Reactor Transient Analysis Research Articles

Whole-core analysis of Watts bar benchmark with three-dimensional MOC code STREAM3D

This paper presents a high-fidelity simulation of the Organization for Economic Co-operation and Development (OECD) Nuclear Energy Agency (NEA) 3D whole-core Watts Bar benchmark using the UNIST in-house STREAM3D (Steady State and Transient Reactor Analysis code with Method of Characteristics) neutronic code. The benchmark encompasses various whole-core exercises, including single physics problems, multi-physics simulations, and depletion problems. When comparing parameters during the zero-power physics tests, including ITC, DBW, CRW, and criticality tests, STREAM3D results indicate a strong agreement with the measured data and KENO-VI. The comparison with the MC21/CTF code in 3D HFP BOC condition demonstrated strong agreement, with only a 0.42% difference in the normalized radial power distribution, a 0.38 K difference in the RMS of the assembly coolant exit temperature, and a mere 4 ppm difference in CBC.

High-Fidelity Transient Analysis with STREAM Based on the Predictor-Corrector Quasi-Static Method

The predictor-corrector quasi-static method (PCQM) is used to solve the transient problem in the STREAM code, a steady-state and transient reactor analysis code with the method of characteristics. In PCQM, the angular neutron flux undergoes a factorized split to form the product of shape and amplitude functions. The time-dependent neutron transport equation is solved to obtain the shape function whereas the amplitude function is obtained by resolving the exact point kinetics equations (EPKEs). A two-level coarse mesh finite difference technique is implemented to reduce the transient running time of the transport solution. Moreover, high-order polynomial interpolation is applied to the kinetics parameters utilized in EPKEs to reduce the error when the reactivity insertion is nonlinear. Several numerical benchmarks are solved to justify the application of the procedure, proving that the method maintains solution accuracy.

Startup analyses of a megawatt heat pipe cooled reactor

Heat pipe cooled reactors experience temperature rises of up to 800 K during startup. The in-core heat pipes and the energy conversion system are initially frozen, which leads to a highly coupled heat transfer system that has significant safety challenges. This work modeled the system startup using a two-dimensional heat pipe model and an open-air Brayton cycle model coupled to the Heat Pipe Reactor TRANsient analysis code, HPRTRAN. The heat pipe model was validated with startup experiments showing that the predicted heat pipe wall temperature was within 30 K of the measured temperatures. The Brayton cycle model was validated against experimental data in the literature. The analysis code was then used to analyze a megawatt heat pipe reactor connected to an open-air Brayton cycle, which was used to study the influence of the external reactivity and the inherent feedback on the startup process. The simulations show that the reactor startup process is sensitive to the heat pipe operating state. The startup process can be divided into the subcritical stage, heat pipe startup stage, and increasing power stage. The power peak amplitudes are significantly reduced by slowing the angular speed of the control drum. Reducing the control drum angular speed from 0.1°/min to 0.05°/min reduced the first power peak from 2000 kW to 1000 kW. A modified reactor startup control strategy was then developed that ensures the core safety with the reactivity introduced in steps. Smaller reactivity insertions reduce the power peaks during the initial startup but lead to much longer startup times. A reasonable balance was obtained by repeated insertions of either 30 pcm or 60 pcm for safe startups of the heat pipe cooled reactor.

Validation of EOPs/FRGs Procedures Using LOHS Scenario

Validation of EOPs (Emergency Operating Procedures) and FRGs (Function Restoration Guidelines) can be achieved either through plant full scope simulator or on desk top exercises. The desk top exercise is conducted when for the given scenario plant full scope simulator is not suitable. In either verification cases predefined scenario should be evaluated and possible branching foreseen. The scenario presented is LOHS, with bleed and feed procedure initiated. Best estimate light water reactor transient analysis code RELAP5/mod3.3 was used in calculation. Standardized detailed plant model was used. Operator actions were modelled from beginning of the scenario to its termination.

