Rod Worth Research Articles

Control rod shadowing effect in PWR core utilizing Urania-Gadolinia fuel

Safety analysis of nuclear power plants requires the assessment of all the systems important to safety. Control rods are one of the important safety systems for nuclear reactors. The control rod worth is affected by location of control rod banks, enrichment of uranium fuel in the assembly where the bank is inserted and the enrichment of gadolinium in the assembly. Also, the Interactions between control rods, phenomena known as shadowing effect, influence the worth of control rods. In this paper shadowing effect and the factors affecting the control rod worth are investigated for four types of control rod banks of an EPR Reactor. Parameters investigated are control rod worth, degree of interaction between rods and amplification factor. Moreover, the effect of interactions between control rod banks on the fluctuation of flux distribution in the core is studied. The calculations are evaluated at BOC and EOC using MCNP6 code. The results showed that the location of control rod bank in the core has the highest effect on the worth of a certain bank, second is the number of control rod bank groups in the core, followed by the fuel enrichment. The gadolinium burnable absorber has a slight effect on the control rod worth. The results obtained represent an important contribution that would support safety analysis of the EPR reactor design.

Utilization of PARCS/Serpent in small-scale reactor – Multiplication factor, rod worth, and transient

The paper is focused on utilization of calculation code PARCS (version 3.3.1) for the VR-1 reactor. Macroscopic cross-sections are generated by stochastic code Serpent (version 2.1.30) with ENDF/B-VIII.0 library and with a high emphasis on a wide range of utilization and reproducibility. The VR-1 reactor is characterized by small-sized core configurations (28.6 × 28.6 cm up to 42.9 × 42.9 cm; height of 60 cm; pitch 7.15 cm) that are imposing special requirements on a cross-section homogenization. Published cross-section generation approaches are used for analyses of 7 highly distinctive core configurations. This allows to asses their performance in a wider range than other papers aiming only at one specific core configuration. Even though predictions of a critical state are not sufficiently accurate for any actual usage (in case of the VR-1 reactor), calculated absorption rod worths reach a high potential for a fast and precise evaluation of safety criteria. Core kinetics parameters generated by Serpent with ENDF/B-VIII.0 library (for all three methods: Meulekamp, Nauchi, IFP) show a continuous underestimation of calculated power in all investigated transients during an insertion of a negative reactivity.

Superphénix Benchmark Part I: Results of Static Neutronics

Abstract In the paper, the specification of a new neutronics benchmark for large sodium cooled fast reactor (SFR) core and results of modeling by different participants are presented. The neutronics benchmark describes the core of the French sodium cooled reactor Superphénix at its startup configuration, which in particular was used for experimental measurement of reactivity characteristics. The benchmark consists of the detailed heterogeneous core specification for neutronic analysis and the results of the reference solution. Different core geometries and thermal conditions from the cold “as fabricated” up to full power were considered. The reference Monte Carlo (MC) solution of serpent 2 includes data on multiplication factor, power distribution, axial and radial reaction rates distribution, reactivity coefficients and safety characteristics, control rods worth, kinetic data. The results of modeling with seven other solutions using deterministic and MC methods are also presented and compared to the reference solution. The comparisons results demonstrate appropriate agreement of evaluated characteristics. The neutronics results will be used in the second phase of the benchmark for the evaluation of transient behavior of the core.

Multischeme equivalence procedure for neutron transport finite element methods

Diffusion equivalence theory applied at the full-core level is well understood and enables preservation of the multiplication factor and key reaction rates. In many cases, however, high-interest regions inside the reactor benefit from a heterogeneous representation solved using a transport scheme. This paper formalizes the multischeme (MS) equivalence procedure in which the capability to use distinct transport operator approximations in different parts of the domain is combined with an equivalence procedure, thus enforcing preservation of the reaction rates in—and (optionally) leakage rates out of—the low-resolution domains, using Super Homogenization (SPH) and discontinuity factors (DFs).Two approaches are proposed: MS-SPH applies SPH factors to the diffusion interface terms, whereas MS-SPH-DF relies on DFs to enforce preservation of the net currents at the interface—in which case, one normalization factor per energy group and connected region is required.The main targeted applications of multischeme equivalence are (1) more accurate reaction rates inside the heterogeneous region and (2) the ability to rely on methods otherwise incompatible with equivalence. Both proposed methods can successfully reproduce the eigenvalue and reaction rates in the heterogeneous region. Although MS-SPH-DF may better capture local effects with very refined meshes, MS-SPH otherwise seems more appealing, due to its comparable accuracy with coarser meshes and its significantly reduced burden on the analyst for large applications, as reference currents are not needed. When global quantities of interest are specifically targeted (e.g., control rod worth), neither method appears superior to a standard, spatially restricted SPH approach.

