Error Estimation of Values Obtained from Practical CFD Analysis

In recent years, it has become common to analyze the detailed, three-dimensional flow features in reactor pressure vessels of boiling water reactors (BWRs) by computational fluid dynamics (CFD) analysis. However, there are few reports on practical examples of estimation or on estimation methodologies of the uncertainties in multi-dimensional CFD analysis. In this paper, to estimate the errors of values obtained from practical CFD analysis of a complex flow field, we propose a quantitative methodology that adopts the numerical analysis errors of “elementary phenomena” as error factors for sensitivity analyses, as well as, for instance, dimensional tolerances or errors of input values. Using this methodology with CSAU methodology, we showed a practical simplified example of error estimation regarding calculated water surface drop along the radial direction obtained from CFD analysis of the hydraulic gradient formed in the reactor pressure vessel of a BWR. We show the validity of the methodology by comparing this “estimated error” with a “reference error” evaluated by comparing numerical and experimental results.     

Numerical Study on Effects of Fuel Mixture Fraction and Li-6 Enrichment on Neutronic Parameters of a Fusion–Fission Hybrid Reactor

This study presents the effects of mixture fractions of nuclear fuels (mixture of fissile–fertile fuels and mixture of two different fertile fuels) and ⁶Li enrichment on the neutronic parameters (the tritium breeding ratio, TBR, the fission rate, FR, the energy multiplication ratio, M, the fissile breeding rate, FBR, the neutron leakage out of blanket, L, and the peak-to-average fission power density ratio, Γ) of a deuterium–tritium (D–T) fusion neutron-driven hybrid blanket. Three different fertile fuels (²³²Th, ²³⁸U and ²⁴⁴Cm), and one fissile fuel (²³⁵U) were selected as the nuclear fuel. Two different coolants (pressurized helium and natural lithium) were used for the nuclear heat transfer out of the fuel zone (FZ). The Boltzmann transport equation was solved numerically for obtaining the neutronic parameters with the help of the neutron transport code XSDRNPM/SCALE4.4a. In addition, these calculations were performed by also using the MCNP4B code. The sub-limits of the mixture fractions and ⁶Li enrichment were determined for the tritium self-sufficiency. The considered hybrid reactor can be operated in a self-sufficiency mode in the cases with the fuel mixtures mixed with a fraction of equal to or greater than these sub-limits. Furthermore, the numerical results show that the fissile fuel breeding and fission potentials of the blankets with the helium coolant are higher than with the lithium coolant.     

Estimation of Neutronic Performance of a High Power Density Hybrid Reactor by Multilayer Perceptron Neural Networks

Artificial neural networks (ANNs) have recently been utilized in the nuclear technology applications since they are fast, precise and flexible vehicles to modeling, simulation and optimization. This paper presents a new approach based on multilayer perceptron neural networks (MLPNNs) for the estimation of some important neutronic parameters (net ²³⁹Pu production, tritium breeding ratio, cumulative fissile fuel enrichment, and fission rate) of a high power density fusion–fission (hybrid) reactor using light water reactor (LWR) spent fuel. A comparison of the results obtained by the MLPNNs and those found by using the code (Scale 4.3) was carried out. The results pointed out that the MLPNNs trained with least mean squares (LMS) algorithm could provide an accurate computation of the main neutronic parameters for the high power density reactor.     

Modification of PROMETHEUS Reactor as a Fusion Breeder and Fission Product Transmuter

This study presents the analyses of the fissile breeding and long-lived fission product (LLFP) transmutation potentials of PROMETHEUS reactor. For this purpose, a fissile breeding zone (FBZ) fueled with the ceramic uranium mono-carbide (UC) and a LLFP transmutation zone (TZ) containing the ⁹⁹TC and ¹²⁹I and ¹³⁵Cs isotopes are separately placed into the breeder zone of PROMETHEUS-H design. The neutronic calculations are performed by using two different computer codes, the XSDRNPM/SCALE4.4a neutron transport code and the MCNP4B Monte Carlo code. A range of analyses are examined to determine the effects of the FF, the fraction of ⁶Li in lithium (Li) and the theoretical density (TD) of Li₂O in the tritium breeder zone (TBZ) on the neutronic parameters. It is observed that the numerical results obtained from both codes are consistent with each other. It is carried out that the profiles of fission power density (FPD) are flattened individually for each FF (from 3 to 10%). Only, in the cases of FF ≥ 8%, the system is self sufficient from the point of view of tritium generation. The results bring out that the modified PROMETHEUS fusion reactor has capabilities of effective fissile breeding and LLFP transmutation, as well as the energy generation.     

