Thermal-hydraulic Feedback Research Articles

On-the-fly treatment of temperature dependent cross sections in the unresolved resonance region in RMC code

With the rapid development of computational power and parallel algorithms, Monte Carlo method has been widely investigated and used in neutron transport simulations due to its advantages in geometry modelling and usage of continuous energy point-wise cross sections. Monte Carlo codes can also be coupled with thermal-hydraulics codes to consider feedbacks. One of the most important aspects of thermal-hydraulics feedback is the detailed temperature distribution, which results in the demands of updates of temperature dependent cross sections in neutron transport simulations. For thermal reactors such as PWR and HTGR, two neutron energy regions should be carefully considered: the resolved resonance region (RRR) and the thermal energy region, especially the resolved resonance region. Besides, the temperature dependence of cross sections in the unresolved resonance energy region (URR) is also important for fast reactors and some experimental critical assemblies. In this paper, the on-the-fly temperature treatment of cross sections in the RRR was implemented in RMC code. The on-the-fly method for the URR was also proposed and implemented in RMC code, which was also combined with the on-the-fly temperature treatments for resolved resonance energy. The proposed method was applied to Monte Carlo transport and depletion calculations. The accuracy and efficiency are compared for different combinations of methods of RRR and URR. The results show that the on-the-fly treatment has high efficiency and satisfactory fidelity. The probability tables with equiprobable bands were also developed to reduce the memory consumption, with keeping the same accuracy of original probability tables.

Nodal diffusion methods and lattice physics data in LWR analyses: Understanding numerous subtle details

Numerous researchers have been unsuccessful in obtaining accurate LWR power distributions using two-group nodal diffusion codes and neutronic data generated from single-assembly lattice calculations. Researchers using the Serpent Monte Carlo code to generate data for the ARES nodal code have determined that large buffer zones surrounding each fuel assembly are required to obtain data that permits accurate nodal calculation of core power distributions. While successful, such larger buffer zones result in extremely large computational requirements for lattice data generation. Since accurate commercial LWR power distributions have been obtained using single-assembly lattice calculations in the CASMO and SIMULATE lattice/nodal codes, it clearly should be possible to use Monte Carlo to replace deterministic lattice calculations.In this paper, we present numerous important refinements of nodal diffusion methods that are required to obtain accurate commercial LWR power distributions using single-assembly lattice data. Many of these refinements have never been published (because of the proprietary nature of their development), and consequently, many subtleties of nodal methods are not well known in the nuclear reactor analysis community. The importance and impact of numerous refinements of basic nodal methods are documented here using the Hot Zero Power (HZP) BEAVRS PWR benchmark. This paper documents only those nodal refinements needed to accurately predict assembly-averaged power distributions without thermal-hydraulic feedback (e.g. isothermal conditions) and fuel depletion. Additional refinements needed for thermal feedback, fuel depletion, and pin power reconstruction are deferred for subsequent publications.

BWR stability analysis with sub-diffusive and feedback effects

The aim of this work is to investigate the Boiling Water Reactor (BWR) stability with sub-diffusive effects and thermal-hydraulics feedback, using frequency domain method. The fractional neutron point kinetics (FNPK) equation is used to approximate the sub-diffusive effects, and a reducer-order model (ROM) is employed for void fraction and fuel temperature feedback. As a consequence a novel linear fractional reducer-order model (F-ROM) is proposed. The F-ROM is a compact set of five differential equations for BWR dynamics. The analysis is carried out for three values of anomalous diffusion coefficient representing three levels of sub-diffusion in reactor core. It is shown with extensive simulations that all the F-ROM exhibit closed-loop stability. The results are compared with the classical ROM.