Impact of Different Nuclear Data Library on Control Rod Reactivity Worth Calculation of Small Pebble Bed Reactor

One of the main critical issues on a nuclear reactor is safety and control system. The control rod worth plays an important role in the safety and control of nuclear reactors. The control rods worth calculation is used to specify the safety margin of the reactor. The main objective of this work is to investigate impact of different nuclear data libraries on calculating the control rod reactivity worth on small pebble bed reactor. Calculation of the control rod reactivity worth in small high temperature gas cooled reactor has been conducted using the Monte Carlo N-Particle 6 (MCNP6) code coupled with a different nuclear data library. Famous evaluated nuclear data libraries such as JENDL-40u, ENDF/B-VII.1 and JEFF-3.2 continuous cross section-energy data libraries were used. The overall calculation results of integral control rod worth show that the ENDF/B-VII.1, JENDL-40u and JEFF-3.2 files give values of - 17.814%☐k/k, -18.0204 %☐k/k and -18.0267%☐k/k, respectively. Calculations using ENDF/B-VII.1 give a slightly lower value than the others, while the JENDL-4.0u file gives results that are close to JEFF-3.2 file. The different nuclear data libraries have a relatively small impact on the control rod worth of small pebble bed reactor. Accurate prediction by simulation of control rod worth is very important for the safety operation of all reactor types, especially for new reactor designs.

Accurate Nodal Diffusion Modelling on the High Temperature Test Reactor (HTTR)

The High Temperature Test Reactor is a 30-MWth helium-cooled, graphite-moderated, prismatic-type gas reactor developed by the Japan Atomic Energy Agency (JAEA). The hexagonal shape of fuel blocks in the HTTR core combined with complex inner structures containing TRISO particles results in the double-heterogeneity effect that increases the simulation challenge of the reactor. This research has a goal to accurately model the HTTR fuel blocks employing the standard two-step procedure of a reactor analysis: employ a lattice physics calculation to generate homogeneous cross sections and use them in a nodal diffusion calculation. The implementation of the diffusion approximation results in a faster calculation with acceptable accuracy compared to the high-resolution lattice calculation. An advanced method called Triangular Polynomial Expansion Nodal (TriPEN) method was used in this work for the nodal diffusion calculation to accurately model the flux discontinuity effect between blocks by generating discontinuity factors in each surface and corner point. To do this, the heterogeneous solutions obtained from the lattice physics calculation, which is done by Serpent Monte Carlo in this case, are utilized by TriPEN to generate the discontinuity factors. Due to its capability to simulate any reactor geometry with a high-resolution, the results generated from Serpent calculation were also used as the reference cases for this work. In this work, the TriPEN method is implemented in the PARCS core neutronic module inside AGREE, a U.S. N.R.C. Multiphysics code system for the High Temperature Reactor (HTR). Test cases conducted for this method involved the original design of the HTTR. The 4-hex model built consisted of the central control-rod block of HTTR together with 6 of the half-fuel-blocks surround it. The differences in material composition in each assembly block in HTTR resulted in flux discontinuity effects on the assembly block interfaces. To correct this discrepancy, discontinuity factors were applied in order to make the homogenous solutions from the nodal calculation agree with the heterogeneous solutions from the lattice physics calculation. Applying this procedure to the HTTR nodal models, TriPEN is able to produce exact results in the eigenvalue compared to Serpent calculation, the rod worth calculated perfectly matched the reference, and the flux and power distribution only has negligible discrepancies.

Study on Implementation Method of Deep Subcritical Rod Worth Measurement Electronics

In order to realize the effective acquisition of data required for deep subcritical rod worth calculation, the overall architecture and key modules of deep subcritical rod worth measurement electronics have been researched and designed. The characteristics of the key modules have been tested through reactor test. The results show that the designed deep subcritical rod worth measurement electronics can effectively measure the detector signal transmitted through about 200 m cable. The pulse signal has a stable waveform width and a proper signal-to-noise ratio. The measured high voltage plateau characteristic curve can provide an effective reference for the high voltage selection of the detector. The measured discrimination characteristic curve is stable, from which the neutron component in the detector signal can be effectively obtained.

