Thermal Conductivity Of Pebble Beds Research Articles

An apparatus to measure thermal conductivity of ceramic pebble beds under uniaxial compressive stress

Pebble beds have various applications in many industrial and research sectors. Lithium ceramic pebble beds have specific application in fusion reactors as one of the most promising candidates for tritium breeding material. During the operation of the fusion reactor, these pebble beds will have to sustain various thermal and mechanical stresses. Therefore, it is necessary to do thermal characterisation of these pebble beds under different stress conditions and generate sufficient data on their thermal properties, which is essential for designing breeder units of fusion reactors. In this work, an apparatus has been designed to evaluate the thermal conductivity of ceramic pebble beds under compressive stress. It can be mounted to any standard universal testing machine with the necessary adjustments. The apparatus is based on the transient hot-wire method, widely used to evaluate the thermal conductivity of porous materials. A platinum wire with a diameter of 0.5 mm was used as a hot-wire. Instead of utilising a thermocouple, the 4-wire approach was used to obtain the temperature. The transient temperature response of the hot-wire was obtained by applying a 7A constant current to it and monitoring the voltage drop along its 40 mm length. The thermal conductivity of the water gel was measured to assess the accuracy of the apparatus; the results showed a less than 1.5 % variation from the reference value. In this study, the thermal conductivity of Li2TiO3 pebbles was measured in an air and helium environment in different stress conditions. In an air environment, measurements were done at atmospheric pressure, whereas in a helium gas environment, they were performed at gauge pressures of 0.05 bar, 0.5 bar, and 1 bar. The measurements were conducted in two scenarios: (i) constant stress condition at 0, 3, and 6 MPa, and (ii) Cyclic loading-unloading of 0.037–3 MPa and 0.037–6 MPa. It was found that the pebble bed's thermal conductivity rose in tandem with increased compressive stress in both the helium and air environments. Pebble bed’s thermal conductivity was found to be higher in a helium gas environment than in air. The thermal conductivity of the pebble bed increased slightly with rising helium gas gauge pressure from 0.05 bar to 1 bar. This work provides a design to incorporate 4-wire temperature measurement in the hot-wire method for thermal conductivity measurement of compressed pebble beds. It also contributes to the thermal conductivity data of Li2TiO3 pebbles in cyclic stress conditions in helium and air environments.

Analysis of Near-Wall Pebble Bed Thermal Conductivity for Energy Applications.

Pebble beds have been employed in thermal storage and energy systems, where they are typically used to promote heat exchange in high-temperature environments. Understanding the heat conduction of the entire pebble bed could aid in the material selection of the pebbles themselves and structural components, system design, and safety monitoring. However, the thermal conductivity of pebble beds can change significantly near geometric boundaries. Using a complex multilayer analytical model in conjunction with a line source probe, we found a substantial increase in the thermal conductivity of a sintered bauxite pebble bed in the near-wall region (7.6 W m-1 K-1) compared to the bulk (0.59 W m-1 K-1). We investigated this difference by comparing porosity results, acquired with micro-CT, of 33.18 and 33.31% at approximately one pebble width surrounding the probe (near-wall) and the bulk of the pebble bed, suggesting that the thermal conductivity is largely altered by thermal contact resistance in the near-wall regime.

Effects of atmospheric gases and compression load on effective thermal conductivity of Li2TiO3 pebble bed

Tritium breeder material in the solid-type of breeding blanket concepts is usually used in a pebble bed form because of the efficiency and convenience of tritium extraction. The pebble bed is continuously heated by the exothermal reaction between neutron and lithium-6 during the operation of a fusion reactor. Thus, a compression pressure is applied on the pebble bed by the thermal expansion of pebbles and container structure. Therefore, the accurate thermal properties of the pebble bed are one of the important design parameters to ensure a function and stability of the breeding blanket. This study aims at the investigation of the change on effective thermal conductivity of Li2TiO3 pebble beds under the operation conditions of breeding blanket.The measurement of effective thermal conductivities of Li2TiO3 pebble beds has been performed by laser flash technique in several atmosphere gases, such as helium, nitrogen, and air, under the statically compression load controlled by specially design pneumatic device incorporated to the laser flash apparatus. Also, in the case of helium atmosphere, the effects of hydrogen concentration from 0.1 wt.% to 1.0 wt.% on the effective thermal conductivity were also investigated. The effective thermal conductivity of the Li2TiO3 pebble bed was strongly dependent on a kind of atmosphere gases, especially its thermal conductivity, in the relatively low temperature. However, the concentration of hydrogen in the helium atmosphere did not significantly affect the effective thermal conductivity of the pebble bed. Applied axial compression load has influenced on the effective thermal conductivity of the Li2TiO3 pebble bed, especially at high temperature. However, the obvious change of effective thermal conductivity with the value of compression load was not observed.

