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The simulation of nuclear power plant accident conditions requires three-dimensional (3D) modeling of the reactor core to ensure a realistic description of physical phenomena. The operational flexibility of Light Water Reactor (LWR) plants can be improved by utilizing accurate 3D coupled neutronics/thermal–hydraulics calculations for safety margins evaluations. There are certain requirements to the coupling of thermal–hydraulic system codes and neutron-kinetics codes that ought to be considered. The objective of these requirements is to provide accurate solutions in a reasonable amount of CPU time in coupled simulations of detailed operational transient and accident scenarios. These requirements are met by the development and implementation of six basic components of the coupling methodologies: ways of coupling (internal or external coupling); coupling approach (integration algorithm or parallel processing); spatial mesh overlays; coupled time-step algorithms; coupling numerics (explicit, semi-implicit and implicit schemes); and coupled convergence schemes. These principles of the coupled simulations are discussed in details along with the scientific issues associated with the development of appropriate neutron cross-section libraries for coupled code transient modeling.

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... By the early '00 point kinetic/1-dimensional thermo-hydraulic modeling shifted to fully coupled three-dimensional neutronic-thermal-hydraulic simulations for transient and accidental analysis [26]; of particular use in PWR having an open lattice with radial cross-flow [45]. Additionally, further core optimization and improvement in best estimate calculations for increase plant availability [46] required an update in the cross section models [45]. ...

... By the early '00 point kinetic/1-dimensional thermo-hydraulic modeling shifted to fully coupled three-dimensional neutronic-thermal-hydraulic simulations for transient and accidental analysis [26]; of particular use in PWR having an open lattice with radial cross-flow [45]. Additionally, further core optimization and improvement in best estimate calculations for increase plant availability [46] required an update in the cross section models [45]. In a asymmetric steam line brake accident for example, that requires a 3D modeling of the moderator density, difference between commercial codes (SIMULATE-3 and CORETRAN) were observed, specifically due to the cross section models [47]. ...

... Higher order approximation (splines) [49] and projection into dedicated sub-libraries can mitigate this to some extent. Splines ensure a smooth interpolating approximation that requires fewer points, sometimes called "High-order table lookup method" [45]. Possible oscillation problems have been reported [46]. ...

Modern nuclear reactors utilize core calculations that implement a thermo-hydraulic feedback requiring accurate homogenized few-group cross sections.They describe the interactions of neutrons with matter, and are endowed with the properties of smoothness and regularity, steaming from their underling physical phenomena. This thesis is devoted to the modeling of these functions by industry state-of-theart and innovative machine learning techniques. Mathematically, the subject can be defined as the analysis of convenient mapping techniques from one multi-dimensional space to another, conceptualize as the aggregated sum of these functions, whose quantity and domain depends on the simulations objectives. Convenient is intended in terms of computational performance, such as the model’s size, evaluation speed, accuracy, robustness to numerical noise, complexity,etc; always with respect to the engineering modeling objectives that specify the multidimensional spaces of interest. In this thesis, a standard UO₂ PWR fuel assembly is analyzed for three state-variables, burnup,fuel temperature, and boron concentration.Library storage requirements are optimized meeting the evaluation speed and accuracy targets in view of microscopic, macroscopic cross sections and the infinite multiplication factor. Three approximation techniques are studied: The state-of-the-art spline interpolation using computationally convenient B-spline basis, that generate high order local approximations. A full grid is used as usually donein the industry. Kernel methods, that are a very general machine learning framework able to pose in a normed vector space, a large variety of regression or classification problems. Kernel functions can reproduce different function spaces using an unstructured support,which is optimized with pool active learning techniques. The approximations are found through a convex optimization process simplified by the kernel trick. The intrinsic modular character of the method facilitates segregating the modeling phases: function space selection, application of numerical routines and support optimization through active learning. Artificial neural networks which are“model free” universal approximators able Artificial neural networks which are“model free” universal approximators able to approach continuous functions to an arbitrary degree without formulating explicit relations among the variables. With adequate training settings, intrinsically parallelizable multi-output networks minimize storage requirements offering the highest evaluation speed. These strategies are compared to each other and to multi-linear interpolation in a Cartesian grid, the industry standard in core calculations. The data set, the developed tools, and scripts are freely available under aMIT license.

... The overall coupling strategy can be very different from one application to another. The coupling between two codes can be classified (Ivanov and Avramova, 2007) according to: ...

... Two approaches are possible (Ivanov and Avramova, 2007): The external approach has been selected for the present work, communication scripts have been written to exchange data between CFX and TRIPOLI. ...

Coupled multi-physics simulations of nuclear reactors represent a very dynamic research topic in the field of nuclear engineering. One of the most important aspects in reactor operation and design, which is considered in this thesis, is the interaction between thermal-hydraulics and neutron physics. Reactivity coefficients are integral parameters that characterise this coupling. Their sign and magnitude are important since they suggest the consequences of sudden changes in operating parameters of a nuclear reactor and have a significant impact on core’s performance and safety of the reactor.
This thesis presents the developed communication interfaces required to couple the neutron transport code TRIPOLI and the computational fluid dynamics code CFX. The methods are applied on the TRIGA Mark II reactor at the Jožef Stefan Institute. Additionally, new coolant temperature measurements were performed in the reactor tank to validate simulations.
This research work produces two original contributions. Firstly, the temperature measurements, apart from the description of the motion of the water driven by buoyancy and of an estimation of the fluid velocity, enable determination of temperature reactivity coefficient for fuel and coolant. Secondly, the development of three-dimensional model of the TRIGA reactor offers the possibility to define a multi-physics benchmark for the research community. It was found that the coupling between neutronics and thermal-hydraulics was rather weak in the TRIGA core. Coolant temperature and density have small influence on the power density distribution. On the contrary, the temperature of the fuel, which also acts as moderator, has a prompt and large effect on the reactivity. This effect was reproduced numerically, local effects on the power density were observed.

... This value is used as an average energy released of $200 MeV (i.e.,), based on the energies released by the fission of the U 235 nuclei [8]. In summary, once the NK model is used to generate the neutron flux distribution in the reactor core, expression (12) can be used to calculate the thermal power being generated along all the nodes in a thermal-hydraulic channel of area Δa and height H. This thermal power can be the axial power profile needed by the TH model to produce the thermal-hydraulic state corresponding to the generated thermal power. ...

... Although reference [12] has important issues to be considered in the development of an NK-TH-coupled model, those issues are not repeated here, but taken into account. The most direct way of coupling NK module and TH module, as implemented in AZKIND, consists simply in that axially both NK mesh and TH mesh have the same partition, making possible to assign an NK node at position z to the TH node in the same position. ...

... Furthermore, a brief description of previous works exemplifies the state of art and relevance of coupled calculations. Since some previous work [4], great enhancements on multiphysics calculations have been made. The reference [5] shows a way to do coupled simulations for reactor safety purposes. ...

... That paper presented OpenFOAM and Serpent coupled calculations in a accident case were the Opal reactor pool was drained [5]. That work links directly with [4] predictions for transient calculations. Moreover, other paper [6] presented a OpenFOAM coupled with Serpent methodology that makes it possible to glimpse a full core simulation as a future possibility. ...

In this work, a single step of coupled calculations for a fuel rod of IPR-R1 TRIGA was performed. The used methodology allowed to simulate the fuel pin behavior in steady-state mode for different power levels. The aim of this paper is to present a practical approach to perform coupled calculations between neutronic (Monte Carlo) and thermal-hydraulic (CFD) codes. For this purpose, is necessary to evaluate the influence of the water thermal-physical properties temperature variations on keff parameter. Besides that, Serpent Nuclear Code was used for the neutronics evaluation, while OpenFOAM was used for thermal-hydraulics. OpenFOAM simulations were made by using a modified chtMultiRegionFoam solver, developed to read Serpent output correctly. The neutronic code was used without any modifications. The results shows that this coupled calculations were consistent and that leads to encouraging further methodology development and its use for full core simulation. Also, the results shows good agreement with calculations performed using other version of OpenFOAM and Milonga as neutronic code.

... Furthermore, a brief description of previous works exemplifies the state of art and relevance of coupled calculations. Since some previous work [4], great enhancements on multiphysics calculations have been made. The reference [5] shows a way to do coupled simulations for reactor safety purposes. ...

... That paper presented OpenFOAM and Serpent coupled calculations in an accident case were the Opal reactor pool was drained [5]. That work links directly with [4] predictions for transient calculations. ...

In this work, a single step of coupled calculations for a fuel rod of IPR-R1 TRIGA was performed. The used me-thodology allowed to simulate the fuel pin behavior in steady-state mode for different power levels. The aim of this paper is to present a practical approach to perform coupled calculations between neutronic (Monte Carlo) and thermal-hydraulic (CFD) codes. For this purpose, is necessary to evaluate the influence of the water thermal-physical properties temperature variations on keff parameter. Besides that, Serpent Nuclear Code was used for the neutronics evaluation, while OpenFOAM was used for thermal-hydraulics. OpenFOAM si- mula-tions were made by using a modified chtMultiRegionFoam solver, developed to read Serpent output correctly. The neutronic code was used without any modifications. The results shows that this coupled calculations were consistent and that leads to encouraging further methodology development and its use for full core simulation. Also, the results shows good agreement with calculations performed using other version of OpenFOAM and Milonga as neutronic code.

... Recently the focus also pointed toward the use of heavy-weight thermal-hydraulic and neutronic codes to solve nuclear reactor problems in a coupled way. It must be remarked that coupled problems have been tackled for a long time (Ivanov and Avramova, 2007), but only recently more computational demanding methods became accessible. These coupled calculations approaches, also called multiphysics (Leppännen et al., 2012;Schmidt et al., 2015;Aufiero et al., 2015;Bennett et al., 2016;Valtavirta et al., 2017), offer an innovative way of modeling the feedback from thermal-hydraulics to neutronics and vice versa. ...

... As an advantage, the use of shared memory poses no overhead in data access greater than any other type of memory access. Some works on coupled thermal-hydraulic and neutronic using external files (Ivanov and Avramova, 2007;Hummel and Novog, 2016) have access time orders of magnitude higher than the achieved using shared memory (Theler et al., 2013). It must be noted that tools for shared memory communication are available as standard in most of the common operational systems available nowadays. ...

