Experimental measurement of effective thermal conductivity of packed lithium-titanate pebble bed

Lithium titanate is a promising solid breeder material for the fusion reactor blanket. Packed lithium titanate pebble bed is considered for the blanket. The thermal energy; that will be produced in the bed during breeding and the radiated heat from the reactor core absorbed must be removed. So, the experimental thermal property data are important for the blanket design. In past, a significant amount of works were conducted to determine the effective thermal conductivity of packed solid breeder pebble bed, in helium atmosphere, but no flow of gas was considered. With increase in gas flow rate, effective thermal conductivity of pebble bed increases. Particle size and void fraction also affect the thermal properties of the bed significantly. An experimental facility with external heat source was designed and installed. Experiments were carried out with lithium-titanate pebbles of different sizes at variable gas flow rates and at different bed wall temperature. It was observed that effective thermal conductivity of pebble bed is a function of particle Reynolds number and temperature. From the experimental data two correlations have been developed to estimate the effective thermal conductivity of packed lithium-titanate pebble bed for different particle Reynolds number and at different temperatures. The experimental details and results are discussed in this paper.     

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.     

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.     

Failure initiation and propagation of Li4SiO4 pebbles in fusion blankets

Lithium orthosilicate (Li₄SiO₄) pebbles are considered to be a candidate as solid tritium breeder in the helium cooled pebble bed (HCPB) blanket. These ceramic pebbles might be crushed during thermomechanical loading in the blanket. In this work, the failure initiation and propagation of pebbles in pebble beds is investigated using the discrete element method (DEM). Pebbles are simplified as mono-sized elastic spheres. Every pebble has a contact strength in terms of critical strain energy, which is derived from a validated strength model and crush test data for pebbles from a specific batch of Li₄SiO₄ pebbles. Pebble beds are compressed uniaxially and triaxially in DEM simulations. When the strain energy absorbed by a pebble exceeds its critical energy it fails. The failure initiation is defined as a given small fraction of pebbles crushed. It is found that the load level for failure initiation can be very low. For example, if failure initiation is defined as soon as 0.02% of the pebbles have been crushed, the pressure required for uniaxial loading is about 2.5 MPa. Therefore, it is essential to study the influence of failure propagation on the macroscopic response of pebble beds. Thus a reduction ratio defined as the size ratio of a pebble before and after its failure is introduced. The macroscopic stress–strain relation is investigated with different reduction ratios. A typical stress plateau is found for a small reduction ratio.     

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.     

堆内辐照氚增殖剂球床有效热导率分析

氘-氚聚变反应堆中,固态氚增殖剂包层能不断为聚变反应提供氚核素,是实现聚变反应堆商用的关键技术之一。由锂陶瓷小球堆积形成的球床形式的固态氚增殖剂包层具有比表面积大、产氚效率高等优点,是我国重点发展的氚增殖剂包层形式。氚增殖剂球床须能支撑在堆内辐照时的高温环境,这就要求氚增殖剂球床有较好的导热特性。球床的有效热导率在球床设计和辐照过程中的安全分析十分重要,因此在中国先进研究堆（CARR）开展了氚增殖剂球床在堆内辐照环境下的有效热导率测量实验。根据MCNP计算得出的球床发热功率,结合实验测量的球床温度分布反推得到氚增殖剂球床的有效热导率,并与广泛应用于球床有效热导率计算的改进型ZBS模型计算结果以及堆外实验结果进行对比分析,理论值与实验值能较好吻合。     

Comparative studies for two different orientations of pebble bed in an HCCB blanket

The Indian Test Blanket Module(TBM) program in ITER is one of the major steps in its fusion reactor program towards DEMO and the future fusion power reactor vision. Research and development(RD) is focused on two types of breeding blanket concepts: lead–lithium ceramic breeder(LLCB) and helium-cooled ceramic breeder(HCCB) blanket systems for the DEMO reactor. As part of the ITER-TBM program, the LLCB concept will be tested in one-half of ITER port no. 2, whose materials and technologies will be tested during ITER operation. The HCCB concept is a variant of the solid breeder blanket, which is presently part of our domestic RD program for DEMO relevant technology development. In the HCCB concept Li_2TiO_3 and beryllium are used as the tritium breeder and neutron multiplier, respectively, in the form of a packed bed having edge-on configuration with reduced activation ferritic martensitic steel as the structural material. In this paper two design schemes, mainly two different orientations of pebble beds, are discussed. In the current concept(case-1), the ceramic breeder beds are kept horizontal in the toroidal–radial direction. Due to gravity, the pebbles may settle down at the bottom and create a finite gap between the pebbles and the top cooling plate, which will affect the heat transfer between them. In the alternate design concept(case-2), the pebble bed is vertically(poloidal–radial) orientated where the side plates act as cooling plates instead of top and bottom plates. These two design variants are analyzed analytically and 2 D thermal-hydraulic simulation studies are carried out with ANSYS, using the heat loads obtained from neutronic calculations.Based on the analysis the performance is compared and details of the thermal and radiative heat transfer studies are also discussed in this paper.     

