Monte Carlo Code RMC Research Articles

MC/sub-channel coupling for steady state and transient simulation of Xi’an Pulsed Reactor

The Monte Carlo (MC) code RMC and sub-channel code CTF are coupled for Xi’an Pulsed Reactor (XAPR) pulse and depletion simulation. A python script is developed to handle data exchange through files. $3.45 pulse and $2 pulse are simulated with the pulsed state core. The pulse peak power and the Full Width at Half-Maximum (FWHM) results are compared with experiments as a validation and good agreement is achieved. Detailed 3-D power and temperature distributions are also obtained. Results show that the core power peak is close to the pulse rod where the reactivity is introduced. The radial power peak of each rod is at the boundary because of the self-shielding effect. The rod temperature distribution follows the same trend with the power, and the coolant temperature is not changed during the pulse period of about 0.12 s, which suggests that the heat transfer plays a negligible role in such a short time. For the steady state core, depletion simulation is carried out for the lifetime of the first fuel cycle of 120 Effective Full Power Days (EFPD). Validation is done by calculating the temperature distribution and the differential worth of the regulating rod at 0 EFPD, which both agree well with experiments. Results show that the power distribution is almost unchanged over time, only slightly more flat, indicating the material is not greatly depleted. The temperature distribution of the core generally agrees with the power distribution, except the radial temperature peak of each rod is at the center because heat is conducted outwards at steady state. Detailed coolant temperature distribution is obtained thanks to the utilization of CTF. Temperatures at the assembly boundary and near the central water chamber is noticeably lower than the other part, which is not shown in the parallel multi-channel models.

Research on the calculation method of sensitivity coefficients of reactor power to material density based on Monte Carlo perturbation theory

The ability to calculate the material density sensitivity coefficients of power with respect to the material density has broad application prospects for accelerating Monte Carlo-Thermal Hydraulics iterations. The second-order material density sensitivity coefficients for the general Monte Carlo score have been derived based on the differential operator sampling method in this paper, and the calculation of the sensitivity coefficients of cell power scores with respect to the material density has been realized in continuous-energy Monte Carlo code RMC. Based on the power-density sensitivity coefficients, the sensitivity coefficients of power scores to some other physical quantities, such as power-boron concentration coefficients and power-temperature coefficients considering only the thermal expansion, were subsequently calculated. The effectiveness of the proposed method is demonstrated in the power-density coefficients problems of the pressurized water reactor (PWR) moderator and the heat pipe reactor (HPR) reflectors. The calculations were carried out using RMC and the ENDF/B-VII.1 neutron nuclear data. It is shown that the calculated sensitivity coefficients can be used to predict the power scores accurately over a wide range of boron concentration of the PWR moderator and a wide range of temperature of HPR reflectors.

Development of CAD geometry converting and correction method in Monte Carlo code RMC

For reactors with complex geometric structures such as fusion reactors, modeling work is relatively complex. The traditional Constructive Solid Geometry (CSG) method in Monte Carlo particle transport simulations shows limitation when constructing the complex geometry accurately. In order to use the CAD models, the Direct Accelerated Geometry Monte Carlo (DAGMC) has been proposed and implemented in many Monte Carlo codes. In the typical workflow of DAGMC method, the commercial mesh generation software Trelis is used. In this work, the DAGMC function was implemented in the Monte Carlo code RMC, and three modifications were also developed in the DAGMC function of RMC. Firstly, a workflow of generating the DAGMC mesh model was proposed using the open-source scripts occ_faceter instead of Trelis. Secondly, a gap correction algorithm was proposed to solve the errors in particle transport process, which is resulted from the existence of gaps between adjacent volumes in the CAD model generated by occ_faceter. Thirdly, the DAG-CSG hybrid geometry method was also developed, which combines the DAG and CSG geometry to construct the geometry more efficiently, and the verification analyses were carried out on the three-dimensional fuel assembly models. Finally, the CAD geometry of the FNG-ITER model was constructed and the developed DAG-RMC was applied to the FNG-ITER benchmark, further verifying the correctness and reliability of the developed DAGMC method.

