Reactivity Insertion Research Articles

Higher orders of Magnus expansion for point kinetics telegraph model

Neutron transport has been still under very active development in research institutions and academia throughout the world. The spatial, temporal, energy and directional angle dependence make it remains one of the most computationally challenging problems in the world. The correct P1 approximation to the neutron transport equation is not the first order diffusion equation, but the second-order in time, which is called telegraph equation. In this paper, a synopsis derivation of the point kinetics telegraph model is obtained from the neutron transport equation as a couple system of stiff differential equations. The problem of the obtained system is formulated in the matrix form and solved by higher orders Magnus expansion, where the first successive three orders of Magnus expansion are derived analytically for the point telegraph equations with multi-group of delayed neutrons and various different types of reactivity. These approximations depend on the exponential function of Magnus matrix, where the calculations are obtained using the eigenvalues of Magnus matrix and the corresponding eigenvectors. The proposed methods are tested using different cases of reactivity such as step, ramp and sinusoidal reactivity insertions. The numerical results indicate that the high order of Magnus expansion approximations is accurate compared with the traditional methods.

Dynamic Analysis on the Safety Criteria of the Conceptual Core Design in MTR-type Research Reactor

One of the high-priority research activit ies in BATAN is designing a new MTR-type research reactor with a new fuel. The core follows a compact core model that consists of 16 fuels and 4 control rods. The increasing heat flux at the fuel will cause the temperature of the fuel and cladding to increas e so that the coolant flow rate needs to b e increas ed . However, the coolant flow rate in the fuel element is limited by the thermal-hydraulic stability in the core. Therefore, dynamic analysis is important in evaluating the design and operation of nuclear reactor safety. The objective of this research work is to carry out a dynamic analysis for a conceptual MTR research reactor core fuelled with the low-enrichment U9Mo-Al dispersion. The calculations were performed using WIMSD-5B, Batan-2DIFF, Batan-3DIFF, POKDYN, and MTRDYN codes. Steady-state thermal-hydraulic parameters and dynamic analysis were determined using the MTRDYN code. The calculation results show that t he maximum temperatures of the coolant, cladding, and fuel meat with the uranium density of 3 . 96 g cm -3 are 76.01 °C, 192.02 °C, and 196.24 °C, respectively. The maximum value of fuel meat temperature for safety limit is 210 °C, which means that the maximum temperatures fulfill the design limit, and therefore the reactor operates safely at the nominal power. The dynamic analysis shows that inherent safety can protect the reactor operation when insertion of reactivity occurs in the core.

Kinetics experiments in ZED-2 using heterogeneous cores of advanced nuclear fuels

Neutronic transient measurements of substitution cores composed of low enriched uranium oxide driver fuel and uranium-plutonium (as simulated mid-burnup natural uranium), plutonium-thorium, or uranium-233-thorium mixed oxide fuels in a heavy water moderated lattice are presented. The measurements recorded flux at several detector locations outside the core while reactivity insertions of varying scale were conducted. The results provide valuable data to explore point and 3D reactor models. Inverse point-kinetics analyses of the recorded flux indicate that delayed parameters tabulated by only the fission-rate per nuclide provide similar results to adjoint-weighted kinetics parameters calculated by MCNP6 via the iterated fission probability method, on the timescale of delayed neutrons. However, the inadequacy of the conventional delayed photoneutron parameters, which are based on measurements of uranium-235 in D2O, is clearly shown in the computed reactivity. The importance of delayed photoneutrons in heavy water reactor kinetics necessitates an improved understanding of the delayed photoneutron group structure by nuclide and appropriate adjoint-weighting for photoneutrons.

New kinetic simulation capabilities for Tripoli-4®: Methods and applications

Thanks to the growing computer power, it is now feasible to apply Monte Carlo methods to the solution of non-stationary transport problems in reactor physics and in criticality-safety, which play an instrumental role in producing reference numerical solutions for the analysis of transients occurring during normal and accidental behaviour. In this respect, a major scientific challenge is represented by the very different time scales of neutrons and precursors, which demand distinct strategies and variance reduction techniques with respect to stationary simulations. In this work we will present the principal algorithms and simulation methods that have been explored and selected for the kinetic capabilities of Tripoli-4®, the production Monte Carlo code developed at CEA. The efficiency of the tested methods will be demonstrated on simple geometries as well as on step reactivity insertion and extraction due to control rod movements for the experimental reactor SPERT-III E-core. The solutions obtained by using Tripoli-4® will be compared to the point-kinetics approximation and to the asymptotic analysis based on alpha eigenvalues.

