A discrete element method study on the evolution of thermomechanics of a pebble bed experiencing pebble failure

The discrete element method (DEM) is used to study the thermal effects of pebble failure in an ensemble of lithium ceramic spheres. Some pebbles crushing in a large system is unavoidable and this study provides correlations between the extent of pebble failure and the reduction in effective thermal conductivity of the bed. In the model, we homogeneously induced failure and applied nuclear heating until dynamic and thermal steady-state. Conduction between pebbles and from pebbles to the boundary is the only mode of heat transfer presently modeled. The effective thermal conductivity was found to decrease rapidly as a function of the percent of failed pebbles in the bed. It was found that the dominant contributor to the reduction was the drop in inter-particle forces as pebbles fail; implying the extent of failure induced may not occur in real pebble beds. The results are meant to assist designers in the fusion energy community who are planning to use packed beds of ceramic pebbles. The evolution away from experimentally measured thermomechanical properties as pebbles fail is necessary for proper operation of fusion reactors.     

Effects of random pebble distribution on the multiplication factor in HTR pebble bed reactors

In pebble bed reactors the pebbles have a random distribution within the core. The usual approach in modeling the bed is homogenizing the entire bed. To quantify the errors arising in such a model, this article investigates the effect on k_eff of three phenomena in random pebble distributions: non-uniform packing density, neutron streaming in between the pebbles, and variations in Dancoff factor. For a 100 cm high cylinder with reflective top and bottom boundary conditions 25 pebble beds were generated. Of each bed three core models were made: a homogeneous model, a zones model including density fluctuations, and an exact model with all pebbles modeled individually. The same was done for a model of the PROTEUS facility. k_eff calculations were performed with three codes: Monte Carlo, diffusion, and finite element transport. By comparing k_eff of the homogenized and zones model the effect of including density fluctuations in the pebble bed was found to increase k_eff by 71 pcm for the infinite cylinder and 649 pcm for PROTEUS. The large value for PROTEUS is due to the low packing fraction near the top of the pebble bed, causing a significant lower packing fraction for the bulk of the pebble bed in the homogenized model. The effect of neutron streaming was calculated by comparing the zones model with the exact model, and was found to decrease k_eff by 606 pcm for the infinite cylinder, and by 1240 pcm for PROTEUS. This was compared with the effect of using a streaming correction factor on the diffusion coefficient in the zones model, which resulted in Δ_streaming values of 340 and 1085 pcm. From this we conclude neutron streaming is an important effect in pebble bed reactors, and is not accurately described by the correction factor on the diffusion coefficient. Changing the Dancoff factor in the outer part of the pebble bed to compensate for the lower probability of neutrons to enter other fuel pebbles caused no significant changes in k_eff, showing that variations in Dancoff factor in pebble bed reactors can be ignored.     

Development of an innovative detection system for pebble bed kinematic studies

Pebble bed reactors enable the circulation of pebble fuel elements when the reactors are in operation.This unique design helps to optimize the burnup and power distribution, reduces the excessive reactivity of the reactor,and provides a mean to identify and segregate damaged fuel elements during operation. The movement of the pebbles in the core, or the kinematics of the pebble bed,significantly affect the above features and is not fully understood. We designed and built a detection system that can measure 3-axis acceleration, 3-axis angular velocity,3-axis rotation angles, and vibration and temperature of multiple pebbles anywhere in the pebble bed. This system uses pebble-shaped detectors that can flow with other pebbles and does not disturb the pebble movement. We used new technologies to enable instant response, precise measurement, and simultaneous collection of data from a large number of detectors. Our tests show that the detection system has a negligible zero drift and the accuracy is better than the designed value. The residence time of the pebbles in a moving pebble bed was also measured using the system.     

Experimental investigation of the overall residence time of pebbles in a pebble bed reactor (PBR) using radioactive pebble

The granular flow of pebbles in a pebble bed reactor (PBR) under the influence of gravity is a dense granular flow with long-lasting frictional contacts. The basic governing physics is not fully understood and hence the dynamic core of a PBR and non-idealities associated with pebbles flow inside the reactor core are of non-trivial significance from the point of view of safety analyses, licensing, and thermal hydraulics. In the current study, overall and zonal pebbles residence time investigation is carried out by implementing noninvasive radioisotope-based flow visualization measurement techniques such as residence time distribution (RTD) and radioactive particle tracking (RPT). The characteristics of overall pebble residence time/transient number, zonal residence time, and the z-component of average zonal velocities at different initial seeding positions of a tracer particle have been summarized. It is found that the overall pebbles residence time/transient number increases (the z-component of average zonal velocities decreases) from the center towards the reactor wall. Also, pebbles’ zonal residence time results (the whole core is divided into three zones) which provide more insight and understanding about PBR core dynamics have been reported. The benchmark data provided could be used for assessment of commercial/in-house computational methodologies related to granular flow investigations.     