Fourier analysis of iteration schemes for k-eigenvalue transport problems with flux-dependent cross sections

A central problem in nuclear reactor analysis is calculating solutions of steady-state k-eigenvalue problems with thermal hydraulic feedback. In this paper we propose and utilize a model problem that permits the theoretical analysis of iterative schemes for solving such problems. To begin, we discuss a model problem (with nonlinear cross section feedback) and its justification. We proceed with a Fourier analysis for source iteration schemes applied to the model problem. Then we analyze commonly-used iteration schemes involving non-linear diffusion acceleration and feedback. For each scheme we show (1) that they are conditionally stable, (2) the conditions that lead to instability, and (3) that traditional relaxation approaches can improve stability. Lastly, we propose a new iteration scheme that theory predicts is an improvement upon the existing methods.

Analysis of BEAVRS two-cycle benchmark using RMC based on full core detailed model

With the increasing demands of high fidelity neutronics analysis and the development of computer technology, Monte Carlo method is becoming more and more attractive especially in criticality analysis of initial core and shielding calculations, due to its advantages of flexible geometry modeling and use of continuous-energy nuclear cross sections. However, nuclear reactors are complex systems with different physics and feedback interactions and coupling. To perform the high fidelity multi-physics simulations of real reactors or benchmark calculations such as two-cycle BEAVRS benchmark based on measurement data of a practical nuclear power plant, several factors must be considered such as large scale detailed depletion, thermal-hydraulics feedback, on-the-fly nuclear cross section processing, criticality search and inter-cycle refueling. In this paper, the abilities mentioned above for multiple burnup cycles simulations in Hot Full Power condition of PWR full core have been developed in continuous-energy Reactor Monte Carlo neutron and photon transport code RMC, which is developed by Department of Engineering Physics at Tsinghua University, Beijing (Wang et al., 2015). RMC has the capacity for lifecycle simulations of nuclear reactor cores. The BEAVRS benchmark was selected as an example and RMC was applied to a full core, two cycle burnup calculation of BEAVRS. All of the parameters given in the BEAVRS benchmark have been calculated and compared with the measured values of BEAVRS benchmark. For other parameters such as pin power distributions, they are compared to the results of other codes. The results of RMC agree well with the measured values of BEAVRS benchmark and also agree well with those of other codes. This was the first time for a Monte Carlo code to perform the full core, two cycle calculation of BEAVRS. This work paves the way for Monte Carlo codes in life cycle simulations of nuclear reactor cores.

Transient coupled calculations of the Molten Salt Fast Reactor using the Transient Fission Matrix approach

In this paper we present transient studies of the Molten Salt Fast Reactor (MSFR). This generation IV reactor is characterized by a liquid fuel circulating in the core cavity, requiring specific simulation tools. An innovative neutronic approach called “Transient Fission Matrix” is used to perform spatial kinetic calculations with a reduced computational cost through a pre-calculation of the Monte Carlo spatial and temporal response of the system. Coupled to this neutronic approach, the Computational Fluid Dynamics code OpenFOAM is used to model the complex flow pattern in the core. An accurate interpolation model developed to take into account the thermal hydraulics feedback on the neutronics including reactivity and neutron flux variation is presented. Finally different transient studies of the reactor in normal and accidental operating conditions are detailed such as reactivity insertion and load following capacities. The results of these studies illustrate the excellent behavior of the MSFR during such transients.

Bifurcation analysis of the simplified models of boiling water reactor and identification of global stability boundary

Nonlinear stability study of the neutron coupled thermal hydraulics instability has been carried out by several researchers for boiling water reactors (BWRs). The focus of these studies has been to identify subcritical and supercritical Hopf bifurcations. Supercritical Hopf bifurcation are soft or safe due to the fact that stable limit cycles arise in linearly unstable region; linear and global stability boundaries are same for this bifurcation. It is well known that the subcritical bifurcations can be considered as hard or dangerous due to the fact that unstable limit cycles (nonlinear phenomena) exist in the (linearly) stable region. The linear stability leads to a stable equilibrium in such regions, only for infinitesimally small perturbations. However, finite perturbations lead to instability due to the presence of unstable limit cycles. Therefore, it is evident that the linear stability analysis is not sufficient to understand the exact stability characteristics of BWRs. However, the effect of these bifurcations on the stability boundaries has been rarely discussed. In the present work, the identification of global stability boundary is demonstrated using simplified models. Here, five different models with different thermal hydraulics feedback have been investigated. In comparison to the earlier works, current models also include the impact of adding the rate of change in temperature on void reactivity as well as effect of void reactivity on rate of change of temperature. Using the bifurcation analysis of these models the globally stable region in the parameter space has been identified. The globally stable region has only stable solutions and does not have even unstable limit cycles. Hence, the system is stable irrespective of the size of the perturbation in these regions.