Effective Thermal Property Estimation of Unitary Pebble Beds Based on a CFD-DEM Coupled Method for a Fusion Blanket

Lithium ceramic pebble beds have been considered in the solid blanket design for fusion reactors.To characterize the fusion solid blanket thermal performance,studies of the effective thermal properties,i.e.the effective thermal conductivity and heat transfer coefficient,of the pebble beds are necessary.In this paper,a 3D computational fluid dynamics discrete element method(CFD-DEM) coupled numerical model was proposed to simulate heat transfer and thereby estimate the effective thermal properties.The DEM was applied to produce a geometric topology of a prototypical blanket pebble bed by directly simulating the contact state of each individual particle using basic interaction laws.Based on this geometric topology,a CFD model was built to analyze the temperature distribution and obtain the effective thermal properties.The current numerical model was shown to be in good agreement with the existing experimental data for effective thermal conductivity available in the literature.     

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.     

Experimental study and analysis of the purge gas pressure drop across the pebble beds for the fusion HCPB blanket

The lithium ceramic and beryllium pebble beds of the breeder units (BU), in the fusion breeding blanket, are purged by helium to extract the bred tritium. Therefore, the objective of this study is to support the design of the BU purge gas system by studying the effect of pebbles diameter, packing factor, pebble bed length, and flow inlet pressure on the purge gas pressure drop. The pebble bed was formed by packing glass pebbles in a rectangular container (56 mm × 206 mm × 396 mm) and was integrated into a gas loop to be purged by helium at BU-relevant pressures (1.1–3.8 bar). To determine the pressure drop across the pebble bed, the static pressure was measured at four locations along the pebble bed as well as at the inlet and outlet locations. The results show: (i) the pressure drop significantly increases with decreasing the pebbles diameter and slightly increases with increasing the packing factor, (ii) for a constant inlet flow velocity, the pressure drop is directly proportional to the pebble bed length and inlet pressure, and (iii) predictions of Ergun's equation agree well with the experimental values of the pressure drop.     

Study of ceramic pebble beds in Post Irradiation Examination of the Pebble Bed Assemblies irradiation experiment

The irradiation experiment Pebble Bed Assemblies (PBA) consists of four mock-up representations (test elements) of the EU Helium Cooled Pebble Bed (HCPB) concept. The four test elements contain a ceramic breeder pebble bed sandwiched between two beryllium pebble beds and are regarded as one of the first DEMO representative HCPB blanket irradiation tests, with respect to temperatures and power densities. The design value of the PBA were to irradiate pebble beds at a power density of 20–26 W/cc in the ceramic breeder, to a maximum temperature of 800 °C.Two test elements contain lithium orthosilicate pebbles (Li₄SiO₄; FZK/KIT) and were irradiated with target temperatures of 600 and 800 °C, respectively. The other test elements have lithium metatitanate (Li₂TiO₃; CEA) with different grain sizes and were both irradiated with a target temperature of 800 °C. The PBA have been irradiated for 294 Full Power Days (12 cycles) in the High Flux Reactor (HFR) in Petten to a total neutron dose of 2–3 dpa in Eurofer, and an estimated (total) lithium burnup of 2–3% in the ceramic pebbles.This work presents results of Post Irradiation Examinations (PIE) on the four HCPB test elements. Using e.g. SEM, the evolution of compressed pebble beds and pebble interactions like swelling, creep, sintering, etc., under irradiation and thermal loads are studied for the candidate pebble materials Li₂TiO₃ and Li₄SiO₄. (Chemical) interactions between ceramic pebbles and Eurofer (e.g. chrome diffusion) are observed. Looking at different sections of the pebble beds, correlations between temperatures and thermal–mechanical behaviour are clearly observed.     

Individual pebble temperature peaking factor due to local pebble arrangement in a pebble bed reactor core

Scientists at the German AVR pebble bed nuclear reactor discovered that the surface temperature of some of the pebbles in the AVR core were at least 200 K higher than previously predicted by reactor core analysis calculations. The goal of this research paper is to determine whether a similar unexpected fuel temperature increase of 200 K can be attributed solely or mostly to elevated power production resulting from exceptional configurations of pebbles. If it were caused by excessive pebble-to-pebble local power peaking, there could be implications for the need for core physics monitoring which is not now being considered for pebble bed reactors. The PBMR-400 core design was used as the basis for evaluating pebble bed reactor safety. Through exhaustive Monte Carlo modeling of a PBMR-400 pebble environment, no simple pebble-to-pebble burn-up conditions were found to cause a sufficiently high local power peaking to lead to a 200 K temperature increase. Simple thermal hydraulics analysis was performed which showed that a significant core coolant flow anomalies such as higher than expected core bypass flows, local pebble flow variation or even local flow blockage would be needed to account for such an increase in fuel temperature. The identified worst case scenarios are presented and discussed in detail. The conclusion of this work is that the stochastic nature of the pebble bed cannot lead to highly elevated fuel temperatures but rather local or core-wide coolant flow reductions are the likely cause.     

