Subcritical Core Research Articles

Neutronic simulation of Traveling Wave Reactor (TWR) core in multi-cycles using Monte Carlo method

Abstract An ingenious design, Traveling Wave Reactor (TWR) has been suggested for full exploitation of uranium resources in next generation of nuclear reactors. This design involves the slow propagation of a nuclear fission wave through a long initially subcritical core and the transmutation of nuclear fuel. It has been widely proven that the initiation and propagation of fission waves are feasible prompting the Terra Power Company to conduct preliminary commercialization studies on this project. In equilibrium state, the shapes of the neutron flux, nuclide densities and power density distribution remain constant but the burning region moves in axial (or radial) directions. In this case the in situ fissile material production and consumption drives the operation. Only natural or depleted uranium is required for fresh fuel region. However, in equilibrium state, the burning region contains a spectrum of fission products as well as higher actinides whose are not easily available for initial TWR core construction. One solution is based on the use of enriched uranium in the first cycle to ignite the fission wave and then employment of the composition in subsequent cycles up to the equilibrium state. The main objective of this work is the feasibility study of forming a fission wave as well as the neutronic analysis of a Gas-Cooled Traveling Wave Reactor in various cycles up to the equilibrium one. The MCNP Monte Carlo code was utilized for the analysis of criticality and burn-up calculation. In each cycle, the axial fresh fuel loading and spent fuel discharge, were subjected to analysis. Results showed that the equilibrium state can be obtained by using special arrays of absorbers, from the third cycle where the shape of neutron flux and the power density distribution in axial direction remain unchanged.

Flux Flattening Large Heavy Water Power Reactors with Accelerator-Driven Photoneutron Source

Flux flattening and power uprating of large heavy water power reactors (HWRs) are demonstrated as an application of an accelerator-driven photoneutron source (ADS) in the ADS-CANDU concept where an array of electron linear accelerators is configured around the periphery of a subcritical CANDU-6 core. The localized ADS generated through (e−,γ,n) reactions in the HWR lattice perturbs the reactor power distribution by increasing the power of low-power bundles and depressing the power at the core center relative to the fundamental mode power distribution. Gross power uprating is feasible when the system is near critical, but the ADS array consumes tens of megawatts electric exceeding the power gained by a factor of more than 2 for the conservative ADS performance specifications assumed in the analysis. Several important challenges of fixed-source Monte Carlo simulations of near-critical multiplying media are investigated including severe load imbalance issues with distributed-memory parallel computing architecture and correlated local tallies in nonanalog (implicit absorption) Monte Carlo radiation transport. All subcritical fixed-source simulations in the study readily exceed the default random number stride used in most production Monte Carlo codes, and the stride exceedance causes both bias in local tally results (bundle powers) and spatial autocorrelation of these errors/biases in the large core. A legacy stride exceedance is critically reviewed, and the conclusions and subsequent interpretations of those conclusions are rejected. Several classes of radiation transport Monte Carlo problems are likely to be susceptible to stride exceedance, and this issue needs to be promptly addressed by the Monte Carlo analyst and code developer communities.

Analysis of the performance of driver MOX fuel in the MYRRHA reactor under Beam Power Jump transient irradiation conditions

This work focuses on the performance analysis of driver fuel pins under transient irradiation conditions in the MYRRHA reactor, which must be considered besides the normal operation towards the design optimization and licensing of the facility. The considered transient scenario is a Beam Power Jump (BPJ) caused by a trip of the MYRRHA accelerator coupled to the sub-critical reactor core. Based on the outcomes of the analysis of the nominal MYRRHA irradiation - NED 386 (2022) 111581, the impact of this over-power scenario on the pin response is investigated both at the beginning and at the end of irradiation as the most critical moments for the fuel maximum temperature and for the potential fuel-cladding mechanical interaction, respectively. The simulation results are achieved with the TRANSURANUS fuel performance code equipped with advanced models for thermal–mechanical properties of U-Pu mixed-oxide (MOX) fuels, for inert gas behaviour and for the specific mechanical response of DIN 1.4970 cladding. The comparison with design limit criteria adopted highlights the safety of the MYRRHA fuel pins under irradiation, complying with satisfactory margins even considering the occurrence of BPJ transients.

