UNCERTAINTY ANALYSIS OF SUB-EXERCISES IN UAM-SFR BENCHMARK WITH THE MCS CODE

In recent years, there has been an increasing demand from nuclear research, industry, safety, and regulation for best estimate predictions to be provided with their confidence bounds. Consequently, Organization for Economic Cooperation and Development (OECD)/Nuclear Energy Agency (NEA) has initiated an international uncertainty analysis in modeling (UAM) benchmark focused on uncertainty analysis in best-estimate coupled code calculations for design, operation, and safety analysis of light water reactors (LWRs). The title of this benchmark is “OECD/NEA UAM-LWR benchmark”. Reference systems and scenarios for coupled code analysis are defined to study the uncertainty effects for all stages of the system calculations. Measured data from plant operation are available for the chosen scenarios. The proposed technical approach is to establish a benchmark for uncertainty analysis in best-estimate modeling and coupled multiphysics and multiscale LWR analysis, using as bases a series of well-defined problems with complete sets of input specifications and reference experimental data. The objective is to determine the uncertainty in LWR system calculations at all stages of a coupled reactor physics/thermal hydraulics calculation. The full chain of uncertainty propagation from basic data, engineering uncertainties, across different scales (multi-scale), and physics phenomena (multiphysics) is tested on a number of benchmark exercises for which experimental data are available and for which the power plant details have been released. The principal idea is (a) to subdivide the complex system/scenario into several steps or exercises, each of which can contribute to the total uncertainty of the final coupled system calculation, (b) to identify input, output, and assumptions for each step, (c) to calculate the resulting uncertainty in each step and (d) to propagate the uncertainties in an integral system simulation for which high quality plant experimental data exist for the total assessment of the overall computer code uncertainty. The main scope covers uncertainty (and sensitivity) analysis (SA/UA) in best estimate modeling for design and operation of LWRs, including methods that are used for safety evaluations. As part of this effort, the development and assessment of different methods or techniques to account for the uncertainties in the calculations are to be investigated and reported to the participants. The general frame of the OECD/NEAUAM-LWR benchmark consists of three phases with different exercises for each phase: Phase I (neutronics phase), Phase II (core phase), and Phase III (system phase). The focus of Phase I is on propagating uncertainties in standalone neutronics calculations and consists of the following three exercises.

A thorough understanding of the reactor core thermal hydraulic behavior is essential for the design and safety analysis of Sodium-cooled Fast Reactors (SFR). Due to the application of hexagonal subassembly, the core thermal hydraulic behavior is significantly affected by the flow field within the subassemblies, the inter-wrapper region and the hot pool. Analysis of the core thermal hydraulic behavior requires a model coupling the three regions mentioned above, which has been identified as one of the thermal hydraulic challenges in SFR. In the present study, a 3D model that covers the three regions was developed for the core of the China Experimental Fast Reactor (CEFR) with the Computational Fluid Dynamic (CFD) code, Fluent. The inter-wrapper region and the hot pool were modeled in detail, while the subassemblies were modeled with a special porous medium model. The core thermal hydraulics behavior under steady state was studied, more specifically, information for the flow field distribution at the core outlet, the inter-wrapper flow and the duct wall temperature distribution was obtained. Under steady state, liquid sodium in the inter-wrapper region is supplied by the inner region of the hot pool. And it enters the inter-wrapper region from the core outer region and returns back to the hot pool inner region from the core central region. The inter-wrapper flow is cooled by non-fuel subassemblies and heated up by fuel subassemblies. For non-fuel subassembly, the ratio of the total heat transfer rate between the inter-wrapper flow and the subassemblies to the heat generated within subassemblies could reaches 96%; for fuel subassemblies, the maximum ratio of the total heat transfer rate between the inter-wrapper flow and the subassemblies to the heat generated within subassemblies is 2.45%. Significant temperature gradients have been observed on the duct wall, with maximum values of 156.69 K/m in the vertical direction and 2,196.00 K/m in the circumferential direction. The largest temperature gradient appears on the duct of subassemblies adjacent to the transition region of fuel subassemblies and non-fuel subassemblies.