Thermo-mechanical test rig for experimental evaluation of thermal conductivity of ceramic pebble beds

The experimental determination of mechanical and thermal properties of ceramic pebble beds, such as the lithium orthosilicate or lithium metatitanate, is a key issue in the framework of fusion power technology, for the reason that they are possible candidates in the design of breeder blankets.The paper deals with an experimental method for the evaluation of the thermal conductivity of ceramic pebble beds versus the temperature and compressive strain, based on a steady state heat flux through a material (alumina) of known conductivity. The alumina thermal conductivity is determined by means of the hot wire method. To assess the experimental method, a thermo-mechanical characterization of alumina pebble beds (a material largely available), having different diameters, considering a wide range of temperatures and compression forces has been carried out.Moreover preliminary tests have been performed on lithium orthosilicate and lithium metatitanate pebble beds.     

Thermo-mechanical modelling of pebble bed-wall interfaces

In HCPB blankets, interfaces between pebble beds and structural material provide for an additional heat resistance, which depends on local mechanical stresses and temperature. The heat transfer coefficient of pebble bed-wall interfaces was investigated by modelling particle-wall contact, radiation effect, and interstitial gas. The predictions of the model were compared to the experimental data. Interfacial modelling as presented by this paper, which takes the coupled thermo-mechanical behaviour of the interface into account, opens up the possibility to implement these effects in a finite element simulation of a structure containing pebble beds.     

Spectral zone selection methodology for pebble bed reactors

A methodology is developed for determining boundaries of spectral zones for pebble bed reactors. A spectral zone is defined as a region made up of a number of nodes whose characteristics are collectively similar and that are assigned the same few-group diffusion constants. The spectral zones are selected in such a manner that the difference (error) between the reference transport solution and the diffusion code solution takes a minimum value. This is achieved by choosing spectral zones through optimally minimizing this error. The objective function for the optimization algorithm is the total reaction rate error, which is defined as the sum of the leakage, absorption and fission reaction rates errors in each zone. The selection of these spectral zones is such that the core calculation results based on diffusion theory are within an acceptable tolerance as compared to a proper transport reference solution. Through this work, a consistent approach for identifying spectral zones that yield more accurate diffusion results is introduced.     

Void fraction and effective thermal conductivity of binary particulate bed

In many industrial processes, solid particles of different sizes are mixed in different volume or mass fractions for various applications, primarily to reduce void volume or to increase the density of the mixture. A few of these processes include; production of high density ceramics, mortar, concrete, graphite, bricks and carbon blocks. Experiments were carried out with alumina and lithium titanate pebbles (size ≥ 1 mm) and particles (size < 1 mm) of different sizes and volume fractions in cylindrical and rectangular vessels to study the variation of void fraction with volume fraction of component pebbles and with large pebble to small pebble or pebble to particle size ratio. It was observed that the variation of void fraction with volume fraction of smaller pebbles or particles is ‘V-shaped’. Thus there exists a minimum void fraction and two different volume fractions of smaller pebbles or particles which can give same void fraction. The effect of void fraction on the effective thermal conductivity of binary bed of lithium titanate and alumina pebbles and particles of different sizes and volume fractions was investigated. From the experimental results it was found that the binary particulate bed has higher effective thermal conductivity that that of a unary particulate bed. Effective thermal conductivity of binary particulate bed is the maximum when its void fraction is the minimum. The binary particulate bed with less volume fraction of small particles has higher conductivity than that of the binary bed of higher volume fraction of small particles and having same void fraction. This is due to the fact that with increase in volume fraction of small pebbles or particles, the number of small-to-small and large-to-small pebbles and or particles contact point increases resulting in higher resistance to heat transfers. The experimental details and results are discussed in this paper.     

规则球床堆熔盐流动压降与对流换热CFD模拟

球床堆复杂的几何结构导致直接建模进行热工水力模拟非常困难,一般使用多孔介质模型简化处理,但多孔介质已有的压降和对流换热公式在熔盐冷却球床中的有效性仍待验证。本文基于固态燃料熔盐堆建立了6 cm直径小球的规则球床模型,给定球床进口熔盐流量和球壳发热功率,模拟了球床内的稳态流动与换热,计算了对应的压降和对流换热系数,并分别得到了球床压降、对流换热Nu随球床内流动Re变化的曲线。对比发现:模拟压降结果与已有公式差异较大,而模拟对流换热Nu结果与已有公式的差异相对较小。结合模拟结果和已有的公式,拟合得到了修正的压降和对流换热Nu公式。将修正公式应用于3 cm直径规则球床中,结果表明多孔介质修正模型与直接模拟结果一致。     

