published version of the manuscript. **Funding:** This research received no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. **Conflicts of Interest:** Authors [PERSON], [PERSON] and [PERSON] were employed by the company China State Shipbuilding Corporation Limited. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. **Nomenclature**