Adsorption Characteristics of Water Vapor on Gamma-Lithium Aluminate

Lithium aluminate (LiAl0₂) is one of the probable candidates for tritium breeding material because of its potential to give a fair tritium breeding ratio, stability at high temperature and stability in atmosphere containing water vapor. Clarification of the adsorption performances of water on LiAl0₂ is important for optimization of the way to recover bred tritium from LiAl0₂ and for estimation of the tritium inventory in the breeding blanket and for quantification of the hydrogen isotope exchange reaction. The amount of water captured on LiAl0₂ was studied in the temperature range of 373~1,100K using the breakthrough curve method, and adsorption isobar and isotherm of water on LiAl0₂ were proposed based on the data obtained. The water capture phenomena of LiAl0₂ was attributed to the dissociative chemisorption, and the apparent activation energy was determined to be 32.2 kJ/mol.K. The tritium inventory by sorption for LiAl0₂ was compared with that for Li₂0.     

Hydrogen Permeation through Incoloy-800

The poloidal distribution of the first wall 14 MeV neutron flux and the tritium breeding ratio in a Tokamak fusion reactor were calculated using Monte Carlo method. The poloidal distribution of the 14 MeV neutron flux in the first wall was found to be quite different from that of the primary incident flux. The tritium breeding ratio calculated by the Monte Carlo method became about 5% larger than the value obtained from S_N transport calculations.     

Investigating Neutronic Parameters of a Thorium Fusion Breeder with Recurrent Neural Networks

Artificial neural networks (ANNs) have recently been introduced to the nuclear engineering applications as a fast and flexible vehicle to modeling, simulation and optimization. In this paper, a new approach based on recurrent neural networks (RNNs) was presented for the neutronic parameters of a thorium fusion breeder. The results of the RNNs implemented for the tritium breeding ratio computation, energy multiplication factor and net ²³³U production in a thorium fusion breeder and the results available in the literature obtained by using Scale 4.3 were compared. The drawn conclusions confirmed that the proposed RNNs could provide an accurate computation of the tritium breeding ratio computation, the energy multiplication factor and the net ²³³U production of the thorium fusion breeder.     

Estimation of Error Propagation in Monte-Carlo Burnup Calculations

A formulation has been established to estimate the error propagation in Monte-Carlo burnup calculations. The uncertainties in cross sections and the statistical errors in Monte-Carlo calculations are considered as error sources, and the error propagation of number densities of individual nuclides over a burnup period is formulated. The present formulation is applied to the burnup calculation of a simplified fast reactor core. The components of the errors in number densities due to the statistical error are up to 0.92% even when the history number is small as 10⁴. On the other hand, the components due to the cross section error are about 2–5% for the number densities of ²³⁵U, ²³⁹Pu, ²⁴⁰Pu, ²⁴¹Pu and ²⁴²Pu, and about 7.3% for the fission-product. Thus the contribution is mainly due to the cross section errors. The error propagation of the number densities due to the statistical errors at individual burnup steps is investigated by dividing the burnup period into two steps. The error propagation is not serious for the problem treated here because the component due to the statistical error is much smaller than that due to the cross section error.     

Permeation Analysis of Tritium Through the Vessel Wall of a Titanium Hydride Storage Container

Abstract

A preliminary design for a stainless steel vessel for the long-term storage of hydrogen isotopes has been proposed. The immobilised hydrogen, as a titanium hydride, could be stored in a stainless steel vessel for this application. The vessel, as a primary package, is designed to form titanium hydride and to contain the hydrogen isotopes and helium-3 produced from the decay of tritium. In order to predict the possibility of contamination and the deterioration of the mechanical properties, a numerical diffusion analysis calculation of the hydrogen isotopes and helium inside the stainless steel vessel was carried out. Numerical results showed that a negligible amount of tritium would be released by permeation through a 0.7 cm thick vessel wall at normal conditions over the entire period of the storage. When the vessel is heated up to a temperature of 600^°C for the routine conditions of activation or exothermic hydriding, tritium loss or contamination would be of little concern. However, if the vessel were exposed to fire conditions with a temperature of 800^°C, permeation of hydrogen through the vessel wall would result in a serious increase in the amount of tritium escaping, in a very short time.     