HEART, a specific code for thermal-electrical analysis of heat pipe cooled nuclear reactor

Heat pipe cooled reactor (HPR) features high power density, compact structure, long operation life and high reliability, which is an excellent candidate for small nuclear power source for deep space or underwater missions. In this paper, a conceptual Nuclear Silent Thermal-Electrical Reactor (NUSTER) is preliminarily designed, using 109 sodium heat pipes for passive cooling. The thermoelectric generators (TEGs) are employed in the reactor to convert fission heat to electric power. Based on the design, a HEat pipe cooled Advanced Reactor Transient analysis code (HEART) is developed, including point reactor kinetics model, multi-channel model, core heat transfer model, heat pipe model, thermoelectric generator model and coolant model. The models proposed in HEART are preliminarily verified against the design value and experiment data, and the maximum deviation is less than 12.3%. Steady-state performance of the NUSTER are successfully predicted by HEART, and results indicate that the solid-state core has good temperature flattening ability. The surface temperature of the heat pipe is less than 1300 K, and the average temperature drop of the TEG module in central channel is 724.1 K, which can produce an electrical power of 301.94 W. The models developed in HEART can also be applied to other heat pipe cooled reactors, providing valuable experience in design and thermal-hydraulic evaluation of HPRs.

Pin-by-Pin Coupled Transient Monte Carlo Analysis Using the iMC Code

In this article, we present a coupled multi-physics Monte Carlo reactor transient analysis framework implemented in the KAIST Monte Carlo iMC code. In the multi-physics framework, the time-dependent neutron transport calculation and the transient heat transfer analysis are done based on the predictor–corrector quasi-static Monte Carlo method and the three-dimensional finite element method, respectively. Using this high-fidelity analysis framework, we demonstrated the negative temperature feedback effect in two pressurized water reactor (PWR) transient scenarios. First, a 3-D burnable absorber-loaded fuel assembly was considered with all reflective boundary conditions. In this simple problem, a positive reactivity-induced transient was analyzed to characterize the reactor responses in view of the pin-wise power and temperature distribution. Second, the iMC multi-physics analysis is applied to a control rod withdrawal transient in the TMI-1 mini core problem, and detailed time-dependent results were provided and compared with the Serpent/SUBCHANFLOW analysis. In both cases, independent MC runs were performed to quantify the uncertainty of the multi-physics MC transient analysis.

Data-driven modeling of coarse mesh turbulence for reactor transient analysis using convolutional recurrent neural networks

Advanced nuclear reactors often exhibit complex thermal-fluid phenomena during transients. To accurately capture such phenomena, a coarse-mesh three-dimensional (3-D) modeling capability is desired for modern nuclear-system code. In the coarse-mesh 3-D modeling of advanced-reactor transients that involve flow and heat transfer, accurately predicting the turbulent viscosity is a challenging task that requires an accurate and computationally efficient model to capture the unresolved fine-scale turbulence.In this paper, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor. The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data to ensure accuracy. A novel neural network architecture, combining a densely connected convolutional network and a long-short-term-memory network, is developed that can efficiently learn from the spatial-temporal CFD transient simulation results. The neural network model was trained and optimized on a loss-of-flow transient and demonstrated high accuracy in predicting the turbulent viscosity field during the whole transient. The trained model’s generalization capability was also investigated on two other transients with different inlet conditions. The study demonstrates the potential of applying the proposed data-driven approach to support the coarse-mesh multi-dimensional modeling of advanced reactors.

