The Transient Reactor Test Facility (TREAT) is a high enriched, graphite moderated, air cooled reactor built for experimental transient fuel testing. Recently, the reactor was returned to operation after having been shut down since 1994. Transients at TREAT are controlled largely by control/transient rod movement and temperature feedback that is attributed to the core’s graphite-fuel matrix. To date, TREAT simulations use the standard ENDF/B-VII.1 graphite thermal neutron scattering cross sections that assume an ideal crystalline form for the core’s graphite. Historically, it has been reported that the use of these cross sections may result in a −2000 pcm discrepancy when attempting to predict TREAT criticality [1]. In this work, a multi-physics simulation of a TREAT transient is performed using the standard ENDF/B-VII.1 graphite thermal scattering cross section libraries and compared with results using graphite libraries that assume a porous graphite structure and a corresponding density consistent with TREAT graphite. The transient simulation methodology couples a full-core transient Monte Carlo calculation in the Serpent code with feedback calculated from temperature estimates derived using the computational fluid dynamics code OpenFOAM. Steady state simulations show that use of the “porous” graphite libraries allows predicting TREAT criticality to within a few hundred pcm. In the current transient simulations, the reactor’s time dependent power behavior is successfully reproduced. With this model, observables such as maximum fuel temperatures and temperature-dependent flux spectra are calculated, using both the traditional ENDF/B-VII.1 and the “porous” graphite thermal scattering libraries.

In the pebble-bed high temperature reactor under construction in China, called HTR-PM, the spherical fuel elements continuously flow downward in the cylindrical core. After the discharge, the burnup of each pebble is checked at the core outlet and, according to the achieved burnup level, the pebble might be disposed or reinserted into the upper section of the core, distributing randomly in the radial direction and defining a variable number of passes necessary to achieve the average maximum burnup of 90 MWd/kgU. Discrete Element Method (DEM) simulations have been carried out to achieve a clear understanding of the movement of 420,000 fuel pebbles in the HTR-PM core. At the same time, neutronic properties have been investigated for a single pebble and for the full core with Serpent 2 Monte Carlo code in order to perform a parametrization of the one-group microscopic cross sections at the core-level. The pebble movement has been coupled with the neutronic behavior of a single pebble in a dedicated burnup script called Moving Pebble Burnup (MPB), developed in Matlab. 3,000 single pebble burnup histories were simulated to obtain sufficient statistics and insight on the burnup process in the HTR-PM. The decrease of the average burnup gained per single pass implies that a miss-handling of recirculated fuel elements is unlikely to lead to exceedance of the maximum allowed burnup of 100 MWd/kgU. Furthermore, the core demonstrates a self-compensation effect of burnup, meaning that it always compensates burnup under- or over-runs in the successive passes. Finally, it is possible to conclude that the fuel cycle of the HTR-PM, as it has been laid out, is well-designed and feasible.

Global-local self-shielding calculation scheme is a new high-fidelity resonance calculation model proposed by NECP laboratory of Xi'an Jiaotong University. Neutron Current Method (NCM) is utilized for resonance calculation in the global aspect to obtain Dancoff factors. Then each fuel pin is transformed into individual 1D cylindrical problems by conserving Dancoff factors. The Pseudo-Resonant-Nuclide Subgroup Method (PRNSM) is used to conduct resonance calculation in the local aspect for each 1D cylindrical pin. Global-local self-shielding calculation scheme has been successfully implemented in high-fidelity numerical nuclear reactor physics code NECP-X. Verification results of global-local self-shielding calculation scheme showed good accuracy for UO2 fuels. The maximum relative error of microscopic absorption cross sections (XSs) for 238 U in resonance range was 1.5% compared with MCNP5 [1]. AIC control rods serve as strong absorbers in reactor. Strong self-shielding phenomenon occurs when AIC control rods are inserted. Analysis was performed to determine the effects of AIC control rods on the accuracy of global-local self-shielding calculation scheme and the sources of error. Evaluation results showed that the main part of error was introduced by NCM and radius searching. The relative errors were larger than 10% in several resonance groups. Therefore, a supercell model is proposed to couple with global-local self-shielding calculation scheme to treat resonance calculation for AIC control rods in this paper. Numerical results show that this model improves the accuracy of the global-local self-shielding calculation scheme. The relative errors of microscopic absorption XSs for AIC in most resonance groups were decreased to less than 2%.