Effect of outside tritium source on tritium balance of a D-T fusion reactor

Attainable tritium breeding ration in the blanket system must be larger than the required breeding ratio when no effective tritium resources from outside are expected. It is revealed recently that a considerable amount of tritium can be trapped to the re-deposition layer of the first wall materials and that the time constant of this phenomenon is rather long. Then, the tritium breeding ratio around 1.1 is required in the blanket system when 3 years is claimed for the tritium doubling time to prepare tritium for the initial inventory of a next reactor. Construction of an outside tritium supply is one of the possible ways to compensate the lack of tritium because it is generally considered that the attainable tritium breeding ratio in the solid breeder system is around 1.05. It is reported recently that a high-temperature gas-cooled reactor can produce 10 kg of tritium per year. The preferable amount of tritium production rate of the outer tritium supply is discussed in this study from the viewpoint of tritium balance in a D-T power reactor.     

Impact Analysis of Helium Cooled Solid Blanket Structures on the Tritium Breeding Performance in CFETR

Chinese Fusion Engineering Test Reactor (CFETR) is a test tokamak reactor to bridge the gap between ITER and future fusion power plant. As its objectives are to demonstrate generation of fusion power and to realize tritium self-sufficiency, the tritium breeding ratio (TBR) is a key design parameter. In the blanket design and optimization, the structures such as the first wall (FW), cooling plate (CP), stiffening plate (SP), cap and some other design parameters in detailed 3-D model have significant impacts on the tritium breeding performance. Based on a helium cooled solid breeder blanket option for CFETR, the impact analysis of the helium cooled solid blanket structures on tritium breeding performance was performed in this paper. Firstly, the detailed 3D neutronics model was built by using of a CAD to Monte Carlo Geometry conversion tool McCad. Then based on the detailed 3D neutronics model, the impact analyses of the blanket structures on tritium breeding performance were carried out, which include the FW, CP, SP, cap and side wall. By the sensitivity study of the blanket structures on the TBR, it gave the TBR variation trend and references for the blanket design and optimization.     

超临界水冷固态实验包层中子学与热工水力特性研究

基于国际热核聚变实验堆(ITER)实验包层方案,提出了一个超临界水冷固态实验包层概念设计方案。设计采用Be作为中子倍增剂,Li4SiO4作为氚增殖剂,CLAM钢作为结构材料。包层第一壁采用多层盘道设计以提高第一壁出口温度,内部采用增殖剂与中子倍增剂分层布置以提高热沉积与氚增殖率。为验证包层设计的可行性,分析计算了三维包层氚增殖率与热沉积的分布,然后根据中子学计算得到的结果对超临界水冷固态实验包层进行了数值模拟研究。结果表明:包层功率密度分布较合理;氚增殖率满足运行中氚自持的要求;在冷却剂出口温度达到500℃条件下材料温度不超过限值。该设计方案能满足中子学设计与热工水力的要求。     

Nuclear design of a heliotron-H fusion power reactor

Nuclear analysis was carried out for the heliotron-H fusion power reactor employing anl=2 helical heliotron field. The neutronics aspects examined were (a) tritium breeding capability, (b) shielding effectiveness for the superconducting magnet (SCM), and (c) induced activity after shutdown. In this reactor design of the heliotron-H, the space available for the blanket and shield is limited due to the reactor geometry. Thus, some parametric survey calculations were performed to satisfy the design requirements. The nucleonic design features of the heliotron-H are as follows. An adequate tritium breeding ratio of 1.17 is obtained when a 10-cm thick Pb neutron multiplier and a 40-cm thick Li₂O breeding blanket are used. In this case, the total nuclear energy deposition is 16.10 MeV per 14.06 MeV incident neutron. The performance of the SCM is assured during 2 yr of continuous operation using a 20-cm thick tungsten shield. Biological dose rate behind the SCM at 1 day after shutdown is too high for hands-on maintenance.     