Burnup-control drum coupling characteristics investigation of lead–bismuth eutectic-cooled solid reactor

As an advanced research tool, neutronics and thermal-hydraulics coupling have a wide range of promising applications in the field of nuclear energy. This paper develops a burnup-control drum coupling code based on the Monte Carlo code RMC and the computational fluid dynamics (CFD) program STAR-CCM +. The dynamic adjustment of the control drums' position and more realistic prediction of reactor neutronics and thermal-hydraulics is achieved by updating the nuclide density, solving the control drum value function and updating the neutronics model in the process of burnup calculation. The core of a lead–bismuth-cooled solid reactor was also studied to investigate the neutronics and thermal-hydraulics properties of the solid core when the effective multiplication factor was kept at about 1.0, and the core's power and temperature variation patterns during the lifetime were obtained. The results of the study show that the simulation of the coupling code achieves the design purpose. In addition, the solid core's maximum fuel and cladding temperatures decrease with the deepening of the burnup.

Concept design and neutronics analysis of a heat pipe cooled nuclear reactor with CERMET fuel

Special off-grid power generations require the energy system to be reliable and compact. The heat pipe cooled reactor (HPR) is passively safe and highly modular, and is well suitable for energy demands ranging from a few kW to several MW. This study proposes a compact HPR design in which the ceramic metal composite (CERMET) fuel is used (HPR-CF). The CERMET fuel has advantages such as high temperature resistance and thermal conductivity. The fuel assembly using the CERMET fuel contains 6 heat pipes and fuel blocks with the hexagonal prism shape. The HPR-CF consists of 36 CERMET fuel assemblies containing 216 lithium heat pipes, 12 control drums, 1 safety control rod and peripheral beryllium dioxide reflector, all of which are mounted in a reactor vessel. The Monte Carlo code RMC is used to calculate the neutronics characteristics. The excess reactivity of the HPR-CF reactor is sufficient for operating at high temperature and 3MWt for over 3000 days. The power distribution and the criticality safety are calculated and discussed. The results show the neutronics availability of the HPR-CF design.

A novel method for calculating annular fuel cell resonance effective temperature

Annular fuels can increase the power density of reactors because of their double-sided cooling design, which is of great significance to the miniaturization and long-life operation of pressurized water reactors. In this study, a thermal–hydraulic analysis code named Thermal-Hydraulic Code of Annular Fuel with Single channel (THCAFS) was developed for annular fuels, and a calculation model for the resonance effective temperature of annular fuel cells was established. An annular fuel cell of a four-loop pressurized water reactor (PWR) designed by Westinghouse company was used as the calculation object, and the numerical results of THCAFS were compared with those of existing sub-channel codes such as VIPRE-01, TAFAX, and NACAF. Meanwhile, the Monte Carlo code RMC was used to simulate the radial power distribution and burnup process of the annular fuel, and its thermodynamic behavior was simulated using the self-developed code THCAFS. The radial power distribution, nuclide density variation, and cell temperature field under different burnup levels were also obtained, and the reaction rate equivalence was used instead of the effective resonance integral to investigate the calculation method used for resonance effective temperature of the annular fuel cell. The results show that THCAFS can be preliminarily applied to annular fuel designs and thermal–hydraulic analysis, while the effective temperature calculation method can provide important reference values for studying the resonance effective temperature of annular fuels.

A better hash method for high-fidelity Monte Carlo simulations on nuclear reactors

With the increasing demand for high-fidelity nuclear reactor simulations, the acceleration of Monte Carlo particle transport codes is becoming a core problem. One of the bottlenecks is locating millions or even billions of cells and fetching their associated parameters in the repeated geometry structure. Typically, Monte Carlo codes utilize a hash function to accelerate the cell locating and parameter indexing process. Specifically, they use the “cell vector → hash → parameter” method to accelerate the direct “cell vector → parameter” method. In this work, we propose a better hash method based on the Cyclic Redundancy Check (CRC) mechanism, which has been mathematically proven to be efficient and produce fewer hash collisions. Experimentally, this new hash method has been compared with some other hash functions and showed its superiority in terms of the calculation speed and collision probabilities. This hash method has been integrated into the Reactor Monte Carlo code RMC and worked well in practical applications.