Stochastic processes during transients in nuclear reactors

Steady state noise techniques are widely known and applied to the monitoring of neutron reacting system. This paper deals with the stochastic analysis of neutron chain systems (nuclear reactors or fissile system) which are changing in time from subcritical states reaching other subcritical, critical or hypercritical states due to an external parametric excitation. Two cases are analyzed: 1) without reactivity feedback, that is from a subcritical state to one with almost zero power, and 2) a supercritical excursion with thermalhydraulic feedback. Our goal is to check in case 1 if the usual noise techniques can be used to monitoring the reactivity changes and in case 2 how to calculate the variance of the power and energy released.

Testing the new stochastic neutronic code ANET in simulating safety important parameters

ANET (Advanced Neutronics with Evolution and Thermal hydraulic feedback) is an under development Monte Carlo code for simulating both GEN II/III reactors as well as innovative nuclear reactor designs, based on the high energy physics code GEANT3.21 of CERN. ANET is built through continuous GEANT3.21 applicability amplifications, comprising the simulation of particles’ transport and interaction in low energy along with the accessibility of user-provided libraries and tracking algorithms for energies below 20MeV, as well as the simulation of elastic and inelastic collision, capture and fission. Successive testing applications performed throughout the ANET development have been utilized to verify the new code capabilities. In this context the ANET reliability in simulating certain reactor parameters important to safety is here examined. More specifically the reactor criticality as well as the neutron fluence and fission rates are benchmarked and validated. The Portuguese Research Reactor (RPI) after its conversion to low enrichment in U-235 and the OECD/NEA VENUS-2 MOX international benchmark were considered appropriate for the present study, the former providing criticality and neutron flux data and the latter reaction rates. Concerning criticality benchmarking, the subcritical, Training Nuclear Reactor of the Aristotle University of Thessaloniki (TNR-AUTh) was also analyzed. The obtained results are compared with experimental data from the critical infrastructures and with computations performed by two different, well established stochastic neutronics codes, i.e. TRIPOLI-4.8 and MCNP5. Satisfactory agreement is found with both measurements and independent computations, verifying thus ANET’s ability to successfully simulate important parameters of critical and subcritical systems.

Current status of the reactor physics code WIMS and recent developments

The WIMS modular reactor physics code has been under continuous development for over fifty years. This paper discusses the current status of WIMS and recent developments, in particular developments to the resonance shielding methodology and 3D transport solvers. Traditionally, WIMS is used to perform 2D lattice calculations, typically to generate homogenized reactor physics parameters for a whole core code such as PANTHER. However, with increasing computational resources there has been a growing trend for performing transport calculations on larger problems, up to and including 3D full core models. To this end, a number of the WIMS modules have been parallelised to allow efficient performance for whole core calculations, and WIMS includes a 3D method of characteristics solver with reflective and once-through tracking methods, which can be used to analyse problems of varying size and complexity. A time-dependent flux solver has been incorporated and thermal-hydraulic modelling capability is also being added to allow steady-state and transient coupled calculations to be performed. WIMS has been validated against a range of experimental data and other codes, in particular for water and graphite moderated thermal reactors. Future developments will include improved parallelization, enhancing the thermal-hydraulic feedback models and validating the WIMS/PANTHER code system for BWRs and fast reactors.