Thermal transient and the temperature profile in a HELICA mock-up simulated by a new finite element homogenous model

This paper deals with a numerical approach for simulating the thermal and mechanical behaviour of pebble beds used as breeder and neutron multiplier in breeding blanket of nuclear fusion reactor. The model of the pebble beds is based on the results of a theoretical and experimental research activity performed by the Authors on ceramic pebble beds (lithium ortosilicate and lithium metatitanate). The results of this activity permitted to determine the effective thermal conductivity of the beds, versus the temperature and the axial pressure and to implement a homogenous model of pebble bed in a FEM code.This paper illustrates an application of the implemented model, considering pebble beds under several cycles of heating and cooling. The examined geometry corresponds to the HELICA mock-up tested by ENEA in the research centre Brasimone. The experimental tests performed on HELICA have been used as a benchmark problem in order to assess the different approaches for simulating pebble beds. In this paper, the simulations performed with two-dimensional models are illustrated. Moreover the numerical results are compared with the experimental ones. Finally, a discussion on results obtained by other authors involved in the benchmark is reported.     

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.     

Mechanics of binary and polydisperse spherical pebble assembly

The micromechanical behavior of an assembly of binary and polydisperse spherical pebbles is studied using discrete element method (DEM) accounting for microscopic interactions between individual pebbles. A in-house DEM code has been used to simulate the assemblies consisting of different pebble diameters and the results of the simulations are compared with that of mono-size pebble assemblies. The effect of relative radii and volume fraction of the pebbles on the macroscopic stress–strain response is discussed. Furthermore, the effect of packing factor and coefficient of friction on the overall stress–strain behavior of the system is studied in detail. The shear (tangential) stiffness between the particles is also another influencing parameter. For a very small shear stiffness the system shows a strong dependence on the packing factor while a pebble material dependent shear stiffness shows a rather moderate dependence on the packing factor. For a similar packing factor, the mono-size assembly shows a stiff behavior during loading compared to binary assembly. However, the simulations do not show a significant difference between the two behaviors in contrast to the observations made in the experiments. The discrepancy can be attributed to (i) probable difference in packing factors for mono-size and binary assemblies in the experiments, (ii) arbitrary friction coefficient in the current model and (iii) the tangential interaction (constant shear stiffness) implemented in the present model which needs further modification as a function of the load history on the pebbles. Evolution of other micromechanical characteristics such as coordination number, contact force distribution and stored elastic energy of individual pebbles as a function of external load and system parameters is presented which can be used to estimate important macroscopic properties such as overall thermal conductivity and crushing resistance of the pebble beds.     

高温球床壁面区域有效导热系数模型优化

有效导热系数用来表征高温气冷球床堆堆芯综合传热能力,提高球床有效导热系数的预测精度对于高温气冷球床堆的热工设计和安全分析十分重要。为了优化球床壁面区域有效导热系数模型,本文针对无序石墨球床有效导热系数开展数值研究,分析了无序堆积球床主体区域、近壁面区域以及壁面区域有效导热系数的分布特性。结果表明：壁面区域有效导热系数相对于主体区域和近壁面区域显著降低,其平均降幅约为22%。因此引入了修正系数C_w对ZBS模型在壁面区域进行优化,对于球床主体区域及近壁面区域修正系数C_w=1,对于壁面区域,修正系数C_w=0.78。通过与前期无序球床实验数据和南非HTTU实验数据的对比,验证了优化后的ZBS模型能较好地预测球床壁面区域有效导热系数。     

高温气冷球床堆有效导热系数模型的改进

有效导热系数是高温气冷球床堆热工设计和安全分析程序中的基本参数,ZBS模型广泛应用于球床结构有效导热系数的预测。本文针对ZBS模型中的关键经验型参数——接触面积系数φ进行了分析,通过对不同堆积结构球床有效导热系数的数值分析,获得了12组接触直径比和配位数及其对应的φ值,然后通过多元线性分析获得φ的计算公式。与德国SANA实验结果进行比较,发现改进后的ZBS模型预测能力优于其他模型。改进后的ZBS模型的计算结果与先前实验测量的球床主体区域的有效导热系数吻合也很好。本文研究结果可为高温气冷球床堆的设计和安全分析提供理论支持。     

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.     

A Measurement Platform Scheme and Data Post-processing Method for Thermal Conductivity of Li<Subscript>4</Subscript>SiO<Subscript>4</Subscript> Pebble Bed

The effective thermal conductivity of tritium breeder pebble bed is an important thermal parameter and must be known for the thermo-mechanical design of solid tritium breeder blankets. In order to obtain the parameter, experimental measurement is an effective method. A measurement platform was designed by University of Science and Technology of China for CFETR solid blanket scheme to measure the immediate thermal conductivity data and study the effect of pebble bed temperature, the purge gas pressure and pebble deformation on the thermal conductivity of pebble bed. Measurements were performed based on about 1 mm diameter Li₄SiO₄ pebbles in the temperature range between 100 and 800 °C, with purge gas pressure ranging from 0.1 to 0.3 MPa. This paper described a measurement platform scheme by thermal probe method. On the other hand, for the sake of increasing the precision of thermal conductivity data transformed from temperature data, some improvements for the data post-processing using Monte Carlo inversion method were made in this paper too.