Investigations of Rod Positions for Treat M8CAL Analyses

The transient reactor test facility (TREAT), a graphite moderated experimental reactor, is scheduled to restart in late 2017. There is now renewed interest in development of capabilities to model and simulate the TREAT transients using three-dimensional coupled physics. To validate existing transient analysis tools as well as those under development, several temperature-limited transients have been modeled and analyzed. These transients are from the M8 calibration (M8CAL) experiment series, a set of experiments performed to calibrate the reactor detectors for the planned M8 series of fuel tests. Detailed reactor models were prepared that were then used to calculate the pretransient and post-transient keff values as well as corresponding reactivity insertions. Alterations to modeled values of shutdown and initial transient rod insertion depths were made to better match the reported experimental values of reactivity insertions assuming just critical pretransient states. It was found that two of the altered media inputs, fuel and Zircaloy-3 cladding, had significant effects on the keff. In addition, increasing shutdown rod insertion by 3–5 cm and decreasing initial transient rod insertion by 1–2 cm gave perfect pretransient keff and total reactivity insertion values. However, the revised positions are as much as a factor of 3–20 different from reported uncertainty of 0.762 cm. This suggests that boron concentration uncertainties may play a significant role in accurately modeling the TREAT transients and should be investigated thoroughly.

Multiphysics Modeling of Pressurized Water Reactor Fuel Performance

Nuclear fuel rods operate under complex radioactive, thermal, and mechanical conditions. Nowadays, fuel rod codes usually make great simplifications on analyzing the multiphysics behavior of fuel rods. The present study develops a three-dimensional (3D) module within the framework of a general-purpose finite element solver, i.e., abaqus, for modeling the major physics of the fuel rods. A typical fuel rod, subjected to stable operations and transient conditions, is modeled. The results show that the burnup levels have an important influence on the thermomechanical behavior of fuel rods. The swelling of fission products causes a dramatically increasing strain of pellets. The variation of the stress and the radial displacement of the cladding along the axial direction can be reasonably predicted. It is shown that a quick power ramp or a reactivity insertion accident can induce high tensile stress in the outer regime of the pellet and may cause further fragmentation to the pellets. Fission products migration effects and differential thermal expansion become more severe if there are flaws or imperfections on the pellet.

Importance of parametric uncertainty in predicting probability distributions for burst wait-times in fissile systems

A method of uncertainty quantification in the calculation of wait-time probability distributions in delayed supercritical systems is presented. The method is based on Monte Carlo uncertainty quantification and makes use of the computationally efficient gamma distribution method for prediction of the wait-time probability distribution. The range of accuracy of the gamma distribution method is examined and parameterised based on the rate and magnitude of the reactivity insertion, the strength of the intrinsic neutron source and the prompt neutron lifetime. The saddlepoint method for inverting the generating function and a Monte Carlo simulation are used as benchmarks against which the accuracy of the gamma distribution method is determined. Finally, uncertainty quantification is applied to models of the Y-12 accident and experiments of Authier et al. (2014) on the Caliban reactor.

Numerical Study of Integral Inherently Safe Light Water Reactor in Case of Inadvertent DHR Operation Based on the Multiscale Method

In detailed previous work by the authors, an innovative decay heat removal (DHR) system has been proposed and designed for the Integral Inherently Safe Light Water Reactor (I2S-LWR). The current paper studies the inadvertent actuation of one DHR system train during I2S-LWR normal operation due to a false signal or operator action. The RELAP5 code is used to perform a one-dimensional study, and important thermal-hydraulic characteristics, including primary loop coolant flow rate, pressure, temperature, DHR primary-side flow rate, and coolant temperature, are achieved during this transient. Then, a detailed computational fluid dynamics simulation utilizing STARCCM+ is carried out to investigate the coolant mixing characteristics in the downcomer and lower plenum and obtain the local thermal-hydraulic conditions at the reactor core inlet. It is found that as a consequence of inadvertent DHR actuation, the maximum overcooling at the reactor core inlet is about 3 K, which would not result in significant reactivity insertion. Furthermore, a more severe transient of inadvertent DHR operation with intermediate loop break is studied, and the results show that this would not lead to more significant overcooling to the I2S-LWR core compared with inadvertent DHR operation without intermediate loop break. This work is an indispensable supplement for DHR system comprehensive assessment in the I2S-LWR project.