Towards optimized designs for control rod absorbers with a high-fidelity simulation method implemented in the RMC code

A high-fidelity simulation method of the control rod absorbers is implemented in the Monte Carlo code RMC. For rare-earth absorbers and B4C, detailed calculations and analyses are conducted for neutronics and depletion characteristics. Three kinds of optimized control rod absorbers are proposed with higher reactivity worth and favorable burnup stability. In these new designs, the composite absorbers possess higher reactivity worth and only average 20% loss of reactivity worth at the end of cycle (EOC). The enriched absorbers have better neutron absorbing capacity and more stable radiation resistance, and the loss of reactivity worth of enriched B4C reduces from 90% to only 7.42% at EOC. For mixed absorbers, the best properties are found for the Dy and B4C mixture when the proportion of Dy is about 60%. The coupling of ZrH2 and Hf achieves a better control efficiency, but unfortunately the loss of reactivity worth increases at EOC.

Analysis of Th and U breeding in a heat pipe cooled traveling wave reactor

Introduction: Heat pipe cooled traveling wave reactor (HPTWR) is a newly proposed heat pipe reactor. The HPTWR can achieve the low enrichment of loaded fuel, small reactivity swing, and long-term continuous operation for the power supply of decentralized electricity markets. Due to the excellent breeding capability of the HPTWR, the Th fuel is also added into the breeding fuel region of the reactor to achieve the Th-U fuel cycle in this work.Methods: The Monte Carlo code RMC is used to obtain the reactivity swing, propagation of axial power peak, burnup, and productions of bred fissile nuclides for the HPTWR with Th and U fuels.Results and Discussion: The results indicate that the HPTWR with 13.6% 235U enrichment of ignition fuel and 20% 235U enrichment of breeding fuel can continuously operate for 18.1 years without refueling when the mass fraction of 232Th in heavy metals of breeding fuel region is 33%. The propagation velocity of axial power peak and total burnup for the HPTWR with Th and U fuels is about 0.5525 cm/years and 24.72 GWd/THM during the 18.1 years operation respectively. The corresponding productions of bred 239Pu, 241Pu and 233U are about 212.99 kg of 239Pu, 0.19 kg of 241Pu and 81.58 kg of 233U at the end of cycle (EOC) respectively. The obtained results in this study demonstrate that the HPTWR can achieve the Th fuel breeding in the case of the low 235U enrichment loading (≤ 20%).

An internal coupling method between neutronics and thermal-hydraulics with RMC and CTF

To tackle the high-fidelity multi-physics coupling challenge in nuclear reactors, an internal coupling method was proposed and implemented to closely couple the neutron transport Monte Carlo code RMC and the sub-channel thermal-hydraulics solver COBRA-TF (CTF) using direct memory data transfers. In this coupling system, fixed-point Picard iteration scheme and Gauss-Seidel iteration method were implemented and evaluated. Two acceleration algorithms were proposed and both proved effective, including the hybrid MPI/OpenMP parallelism scheme and the asymptotic batch coupling method. The coupling system was validated against the VERA benchmarks and compared with literatures. The k eigenvalue differed by 7 pcm and the relative differences in the radial power profiles were less than 0.30%. Moreover, the simulation time was reduced by 48.1% due to quicker convergence with the two acceleration methods. Further analyses also proved the superior precision of this method, especially for asymmetric problems.

Nuclear Data Sensitivity and Uncertainty Study for the Pressurized Water Reactor (PWR) Benchmark Using RMC and SCALE

In order to improve the safety and economy of nuclear reactors, it is necessary to analyze the sensitivity and uncertainty (S/U) of the nuclear data. The capabilities of S/U analysis has been developed in the Reactor Monte Carlo code RMC, using the iterated fission probability (IFP) method and the superhistory method. In this paper, the S/U capabilities of RMC are applied to a typical PWR benchmark B&W’s Core XI, and compared with the multigroup and continuous-energy S/U capabilities in the SCALE code system. The S/U results of the RMC-IFP method and the RMC-superhistory method are compared with TSUNAMI-CE/MG in SCALE. The sensitivity results and the uncertainty results of major nuclides that contribute a lot to the uncertainties in keff are in good agreement in both RMC and SCALE. The RMC-superhistory method has the same precision as the IFP method, but it reduces the memory footprint by more than 95% and only doubles the running time. The superhistory method has obvious advantages when there are many nuclides and reaction types to be analyzed. In addition, the total uncertainties in the keff of the first-order uncertainty quantification method are compared with the stochastic sampling method, and the maximum relative deviation of total uncertainties in the keff is 8.53%. Verification shows that the capabilities of S/U analysis developed in the RMC code has good accuracy.