Experimental Analyses of Capture Reaction Rates for Epithermal and Resonance Neutrons in Source-Driven Subcritical Cores

Neutron irradiation experiments are carried out in source-driven subcritical cores with high-energy neutrons generated by spallation reactions between a 100-MeV proton beam and a lead-bismuth target at the Kyoto University Critical Assembly. The main objective of the experiments is to investigate the effect of epithermal and resonance neutrons on the accuracy of capture reaction rates with respect to a subcriticality variation. Activation foils of copper, indium, tantalum, and tungsten are employed to obtain capture reaction rates for epithermal and resonance neutrons by applying the cadmium difference method. Also, the applicability of the foils for the measurement of the reaction rates for epithermal and resonance neutrons is substantiated in the critical irradiation experiments performed prior to the subcritical experiments. The subcritical experiments are conducted with three different subcriticalities by changing the control rod insertion pattern. The measured reaction rates are compared with the calculated values obtained by the Monte Carlo code MVP with JENDL-4.0, and the ratio of the calculation and experiment values of the reaction rates shows equivalent values within the 1σ errors regardless of a difference in the subcriticality. The compared results indicate that the numerical analyses have a consistent accuracy of reaction rates in epithermal and resonance energy regions for a subcriticality variation in source-driven subcritical cores.

Study on the basic of spallation target for accelerator driven system

A study on the basic of spallation target for Accelerator Driven System (ADS) has been done. ADS is a subcritical assembly combined with a high-power proton accelerator. In the center of the subcritical assembly, there is a spallation target for producing primary neutrons that will be multiplied by the subcritical core surrounding it. The neutrons are produced via spallation reaction which occurs when the spallation target is bombarded by high-energy protons. The spallation target has to be designed so that the number of neutrons escaping from the target per incident proton is maximum and the power density deposited on it is high (~1 MW/litter). The spallation target can be made of a solid or liquid material such as Pb, Hg, U, W, Ta, or Pb-Bi which are the most preferred materials for spallation targets. But, today Pb-Bi is the reference material for ADS applications. The spallation target has a large thermal load due to the conversion of about 10 MW proton into a neutron. Therefore, the target needs a cooling system; there are two options that can be considered i.e., cooling by means of the subcritical reactor primary system coolant and cooling by means of an independent loop.

Implementation and optimization of WDT algorithm on IMPC-Neutron and comparison of efficiency of various algorithms

In Monte Carlo code, the use of Delta-tracking algorithm can greatly improve the computational efficiency, but the existence of virtual collision will waste computing resources because the virtual collision introduced by Delta-tracking algorithm does not make any contribution to the statistical results. The Weighted Delta-tracking algorithm makes the virtual collision contribute to the statistics and improves the efficiency of Delta-tracking algorithm. We implemented Weighted Delta-tracking algorithm into the IMPC-Neutron code, then we optimized the Weighted Delta-tracking algorithm to improve its computational efficiency, and analyzed the effects and limitations of Weighted Delta-tracking algorithm in different assemblies. The optimal parameters of Weighted Delta-tracking algorithm are tested in the full reactor models of PWR core and sub-critical fast reactor core. Finally, the calculation efficiency of various neutron transport methods is compared by using IMPC-Neutron.

Application of the improved quasi-static coupled probability theory method to transient safety analysis of an experimental facility

The accelerator-driven sub-critical system is driven by external neutron sources, which are generated by the spallation reaction and maintain the stable operation of the sub-critical core, while the external neutron source increases the complexity of reactor neutron kinetic processes. This article focuses on simulation analysis of neutron space–time kinetics with a dynamic analysis code, which is developed based on the improved quasi-static approximation and Monte Carlo neutron transport method. The amplitude function and shape functions are solved to achieve the dynamics simulation process. Then, the transient responses of beam interruptions and reactivity insertions are calculated and analyzed for an experimental facility. To further verify the correctness and reliability of dynamic behavior, the simulation results are compared with experimental values, and the results show that the normalized neutron fluxes varying with time are in good agreement with the corresponding values. It can be concluded that the improved quasi-static coupled probability theory method can be used to solve the neutron space–time kinetic problem of the experimental facility, and the results are reliable.

Gamma-Ray Spectrum Measurement from Capture Reactions of Uranium-238 for Thermal and Resonance Energy Neutrons

γ-ray spectrum from the capture reaction of 238U is measured for the thermal and resonance energy neutrons at KURNS-LINAC facility. Prominent primary γ ray of 3.297 MeV listed in CapGam is not observed for the thermal energy neutrons. The measured γ-ray spectrum is varied with neutron energy so that we can expect neutron spectrum inducing 238U(n,γ) reactions in critical / subcritical cores could be deduced by the γ-ray spectroscopy for the cores. Preliminary deduced ratio of 4.060 MeV γ-ray emission to capture for the thermal energy neutron agrees with CapGam so that the deduction scheme is considered adequate.