PCI analysis of Zircaloy coated clad under LWR steady state and reactor startup operations using BISON fuel performance code

Research following the earthquake and subsequent tsunami that devastated the Fukushima Daiichi nuclear power plant, causing severe damage to the reactor cores, has led to the development of accident tolerant fuel designs. Accident tolerant fuels are described as a fuel form which exhibits improved material response, when compared to traditional uranium dioxide fuel clad by a zirconium alloy, during accident (e.g., loss of coolant accident or reactivity insertion accident) while maintaining or exceeding normal reactor operational expectations. One of the primary goals of accident tolerant fuel concepts is to reduce cladding corrosion by either replacing traditional Zircaloy cladding with a new material or by applying a coating to the outer surface of the cladding with enhanced resistance to corrosion at high temperatures. However, while coating the clad may provide an increase in high temperature corrosion resistance, it also changes the mechanical state of the cladding and potentially creates alternate failure mechanisms during reactor operations or accident conditions. This research has primarily focused on the pellet-cladding interactionmechanical response of FeCrAl (Iron-Chromium-Aluminum alloy) coated cladding during light water reactor steady state and reactor startup operations. Using the MOOSE-based, finite-element fuel performance code BISON and commercial pressurized water reactor data obtained from Diablo Canyon Unit 2, a preliminary analysis was performed to evaluate the performance of FeCrAl coated cladding under steady state operation and its mechanical stability under pellet-cladding interaction during a reactor startup. This work summarizes BISON 2-D radial-axially symmetric (R-Z) and radial-circumferentially symmetric (R-θ) simulation results by comparing 20, 50, and 100-µm FeCrAl coating thicknesses as well as FeCrAl cladding to traditional Zr-4 cladding under pellet-cladding interaction condition. The results of this study will provide a feasibility analysis for steady state and transient operational response of FeCrAl coated, Zircaloy cladding. Furthermore, this work will provide a fundamental basis for the assessment of the ability of coated cladding, as an ATF candidate, to maintain or exceed current steady state reactor operating expectations.

Abnormal control rod withdrawal analysis for innovative research reactor using PARET-ANL codes

Abstract Innovative Research Reactor 50 MW (RRI-50) is a conceptual design of an Indonesia's high-power innovative research reactor, which is designed to produce a maximum neutron flux as high as 1.0 × 1015 n/cm2 s and thermal neutron flux of 5.0 × 1014 n/cm2 s. In this study, the design basis accident slow reactivity insertion is carried out. Reactivity insertion accident (RIA) caused by the inadvertent withdrawal of all fuel rod at normal rate is simulated by using PARET-ANL transient code. In the simulation accident is assumed to occur when the reactor is in operation at high power and at low power level. During transient, the fuel rods are assumed to be in the most effective positions with insertion rate of 0.049 $/s. This reactivity worth will give effect only if the fuel rod interlock system is failed to function properly and the operator action does not follow the standard operation procedure. The analysis results show that the reactor experiences scram when it reaches its protected power at high power level of 110 % (55 MW) at period of 5 s and at low power level of 3 MW at period of 120 s, and there is sufficient safety margin for the anticipated RIA caused by reactivity feedback.

Coupling of neutronics and thermal-hydraulics codes for the simulation of reactivity insertion accident for LFR

As one of the advanced reactors proposed by the Generation IV International Forum (GIF), Lead-bismuth eutectic (LBE) coolant cooled fast reactor has shown great advantages over the other reactors. To analysis this reactor, several steps are carried out covering the code development and the coupled analysis. Firstly, the physical property of lead-bismuth, heat transfer correlation, turbulent mixing and pressure drop models are implemented into the thermal-hydraulics code COBRA-YT, where the inlet flow rate boundary condition is calculated by Computational Fluid Dynamics (CFD). The neutronics model has seven neutron energy groups and six groups of delayed neutron precursors. The neutronics parameters such as cross-section and feedback coefficient are calculated by the DRAGON code with endfb7 library. Secondly, based on sub-channel code COBRA-YT and neutron code SKETCH-N, the coupled of neutronics and thermal-hydraulics code has been developed via Parallel Virtual Machine (PVM) software platform. COBRA-YT code performs the thermal-hydraulics calculation and transfers its results such as coolant density and fuel temperature to the neutronics code SKETCH-N to update the cross-section; then SKETCH-N carries out the neutron-physical simulation of the reactor and provides the power density to the thermal-hydraulics code COBRA-YT as boundary conditions. Finally, this coupled code platform is exploited to the lead-bismuth fast reactor design to simulate some transient and control rod withdrawal accidents. The results achieved so far indicates that an increase of the reactor power and cladding temperature occurs after the control rod withdrawal, but the thermal-hydraulics results exceed their design limits. Time step size effect and withdrawal velocity analysis are also discussed.