Nuclear Thermal-Hydraulic Phenomena: Bases and Challenges

In the domain of reactor transient simulation, the identification of thermal-hydraulic phenomena (THPs) plays a major role. The system codes should model all influential THPs and should be validated against integral effect tests and separate effect tests which cover all influential THPs. The validation and the uncertainty quantification should cover every model related to an influential THP. A list of 116 THPs, recently established, covers all water-cooled reactors and design basis accident (DBA) analyses. It synthesizes more than 30 years of Organisation for Economic Co-operation and Development and International Atomic Energy Agency activities conducted by several safety specialists. A new tentative method to identify THPs was proposed based on two sources of information, the parameter evolutions in transients (depressurization, voiding, refill, heating, ...) and the set of balance equations with source and sink terms for convection, diffusion, interfacial transfers, and wall transfers. This method is just based on Gen-2 pressurized water reactor (PWR) transient analysis at the system, component, and basic process levels. The comparison of the 116 THP list with the list of the tentative methods is made in this paper for the particular case of GEN-2 PWRs. No major contradiction was found. Both methods identified phenomena at the system, component, and process level. The 116 list better identified special components that require “special models” in system codes. The use of equations identified many more local process THPs, which may help ranking phenomena in a scaling analysis and identifying validation needs. The comparison confirms a potential synergy and complementarity between approach 1, which is based on the 116 THP list, and approach 2, which is based on the tentative method; the outcome of this comparison suggests further efforts to combine them and complement them in a new international collaborative context. This analysis reports ongoing discussions between members of the Forum and Network of System Thermal Hydraulics Codes in Nuclear Reactor Thermal-Hydraulics network of system code developers.

Semi wavelet-based improved quasi static method for the analysis of PHWR transients

A new computational method, by incorporating wavelets in the improved quasi static (IQS) scheme, is developed and presented here for the analysis of CANDU PHWR and TWIGL reactor transients. According to this method the time dependent neutron diffusion equation is split into amplitude function and shape function. The amplitude function is solved using the Haar wavelet and its solution is used in the estimation of shape function. The advantage of this computational method is that the concept of micro time step and macro time step, adopted in the IQS scheme, does not arise here at all and the transient can be estimated with only one time step, i.e. single time step. In this method, the transient estimation methodology is different from the improved quasi static scheme. This computational method is applied to estimate the transients in CANDU 3D-PHWR benchmark, CANDU-2D and TWIGL reactors. In TWIGL reactor, a Doppler temperature feedback in introduced and the transient is estimated with feedback. The estimated transients are compared with the reference. From the comparison of results, it is observed that this method is capable of estimating the reactivity initiated transients in heterogeneous reactors to a good accuracy, by adopting only one time step. This computational method is first of its kind in the estimation of reactor transients. It is also shown that as the order of resolution of wavelet is increased, the error in the estimation of transient is reduced.

Time-dependent Green's function generation with Monte Carlo for transient analysis of source-driven systems

The transient analysis of nuclear reactors is an important issue from a safety point of view. The deterministic methods, by considering different approximations, are extensively used to solve the neutron transport equations. Nowadays, by the continuous increase of computational resources, the feasibility of utilization of pure Monte Carlo methodology in the nuclear reactor transient analysis, without using different approximations, is being increased. In the present work, a detailed Dynamic Monte Carlo (DMC) methodology is developed and employed to investigate the transient analysis of source driven nuclear systems. Analytically solvable time and space and time dependent problems are introduced and solved to verify variance reduction tools used in the DMC methodology. Then, the DMC method is utilized to generate time dependent Green's functions for transient analysis of the source-driven systems (SDSs) studied in literature. The equilibrium and post perturbation transient responses of source driven systems are obtained by utilizing the Green's functions generated for those systems. The newly developed novel method is applied to different transient benchmark problems of SDSs. The performance and validity of the proposed method are discussed through qualitative and quantitative comparisons with the results given for the test and benchmark problems.

Polynomial relaxation in the quasi-static approach and its implementation in nonlinear reactor transient analyses

The quasi-static (QS) method had been devised for efficient analyses of reactor transients, and two different approaches are widely implemented, which are namely Improved Quasi-Static Method (IQM) and Predictor-Corrector Quasi-Static Method (PCQM). Conventionally, both methods regard the shape to be static while deducing the variation of the amplitude. In this paper, the formulation of standard IQM and PCQM methods based on a multi-group neutron diffusion equation is presented along with a description for implementing such methods to feedback-encompassed nonlinear transient calculation. The idea of relaxation in the quasi-static treatment of the shape through polynomial interpolation is proposed, and comparison among the ramifications of having different conjectures, e.g., static, linear, and quadratic relaxation, has been made based on a thermal-hydraulics-coupled one-dimensional two-group reactor representing the pressurized water reactor. It is found that performance of both IQM and PCQM could be clearly improved with polynomial relaxations even for strongly non-linear reactor problems.

