Types Of Reactors Research Articles

Effect of Cooling Pump Transient Power Supply on ETRR-2 Safety Parameters

The primary goals of the engineering design for nuclear reactors involve safeguarding the integrity of the reactor core. Preserving the integrity of the cladding material is especially crucial, as it serves as the initial defense against the potential dangers posed by radioactive materials. In this work, an accident analysis of core cooling pump power transients of different ratios of the nominal pump power in a typical material test reactor is conducted. Phase failure is a very common electrical fault experienced by three-phase motors. Pump power reduction can be initiated due to several causes, like phase failure, voltage reduction, winding failure, and other causes. The nuclear reactor analysis code PARET/ANL version 7.6 is used to carry out these calculations. The accident scenario began with the reactor operating steadily, then experiencing a transient in the core pump power. This caused the core flow rate to decrease and eventually stabilize at a lower level as the pump power decreased. Core cooling pump power variations ratios of 20%, 33.3%, 50%, and 70% of the nominal pump power are considered in this work. The accident analysis is conducted under the availability and unavailability of reactor safety systems. Reactor safety parameters are reported for all cases of the core pump power variations.

Study on the flow characteristics of heterogeneous particles in three types of biomass fast pyrolysis down-tube reactors

A novel staircase down-tube reactor has been developed to solve the problem of the short residence time of ceramic balls in a vertical down-tube reactor and flow separation of biochar powder and ceramic balls in a V-shaped down-tube reactor. Numerical simulation was performed using a coupled approach that combined the Discrete Element Method (DEM) and Computational Fluid Dynamics (CFD) to simulate the mixing flow of heterogeneous particles (biochar powder and ceramic balls) in three types of down-tube reactors: staircase, vertical, and V-shaped structure. The results show that at an equivalent vertical height. The average residence time for ceramic ball in a staircase down-tube reactor is longer than that of the other two types (tstaircase structure = 1.6 s > tV-shaped structure = 1.0 s > tvertical structure = 0.6 s). The average residence time of biochar powder in three types of down-tube reactors can be classified as follows: tV-shaped structure = tstaircase structure = 1.2 s > tvertical structure = 1.1 s. The flow separation and centripetal motion of heterogeneous particles were observed in V-shaped down-tube reactor. A distinct periodic motion is exhibited in staircase down-tube reactor, it has great significance for exploring the flow and heat transfer regularity of heterogeneous particles. Eccentric distance (E.d) was proposed as a measure of the spatial utilization efficiency of the device. While the degree of coherence (D.c) was used to assess the degree of flow separation among heterogeneous particles.

Pollution Load Reduction from Domestic Wastewater with Electrocoagulation Process for Agricultural Reuse

Objectives: The present study is aimed to investigate electrocoagulation of domestic wastewater and assessment of pollutants removal efficiency for potential reuse in agriculture. Methods: The electrocoagulation treatment of domestic wastewater with Fe – Fe electrodes was performed under optimal conditions of pH (8.0), current density (0.6 mA/cm2), treatment time (45 minutes), and NaCl dose (2.8 g/L) in a slurry type of reactor. The primary clarified and biotreated domestic wastewaters were subjected to electrocoagulation with Direct Current (DC) as power source. Findings: There was observed higher pollutants removal efficiency from the biotreated wastewater as compared with the primary clarified wastewater after electrocoagulation. The treated wastewaters showed significant removal of pollutants in terms of BOD (79.5% – 87.9%), COD (86.8% – 89.5%), TDS (87.4% – 89.9%), TSS (66.7% – 75.3%), conductivity (77.8% – 78.4%), turbidity (74% – 81.2%), colour (77.7% – 86.2%), nitrates (44.1% – 51.7%), and phosphates (48.7% – 55.9%) after electrocoagulation treatment. Electrocoagulation considerably improved the biodegradability index of the primary clarified (0.59 to 0.92) and biotreated (0.69 to 0.8) wastewaters. This indicates easy removal of the pollutants further by biological processes in the aquatic ecosystems. Electrocoagulation demonstrated potential for removal of pollution from the domestic wastewater for productive reuse in agriculture and urban areas. Novelty: There exist few studies of use of electrochemical process for treatment and reuse of domestic wastewater. The treated waters complied with the regulatory standards and had satisfactory quality for reuse in agriculture and urban activities. Keywords: Electrocoagulation, Domestic wastewater, Biodegradability index, Agricultural reuse, National Green Tribunal