The development of a fine mesh coupled neutronics/thermal-hydraulics framework mainly using free open source software is presented. The proposed contributions go in two different directions: one, is the focus on the open software approach development, a concept widely spread in many fields of knowledge but rarely explored in the nuclear engineering field; the second, is the use operating system shared memory as a fast and reliable storage area to couple the computational fluid dynamics (CFD) software OpenFOAM to the free and flexible reactor core analysis code milonga. This concept was applied to model the behavior of a TRIGA-IPR-R1 reactor fuel pin in steady-state mode. The macroscopic cross-sections for the model, a set of two-group cross-sections data, were generated using the Serpent code. The results show that this coupled system gives consistent results, encouraging system further development and its use for complex geometries simulations.

... The data exchange and the geometry mapping between codes are further issues that should be addressed. According to the classification proposed by [78] there are to methods of coupling regarding the data exchange. The internal coupling is more sophisticated and requires modification of the codes. ...

Long term sustainable nuclear energy scenarios envisage a fleet of Liquid Metal Fast Reactors (LMFR) for the Pu recycling and minor actinides (MAs) transmutation or combined with some accelerator driven systems (ADS) just for MAs elimination. Design and licensing of these innovative reactor concepts require accurate computational tools, implementing the knowledge obtained in experimental research for new reactor configurations, materials and associated systems. Although a number of fast reactor systems have already been built, the operational experience is still reduced, especially for lead reactors, and not all the transients are fully understood. The safety analysis approach for LMFR is therefore based only on deterministic methods, different from modern approach for Light Water Reactors (LWR) which also benefit from probabilistic methods. Usually, the approach adopted in LMFR safety assessments is to employ a variety of codes, somewhat different for the each other, to analyze transients looking for a comprehensive solution and including uncertainties. In this frame, new best estimate simulation codes are of prime importance in order to analyze fast reactors steady state and transients. This thesis is focused on the development of a coupled code system for best estimate analysis in fast critical reactor. Currently due to the increase in the computational resources, Monte Carlo methods for neutrons transport can be used for detailed full core calculations. Furthermore, Monte Carlo codes are usually taken as reference for deterministic diffusion multigroups codes in fast reactors applications because they employ point-wise cross sections in an exact geometry model and intrinsically account for directional dependence of the ux. The coupling methodology presented here uses MCNP to calculate the power deposition within the reactor. The subchannel code COBRA-IV calculates the temperature and density distribution within the reactor. COBRA-IV is suitable for fast reactors applications because it has been validated against experimental results in sodium rod bundles. The proper correlations for liquid metal applications have been added to the thermal-hydraulics program. Both codes are coupled at steady state using an iterative method and external files exchange. The main issue in the Monte Carlo/thermal-hydraulics steady state coupling is the cross section handling to take into account Doppler broadening when temperature rises. Among every available options, the pseudo materials approach has been chosen in this thesis. This approach obtains reasonable results in fast reactor applications. Furthermore, geometrical changes caused by large temperature gradients in the core, are of major importance in fast reactor due to the large neutron mean free path. An additional module has therefore been included in order to simulate the reactor geometry in hot state or to estimate the reactivity due to core expansion in a transient. The module automatically calculates the fuel length, cladding radius, fuel assembly pitch and diagrid radius with the temperature. This effect will be crucial in some unprotected transients. Also related to geometrical changes, an automatic control rod movement feature has been implemented in order to achieve a just critical reactor or to calculate control rod worth. A step forward in the coupling platform is the dynamic simulation. Since MCNP performs only steady state calculations for critical systems, the more straight forward option without modifying MCNP source code, is to use the flux factorization approach solving separately the flux shape and amplitude. In this thesis two options have been studied to tackle time dependent neutronic simulations using a Monte Carlo code: adiabatic and quasistatic methods. The adiabatic methods uses a staggered time coupling scheme for the time advance of neutronics and the thermal-hydraulics calculations. MCNP computes the fundamental mode of the neutron flux distribution and the reactivity at the end of each time step and COBRA-IV the thermal properties at half of the the time steps. To calculate the flux amplitude evolution a solver of the point kinetics equations is used. This method calculates the static reactivity in each time step that in general is different from the dynamic reactivity calculated with the exact flux distribution. Nevertheless, for close to critical situations, both reactivities are similar and the method leads to acceptable practical results. In this line, an improved method as an attempt to take into account the effect of delayed neutron source in the transient flux shape evolutions is developed. The scheme performs a quasistationary calculation per time step with MCNP. This quasistationary simulations is based con the constant delayed source approach, taking into account the importance of each criticality cycle in the final flux estimation. Both adiabatic and quasistatic methods have been verified against the diffusion code COBAYA3, using a theoretical kinetic exercise. Finally, a transient in a critical 100 MWth lead-bismuth-eutectic reactor concept is analyzed using the adiabatic method as an application example in a real system.

... The determination of the thermal power generated in a nuclear reactor is a coupled multiphysics problem, involving neutron physics and thermal-hydraulic models. The solution of the whole problem is generally addressed by separate linearized problems coupled through successive iterations up to a fixed point [1]. ...

Several types of nuclear reactors rely on lattices of fuel rods, where the fuel cells constitute the basic units of energy production by the nuclear reactions and of energy removal by the flowing coolant. The coolant channel is physically identified by the volume within adjacent fuel cells, and it is the fundamental purview of design and safety studies resolving coupled thermal-hydraulic and neutron problems. Although channels are generally open to increase the flow mixing, its closed version is often in use to describe representative channels in boxed fuel assemblies, or simply faster predictive modelling. This work aims to find a solution to the coupled closed channel problem without solving separately for the different physics in an iterative scheme. The new methodology developed hereafter is demonstrated on a realistic PWR channel with UO2 fuel, and compared against the traditional one based on operator-splitting. The simple model presented in this work serves both research and educational purposes.

... The SHARP toolset, part of the Nuclear Energy Advanced Modeling and Simulation (NEAMS) project, is an example of an effort to combine models of neutronics, thermal-hydraulics, and structural mechanics in a coupled simulation to model any type of nuclear reactor [1]. The multi-physics coupling in these codes required experimental validation that is in addition to the validation data that exists for the individual physics routines, with benchmark experiments specifically designed for that purpose [2]. To focus on the feedback between thermal-hydraulics and neutronics, a set of experiments are developed in which the temperature conditions can be adjusted in a controlled manner to affect the reaction rate. ...

Modern reactor simulation tools provide advanced prediction capabilities by coupling multi-physics models to simulate reactor behaviors, involving thermal, neutronic, and mechanical interactions. To assure high-fidelity predictions by these tools, experimental data are needed to validate coupled-physics models deployed by these tools. In order to provide data to benchmark the feedback between temperature and neutronic simulations, coupled-physics critical experiments have been designed and performed at a Reactor Critical Facility (RCF). The facility's low power and open-pool atmospheric pressure configuration allows for many unique critical experiments. Recently, a water loop system has been designed and installed in the facility with the heated water circulating through the center of the core, which broadens the range of validation experiments available. Direct effects of the temperature on reactor state and excess reactivity are demonstrated, through a series of different measurements, including reactor change of state through moderator temperature change, influence of heated water in the center of the core on the reactivity, and transient temperature influence on reactor power evolution. Changes as low as of 1% in the reactor power caused by small water temperature perturbations are observable experimentally.

... (1) and (2). Because of the complex structure in the TRISO fuel sphere, the interior temperature distribution in the fuel sphere is calculated in TINTE to consider the temperature feedback mechanisms accurately, as shown in Eq. (3). The global graphite temperature (also known as the pebble-bed temperature) Two-group diffusion equation: ...

This paper evaluates the performance of neutronic and thermal-hydraulic coupling algorithms in transient problems based on the high-temperature gas-cooled reactor simulator TINTE. In particular, the operator splitting semi-implicit (OSSI), Picard iteration, and Jacobian-free Newton-Krylov (JFNK) methods are compared by a practical engineering model. The OSSI method is employed in the original TINTE. The fully implicit algorithms TINTE-Picard and TINTE-JFNK are implemented in this study. Several special numerical technologies are discussed to improve the performance of JFNK. First, a novel JFNK variant is employed to deal with the multiscale coupling between local fuel sphere temperature and global solid porous media temperature. Second, the preconditioning strategy is determined by making a balance between performance and code burden. Finally, the scaling modifications of the Jacobian matrix and perturbation size are investigated to solve the ill-posed problem. What is more, the framework of TINTE-Picard and TINTE-JFNK is presented, and the key points of implementation are discussed. Numerical results indicate that the advanced coupling algorithms Picard and JFNK can achieve higher computational performance than the original semi-implicit coupling algorithm in TINTE due to the accuracy and stability advantage.

... Such multi-physics and multi-scale modelling remain a particularly challenging task for the future (Ivanov and Avramova, 2007). One of the key multi-physics interactions appears in the reactor core between neutronics and thermal-hydraulics. ...

The computational model of the JSI TRIGA Mark II, coupling Monte-Carlo neutron transport code TRIPOLI and computational fluid dynamics code CFX was used to reproduce the behaviour of the reactor after extraction of a control rod. To tackle the time dependent Boltzmann equation, a quasistatic approach has been used and compared with point kinetic. Qualitative assessment of the model was performed by comparison with measured fuel temperature and power. Time evolutions of power and fuel temperature were reproduced. The quasistatic approximation was justified by updating the shape function at different time intervals. The quasistatic approach successfully reproduces the experimental results obtained with the TRIGA reactor. It was shown that most of the local effects (temperature, power density) were due to the control rod and that local effects of coupling were small.

... On the other hand, in the loose coupling, the different physics are solved separately using an external iteration scheme to track the convergence of the coupled solution. Furthermore, loose coupling methods can be divided into internal and external coupling schemes [13]. The internal coupled codes are compiled in the same project, and the communication and data exchanges take place by sharing their internal memory. ...