Experimental investigation of pebble beds thermal hydraulic characteristics

The purpose of this paper is to present the results of the experimental investigation of the thermal hydraulic characteristics for two types of test sections—thin annular pebble beds (i.e. spheres dumped in thin annular slots) and pebble beds placed between cylinders. The experimental results of heat transfer from the spheres and from a cylinder, as well as hydraulic drag for both types of test sections are presented in this paper. The results of performed experiments in the case of thin annular pebble beds demonstrated that maximum heat transfer and hydraulic drag is at the relative width of the annular slot K equal to 1.07 and 1.75 of spheres diameter. The heat transfer in internal layers at these values of K is equal to the heat transfer in the internal layers of large (unlimited) rhombic packing. The results of the experimental investigation of pebble beds between cylinders demonstrated that the randomly arranged pebble bed is preferable to the regular rhombic structure from the point of view of design simplicity, heat transfer from the cylinder and drag coefficient.     

Experimental characterization of the effective particle diameter of a particulate bed packed with multi-diameter spheres

This paper is concerned with uncertainty reduction in coolability analysis of a debris bed formed in fuel-coolant interactions (FCI) during a postulated severe accident of LWRs. A test facility named POMECO-FL was designed and set up to investigate the friction laws of adiabatic single and two-phase flow through particulate beds which have the characteristics of the prototypical debris bed, such as packed with particles of multiple sizes or irregular shapes. The emphasis of the present study is placed on quantification of effective particle diameter of a particulate bed composed of multi-diameter spheres. Pressure drops are measured for water/air flow through the particulate beds packed with various combinations of spheres, and the effective particle diameters of the beds are obtained based on the pressure gradients and the Ergun equation. The results show that at low flowrate (Re < 7) the effective particle diameters can be represented by the area mean diameters of the particles in the beds, while at high velocity (Re > 7) the effective particle diameters are closer to the length mean diameters. If the area mean diameters are chosen as the effective particle diameters, the frictional pressure drops of two-phase flow in the beds can be predicted by the Reed model with good agreements.     

Effect of the Cu-rich precipitates on thermal conductivity of RPV model steel

Cu-rich precipitates are the important influence factors for the irradiation embrittlement of the reactor pressure vessel model steels. The microstructure of the Cu-rich precipitates could be revealed by mechanical and magnetic properties. In this article, the effect of the Cu-rich precipitates on thermal conductivity was studied. The reactor pressure vessel (RPV) model steels were aged for different time at 500°C. The results show that the thermal conductivity of RPV model steel is first decreased and then increased during the experiment, with a minimum value at 48.33 ± 0.21 W·m^?1·K^?1 after being aged for 200 h. The changing thermal conductivity is decided by the synergistic effect of the following three factors: (1) the crystal structure transformation of Cu-rich precipitates, (2) the orientation relationship between the matrix and Cu-rich precipitates, (3) the content of Cu atoms in the matrix.     

Synthesis and thermal conductivity of Y6UO12

Y₆UO₁₂ was synthesized by solid-state reactions of Y₂O₃ and U₃O₈. The high-density pellet of Y₆UO₁₂ was prepared by the spark plasma sintering followed by heat treatment in air for oxygen supplementation. The thermal conductivity (κ) was evaluated using the laser flash method from room temperature to 1173 K. The κ of Y₆UO₁₂ decreased with increasing temperature in the whole temperature range, indicating that the phonon contribution was predominant. The room temperature κ value of Y₆UO₁₂ was 4.90 Wm^?1K^?1. The magnitude relationship of κ among Y₆UO₁₂, Y₆WO₁₂, and Yb₆WO₁₂, i.e. κ of Yb₆WO₁₂ < κ of Y₆UO₁₂ < κ of Y₆WO₁₂, was discussed based on the general lattice thermal conductivity theory.     

Fabrication of beryllide pebble as advanced neutron multiplier

Fusion reactors require advanced neutron multipliers with great stability at high temperatures. Beryllium intermetallic compounds, called beryllides such as Be₁₂Ti, are the most promising materials for use as advanced neutron multipliers. However, few studies have been conducted on the development of mass production methods for beryllide pebbles. A granulation process for beryllide needs to have both low cost and high efficiency. To fabricate beryllide pebbles, a new granulation process is established in this research by combining a plasma sintering method for beryllide synthesis and a rotating electrode method using a plasma-sintered electrode for granulation. The fabrication process of the beryllide electrode is investigated and optimized for mass production. The optimized beryllide electrode exhibits higher ductility and can be sintered at a lower temperature for a shorter time, indicating that it is more suitable not only for withstanding the thermal shock from arc-discharge during granulation but also for producing the beryllide pebbles on a large scale. Accordingly, because these optimization results can reduce the time required for electrode fabrication by 40%, they suggest the possibility of great reductions in time and cost for mass production of beryllide pebbles.     

