Reactor Kinetic Parameters Research Articles

Verification of Adjoint Solution Commutativity with the New OpenNode Nodal Diffusion Code

This paper presents in-depth exploration and verification of the OpenNode nodal diffusion code, a robust tool designed for multigroup neutron diffusion simulations under steady-state conditions. Leveraging the Nodal Expansion Method with a quartic polynomial and moments weighting method, OpenNode demonstrates exceptional accuracy in approximating nodal surface fluxes, further enhanced by the Quadratic Transverse Leakage approximation. The critical concept of commutativity between adjoint and forward solutions is thoroughly investigated, serving as a benchmark for the code’s reliability in predicting system responses, determining single-point reactor kinetics parameters, and facilitating perturbation analyses. The paper meticulously details OpenNode’s methodology for adjoint neutron flux computation, unraveling its rigorous approach through transposition operations and intricate mathematical transformations. Noteworthy features, including support for second and fourth polynomial orders; versatile computation modes; different mesh points; and seamless integration with Python, PyQt5, and Blender, underscore OpenNode’s adaptability. Results from comprehensive analysis of the two-dimensional and three-dimensional International Atomic Energy Agency core benchmark problem showcase OpenNode’s prowess. The code excels in reactor geometry visualizations, benchmark parameters, and neutronic analysis, with a particular emphasis on commutativity verification against various benchmarked codes. The precision of OpenNode is further demonstrated in power distribution analyses, revealing remarkable proximity to reference values and symmetrical power distribution patterns.

Measurement of Isfahan heavy water zero-power reactor kinetic parameters using advanced pulsed neutron source method in a near critical state

The pulsed neutron source (PNS) technique was used to determine the prompt neutron decay constant for two different lattice pitches in the HWZPR heavy water zero power reactor. The results were compared to the variance-to-mean ratio (VTM) method. The neutron mean generation time was also calculated for both pitches, and the results were compared to previous Monte Carlo calculations. The findings of this research can be used as a benchmark nuclear codes to validate kinetic parameters.

Neutron multiplication and reactor kinetics parameters in stochastic media based on randomized noise functions

The modelling of stochastic media is of considerable interest for criticality safety and reactor physics applications. Novel methods for modelling highly disordered, random heterogeneous mixtures based on randomized Weierstrass functions and Perlin noise have been implemented in the MONK® Monte Carlo code using Woodcock tracking. Perlin noise in particular is shown to be well suited to the application, efficiently producing random geometries with much greater physical realism than the artificial nature of alternative methods. The effect of geometry randomization on neutron multiplication and reactor kinetics parameters in a simple benchmark configuration has been investigated, and results are compared with previous research based on tessellation algorithms. While the results are found to be broadly consistent with previous work, the new methods presented here offer significant benefits in terms of increased physical realism, conservation of material volume fractions, computational efficiency and ease of use.

Neutronic Evaluation of Using a Thorium Sulfate Solution in an Aqueous Homogeneous Reactor

Radioisotope 99 Mo is one of the most essential radioisotopes in nuclear medicine. Its production in an Aqueous Homogeneous Reactor (AHR) could be potentially advantageous compared to the traditional technology, based on target irradiation in a heterogeneous reactor. An AHR conceptual design using low-enriched uranium for the production of 99 Mo has been studied in depth. So far, the possibility of replacing uranium with a non-uranium fuel, specifically a mixture of 232 Th and 233 U, has not been evaluated in the conceptual design. Therefore, the studies conducted in this article aim to evaluate the neutronic behavior of the AHR conceptual design using thorium sulfate solution. Here, the 232 Th- 233 U composition to guarantee ten years of operation without refueling, conversion ratio, medical isotopes production levels, and reactor kinetic parameters were evaluated, using the computational code MCNP6. It was obtained that 14 % 233 U enrichment guarantees the reactor operation for ten years without refueling. The conversion ratio was calculated at 0.14. The calculated 99 Mo production in the AHR conceptual design resulted in 24.4 % higher with uranium fuel than with thorium fuel.