Best Estimate Plus Uncertainty (BEPU) approaches for nuclear reactor applications have been extensively developed in recent years. The challenge for BEPU approaches is to achieve multi-physics modeling with an acceptable computational cost while preserving a reasonable fidelity of the physics modeled. In this work, we present the core multi-physics computational framework developed for the efficient computation of uncertainties in Light Water Reactor (LWR) simulations. The subchannel thermal-hydraulic code CTF and the nodal expansion neutronic code PARCS are coupled for the multi-physics modeling (CTF-PARCS). The computational framework is discussed in detail from the Polaris lattice calculations up to the CTF-PARCS coupling approaches. Sampler is used to perturb the multi-group microscopic cross-sections, fission yields and manufacturing parameters, while Dakota is used to sample the CTF input parameters and the boundary conditions. Python scripts were developed to automatize and modularize both pre- and post-processing. The current state of the framework allows the consistent perturbation of inputs across neutronics and thermal-hydraulics modeling. Improvements to the standard thermal-hydraulics modeling for such coupling approaches have been implemented in CTF to allow the usage of 3D burnup distribution, calculation of the radial power and the burnup profile, and the usage of Santamarina effective Doppler temperature. The uncertainty quantification approach allows the treatment of both scalar and functional quantities and can estimate correlation between the multi-physics outputs of interest and up to the originally perturbed microscopic cross-sections and yields. The computational framework is applied to three exercises of the LWR Uncertainty Analysis in Modeling Phase III benchmark. The exercises cover steady-state, depletion and transient calculations. The results show that the maximum fuel centerline temperature across all exercises is 2474 K with 1.7% uncertainty and that the most correlated inputs are the U-238 inelastic and elastic cross-sections above 1 MeV.

... Loose coupling can be further divided into internal and external coupling (Ivanov and Avramova, 2007). Internal coupling refers to embedding neutronic code as sub-code into thermal-hydraulic code or embedding thermal-hydraulic code as sub-code into neutronic code. ...

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.

... The multi-physics coupling in these codes required experimental validation that is in addition to the validation data that exists for the individual physics routines, with benchmark experiments specifically designed for that purpose [2]. The purpose of this work is to develop a set of experiments at the Walthousen Reactor Critical Facility (RCF) at Rensselaer Polytechnic Institute (RPI) that will provide data for multi-physics coupling validation of the SHARP toolset, and which may be applied to other code sets as well. ...

... So far, most of the attempts to couple stochastic neutronic with T-H solvers for coupled static analysis use a kind of serial coupling like Joo et al., 2004;Waata et al., 2005;Ivanov and Avramova, 2007;Seker et al., 2007;Grieshemer et al., 2008;Hu, 2008;Shan et al., 2010;Kotlyar et al., 2011;Cardoni, 2011;Vasquez et al., 2012;Chaudri et al., 2012;Espel et al., 2013;Guoa et al., 2013;Bettencourt et al., 2013;Mylonakis et al., 2014;Bernnat et al., 2014;Wu and Kozlowski, 2015. This type of coupling is a Picard Iteration (PI). ...

In the field of nuclear reactor analysis, multi-physics 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 a kind of “serial” algorithm has been mainly used for coupling with thermal-hydraulics. The main motivation of this work is the interest for an algorithm that could maintain the distinct treatment of the involved fields within a tight coupling context that could be translated into higher convergence rates and more stable behaviour. This work investigates the possibility of replacing the usually used “serial” iteration with an approximate Newton algorithm. The selected algorithm, 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 creation of the Jacobian matrix. A coupling algorithm between Monte-Carlo neutronics and thermal-hydraulics based on the above-mentioned methodology is developed and its performance is analysed. More specifically, OpenMC, a Monte-Carlo neutronics code and COBRA-EN, a thermal-hydraulics code for sub-channel and core analysis, are merged in a coupling scheme using the Approximate Block Newton method aiming to examine the performance of this scheme and compare with that of the “traditional” serial iterative scheme. First results show a clear improvement of the convergence especially in problems where significant coolant density gradients appear.

... Multi-physics and multi-scale modelling is a particularly challenging task for the future (Ivanov and Avramova, 2007). More precisely, the coupled phenomena occurring in the core between neutronics and thermal-hydraulics are known as reactivity or thermal feedback. ...

A new computational model of the JSI TRIGA Mark II, coupling Monte Carlo neutron transport code
TRIPOLI and fluid dynamics code CFX was built and verified with a set of new experimental data. A set
of subroutines was developed to allow the communication between the Monte-Carlo transport code
and CFD code. First, test of the coupling scheme is presented: for a given thermal power of the reactor,
the coupled model numerically reproduced fuel temperature monitored during reactor operation and
axial water temperature profile measured in the coolant channels. Then axial temperature profiles in
the coolant channels were measured with a newly developed sensor during steady-state operation.
Predictions of the coupled model are in expected agreement with experimental data recorded during
reactor operations. Influence of the coupling has been investigated.

... Extensively study has been made on this type of coupled multi-physics approach [1][2][3][4][5][6]. K. Ivanov [7] summarized the main issues in a coupled neutronics and thermal-hydraulics system to be: ...

Coupled multi-physics approach plays an important role in improving computational accuracy. Compared with deterministic neutronics codes, Monte Carlo codes have the advantage of higher resolution level. In the present paper, a three-dimensional continuous-energy Monte Carlo reactor physics burnup calculation code, Serpent , is coupled with thermal-hydraulics safety analysis code, RELAP5. A new convergence criterion for the coupled simulation is developed based on the statistical uncertainty in power distribution in Monte Carlo code, rather than an arbitrarily chosen criterion in previous research. The coupled simulation is based on the OECD-NEA/NRC PWR MOX-UO 2 Core Transient Benchmark. The convergence criterion of normalized axial power distribution is tested on both UO 2 and MOX single assembly models. Compared with previously implemented convergence criteria based on temperature, eigenvalue or flux (or power), it takes into account both the local and global convergence. It does not use a pre-set tolerance limit and is decided by the statistical accuracy of the Monte Carlo code itself. This new convergence criterion is shown to be stable, more stringent and direct, equally convenient to use but may need a few more steps to converge.

... For coupling the neutronic and thermal-hydraulic calculation, the traditional technique is the Operator Splitting (OS) method [24,25]. By this method, different physical processes are solved separately. ...

Response Surface Methodology (RSM) is introduced to optimize the control rod positions in a pressurized water reactor (PWR) core. The widely used 3D-IAEA benchmark problem is selected as the typical PWR core and the neutron flux field is solved. Besides, some additional thermal parameters are assumed to obtain the temperature distribution. Then the total and local entropy production is calculated to evaluate the energy dissipation. Using RSM, three directions of optimization are taken, which aim to determine the minimum of power peak factor Pmax, peak temperature Tmax and total entropy production Stot. These parameters reflect the safety and energy dissipation in the core. Finally, an optimization scheme was obtained, which reduced Pmax, Tmax and Stot by 23%, 8.7% and 16%, respectively. The optimization results are satisfactory.

... The validation of multi-physics coupling techniques requires new experimental benchmark experiments specifically designed for that purpose [2]. As a preliminary step towards design of these experiments, a series of measurements have been performed to demonstrate the temperature-dependent neutronic behavior of a wellcharacterized reactor assembly for comparison with the available codes. ...

... It was shown before in Refs. 89,90 that starting the loop with the thermal-hydraulics code yields faster convergence. ...

A novel and modern framework for energy modeling is developed in this paper with a focus on nuclear energy modeling and simulation. The framework combines multiphysics simulations and real data, with validation by uncertainty quantification tasks and facilitation by machine and deep learning methods. The hybrid framework is built on the basis of a wide range of physical models, real data, mathematical and statistical methods, and artificial intelligence techniques. The framework is demonstrated in different applications, including quantifying uncertainties in computer simulations, multiphysics coupling, analysis of variance using machine learning surrogate models, deep learning of time series phenomena, and propagating parametric uncertainties of nuclear data. The applications demonstrated are oriented to nuclear engineering simulations, even though majority of the methods are applicable to other energy sources (eg, renewable). Efficient utilization of this framework is expected to yield a much better understanding of the physical phenomena analyzed as well as an improvement in the performance of the energy design/model under construction. A novel framework is developed to model advanced energy systems, where mathematical, statistical, and artificial intelligence methods are integrated. The multiphysics simulations are validated with real data. Various underlying uncertainties are propagated using uncertainty quantification methods. The high dimensionality and computational costs are handled by deep learning. The integrated framework is demonstrated using nuclear power applications, with the possibility of applications to other energy systems.

... The traditional methods used for the representation of cross sections were developed mostly for the analysis of reactors during steady state operations. Creation of cross section libraries suitable for use during reactor transients and accidents result in additional challenges due to the increased intervals of the state parameters (Ivanov and Avramova, 2007). The most straightforward solution to this challenge would be to increase the number of state parameter points at which homogenised cross sections are pre-calculated so that an accurate representation may be constructed. ...

Nodal diffusion methods are often used for full core neutronic analysis. They require few-group homogenised neutron cross sections for every heterogeneous sub-region of the core. The homogenised cross sections are pre-calculated at various reactor states and represented in a way that facilitates the reconstruction of cross sections at other possible states. In this study hierarchical Lagrange interpolation on Clenshaw–Curtis sparse grids was used to represent the homogenised cross sections of a MOX (mixed oxide) fuel assembly. Representations were produced for the homogenised cross sections of a number of individual isotopes, as well as the effective (lumped) cross section of all the materials in the assembly. The impact of increasing the number of neutron energy groups from two to six, as well as using different state parameter intervals, on both the representation accuracy and the way in which the cross sections depend on the state parameters, was investigated. The two sets of state parameter intervals were designed to be applicable to the simulation of standard reactor operations and transient analysis, respectively. The anisotropy feature of the representation procedure, which allows more samples to be taken for state parameters that are known to be more important to the representation accuracy than others, was applied, and the effect this refinement to the method has on the representation accuracy was studied. Results of this study show that the sparse grid method is capable of constructing efficient representations to an accuracy that is considered acceptable in practical applications, if the anisotropy feature is used.

... The existing coupled code development technologies mainly include PVM, dynamic link library (DLL) (Li et al., 2014), and boundary files modification methods. Challenges in the coupling process (Ivanov and Avramova, 2007) mainly concern the method of coupling, coupling approach, spatial mesh overlays, time step algorithms, and coupling numeric and convergence schemes. Spatial mesh mapping, especially the data exchange at the coupling interface plays a key role in simulation accuracy and numerical convergence. ...