Analysis of effective thermal conductivity of pebble bed by artificial neural network and its computational and experimental verification

While dealing with a solid-type ceramic breeding blanket for a fusion reactor, it is critical to determine the basic and thermal properties of the functional material in the form of a pebble bed. In the form of pebbles, lithium ceramics serve as the tritium breeder material in the fusion blanket. Effective thermal conductivity (keff) is one of the important thermal properties for the design and useful parameter to determine the performance of the blanket component. Artificial Neural Networks (ANN) are a popular machine learning technique for tuning between input and output parameters. These networks can learn from examples (data set) and apply them when a homogeneous event arises, making them able to work through genuine-time events. Hence, it can save a lot of time and money for doing repetitive experiments and high-end simulations. This will aid in the creation of a huge database on the pebble bed's keff, which will be useful in the design and development of fusion blankets. The findings of simulations and experiments are compared to those predicted by the ANN model for the pebble bed's thermal conductivity.At IPR, a test setup for experiments has been developed using the steady-state and axial heat flow approach. keff of Li2TiO3 has been measured for the pebbles of diameter of 0.8–1.2 mm having packing fraction of ∼62% and using helium environment at different temperatures ranging from 100 °C to 600 °C at constant atmospheric pressure. keff has been compared with pebble bed of stainless steel pebbles of different diameters (1, 2, 3, 1&3, & 2&3 mm) as well. DDPM-DEM model has been used to generate the pebble bed and ANSYS-CFD simulations using FLUENT have been performed to validate the results. The projected values using ANN are within 5% of the results obtained from simulations and experiments. The details of the DDPM-DEM and ANN models, FLUENT simulations, and experimental results will be discussed in this paper.

A review of recent study on the characteristics and applications of pebble flows in nuclear engineering

This paper reviews the recent three-year progress on the investigations of pebble bed flows in nuclear engineering. Both the application of pebble beds in the fission reactors and the fusion reactors are included. The fundamental characteristics of packing, flows, conduction, convection, radiation, and the effective thermal conductivity of pebble beds are reviewed. The important issues on the design of the pebble beds as well as that related to the reactor safety are also introduced. In addition, the advances in measurement techniques and numerical coupled methods for exploring the pebble flow characteristics are categorized and summarized too.

Effect of packing structure on anisotropic effective thermal conductivity of thin ceramic pebble bed

Helium cooled solid breeder blanket as an important blanket candidate of the Tokamak fusion reactor uses ceramic pebble bed for tritium breeding. Considering the poor effective thermal conductivity of the ceramic breeder pebble bed, thin structure of tritium breeder pebble bed is usually adopted in the blanket design. The container wall has a great influence on the thin pebble bed packing structure, especially for the assembly of mono-sized particles, and thin pebble bed will appear anisotropic effective thermal conductivity phenomenon. In this paper, thin ceramic pebble beds composed of 1 mm diameter Li4SiO4 particles are generated by the EDEM 2.7. The effective thermal conductivity of different thickness pebble beds in the three-dimensional directions are analyzed by three-dimensional thermal network method. It is observed that thin Li4SiO4 pebble bed showing anisotropic effective thermal conductivity under the practical design size. Normally, the effective thermal conductivity along the bed vertical direction is higher than the horizontal direction due to the gravity effect. As the thickness increases from 10 mm to 40 mm, the effective thermal conductivity of the pebble bed gradually increases.