Inverse uncertainty quantification of reactor simulations under the Bayesian framework using surrogate models constructed by polynomial chaos expansion

Modeling and simulations are naturally augmented by extensive Uncertainty Quantification (UQ) and sensitivity analysis requirements in the nuclear reactor system design, in which uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. Historically, expert judgment has been used to specify the nominal values, probability density functions and upper and lower bounds of the simulation code random input parameters for the forward UQ process. The purpose of this paper is to replace such ad-hoc expert judgment of the statistical properties of input model parameters with inverse UQ process. Inverse UQ seeks statistical descriptions of the model random input parameters that are consistent with the experimental data. Bayesian analysis is used to establish the inverse UQ problems based on experimental data, with systematic and rigorously derived surrogate models based on Polynomial Chaos Expansion (PCE).The methods developed here are demonstrated with the Point Reactor Kinetics Equation (PRKE) coupled with lumped parameter thermal-hydraulics feedback model. Three input parameters, external reactivity, Doppler reactivity coefficient and coolant temperature coefficient are modeled as uncertain input parameters. Their uncertainties are inversely quantified based on synthetic experimental data. Compared with the direct numerical simulation, surrogate model by PC expansion shows high efficiency and accuracy. In addition, inverse UQ with Bayesian analysis can calibrate the random input parameters such that the simulation results are in a better agreement with the experimental data.

A nonlinear reactivity method with application to accident-tolerant fuels

A nonlinear reactivity model with thermal-hydraulic feedback is presented for analysis of PWR fuel with various cladding materials. The simplified, batch-wise neutronic model requires batch reactivities and migration areas as predetermined functions of burnup, temperature (fuel and coolant), and any design parameters having neutronic significance (e.g., enrichment or cladding composition). Here, such functions are found by using symbolic regression, a unique approach that finds both a functional form and any model coefficients simultaneously. Core thermal-hydraulics are modeled using single-channel, axially-averaged values. The models were implemented in an open-source, Python-based tool, used here to the analyze fuel with Zr-based cladding having outer, protective layers of either FeCrAl or SiC, two materials proposed for use in next-generation, accident-tolerant fuel.

A Multilevel Quasi-Static Kinetics Method for Pin-Resolved Transport Transient Reactor Analysis

Three-dimensional (3D), full-core transport modeling with pin-resolved detail for reactor dynamic simulation is important for some multiphysics reactor applications. However, it can be computationally intensive due to the difficulty in maintaining accuracy while minimizing the number of time steps. An innovative Predictor-Corrector Quasi-static Method (PCQM) is introduced that is based on a Transient MultiLevel (TML) methodology. Two levels of couplings are used between 3D-transport/3D-CMFD (coarse-mesh finite difference) and 3D-CMFD/EPKE (exact point-kinetics equation). In each level, the original flux equation is solved in the coarse predictor step and then is factorized as an amplitude and a shape function in the corrector step, where the predicted solution is adjusted using multiple fine steps. In the first-level 3D-transport/3D-CMFD coupling, the angular and subpin flux shape functions in the Boltzmann transport equation are assumed to vary slowly over time, and the CMFD cellwise amplitude function is solved using multiple steps by the 3D-CMFD transient equation. In the second level, the CMFD scalar flux calculated in the last step is further corrected by a whole-core-wise amplitude function generated by the EPKE solver. The utilization of hierarchical multilevel neutronics transient solvers achieves the goal to balance the numerical accuracy and computational efficiency. In addition, a new iteration scheme with pin-resolve thermal-hydraulic feedback and theoretical proof for the accuracy of PCQM are also presented. Finally, a stripe assembly case adopted from the SPERT (Special Power Excursion Reactor Test) transient tests is used to demonstrate the accuracy and efficiency of the TML method.

