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.     

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.     

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.     

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.     

Design and validation of breeder unit of helium-cooled pebble bed blanket for demo fusion reactor

In the framework of European helium-cooled pebble bed (HCPB) blanket development, an HCPB breeder unit based on the design of pebble beds between flat cooling plates is proposed for a DEMO fusion reactor. The performances of the designed breeder units are validated by supporting analyses. By applying the thermal boundary conditions obtained by neutronics simulations for the DEMO reactor, results of finite element calculations of the breeder unit are analyzed in views of thermal-hydraulics and thermal stress to identify the adherence to maximum temperatures in structural and functional materials and the abidance by the stress criterion imposed by the structural material. The layout of the internal meandering channels in the cooling plates is optimized by using numerical methods. Finally, possible improvements of the new designed breeder unit are proposed.     

Thermal characterisation of ceramic/metal joining techniques for fusion applications using X-ray tomography

This work investigates the thermal performance of four novel CFC–Cu joining techniques. Two involve direct casting and brazing of Cu onto a chromium modified CFC surface, the other two pre-coat a brazing alloy with chromium using galvanisation and sputtering processes. The chromium carbide layer at the interface has been shown to improve adhesion. Thermal conductivity across the join interface was measured by laser flash analysis. X-ray tomography was performed to investigate micro-structures that might influence the thermal behaviour. It was found that thermal conductivity varied by up to 72%. Quantification of the X-ray tomography data showed that the dominant feature in reducing thermal conductivity was the lateral spread of voids at the interface. Correlations were made to estimate the extent of this effect.     

Transient thermo-mechanical behavior of a direct-drive target during injection in an inertial fusion energy chamber

During injection in an inertial fusion energy (IFE) chamber, a direct-drive target is subject to heat loads from chamber wall radiation and energy exchange from the chamber gas constituents. These heat loads can lead to the deuterium-tritium (DT) reaching its triple point temperature and even undergoing phase change, leading to unacceptable non-uniformity based on target physics requirements for compression and ignition of the DT fuel pellets using multiple laser beams. A two-dimensional bubble nucleation mode was added to the previously presented thermo-mechanical model to help better define the design margin for direct-drive IFE targets. The new model was validated by comparison with analytical results for controlled cases. It was then used to simulate heating experiments on DT targets conducted at the Los Alamos National Laboratory (LANL), where the ³He present in the DT due to tritium decay was found to affect the nucleation process.The previous requirement for target survival was for the temperature of the DT to remain below triple point of DT (19.79 K). If the existence of a melt layer does not violate the symmetry requirements on the target for successful implosion, the constraint could be relaxed by assuming a limit based on the avoidance of bubble nucleation. This study shows that the thresholds for melting and bubble nucleation are significantly different, allowing for extra margin in target survival under this assumption.     

Improvements in performance and microstructure of doped graphites as plasma-facing materials by a new process

Multi-elemental (B, Si and Ti) doped graphite was prepared from fillers of petroleum coke, dopants and binder of coal tar pitch by a new liquid mixing method. Such composite has not only high thermal conductivity (233 W/m K) but also excellent mechanical strength compared with the material prepared by the conventional solid mixing method. Scanning electron microscopy (SEM) results show that such material has a fine-grained structure as well as little pore diameter. The effects of the manufacturing procedure of doped graphites on the performance and microstructure are investigated. In addition, correlations between properties and microstructure are also discussed in detail.     

Multidimensional gap conductance model for thermo-mechanical simulation of LWR fuel behavior using a virtual link element

In light water reactor (LWR) fuel, the modeling of the heat transfer across the gap between the fuel pellets and the protective cladding is essential to understanding the fuel behavior. Based on the Ross and Stoute model, the gap conductance that specifies the temperature gradient within the gap depends on the gap thickness, which is related to the mechanical behavior. A multidimensional gap conductance problem can be challenging in terms of convergence and nonlinearity. In this work, a virtual link gap (VLG) element has been proposed to resolve the convergence issue and nonlinear characteristic of multidimensional gap conductance. The elements that link the node of a pellet surface with the node of the cladding surface are virtually generated so as to transfer heat as a function of gap thickness at every iteration step. To evaluate the proposed methodology for the simulation of the gap conductance, a thermo-mechanical model has been established using ANSYS Parametric Design Language (APDL) for a preliminary study, and a 3D thermo-mechanical module using FORTRAN77 has been implemented. In terms of calculation accuracy and convergence efficiency, the proposed VLG model has been evaluated. As a result, the convergence criterion of the thermo-mechanical calculation considering the iteration characteristics of the VLG element has been proposed. To demonstrate the effect of the VLG model in a 3D simulation with the implemented thermo-mechanical module, the simulation results of a missing pellet surface (MPS) have been compared.     