Deep Subcriticality Determination Using the Source Jerk Integral Method in the SALMON Program

The Source Jerk Integral (SJI) method has been extensively used to determine the subcriticality in VENUS-F zero-power experiments since 2012. The obtained results were in the range from −5 $ to about −20 $ and concerned the subcriticalities of accelerator-driven system MYRRHA mockup cores. Within the SALMON program, which is dedicated to the safe loading procedure of pressurized power reactors, five subcritical core configurations were assembled and studied in the VENUS-F reactor in 2019. These cores simulated the loading process in inverse mode: from more reactive to deep subcritical. The subcriticality of five variants of the SC11 VENUS-F core was changed in steps from −20 $ to about −100 $ by replacing the fuel assemblies with lead reflector assemblies. The subcriticality levels were determined with the pulsed neutron source (PNS) and SJI methods. The GENEPI-3C deuterium accelerator coupled with VENUS-F was used as an external neutron source. The results of the measurements obtained with the SJI method are presented in this paper. Time-dependent Monte Carlo calculations were performed to simulate the SJI experiments and to determine spatial-energy correction factors. Static Monte Carlo simulations were performed to calculate neutron spectra and reactivity. The results of the measurements (both SJI and PNS) are compared with the static MCNP calculations.

The feasibility study of the Sub-criticalization of the Holos small modular reactor driven by an electron accelerator

Small modular reactors (SMRs) and accelerator-driven subcritical reactors (ADSs) have many potentials, which have attracted the attention of many researchers. The present study proposes the sub-criticalization of a small portable reactor to increase its safety. The operation of the Holos mobile power generator is examined at the subcritical level to produce cost-effective power. The UO2-fueled Holos subcritical core is modelled by the MCNPX2.6 code. The external photoneutron source was considered with a 100 MeV, 1 mA electron accelerator. The Holos simulated core is discussed in the subcritical level to evaluate the neutronic performance and safety parameters. Power distributions were compared inside the Holos simulated core in critical and subcritical levels. The carried-out calculations show that in addition to the subcritical level operation, negative reactivity coefficient in the Holos subcritical core ensures the core inherent safety. Results show that the neutron and photon flux magnitudes within the Holos core in the subcritical level are greater than the critical state.

Inherent Safety Characteristics of Lead Bismuth Eutectic-Cooled Accelerator Driven Subcritical Systems

An accelerator driven subcritical system (ADS) is a new nuclear energy system which could not only produce clean energy but also incinerate nuclear waste. In this paper, inherent safety analysis of an ADS is performed with neutronics and thermal-hydraulics coupled code named ARTAP. Five typical accidents are carried out, including the cases of proton beam interruption, transient overpower, reactivity insertion, loss of flow, and loss of heat sink. The transient simulations are performed in the average channel and the hottest channel of the fuel pin in the ADS core. The simulation results for beam interruption show that the highest temperature of the pellet is in the middle of the fuel element in the average channel, while the peak temperature of the cladding is in the top of the fuel element. After the beam is interrupted for 20s, the maximum temperature drops at the fuel center, the cladding inner surface, and the outlet coolant in the hottest channel are 644.46K, 162.27K, and 136.42K respectively. For transient overpower accidents with the increase of beam intensity, the maximum temperature of the fuel and the cladding are below the safety limit. Concerning the reactivity insertion accident, it is found that the ADS has good inherent safety and its margin of criticality safety is large. The calculation results for loss of flow show that the power drop is small due to low sensitivity of the subcritical core to negative reactivity feedback, and the maximum temperature of the cladding reaches 1726K, which means the fuel element would rupture. However, the power and the temperatures of fuel, cladding, and coolant could decrease quickly to the safety level after the proton accelerator is cut off under a loss of flow accident. The results also show that the peak temperature of the cladding is lower than the safety limit under a loss of heat sink accident. The present simulation results reveal that the ADS has a remarkable advantage against severe accidents. It also implies that its inherent safety characteristics could ensure reactor shutdown by cutting off the proton beam after accidents occur.

A « Water Motor » With an Accelerator, Water With High Natural Radioactivity and Fission

The concept relies on the most recent innovations in laser spallation of neutrons altogether with the naturally radioactive waters available in profusion to develop fission power and propel a vehicle. It consists in a subcritical fission core of a new type designed to make use of the small but existing period in which low-weight radioactive elements, after neutron capture become fissile.