This paper provides a description of the education and training activities related to sodium fast reactors, carried out respectively in the French Sodium and Liquid Metal School (ESML) created in 1975 and located in France (at the CEA Cadarache Research Centre), in the Fast Reactor Operation and Safety School (FROSS) created in 2005 at the Phenix plant, and in the Institut National des Sciences et Techniques Nucléaires (INSTN). It presents their recent developments and the current collaborations throughout the world with some other nuclear organizations and industrial companies. Owing to these three entities, CEA provides education and training sessions for students, researchers, and operators involved in the operation or development of sodium fast reactors and related experimental facilities. The sum of courses provided by CEA through its sodium school, FROSS, and INSTN organizations is a unique valuable amount of knowledge on sodium fast reactor design, technology, safety and operation experience, decommissioning aspects and practical exercises. It is provided for the national demand and, since the last ten years, it is extensively opened to foreign countries. Over more than 35 years, the ESML, FROSS, and INSTN have demonstrated their flexibility in adapting their courses to the changing demand in the sodium fast reactor field, operation of PHENIX and SUPERPHENIX plants, and decommissioning and dismantling operations. The results of this ambitious and constant strategy are first sharing of knowledge obtained from experimental studies carried out in research laboratories and operational feedback from reactors, secondly standardized information on safety, and finally the creation of a “sodium community” that debates, shares the knowledge, and suggests new tracks for a better definition of design and operating rules.

Challenges and progress of uncertainty analysis for the pebble-bed high-temperature gas-cooled reactor

The Super System Code of the Korea Atomic Energy Research Institute (SSC-K) has been developed for the transient analysis of the Korea Advanced LIquid MEtal Reactor (KALIMER) system. Recently, a detailed three-dimensional (3-D) core thermal-hydraulic model was developed to describe nonuniformities of radial temperature and flow within a subassembly and to decrease the uncertainties in the reactor safety margins during accident situations. The Shutdown Heat Removal Test-17 (SHRT-17) performed in the Experimental Breeder Reactor-II (EBR-II) and the postulated unscrammed events for the KALIMER conceptual design have been analyzed using a code system that has coupled a detailed 3-D core thermal-hydraulic model with SSC-K. The coupled code predicted behaviors for the experimental trends for the protected loss-of-flow SHRT-17. The KALIMER-150 design was adopted for a plant application of the same code system. Three events, unprotected transient overpower (UTOP), unprotected loss of flow (ULOF), and unprotected loss of heat sink (ULOHS) were analyzed, and the simulation results were compared to those obtained using another code system that has coupled the Safety Analysis Section SYStem (SASSYS)-1 code with the same detailed 3-D core thermal-hydraulic model. The results, calculated with SSC-K coupled with the detailed 3-D core thermal-hydraulic model showed good agreement with the calculated results of the SASSYS-1 coupled code system for the UTOP and ULOF; however, some discrepancies were shown in the results for the ULOHS. These were found to have occurred because of a difference of the modeling for the decay heat removal system and primary coolant inventory. Through these analyses, the coupled code system was validated in order to be available for the safety analysis of a liquid-metal reactor (LMR) plant.