A best estimate plus uncertainty safety analysis framework based on RELAP5-3D and RAVEN platform for research reactor transient analyses

This paper develops a best estimate plus uncertainty (BEPU) framework for research reactor transient safety analysis. The BEPU framework is developed based on the system level reactor safety analysis code RELAP5-3D and the data analysis platform RAVEN developed by Idaho National Laboratory. Within the framework, a sensitivity analysis procedure is first conducted to identify the contributions and ranks of individual input parameters to the user-defined figures-of-merit (FOMs) associated with specific transient phenomena. An uncertainty analysis procedure is then performed to quantify the uncertainties of the FOMs resulting from the uncertainties of the input parameters. Many useful outcomes can be realized through the BEPU analysis. Specifically, the sensitivity information obtained from the sensitivity analysis will provide insights about the influence of each different input parameter on FOMs. The uncertainty information obtained from the uncertainty analysis will imply the range of response deviations caused by the propagation of errors existing in various input components.As a case study for research reactors, the developed BEPU framework was employed to perform design-basis accident (DBA) analysis for one conceptual research reactor design proposed at the National Institute of Standards and Technology (NIST). Two hypothetical DBA scenarios, namely the reactivity insertion accident (RIA) and the loss of flow accident (LOFA), were modeled and analyzed through the BEPU framework. To demonstrate the value of the BEPU framework, the BEPU analysis results were compared to that obtained from the conventional transient safety analysis procedure, which was conducted by using commonly used transient safety analysis codes including RELAP5-3D and PARET. The comparison shows that the BEPU analysis is capable of providing additional sensitivity and uncertainty information that help confirm safety margins of the NIST conceptual research reactor during both RIA and LOFA situations, which justifies the advantages and benefits of the BEPU safety analysis framework developed in this work.

Modeling and simulation of a High Flux Isotope Reactor representative core model for updated performance and safety basis assessments

A high-fidelity neutronics model of the Oak Ridge National Laboratory High Flux Isotope Reactor (HFIR) with a representative core and experiment loading was developed to serve as the new basis for performance and safety basis assessments. HFIR provides one of the highest steady-state neutron fluxes of any research reactor in the world to support high-impact applied and basic neutron science research. The newly developed model better characterizes ongoing and envisioned research activities at HFIR, in comparison to the legacy Cycle 400 (operated in 2004) model. The new reactor model serves as the reference for safety basis, reactor operation, in-core experiment, reactor upgrade, and other research activities. It also serves as the reference for high-enriched uranium to low-enriched uranium conversion studies, enabling consistent performance and safety metrics comparisons.Neutronic performance and safety metrics calculational methods and results including, but not limited to, cycle length estimates, flux and fission distributions, point kinetics data, reactivity coefficients, intra cycle and post shutdown source terms, and control element worths are documented herein. These neutronics results provide essential input to higher accuracy follow-on heat deposition, thermal–hydraulic, thermal-structural, reactor transient, and severe accident analyses and directly support safety analysis upgrades, startup and operations calculations, and fuel storage and transportation evaluations.Furthermore, thermal–hydraulic safety limit calculations for inlet coolant temperature, flux-to-flow, and inlet vessel pressure that utilized the neutronics results obtained with the new reactor model are discussed herein. The use of the new neutronics results led to a significant gain in thermal safety margin and enabled the removal of previous conservatism based on low-fidelity calculations.