Analysis of thermal problems in development of spent fuel transport cask for research reactors

A packaging for the transport of irradiated fuel from research reactors was designed by a group of researchers to improve the capability in the management of spent fuel elements from the reactors operated in the region. Two half scale models for MTR fuel were constructed and tested so far and a third one for both MTR and TRIGA fuels will be constructed and tested next. Four test campaigns have been carried out, covering both normal and hypothetical accident conditions of transportation. The thermal test is part of the requirements for the qualification of transportation packages for nuclear reactors spent fuel elements. In this paper, both the numerical modelling and experimental thermal tests performed are presented and discussed. The cask is briefly described as well as the finite element model developed and the main adopted hypotheses for the thermal phenomena. The results of both numerical runs and experimental tests are discussed as a tool to validate the thermal modelling. The impact limiters, attached to the cask for protection, were not modelled.     

Numerical solutions for the kinematic model of pebble flow velocity profiles and its applications in pebble-bed nuclear reactor

The modular pebble-bed nuclear reactor (PBR) is a candidate Generation IV reactor being developed. The pebble flow in the very slow draining of fuel pebbles draws attention for its implications on core physical design and reactor physics analysis. One of the effective and simplified methods to address this problem is the kinematic model which is based on continuous theory to derive a diffusion equation for vertical velocity. This paper investigates the appropriate numerical solutions for the kinematic model of pebble flow velocity profiles in PBR geometry. Our method is based on a previously proposed transformed Cartesian coordinates and uses the implicit Crank–Nicholson integration scheme with two different treatments of the boundary conditions. Validations show that this numerical solution gives preferable agreements with the experimental results in the reference. Finally, the simulated velocity profiles are applied in the investigation of two pebble burnup-related issues, which are the pebble residence time prediction and the channel scheme in realistic high-temperature reactor pebble-bed modules reactor core geometry.     

Assessment of a RELAP5 model for the IPR-R1 TRIGA research reactor

RELAP5 code was developed at the Idaho National Environmental and Engineering Laboratory and it is widely used for thermal hydraulic studies of commercial nuclear power plants and, currently, it has been also applied for thermal hydraulic analysis of nuclear research systems with good predictions. This work is a contribution to the assessment of RELAP5/3.3 code for research reactors analysis. It presents steady-state and transient calculation results performed using a RELAP5 model to simulate the IPR-R1 TRIGA research reactor conditions operating at 50 and 100 kW. The reactor is located at the Nuclear Technology Development Centre (CDTN), Brazil. The development and the assessment of a RELAP5 model for the IPR-R1 TRIGA are presented. Experimental data were considered in the process of code-to-data validation. The RELAP5 results were also compared with calculation performed using the STHIRP-1 (Research Reactors Thermal Hydraulic Simulation) code. The use of a cross flow model has been essential to improve results in the transient condition respect to preceding investigations.     

Analytical model for calculation of the thermo hydraulic parameters in a fuel rod assembly

The paper presents the procedure of the cellular calculation of thermo hydraulic parameters of a single-phase gas flow in a fuel rod assembly. The procedure is implemented in the DARS program. The program is intended for calculation of the distribution of the gaseous coolant parameters and wall temperatures in case of arbitrary, geometrically specified, arrangement of the rods in fuel assembly and in case of arbitrary, functionally specified in space, heat release in the rods.In mathematical model the flow cross-section of the channel of intricate shape is conventionally divided to elementary cells formed by straight lines, which connect the centers of rods. Within the limits of a single cell the coolant parameters and the temperature of the corresponding part of the rod surface are assumed constant. The entire fuel assembly is viewed as a system of parallel interconnected channels.Program DARS is illustrated by calculation of a temperature mode of 85-rod assembly with spacers of wire wrapping on the rods.     

Application of laser-induced breakdown spectroscopy for characterization of material deposits and tritium retention in fusion devices

Laser-induced breakdown spectroscopy (LIBS) is discussed as a possible method to characterize the composition, tritium retention and amount of material deposits on the first wall of fusion devices. The principle of the technique is the ablation of the co-deposited layer by a laser pulse with P (power density) ≥ 0.5 GW/cm² and the spectroscopic analysis of the light emitted by the laser induced plasma. The typical spatial extension of the laser plasma plume is in the order of 1 cm with typical plasma parameters of n_e ≈ 3 × 10²² m^?3 and T_e ≈ 1–2 eV averaged over the plasma lifetime which is below 1 μs. In this study “ITER-Like” mixed deposits with a thickness of about 2 μm and consisting of a mixture of W/Al/C and D on bulk tungsten substrates have been analyzed by LIBS to measure the composition and hydrogen isotopes content at different laser energies, ranging from about 2 J/cm² (0.3 GW/cm²) to about 17 J/cm² (2.4 GW/cm²) for 7 ns laser pulses. It is found that the laser energies above about 7 J/cm² (1 GW/cm²) are needed to achieve the full removal of the deposit layer and identify a clear interface between the deposit and the bulk tungsten substrate by applying 15–20 laser pulses while hydrogen isotopes decrease strongly after the first laser pulse. Under these conditions, the evolution of the spectral line intensities of W/Al/C/hydrogen can be used to evaluate the layer composition.     