Monte Carlo (MC) burnup calculation method, implemented through coupling neutron transport and point depletion solvers, is widely used in design and analysis of nuclear reactor. Burnup calculation is generally solved by dividing reactor lifetime into steps and modeling geometry into numbers of burnup areas where neutron flux and one group effective cross sections are treated as constant during each burnup step. Such constant approximation for neutron flux and effective cross section will lead to obvious error unless using fairly short step. To yield accuracy and efficiency improvement, coupling schemes have been researched in series of MC codes. In this study, four coupling schemes, beginning of step approximation, predictor-corrector methods by correcting nuclide density and flux-cross section as well as high order predictor-corrector with sub-step method were researched and implemented in RMC. Verification and comparison were performed by adopting assembly problem from VERA international benchmark. Results illustrate that high order coupled with sub-step method is with notable accuracy compared to beginning of step approximation and traditional predictor-corrector, especially for calculation in which step length is fairly long.

To solve three-dimensional kinetics problems, a high order nodal expansion method for hexagonal-z geometry (HONEM) and a Runge-Kutta (RK) method are respectively adopted to deal with the spatial and temporal problem. In the HONEM, 1D partially-integrated flux are approximated by using four order polynomial. The two order polynomial is adopted to the approximation of partially-integrated leakages. The Runge-Kutta method is adopted as a tool for dispersing the time term of 3D kinetics equation. A flux weighting method (FWM) is used for obtaining homogenized cross sections of mix node. The three-dimensional hexagonal kinetics code has been developed based on this method and tested with two benchmark problems of VVER which are the control rod ejection without any feedback and with simple adiabatic Doppler feedback. The results calculated by this code agree well with the reference results and the code is validated.

Deep penetration problems exist widely in reactor applications, such as SPRR300 (Swimming Pool Research Reactor 300), a light water moderated, enriched uranium fueled research reactor in China. Deterministic transport theory is intrinsically suitable for deep penetration. But there exist some problems when it’s applied in SPRR-300research reactors. First, the reactor core is complicated for geometry description in deterministic theory codes. Monte Carlo method has advantages in complex geometry modeling. And it uses continuous energy cross sections which are independent with specific reactor types and research objections. But usually it’s difficult to converge well enough to deal with deep penetration problems, even though there are a number of variance reduction techniques. Based on the advantages and disadvantages of Monte Carlo and Deterministic method, we proposed a coupled neutron transport calculation method for deep penetration. It combines advantages of these two methods. Firstly, we use Monte Carlo code to finish fine modeling and do the whole reactor core calculation. Domestically developed Monte Carlo code JMCT is used to do the neutron transport calculation. Then homogenized group constants in each mesh are calculated from JMCT output by a self-developed script. Afterwards, we do the whole reactor calculation with deterministic theory code TORT. It directly uses group constants generated by Monte Carlo code. Finally, we can get the deep penetration calculation results from TORT output. Verification is carried out by comparing the group constants of benchmark problem, and by comparing k eff calculated by this method with continuous energy Monte Carlo method. Benchmark calculation is conducted with OECD/NEA slab benchmark problem. The comparison shows that group constants generated by this study are in good agreement with results from published references. Then above group constants are applied to 3-dimensional discrete ordinates deterministic theory transport code TORT. But k eff calculated by TORT is a little lower than that calculated by Monte Carlo code JMCT. To minimize other influence factors, different Sn/Pn order, and different mesh size in TORT has been tried. Unfortunately the k eff difference between these two methods remains. Even though the k eff results in this benchmark are less than k eff calculated by continuous energy MC method, Benchmark results show that all the group constants generated by this method are in good agreement with existing references. So it can be expected that after further verification and validation, this coupled method can be effectively applied to the deep penetration problem in such kind of research reactors.

