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Investigating a Matrix-free, Newton-based, Neutronic-Monte Carlo/Thermal-Hydraulic Coupling Scheme
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In the field of nuclear reactor analysis, multiphysics calculations that account for the bonded nature of the neutronic and thermal-hydraulic phenomena are of major importance for both reactor safety and design. So far in the context of Monte-Carlo neutronic analysis, the Gauss-Seidel iterative scheme, in a version for individual single-physics solvers, is mainly used for coupling with thermal-hydraulics. This work investigates the possibility of replacing the previous scheme with an approximate Newton algorithm. The proposed method, called Approximate Block Newton, is actually a version of the Jacobian-free Newton Krylov method suitably modified for coupling mono-disciplinary solvers. Within this Newton scheme the linearised system is solved with a Krylov solver in order to avoid the need for creation of the Jacobian matrix. Main motivation for this approach is the interest for an algorithm that could maintain the distinct treatment of the involved fields within a tight coupling context. This work performs preliminary analysis in order to investigate the behaviour of the proposed method in reactor analysis. More specifically, OpenMC, a Monte-Carlo neutronic code and COBRA-EN, a thermal hydraulic code for sub-channel and core analysis, are merged in a coupling scheme using the Approximate Block Newton method with the aim to examine the performance and the accuracy of this coupling scheme and compare with those of the traditional sequential iterative scheme.
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... In this review, Wang et al. (2020), the authors make an extensive state-ofthe-art of the coupled codes, subdividing them by the coupling method (e.g., implicit as Jacobian Free Newton Krylov (JFNK), or explicit as Operator Splitting or Picard iteration) and by application (e.g., PWR, BWR, MSR, PB etc.). Analysing the couplings that consider explicit methods, the following can be mentioned: MCNPX was coupled with the 2D subchannel code COBRA-IV for the analysis of a SFR (Vazquez et al., 2012); MCNP6 was used with ANSYS-FLUENT for the investigation of a PWR facility (Gurecky and Schneider, 2016); OpenMC, along with the 2D code COBRA-EN, was adopted to study both PWR and BWR systems (Mylonakis et al., 2015); Serpent was coupled with both the 2D thermal-hydraulic code RELAP5 (Wu and Kozlowski, 2015) to investigate a PWR system, as well as to the 3D code OpenFOAM in the analysis of PWR (Tuominen et al., 2016;Castagna et al., 2020), research reactors (Castagna et al., 2022), Pebble bed reactors (Aufiero and Fratoni, 2016) and transient scenarios (Aufiero et al., 2015). OpenFOAM and OpenMC (Bullerwell, 2020) and Nek5000 with OpenMC (Novak et al., 2018;Romano et al., 2021). ...
The state of an operating nuclear reactor depends on several physical phenomena that coexist and are interdependent: they can be taken into account simultaneously by adopting a multi-physics approach, allowing a higher level of detail of the system's properties. Neutron physics and thermal hydraulics are of great importance in this framework, their interdependence being the most fundamental coupling effect in nuclear reactors, as their interaction determines the power and temperature profiles, being quantities of interest during the design and safety analysis phases. This work focuses on developing a fully open-source multi-physics and multi-scale tool capable of determining the temperature profile of a characteristic fuel pin of a PWR when the power generated by the system is known. This methodology is implemented in a Python environment coupling the open source library FEniCSx for the thermal-hydraulic analysis with the OpenMC Monte Carlo code for the description of the fissionable system: regarding the former, FEniCSx handles the thermal calculations, whereas a 1D model is used to predict the axial coolant temperature distribution. The coupling applies an explicit method, whose convergence is based on a Picard scheme, using an adaptive relaxation scheme. This coupling strategy is compared with literature data, providing a good agreement with a fully Multi-Physics solver.
... As the convergence of an algorithm is always an important issue, an improvement of the convergence behaviour by adopting a new numerical technique (Approximate Block Newton method) and developing an innovative neutronic-MC/T-H coupling scheme, was attempted. It was found that the proposed coupling methodology outperforms the traditional sequential one as shown in [40]. The improvement seems to be more significant in the BWR cases, however further investigation especially in larger scale problems is needed in order to exploit in more detail the features, the advantages and disadvantages of this innovative coupling scheme. ...