Determination of volume of radioactive waste in activated VVER-1200 reactor structures

The results of calculation studies of the amount of solid high-level, intermediate-level, low-level, very lowlevel radioactive waste (HLW, ILW, LLW, VLLW, respectively) generated during neutron activation of structural materials adjacent to the core of the VVER-1200 reactor plant, depending on the time after the final stopping it. An assessment of the volumes of radioactive waste (RAW) of activation origin generated over 60 years of operation of a VVER-1200 type reactor was carried out on the basis of computational studies of the induced activity of structural and protective materials using reactor and Monte Carlo program codes (SERPENT 2, TVS-M, DYN3D , MCU-PD). Specific activities for each isotope, total specific activities and activities, masses and volumes of activated structural and protective reactor materials for various categories of radioactive waste were calculated after the specified period of operation of VVER-1200 and over time after the final shutdown of the reactor. The obtained dependences of changes in the masses and volumes of activated materials over time after the final shutdown of the reactor make it possible to determine these parameters of materials separately for each category of radioactive waste and in total at any point in time. Thus, the masses of activated materials related to radioactive waste will decrease by 264 tons (from 713 to 449 tons) over 200 years of aging, and the volumes will decrease by 74.3 m3 (from 169 to 94.7 m3). Forecast quantitative data on the volumes and mass of activated reactor structures, depending on the duration of their exposure after the final shutdown of the power unit, will make it possible to develop technical proposals, forecast plans and schedules for organizing a radioactive waste management system during the decommissioning of the VVER-1200 reactor plant, as well as possible technological and design solutions for the disposal system for these radioactive waste.

Behavior of Nanocatalysts in Fischer–Tropsch Synthesis in Various Types of Three-Phase Slurry Reactors

Behavior of Nanocatalysts in Fischer–Tropsch Synthesis in Various Types of Three-Phase Slurry Reactors

Best Estimate Plus Uncertainty Analysis of Station Blackout Transient in Pool-Type Research Reactor

Simulation of a station blackout (SBO) scenario was carried out for an open pool–type nuclear research reactor. The SBO transient was analyzed using the best estimate (BE) thermal-hydraulic code RELAP5/MOD3.2 to evaluate the performance of safety systems and inherent thermal inertia provided by the reactor pool in ensuring adequate core cooling during a prolonged SBO condition lasting up to 7 days. This encompasses assessment of cooling provided by battery-operated auxiliary pumps in the initial phase followed by setup of the natural convection cooling mode for the extended period. Best Estimate Plus Uncertainty (BEPU) methodology was applied for assessment of safety margins. This involved estimation of required simulations using the Wilks first-order formulation to achieve results within the tolerance limit of 95/95. Identification of relevant uncertainties and their propagation was carried out; subsequently, a case matrix for 59 simulation runs was generated using the Latin hypercube sampling method. The upper/lower bounds of uncertainty results were analyzed and compared with the BE code results. Later, sensitivity analysis was carried out using sensitivity coefficients generated using the Pearson and Spearman coefficient. The results show that the values of the crucial thermal-hydraulic parameters obtained with the tolerance limit of 95/95 met the acceptance criteria, with adequate safety margins.