On the effects of pre- and post-transient rod positions for TREAT temperature-limited transient powers

A set of KENO models to simulate select TREAT temperature-limited transients using the Transient Reactor eXcursion simulator (T-ReX), a hybrid deterministic-stochastic code, has been prepared. These transients are from the M8CAL experiment series, which are a set of experiments performed to determine the relationship between the fission power generated in the TREAT core and the fission power generated in experiment fuel located in an experiment vehicle. The experiments were performed to provide necessary calibration information specifically needed for planning and analysis of the M8 test series. The models have been prepared using best available information on materials and geometry. These models resulted in somewhat different reactivity values than those that were reported. Control rod positions prior to and post transient were adjusted to yield the reported critical values as well as the reactivity insertions. The effect of using different cross-section libraries as well as continuous energy vs. multigroup treatments were assessed. Finally, transient analyses were performed using T-ReX for both unmodified and modified cases and compared to experimental results. It was observed that the modified rod positions result in better agreement for maximum yield measured during the M8CAL experiments.

Dose Rates From the Accidental Withdrawal of a Fuel Element From an Open Pool-Type Reactor

This paper studies the radiological consequences resulting from withdrawal of nuclear fuel element (FE) from a core of open pool type reactor during normal operation. The FE withdrawal accident may be occurred due to human error during routine transport of spent FE process or from failure of FE clamp during reactor normal operation. For both cases, the FE will move vertically upward toward pool water surface. In case of accidental failure of fuel clamp, a negative reactivity insertion in the core after FE withdrawal and the reactor will be shutdown. MCNP5 code was used in this study to calculate the radiation dose rate levels in the reactor hall and inside the control room during FE withdrawal. The results show that the operator in control room will receive dose rate lower than permissible dose rate limit when FE reaches at depths more than to 211 cm for vertical FE and at depths more than to 246 cm for horizontal FE.

Analysis of the thermal feedback and burn up effects on kinetic parameters in TRR by the Monte Carlo method

In the safety analysis of nuclear reactors, the knowledge about kinetic parameters is significant. Effective delayed neutron fraction and prompt neutron life time depend on the time behaviour of the reactor power transient after reactivity insertion. Thus, in this article, the sensitivity analysis of the kinetic parameters to physical parameters such as fuel enrichment, fuel consumption (burn-up) and temperature changes in Tehran Research Reactor (TRR) has been investigated. For this purpose, this research has used MCNPX code for these parameters. According to the results, the amounts of ℓp parameter for poisoning method and Safety Analysis Report (SAR) are 47.9 and 45.0 μs, respectively. The obtained results have been compared to SAR. It was found that the relative difference is 6.4% for parameter. Moreover, the values of parameter for MCNPX code and SAR are 785.64 and 777.7 pcm, respectively. When compared to the available SAR data, a relative difference of 1.1% was obtained for parameter. In most cases, raising the temperature produces higher values of but reduces parameters in both LEU and HEU cases. Also, any increment in burn-up no changes in parameter but parameter reduces for both LEU and HEU cases.

Kernel approaches for fault detection and classification in PARR-2

Safety and reliability of nuclear power plants is of utmost importance. For that purpose, modern fault detection and classification (FDC) techniques are being devised to compliment the existing hardware redundancy and limit checking techniques. Among these modern techniques, Fisher discriminant analysis (FDA) and support vector machines (SVM) have been shown to be successful for FDC of nuclear reactors. By considering the fact that both FDA and SVM are basically established for linear systems and nuclear reactors are highly nonlinear processes, it becomes more intuitive to utilize some nonlinear FDC technique. To this end, application of kernel based non-linear approaches including kernel FDA (KFDA) and kernel SVM (KSVM) is proposed in this paper for fault detection and classification in Pakistan Research Reactor-2. Control rod withdrawal and accidental external reactivity insertion faults are manually executed at PARR-2, and training data is collected from the reactor based on which KFDA and KSVM models are developed. The online data is subsequently tested using the developed models which resulted into reliable fault classification.