STUDY ON MCNP6 MODEL IN THE CALCULATION OF KINETIC PARAMETERS FOR PEBBLE BED REACTOR

When conducting a nuclear reactor transient analysis, the most important parameter, called the kinetic parameter, is required. The calculation of kinetic parameters can be conducted using several methods. The deterministic method is one possible method that relies on the forward and adjoint neutron fluxes to provide the kinetic parameters calculation based on the perturbation theory. In this study, the Monte Carlo transport code MCNP6 was utilized to perform the exact prediction of the kinetic parameters of a pebble bed reactor. The core was modelled with a different fuel composition of uranium loading per pebble, <sup>235</sup>U enrichment and H/D ratio. It was found that <em>k</em>eff strongly depends on the uranium loading, uranium enrichment and H/D ratio while the <em>β</em>eff dependence is insignificant. The increase in the prompt neutron lifetime (ℓ) and mean generation time (Ʌ) as a function of H/D ratio are insignificant as compared to the decrease of those parameters in the case of uranium loading or uranium enrichment. These results conclude that the selection of uranium loading per pebble, <sup>235</sup>U enrichment and H/D ratio should be considered carefully for the control and inherent safety performances

Transient Studies on Low-Enriched-Uranium Core of Ghana Research Reactor–1 (GHARR-1)

Following the core conversion of Ghana’s miniature neutron source reactor (MNSR) from highly enriched uranium (HEU) to low-enriched uranium (LEU), there has been a change in the fuel composition, fuel, clad, and other reactor core parameters. Since the allowable core power in a nuclear reactor is limited by thermal considerations, this study presents transient analysis of the LEU core of Ghana Research Reactor−1 (GHARR-1). The transient study has been carried out using the Monte Carlo N-Particle code version 5 (MCNP5) and the Program for the Analysis of Reactor Transients (PARET)/Argonne National Laboratory (ANL) computational tools. The behavior of the reactor core at normal and accident conditions of large reactivity insertions was studied. Transient results obtained for accidental large reactivity insertions of 6.71 mk indicated that boiling might occur in the coolant because under such large reactivity insertions, the coolant temperature was close to the saturation temperature of the coolant. The results show that boiling will not occur in the core for other reactivity insertions of 1.94, 2.1, 2.99, 3.87, and 4.0 mk considering that the outlet coolant temperatures obtained are far below the saturation temperature of 100°C at a pressure of 1 atm. The clad and fuel meat temperatures obtained for all the reactivity insertions are far below the melting points of Zircaloy-4 clad material and UO2 fuel. The results of the power profiles obtained show that the reactor is inherently safe even under large reactivity insertion conditions. The results obtained were found to agree well with the available experimental results. Comparison of the results of the LEU core with the previous HEU core has shown that temperature rise in the LEU core is lower than that in the HEU core under reactor transient conditions.

Quasi-Diffusion Method with 3-D Cross Sections for TREAT Core Analysis

The conventional two-step neutronics method used to perform full-core reactor neutronics simulation has been used successfully for light water reactor steady-state and transient analysis. The first step in the method is to generate assembly homogenized few-group cross sections from a lattice transport calculation at the anticipated range of core conditions. The resulting cross sections are then used in the second step to calculate the whole-core flux distribution using nodal diffusion methods. However, when applying this method to small reactors or some experimental reactors such as the Transient Reactor Test (TREAT) Facility, the bias from approximations used in the conventional two-step method can become significant. A large source of error can be the cross sections that are generated from the assembly calculations with reflective boundary conditions since interassembly neutron leakages in small reactors can be significant. Another source of error can be the presence of large void regions such as in the TREAT core. In the work here, the shortcomings of the two-step method were addressed by using the quasi-diffusion method with cross sections obtained from a whole-core three-dimensional Monte Carlo simulation. For the nonvoid region, the group-averaged cross sections were obtained directly from Monte Carlo simulation results, and the directional diffusion coefficients were generated from flux-weighted transport cross sections and the Edington factors directly from the angular flux distribution from the Monte Carlo results. Discontinuity factors were also used in the nodal solution to preserve the neutron currents between nodes based on the Monte Carlo results. For the void region, the directional diffusion coefficients were optimized to minimize the magnitude of the discontinuity factors and thereby mitigate potential numerical problems in the quasi-diffusion method for full-core simulations. The numerical results from the TREAT core steady-state and transient analysis show that the quasi-diffusion method can reproduce the Monte Carlo whole-core results in steady state and that the transient results are in good agreement with experimental measurements.