In nuclear reactor system research, the multiscale coupled thermal-hydraulic (T-H) system code and CFD code is one of the most prevalent research areas, and it could help improve simulation fidelity and optimize nuclear reactor design. Additionally, a new idea known as the function fitting method (FFM) for coupling parameter distribution has been newly proposed for exchanging data on the coupling interface, which uses math equations to present the velocity distribution characteristics at the coupling interface. This method could improve the simulation error and numerical instability. To verify and validate the abovementioned FFM, a comparison between the velocity function shape by FFM and real velocity distribution was completed. Besides, the Edwards pipe blowdown test results were used to verify the coupled code. The results showed good agreement with experiment results, and a better simulation accuracy compared to previous work. The current work will establish the ability to explore multiscale coupled thermal-hydraulic operation characteristics which permit precise local parameter distribution.

... Traditionally, in order to obtain the solution of such a multiphysics nonlinear system, the coupled fields are solved separately by dividing them into sub-fields. The whole system is coupled by transferring boundary conditions between subfields [1], such as typical operator splitting and Picard iteration method. They could be called fixed point method. ...

The design and safety of nuclear reactor are strongly dependent on the neutronics and thermal conduction. The interaction between these coupled issues forms multi-physics nonlinear system, which has limited the economy of the nuclear power plant because of the complexity. And the accurate prediction of the reactor behavior still remains a challenge for the nuclear engineering. Traditionally, the neutronics and thermal conduction are solved separately by operator-splitting, which may be unstable and introduce significant errors. In recent years, fully coupled Newton-Krylov methods are prefer to be adopted due to these methods are more robust, accurate and efficient. However, each Newton-Krylov method has merits and demerits. In this study, finite difference Jacobian based Newton-Krylov (DJNK) and widely used Jacobian-free Newton-Krylov (JFNK) method are employed to solve the coupled neutronics/thermal conduction problems of a high-temperature gas-cooled reactor (HTGR). A steady state at thermal power of 250 MW and a transient state of supercritical accident are simulated. The results show that, DJNK is more efficient compared with JFNK, because DJNK performs better in preconditioning, which is the key to successful application of Newton-Krylov methods. And different preconditioning methods are utilized to reduce the number of Krylov iterations. A speedup ratio of DJNK over JFNK is observed to be 3. Synthesis results indicate that compared with JFNK, DJNK is a more potential method, contributing to a deeper understanding of the reactor behavior in a more efficient way.

... Inherent feedback mechanisms in reactors necessitate a multi-physics approach, particularly between neutronics and thermal-hydraulics [9,10]. Numerous neutronics and thermal-hydraulics coupling research studies have been done with simplified physical models, such as nodal diffusion theory and subchannel or single-channel thermal hydraulic codes [11][12][13][14]. ...

This paper develops a multi-physics interface code MC-FLUENT to couple the Monte Carlo code OpenMC with the commercial computational fluid dynamics code ANSYS FLUENT. The implementations and parallel performances of block Gauss–Seidel-type and block Jacobi-type Picard iterative algorithms have been investigated. In addition, this paper introduces two adaptive load-balancing algorithms into the neutronics and thermal-hydraulics coupled simulation to reduce the time cost of computation. Considering that the different scalability of OpenMC and FLUENT limits the performance of block Gauss–Seidel algorithm, an adaptive load-balancing algorithm that can increase the number of nodes dynamically is proposed to improve its efficiency. Moreover, with the natural parallelism of block Jacobi algorithm, another adaptive load-balancing algorithm is proposed to improve its performance. A 3 x 3 PWR fuel pin model and a 1000 MWt ABR metallic benchmark core were used to compare the performances of the two algorithms and verify the effectiveness of the two adaptive load-balancing algorithms. The results show that the adaptive load-balancing algorithms proposed in this paper can greatly improve the computing efficiency of block Jacobi algorithm and improve the performance of block Gauss–Seidel algorithm when the number of nodes is large. In addition, the adaptive load-balancing algorithms are especially effective when a case demands different computational power of OpenMC and FLUENT.

... The nuclear reactor is a typical multi-physics system, in which the coupled neutronics-thermal-hydraulics (NTH) process (Guo et al., 2017;Liu et al., 2020) is one of the main considerations in nuclear reactor simulation and engineering, especially the nuclear reactor design and safety analysis (Chen et al., 2015;Ivanov and Avramova, 2007;Liu et al., 2016). The neutron transport process determines the amount of energy generated by neutron fission in the nuclear fuel, while the thermal-hydraulics process determines the temperature distribution and affects the macroscopic neutron cross-sections via the Doppler effect (Jareteg et al., 2015). ...

This work establishes the unified lattice Boltzmann (LB) framework, namely lbmNTH, to simulate the fully coupled neutronics-thermal-hydraulics (NTH) process in nuclear reactor. The neutron transport and delayed neutron precursor balance are simulated using the finite-Boltzmann schemed LB models with considering the temperature feedback. The fluid flow is simulated using the large-eddy-based LB model, and the convection heat transfer with fission generation also is considered under the LB framework. All the LB models have the same data structure and implementation, which simplifies the data exchange between different physical fields, and no extra data interpolation is required. Numerical results show that the proposed lbmNTH framework can simulate the coupled NTH process flexibly. The temperature feedback has a strong effect in high-temperature conditions, while the high flow velocity can effectively improve the heat transfer capability. This work can provide an optional multi-physics technique to analyze the coupled neutronics-thermal-hydraulics process in nuclear reactor engineering.

... Multiphysics analysis attracts a lot of attention of nuclear engineers worldwide as it helps to produce more realistic results in terms of reactor core safety margins. Nowadays there are many codes progressing towards the high-fidelity multiphysics simulation of light water reactors [1,2]. Recent works [3,4] demonstrate the coupling experience of MCS [5], CTF [6] and FRAPCON [7] codes for reactor core pin-by-pin analysis taking into consideration the pellet-to-cladding transfer and coolant cross-flow phenomena. ...

A new reactor core multi-physics system addresses the pellet-to-cladding heat transfer modeling to improve full-core operational transient and accident simulation used for assessment of reactor core nuclear safety. The rigorous modeling of the heat transfer phenomena involves strong interaction between neutron kinetics, thermal-hydraulics and nuclear fuel performance, as well as consideration of the pellet-to-cladding mechanical contact leading to dramatic increase in the gap thermal conductance coefficient. In contrast to core depletion where parameters smoothly depend on fuel burn-up, the core transient is driven by stiff equation associated with rapid variation in the solution and vulnerable to numerical instability for large time step sizes. Therefore, the coupling algorithm dedicated for multi-physics transient must implement adaptive time step and restart capability to achieve prescribed tolerance and to maintain stability of numerical simulation. This requirement is met in the MPCORE (Multi-Physics Core) multi-physics system employing external loose coupling approach to facilitate the coupling procedure due to little modification of constituent modules and due to high transparency of coupling interfaces. The paper investigates the coupling algorithm performance and evaluates the pellet-to-cladding heat transfer effect for the rod ejection accident of a light water reactor core benchmark.

... Since the computing power at that time was limited, such codes could not provide higher level of nodalization and precision. At present, coupled calculations are very widespread and allow user to prepare highly accurate modelling for almost all types of nuclear reactors and nuclear power plants [1][2][3][4][5][6][7][8][9][10][11]. The main idea of coupled calculations is to conduct modelling as accurate as possible, considering the largest possible number of phenomena, while keeping an acceptable computation time [12]. ...

The paper describes recent developments in the multi-physics coupling scheme between the SKETCH-N nodal neutronics code and the best-estimate thermohydraulic code ATHLET v3.2. The boundary conditions plugin was implemented. The verification and validation were performed using the transient of the Kalinin-3 international Benchmark. The simulation results using the boundary conditions plugin show good agreement with experimental data and calculations performed by using SKETCH-N/ATHLET direct calculations. The calculations of the transient "Switch off of one MCP (Main Coolant Pump) at nominal power" is performed applying a simple core thermohydraulic model without taking into account inter-channel mass transfer.

... The main feature of coupled simulation is the modelling of several phenomena from different scientific fields at once taking into account the influence of some phenomena on other (so-called feedbacks), thus allowing a more accurate modelling. The main idea of coupled calculations is to conduct modelling as accurate as possible, considering the largest possible number of phenomena, while keeping an acceptable computation time [1]. ...

The paper describes the multi-physics coupling scheme between the SKETCH-N nodal neutronics code and the best-estimate thermohydraulic code ATHLET v3.2. Some first results are discussed. Various possible options of coupling have been considered. A scheme is selected and applied for data exchange between the codes based on MPI library. The verification and validation were performed using the transient of the Kalinin-3 international Benchmark. The simulation results show good agreement with experimental data and calculations performed by the participants of the benchmark. Parallel to the coupling scheme development, a visualization system to process the results is being created. The steady-state analysis is carried out using both simple and complex thermohydraulic models. The calculations of the transient \Switch off of one MCP (Main Coolant Pump) at nominal power" is performed applying a more elaborate thermohydraulic model taking into account inter channel mass transfer.

... On the other hand, the reactor TH will only be properly captured with the appropriate power flux distribution, that comes from neutronics (Ivanov and Avramova, 2007). Hence, reactor analysis must take this TH-N correlation into account. ...

In this work, a fine-mesh 1:1 Computational Fluid Dynamics (CFD) – Monte Carlo Neutron Transport (MC) coupled calculations for a IPR-R1 TRIGA MARK I fuel pin was performed. The proposed methodology allowed the simulation of the fuel pin behavior in steady-state for different meshes and the evaluation of the discretization uncertainty. Comparison between mesh-based and Constructive Solid Geometry (CSG) MC simulations was performed. An extended Grid Convergence Index (GCI) method was applied to quantify numerical discretization uncertainty for keff, temperature and power density profiles. Serpent Nuclear Code was used for neutronics simulations, while OpenFOAM was used for thermal–hydraulics calculations. The proposed coupling method was proved convergent. This coupling method did not produce a smooth power density profiles. In order to achieve high-quality profiles, neutronic noise reduction procedure was performed. The results were encouraging, nevertheless, the methodology should be employed on the study of problems with increased complexity for further assessment.