Penn State University TRIGA Reactor Digital Reactivity Computer: Development and Testing

A digital control rod reactivity computer (DRC) has been developed using commercially available software (National Instruments LabView) for use to determine control rod worth curves for the Penn State University TRIGA research reactor. For low-worth reactivity steps, use of the prompt-jump approximation to the point kinetics equations enabled rapid calculation of rod reactivity insertions and minimized measurement noise effects. In contrast, use of the In-Hour method (an historically-effective way of determining control rod reactivity) would take several hours, compared to 30 min with the DRC for a complete control rod worth curve. All of the data acquisition, reactivity calculations, and integral control rod worth curve fitting are performed in LabView, which additionally provides for development of the graphical user interface. Results demonstrate the LabView DRC developed provides a platform for these measurements that calculates accurate control rod reactivity measurements in significantly less time than the historically accepted In-Hour method.

Application of Backward Differentiation Formulas to Neutron Kinetics Problems

The neutron kinetics equations belong to the class of stiff equations for numerical time integration schemes. In this work, the accuracy and speed of algorithms based on backward differentiation formulas (BDFs) are studied with regard to point and spatial neutron kinetics problems. Using a BDF algorithm with the automatic selection of time step and order, solutions to a number of model problems with both a positive and negative reactivity insertion are analyzed. Plots of numerical cost dependences on local and global errors are presented. The results indicate that algorithms based on BDFs are highly efficient and that their application to nuclear reactor simulation is justified.

Thermal-hydraulic Feasibility Study of a Convex shaped Fast Reactor Core

The objective of the present study is to evaluate the temperature profile of a convex shaped reactor core to confirm the thermal hydraulic feasibility. The convex core configuration intends to achieve negative reactivity insertion by fuel compaction in case of CDA. For the preliminary study, a convex core with fuel length 1.585m in the inner-core region and 0.52m in the outer-core region is modeled by RELAP5-3D code. The calculation model consists of the reactor core with 10 different channels, two IHXs, two main pumps, and lower and upper plena. The basic parameters are assumed similar to the existing study for Monju and JSFR. Considering well-balanced flow distribution to the core, the linear heat rate of the outer-core region is within the upper limit. The pressure loss and temperature distribution of the core are calculated. It is confirmed that no major issue to deny the feasibility of the fundamental thermal-hydraulics.

Machine learning based system performance prediction model for reactor control

A machine learning based system performance prediction model is currently created to support the development of autonomous control for small reactors, such as the Transportable Fluoride-salt-cooled High-temperature Reactor (TFHR), which is a 20 MWth compact core proposed by MIT for remote site applications. The prediction model consists of a reactor physics model and a thermal-hydraulic model. It is presently constructed using support vector regression (SVR) with training data generated by multiple cases of a one-dimensional reactor system model. A particle filtering framework is utilized to estimate and update model parameters with noisy instrument measurements. Verifications of the prediction and filtering models have been carried out using the TFHR reactivity insertion events. Satisfactory performance in predicting the core behavior and in recognizing transient parameters such as reactivity insertion timing and rate is concluded.

Status of severe accident studies at the end of the conceptual design of ASTRID: Feedback on mitigation features

The ASTRID reactor developed by the CEA with its industrial partners, will be used for demonstration of the safety and operability, at the industrial scale, of sodium fast reactors of the 4th generation. Among the goals assigned to ASTRID, one is to improve the safety and the reliability of such reactor (compared to previous built sodium-cooled fast reactors). Regarding the innovations promoted in the ASTRID design, a low sodium void worth core concept (CFV core) has been developed. By means of various design provisions enhancing the neutron leakage in case of sodium draining, the overall sodium void effect of the ASTRID core is near zero and could even be negative. Additionally, mitigation devices should be implemented into the core in order to limit the thermal energy released in the fuel during a severe accident. This paper deals with a synthesis of severe accident studies performed during the second period of the pre-conceptual design stage of the ASTRID project (2013–2015). The main insights of the studies in term of mitigation strategy and of mitigation device design are highlighted in the paper. The CFV core transient behavior has been investigated in case of generalized core melting situations initiated by postulated reactivity insertion ramps (UTOP) and unprotected loss of flow (ULOF). In case of UTOP transients, according to our calculations, the mechanical energy released by molten fuel vapor expansion does not exceed several tenths of megajoule. Simulated ULOF transients do not lead to energetic power excursions thanks to the mitigation provisions and to the core design. Regarding ULOF transients, early boiling phase leads to core power decrease and the primary phase of the accident is not governed by a power excursion. The paper deals with the approach and the presentation of preliminary findings regarding mitigation provisions. Those provisions are investigated by considering a postulated core degraded state representative of the end of the transition phase. The possible scenario evolutions from this degraded state provide the following parameters: mass and temperature of molten materials, mass and flow rates of materials relocated on the core catcher and possible ejected material mass above the core. Those parameters are used for the determination of approximate loadings for the primary vessel and for the core catcher.