ANET is being developed targeting to a multiple capabilities code which can inherently, dynamically and accurately simulate GEN II/III reactors as well as Accelerator Driven Systems (ADSs). ANET is oriented towards an open-source pure Monte-Carlo transient code with Thermal-Hydraulics (T-H) feedback. It incorporates the treatment of all types of particles’ creations and collisions as existing in the High Energy Physics code GEANT while its capabilities have been extended to energies below 20 MeV so as to cope with fission neutrons and their possible reactions in a reactor core (transport, elastic and inelastic scattering, capture and fission). The developed code aims to account for core evolution in both short and long time-scales, allowing for T-H feedback and assessment of the fuel isotopic composition variations, including neutron poisons’ evolution. In order to analyze ADSs, ANET can incorporate specific codes (such as FLUKA and INCL/ABLA) for the treatment of spallation targets of various materials and geometries. Regarding verification and validation (V&V) studies ANET has been successfully tested against measurements and/or independent numerical results with respect to its capability to compute criticality, neutron fluence and reaction rates. Also ANET neutron yield computations for three of the most popular spallation target materials (Pb, W and U) hit by accelerated protons of various energies are satisfactorily compared with independent simulations and experimental results. Moreover, preliminary ANET applications for the prediction of changes in the fuel isotopic composition show encouraging results compared with measurements as well as corresponding simulations.
In an operating nuclear reactor system, various physical phenomena of different properties are intimately linked. These multiphysics phenomena include neutronics (N), thermal-hydraulics (TH), materials science, and other subjects. Among them, the interaction between neutronics and thermal-hydraulics is of great significance in reactor design and safety analysis. In this work, different N/TH coupling methods are reviewed, including loose and tight coupling. For the studies on loose coupling, in which two physical fields are decoupled, the current research status is summarized and classified based on the coupling methods of neutronics and thermal-hydraulics. The studies of tight coupling are introduced based on multiphysics coupling platforms. The investigation shows that the number and objectives of loose coupling studies are more abundant and extensive than those of tight coupling. This indicates that loose coupling strategies are the mainstream coupling solutions in recent research. Furthermore, the solution approaches of N/TH coupling are reviewed with respect to the aspects of performance improvement and application studies, including the operator splitting (OS), Picard iteration, and Jacobian-Free Newton–Krylov (JFNK) methods. A comprehensive study of the solution approaches shows that most of the current loose coupling numerical simulations adopt the Picard iteration method, because it has higher calculation accuracy than the OS method. In contrast to the decoupling approaches such as the OS and Picard iteration methods, the JFNK method updates all physical quantities synchronously, which makes it more accurate. Hence, there are broad application prospects for N/TH tight coupling of the JFNK method.
Within the context of an operating nuclear reactor core, multi-physics calculations that account for the bonded nature of the neutronic and thermal-hydraulic phenomena are of major importance in reactor safety and design. In this work, the ongoing development of a tool for neutronic/thermal-hydraulic coupled calculations is presented. OpenMC, a Monte-Carlo 3D neutronic code and COBRA-EN, a thermal-hydraulic code for sub-channel and core analysis, are integrated in a single tool for coupled calculations. This new coupled system (OpenMC/COBRA) is capable of performing coupled Neutronic/Thermal-Hydraulic analysis in both sub-channel and core level. As regards the main key parameters related to the coupled problems, these mainly include the handling of the involved feedbacks between the two physical processes, the accuracy of the Monte-Carlo calculation and the convergence behavior of such an iterative scheme. Another issue which should be considered carefully is the optimal, in terms of computational time, use of the neutronic Monte-Carlo code, since the main disadvantage of such codes is the high computational cost. This work investigates the role of these parameters in the coupled neutronic/thermal-hydraulic calculations performed by OpenMC/COBRA while it examines the direction towards which their optimization should move in order to achieve accurate results with reasonable computational cost. The results show that satisfying accuracy can be obtained in reasonable computational time when Monte-Carlo multi-processing is combined with proper selection of the Monte-Carlo parameters, as well as of the parameters concerning the coupled iterative scheme.