The adjoint neutron flux is vital in the analysis of reactor kinetics parameters and reactor transient events. Both deterministic and Monte Carlo methods have been developed for the adjoint neutron flux calculation on the basis of multi-group cross sections which may vary significantly among different types of reactors. The iterated fission probability (IFP) method is introduced to calculate the neutron importance which is able to represent the adjoint neutron flux in continuous energy problem and have been applied to the calculation of kinetics parameters. However, the adjoint neutron flux can’t be obtained directly and applied to both Monte Carlo transient event analysis and deterministic methods. In this study, a method based on IFP is studied and implemented in Monte Carlo code RMC. The multi-group adjont neutron flux can be obtained directly through the discretization of energy and space with the modification of fission neutrons through continuous energy Monte Carlo calculations. The obtained multi-group adjoint neutron flux can be used in both Monte Carlo transient analysis and deterministic methods.

Uncertainty quantification is an indispensable analysis for nuclear reactor simulation as it provides a rigorous approach by which the credibility of the predictions can be assessed. Focusing on propagation of multi-group cross-sections, the major challenge lies in the enormous size of the uncertainty space. Earlier work has explored the use of the physics-guided coverage mapping (PCM) methodology to assess the quality of the assumptions typically employed to reduce the size of the uncertainty space. A reduced order modeling (ROM) approach has been further developed to identify the active degrees of freedom (DOFs) of the uncertainty space, comprising all the cross-section few-group parameters required in core-wide simulation. In the current work, a sensitivity study, based on the PCM and ROM results, is applied to identify a suitable compressed representation of the uncertainty space to render feasible the quantification and prioritization of the various sources of uncertainties. While the proposed developments are general to any reactor physics computational sequence, the proposed approach is customized to the TRITON-NESTLE computational sequence, simulating the BWR lattice model and the core model, which will serve as a demonstrative tool for the implementation of the algorithms.

Nuclear reactor simulation is often based on multi-group cross-section libraries. The structure and resolution of these libraries have a strong influence on the accuracy and computational time; hence, number of groups and energy structure must be carefully considered. The relationship between group structures and how they impact generated cross-sections can be a critical parameter. Common energy boundaries shared among major group structures were identified and the relative kinship among those was reconstructed in an effort to build a family tree of major group structures. Stochastic code Serpent2 [1] was employed to generate cross-sections of selected isotopes at different reactor compositions and conditions, using the investigated energy group structures. The impact on their generation was quantified by spectral weighted deviation. The 35 major energy structures were divided into three basic families. The key parameters distinguishing them were their applicability to thermal or fast reactors and their applicability in neutronic or multiphysics investigations. A sensitivity threshold of the generated cross-sections over the group structure resolution was investigated. The aim was to identify a group structure with very low dependency on the actual reactor spectrum.

Helically coiled tubes are widely used in many industrial applications such as the steam generator in the high-temperature gas-cooled reactor which is recognized as one of the new generation advanced reactors. The thermophysical properties of fluids exhibit drastic and fast changes in the pseudocritical region so that the flow and heat transfer characteristics of supercritical pressure fluids are greatly different from those at the subcritical pressure. The paper presents results of numerical investigation on turbulent heat transfer of supercritical CO 2 in a helically coiled tube with a tube diameter of 9 mm, a coil diameter of 283 mm and a coil pitch of 32 mm under the constant wall heat flux. Both the RNG k-ε model with enhanced wall function and the SST k-ω model were applied in the simulations, and the results showed that the SST k-ω model agreed better with the experimental results in the literature. Effects of buoyancy and flow acceleration were evaluated. Details of developing heat transfer characteristics at three specific cross sections were analyzed. The heat transfer regularity and mechanism presented in this work can be useful for the design and development of more economic and safer design of the supercritical steam generator.

The Czech Republic National Radiation Protection Institute (SURO) provides technical support to the Czech Republic State Office for Nuclear Safety, providing safety analysis and reviewing of the technical documentations for Nuclear Power Plants (NPPs). For this reason, several computational models created in SURO were prepared using different codes as tools to simulate and investigate the design base and beyond design base accidents scenarios. This paper focuses on the creation of SCALE and PARCS neutronic models for a proper analysis of the VVER-440 reactor analysis. In particular, SCALE models of the VVER-440 fuel assemblies have been created in order to produce collapsed and homogenized cross sections necessary for the study with PARCS of the whole VVER-440 reactor core. The sensitivity study of the suitable energy threshold to be adopted for the preparation with SCALE of collapsed two energy-group homogenized cross sections is also discussed. Finally, the results obtained with PARCS core model are compared with those reported in the VVER-440 Final Safety Report.