In recent years, the demand to provide best-estimate predictions with confident bounds is increasing for the nuclear reactor performance and safety analysis. The Organisation for Economic Co-operation and Development Nuclear Energy Agency has been developing an international benchmark of the light water reactor (LWR) uncertainty analysis in modeling (UAM) for the examination of uncertainty quantification and propagation methodologies with various modeling and simulation code systems. The objective of the present work is to develop an uncertainty propagation mechanism based on the stochastic sampling method by taking into account the uncertainties of both basic nuclear data and fuel modeling parameters in the simulation of pressurized water reactors (PWRs) that can be incorporated in the conventional LWR simulation approach. More specifically, the Three Mile Island Unit 1–related exercises from the LWR-UAM benchmark have been modeled using the coupled TRACE/PARCS code system in the three-dimensional core representation. The input uncertainties of the neutronics simulation include few-group cross sections and kinetics parameters generated using the Sampler/Polaris sequence of SCALE 6.2.1. Several heat transfer–related variables for the fuel modeling were considered as sources of input uncertainty of the thermal-hydraulics simulations, including the thermal conductivity of fuel and cladding, fuel heat capacity, and the gap conductance. Dakota was used to sample input parameters of the coupled code system and to perform the uncertainty analysis. Two types of simulations were conducted: steady-state calculation at hot full-power condition and transient scenario initiated by the spatially asymmetric rod ejection accident. Quantities of interest for the steady-state calculation, including core multiplication factor and power peaking factors, were calculated with associated uncertainties. For transient calculations, best-estimate plus uncertainty results of the time evolution of core reactivity, core power, and peak fuel temperature were generated and analyzed. The Wilks’ formula was used to determine the necessary sample size to achieve a 95% confidence of the 95% limit of output quantities of interest. Although the uncertainty propagation and quantification method presented in this paper was developed for PWRs, it could be in general applicable to the multiphysics uncertainty quantification of other types of LWR cores.

3D numerical simulation on thermal hydraulic characteristics in integrated sodium pool of PHENIX reactor during dissymmetric test

Quantification and propagation of neutronics uncertainties of the Kozloduy-6 VVER-1000 fuel assembly using SCALE 6.2.1 within the NEA/OECD benchmark for uncertainty analysis in modelling of LWRs

The Ramm-Johannsen correlation of eddy diffusivity for momentum is used to compute the onset and growth of flow laminarization in triangular rod bundles. The laminarization is indicated by Reynolds numbers based on the bulk flow condition in the coolant channel. Simple correlations that qualitatively estimate the transition Reynolds numbers are developed for applications in the safety analysis of liquid-metal fast breeder reactors.

The postulated core disruptive accidents (CDAs) are regarded as particular difficulties in the safety analysis of liquid-metal fast reactors (LMFRs). In CDAs, the motions and interactions of solid particles, such as refrozen fuels, disrupted pellets, etc., not only dominate fundamental behaviors of multiphase flows, but also drastically influence the process of CDAs. The fast reactor safety analysis code, SIMMER-III, which is a 2D, multi-velocity-field, multiphase, multicomponent, Eulerian, fluid dynamics code coupled with a fuel-pin model and a space- and energy-dependent neutron kinetics model, was successfully applied to a series of CDA assessments. However, strong interactions among solid particles as well as particle characteristics in multiphase flows with rich solid particles were not taken into consideration for fluid-dynamics models of SIMMER-III. In this article, a hybrid method for multiphase flows analysis is developed by coupling the discrete element method (DEM) with the multi-fluid model of SIMMER-III. In the coupling algorithm, motions of liquid and gas phases are solved by a time-factorization (time-splitting) method. For the solid phases, contacts among particles and interactions with fluid phases are considered through DEM. Numerical simulations of dam-break behavior with rich solid particles show reasonable agreements with corresponding experimental results. It is expected that SIMMER-III coupled with DEM could provide a promising and useful computational tool for complicated multiphase-flow phenomena with high concentration of solid particles.Copyright © 2012 by ASME

Uncertainty and sensitivity analyses as a validation tool for BWR bundle thermal–hydraulic predictions

