# Kinetic Modeling and Analysis of Fuel Element Pneumatic Lifting System in Pebble Bed Reactors
## 1 Introduction  
In order to achieve carbon neutrality, many countries have introduced policies to support non-fossil energy sources, and nuclear energy is developing rapidly as a low-carbon non-fossil energy source [1; 2; 3; 4]. However, the development of nuclear energy has also brought tragic accidents to mankind [5], which makes nuclear safety ever more important [6]. There are six types of Generation IV nuclear reactors designed with safety in mind, namely, VHTR, GFR, MSR, LFR, SFR, and SCWR [7], which are considered to solve the obvious problems of existing reactor types [8]. The high-temperature gas-cooled reactor (HTR) is considered a promising Generation IV nuclear reactor due to its inherent safety [9; 10; 11]. The construction of the first commercial HTR-PM was initiated at Shidao Bay, Rongcheng, Shandong province, China, in 2012, and is in the commissioning stage [12; 13; 14]. HTR can be divided into hexagonal prismatic and pebble-bed high-temperature gas-cooled reactors based on the geometry of the fuel. The fuel elements of prismatic high-temperature gas-cooled reactors use hexagonal graphite blocks and are arranged in the longitudinal direction of the core, with the active cores distributed in an annulus shape in the lateral direction, and each standard fuel element consists of burnable poison rods, compact fuel rods, large coolant channels, and small inner coolant channels [15; 16; 17]. The fuel element of a pebble-bed high-temperature gas-cooled reactor is a fuel sphere consisting of a fuel core and a fuel-free shell, which takes advantage of the fluidity of the sphere to ensure its circulation capability, allowing the input of fresh and unexhausted fuel without stopping the reactor. When the fuel elements are discharged from the bottom of the core,the unexhausted fuel elements are screened and fed into the reactor together with fresh fuel through the fuel-lift system, which ensures fuel utilization. The fuel-element pneumatic lifting system uses pneumatic transportation to cycle the fuel element. Thousands of elements are discharged from the bottom of the core and lifted to the top of the core by the continuous airflow in a spatially oriented transport pipeline [18]. The diameter of spherical fuel elements is very close to the inner diameter of the conveying pipeline, with the diameter ratio ranging from 0.92 to 0.97. Therefore, this conveying method is called \"near-equal diameter spherical flow pipeline pneumatic conveying.\"  
Figure 1 shows a schematic diagram of the motion of the fuel element. A Cartesian system attached to the sphere is used to express the axial, lateral, and rotational motions. During its motion from the steering section of the bend to the vertical section, the fuel element will move in the plane where the axis of the bend is located due to the centrifugal force in the bend, and the dotted line in the figure illustrates the trajectory of the center of mass of the fuel element. The motion of the fuel element can be decomposed into translational motion \(v_{z}\) along the axis of the pipe (along the \(z\)-axis direction), transverse motion \(v_{\mathrm{x}}\) perpendicular to the axis of the pipe (along the \(x\)-axis direction), and rotational motion w. [PERSON] et al. [19] pointed out that in the process of pneumatic transportation of fuel balls, the collision will lead to the formation of graphite dust, and the accumulation of graphite dust will affect the stability and reliability of the reactor. Therefore, it is imperative to analyze the dynamics of the motion process. [PERSON] et al. [20] studied the process of pipeline transport of fuel elements with water as the medium and explored the effect of each parameter of the element but did not carry out a kinetic study.