Improved analytical methodology for calculation assessment of material parameters in the nuclear installation decommissioning process

The process of nuclear installation decommissioning is, besides other features, characterized by production of large amount of various radioactive and non-radioactive materials or waste that have to be managed, taking into account its physical, chemical, toxic and radiological characteristics. Waste management is considered to be one of the key issues within the frame of the decommissioning process from the technological and also financial point of view. Because of that mentioned fact, the evaluation of costs and other parameters is necessary to be done as precise as possible in the decommissioning planning period. The calculation code OMEGA with its implemented module of integrated material flow, is suitable for the assessment and further optimization of the various decommissioning waste management scenarios considering the different input parameters.In the paper, the improved analytical methodology based on the identification of decommissioning materials, definition of detailed material streams, development of scenarios, calculation of output parameters and final optimization, is presented. The process of implementation of such methodology to the existing OMEGA material flow system, including the new or perspective technologies and methods for the waste managing, is also discussed more in details.Finally, the summarizing conclusions and recommendations resulting from the model calculation results, done for the verifying the suggested methodology and functionality of new improved material flow system of the OMEGA code, are presented.     

Neutronics shielding analysis for the end plug of a tandem mirror fusion reactor

A neutronics analysis using the Monte Carlo method is carried out for the end-plug penetration and magnet system of a tandem mirror fusion reactor. Detailed penetration and the magnets' three-dimensional configurations are modeled. A method of position dependent angular source biasing is developed to adequately sample the DT fusion source in the central cell region and obtain flux contributions at the penetration components.To assure cryogenic stability, the barrier cylindrical solenoid is identified as needing substantial shielding of about 1 m of a steel-lead-boron-carbide-water mixture. Heating rates there would require a thermal-hydraulic design similar to that in the central cell blanket region. The transition coils, however, need a minimal 0.2 m thickness shield. The leakage neutron flux at the direct converters is estimated at 1.3×10¹⁵ n/(m²·s), two orders of magnitude lower than that reported at the neutral beam injectors for tokamaks around 10¹⁷ n/(m²·s) for a 1 MW/m² 14 MeV neutron wall loading. This result is obtained through a coupling between the nuclear and plasma physics designs in which hydrogen ions rather than deuterium atoms are used for energy injection at the end plug, to avoid creating a neutron source there. This lower and controllable radiation leakage problem is perceived as a potential major advantage of tandem mirrors compared to tokamaks and laser reactor systems.     

Response of multi-step compound pre-equilibrium reaction cross sections for the (p,n) reactions to forms of optical model parameters

In furtherance to improving agreement between calculated and experimental nuclear data, the nuclear reaction code GAMME was used to calculate the multistep compound(MSC) nucleus double differential cross sections(DDCs) for proton-induced neutron emission reactions using the Feshbach-Kerman-Koonin(FKK) formalism. The cross sections were obtained for reactor structural materials involving ~(52)Cr(p, n)~(52)Mn,~(56)Fe(p,n)~(56)Co, and ~(60)Ni(p, n)~(60)Cu reactions at 22.2 MeV incident energy using the zero-range reaction mechanism. Effective residual interaction strength was 28 MeV, and different optical potential parameters were used for the entrance and exit channels of the proton-neutron interactions. The calculated DDCs were fitted to experimental data at the same backward angle of 150°, where the MSC processes dominate. The calculated and experimental data agree well in the region of pre-equilibrium(MSC) reaction dominance against a weaker fit at the lower emission energies. We attribute underestimations to contributions from the other reaction channels and disagreement at higher outgoing energies to reactions to collectively excited states. Contrary to the FKK multi-step direct calculations, contributions from the higher stages to the DDCs are significant. Different sets of parameters resulted in varying levels of agreement of calculated and experimental data for the considered nuclei.     

Numerical model for separation of H-D gas mixture in batch-type concentric-tube thermal diffusion columns

The modeling simulation for the separation of H-D gas mixture in batch-type concentric-tube thermal diffusion columns have been analyzed from the transport equation coupled with the application of mass balance. The most important assumption is that the concentrations of H₂, HD and D₂ are locally equilibrium at every points in the column as H₂ + D₂ ↔ 2HD. The concentration distribution equation was derived and the concentration difference between the bottom and top ends of the column could be estimated. The degree of separation and separation factor for recovery of deuterium from H-D gas mixture in the batch-type cryogenic-wall thermal diffusion column were estimated.     

Influence of geometrical and material parameters on flow rate in simplified ADS dense granular-flow target: a preliminary study

The spallation target is one of the key components of an accelerator-driven subcritical system (ADS). Following previous designs such as plate targets, rod targets, rotating targets, and liquid metal targets, the gravity-driven dense granular-flow target (DGT), which combines the advantages of solid and liquid metal targets, becomes a new attractive choice. The geometry of DGT consists of a cylindrical hopper and an internal coaxial cylindrical beam pipe. In this paper, using discrete element method simulations on graphics processing units, we research into the relations of the flow rate with the geometrical as well as the material parameters. For geometrical parameters, it is found that the existence of an internal pipe does not influence the flow rate when the distance from the bottom of the pipe to orifice is large enough. The results also reveal how the material parameters influence the flow rate. The whole research is helpful for the design of DGT.