Study of neutronic performance analysis of Sodium-Cooled Fast Reactor (SFR) design based on the variations of output power using radial fuel suffling strategy has been performed. SFR is a type of the generation IV reactor that is widely researched for application on a commercial scale. The reactor design uses natural uranium as a fuel and Sodium as a coolant. The research has been carried out by using the SRAC code and JENDL-3.2 as a library with two dimensional R- Z suffling strategy of cylinder core for variations of power output 300, 350, 400, 450 and 500 MWTh. The neutronic parameters such as a multiplication factor (k-eff and k-inf) and burn-up analysis are observed. The SFR core is separated into 10 regions having the same volume fraction in the radial direction. At beginning of burn-up process, the reactor core is only filled with natural uranium fuel called fresh fuel and prepared for the one cycle of 10 years of burn-up time. The burn-up result in the first region is shifted into the second region, the burn-up result in the second region is shifted into the third region, and so on until burn-up result into the tenth region. The burn-up result in the tenth region is removed from the reactor core, then the first region can be filled with fresh natural uranium fuel and so on up to 10 times fuel cycles of reactor operation. The neutron calculation results indicate that the multiplication factors (k-eff and k-inf) in a critical condition are occurred on the 300 MWTh of output power. Overall, the output power of 300 MWTh has requirements and a greater chance of being operated for SFR designed.

Safety issues are particularly crucial for sodium-cooled fast reactors (SFRs). Data obtained from SFR safety analyses over recent years have shown that a specific type of sloshing motion probably occurs in the molten pool during core disruptive accidents (CDAs) of SFRs due to local neutronic power excursion or pressure developments, thereby significantly influencing recriticality. Recognizing the importance of improving the evaluation of CDAs of SFRs, extensive knowledge about this phenomenon has been garnered through experimental studies of their thermal-hydraulic mechanism and characteristics. Based on these studies, simulations using various numerical approaches, such as SIMMER code, the finite volume particle method, and the smoothed particle hydrodynamic method, have attempted to reproduce the sloshing motion under various experimental conditions to verify their reasonability and applicability, thereby promoting the development of SFR safety analysis. To provide useful references for future SFR safety analyses and assessments, we have systematically reviewed and summarized these experimental and numerical investigations into the thermal-hydraulic aspect of molten-pool sloshing motion. In addition, to enhance deeper and more comprehensive research into sloshing motion, we have also discussed future prospects. Knowledge gained from experimental and numerical investigations into molten-pool sloshing motion is valuable not only for improving and verifying SFR safety analysis codes but also for providing reference data for studies of sloshing motion in other fields of engineering.

The demonstrated technological feasibility of Sodium-cooled Fast Reactors (SFRs) makes them stand out among the other reactor concepts proposed by Generation IV International Forum (GIF) for short-term deployment. The availability of reliable computational tools in support of safety analyses and plant simulations under complex transient scenarios is essential to assure SFR’s compliance with the highest safety goals.Answering this need, a multi-physics three-dimensional core and system model is being developed to enable a more detailed representation of the physics of the plant and to anticipate more accurately plant behaviour, even under wider three-dimensional scenarios, such as asymmetric transients. The coupling will be performed using the U.S.NRC system codes TRACE-PARCS, modified to simulate more accurately when using sodium as coolant.The publicly available end-of-life tests conducted in the French SFR Phenix were chosen as baseline to perform a first validation of the computational model. The development of the tool started with a three-dimensional thermal-hydraulic nodal system of Phenix using the TRACE system code.The system simulates the Phenix end-of-life natural circulation test and the result have been compared with published experimental and benchmark results. The main physical phenomena of the 3 phases of the transient (rise in temperature in the low part of the reactor vessel, establishment of natural convection and subsequent cooling of the lower and upper part of the vessel) are predicted by the developed nodal system. More specifically, the analysis of parameters such as Intermediate Heat Exchangers (IHX), primary pumps and core temperatures, shows that the developed system is able to predict and study natural convection phenomena in Phenix-type reactors.The three-dimensional nodal system is able to clearly illustrate the existing thermal stratification in the hot pool, which is neglected by one-dimensional systems and enables the modelling of thermal hydraulic asymmetric behaviour, as it is shown by the uneven flow distribution in Phenix’s primary IHXs as they are asymmetrically located in the reactor vessel.

Nuclear data uncertainty and sensitivity analysis of the VHTRC benchmark using SCALE