Bias factor method using random sampling technique

ABSTRACTToward the practical use of the bias factor method for actual light water reactor core analyses, the bias factor method using the random sampling technique is newly proposed. The bias factor method is one of the correction methods using information of E/C values in existing measurable systems, to reduce biases and uncertainties of predicted core characteristics parameters. By the aid of the random sampling technique, our proposed bias factor method can be carried out using only forward calculations without any adjoint calculations, and can easily take into account burnup and thermal-hydraulic feedback effects, which are difficult points in the practical application to actual core analyses. Although the statistical error due to the random sampling technique is inevitable in the proposed method, the statistical error can be simply quantified by the resampling technique such as the bootstrap method. As one of the feasibility studies, effectiveness of the proposed method is verified through a numerical experiment which virtually simulates a typical equilibrium pressurized water reactor core. In this verification problem, it is clarified that E/C values of control rod worth at the beginning of cycle under the hot zero power condition are useful information to reduce biases and uncertainties of predicted assembly-wise power distributions during operation of hot full power.

Coupled 3D neutron kinetics and thermalhydraulic characteristics of the Canadian supercritical water reactor

The Canadian Supercritical Water-cooled Reactor concept, as an evolution of the CANada Deuterium Uranium (CANDU) reactor, includes both pressure tubes and a low temperature heavy water moderator. The current Pressure Tube type SCWR (PT-SCWR) concept features 64-element fuel assemblies placed within High Efficiency Re-entrant Channels (HERCs) that connect to core inlet and outlet plena. Among current SCWR concepts the PT-SCWR is unique in that the HERC separates multiple coolant and moderator regions, giving rise to coupled neutronic-thermalhydraulic feedbacks beyond those present in CANDU or contemporary Light Water Reactors. The objective of this work was thus to model the coupled neutronic-thermal hydraulic properties of the PT-SCWR to establish the impact of these multiple regions on the core's transient behavior. To that end, the features of the PT-SCWR were first modeled with the neutron transport code DRAGON to create a database of homogenized and condensed cross-sections and thermalhydraulic feedback coefficients. These were used as input to a core-level neutron diffusion model created with the code DONJON. The behavior of the primary heat transport system was modeled with the thermalhydraulic system code CATHENA. A procedure was developed to couple the outputs of DONJON and CATHENA, facilitating three-dimensional spatial neutron kinetics and coupled thermalhydraulic analysis of the PT-SCWR core. Several postulated transients were initiated within the coupled model by changing the core inlet and outlet boundary conditions. Decreasing coolant density around the fuel was demonstrated to produce positive power excursions (i.e., the coolant void reactivity around the fuel was positive), but such power transients were found to be inherently self-terminating as low density coolant inevitably reaches other parts of the HERC geometry (where the void reactivity is highly negative). Nevertheless, the observed power excursions potentially demonstrate the need for fast-acting shutdown system intervention, similar to CANDU designs.

Uncertainty Quantification of LWR Core Characteristics Using Random Sampling Method

Uncertainties of various neutronics characteristics in commercial boiling water reactor (BWR) and pressurized water reactor (PWR) cores due to cross-section covariance are evaluated by the Latin Hypercube Sampling (LHS) method, which is an efficient random sampling algorithm. Thermal-hydraulic feedback and burnup effects are fully and explicitly taken into account using a licensing-grade core simulator. Uncertainties for various core characteristics are evaluated by the statistical processing of core calculation results based on the LHS method. The calculation results indicate that uncertainty of critical eigenvalue (i.e., core reactivity) in the BWR core is comparable to that of a typical PWR core. On the other hand, uncertainties of assembly relative power distribution and maximum assembly burnup in the present BWR core are much smaller than those of the present PWR core. The strong thermal-hydraulic feedback effect in the BWR core significantly contributes to the difference of uncertainties in BWR and PWR cores.