SERPENT CODE POINT KINETIC PARAMETERS ANALYSIS: A NEXUS FOR NIGERIA RESEARCH REACTOR – 1 CORE CONVERSION USING ENRICHED URANIUM DIOXIDE FUEL

The International Atomic Energy Agency (IAEA) requires that all test and research reactors operating on Higher Enriched Uranium (HEU) should be converted to Low Enriched Uranium (LEU) for safety and security purposes. Nigeria having a Miniature Neutron Source Reactor (MNSR) has been long interested in fuel technological research not just to develop the area but also to meet with resolution on the nuclear treaty set out by the global nuclear regulatory body. In this study, reactor kinetic parameters such as effective delayed neutron fractions, prompt neutron lifetime as well as mean neutron generation time were analysed for Nigerian Research Reactor-1 (NIRR-1). Serpent Monte Carlo code 1.17 is used in the analysis. For delayed neutron parameters determination, we used fission probability iteration under one averaged generation time and neutron population rate.The calculated values for delayed neutron were recorded as analogue prompt and implicit prompt neutron lifetime, reproduction time and emission time are in the order of 3×10-7 (s), in agreement with the calculated data from the nuclear data libraries and some literature.The result for delay neutron fraction and other time-based parameters support the fuel core conversion for NIRR-1.The computational and pictorial results obtained from Serpent code simulation described well the transient behavior of the delayed neutron in this reactor.The analytical results also spelled out the relevance and compatibility of low enriched uranium dioxide fuel over higher enriched type.The result of this study conforms with other results obtained from similar reactors but with different Monte Carlo codes and with higher enriched uranium

Neutron Multiplication and Reactor Kinetics Parameters in Stochastic Media Based on Randomized Noise Functions

Neutron Multiplication and Reactor Kinetics Parameters in Stochastic Media Based on Randomized Noise Functions

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

Calculation of kinetic parameters βeff and Λ with modified open source Monte Carlo code OpenMC(TD)

This work presents the methodology used to expand the capabilities of the Monte Carlo code OpenMC for the calculation of reactor kinetic parameters: effective delayed neutron fraction βeff and neutron generation time Λ. The modified code, OpenMC(Time-Dependent) or OpenMC(TD), was then used to calculate the effective delayed neutron fraction by using the prompt method, while the neutron generation time was estimated using the pulsed method, fitting Λ to the decay of the neutron population. OpenMC(TD) is intended to serve as an alternative for the estimation of kinetic parameters when licensed codes are not available. The results obtained are compared to experimental data and MCNP calculated values for 18 benchmark configurations.

Safety Analysis of Indonesia's Multipurpose Reactor During Irradiation of Natural UO2 Pin Target at Power Ramp Test Facility

Abstract To support the utilization of the power ramp test facility (PRTF) at the reactor Serba Guna GA Siwabessy (RSG-GAS) reactor, the investigation of safety parameters both on the target and the reactor during the irradiation of natural UO2 has been conducted. The program for the analysis of reactor transient (PARET) and Monte Carlo N-particle version 6 (MCNP6) codes were integrated for thermal-hydraulic and neutronic analysis under the reactivity insertion phenomenon. The reactivity insertion and linear heat rate (LHR) were calculated by MCNP6 to confirm that the maximum values are well below the safety limits. Also, the code computed the reactor kinetic parameters to provide inputs for the PARET code to evaluate the reactor response due to the target movement at the PRTF. The target moves from the farthest position to the nearest one traveling 440 mm and then moves back to the original position. The safety analysis indicated that both maximum reactivity insertion and LHR values did not exceed the safety limits. The target induces maximum reactivity insertion of 0.023%dk/k and produces the maximum LHR of 137.53 W/cm and 275.06 W/cm; when the reactor operates at 15 MW and 30 MW, respectively. The PARET simulation results showed that the reactor power oscillated due to the target movement. Therefore, the recommended velocities of the target are below 0.17 m/s and 0.08 m/s for reactor power of 15 MW and 30 MW, respectively, to avoid the reactor scram, and no safety limits are exceeded.