Experimental and analytical determination of irradiated control rod worth of a low power research reactor

The NIRR-1 has a single control rod that performs the function of shutting down, shimming and bringing the reactor to power. Assessment of the efficiency of control rod is very important especially after modification. In this work, the efficiency of the control rod prior to the removal of cadmium rabbit in one of the irradiation channels of NIRR-1 was assessed using experimental and analytical methods. The measured and calculated safety parameters of the control rod such as control rod worth, shutdown margin and safety reactivity factor were found to be (6.41 mk and 6.37 mk), (2.52 mk and 2.48 mk) and (1.65 and 1.64) respectively, which meet safety requirements of NIRR-1 in the SAR. The result from analytical methods was found to be within maximum of 3σ of the measured value, indicating that the analytical method can be used to obtain a good approximation of control rod worth. Results obtained in both methods indicate that it was safe to continue to use the control rod after removal of the cadmium rabbit.

Steady State Calculations of the PWR MOX/UO2 Core with the Monte Carlo Code MCNP6

This paper presents the steady-state analysis results of the OECD/NEA and U.S. NRC PWR MOX/UO2 (MOX: Mixed Oxide) Core Transient Benchmark with the modern MCNP6 Monte Carlo code based on the ENDF/B-VII.1 evaluated nuclear data library. The purpose was to verify an MCNP6 model proposed for calculations of a heterogeneous MOX/UO2 fuelled PWR core, which has different neutronic characteristics from the popular homogeneous ones loaded with the UO2 fuel due to its partial loading of the MOX fuel. The effective neutron multiplication factors, assembly power distributions, and control rod worths calculated using MCNP6 showed a reasonable agreement within 390 pcm, 6%, and 175 pcm, respectively, with the available benchmark data. The discrepancies between the MCNP6 results and the benchmark data were also discussed. Consequently, these results obtained with MCNP6 and ENDF/B-VII.1 can be considered as a new full-core heterogeneous transport solution to supplement for the available benchmark solutions at the steady-state conditions.

Chemical spectral shift control method for VVER-1000 LEU fuel assembly benchmark

The spectral shift control (SSC) is a promising method to decrease the fuel cycle cost and enhance the utilization of fuel resources (U, Pu) in nuclear reactors. In the chemical SSC method, reactivity control is accomplished by varying the ratio of heavy water to light water moderator (D2O/H2O). In the current work, we apply the chemical SSC method to analyze the VVER-1000 LEU fuel assembly from the OECD benchmark. Additionally, we compare the chemical SSC method to the conventional poison method presented in the benchmark. The results showed that the discharge burnup was improved by 60% and the conversion ratio value reached 0.83. The k∞ was suppressed at the beginning of cycle by −8% compared to the benchmark model. Furthermore, the dedication of 12 burnable absorber rods with 4.0 wt% Gd2O3 would save the D2O quantity during the adjustment process resulting in reducing the capital cost of the SSC method. However, it’s found that the physical changes associated with applying the SSC method including a high contribution of 239Pu and 241Pu to power generation, the low effect of 135Xe and 149Sm on the reactivity system, and reduction of control rod worth should be considered in the safety analysis of the SSC design.

Study on Reactor Core Physics Calculation of Marine Nuclear Power Platform

The marine nuclear power platform is an organic combination of small nuclear reactor and ship engineering technology. It has the characteristics of good manoeuvrability, long on-time charging operation cycle, high power density, low operating cost, energy saving and environmental protection. In this paper, The core geometry model is built based on the design of the marine nuclear power platform reactor core. The core reactivity and control rod worth are calculated by a Monte Carlo code MCNP for this core design at first cycle, initial loading, normal temperature, and normal pressure condition. The results of the calculation are compared with nuclear design values. It shows that MCNP code is suitable for marine nuclear power platform core design calculation, and can be verified with nuclear design values.

Static and transient analyses of Advanced Power Reactor 1400 (APR1400) initial core using open-source nodal core simulator KOMODO

The United Arab Emirates is currently building and operating four units of the APR-1400 developed by a South Korean vendor, Korea Electric Power Corporation (KEPCO). This paper attempts to perform APR-1400 reactor core analysis by using the well-known two-step method. The two-step method was applied to the APR-1400 first cycle using the open-source nodal diffusion code, KOMODO. In this study, the group constants were generated using CASMO-4 fuel transport lattice code. The simulation was performed in Hot Zero Power (HZP) at steady-state and transient conditions. Some typical parameters necessary for the Nuclear Design Report (NDR) were evaluated in this paper, such as effective neutron multiplication factor, control rod worth, and critical boron concentration for steady-state analysis. Other parameters such as reactivity insertion, power, and fuel temperature changes during the Reactivity Insertion Accident (RIA) simulation were evaluated as well. The results from KOMODO were verified using PARCS and SIMULATE-3 nodal core simulators. It was found that KOMODO gives an excellent agreement.