... The coupling between phenomena is necessary to understand the physics in the core undergoing feedback processes, i.e. the feedback between the neutronic and thermofluid phenomena [18][19][20][21]. There is a strong coupling of different physical processes in nuclear reactors, resulting in nonlinear feedback effects inherited in the mathematical model. ...

The heat transfer phenomena are crucial in nuclear reactors' design and safety analysis due to the feedback effects with the neutronic processes for power generation. Nuclear reactors are heterogeneous systems containing hundreds of thousands of fuel pins that exhibit power distribution through the space, and the temperatures between the coolant fluid and pins are different. This work analyzes the heat transfer process in liquid metal-cooled fast nuclear reactors with two upscaled energy equations based on the volume averaging method, which is widely applied for the analysis of transport in multiphase systems. The upscaled heat transfer model is coupled with a neutronic reflected core model including feedback effects from the nuclear fuel and liquid metal temperatures. The coupled mathematical models are employed within a called downscaling procedure, which represents a novel methodology with scopes beyond conventional problems in heat transport processes in nuclear reactors. The downscaling process allows us to increase the degree of resolution in the reactor core since this considers the scale of the fuel assembly and that of individual pins at the smallest scale, i.e. a single fuel pin surrounded by liquid metal. This point is crucial for analyzing hot spots in the reactor core.

... Then, the entire system is coupled together by transferring information (i.e. boundary conditions) between subfields (Ivanov and Avramova, 2007). For instance, in order to analyse the reactivity initiated accident, Hursin et al. (2013) used neutronic codes to provide power density for fuel performance code. ...

Newton-Krylov (NK) method with the explicit Jacobian matrix is a promising method to solve the nonlinear multi-physics coupling system. However, how to form the Jacobian matrix efficiently is a key issue that is the most cumbersome step in NK method. In this work, a new solution with the finite difference Jacobian based NK (DJNK) method is proposed, where the Jacobian matrix is calculated by finite difference approximation instead of the analytical form. Moreover, DJNK is further improved to form Jacobian by calculating the diagonals of the submatrixes, leading to significant reduction of the time cost. Two benchmarks and a complicated transient neutronics/thermal-hydraulics coupling problem are conducted. Results show that DJNK outperforms widely used Jacobian-free NK (JFNK) method, because of the higher performance in matrix-vector product calculation and the more efficient preconditioning in Krylov iteration. A speedup ratio of DJNK over JFNK is observed to be 1.7.

... Neutronics and thermal-hydraulics coupling involves exchanging data on axial power distribution and coolant characteristics across physics codes [12]. is process can be done with external coupling [13], which is the method used in this study for validation of spent fuel isotopic composition (see Section 3). A variety of neutronics and thermal-hydraulics coupling studies have been conducted previously, which include coupling to subchannel codes (e.g., CTF), coupling to system codes (e.g., TRACE), and coupling to computational fluid dynamics codes (e.g., ANSYS/FLU-ENT). ...

Multiphysics coupling of neutronics/thermal-hydraulics models is essential for accurate modeling of nuclear reactor systems with physics feedback. In this work, SCALE/TRACE coupling is used for neutronic analysis and spent fuel validation of BWR assemblies, which have strong coolant feedback. 3D axial power profiles with coolant feedback are captured in these advanced simulations. The methodology is applied to two BWR assemblies (2F2DN23/SF98 and 2F2D1/F6), discharged from the Fukushima Daini-2 unit. Coupling is performed externally, where the SCALE/T5-DEPL module transfers axial power data in all axial nodes to TRACE, which in turn calculates the coolant density and temperature for each of these nodes. Within a burnup step, the data exchange process is repeated until convergence of all coupling parameters (axial power, coolant density, and coolant temperature) is observed. Analysis of axial power, criticality, and coolant properties at the assembly level is used to verify the coupling process. The 2F2D1/F6 benchmark seems to have insignificant void feedback compared to 2F2DN23/SF98 case, which experiences large power changes during operation. Spent fuel isotopic data are used to validate the coupling methodology, which demonstrated good results for uranium isotopes and satisfactory results for other actinides. This work has a major challenge of lack of documented data to build the coupled models (boundary conditions, control rod history, spatial location in the core, etc.), which encourages more advanced methods to approximate such missing data to achieve better modeling and simulation results.

... In this challenging landscape, multi-physics (MP) approaches (Fiorina et al., 2015;Ivanov and Avramova, 2007;Mylonakis et al., 2014;Zerkak et al., 2015) have emerged as a promising strategy for a comprehensive modeling of a nuclear reactor, thanks to the intrinsic coupling of the different "physics" within the system, e.g. the neutronics, fluid-dynamics, heat-transfer and thermal elasticity, mass transport, etc. In recent years, MP has been used to perform multi-scale neutronic/thermal-hydraulics coupled calculations for LWRs (Ellis et al., 2013;Kotlyar et al., 2011;Zare et al., 2010), SFRs (Radman et al., 2018;Vazquez et al., 2012;Yu et al., 2020), LFRs (Aufiero et al., 2013;Bonifetto et al., 2013), and MSRs (Aufiero et al., 2014;Cervi et al., 2019;Guo et al., 2013;Křepel et al., 2007;Yamamoto et al., 2006). ...

The development of a new generation of reactor presents several modelling challenges that cannot be effectively addressed by traditional tools used for Light Water Reactors. Multi-physics approaches allow for a comprehensive modeling of reactor cores, as they intrinsically couple the involved physics (i.e. fluid-dynamics, heat transfer, neutronics, thermo-mechanics), but require intense computational efforts that preclude their use in reactor control applications. This work aims at applying a Reduced Order Model (ROM) technique to multi-physics modelling. Such objective is achieved through a ROM technique previously used for Navier-Stokes equations and thermal-hydraulics problems (POD-FV-ROM). The technique used in this article, is built on a modeling framework developed ad-hoc for the Finite Volume (FV) scheme and relies on the Proper Orthogonal Decomposition (POD) and the Method of Snapshots. The reduced order multi-physics approach outlined in this work has been tested with success on a Lid-Driven-Cavity-based homogeneous reactor model. Reduced-order simulations have reproduced accurately the full order velocity, temperature, neutron flux and precursor concentration fields, resulting in relative L² norms of the differences between full order and reduced order simulations below 1 % for all the considered fields.

Large-scale reactor calculations with Monte Carlo (MC), including nonlinear feedback effects, have become a reality in the course of the last decade. In particular, implementations of coupled MC and thermal-hydraulic (T-H) calculations have been separately developed by many different groups. Numerous MC codes have been coupled to a variety of T-H codes (system level, subchannel, and computational fluid dynamics). In this work we review the numerical methods that have been used to solve the coupled MC-T-H problem with a particular focus on the formulation of the nonlinear problem, convergence criteria, and relaxation schemes used to ensure stability of the iterative process. We use a simple pressurized water reactor pin cell problem to numerically investigate the stability of commonly used schemes and which problem parameters influence the stability - or lack thereof. We also examine the role that the running strategy used in the MC calculation plays in the convergence of the coupled calculation. Results indicate that the instability in fixed-point iterations is driven by the Doppler feedback effect and that underrelaxation can be used to restore stability. We also observed that a form of underrelaxation could be achieved by performing the coupled iterations without converging the MC fission source each iteration. By performing many iterations of few histories, we observed rapid convergence to the coupled MC-T-H solution in a relatively small number of batches. Numerical results also showed that the presence of instability in the fixed-point iteration is independent of the stochastic noise in the MC simulation.

The design and the analysis of nuclear power plants (NPPs) require computational codes to predict the behavior of the NPP nuclear components and other systems (i.e., reactor core, primary coolant system, emergency core cooling system, etc.). Coupled calculations are essential to the conduct of deterministic safety assessments.
Inasmuch as the physical phenomena that govern the performance of a nuclear reactor are always present simultaneously, ideally computational modeling of a nuclear reactor should include coupled codes that represent all of the active physical phenomena. Such multi-physics codes are under development at several institutions and are expected to become operational in the future. However, in the interim, integrated codes that incorporate modeling capabilities for two to three physical phenomena will remain useful. For example, in the conduct of safety analyses, of paramount importance are codes that couple neutronics and thermal-hydraulics, especially transient codes. Other code systems of importance to safety analyses are those that couple primary system thermal-hydraulics to fission product chemistry, neutronics to fuel performance, containment behavior and structural mechanics to thermal-hydraulics, etc. This paper surveys the methods used traditionally in the coupling of neutronic and thermal-hydraulics codes.
The neutron kinetics codes are used for computing the space-time evolution of the neutron flux and, hence, of the power distribution. The thermal-hydraulics codes, which compute mass, momentum and energy transfers, model the coolant flow and the temperature distribution. These codes can be used to compute the neutronic behavior and the thermal-hydraulic states separately. However, the need to account with fidelity for the dynamic feedback between the two sets of properties (via temperature and density effects on the cross section inputs into the neutronics codes) and the requirement to model realistically the transient response of nuclear power plants and to assess the associated emergency systems and procedures imply the necessity of modeling the neutronic and thermal-hydraulics simultaneously within a coupled code system. The focus of this paper is a comparison of the methods by which the coupling between neutron kinetics and thermal-hydraulics treatments has been traditionally achieved in various code systems. As discussed in the last section, the modern approaches to multi-physics code development are beyond the scope of this paper.
From the field of the most commonly used coupled neutron kinetic-thermal-hydraulics codes, this study selected for comparison the coupled codes RELAP5-3D (NESTLE), TRACE/PARCS, RELAP5/PARCS, ATHLET/DYN3D, RELAP5/SCDAPSIM/MOD4.0/NESTLE. The choice was inspired by how widespread the use of the codes is, but was limited by time availability. Thus, the selection of codes is not to be construed as exhaustive, nor is there any implication of priority about the methods used by the various codes.
These codes were developed by a variety of institutions (universities, research centers, and laboratories) geographically located away from each other. Each of the research group that developed these coupled code systems used its own combination of initial codes as well as different methods and assumptions in the coupling process. For instance, all these neutron kinetics codes solve the few-groups neutron diffusion equations. However, the data they use may be based on different lattice physics codes. The neutronics solvers may use different methods, ranging from point kinetics method (in some versions of RELAP5) to nodal expansion methods (NEM), to semi-analytic nodal methods, to the analytic nodal method (ANM). Similarly, the thermal-hydraulics codes use several different approaches: different number of coolant fields, homogenous equilibrium model, separate flow model, different numbers of conservation equations, etc. Therefore, not only the physical models but also the assumptions of the coupled codes and coupling techniques vary significantly. This paper compares coupled codes qualitatively and quantitatively. The results of this study are being used both to guide the selection of appropriate coupled codes and to identify further developments into coupled codes.