Defining the performance envelope of reactivity-initiated accidents in a high-temperature gas-cooled reactor

The purpose of this study is to define an envelope of possible transient conditions during two reactivity-initiated accidents (RIAs) in a modular high-temperature gas-cooled reactor (mHTGR). The accident scenarios studied were a group control rod withdrawal (CRW), a design basis accident, and a control rod ejection (CRE), a beyond design basis accident. Variance-based sensitivity analysis methods were employed to obtain realistic bounds on the reactor power and maximum temperature, energy deposition, and heating rate in the fuel during these accidents. Key reactor kinetic parameters and the heat transfer properties of the fuel and moderator were varied in a RELAP computer model of a 350-megawatt mHTGR to obtain these bounds. Sobol sensitivity indices were calculated to highlight which inputs account for the most variance in the outputs. Results showed that the kinetic properties and reactivity temperature coefficients were the most dominant inputs, while thermal properties had little impact on the outputs. Compared to previous experimental work, the fuel particle energy deposition from the simulated RIAs would not be expected to cause fuel failure in any design basis or beyond design basis reactivity accident we investigated. The predicted energy deposition in fuel kernels ranged from 98 to 331 J/g-fuel, significantly less than the expected failure threshold of approximately 1500 J/g-fuel. However, the power pulse widths and heating rates used in previous fuel safety experiments were different from the values predicted in this study for both accident scenarios. Regardless of these differences, this analysis shows that the safety margins in graphite-moderated mHTGRs for reactivity accidents are very large, and additional fuel safety tests are not expected to be necessary for this application.

Calculation of effective point reactor kinetic parameters combined with the Galerkin finite element method

Precise point reactor kinetic parameters are essential in the study of reactor dynamics. Point reactor kinetic parameters include the effective delayed neutron fraction and prompt neutron lifetime. In this work, effective point reactor kinetic parameters, which can be applied to unstructured grids, were calculated based on the Galerkin finite element method. First, two-dimensional and three-dimensional benchmarks were used to verify the calculation of steady-state neutronic parameters. Then, the Tehran research reactor core was divided into hexahedral meshes, and the forward flux and adjoint flux were calculated. Finally, the effective point reactor kinetic parameters of the Tehran research reactor were obtained by comprehensively processing the steady-state neutronic parameters.

Review of kinetic modulation experiments in low power nuclear reactors

The safety improvement of nuclear reactors requires continuous efforts in understanding the fundamental physical quantities related to the fission process. In neutronic models, the reactor dynamics is covered by the kinetic parameters to characterize the temporal behavior of the neutron population subject to perturbations. The reactor transfer function is a frequency domain analogy of this temporal description. It can be measured experimentally through transfer function analysis via noise analysis or kinetic modulation, for the study of reactor stability and kinetic parameters. This paper summarizes the experimental measurements of reactor transfer function through kinetic modulation. Extensive work have been conducted experimentally, starting from the beginning of reactor physics research. An overview is given regarding various experimental designs and conducted analyses. The concepts of the modulation system are also discussed. The current work is limited to online contents and internal archives of CEA Cadarache due to difficulties in accessing references traced back to 1950s.

The CRANK System—A Simple, Robust Apparatus for Measurement of Cherenkov Light at Open-Pool Reactor

Recently, techniques for qualitative inspections of spent fuel using Cherenkov light have advanced the International Atomic Energy Agency’s ability to perform defect verification measurements following discharge of the fuel from the reactor. Unfortunately, these measurements are limited in their value for safeguards and nuclear material accountancy since they do not quantify the fissile material quantities and cannot characterize a reactor during operations. The Cherenkov Radiation Assay for Nuclear Kinetics (CRANK) system has been devised to quantify the fissile material in the Oregon State TRIGA Reactor (OSTR) during two or more reactor pulses through the measurement of Cherenkov light. The results from the OSTR experiments have shown that the CRANK system is capable of determining the ratio of reactor kinetics parameters (RKP) through the measurement of Cherenkov light in an assay of a research reactor capable of pulsing. There exists excellent agreement between the declared value of the RKP ratio in the OSTR Final Safety Analysis Report and four separate reactor pulse comparisons using the CRANK system. Future applications of the CRANK system can provide independent determination of a pulsing research reactor with an unknown RKP ratio.