Design of a multipurpose laboratory scale apparatus for the investigation of hydrogen isotopes in PbLi and permeation technologies

The knowledge of the tritium transport parameters in lead lithium is fundamental for the design of the HCLL (helium cooled lead lithium) blanket. In fact, the inventory of tritium in fusion reactors blankets and the permeation of tritium into the blanket coolant, with the consequent leaks toward the environment, are strongly depending on its solubility and diffusivity in the lead alloy PbLi. Several experiments, devoted to investigate the function linking the tritium solubilised in lead lithium with the corresponding tritium partial pressure at equilibrium, were carried out in the past, but significant uncertainties still remain.A detailed analysis of the past experimental works is carried out in this paper with the aim to investigate the main problems occurred in the facilities used to measure the tritium solubility in PbLi that caused such a big spread in the achieved results. On the basis of this analysis, a new a multipurpose laboratory scale apparatus has been designed. The apparatus is able to measure the tritium solubility and diffusivity in PbLi in the range of temperature 300–550 °C and it will be operated with hydrogen partial pressure in the range 10²–10⁴ Pa. The facility can work with desorption and absorption technique.Moreover, the apparatus has been designed to allow the testing of H/D concentration sensors in Pb–15.7Li in operative conditions relevant to the HCLL–TBM and the characterisation of hydrogen permeation barrier.     

Numerical and Statistical Analysis of FR Spent Fuel Transmutation in a Thorium Fusion Breeder

In this study, a numerical analysis and an analysis of variance (ANOVA) are applied to find the best suitable neutronic parameters for the performance analysis in a thorium fusion rector. The numerical and ANOVA approach are employed to investigate the neutronic characteristics of a fusion reactor using ThO₂ 90% + FR spent fuel 10% fuel mixtures. Three different neutronic parameters for the ANOVA and numerical approach, namely, moderator/fuel volume fractions (V_m/V_f), plasma chamber dimensions (PCD) and neutron wall loading (NWLs) as time dependent are selected for neutronic performance characteristics including tritium breeding ratio (TBR), multiplication factor (M), total fission rate (Σ_f), ²³²Th(n,γ) reaction, burn up and/or transmutation (B/T) and fissile fuel breeding (FFBR). Moreover, effects of the NWLs, V_m/V_f fractions and PCD in the B/T of FR spent fuel mixed thorium are investigated. Numerical and statistics approach results are evaluated for TBR, M, Σ_f fission rate, ²³²Th(n,γ) reaction, B/T and FFBR.     

Tritium implantation and depth profiling in fusion related materials

Tritium behaviour in solids and particularly its permeation and inventory in the first wall, limiters, breeding blanket materials and in other structural elements of fusion reactors is a subject of great concern in all projects aiming at D + T fusion. In the present work elastic recoil detection (ERD) under ⁴He bombardment and the T(d, α)n nuclear reaction analysis (NRA) in the forward detection geometry were applied to the depth profiling of tritium at submicron distances below the surface of selected fusion related materials. Experimental results obtained for tritium implanted in titanium, graphite and lithium aluminate LiAlO₂ are presented as the examples.     

Estimation of modeling approximation errors using data assimilation with the minimum variance approach

In this paper, we estimate prediction errors owing to approximations in calculation models (modeling approximation error) using the data assimilation method. Correlations between the modeling approximation error and neutronics parameters obtained through calculations are evaluated in test configurations and then the evaluated correlations are used to predict the modeling approximation errors in design configuration. Formulae to estimate the modeling approximation error using the correlations are derived based on the minimum variance approach and the physical interpretation of the formulae is discussed through simple cases. The proposed method is applied in 2 × 2 and 3 × 3 fuel assembly geometries using specifications of the KAIST benchmark problem. The correlation between the modeling approximation error and parameters (neutron leakage in each fuel assembly) is estimated in 2 × 2 fuel assemblies and then the modeling approximation error in 3 × 3 fuel assemblies is predicted using the correlation. The calculation results not only indicate feasibility of the present method, but also suggest a need for further investigation on the assumptions used in the present study, i.e. applicability and robustness of the correlation among different geometries.     