At UPM, in-depth modifications of the core simulator COBAYA, able to perform neutronics diffusion calculations at both nodal and pin-by-pin levels, have been accomplished during the 7th Framework EURATOM NURESAFE project. The main goal was to upgrade its integration in the European Platform for Nuclear Reactor Safety Simulation in order to facilitate the coupling with any other code of the platform for multi-physics analysis, focusing also on the code legibility and maintainability.
An external and flexible coupling with the thermal-hydraulics code COBRA-TF was designed. As a result, COBAYA4/COBRA-TF allows multiscale coupled calculations, enabling both nodal and pin-by-pin neutronics resolutions using both assembly-based channels and pin-based subchannels at the thermal-hydraulics domain. Flexible mapping schemes also in axial direction can be defined.
The coupled system was applied to a Main Steam Line Break transient benchmark. Pin-by-pin 3D simulations using one thermal-hydraulic channel per assembly were carried out in a reasonable computing time, and results compared to nodal solutions demonstrating the multiscale coupling capability for full core transients. Pin-by-pin calculations using thermal-hydraulics subchannels will be performed in a near future to assess the role that a very detailed mapping can play to predict realistic local parameters. While in asymmetric transients the effect can be important, it is expected that in symmetric transients assembly-based thermal-hydraulics channels can provide accurate pin-by-pin solutions in execution times suitable for routine analysis.
The performed work will bring the ability to explore in an easy way multiscale effects on safety transient evaluations and give recommendations for the neutronics/thermal-hydraulics mapping depending on the application.

The traditional modeling approach for sodium fast reactor cores relies on separate physics models, where the fuel performance, thermal–hydraulics, and neutronics calculations required to predict the core physics characteristics for nominal conditions are decoupled by relying on user-imposed boundary conditions. This paper aims at evaluating the impact of multiphysics simulations for predicting the core characteristics of the Versatile Test Reactor, which is being designed as a 300-MWt sodium-cooled fast reactor. The purpose of the Versatile Test Reactor is to accelerate the testing of advanced nuclear materials in the United States. The proposed multiphysics model relies on the Griffin reactor physics code, the SAM thermal–hydraulic system code, the BISON fuel performance code, as well as generic Multiphysics Object-Oriented Simulation Environment capabilities implemented in the open-source tensor mechanics module. For keff calculations, the introduction of a tight coupling between the neutronics, thermo-mechanical and thermal–hydraulics models induces a change of around 543 pcm in the eigenvalue, compared to the traditional standalone neutronics calculation where approximate temperature profiles are used. The multiphysics model is then employed for quantifying the impact of the thermal conductivity uncertainties on some of the key figures of merit, such as the fuel centerline temperature, assembly powers, and keff for nominal core conditions. As anticipated, uncertainties on fuel thermal conductivity mostly impact the fuel centerline temperature, and to a lesser extend the keff.

For offshore floating nuclear power plant the complex ocean conditions must be considered for safe design and review. And the neutron kinetics decides the power distribution and variation. Both of them will change the characteristics of the core instability. In this paper the ocean condition mode and diffusion models are added into the parallel channel system thermal-hydraulic model. An imaginary 36-channels reactor core is selected as research object. The stable and unstable cases of the system are analyzed firstly. The oscillation characteristics of mass flow rate and total power are studied. Then the instability boundaries under ocean condition and neutron feedback are obtained, which is compared with the inherent boundary. The results indicate that the combined effect have powerful influence on the system instability and should be noticed.

The objective of this work is to obtain the eigenvalue in steady neutron diffusion problem by Newton based method. Unlike the traditional methods, Newton based methods are suitable for solving nonlinear equations. The method is implemented to solve coupled equations simultaneously, and second order convergence rate can be reached meanwhile. Generally the steady-state neutron calculation is regarded as a linear eigenvalue problem. However, the equations will become nonlinear if the eigenvalue is treated as a variable, and additional equation is required during the iteration. Besides, the solution will not converge to the dominant eigenvalue because Newton based method can only guarantee local convergence. Thus, a suitable initial guess strategy is proposed under the framework of Newton based method. In this paper, a code has been developed to solve the steady state using SLEPc and PETSc library. The effectiveness of the code is demonstrated on a 2D homogeneous reactor benchmark and High-Temperature Gas-Cooled Reactor–Pebble bed Module problems, and a comparison is presented between the Newton based method and Power Iteration method.

PWR core phenomena can be simulated and predicted more precisely and in more details with high-fidelity neutronics and thermal-hydraulics coupling calculation. An in-house subchannel code SUBSC was developed as the thermal-hydraulics solver. The steady-state bundle benchmark of PSBT benchmark was calculated to validate SUBSC; the results showed that the channel-averaged quality provided by SUBSC agreed well with the measured data at various conditions. Then a coupling code written in python language was employed to couple SUBSC and the Monte Carlo code OpenMC. The coupling code SUBSC/OpenMC was applied for a typical PWR 3x3 pin cluster coupling calculation. The numerical results demonstrated that the subchannel code SUBSC developed in this paper is applicable for high-fidelity coupling calculation.

Critical flow has significant impact on the reactor safety. Critical flow models are considered as an important module in all system thermal–hydraulic (STH) codes, with several optional models. But each model has its own scope of application. Consequently, the STH simulation results largely dependent on the model choice, i.e. on the user effect. A full-range critical flow model may be used to deal with this issue. The aim of this work was to develop a full-range 6-equation critical flow model with higher accuracy and plug it into ATHLET. The model was validated in Henry tests. The results show that the new model could predict mostly within the error band ±20%, better than other models of ATHLET. To verify the ability of ATHLET with the new model, it was applied to several Marviken full scale critical flow tests in transient, showing better (or at least comparable) results than before.

Application of the Virtual Environment for Reactor Applications (VERA) to BWR analysis is assessed in this paper by comparing results to those calculated using other widely-used modeling tools, namely the U.S. Nuclear Regulatory Commission’s PARCS/PATHS and the Serpent Monte Carlo particle transport code. Additionally, VERA is used to calculate 3-D temperature and fast neutron flux distributions in silicon carbide (SiC) fiber-reinforced, SiC matrix composite (SiC/SiC) BWR channel boxes, which are being studied as an Accident Tolerant Fuel core structural material concept. The code-to-code comparisons were favorable, and the SiC/SiC channel box evaluation demonstrates the many advanced modeling features VERA provides while also highlighting the non-uniformity in fast neutron flux distributions that can play a role in potential SiC/SiC channel box deformation. Traditional BWR analysis tools do not have the calculation fidelity necessary for coupled assessment of flux and temperature gradients in a SiC/SiC channel box. VERA is a state-of-the-art modeling environment that was developed to increase the safety and economic competitiveness of nuclear power through improved modeling accuracy. While VERA has already been deployed in the nuclear industry for PWR applications, the current study is a vital initial step in the extensive development, validation, and verification that VERA must go through to be useful for BWR applications.

Picard Iteration is a widely used coupling method for multiphysics simulations. This method allows one to directly leverage existing and well-developed single-physics programs without re-writing large portions of the codes. In Picard Iteration, single-physics codes just iteratively pass solutions to each other as inputs until each code has reached a converged solution. However, multiphysics computation linked by Picard Iteration is susceptible to over-solving, which can make the overall computation much less efficient. Over-solving means that each single-physics code provides an accurate solution in each Picard Iteration, which is not necessary in practice. Solving the single-physics codes in an inexact manner, i.e. with relaxed termination criteria, can help avoid this problem. This work develops a modified Picard Iteration coupling method with adaptive, inexact termination criteria for the underlying single-physics codes. Also, nested within the inexact Picard Iteration, inexact Newton methods were applied in the single-physics codes. The effect on the overall computation efficiency due to the inexact (relaxed) termination criteria at both levels is investigated by applying them to solve reactor transient problems. A reactor dynamics problem with temperature feedback in one-dimensional slab geometry is used to scope the behavior of nested inexact solvers. Then these methods are applied to a larger two-dimensional Boiling Water Reactor (BWR) problem. Computational time savings reach 55% for the two-dimensional problem. Additionally, applying an inexact termination criterion (inexact Newton method) to each single-physics code results in a further time savings of up to 18%.

One of the main subjects related with the use of nuclear energy is Nuclear Safety. Nowadays, safety analyses are commonly carried out based on a Best-Estimate (BE) approach, trying to simulate the physical phenomena taking place in the core, the coolant loops and the balance of plant as accurately as possible. In order to achieve the most realistic description of the neutron flux distribution and its coupling to the thermal-hydraulic phenomena within the core, advanced multidimensional reactor dynamics codes have been developed and validated in the last decades. These state-of-the-art codes are able to predict, for instance, non-symmetrical core power perturbations and they can calculate safety margins more accurately than the former developments (based in point kinetics), by using 3D core models with a spatial resolution at fuel assembly level for a wide range of operational transients and postulated accidents. Such a level of approximation is acceptable to predict most safety-relevant variables, but there are also some important variables for safety, which must be evaluated based on local pin-level conditions, e.g. maximal cladding and fuel centreline temperatures.
This dissertation has followed two goals that extend currently used nodal reactor simulations at the fuel assembly level to heterogeneous reactor simulations at fuel rod level for detailed design and safety evaluations of nuclear reactors.
The first one considers the extension of the pin power reconstruction method used in the reactor dynamics code DYN3D in connection with nodal diffusion solutions. The flexibility of the new development allows local refinement in the spatial mesh for specific regions of interest (where a local perturbation occurs) or even having a whole core with pin-by-pin resolution. A detailed description of the integration of this extended version of DYN3D in the European Nuclear Reactor Simulation Platform (NURESIM) is also presented. This integration is a step forward in the direction of two-level coupling with a subchannel analysis code, which is one of the major objectives of NURESIM platform.
The second one focuses on the development of a novel two-way pin-based coupling of the simplified transport (SP3) version of DYN3D with the subchannel code SUBCHANFLOW. The new coupled code system (DYNSUB) allows for a more realistic description of the core
behaviour under steady state and transients conditions. The details of the internal coupling approach of both codes together with the implementation as well as selected results of the verification and validation work are presented and discussed. The comparison of the results predicted by DYNSUB with the ones of coarser coupled solutions have shown important deviations in the local safety parameters demonstrating the novel capabilities of the developed coupled system DYNSUB. The implications of such deviations for the assessment of the safety features of nuclear reactors are discussed.
Finally, further work related to physical model developments and validation for the improvement of DYNSUB is proposed.