Reactivity Effect Evaluation of Fast Reactor Based on Angular-Dependent Few-Group Cross Sections Generation

Among all the possible occurring reactivity effects of a fast reactor, the situations whereby the control rod was inserted, or the coolant was voided could lead to strong anisotropy of neutron flux distribution, therefore the angular dependence on neutron flux should be considered during the few-group cross-sections generation. Therefore, the purpose of this paper is to compare the influence whether the angular dependence on neutron flux is considered in the calculation of few-group cross sections for the reactivity effect calculation. In the study, the 1-D SN finite difference neutron transport equation solver was implemented in the TULIP of SARAX code system so that the high-order neutron flux could be obtained. Meanwhile, the improved Tone’s method was also applied. The numerical results were obtained based on three experimental FR cores, the JOYO MK-I core, ZPPR-9 core, and ZPPR-10B core. Both control rod worth and sodium void reactivity were calculated and compared with the measurement data. By summarizing and comparing the results of 46 cases, significant differences were found between different consideration of the neutronic analysis. The consideration of angular dependence on neutron flux distribution in the few-group cross-sections generation was beneficial to the neutronic design analysis of FR, especially for the reactivity effect calculation.

An investigation on the control rod homogenization method for next-generation fast reactor cores

A Japanese next-generation fast reactor core design adopts the reaction rate ratio preservation (RRRP) method for control rod homogenization with a super-cell model in which a control rod is surrounded by fuel assemblies. An earlier study showed that the RRRP method with the conventional super-cell model could estimate the control rod worth (CRW) of a 750-MWe large fast reactor core within the error of 1.5%. The estimation of radial power distribution (RPD) tends to have relatively large error especially for large fast reactor cores with the control rods inserted. In order to reduce the radially-dependent error of CRW and RPD, this study evaluated the modeling error and refined the surrounding fuel assemblies of the super-cell model for all control rods in the RRRP method. This refinement significantly decreased the radially-dependent modeling error: the error of CRW and RPD were reduced to less than 0.1% and 0.4%, respectively.

Direct whole core modeling and simulation of the SPERT III E-Core experiments by nTRACER

The SPERT III E-core experiments are modeled and simulated by a direct whole core calculation code nTRACER as an effort to validate its dynamics calculation capability. The control rod ejection experiments performed for the E-core of the Special Power Excursion Reactor are faithfully modeled by explicitly representing all the complex components such as fuel cans and the cruciform transient rod. The unknown experiment conditions such as the initial position of the ejected rod is estimated rigorously to yield the proper rod worth. The simulations are performed in the one-step manner such that the entire calculation for rod ejection is carried out with a single input deck without any prior calculation. All the kinetics data such as the fractions and decay constants of the delayed neutron precursors are directly obtained from the suitable evaluated nuclear data files. Doppler feedback is modeled by the direct estimation of the fuel temperature profiles inside each pellet. The transient results for the five ejection tests are compared with the measured data such as the peak time and magnitude of the power pulse, the net power release up to the power peak, and the post-burst power level. The good agreement between the nTRACER results and measured data demonstrates the efficacy of direct whole core dynamics calculation as well as the accuracy of nTRACER. In addition, a comparison is made with a two-step calculation to demonstrate the advantage of the direct whole core transient calculation.

COMPARISON OF MEASURED AND CALCULATED CONTROL ROD REACTIVITY OF THE RSG-GAS CORE

COMPARISON OF MEASURED AND CALCULATED CONTROL ROD REACTIVITY OF THE RSG-GAS CORE . The reactivity worth and a calibration curve of control rods are important physical parameters on account of the nuclear safety of the RSG-GAS reactor core. Reactivity characteristics of control rods must be determined not only, but also in the first criticality and also after any substantial changes in the reactor core. The required time to measure the reactivity worth by various methods depends mostly on the quality of the reactivity measurement devices. The rod-insertion method has some specific advantages which make such compensation unnecessary while yielding both integral and differential reactivity worth curves, as well as total reactivity worth. In this study, the total control rod worth of RSG-GAS is calibrated experimentally using a rod-insertion method to verify calculation results for the new core configuration. Calculations were done by diffusion and Monte Carlo methods using Batan-3DIFF and MCNP5 codes. Total control rod reactivity worth of the control rod is obtained 17.54 $, 17.03 $, and 17.87 $ by experiment, Batan-3DIFF, and MCNP5 calculations, respectively. The relative difference between the experimental and calculated values of control rod reactivity worth is about 3.0 %, which indicates a good agreement between the applied experimental method and calculation.