Zeolite-templated carbons process with recycled materials and characterisation for energy storage applications

Quantity and quality are the two most important challenges for applying zeolite-templated carbons (ZTCs) into the industry. To provide more information on the mass production in the large-scale facility, depreciation of the quasi-crystal graphite carbon, utilisation of recycled acetylene and zeolite, and online quick quality control for the production of ZTCs, three types of reactors were applied under similar experimental conditions to investigate the ZTC production rate and the generation of the quasi-crystal graphite carbon on the uppermost layer of ZTC. The best specific surface area and carbon yield efficiency from the generation of ZTC were obtained using a fluidised-bed reactor (FBR). The occurrence of the quasi-crystal graphite carbon also disappeared using a FBR. The fluidised-bed-particle kinetic model was also established to demonstrate the feasibility of accomplishing the yield of 0.5 kg per day in the pilot-scale FBR experiments. The utilisation of recycled acetylene could reach 85% and the recovered rate of zeolite was around 60%. An on-site standard operating procedure (SOP) for QA/QC was also proposed for ZTC preparation and characterisation, which prominently shortened the production time for the laboratory preparation of ZTC and achieved superior hydrogen storage and electrochemical capacity.

Features of the architecture of nuclear power plants

The article analyses the peculiarities of the specific industrial landscape of nuclear power plants on the basis of domestic and foreign experience and highlights the importance of adapting these industrial complexes with a heavy technological regime to modern architectural post-industrial requirements. The architecture of nuclear power plants (hereinafter referred to as NPPs) is often a subject of debate. Some people believe that NPPs are a symbol of technological progress and should be presented as monumental structures. Others believe that NPPs are potentially dangerous facilities and should be built in a more modest style. Most industrial facilities, such as NPPs, were built in the industrial era and do not meet the requirements of the post-industrial era in terms of environmental friendliness, adaptability and architectural coherence. This is due to the duration of their construction and the environment in which they are located. Therefore, they need to be modernised. Analysing the architectural features of nuclear power plants, the author has determined that, regardless of the architectural style, NPPs usually have several common features, namely: large, monumental buildings that emphasise their importance, features that reflect their technological nature, such as cooling towers and reactor units. Due to the regional location, NPPs have their own peculiarities in composition and architectural decoration, which can not only modernise the appearance, but also depict elements of national identification. Due to their location on the ground, in a certain established natural environment, NPPs require a large amount of water resources due to the peculiarities of the heavy technological regime (reactor type) that takes place at the enterprise, so they are located on the ground near water bodies and reservoirs, and sometimes absorb entire rivers and lakes for the needs of technological processes. The mountainous terrain factor is equally important. It affects the architectural landscape of NPPs and their authenticity. Equally important is the period in which the plant was designed and built, as nuclear power is an important economic and political component of the country where it is produced. In terms of form, space and volume solutions, typology, and architectural and planning principles, it is possible to draw an analogy with the stage of development of a state.

Computational substantiation of technological characteristics of the closure stage of nuclear fuel cycle using code VIZART

There exist different variants of organizing the closure of nuclear fuel cycle (CNFC) depending on fast reactor type, fuel types, station or centralized allocation of closed nuclear fuel cycle stages. One of the ways to verify and estimate engineering solution is mathematical modeling of radiochemical technology which in the end will allow to optimize composite technological process in order to increase effectiveness and reduce cost. In order to calculate the balance of material flows of process circuits and individual production sections in the stationary and dynamic modes, with taking into account the isotopic composition evolution, a software package VIZART (Virtual Plant of Radiochemical Technologies) was developed, allowing the user to assemble the required sequence of operations for any part of the process scheme and perform the calculation of material balance for all flows of the circuit, as well as to optimize the equipment operating modes and provide the necessary data to justify the safety of certain limits and the entire process circuit. The following capabilities of code VIZART for computational substantiation of CNFC technology design and characteristics are considered: material balance calculation, cyclogram creation, determination of the most loaded parts of processing lines, estimation of fissile materials accumulating in devices and intermediate vessels, optimization of productivity of nodes and devices.