The aim of this study is to analyze the effect of radial void fraction distribution, considered at three degrees of fidelity, on lattice k∞ and 2-group homogenized cross sections. The novelty of this work lies in its use of experimentally-determined radial void fraction distributions which allows for fine-scale coolant density data with no predictive uncertainty and which could be prohibitively expensive to simulate over the range of operational parameters used in the experiments. The experimentally-determined radial void fraction distributions are also characterized using a statistical tool called a semi-variogram in order to determine the scale of continuity. Void fraction distributions are averaged at the lattice and subchannel level for comparison with the fine-scale model. Models averaged at the subchannel and lattice level show a difference in k∞ about 68% of the time. Also, by comparing 2-group homogenized cross-sections, the differences between the subchannel and homogeneous cases are measurable.

Modern reactor simulation tools provide advanced prediction capabilities by coupling multiphysics models to simulate reactor behaviors, involving thermal, neutronic, and mechanical interactions. To assure high-fidelity predictions by these tools, experimental data are needed to validate coupled-physics models deployed by these tools. In order to provide data to benchmark the feedback between thermal-hydraulic and neutronic simulations, coupled-physics critical experiments are designed and performed at a Reactor Critical Facility (RCF). The facility houses a low power and open-pool type light water reactor operated at the atmospheric pressure. The reactor allows flexible reconfigurations for many unique critical experiments. Recently, a water loop system has been designed and installed in the facility with the heated water circulating through the center of the reactor core, which broadens the range of validation experiments available for neutronics/thermal-hydraulics couplings. Direct effects of the loop water thermal dynamic change on reactor power and derived reactivity are demonstrated through a series of different experiments, including reactivity change over different loop water temperatures and reactor power evolution under influence of flow transient conditions in the water loop. Changes as low as 1% in the reactor power/neutron flux caused by small water temperature perturbations are observable experimentally.

In this paper, development of coupled codes using two-group neutron diffusion kinetics code and computational fluid dynamics (CFD) solver Fluent has been introduced. Way of coupling, time step control algorithm and spatial mesh overlays have been summarized in detail which are basic components and challenges of the coupling methodologies. The implement and verification of coupled code have been modeled on integral pressurized water reactor (IPWR) IP200 with hexagonal fuel assembly in the core and once-through steam generators. The steam line break core transient was analyzed in coupled code simulation of a core boundary conditions derived from system code simulation results. The results presented transient three-dimensional distribution of the key operation parameters such as reactor power and coolant temperature, also demonstrated the inherent safety features of IP200. The current work will bring about the ability to explore multi-scale and multi-dimensional safety transient evaluations and give more precise neutronics/thermal-hydraulics mapping.

Group Method of Data Handling (GMDH) is considered one of the earliest deep learning methods. Deep learning gained additional interest in today's applications due to its capability to handle complex and high dimensional problems. In this study, multi-layer GMDH networks are used to perform uncertainty quantification (UQ) and sensitivity analysis (SA) of nuclear reactor simulations. GMDH is utilized as a surrogate/metamodel to replace high fidelity computer models with cheap-to-evaluate surrogate models, which facilitate UQ and SA tasks (e.g. variance decomposition, uncertainty propagation, etc.). GMDH performance is validated through two UQ applications in reactor simulations: (1) low dimensional input space (two-phase flow in a reactor channel), and (2) high dimensional space (8-group homogenized cross-sections). In both applications, GMDH networks show very good performance with small mean absolute and squared errors as well as high accuracy in capturing the target variance. GMDH is utilized afterward to perform UQ tasks such as variance decomposition through Sobol indices, and GMDH-based uncertainty propagation with large number of samples. GMDH performance is also compared to other surrogates including Gaussian processes and polynomial chaos expansions. The comparison shows that GMDH has competitive performance with the other methods for the low dimensional problem, and reliable performance for the high dimensional problem.

In nuclear industry, using coupling of different best estimate 3-D neutron kinetic (N-K) and thermal hydraulic (T-H) codes to analyze neutronic-thermohydraulic features of reactor core is one of the most concerned research areas, which could help improve simulation fidelity and optimize nuclear design. In this paper, to further understand low power operation features of Integral PWR-200 (IP200), the coupled code combining RELAP5 and 3-D two-group neutron diffusion code had been developed. This paper reported the detailed processing of synchronizing different time steps explicitly and spatial mapping between T-H and N-K codes. To verify and validate the coupled code, the benchmark test results showed good agreement with the existing Qinshan nuclear power plant (NPP) operation data. IP200′s entire system and reactor core were modeled using the coupled code. The simulation tasks gave descriptions of different scenarios of operation strategies, including rated power, natural circulation (NC) and once-through steam generators’ (OTSGs) group operation under low power conditions. For forced circulation (FC) operation, reactor power, coolant flow and temperature features were mainly influenced by fuel assembly enrichment, control rods configuration and pumps’ thrust. Under 25%FP low power operation, NC showed different coupled effects with that of FC, whose above core features were mainly influenced by loss of pumps’ driven force. Besides, 25%FP OTSGs group operation transient conquered secondary-side flow instability, but also characterized by a strongly asymmetric behavior of the primary system which was caused by non-uniform coolant temperature distribution at the core inlet. The coupled code improved simulation precision of different low power operation strategies under the premise that it could fully generalize characteristics and performance of the whole system. Furthermore, the obtained knowledge of coupled code provided a better understanding of integral pressurized water reactor (IPWR) operation features with strong neutronic-thermohydraulic coupling effects, which would be beneficial to improve coupling other codes in future work.

The sub-channel code COBRA-TF has been introduced for the evaluation of the thermal margins on the local pin-by-pin level in PWR. The coupling of COBRA-TF with TRAC-PF1/NEM is performed by providing the axial and radial boundary conditions and the relative pin power profiles obtained with the pin power reconstruction. Efficient algorithm for coupling of the sub-channel code COBRA-TF with TRAC-PF1/NEM in PVM environment was developed addressing the issues of time-synchronization, data exchange, spatial overlays, and coupled convergence. The local feedback modeling on the pin level was implemented. The update of the local form functions and the recalculation of the pin powers after obtaining the local feedback parameters were introduced. The coupled TRAC-PF1/NEM/COBRA-TF code system was tested on the REA and MSLB benchmark problems. In both problems the local results are closer to the correspondent critical limits. The maximum value of fuel enthalpy reached after the power spike during REA is around 48 cal/g compared to 43 cal/g obtained with the assembly average model. The minimum departure from nucleate boiling ratio does not drop below 3.5 during the MSLB transient (1.3 is the critical value). The possibility of local on-line refine safety evaluation is demonstrated and the obtained results demonstrate the importance of undertaken efforts.

Incorporating full three-dimensional models of the reactor core into system transient codes allows for a "best-estimate" calculation of interactions between the core behavior and plant dynamics. Considerable efforts have been made in various countries and organizations on the development of coupled thermal-hydraulic and neutronics codes. Appropriate benchmarks have been developed in international co-operation led by NEA/OECD that permits testing the neutronics/thermal-hydraulics coupling, and verifying the capability of the coupled codes to analyze complex transients with coupled core-plant interactions. Three such benchmarks are presented in this paper – the OECD/NRC PWR MSLB benchmark, the OECD/NRC BWR TT benchmark, and the OECD/DOE/CEA V1000CT benchmark. In order to meet the objectives of the validation of best-estimate coupled codes a systematic approach has been introduced to evaluate the analyzed transients employing a multi-level methodology. Since these benchmarks are based on both code to code and code to data comparisons further guidance for presenting and evaluating results has been developed. During the course of the benchmark activities a professional community has been established, which allowed carrying out in-depth discussions of different aspects considered in the validation process of the coupled codes. This positive output has certainly advanced the state-of the art in the area of coupling research.

The advanced thermal-hydraulic subchannel code COBRA-TF has been recently improved and applied for stand-alone and coupled LWR core calculations at the Pennsylvania State University in cooperation with AREVA NP GmbH, Germany and the Technical University of Madrid. To enable COBRA-TF for academic and industrial applications including safety margins evaluations and LWR core design analyses, the code programming, numerics, and basic models were revised and substantially improved. The code has undergone through an extensive validation, verification, and qualification program.

Incorporating full three-dimensional models of the reactor core into system transient codes allows for a "best-estimate" calculation of interactions between the core behavior and plant dynamics. Considerable efforts have been made in various countries and organizations on the development of coupled thermal-hydraulic and neutronics codes. Appropriate benchmarks have been developed in international cooperations led by the Nuclear Energy Agency (NEA) of the Organization for Economic Cooperation and Development (OECD) that permit testing of the neutronics-thermal-hydraulics coupling and verification of the capability of the coupled codes to analyze complex transients with coupled core-plant interactions. Three such benchmarks are presented in this paper - the OECD/U.S. Nuclear Regulatory Commission (NRC) pressurized water reactor main steam line break benchmark, the OECD/NRC boiling water reactor turbine trip benchmark, and the OECD/U.S. Department of Energy/Commissariat à l'Energie Atomique V1000 coolant transient benchmark. To meet the objectives of the validation of best-estimate coupled codes, a systematic approach has been introduced to evaluate the analyzed transients employing a multilevel methodology. Since these benchmarks are based on both code-to-code and code-to-data comparisons, further guidance for presenting and evaluating results has been developed. During the course of the benchmark activities, a professional community has been established, which allowed our carrying out in-depth discussions of different aspects considered in the validation process of the coupled codes. This positive output has certainly advanced the state of the art in the area of coupling research.