Influence of bed conditions on the effective thermal conductivity of ceramic breeder pebble beds using thermal DEM (TDEM)

Abstract The knowledge of effective thermal conductivity (ETC) of the pebble beds is vital in designing the breeder units for fusion reactors. The ETC of pebble beds in general depends on various parameters characterizing the bulk material and microstructural properties. Establishing correlations between the ETC and the governing system parameters through experiments is very expensive and not feasible in some cases as the particle scale data is not readily available. Hence, Thermal Discrete Element Method (TDEM) is employed in this paper to investigate the influence of various parameters on the effective thermal conductivity of pebble beds. Influence of parameters such as packing fraction, stress, bed temperature, pebble size and stagnant gas pressure on the ETC is investigated for lithium ceramic pebble beds in stagnant Helium/Air. Further, the variation of the ETC from the wall region to the bulk for pebble beds formed in prismatic containers is presented. Subsequently, dual phase pebble beds have been investigated to identify configurations that will enhance the ETC of the bed.

Experimental measurements for the effective thermal conductivity of pebble beds with uncertainty analysis

• An experimental platform including a test section and a helium loop was designed to measure the ETC. • The uncertainty of the measured values combining standard uncertainties isaround 5.5 % for a level of confidence of 95 %. • An increase of the ETC of the Li 2 TiO 3 and the Li 4 SiO 4 pebble bed was detected in the temperature range RT-400 °C. • The ETC of binary glass pebble beds in helium and air at room temperature is strongly dependent on the packing factor. The lithium ceramic pebble bed is a vital functional component of solid blankets in fusion reactors to realize tritium breeding. The effective thermal conductivity of the lithium ceramic pebble bed is a key thermal property which has a significant impact on the design and analysis of the fusion blanket. An experimental platform including a test section and a helium loop was designed to measure the effective thermal conductivity. The test section was based on the principle of the hot wire method and the helium loop was designed to satisfy different experimental conditions. For the Li 2 TiO 3 and the Li 4 SiO 4 pebble bed, experiments were performed in the presence of stagnant helium at atmospheric pressure. An increase of the effective thermal conductivity was detected in the temperature range RT-400 °C and the results were compared with numerical results. For the binary glass pebble beds with different diameter ratios, experiments were performed at room temperature in the presence of stagnant helium and air. The effective thermal conductivity was found strongly dependent on the packing factor.

A DEM-CFD numerical model for the prediction of the effective thermal conductivity of pebble beds with contact conduction

Pebble beds are main schemes for tritium breeding zones in the solid blanket for fusion reactors. The effective thermal conductivity of pebble beds (keff) is an important thermal property used in the thermal hydraulic design of solid blankets. In this study, a 3D DEM-CFD one-way coupling method considering contact conduction is applied to analyze the influence of solid contact conduction and solid-fluid-solid conduction on the effective thermal conductivity of pebble beds. The current numerical model gives a keff consistent with experimental data in a wide range of solid-to-fluid conductivity ratio ks/kf from 1 to 10,000. It can be concluded that when the ks/kf is more than 20, contact conduction should be taken into account to make a good prediction for keff.

Measurement of thermal conductivity of Li2TiO3 pebble bed by laser flash method

In order to verify the performance and safety of the solid-type breeding blanket concept, the thermal conductivity of the pebble bed is required as an essential parameter for design and analysis of the blanket. The hot wire, hot disk, guarded hot plate, and laser flash method are considered as measurement technique for the thermal conductivity of pebble bed. This study aims at the provision of the thermal conductivity of Li2TiO3 pebble bed, which is one of the candidates for tritium breeder material in the solid-type breeding blanket. The laser flash method was adopted due to its advantages compared with other methods, such as high accuracy and repeatability, easy sample preparation, absolute measurement technique, and so on. In this method, the thermal diffusivity is directly measured by the laser flash system, and then the thermal conductivity is obtained by multiplying density and specific heat to the measured thermal diffusivity. The thermal conductivity of the Li2TiO3 pebble bed with packing factor of 57% increased with increasing temperature up to 500 °C and was saturated to 1.3 W/m/K at more than 500 °C.

Numerical prediction of packing behavior and thermal conductivity of pebble beds according to pebble size distributions and friction coefficients

In the design process of a solid-type ceramic breeding blanket, it is important to identify the characteristics of functional materials in the form of pebble beds. In this study, the mechanical and thermal behaviors of lithium ceramic pebbles are numerically simulated using an in-house code developed for the discrete element analysis. First, the packing configurations of pebble beds under cyclic loadings are found and discussed in terms of the packing factor, average stress, and average coordination number. In particular, we investigate the effects of pebble size distributions and friction coefficients on the pebble packing. Subsequently, based on the resulting packing configurations, we analyze the heat conduction through the lithium ceramic pebble beds considering the elastic contact between the spherical pebbles. We then qualitatively evaluate the effective thermal conductivities of pebble beds, which also depend upon the pebble size distributions and friction coefficients. The results of the discrete element simulations reveal that a large size difference and low friction coefficient of pebbles lead to close packing and high thermal conductivity of the pebble beds.