Comparing dynamic and quasi-static methods for rod-drop transients with TRIPOLI-4®

Since dynamic reactivities measured on actual reactors are significantly impacted by delayed nuclear data and technological uncertainties, it is of major importance to validate at first the methodology of interpretation against state-of-the-art simulation. In this way, we set up a reference simulation of rod-drop transients with a subcritical core from 3 to 16 $ in the CABRI reactor using the dynamiafforganizationc capabilities of the Monte-Carlo code TRIPOLI-4®. With this tool, the fission-shape evolution and the reactivity are computed for each time step. These quantities are then compared to the output of static stochastic methods based on eigenvalue computations and the Modified Source Method (MSM) to validate the hypotheses of those methods. There is a reactivity discrepancy of 2 % between the MSM model and the dynamic simulation. The fission shape is predicted with a maximum of 2 % discrepancy by the MSM method. This is significantly lower than the direct comparison to the fundamental mode, which proves the interest of a constant-delayed source hypothesis for a quasi-static approach. The nature of the rod-drop (instant or ramp-like) does not influence the fission shape and reactivity values so much, confirming the validity of the prompt-drop hypothesis. The sensitivity of reactivity to kinetic parameters is limited. These results contribute to the identification of the validity domain of the MSM method. Hypotheses investigation and sensibility studies produced pave the way to even better experimental interpretations.

Beam-target configurations and robustness performance of the tungsten granular flow spallation target for an Accelerator-Driven Sub-critical system

The dense granular flow spallation target is a new target concept proposed for an Accelerator-Driven Sub-critical (ADS) system. In this paper, the beam-target configurations of a tungsten granular flow target for the ADS with a thermal power of 1 GW is explored. The beam profile options using different scanning methods are discussed. The critical geometry parameters are adjusted to investigate the performance of the granular target from the aspects of neutron efficiency, stability and temperature distribution in target medium. To figure out how the target under accident conditions would behave, different clogging conditions are induced in the simulation. The dynamic processes are analyzed and some important parameters such as abnormal temperature rise and beam cutoff time window are obtained. The response of the sub-critical reactor to a clogging accident is also investigated. It is indicated that the monitoring of the granular flow by the neutron detectors in the sub-critical core will be effective.

On the calculation of neutron sources generating steady prescribed power distributions in subcritical systems using multigroup X,Y-geometry discrete ordinates models

In this paper a methodology is described to estimate multigroup neutron source distributions which must be added into a subcritical system to drive it to a steady state prescribed power distribution. This work has been motivated by the principle of operation of the ADS (Accelerator Driven System) reactors, which have subcritical cores stabilized by the action of external sources. We use the energy multigroup two-dimensional neutron transport equation in the discrete ordinates formulation (SN) and the equation which is adjoint to it, whose solution is interpreted here as a distribution measuring the importance of the angular flux of neutrons to a linear functional. These equations are correlated through a reciprocity relation, leading to a relationship between the interior sources of neutrons and the power produced by unit length of height of the domain. A coarse-mesh numerical method of the spectral nodal class, referred to as adjoint response matrix constant-nodal method, is applied to numerically solve the adjoint SN equations. Numerical experiments are performed to analyze the accuracy of the present methodology so as to illustrate its potential practical applications.

Determination of Reactor Parameters for Different Subcritical Configurations of the Philippine Research Reactor-1 TRIGA Nuclear Fuel

The Philippine Research Reactor-1 (PRR-1) will be revived as a subcritical assembly for training, education, and research (SATER) in the field of nuclear science and technology. SATER will utilize the existing slightly irradiated nuclear fuel rods that have been maintained in the PRR-1 facility for more than 30 years. A subcritical arrangement for the fuel rods was chosen considering the inherent safety of this configuration. In this paper, we calculate relevant reactor parameters that characterize different annular and hexagonal subcritical configurations of 44 PRR-1 fuel rods. These parameters include the neutron multiplication factor ( ), the effective delayed neutron fraction ( ), and the mean neutron generation time ( ), which are essential quantities to describe reactor behavior. Calculations were performed using the well-validated Monte Carlo radiation transport code MCNP5 v.1.6 together with the ENDF/B- VII.1 evaluated nuclear data library. The maximum value is at 4.0 cm pitch for the chosen annular arrangement, while the maximum value is at 4.3 cm pitch for the chosen hexagonal arrangement. For these configurations, the reactor kinetic parameters were and for the annular arrangement, while and for the hexagonal arrangement. Results demonstrate that with 44 fuel rods, different fuel arrangements remain subcritical with a subcriticality margin that is at least or maximum of 0.97. The key reactor performance characteristics determined in this study can aid in the analysis of transient behavior and safety assessment of subcritical core configurations with TRIGA fuel rods. Our results provide support in expanding the utilization options for irradiated TRIGA fuel rods, even for other TRIGA facilities