Neutronic evaluation of the steady-state operation of a 20 kWth Aqueous Homogeneous Reactor for Mo-99 production

Nowadays, 99mTc is the most common radioisotope used in nuclear medicine, with up to 30–40 million procedures worldwide every year. Furthermore, medical diagnostic imaging techniques using 99mTc represent approximately 80% of all nuclear medicine procedures. Currently, 99mTc is almost exclusively produced from the beta-decay of its 66-h parent 99Mo. The 99Mo production in an Aqueous Homogeneous Reactor (AHR) is potentially advantageous because of its low cost, small critical mass, inherent passive safety, and simplified fuel handling, processing, and purification characteristics. This paper studies an AHR conceptual design using low-enriched uranium for the production of 99Mo. Aspects related to the neutronic behavior such as critical height, medical isotopes production, uranium consumption, plutonium production and the reactivity feedback introduced in the solution by the volumetric expansion of the fuel solution were evaluated using the computational code MCNPX version 2.6e. In addition, important reactor kinetic parameters such as the effective delayed neutron fraction, βeff, and mean neutron generation time, Λ, were calculated. A benchmarking exercise was solved using available results of critical experiments performed at the Russian Research Center “Kurchatov Institute”. The neutronic calculations demonstrated that the reactor is able to produce 99 six-day Ci of 99Mo in operation cycles of five days. The reactivity feedbacks introduced by the volumetric expansion of the fuel solution is at about −1460 pcm, which represents approximately the 48% of the planned initial reactivity reserve in the core. The calculated effective delayed neutron fraction and the average mean neutron generation time were 785 pcm and 134.08 µs, respectively.

A new framework for sampling-based uncertainty quantification of the six-group reactor kinetic parameters

Delayed neutrons, which are described by kinetic parameters, are significant for nuclear reactor operation as they make nuclear reactors controllable. Modern lattice physics codes such as TRITON and Polaris in SCALE code system, generate kinetic parameters for a given material composition. The calculation is performed by summation of the delayed neutron data for each precursor isotope and then weighting is performed by real and/or adjoint neutron spectrum. Quantifying uncertainties in the weighted kinetic parameters is important for assembly and core calculations. Understanding uncertainty in modeling scenarios involve kinetic parameters (e.g. transients), requires propagating uncertainty in the weighted kinetic parameters due to uncertainties in the fundamental nuclear data libraries, including delayed neutron data. In this work, uncertainty analysis of the homogenized (also called weighted or macroscopic) kinetic parameters has been performed using Sampler, a module in SCALE code system, to investigate the effect of fundamental nuclear and delayed neutron data uncertainties on the weighted kinetic parameters. Two major sources of uncertainties were considered: (1) fundamental nuclear data (i.e. cross-sections, fission yield, decay data) and (2) nuclide-dependent group-wise delayed neutron data based on reported experimental measurements. In this study, a new capability was developed through SCALE code system to allow propagation of delayed neutron data uncertainties. Preliminary analysis demonstrated 7% uncertainty in βeff at Beginning of Life (BOL) and increased to 15% after fuel burnup. Decay constant groups showed lower uncertainty than delayed neutron fraction groups, both at BOL and End of Life (EOL). Delayed neutron fraction responses showed high correlation to each other which is expected to be due to the cross-section covariances reported in SCALE data libraries as well as the normalization condition of the nuclide-dependent DNF. Different sources of U-235 delayed neutron data were compared, and the results showed that the uncertainty calculated by Tuttle data was bounded by other sources. The current study can be extended to calculate kinetic parameters and their uncertainties for more advanced LWR applications.

Modified Fuchs-Nordheim model for use in reactor pulse measurements

Experimental reactor physics is constantly advancing new methods to determine parameters of interest in reactor systems. The development of analytical and semi-analytical solutions to characterize complex systems relies on the ability to isolate specific phenomena that may be represented by governing equations. Two values in particular, the delayed neutron fraction, β, and the prompt neutron lifetime, l, are directly related to the performance of a pulse-type reactor during a reactor transient. A great deal of research has been performed to determine these quantities with limited success, especially at high power conditions. The Fuchs-Nordheim model is capable of qualitatively predicting reactor power during the transient, but assumptions limit its ability to determine reactor kinetics parameters during the transient.A modification to the FN model is presented and compared with the FN model along with experimental data from the Oregon State University TRIGA reactor to independently measure of the β/l ratio of the OSTR experimentally with quantifiable uncertainty.