Effective thermal conductivity of a compacted pebble bed in a stagnant gaseous environment: An analytical approach together with DEM

An analytical estimate of the effective thermal conductivity of a pebble bed with mono-sized pebbles in the presence of a stagnant gas is presented. The Discrete Element Method (DEM) is used to simulate granular assemblies under uniaxial compression and Resistor Network (R-N) model is applied for estimating the effective thermal conductivity numerically. In this paper, two heat transfer paths, i.e., conduction through pebble–pebble contact and pebble–gas–pebble interface are considered. The effect of the cutoff range for gap and the strain on the effective conductivity is studied. The validity of the analytical model is verified with the results from the R-N Model for different solid-to-gas thermal conductivity ratios and for different packing fractions. The analytical and numerical models show a good agreement with the experimental results of the effective thermal conductivity for lithium orthosilicate pebble beds in the presence of helium and air at different temperatures.

Discrete element method for effective thermal conductivity of packed pebbles accounting for the Smoluchowski effect

In this paper, a Discrete Element Method (DEM) for the evaluation of the effective thermal conductivity of pebble beds in fusion blankets is presented. Pebble beds are multiphase materials in which both the solid and the gas phase filling the voids between particles coexist. The effective thermal conductivity of a pebble bed depends on the thermal properties of the two phases as well as on the system properties (e.g. gas pressure, temperature etc.). In particular, the pressure of the system is a key parameter for the heat transfer in a packed granular assembly since the thermal conductivity of a confined gas decreases with decreasing pressure (known as Smoluchowski effect). In this work, the influence of the gas pressure on the effective thermal conductivity in the Knudsen domain was implemented, to our knowledge, for the first time in a DEM code. The heat transfer mechanisms implemented are: when two particles touch each other the conduction through the contact area between them and, in any case, the conduction through the gas phase in the gap between neighbouring solid particles, may they be touching or not. These mechanisms are expected to dominate the heat transfer in a fusion breeder packed bed. Parametric studies were carried out to investigate the influence of the solid and gas materials, temperature, pressure and compression state. Numerical results were compared with existing experimental literature data and recent experiments carried out at Karlsruhe Institute of Technology (KIT).

Theoretical and experimental study on effective thermal conductivity of pebble bed for fusion blanket

The effective thermal conductivity of breeder pebble bed as an important thermal physical parameter directly affects the thermal and mechanical properties of solid blanket. Theoretical and experimental studies on effective thermal conductivity of Li4SiO4 pebble bed were introduced in this paper. First, a theoretical model coupling the contact areas with bed strains was presented to predict the effective thermal conductivity of mono-sized pebble bed. Taken into account in this theoretical model is the influence of factors, such as properties of pebbles and gas, bed porosity, pebble size, gas flow, contact areas, thermal radiation and contact resistance. Second, experimental platforms were built up to measure the effective thermal conductivity of Li4SiO4 pebble bed. One is based on transient thermal probe method and the other is based on transient plane source method. The effective thermal conductivity of Li4SiO4 pebble bed with pebbles in a diameter of around 1mm were measured in the temperature range of RT∼550°C. The helium at 0.1MPa and air at atmospheric pressure were used as filling gas respectively to assess the influence on effective thermal conductivity of pebble bed. The comparison between the experimental results and calculation results by theoretical model was also discussed.

Influence of gas pressure on the effective thermal conductivity of ceramic breeder pebble beds

Lithium ceramics have been considered as tritium breeder materials in many proposed designs of fusion breeding blankets. Heat generated in breeder pebble beds due to nuclear breeding reaction must be removed by means of actively cooled plates while generated tritiums is recovered by purge gas slowly flowing through beds. Therefore, the effective thermal conductivity of pebble beds that is one of the governing parameters determining heat transport phenomenon needs to be addressed with respect to mechanical status of beds and purge gas pressure. In this study, a numerical framework combining finite element simulation and a semi-empirical correlation of gas gap conduction is proposed to predict the effective thermal conductivity. The purge gas pressure is found to vary the effective thermal conductivity, in particular with the presence of various sized gaps in pebble beds. Random packing of pebble beds is taken into account by an approximated correlation considering the packing factor and coordination number of pebble beds. The model prediction is compared with experimental observation from different sources showing a quantitative agreement with the measurement.

