# Kinetic Modeling and Analysis of Fuel Element Pneumatic Lifting System in Pebble Bed Reactors
## 6 Conclusions  
In this paper, a fuel-element lifting-system kinetic model is proposed and developed to describe the fuel-element transport process in a pebble-bed reactor. On this basis we calculated important parameters, such as axial velocity, rotation speed, and lateral displacement of the fuel element. The results are as follows:  
1. The fuel element accelerated to 85% of the airflow velocity in the first 0.2 s of the accelerating-duct-section movement and finally stabilized at 93% of the airflow velocity. The collision occurred in the first 0.25 s, in which the collision between the fuel element and the lower wall of the pipe is dominant.
2. The motion speed of the fuel element in the vertical-lifting-pipe section first plummeted from 5.1 m/s to 3.8 m/s in the first 0.1 s, then gradually increased and stabilized at 5.1 m/s in 0.6 s, where the collision occurred in the first 0.7 s, and then entered a stable lifting state.
3. The velocity change of the fuel-element movement in the bend was similar to that of the vertical-lifting-pipe section, and its collision occurred mainly between the fuel element and the outer side of the inner wall of the bend, which was maintained for about 0.15 s.  
The experimental results verify the accuracy of the analysis. This study provides the basis for optimization of the pebble-bed-reactor fuel-element delivery system, including:  
1. When designing the acceleration-pipe section, the acceleration time can be shortened by increasing the sphere/pipe-diameter ratio and the pipe-inclination angle.
2. When designing the vertical-lifting-pipe section, the intensity and frequency of collisions can be reduced by decreasing the recovery factor \(\lambda\), with the setting bellows at the front of the vertical-lifting-pipe section serving as an effective way to reduce the recovery factor \(\lambda\); the efficiency can also be improved by increasing the sphere/pipe-diameter ratio.
3. When designing the reduction section, the axial velocity of the fuel element can be reduced by decreasing the sphere/pipe-diameter ratio and the bending radius of the pipe to ensure the integrity of the fuel element and the safety of the reactor core.
4. When designing the pipe thickness and support, according to the collision strength and frequency, the thickness or support of the lower half of the acceleration section of the piping and the outside of the bend can be added.  
Most of the current research on fuel-lifting systems is about the lifting process of a single fuel element, but multi-fuel-element lifting in groups is a promising research direction for improving efficiency.  
Conceptualization, P.S.; methodology, P.S.; software, R.Z.; validation, R.Z. and P.S.; investigation, R.Z.; data curation, Z.W.; writing--original draft preparation, R.Z.; writing--review and editing, J.C.; supervision, J.C.; project administration, Z.W.; funding acquisition, P.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Opening Foundation of Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Dalian University of Technology), Ministry of Education, grant number KF1801.  
Not applicable.  
The data presented in this study are available in article.