Design study of long-life small modular sodium-cooled fast reactor

Summary This paper presents a new design for a small modular sodium-cooled fast reactor core with an optimized lifetime and reactivity swing through the analysis of various breed-and-burn strategies and its neutronic analyses in terms of active core movements, isotopic mass balance, kinetic parameters, and inherent safety. The new core design aims at a power level of 260 MW with a long lifetime of 30 years without refueling and a reactivity swing smaller than 1000 pcm. Starting from five initial candidate cores with various breed-and-burn strategies, an optimum core was selected from a combination of the two candidates that shows a proper breeding behavior with the optimized uranium enrichment in the low-enriched uranium region and the optimized size of the blanket region. The depletion analysis of the new core provides various reactor design parameters such as the core multiplication factor, breeding ratio, heavy metal mass change, power distribution, and summary of neutron balance. In addition, the perturbation analysis provides the reactor kinetic parameters and reactivity feedback coefficients for the inherent safety analysis of the core. The integral reactivity parameters of the quasi-static reactivity balance analysis demonstrate that the new core is inherently safe in cases of unprotected loss of flow, unprotected loss of heat sink, and unprotected transient over power. Copyright © 2016 John Wiley & Sons, Ltd.

Neutronics and thermal hydraulics analysis of a small modular reactor

The small modular reactor (SMR) offers many feasible pathways for the construction of more nuclear power plants. A physics model of a near term deployable SMR of the integral pressurized water reactor (IPWR) design is developed. Fuel depletion simulations are performed to optimize the active fuel length, fuel enrichment and core loading pattern in order to achieve a uniform core power distribution. The optimized core can produce 500MW of thermal power with a four year core life-time at a capacity factor of 87%. The core consists of 69 uranium dioxide (UO2) fuel assemblies; 5 assemblies at 4.4at% 235U enrichment and 64 assemblies at 4.95at% 235U enrichment. The active fuel length is 200cm and the core diameter is 194.55cm for an active core height-to-diameter ratio of 1.03. As part of the study the active fuel length is increased to 240cm resulting in an increased capacity factor of 95% at 530MW of thermal power output for an active core height-to-diameter ratio of 1.23. Rod cluster control assemblies (RCCAs) are placed strategically to reduce the overall core power peaking factor to 1.3. Estimated reactor kinetics parameters such as the delayed neutron fraction and mean neutron generation time are typical of existing larger pressurized water reactors (PWRs) from which much of the IPWR based SMR design is derived. This study showed that Doppler, moderator temperature, void and power reactivity coefficients are all negative over the core life-time of four years indicating the possibility of safe reactor operation. A semi-analytical thermal hydraulics analysis reveals acceptable radial and axial fuel element temperature profiles with significant safety margin from industry standards on peak fuel and clad surface temperature limits. The critical heat flux (CHF) is calculated and is not exceeded even in 10% overpower conditions. In addition the nucleate boiling ratio (DNBR) is calculated and found to be above 4.8 for the entirety of the active core region. These parameters further engender confidence in the safety of the SMR design.

Calculation of reactor kinetics parameters with Monte Carlo differential operator sampling

The methods to calculate the reactor kinetics parameters of βeff and Λ with the differential operator sampling have been reviewed. The comparison of the results obtained with the differential operator sampling and iterated fission probability approaches has been performed. It is shown that the differential operator sampling approach gives the same results as the iterated fission probability approach within the statistical uncertainty. In addition, the prediction accuracy of the evaluated nuclear data library JENDL-4.0 for the measured βeff/Λ and βeff values is also examined. It is shown that JENDL-4.0 gives a good prediction except for the uranium-233 systems. The present results imply the need for revisiting the uranium-233 nuclear data evaluation and performing the detailed sensitivity analysis.

Benchmarking of the HTR-10 reactor's kinetic parameters: Effective delayed neutron fraction

A number of methods have been proposed to calculate the effective delayed neutron fraction using Monte Carlo codes. The present work aims at assessing the possibility of using the prompt method to calculate the effective delayed neutron fraction for the HTR-10 reactor. The prompt method in Monte Carlo codes is based on a simple assumption: negligibility of the effect of delayed neutrons on neutron flux shape and distribution. Hence one way to prove the applicability of the aforementioned would be to assess those effects. To this end, we modeled the HTR-10 reactor core using the MCNP4c code and extracted such parameters as the neutron spectrum and radial neutron flux distribution. These calculations were performed for two distinct core configurations, corresponding to the start-up and full power modes. Finally, the effective delayed neutron fractions were calculated and compared to previously reported values. Given the simplicity of the prompt method, the innate geometrical flexibility of Monte Carlo based neutronic simulation codes and the results obtained for the HTR-10, this combination method is proposed as an acceptable reactor core kinetic analysis tool for PBM-type reactors.