Conceptual design of a water cooled breeder blanket for CFETR

China Fusion Engineering Test Reactor (CFETR) is an ITER-like superconducting tokamak reactor. Its major radius is 5.7 m, minor radius is 1.6 m and elongation ratio is 1.8. Its mission is to achieve 50–200 MW of fusion power, 30–50% of duty time factor, and tritium breeding ratio not less than 1.2 to ensure the self-sufficiency. As one of the breeding blanket candidates for CFETR, a water cooled breeder blanket with superheated steam is proposed and its conceptual design is being carried out. In this design, sub-cooling water at 265 °C under the pressure of 7 MPa is fed into cooling plates in breeding zone and is heated up to 285 °C with saturated steam generated, and then this steam is pre-superheated up to 310 °C in first wall (FW), final, the pre-superheated steam coming from several blankets is fed into the other one blanket to superheat again up to 517 °C. Due to low density of superheated steam, it has negligible impact on neutron absorption by coolant in FW so that the high energy neutrons entering into breeder zone moderated by water in cooling plate help enhance tritium breeding by ⁶Li(n,α)T reaction. Li₂TiO₃ pebbles and Be₁₂Ti pebbles are chosen as tritium breeder and neutron multiplier respectively, because Li₂TiO₃ and Be₁₂Ti are expected to have better chemical stability and compatibility with water in high temperature. However, Be₁₂Ti may lead to a reduction in tritium breeding ratio (TBR). Furthermore, a spot of sintered Be plate is used to improve neutron multiplying capacity in a multi-layer structure. As one alternative option, in spite of lower TBR, Pb is taken into account to replace Be plate in viewpoint of safety. In this contribution, study on neutronics and thermal design for a water cooled breeder blanket with superheated steam is reported.     

Neutronics analysis for the moving ring fusion reactor,KARIN-1

Monte Carlo calculations on the tritium breeding ratio in the blanket and the heating rate in the first wall were carried out for moving ring reactor, KARIN-1. The blanket adopted in this calculation consists of a 2-cm thick silicon carbide (SiC) first wall, a 25-cm thick lithium (Li) layer, and a 10-cm thick lithium oxide (Li₂O) layer. It was found that the tritium breeding ratio in the blanket and the heating rate in the first wall are changing cyclically with a 1 s period. The maximum tritium breeding ratio obtained is 1.12, the minimum is 1.01, and the average value over a 1 s period is 1.10. As for the heating rate at the center of the burning section, the maximum is ～26 W/cc, the minimum ～10 W/cc, the average ～ 15 W/cc, and the ratio of the maximum to the minimum is ～2.6. The corresponding values at the entrance of the burning section are ～24 W/cc, ～4 W/cc, ～12 W/cc, and ～6.7, respectively. These results provide the basic information for thermal and mechanical design of the reactor system.     

Investigation of the infinite medium integral neutronic data for incident fusion source neutrons

In the present work, the physical behavior of integral data in infinite medium has been evaluated for incident fusion neutrons with the help to the 3-D Monte Carlo code. In a fusion reactor blanket with finite dimension, the integral quantities will be more or less different from the infinitive medium results, depending on the neutron leakage fraction. Design studies foresee the reduction of the neutron leakage out of the blanket as possible in order to prevent the nuclear heating in super conducting fusion magnets and to keep all neutrons primarily in the coolant. The most important materials in fusion technology, namely tritium, beryllium, lead, thorium, and uranium have been investigated in infinitive medium. The main purpose of this work is to calculate the integral tritium breeding ratio, ²³³U breeding rate, ²³⁹Pu breeding rate, heat release, neutron multiplication ratio through (n,x) and fission (when applicable) reactions in those mixtures which are composed when first UO₂ and ThO₂ are mixed with natural lithium (Nat.Li) or ⁶Li for a volume fraction from 0 to 100%. Then the variable UO₂-Nat.Li (UO₂ mixed with Nat.Li) and UO₂-⁶Li (UO₂ mixed with ⁶Li) compositions will be mixed with Beryllium (Be) and Lead (Pb) for a volume fraction from 0 to 100%. However, the variable TO₂-Nat.Li (ThO₂ mixed with Nat.Li) and ThO₂-⁶Li (ThO₂ mixed with ⁶Li) compositions will be mixed with Be and Pb for a volume fraction mentioned above.