CAP1400 is a large passive pressurized water reactor nuclear power plant, which relies on engineering safety features such as passive containment cooling system (PCS) to remove the decay heat in the containment and mitigate accident consequences. PCS is designed to perform passive containment cooling which is mainly dependent on natural convection inside the containment and inner wall condensation heat transfer, outer containment surface water film coverage and evaporation heat transfer and external air flow path cooling performance, etc. Among them, the key factors that affect the performance of the external air flow path include the flow resistance characteristics of the air flow path and the wind-direction neutrality characteristics. The relevant performance will be the important design input of the accident analysis, which will directly affect the safety of the power plant. During the normal operation of power plant, the PCS air flow path is influenced by the external environment, and its internal flow is very complicated. Designers are often lack of data support, and can’t fully consider the impact of environmental flow. In order to fully study the performance of PCS air flow path, it is necessary to perform PCS integrated scaled wind tunnel test. According to the original design of CAP1400 PCS system, the model scale research is developed and CAP1400 PCS wind tunnel test scaled model is established and the scale is 1:100. The test model includes shield building model and the surrounding plant model, which contain pressure measuring points uniformly distributed in 6 horizontal cross sections of the shield building. The pressure measuring point arrangement does not affect air flow in the air flow path. The following wind tunnel tests are simulated in different wind speed including 15m/s, 20m/s, 10m/s, 25m/s. The air flow pressure, wind velocity at the inlet and outlet of air flow path and the pressure distribution of inner annulus and outer annulus are measured in order to study the air flow pressure drop and wind-direction neutrality characteristics, and the wind tunnel test also considers the different wind direction angle, with and without the surrounding buildings and the effects of different landforms. The test results show that the flow rate of inlet and outlet of air flow path is balanced and the wind velocity at the upwind and central area of the flow path outlet is larger than other area, and a large vortex comes on the leeward side near the wall. The local uneven flow phenomenon exists in the outer annulus of the air flow path, but the wind pressure distribution of inner annulus is not affected by environment wind speed, wind direction angle, landforms and the surrounding buildings. So CAP1400 PCS air flow path has the characteristics of wind direction neutrality, and the natural convection of the air flow path will not be adversely affected by the environment wind.

Lattice code generates homogenized few-group cross sections for core neutronics code. It is an important component of the nuclear design code system. The development and improvement of lattice codes are always significant topics in reactor physics. The PANDA code is a PWR lattice code developed by Shanghai Nuclear Engineering Research and Design Institute (SNERDI). It starts from the 70-group library, and performs the resonance calculation based on the Spatially Dependent Dancoff Method (SDDM). The 2D heterogeneous transport calculation is performed without any group collapse and cell homogenization by MOC with two-level Coarse Mesh Finite Difference (CMFD) acceleration. Matrix exponential methods are used to solve the Bateman depletion equation. Based on the methodologies, the PANDA code is developed. The verifications on different levels preliminarily demonstrate the ability of the PANDA code.

A code system has been developed in this paper for the dynamics simulations of MSRs. The homogenized cross section data library is generated using the continuous-energy Monte-Carlo code OpenMC which provides significant modeling flexibility compared against the traditional deterministic lattice transport codes. The few-group cross sections generated by OpenMC are provided to TANSY and TANSY_K which is based on OpenFOAM to perform the steady-state full-core coupled simulations and dynamics simulation. For verification and application of the codes sequence, the simulation of a representative molten salt reactor core MOSART has been performed. For the further study of the characteristics of MSRs, several transients like the code-slug transient, unprotected loss of flow transient and overcooling transient have been analyzed. The numerical results indicated that the TANSY and TANSY_K codes with the cross section library generated by OpenMC has the capability for the dynamics analysis of MSRs.