A comprehensive analysis of thermal–hydraulic signatures in neutron noise of WWER-type reactors

The neutron noise phenomenon, occurring in all types of nuclear reactors, provides valuable insights into the dynamic behavior of these reactors. In this work, a well-justified approach for modeling neutron noise induced by thermal–hydraulic sources in a hexagonal reactor core is presented in detail. These sources encompass fluctuations in key features of the inlet coolant, including flow rate, temperature, and boric acid concentration. Our proposed approach touches on various aspects of the distribution of thermal–hydraulic parameters among coolant loops, accounting for both uniform and non-uniform distributions. The latter allows for the asymmetric and asynchronous distribution of their fluctuating component among the coolant loops. To manage such complexity, it becomes imperative to determine the contribution of each fuel assembly based on each coolant loop. To achieve this, CFD simulations are conducted for the downcomer and lower plenum of the reactor pressure vessel. These simulations provide essential data to establish the coolant mixing matrix, which accounts for non-uniform distributions. The obtained mixing matrix is subsequently integrated into our neutron noise simulator, DYNOSIM, ensuring the faithful reproduction of neutron noise. Our study comprehensively analyzes both uniform and non-uniform scenarios. The radial and axial distributions of neutron noise amplitude and phase are examined for these scenarios. Their qualitative verifications are conducted by prior works in this field. Furthermore, we compare one of the uniform scenarios with reference results obtained using a frequency domain simulator. Notably, our CFD simulation results closely match the experimental data. Our findings demonstrate the effectiveness and efficiency of this methodology in modeling and understanding neutron noise in hexagonal reactor cores.

Assessment of the efficiency and stability of enzymatic membrane reaction utilizing lipase covalently immobilized on a functionalized hybrid membrane

Enzyme immobilization in membrane bioreactors has been considered as a practical approach to enhance the stability, reusability, and efficiency of enzymes. In this particular study, a new type of hybrid membrane reactor was created through the phase inversion method, utilizing hybrid of graphene oxide nanosheets (GON) and polyether sulfone (PES) in order to covalently immobilize the Candida rugosa lipase (CRL). The surface of hybrid membrane was initially modified by (3-Aminopropyl) triethoxysilane (APTES), before the use of glutaraldehyde (GLU), as a linker, through the imine bonds. The resulted enzymatic hybrid membrane reactors (EHMRs) were then thoroughly analyzed by using field-emission scanning electron microscopy (FE-SEM), contact angle goniometry, surface free energy analysis, X-ray diffraction (XRD), Fourier transform infrared (FT-IR) spectroscopy, attenuated total reflection (ATR), and energy-dispersive X-ray (EDX) spectroscopy. The study also looked into the impact of factors such as initial CRL concentration, storage conditions, and immobilization time on the EHMR's performance and activity, which were subsequently optimized. The results demonstrated that the CRLs covalently immobilized on the EHMRs displayed enhanced pH and thermal stability compared to those physically immobilized or free. These covalently immobilized CRLs could maintain over 60% of their activity even after 6 reaction cycles spanning 50 days. EHMRs are valuable biocatalysts in developing various industrial, environmental, and analytical processes.

Optimization of physical design for small long life Lead Cooled fast Reactor based on SARAX

The Offshore Fixed Lead-Cooled Reactor is a Small Long Life Lead Cooled Fast Reactor. In order to verify the rationality of the physical design and applicability of SARAX and the core equivalent model method to the corresponding reactor type, the calculation of the key physical parameters of the Offshore Fixed Lead-Cooled Reactor and the physical design characteristics of the core were investigated and compared with the Monte-Carlo code OpenMC. The initial physical design has been shown to meet the design requirement. The reactivity coefficient of the core during life were calculated and verified, which proved the rationality of the initial core design. In order to solve the problem of high radial power peak factor at end-of-life, analysis of radial fuel zoning was conducted and the core optimization was carried out. The calculation of the key physical parameters of the optimization schemes was conducted, which proved the rationality of optimization schemes.