Summaries of RELAP5/MOD3 code assessments, a listing of the assessment matrix, and a chronology of the various versions of the code are given. Results from these code assessments have been used to formulate a compilation of some of the strengths and weaknesses of the code. These results are documented in the report. Volume 7 was designed to be updated periodically and to include the results of the latest code assessments as they become available. Consequently, users of Volume 7 should ensure that the latest revision is available.

Incorporating full three-dimensional (3-D) models of the reactor core into system transient codes allows for a 'best-estimate' calculation of interactions between the core behavior and plant dynamics. Recent progress in computer technology has made the development of coupled thermal-hydraulic (T-H) and neutron kinetics code systems feasible. Considerable efforts have been made in various countries and organizations in this direction. Appropriate benchmarks need to be developed that will permit testing of two particular aspects. One is to verify the capability of the coupled codes to analyze complex transients with coupled core-plant interactions. The second is to test fully the neutronics/T-H coupling. One such benchmark is the Pressurized Water Reactor Main Steam Line Break (MSLB) Benchmark problem. It was sponsored by the Organization for Economic Cooperation and Development, U.S. Nuclear Regulatory Commission, and The Pennsylvania State University. The benchmark problem uses a 3-D neutronics core model that is based on real plant design and operational data for the Three Mile Island Unit 1 nuclear power plant. The purpose of this benchmark is threefold: to verify the capability of system codes for analyzing complex transients with coupled core-plant interactions; to test fully the 3-D neutronics/T-H coupling; and to evaluate discrepancies among the predictions of coupled codes in best-estimate transient simulations. The purposes of the benchmark are met through the application of three exercises: a point kinetics plant simulation (exercise 1), a coupled 3-D neutronics/core T-H evaluation of core response (exercise 2), and a best-estimate coupled core-plant transient model (exercise 3).In this paper we present the three exercises of the MSLB benchmark, and we summarize the findings of the participants with regard to the current numerical and computational issues of coupled calculations. In addition, this paper reviews in some detail the sensitivity studies on exercises 2 and 3 performed by the benchmark team using the coupled code TRAC-PF1/NEM. The purpose of these supporting studies was to aid participants in developing their models.

A multilevel methodology has been developed to extend the TRAC-BF1/NEM coupled code capability to obtain the transient fuel rod response. The COBRA-TF thermal-hydraulics subchannel analysis code is coupled to TRAC-BF1/NEM in the parallel virtual machine environment. The power information obtained from the nodal expansion method three-dimensional neutronic calculation is used by the hot subchannel analysis module. The TRAC-BF1 thermal-hydraulic system analysis code provides the COBRA-TF thermal-hydraulic boundary conditions. The subchannel analysis module uses this information to recalculate the fluid, thermal, and hydraulics conditions in the most limiting node (axial region of assembly/channel) within the core at each time step. A dynamic algorithm has been developed to identify the most limiting channel and fuel assembly (radially) and axial region (node) based on the current state of the core. Results, obtained with the new parallel multilevel coupled methodology, are presented and discussed for the Mexican Laguna Verde 1 nuclear power plant control rod drop accident.

An Organisation for Economic Co-operation and Development (OECD)/U.S. Nuclear Regulatory Commission (NRC)-sponsored coupled-code benchmark has been initiated for a boiling water reactor (BWR) turbine trip (TT) transient. Turbine trip transients in a BWR are pressurization events in which the coupling between core space-dependent neutronic phenomena and system dynamics plays an important role. In addition, the available real plant experimental data make this benchmark problem very valuable. Over the course of defining and coordinating the BWR TT benchmark, a systematic approach has been established to validate best-estimate coupled codes. This approach employs a multilevel methodology that not only allows for a consistent and comprehensive validation process but also contributes to the study of different numerical and computational aspects of coupled best-estimate simulations. This paper provides an overview of the OECD/NRC BWR TT benchmark activities with emphasis on the discussion of the numerical and computational aspects of the benchmark.

A temporal adaptive algorithm was developed to perform the synchronization and optimization of the performance of TRAC-BF1/NEM/COBRA-TF three-dimensional neutron/thermal-hydraulics sub-channel analysis coupled code system. The multi-level coupling scheme for time synchronization of the TRAC-BF1/NEM and COBRA-TF under PVM is developed considering the different time-step selection algorithms of TRAC-BF1, NEM and COBRA-TF codes. The developed methodology allows one to synchronize the codes in time without doing significant code modifications to the time-step selection logic of the involved codes. The advantage of this approach is that COBRA-TF can capture the nature of a given transient, without losing any time-dependent data. Results for steady state and transient calculations that show how the implemented temporal adaptive algorithm works are presented. In addition selected results are presented to illustrate dynamic behavior and the type of thermal-hydraulic boundary conditions provided by the system code.

The purpose of this paper is to introduce a more accurate and sophisticated methodology for use in three-dimensional coupled neutronic/thermal hydraulic analysis. The approach described in this paper is an original method of modeling cross-section variations for off-nominal core conditions, which is becoming an important issue with the increased use of coupled three-dimensional neutronic/thermal hydraulic simulations. This proposed method improves the accuracy of the cross-section modeling for transient applications and it is called the adaptive high-order table lookup method (AHTLM). During nuclear power plant (NPP) transient and accident simulations AHTLM interpolates into multi-dimensional cross-sections tables, which form a box envelope bounding the expected range of change of both nominal and off-nominal NPP conditions. This paper further addresses the methodologies for the development of the cross-section libraries and issues that affect the proper formulation of accurate data. The automated generation procedure outlined in this paper gives the user the tools and the ability of generating accurate cross-sections that cover a large range of thermal hydraulic parameters. Further improvements and expansions for future applications are also discussed.

The Transient Reactor Analysis Code (TRAC) was developed to provide advanced best-estimate predictions of postulated accidents in light-water reactors. The TRACPFl/MOD2 program provides this capability for pressurized water reactors and for many thermal-hydraulic test facilities. The code features either a one- or a three-dimensional treatment of the pressure vessel and its associated internals, a two-fluid nonequilibrium hydrodynamics model with a noncondensable gas field and solute tracking, flow-regime-dependent constitutive equation treatment, optional reflood tracking capability for bottom-flood and falling-film quench fronts, and consistent treatment of entire accident sequences including the generation of consistent initial conditions. The stability-enhancing two-step numerical algorithm is used in both the one- and three-dimensional hydrodynamics and permits violation of the material Courant condition. This technique permits large time steps and, hence, reduced running time for slow transients. In addition to the components contained in previous TRAC versions, TRAC-PFl/MOD2 includes a heat-structure component that allows the user to accurately model complicated geometries. An improved reflood model based on mechanistic and defensible models has been added. The new code also contains improved constituative models and additions and refinements for several components. This guide describes the components and control systems used in TRAC and gives detailed information the user needs to prepare an input deck and carry out simulations using TRAC-PFl/MOD2.

The subchannel code COBRA-TF has been introduced for an evaluation of thermal margins on the local pin-by-pin level in a pressurized water reactor. The coupling of COBRA-TF with TRAC-PF1/NEM is performed by providing from TRAC to COBRA-TF axial and radial thermal-hydraulic boundary conditions and relative pin-power profiles, obtained with the pin power reconstruction model of the nodal expansion method (NEM). An efficient algorithm for coupling of the subchannel code COBRA-TF with TRAC-PF1/NEM in the parallel virtual machine environment was developed addressing the issues of time synchronization, data exchange, spatial overlays, and coupled convergence. Local feedback modeling on the pin level was implemented into COBRA-TF, which enabled updating the local form functions and the recalculation of the pin powers in TRAC-PF1/NEM after obtaining the local feedback parameters. The coupled TRAC-PF1/NEM/COBRA-TF code system was tested on the rod ejection accident and main steam line break benchmark problems. In both problems, the local results are closer than before the introduced multilevel coupling to the corresponding critical limits. This fact indicates that the assembly average results tend to underestimate the accident consequences in terms of local safety margins. The capability of local safety evaluation, performed simultaneously (online) with coupled global three-dimensional neutron kinetics/thermal-hydraulic calculations, is introduced and tested. The obtained results demonstrate the importance of the current work.

The TRAC-BWR code development program at the Idaho National Engineering Laboratory has developed versions of the Transient Reactor Analysis Code (TRAC) for the US Nuclear Regulatory Commission and the public. The TRAC-BF1/MODl version of the computer code provides a best-estimate analysis capability for analyzing the full range of postulated accidents in boiling water reactor (BWR) systems and related facilities. This version provides a consistent and unified analysis capability for analyzing all areas of a large- or small-break loss-of-coolant accident (LOCA), beginning with the blowdown phase and continuing through heatup, reflood with quenching, and, finally, the refill phase of the accident. Also provided is a basic capability for the analysis of operational transients up to and including anticipated transients without scram (ATWS). The TRAC-BF1/MODI version produces results consistent with previous versions. Assessment calculations using the two TRAC-BF1 versions show overall improvements in agreement with data and computation times as compared to earlier versions of the TRAC-BWR series of computer codes.

The following issues related to the numerical and computational aspects of coupled calculations were studied using the OECD/NRC MSLB Benchmark: dimensionality and geometry approximations (including nodalization) of neutronics, heat structure, thermo-hydraulic models, spatial and temporal mesh overlays (coupling schemes), cross-section interpolation procedures and feedback models, decay heat modeling, reflector modeling, and coupled convergence strategies. The findings are summarized, and the results obtained by the Penn State University benchmark team using the TRAC-PF1/NEM coupled code are discussed in some detail.

The TRAC-BWR code development program at the Idaho National Engineering Laboratory has developed versions of the Transient Reactor Analysis Code (TRAC) for the US Nuclear Regulatory Commission and the public. The TRAC-BF1/MODI version of the computer code provides a best-estimate analysis capability for analyzing the full range of postulated accidents in boiling water reactor (BWR) systems and related facilities. This version provides a consistent and unified analysis capability for analyzing all areas of a large- or small-break loss-of-coolant accident (LOCA), beginning with the blowdown phase and continuing through heatup, reflood with quenching, and, finally, the refill phase of the accident. Also provided is a basic capability for the analysis of operational transients up to and including anticipated transients without scram (ATWS). The TRAC-BF1/MOD1 version produces results consistent with previous versions. Assessment calculations using the two TRAC-BFI versions show overall improvements in agreement with data and computation times as compared to earlier versions of the TRAC-BWR series of computer codes.

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