The Modeling of Advanced BWR Fuel Designs with the NRC Fuel Depletion Codes PARCS/PATHS

The PATHS (PARCS Advanced Thermal Hydraulic Solver) code was developed at the University of Michigan in support of U.S. Nuclear Regulatory Commission research to solve the steady-state, two-phase, thermal-hydraulic equations for a boiling water reactor (BWR) and to provide thermal-hydraulic feedback for BWR depletion calculations with the neutronics code PARCS (Purdue Advanced Reactor Core Simulator). The simplified solution methodology, including a three-equation drift flux formulation and an optimized iteration scheme, yields very fast run times in comparison to conventional thermal-hydraulic systems codes used in the industry, while still retaining sufficient accuracy for applications such as BWR depletion calculations. The capability to model advanced BWR fuel designs with part-length fuel rods and heterogeneous axial channel flow geometry has been implemented in PATHS, and the code has been validated against previously benchmarked advanced core simulators as well as BWR plant and experimental data. The modifications to the codes and the results of the validation are described in this paper.

Analysis of parallel channel instabilities in the CANDU supercritical water reactor

The present work investigates the parallel channel density wave instability in the CANDU supercritical water reactor (SCWR) using a 1-D thermal-hydraulic model in the time domain. The model, which was used to analyze a single channel in-phase mode of instability in the SCWR, is extended for parallel channels in the reactor core to determine both in-phase and out-of-phase modes of oscillations considering the origination of the instabilities purely due to the thermal-hydraulic feedbacks without taking into account the influence of neutronic reactivity feedback effects. The capability of the proposed model to analyze the parallel channel instability is validated against the available experimental data. Extensive numerical investigations are carried out to determine the marginal stability boundary for each of the modes of oscillations in the working regime of the CANDU SCWR. The effect of the asymmetric heating power on the instability thresholds is also studied. Finally, the relative dominance between the in-phase and out-of-phase modes of oscillations at the operating regime of the CANDU SCWR is determined.

Coupling of dynamic Monte Carlo with thermal-hydraulic feedback

Transient analysis of nuclear reactors is traditionally the domain of deterministic methods, even tough these methods are known to have limitations. With the development of dynamic Monte Carlo and the development of coupled-steady state Monte Carlo calculations the road has been paved to perform transient analysis of high power reactors using Monte Carlo. By this way, it is possible to take into account the thermal-hydraulic feedback, while the neutron transport is modelled in full detail.In this paper a new method is described, which can perform such stochastic analysis of a transient scenario.

Coupled 3D neutronics/thermal hydraulics modeling of the SAFARI-1 MTR

The purpose of this study was to develop a coupled accurate multi-physics model of the SAFARI-1 Material Testing Reactor (MTR), a facility that is used for both research and the production of medical isotopes. The model was developed as part of the SAFARI-1 benchmarking project as a cooperative effort between the Pennsylvania State University (PSU) and the South African Nuclear Energy Corporation (Necsa). It was created using a multi-physics coupling of state of the art nuclear reactor simulation tools, consisting of a neutronics code and a thermal hydraulics code.The neutronics tool used was the PSU code NEM, and the results from this component were verified using the Necsa neutronics code OSCAR-4, which is utilized for SAFARI-1 core design and fuel management. On average, the multiplication factors of the neutronics models agreed to within 5pcm and the radial assembly-averaged powers agreed to within 0.2%.The thermal hydraulics tool used was the PSU version of COBRA-TF (CTF) sub-channel code, and the results of this component were verified against another thermal hydraulics code, the RELAP5-3D system code, used at Necsa for thermal–hydraulics analysis of SAFARI-1. Although only assembly-averaged results from RELAP5-3D were available, they fell within the range of values for the corresponding assemblies in the comprehensive CTF solution. This comparison allows for the first time to perform a quantification of steady-state errors for a low-powered MTR with an advanced thermal–hydraulic code such as CTF on a per-channel basis as compared to simpler and coarser-mesh RELAP5-3D modeling. Additionally, a new cross section representation was used to ensure that the thermal hydraulic feedback effects on the core neutronics were captured as accurately as possible. This cross section representation was applied to SAFARI-1 core calculations for the first time in this work. Such implementation helps to quantify the effect of detailed modeling of thermal–hydraulics feedback effects on neutronics results in multi-physics simulations.The outcome of the study is the intended coupled neutronics/thermal–hydraulics model of the SAFARI-1 reactor.