Anammox process in anaerobic baffled biofilm reactors with columnar packings: Characteristics of flow field and microbial community

The enrichment of anammox bacteria is a key issue in the application of anammox processes. A new type of reactor － anaerobic baffle biofilm reactor (ABBR) developed from anaerobic baffle reactor (ABR) was filled with columnar packings and established for effective enrichment of anammox bacteria. The flow field analysis showed that, compared with ABR, ABBR narrowed the dead zone so as to improve the substrate transferring performances. Two ABBRs with different types of columnar packings (Packings 1 and Packings 2) were constructed to culture anammox biofilms. Packings 1 consisted of the single-form honeycomb carriers while Packings 2 was modular composite packings consisting of non-woven fabric and honeycomb carriers. The effects of different types of columnar packings on microbial community and nitrogen removal were studied. The ABBR filled with Packings 2 had a higher retention rate of biomass than the ABBR filled with Packings 1, making the anammox start-up period be shortened by 21.28%. The enrichment of anammox bacteria were achieved and the dominant anammox bacteria were Candidatus Brocadia in both R1 and R2. However, there were four genera of anammox bacteria in R2 and one genus of anammox bacteria in R1, and the cell density of anammox bacteria in R2 was 95% higher than that in R1. R2 has the advantage of maintaining excellent and stable nitrogen removal performance at high nitrogen loading rate. The results revealed that the packings composed of two types of carriers may have a better enrichment effect on anammox bacteria. This study is of great significance for the rapid enrichment of anammox bacteria and the technical promotion of anammox process.

On the Employment of a Chloride or Floride Salt Fuel System in Advanced Molten Salt Reactors, Part 2; Core Inventory, Fuel Burnup, and Salt Clean-Up System

Breed and Burn (B&B) fuel cycle in molten salt reactors (MSRs) qualifies this reactor type as one of the best candidates to be developed for the Gen-IV R&D program. This feature can be approached by employing a closed fuel cycle and application of a molten salt reactor as a spent nuclear fuel burner; the features promise sustainable and clean energy in the future. In this study, a complete package has been developed to calculate core inventory, fuel burnup, and salt clean-up systems of molten salt reactors during their lifetime. To achieve this, the iMAGINE-3BIC package (“iMAGINE 3D-Reg Burnup & Inventory Calculator package”) has been developed in MATLAB R2023a by employing a CINDER90 module of MCNPX 2.7 for burnup-calculation and multi-linear regression method (MLR). The package can estimate the core inventory (concentration of 25 actinides and 245 non-actinides elements) and the burnup of the reactor core during MSR lifetime (up to 100 years) while optimizing the computational resources (time, CPU and RAM), and it can even be hassle-freely executed on standalone PCs in an appropriate time due to its generous database. In addition, the salt clean-up module of the iMAGINE-3BIC package can be employed to evaluate the effects of the salt clean-up system on the above parameters over the MSRs’ lifetime. Finally, the iMAGINE-3BIC package has been applied to an iMAGINE reactor core design (University of Liverpool, UK—chloride-based salt fuel system) and an EVOL reactor core design (CNRS, Grenoble, France, fluoride-based salt fuel system) to evaluate and compare the performance of chloride/fluoride-based salt fuel MSRs from the point of burnup, core inventory, and salt clean-up systems. The results confirm that while a chloride-based salt fuel system has some advantages in less dependency on the salt clean-up system and fewer poisoning elements inventory, the fluoride-based system can achieve higher burnup during the reactor lifetime. The outcome of this study, along with the first part of this article, provides evidence to support the neutronic decision matrix as well as the pros and cons of employing chloride- or fluoride-based fuel systems in MSR cores.

Experimental investigation and prediction of CHF in wire-wrapped rod bundles

The wire-wrapped tight lattice fuel assembly is one of the options for small modular reactors. To clarify the characteristics of critical heat transfer for departure from nucleate boiling, experiments were conducted to investigate the critical heat flux in a wire-wrapped 19-rod bundle. The critical heat flux coincident with associated thermal–hydraulic parameters was obtained under typical pressurized water reactor conditions. Validation of data accuracy was performed to provide confidence in the experiment results. It was found that the critical heat flux in the wire-wrapped rod bundle is sensitive to the change in steam quality at some steam quality regions. Besides, the critical heat flux in wire-wrapped rod bundles has a similar reflection under the effects of local pressure, local mass flux, and steam quality. However, the current correlations tend to overestimate the critical heat flux for a wire-wrapped rod bundle. Hence, further development of KfK-3 correlations was proposed for better prediction of the critical heat flux in wire-wrapped bundles. This work is helpful for rod bundle designs of advanced pressurized water reactors.