Uncertainty and sensitivity analysis is an essential component of nuclear engineering calculations. Uncertainties in the cross-section input data directly affect uncertainties in the results. The covariance values between different types of cross-sections are considered in the NJOY covariance library. However, the correlation coefficient between isotopes can depend on the specific problem. The correlation coefficient between 235 U and 238 U in a pressurized water reactor (PWR) might be different from that in a fast reactor. In this study, a new Monte Carlo-based method is proposed for calculating this effect. The correlation coefficients between different isotopes are calculated using a problem-dependent fraction parameter. The correlation coefficients between the capture cross-sections of 235 U, 238 U, 239 Pu, and 241 Pu are calculated. The same method can be extended to other reaction types. The correlation coefficients as a function of the isotopic atomic density uncertainty and the average one-group microscopic cross-section uncertainty are also studied. It is shown that the correlation coefficients vary very little with the uncertainty in the average one-group microscopic cross-section. The correlation coefficient of an isotope pair changes slightly over the course of a cycle because of atomic density and microscopic cross-section changes.

Fully ceramic micro-encapsulated (FCM) fuels generate double heterogeneity (DH) challenging greatly for classical resonance self-shielding calculation method. New methodologies have been proposed and verified in this research. The target of this study is to provide homogeneous multi-group cross sections reflecting the effect of DH. Embedded Self-Shielding Method (ESSM) [1] was selected to perform resonance self-shielding calculation. Therefore, Monte Carlo code MVP [2] which is capable of well modeling the stochastic dispersed tri-structural isotropic (TRISO) coated fuel particle throughout carbide matrix and method of characteristics (MOC) were chosen to develop the heterogeneous resonance integral (RI) tables for DH problems. Benchmark problems from reference [3] were provided to verify the new methodologies. The results show that ESSM with RI tables from MVP and MOC could well address the resonance calculation for DH problems.

In order to generate cross sections for fast reactor calculation, a code named TXMAT based on object–oriented programming and allocate memory technology has been developed. It has the capability to generate macroscopic cross sections for transport or diffusion calculation and microscopic cross sections for burnup calculation, and can also deal with the ultrafine group cross sections (more than 2000 groups and P 5 Legendre order) which TRANSX 2.15 can’t do. It works together with a generalized cross section data library called MATXS to give the transport code users easier access to appropriate nuclear data and capabilities which are difficult or impossible to get with any other systems. The TXMAT can handle the shielding effects of many isotopes through background cross section iteration. Several critical benchmarks are calculated. It is shown that the total cross section, absorption cross section, fission neutron spectrum and zero Legendre scattering matrix have been verified using TRANSX 2.15, and the maximum relative difference for the main groups is less than 0.2%. After the critical benchmark calculation, the RBEC-M benchmark is used for the whole core calculation. It is shown that the effective multiplication factor of the calculation is consistent with that of other codes, and the power distribution is also in good agreement with that of other codes except for the blankets. The maximum relative difference of the power distribution among core-1, core-2 and core-3 regions is less than 2.3%. But in the blankets the relative error is about 33%, which may be caused by the difference of the weight function between IWT = 8 and real model. Further analysis will be performed in the future.

This work aims to develop an uncertainty analysis methodology for the propagation and quantification of the effects of nuclear cross-section uncertainties on important core-wide attributes, such as power distribution and core critical eigenvalue. Given the computationally taxing nature of this endeavor, our goal is to develop a methodology capable of preserving the accuracy of brute force sampling techniques for uncertainty quantification while realizing the efficiency of deterministic techniques. To achieve that, a reduced order modeling (ROM) approach is proposed to deal with the enormous size of the uncertainty space, comprising all the cross-section few-group parameters required in core-wide simulation. The idea is to generate a compressed representation of the uncertainty space, as represented by a covariance matrix, that renders sampling techniques computationally a feasible option for quantifying and prioritizing the various sources of uncertainties. While the proposed developments are general to any reactor physics computational sequence, we customize our approach to the NESTLE [1]-TRITON [2] computational sequence, which will serve as a demonstrative tool for the implementation of our approach. NESTLE is a software used for core wide simulation, which relies on the few-group cross-sections to calculate core wide attributes over multiple cycles of depletion. Its input cross-sections are generated using a matrix of conditions evaluated using a lattice physics code, which in our implementation is done using the TRITON software of the ORNL’ SCALE suit. This manuscript presents one of the early steps towards this goal. Specifically, we focus here on the development of the algorithms for determining the reduced dimension of covariance matrix. Numerical experiment using the TRITON software is employed to demonstrate how the reduction is achieved.