Razorback – A reactor transient analysis code for large rapid reactivity additions in a natural circulation research reactor

Research reactors play an important role in higher education, scientific research, and medical radioisotope production around the world. It is thus important to ensure the safety of facility workers and the public. This work presents a new reactor transient analysis code referred to as Razorback. The code has been developed for the evaluation of large rapid reactivity addition in research reactors. Its initial focus is the Annular Core Research Reactor (ACRR) at Sandia National Laboratories. Results have been validated against ACRR pulse operations. Razorback models the reactor kinetics, fuel element heat transfer, fuel element thermal expansion, and natural circulation coolant channel thermal-hydraulic response. Simulation results for ACRR pulse operations are shown to agree very well with operational data obtained from the ACRR. Razorback is expected to be a valuable tool for ACRR pulse performance prediction and ACRR reactor safety analyses.

Coupling of Neutronics and Thermal-Hydraulic Codes for Simulation of the MNSR Reactor

This study aims to evaluate a simplified one-dimensional thermal-hydraulic module (THM) established by the DRAGON5/DONJON5 codes that allow a multiphysics study of the Syrian Miniature Neutron Source Research (MNSR) reactor both in steady-state and transient conditions. The purpose of this paper is therefore to describe the THM, fully integrated and implanted in DONJON5 to allow coupling with neutronic modules existing in the same code and to perform steady-state thermal-hydraulic and safety analyses of the reactor. Then we compare the results given by the THM with the results obtained by the Program for the Analysis of REactor Transients (PARET)/Argonne National Laboratory (ANL) thermal-hydraulic code. In order to validate our PARET/ANL and the THM in DONJON5, the fuel center temperature as a function of core power was calculated and compared with the corresponding values of the PARET code. Moreover, we have calculated the departure from nucleate boiling ratio. The comparison of the results of this study showed a good correlation between the values obtained with the THM and the thermal-hydraulic PARET/ANL code.

Assessment of the TRACE Code for the He-Cooled Systems Simulation Capability Against Some He-FUS3 Experimental Measurements

This paper focuses on the TRACE code assessment for helium-cooled systems thermal-hydraulic analysis. In the frame of the GoFastR (gas cooled fast reactor) European Collaborative Project, ENEA has offered some selected experimental data for the organization of a benchmark exercise aimed at the validation of the system and CFD codes for the gas reactor transient analyses. One of the Research Center Řež teams participated in it with a CFD code application. Now, the experimental data are used in order to assess the TRACE code for the ongoing high-temperature helium loop (HTHL-2) licensing process. The results of the TRACE calculations agreed very well with the experimental measurements (often within the experimental uncertainties) data provided by the He-FUS3 facility, indicating that the code, despite developed for water coolant applications, if an appropriately tuned input is adopted, it can also be suitable for reasonably accurate gas technology thermo-hydraulic simulations.

A Reduced Order Model for the Fast Predictions of Reactivity and Neutron Distributions within Reactor Cores

A new Reduced Order Model (ROM) is developed for solving the neutron eigenvalue problem for the fast and accurate prediction and simulation of the neutron flux within light water reactor cores. The method of Proper Orthogonal Decomposition is employed to form the ROM which uses snapshots obtained from a full order model based on the finite element discretisation of the spatial dependence of the multi-group neutron diffusion equation. We detail how the temperature variation and control rod adjustments can be efficiently integrated into the model and their influence then accurately predicted within the model's solution. This is particularly important as the former poses the non-linearities that form within the neutron transport equations, whilst the later can easily form challenging fluxes for the ROM to resolve. <br/> The ROM is used to predict eigenvalues for studying the reactivity of a PWR assembly under varying operating conditions, with varying temperatures, control rod settings and fuel compositions. It is able to accurately resolve reactivity under these different scenarios and provide detailed solutions of the energy dependent neutron scalar flux distributions. Importantly the run times to produce these solutions are drastically reduced, amounting to several orders of magnitude in comparison to a full order model using methods such as the finite element method. Thus it allows extremely fast solutions to a large array of calculations that may be required in scoping calculations, uncertainty quantification, and time dependent reactor transient analysis.