Ion migration mechanism of electrochemical water softening in dual-chamber reactors and their performance for real circulating cooling water

Electrochemical water softening studies often use ion exchange membrane (IEM) reactors. However, their practical application is limited because of inevitable cathodic scaling. To overcome this challenge, one necessary approach is to understand the ion migration mechanism in the typical IEM reactor. In this study, we used operando visualization to reveal that the divider such as IEM or nylon nets was essential to confine the neutralization reaction between H+ and OH−. Ca2+ and Mg2+ may transfer from the anode chamber through the divider into the cathode chamber via electromigration. Using mesh electrodes instead of plate electrodes, the total hardness removal in the cathode chamber and anode chamber was 94.2% and 92.5%, respectively. The high removal rate was attributed to H2 microbubbles produced by cathodic water electrolysis, which drove OH− ions diffusion into solution and sequentially strengthened the nucleation of scale crystals in solution rather than on the cathode surface. On the basis of the above ion migration mechanism, the revolutionized reactor with mesh electrode module and nylon-net divider exhibited good performance in softening real circulating cooling water, and the total hardness removal exceeded 93.1% during 30 h running. These results open new horizons for improving the practicability of electrochemical water softening.

Fabrication Aspects and Performance Characterization of α-Al2O3/AlPO4 Based Sandwich Configuration Flow Channel Inserts and Coatings for High Temperature Liquid Metal Applications

Abstract Liquid metals (LMs) exhibit several key characteristics justifying their utilization as coolants and breeders for nuclear fusion reactors and advanced fission reactors. In fusion reactors, the LMs confront an exorbitantly high flow retarding force, due to the magneto-hydro-dynamics (MHD) effect, imposing significant demands on the pumping power and designs of ancillary coolant systems. Corrosion of structural materials leading to activated corrosion products and coolant chemistry control are some of the vital issues common to both fusion and fission reactors employing liquid lead (Pb) and its alloys. To address these concerns, different technological solutions such as flow channel inserts (FCIs) and high temperature compatible corrosion resistant coatings are being investigated to provide a chemical and/or electrical isolation between the LM and structural material for advanced reactors. In this study, three different prototype geometries (circular, square, and 90 deg bend) of steel-insulator-steel sandwich FCIs are fabricated for fusion reactor applications and an extensive characterization of the electrical insulation is performed over an operating temperature range of 100 °C–600 °C. Welding trials and pneumatic pressure tests up to 10 kg/cm2 (g) are performed on the assemblies to validate the electrical and mechanical integrity over typical fusion reactor operational regime. This paper presents detailed fabrication aspects along with quantitative estimations of insulation filling density, electrical insulation performance and, for the first time, a detailed systematic study of insulation degradation resulting from the combined effects of tungsten inert gas (TIG) welding, exposure to pressure and machining operations on these FCIs. The paper also provides critical details derived from the metallurgical examinations and visual observations from the destructive tests executed on the prototypes. Further, from an implementation perspective toward Lead-cooled Fast Reactors (LFRs), a preliminary feasibility assessment of the α-Al2O3/AlPO4 coating is performed through thin film deposition trials on planar and non-planar substrates followed by mechanical characterizations, such as coating thickness, surface roughness, adhesion strength and microhardness. Metallurgical analyses are presented and discussed to assess Pb ingress after 700 h of continuous exposure to molten Pb alloy at 300 °C–400 °C.

Subtle magnesium liberation of self-fabricated functional filler actuates highly efficient phosphorus removal from source-separated urine by SBBR.