The modular High-Temperature Gas-cooled Reactor (HTGR) is one of the six generation IV advanced nuclear reactors. With the final purpose of operator training and licensing, the engineering simulation system (ESS) has been studied to model the pebble-bed type reactor core and has been successfully implemented into the full scope simulator of HTR-PM. As stated in corresponding industrial standards, one important feature of the nuclear power plant simulator is real-time calculation, and the other one is simulation results with high fidelity (compared to design parameters or operational data in different stages). In ESS, each macro cross-section was in the form of polynomial by function of several variables (like burn-up, buckling, temperatures), the expression of which was finalized by multivariate regression analysis from large scattered database generated by the VSOP. Since the polynomial is explicit and prepared in advance, the macro cross-sections are quickly calculated in running ESS. However, some variables (such as temperature) in HTGR are in larger scope so that the polynomial is not easy to meet full range accuracy. One normal idea is to optimize the expression of polynomial, while another means was proposed and tested in present paper. Other than focusing on the polynomials, a new method, called the fast searching, was described to significantly improve the accuracy of macro cross-section calculation while it was also fast to maintain the real-time feature. Instead of setting up a regression polynomial from the large cross-section database, the fast searching method treated the database as scatted points in the multi-dimension space, and aimed to locate the target position of unknown macro cross-section by fast searching and interpolating. Searching was to find the neighbouring database points around the target point in the multi-dimension space, which naturally improved the accuracy. While interpolating was to predict the macro cross-section of target point based on those neighbouring database points. To keep the searching and interpolating fast, the original database of macro cross-sections was analysed. A series of searching and interpolating methods have been described, programmed, tested and compared to find appropriate methods to calculate all the macro cross-sections in limited time cost. Finally, the fast searching method and its program was implemented into ESS to show better performances.

The RBWR-TR is a thorium-based reduced moderation BWR (RBWR) with a high transuranic (TRU) consumption rate. It is charged with LWR TRU and thorium, and it recycles all actinides an unlimited number of times while discharging only fission products and trace amounts of actinides through reprocessing losses. This design is a variant of the Hitachi RBWR-TB2, which arranges its fuel in a hexagonal lattice, axially segregates seed and blanket regions, and fits within an existing ABWR pressure vessel. The RBWR-TR eliminates the internal axial blanket, eliminates absorbers from the upper reflector, and uses thorium rather than depleted uranium as the fertile makeup fuel. This design has been previously shown to perform comparably to the RBWR-TB2 in terms of TRU consumption rate and burnup, while providing significantly larger margin against critical heat flux. This study examines the uncertainty in key neutronics parameters due to nuclear data uncertainty. As most of the fissions are induced by epithermal neutrons and since the reactor uses higher actinides as well as thorium and 233 U, the cross sections have significantly more uncertainty than in typical LWRs. The sensitivity of the multiplication factor (k eff ) to the cross sections of many actinides is quantified using a modified version of Serpent 2.1.19 [1]. Serpent [2] is a Monte Carlo code which uses delta tracking to speed up the simulation of reactors; in this modified version, cross sections are artificially inflated to sample more collision, and collisions are rejected to preserve a “fair game.” The impact of these rejected collisions is then propagated to the multiplication factor using generalized perturbation theory [3]. Covariance matrices are retrieved for the ENDF/B-VII.1 library [4], and used to collapse the sensitivity vectors to an uncertainty on the multiplication factor. The simulation is repeated for several reactor configurations (for example, with a reduced flow rate, and with control rods inserted), and the difference in k eff sensitivity is used to assess the uncertainty associated with the change (the uncertainty in the void feedback and the control rod worth). The uncertainty in the RBWR-TR is found to be dominated by the epithermal fission cross section for 233 U in reference conditions, although when the spectrum hardens, the uncertainty in fast capture cross sections of 232 Th becomes dominant.