Preliminary Multi-Physics Performance Analysis and Design Evaluation of UO2 Fuel for LBE-Cooled Subcritical Reactor of China Initiative Accelerator Driven System

The China initiative Accelerator Driven System (CiADS) and the corresponding lead-bismuth eutectic (LBE) cooled subcritical reactor, as the research subject of one of the major national science and technology infrastructure projects, are undertaken by the Institute of Modern Physics-Chinese Academy of Sciences (IMP-CAS). And in the first phase, UO2 fuels will be loaded in the subcritical core to test the coupling technology and achieve a long-term steady operation. A brief description of CiADS subcritical reactor, fuel assembly and fuel element are presented here, and a multi-physics performance analysis and design evaluation of CiADS UO2 fuel are carried out by means of the FUTURE code. FUTURE is a fuel performance analysis code to evaluate the synergy of phenomena occurring in the fuel element and their impact on the fuel design improvement for the liquid metal fast reactor, which was developed jointly by IMP-CAS and Xi’an Jiaotong University (XJTU). In this paper, the FUTURE code was modified and updated focusing on characteristics of CiADS fuels. Relocation and densification models were added. Results of the hottest fuel element, mainly concerning the thermo-mechanical behaviors, are discussed concerning both fuel and cladding performance on the basis of indicative design limits. According to the preliminary design, the CiADS UO2 fuel exhibits good performance, and the main safety parameters are far below the indicative limits. The Fuel Cladding Mechanical Interaction (FCMI) is not very serious, and the permanent cladding strains and Cumulative Damage Fraction (CDF) are small and even negligible thanks to the low level of fuel temperature and corresponding stress. However, some critical issues may still exist, especially on LBE corrosion near the coolant inlet, where protective oxide layers are very thin from BoL to EoL. The modeling is useful for providing feedback to the conceptual design of the CiADS LBE-cooled subcritical reactor and the update of FUTURE code.

Proposal and applicability of estimated criticality lower-limit multiplication factor using the bootstrap method

ABSTRACT To judge whether an application system is a subcritical state or not based on numerical results of the effective neutron multiplication factor , an evaluation method of the estimated criticality lower-limit multiplication factor (ECLLMF) using the bootstrap method is newly proposed. By utilizing numerical results of for critical benchmark-problems that are selected depending on neutronic similarity to the application system, the ECLLMF should be carefully and conservatively estimated based on uncertainties of due to a criticality safety analysis code, experimental uncertainty, and covariance matrix of the nuclear data library. Furthermore, the frequency distribution of for these problems does not necessarily obey an ideal normal distribution. Using a resampling technique called ‘bootstrap method,’ the proposed method can reasonably estimate the ECLLMF considering the uncertainties and nuclear data-induced correlation between each critical benchmark-problem without the assumption of normality. To investigate the applicability of the proposed method, the approach-to-criticality experiment was carried out at the Kyoto University Critical Assembly (KUCA). Comparison of numerical results of and the ECLLMF using the bootstrap method indicated that the proposed method was able to judge an actual subcritical core as subcritical state.

Spent Nuclear Fuel Incineration by Fusion-Driven Liquid Transmutator Operated in Real Time by Laser

We introduce a concept of laser-generated neutrons to transmute transuranic elements separated from spent nuclear fuel (SNF) and dissolved in a molten salt to form a subcritical core whose liquid state allows and facilitates safety, laser irradiation, and monitoring of chemical and physical properties. In this transmutation concept (the transmutator), the neutrons are generated via beam-target fusion whereas the beam is created by laser irradiation of nanometric foils through the Coherent Acceleration of Ions by Laser (CAIL) process. This relatively low deuteron energy is catapulted by fusion and eventually by secondary fission processes. The combination of the use of molten salt and laser allows us to introduce rapid feedback control of the system’s operation. The transmutator is an integral part of the partitioning and transmutation concept whereby the radiotoxicity of SNF is significantly reduced together with the required storage duration and volume. To enable this transmutator, we introduce integrated ideas and processes in the areas of lasers, neutronics, first-wall material, and chemistry.

Comparison of spallation and fusion neutron sources in fuel transmutation and regeneration

In this work, a comparison between the capabilities of a spallation source and a fusion source in the burnup of reprocessed fuels and in the regeneration of thorium was carried out. We have performed Monte Carlo simulations of a sub-critical core loaded with thorium and reprocessed fuel under irradiation of two different neutron sources. Two different fuels reprocessed by the GANEX technique were evaluated, one spiked with depleted uranium and the other one spiked with thorium. The aim is to investigate the neutronic behavior of thorium and reprocessed fuels under different neutron sources and analyze the fuel evolution during 10 years of burnup.