A Measurement Platform Scheme and Data Post-processing Method for Thermal Conductivity of Li4SiO4 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.

Thermal analysis with contact resistance of packed bed by a homogenization method

Effective thermal conductivity with contact resistance is analyzed by a homogenization method that can precisely represent the microstructure of a packed bed. The homogenization used in this study explains the heat transfer due to conduction through the solid, the fluid phase, and the contact area between particles, and radiation between solid surfaces. In particular, the effects of parameters, such as the hardness, contact pressure, roughness, temperature, and particle size of the packed bed, on conductivity are estimated in order to clarify the thermal conduction mechanism for the complex packed structure. Heat transfer with thermal contact resistance does not dominate if the Biot number is near 100. In case of larger particle size and no convective heat transfer, the micro-hardness, contact pressure, surface roughness are important factor for effective thermal conductivity. Moreover, thermal radiation in the bed becomes more important for larger particles (>1mm) and contact resistance can be neglected. However, effective thermal conductivity of pebble bed is dependent on the void fraction.

Design and research on the measurement platform of the effective thermal conductivity for Li4SiO4 and Li2TiO3 pebble bed

China is carrying out the conceptual design of Chinese Fusion Engineering Testing Reactor (CFETR), and the Helium Cooled Pebble Bed (HCPB) blanket concept is one of the main choices for tritium production. Li4SiO4 and Li2TiO3 are the candidate breeder materials for the HCPB blanket concept. In the HCPB blanket, breeding pebbles with the diameter range of 0.6–1.2mm are placed between two plates and the bed shall be cooled. Accordingly, effective thermal conductivity of pebble beds needs to be determined for the heat transfer calculation. Measurements of the heat transfer parameters of Li4SiO4 and Li2TiO3 pebble beds are being performed at the University of Science and Technology of China (USTC). Two measurement methods are being used. One is the steady state method with the use of thermocouples to measure the temperature distribution of the pebble bed. Another is transient thermal probe method using the temperature variation of the thermal probe and Monte Carlo inversion method to calculate the heat transfer parameters of the pebble bed. This paper will report on the progress of these measurement platforms.

Thermal Analysis of Breeder Unit for Helium Cooled Solid Breeder Blanket of Chinese Fusion Engineering Test Reactor

As one of the candidate tritium breeding blankets for Chinese Fusion Engineering Test Reactor, a kind of helium cooled solid tritium breeder blanket was proposed. The blanket uses the pebbles of lithium ceramics (Li4SiO4) and beryllium as tritium breeder and neutron multiplier, respectively. The thermal conditions of breeder unit directly affect the performance of tritium breeding and the safety of blanket. Therefore, thermal analysis of the pebble beds is of vital importance for a reliable blanket design. State steady thermal hydraulic analysis of the breeder unit has been performed, showing that the temperature satisfied the corresponding material temperature limits. State steady thermo-mechanical analysis has also been carried out. The maximum von Mises stress was within the allowable stress. Parametric sensitivity studies have been conducted to investigate the influence of main parameters (e.g. coolant mass flow rate, inlet temperature and pebble bed thermal conductivity) on the temperature distribution of the pebble beds and cooling plates.

Preliminary experimental evaluation of thermal conductivity of ceramic pebble beds

This paper illustrates the preliminary experimental tests for determining the effective thermal conductivity of ceramic pebble beds versus temperature and compression strains.Ceramic pebble beds are promising candidates to be used in breeding blankets for nuclear fusion reactor as breeder and neutron multiplier.The tests were performed with an experimental rig, built at the DICI-University of Pisa, which permits to determine the thermal conductivity of pebble beds in steady state conditions, at several temperatures and compression forces. The values of thermal conductivity of pebble beds are obtained as function of a known conductivity of an alumina disc.The assessment of the method has been performed determining the effective thermal conductivity of alumina pebbles beds of different diameters. Void fraction and compression strains are the parameters that mainly influence the variability of the thermal conductivity of the beds.