The Monte Carlo performance benchmark for detailed power density calculation in a full-size reactor core is organized under the auspices of the OECD NEA Data Bank. It aims at monitoring over a range of years the increase in performance, measured in terms of standard deviation and computer time, of Monte Carlo calculation of the power density in small volumes. A short description of the reactor geometry and composition is discussed. One of the unique features of the benchmark exercise is the possibility to upload results from participants at a website of the NEA Data Bank which enables online analysis of results and to graphically display how near we are at the goal of doing a detailed power distribution calculation with acceptable statistical uncertainty in an acceptable computing time. First results are discussed which show that 10 to 100 billion histories must be simulated to reach a standard deviation of a few percent in the estimated power of most of the requested the fuel zones. Even when using a large supercomputer, a considerable speedup is still needed to reach the target of 1 hour computer time. An outlook is given of what to expect from this benchmark exercise over the years. Possible extensions of the benchmark for specific issues relevant in current Monte Carlo calculation for nuclear reactors are also discussed.
As part of the European NURISP research project, a single pin BWR benchmark problem was defined. The aim of this initiative is to test the coupling strategies between Monte Carlo and subchannel codes developed by different project participants. In this paper the results obtained by the Delft University of Technology and Karlsruhe Institute of Technology will be presented. The benchmark problem was simulated with the following coupled codes: TRIPOLI-SUBCHANFLOW, MCNP-FLICA, MCNP-SUBCHANFLOW, and KENO-SUBCHANFLOW.
In an operating nuclear reactor core, various physical phenomena of different nature are interrelated. Multi-physics calculations that account for the interrelated nature of the neutronic and thermal–hydraulic phenomena are of major importance in reactor safety and design and as a result a special effort is developed within the nuclear engineering scientific community to improve their efficiency and accuracy. In addition, the strongly heterogeneous nature of reactor cores involves phenomena of different scales. The interaction between different scales is a specificity of these systems, since a local perturbation might influence the behavior of the whole core, or a global perturbation can influence the properties of the media on all scales. As a consequence, multi-scale calculations are required in order to take the reactor core multi-scale nature into account. It should be mentioned that the multi-physics nature of a nuclear reactor cannot be separated from the multi-scale one in the framework of computational nuclear engineering as reactor design and safety require computational tools which are able to examine globally the complicated nature of a nuclear reactor in various scales. In this work a global overview of the current status of two physics (neutronic/thermal–hydraulic) and multi-scale neutronic calculations techniques is presented with reference to their applications in different nuclear reactor concepts. Finally an effort to extract the main remaining challenges in the field of multi-physics and multi-scale calculations is made.
S>The resonance absorption of neutrons by bodies having complicated
shapes and nonuniform temperature distributions is studied. An effective
temperature T is defined for the body as a fanction of the actual temperature
distribution, the neutron flux distribution, and the shape of the body. The
resonance absorption is then found to be the same as that for a body having the
actual shape but temperature T. The results of this treatment are shown for
slabs, spheres, and cylinders having parabolic temperature distributions. It is
assumed throughout that scattering processes can be ignored. (T.F.H.)
Multi-scale and multi-physics simulations, such as the computational modeling of crystal growth processes, will benefit from the modular coupling of existing codes rather than the development of monolithic, single-application software. An effective coupling approach, the approximate block Newton approach (ABN), is developed and applied to the steady-state computation of crystal growth in an electrodynamic gradient freeze system. Specifically, the code CrysMAS is employed for furnace-scale heat transfer computations and is coupled with the code Cats2D to calculate melt fluid dynamics and phase-change phenomena. The ABN coupling strategy proves to be vastly more reliable and cost efficient than simpler coupling methods for this problem and is a promising approach for future crystal growth models.
A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss–Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.
Covering the last half of the 20th century, we present some of the basic and well-known results for the SOR theory and related methods as well as some that are not as well known. Most of the earlier results can be found in the excellent books by Varga (Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962) Young (Iterative Solution of Large Linear systems, Academic Press, New York, 1971) and Berman and Plemmons (Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA, 1994) while some of the most recent ones are given in the bibliography of this paper. In this survey, both the point and the block SOR methods are considered for the solution of a linear system of the form Ax=b, where and Some general results concerning the SOR and related methods are given and also some more specific ones in cases where A happens to possess some further property, e.g., positive definiteness, L-, M-, H-matrix property, p-cyclic consistently ordered property etc.