Improved design of LBE cooled solid reactor using 3D neutronics thermal-hydraulics coupling method

The goal of this study is to improve a micro reactor core into uniform power distribution, a smaller and safer core. Neutronic thermal-hydraulics coupling is an effective means to study the characteristics of microreactors. This paper performs an improvement work of lead–bismuth eutectic alloy (LBE) cooled solid core using the three-dimensional neutronics/thermal-hydraulics coupling method. Based on the Monte Carlo code RMC and the three-dimensional thermal-hydraulics code STAR-CCM+, the coupling code processes the power distribution, fuel temperature, coolant temperature, and coolant density. The improvement of the solid core is carried out in these aspects: reflector material, reflector dimensions, fuel materials, coolant channel dimensions, the volume fraction of fuel phase in dispersion fuel, and critical enrichment. This paper studies the effect of reflector material and dimensions on the solid core and its mechanism. After improvement, the power peaking factor is effectively reduced, while the size and weight of the solid core are also reduced than before due to the excellent ability of beryllium oxide (BeO), making it compact and lightweight. In addition, the core eigenvalues keff and thermal characteristics of different ceramic fuels, uranium dioxide (UO2), uranium nitride (UN), and uranium carbide (UC), are compared. UO2 was replaced by UN, which improves the thermal conductivity and reduces the maximum temperature of the solid core. At the same pressure difference, the mass flow rate of the coolant and temperature distribution of the fuel and the variation trend of neutron characteristics are studied when the coolant channel diameter changes. The results indicate that the coolant channel diameter of 1.775 cm has the best safety effect on the core. The variation of critical enrichment and thermal conductivity of the fuel at different volume fractions is compared, and 60 % is chosen as the volume fraction of the fuel phase. The final design of the shutdown rod and control drums is performed to ensure that the core is subcritical under all conditions. The improved core can operate at full power for five years and is characterized by miniaturization, high thermal conductivity, low volumetric swelling rate, flattened power distribution, and abundant reactivity control measures.

Neutronics performance improvement based on the small lead-based fast reactor SLBR-50

The design of high-performance lead-based fast reactors (LFRs) has become a hotspot in the advanced reactor system. This study evaluates the neutronics performance improvement based on the small LFR SLBR-50. Parameter sensitivity analyses are conducted, including height-to-diameter ratio (H/D), reflector assembly arrangement, and pitch-to-diameter ratio in fuel assembly, fuel material, and fuel enrichment partitioning. Numerical results of eigenvalue in burnup procedure, assembly power distribution, and energy spectrum are analyzed using the Monte-Carlo code RMC. Our findings indicate that the fuel material, fuel partitioning, and H/D are the three most important factors in LFR design. The neutronics performance analyses will assist in LFR design.

Verification of the direct transport code SHARK with the JRR-3M macro benchmark

The JRR-3M reactor is a water-cooled plate-type reactor for research. A macro benchmark based on the JRR-3M reactor is established with the Monte-Carlo code RMC and deterministic direct transport code SHARK with accurate and explicit geometry modeling. A series of cases from 2D lattice to 3D whole-core are adopted for the verification of SHARK. In the verification, sensitivity analyses are conducted with the 2D lattice case and applied in the 3D whole-core calculation. Numerical results indicate the good accuracy of SHARK for the plate-type JRR-3M macro benchmark.

A new functional expansion tallies (FET) method based on cutting track-length estimation in RMC code

The traditional Monte Carlo method is unable to describe the continuous distribution of parameters in space. The accuracy of a tally does not coexist with the efficiency of a calculation. The functional expansion tallies method (FET method) can obtain the continuous distribution of parameters in the solution space and can solve the problem of the coexistence of computational efficiency and precision.In this paper, an innovative FET method based on track-length estimation is proposed in the Monte Carlo code RMC. Track-length estimation can solve the variance fluctuation problem of collision estimation. In addition, the Legendre polynomials and Zernike polynomials are combined to calculate a continuous distribution of the parameters in a three-dimensional cylindrical space. Moreover, to solve the numerical instability of the FET method on the boundary of the tally region, this paper proposes a track-length cutting method. As a result, the new FET method can obtain a continuous distribution of the parameters in cases of a 10%–80% reduction in computing time compared with the finely divided mesh tally method. The method can also solve the problem where the traditional mesh tally method occupies too much simulation memory. Therefore, the new FET method can obtain more accurate results with less simulation memory (less than 10%).