Domestic wastewater source-separated treatment has attracted wide attention due to the efficiency improvement of sewage treatment systems, energy saving, resource reuse, and the construction and operation cost saving of pipeline networks. Nonetheless, the excess source-separated urine still demands further harmless treatment. Sequencing batch biofilm reactor (SBBR), a new type of composite biofilm reactor developed by filling different fillers into the sequential batch reactor (SBR) reactor, has higher pollutant removal performance and simpler operation and maintenance. However, the phosphorus removal ability of the SBBR filling with conventional fillers is still limited and needs further improvement. In this study, we developed two new fillers, the self-fabricated filler A and B (SFA/SFB), and compared their source-separated urine treatment performance. Long-term treatment experimental results demonstrated that the SBBR systems with different fillers had good removal performance on the COD and TN in the influent, and the removal rate increased with the increasing HRT. However, only the SBBR system with the SFA showed excellent PO43--P and TP removal performance, with the removal rates being 83.7 ± 11.9% and 77.3 ± 13.7% when the HRT was 1 d. Microbial community analysis results indicated that no special bacteria with strong phosphorus removal ability were present on the surface of the SFA. Adsorption experimental results suggested that the SFA had better adsorption performance for phosphorus than the SFB, but it could not always have stronger phosphorus adsorption and removal performance during long-term operation due to the adsorption saturation. Through a series of characterizations such as SEM, XRD, and BET, it was found that the SFA had a looser structure due to the use of different binder and production processes, and the magnesium in the SFA gradually released and reacted with PO43- and NH4+ in the source-separated urine to form dittmarite and struvite, thus achieving efficient phosphorus removal. This study provides a feasible manner for the efficient treatment of source-separated urine using the SBBR system with self-fabricated fillers.

Failure simulation of nuclear pressure vessel under LBLOCA scenarios

This paper presents the finite element deformation and failure simulation of a typical Korean high-power reactor vessel under a severe accident characterized by large break loss of coolant (LBLOCA) with in-vessel retention of molten corium through external reactor vessel cooling (IVR-ERVC) conditions. Temperature distributions calculated using Modular Accident Analysis Program Version 5 (MAAP5) as thermal boundary conditions were used, and ABAQUS thermal and structural analyses were performed. After full ablation, the temperature of the inner surface in the thinnest section remained high (920 °C), but the stress remained relatively low (less than 6 MPa). At the outer surface, the stress was as high as 250 MPa; however, the resulting plastic strain was small owing to the low temperature of 200 °C. Variations in stress, inelastic strain, and temperature with time in the thinnest section suggest that the plastic and creep strains are saturated owing to stress relaxation, resulting in low cumulative damage. Thus, the lower head of the vessel can maintain its structural integrity under LBLOCA with IVR-ERVC conditions. The sensitivity analysis of internal pressure indicates the occurrence of failure in the thinnest section at an internal pressure >9.6 MPa via local necking followed by failure due to high stresses.

Analytic Error Analysis of the Partial Derivatives Cross-Section Model—I: Derivation

Accurate assessment of uncertainties in cross-section data is crucial for reliable nuclear reactor simulations and safety analyses. In this study, we focus on the interpolation procedure of the partial derivatives (PD) cross-section model used to evaluate nodal parameters from pregenerated multigroup libraries. Our primary objective is to develop a systematic methodology that enables prediction of the incurred errors in the cross-section model, leading to the development of optimal case matrices, more efficient cross-section models, and informed case matrix construction for reactor types lacking substantial data and experience. We make progress toward this objective through a rigorous analytic error analysis enabled by the derivation of error expressions and bounds for the PD model based on the discovery that the method is a form of Lagrange interpolation. Our investigations reveal distinct outcomes depending on the chosen cross-section functionalizations, achieved by identifying the sources of error. These error sources are found to include interpolation error, which is always present, and model form error, which is a property of the supplied case matrix. We show that simply increasing grid refinement through the addition of branches may not always lead to decreased cross-section errors, particularly in cases where the model form error predominantly contributes to the total error. We present numerical results and verification in a companion paper, showing these different error characteristics for various cross-section functionalizations. Although applied to current light water reactor environments, our methodology offers a means for advanced reactor analysts to develop case matrices with quantified error levels, advancing the goal of a general methodology for robust two-step reactor analysis. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multilattice problems, and investigating historical effects within the macroscopic depletion model.