Evaluation of Fixed Absorber Reactivity Measurement in the Prototype Fast Reactor Monju

In the prototype fast breeder reactor Monju, fixed absorber worth was measured as the difference of core reactivity measured by control rod worth between cores with and without a single fixed absorber or three fixed absorbers. In this paper, the measurements are evaluated in detail, and their reliability and usefulness as validation data are investigated through a comparison with calculations using the latest neutronics design methodology developed at Japan Atomic Energy Agency. Calculated-to-experiment values and their uncertainties of fixed absorber worth were 1.00 ± 0.05 and 1.02 ± 0.04, respectively. Through this study, the measurements and calculations were found consistent and reliable.

Delayed fast neutron as an indicator of burn-up for nuclear fuel elements

Feasibility study of burn-up analysis and monitoring using delayed fast neutrons was investigated at Missouri University of Science and Technology Reactor (MSTR). Burnt and fresh fuel elements were used to collect delayed fast neutron data for different power levels. Total reactivity varied depending on the burn-up rate of fuel elements for each core configuration. The regulating rod worth was 2.07E-04 Δk/k/in and 1.95E-04 Δk/k/in for T121 and T122 core configurations at 11 inch, respectively. Delayed fast neutron spectrum of F1 (burnt) and F16 (fresh) fuel elements were analyzed further, and a strong correlation was observed between delayed fast neutron emission and burn-up. According to the analyzed peaks in burnt and fresh fuels, reactor power dependency was observed and it was determined that delayed neutron provided more reliable results at reactor powers of 50 kW and above.

The effect of control rods on the reactivity and flux distribution of BWR 4 bundle using MCNPX Code

This paper has three main objectives related to the neutronic and burnup analysis of the BWR (Boiling Water Reactor) Four-Lattice. The first objective is to provide partial validation of the MCNPX code for this lattice by comparing its results with Scale-5.1 results. Validation of the MCNPX to calculate effective multiplication factor and reactivity rod worth for the F-Lattice is provided. This is carried out in case of instantly removing the control blade and replacing it with a graphite moderator. Moreover, spatial neutron flux distributions using F-mesh card over the bundle and the control blade are investigated at inserting and withdrawing the B4C. The second objective is to perform parametric design studies of the F-Lattice. Areas of particular interest are the effect of increased or decreased blade width on the neutron flux throughout the bundle. It is found that the presence of carbon in the control blade at withdrawing the B4C makes the reactor supercritical, (K-eff = 1.22206). On the other hand, the use of B4C blade presents (K-eff = 0.93521). Consequently, the reactivity of 10% B4C thinner case is higher that of 10% B4C thicker. The simulation also showed that the B4C blade had an effective role in decreasing the thermal flux at the periphery of the bundle. This is contrast to the effect of carbon that moderates fast to thermal neutrons. The third part of this work aims at studying the burnup calculations using MCNPX code for 30 days burn with 1 day time step then for 20 months burn with 2 week time steps for the lattice. At the end of the work, it is very important to determine the most proper bundle model that achieves a prolonged fuel burn and flatting thermal flux distribution. For reaching this goal, three cases (B4C, 10% thinner of B4C and 10% thicker) are simulated by MCNPX code till 70 GWd/ton. It is found that the B4C and 10% thicker are the appropriate models that can satisfy the safety considerations of the Compact Modular Boiling Water Reactor.

A fast online procedure of background current elimination from dynamic rod worth measurement

The Dynamic Rod Worth Measurement (DRWM) is a fast and accurate method for measuring the value of control rods. During the process of DRWM, the minimum value of the detector current will reach the order of 10-11A. At this time, the impact of the gamma background current on the rod worth estimation is so big that the results of the reactivity calculation will deviate significantly from its true value. This paper presents a fast online procedure of background current elimination, with the verification results of the algorithm from the actual measured data of Tianwan Nuclear Power Plant 1# unit. The test results show that the algorithm displays the superior performance under the actual measurement noise level. The relative deviation between the result and the theoretical value is within 10%.