A study of bubble behaviors in the volumetrically heated packed bed

The volumetrically heated packed bed has been widely utilized in modern industry, however, no research on the bubble behaviors in forced convection subcooled boiling was studied. To study the bubble behaviors in the volumetrically heated packed bed, here electromagnetic induction heating method was used to heat oxidized carbon steel balls adopted to stack packed bed, while water was utilized as the refrigerant in the experiment. Bubble behaviors were observed by a high speed camera for particle diameter varying from 8 mm to 12 mm, mass flux varying from 29.3 kg m⁻² s⁻¹ to 84.2 kg m⁻² s⁻¹, heat flux varying from 14.5 kW m⁻² to 50 kW m⁻², inlet pressure varying from 0.116 MPa to 0.125 MPa, inlet subcooling varying from 7 k to 9.2 k and porosity = 0.39. Obtained flow visualization images were analyzed. The experimental results indicated that the bubbles were blocked by steel balls and easily attached to the surface of balls, then slipped along the surface of steel balls. There was “regrowth phenomenon” in the packed bed and generated bubbles repeated growth several times in the lifetime. The nucleate boiling was firstly observed in the contact surface. Structures of contact surface had great impacts on the bubble shapes, departure diameter and frequency.     

基于辐射原理狭窄垂直封闭空腔热阻强化措施的实验研究

列车车体围护结构中普遍存在的狭窄空腔增加了车体围护结构的热阻,同时也为进一步降低空腔的辐射换热份额创造了条件。通过实验方法,利用粘贴铝箔方式改变空腔内壁面辐射特性,以期改善空腔热工性能效果进行了研究。结果发现:常规车体壁面空腔辐射换热份额很大,不容忽视;在空腔内壁面附着铝箔等高反射率表层,可有效降低空腔的辐射换热份额,且随着空腔厚度的增大,空腔当量导热系数降低的效果更为明显,最大可达无铝箔空腔的62%左右;冷面单面粘贴铝箔方式的效果与热面单面粘贴铝箔方式的效果几乎相同,双面粘贴铝箔方式效果最好,优于单面铝箔方式5%左右。     

Melting behavior and thermal conductivity of solid sodium-concrete reaction product

This study revealed melting behavior and thermal conductivity of four samples generated by sodium-concrete reaction (SCR). We prepared the samples using two methods such as firing mixtures of sodium (Na) and grinded concrete powder, and sampling depositions after the SCR experiments. In the former, the mixing ratios were determined from the past experiment. The latter simulated the more realistic conditions such as the temperature history and the distribution of Na and concrete. The thermogravimetry-differential thermal analyzer (TG-DTA) measurement showed the temperatures of the onset of the melting (solidus temperatures) were 865–942°C, but those of the samples containing metallic Na could not be clarified. In the two more realistic samples, the compression moldings in a furnace were observed. The observation revealed the softening temperature was 800–840°C and the solidus temperature was 840–850°C, which was 10–20°C lower than the TG-DTA results. The thermodynamics calculation of FactSage 7.2 revealed the solidus temperature was caused by melting of the some components such as Na₂SiO₃ and/or Na₄SiO₄ and NaAlO₂. Moreover, the thermal conductivity was λ ~ 1–3 W/m-K, which was comparable to xNa₂O - (1 - x)SiO₂ (x = 0.5, 0.33, and 0.25), and that at 700°C was explained by NBO/T of Equation (1).     

A review of correlations to model the packing structure and effective thermal conductivity in packed beds of mono-sized spherical particles

This paper presents a review of the literature describing the packing structure and effective thermal conductivity of randomly packed beds consisting of mono-sized particles. In this study particular attention was given to the packing structure (porosity, coordination number, and contact angles) and heat transfer by solid conduction, gas conduction, contact area, surface roughness, as well as thermal radiation. New methods to analyse the models were developed giving new insights into the shortcomings of the correlations to predict and define the packing structure, as well as to simulate the effective thermal conductivity in the near-wall region. This information is of particular importance in the design and operation of high temperature packed bed nuclear reactors.     

Stochastic techniques for the control and surveillance of a modular pebble bed reactor

This paper represents the first of a series of publications describing work in progress on the research, design and testing of a control and surveillance system for a Modular Pebble Bed Reactor.

The scope of the project involves the design of a simple state of the art control system for the reactor and a surveillance system based on smart instrumentation and expert system logic. It is noted that there are some physical and experimental problems unique to the MPBR family. These problems are connected with long neutron lifetimes, the need for a new evaluation of kinetic parameters and reactivity effects, and the need for very high sensitivity counting channels.