High-Fidelity MC-DEM Modeling and Uncertainty Analysis of HTR-PM First Criticality

A high-fidelity model for the first criticality of pebble-bed reactor HTR-PM is built using Monte Carlo (MC) code RMC and discrete element method (DEM) code LAMMPS. Randomly packed TRi-structural ISOtropic (TRISO) particles and fuel pebbles are modeled explicitly. A cone structure on the top of the pebble bed is also taken into account. Criticality calculation result agrees well with the experiment. Uncertainty analysis is carried out considering three inherent aspects: the randomness of MC code, the randomness of TRISO particle and pebble position, and the randomness of mixed pebbles. Results show that these factors have a significant impact on the uncertainty of effective multiplication factor (keff). And the most influential factor is expected to be the randomness of mixed pebbles. The influence of several configuration factors is studied as well. It is observed that the effects of cross-section library, the heterogeneity of TRISO particles, and the angle of pebble bed cone are nonnegligible contributors. However, the results between randomly and regularly placed TRISO particles are not noticeably different.

Preliminary conceptual design and neutroncis analysis of a heat pipe cooled traveling wave reactor

The heat pipe cooled nuclear reactor is becoming a suitable choice compared to conventional power sources in decentralized electricity markets. In this paper, a 65.5 MWth heat pipe cooled traveling wave reactor (HPTWR) design is proposed. The concept design uses neutron traveling wave to improve the continuous operation time and reduce the enrichment of loaded fuel comparing to the currently existing heat pipe reactor designs. The Monte Carlo code RMC is used to obtain the propagation of axial power peak, reactivity swing, burnup and the inventories of bred fissile nuclides for the HPTWR core. The study shows that the HPTWR design with 14% enrichment of ignition fuel and 8.5% enrichment of breeding fuel can operate for 59 years without refueling, which meets the requirements of the low enrichment of loaded fuel, high power output, and long-term continuous operation for the power supply of decentralized electricity markets as a superior choice.

Optimization of spatial structure designs of control rod using Monte Carlo code RMC

Optimization of spatial structure designs of control rod using Monte Carlo code RMC

Application of the Spectral-Shift Effect in the Small Lead-Based Reactor SLBR-50

In the design of a nuclear reactor, improving fuel utilization and extending burnup are two of the most important goals. A concept design of spectral-shift control rods is presented to extend cycle length and fuel utilization. First, a small lead-based reactor, SLBR-50, is preliminarily designed, and the design rationality is proved. Next, the concept design of spectral-shift control rods is presented and analyzed. Finally, numerical results of the small reactor design show that the burnup depth is extended by 73.3% and the fuel utilization rate for 235U and 238U is improved by 66.6 and 68.4%. All results are calculated using a Monte-Carlo code RMC. These results show advantages of the concept design for the spectral-shift control rod.

Development and application of Monte Carlo and COMSOL coupling code for neutronics/thermohydraulics coupled analysis

The tightly coupled solution of neutronics and thermal-hydraulics play an important role in precise simulation of fuel designs. Fully Ceramic Microencapsulated (FCM) fuel was one of the popular designs for accident tolerant fuel. To simulate advanced fuel types such as FCM fuel, a new method was proposed to couple the Monte Carlo code RMC with multi-physical software COMSOL. The MATLAB interface was adopted for coupling, and the superimposed structured mesh was applied to the mesh mapping and data interpolation between the structured meshes of RMC and unstructured meshes of COMSOL. Then the coupling code was verified by a typical PWR fuel rod and a FCM case. Results show that the calculated power and temperature distributions are reasonable, which can capture the self-shielding effect of thermal neutrons. Comparing with the traditional “cell-to-cell” mapping, the proposed method has advantages of good geometric flexibility and high accuracy, which can be applied to multi-physics simulations of different fuel designs.