Numerical simulations of gas–liquid–particle three-phase flows using a hybrid method

For the analysis of debris behavior in core disruptive accidents of liquid metal fast reactors, a hybrid computational tool was developed using the discrete element method (DEM) for calculation of solid particle dynamics and a multi-fluid model of a reactor safety analysis code, SIMMER-III, to reasonably simulate transient behavior of three-phase flows of gas–liquid–particle mixtures. A coupling numerical algorithm was developed to combine the DEM and fluid-dynamic calculations, which are based on an explicit and a semi-implicit method, respectively. The developed method was validated based on experiments of water–particle dam break and fluidized bed in systems of gas–liquid–particle flows. Reasonable agreements between the simulation results and experimental data demonstrate the validity of the present method for complicated three-phase flows with large amounts of solid particles.     

Simulation of molten metal freezing behavior on to a structure

In the severe accident analysis of liquid metal reactors (LMRs), understanding the freezing behavior of molten metal onto the core structure during the core disruptive accidents (CDAs) is of importance for the design of next-generation reactor. CDA can occur only under hypothetical conditions where a serious power-to-cooling mismatch is postulated. Material distribution and relocation of molten metal are the key study areas during CDA. In order to model the freezing behavior of molten metal of the postulated disrupted core in a CDA of an LMR and provide data for the verification of the safety analysis code, SIMMER-III, a series of fundamental experiments was performed to simulate the freezing behavior of molten metal during penetrating onto a metal structure. The numerical simulation was performed by SIMMER-III with a mixed freezing model, which represents both bulk freezing and crust formation. The comparison between SIMMER-III simulation and its corresponding experiment indicates that SIMMER-III can reproduce the freezing behavior observed on different structure materials and under various cooling conditions. SIMMER-III also shows encouraging agreement with experimental results of melt penetration on structures and particle formation.     

Development of the evaluation methodology for the material relocation behavior in the core disruptive accident of sodium-cooled fast reactors

The in-vessel retention (IVR) of core disruptive accident (CDA) is of prime importance in enhancing safety characteristics of sodium-cooled fast reactors (SFRs). In the CDA of SFRs, molten core material relocates to the lower plenum of reactor vessel and may impose significant thermal load on the structures, resulting in the melt-through of the reactor vessel. In order to enable the assessment of this relocation process and prove that IVR of core material is the most probable consequence of the CDA in SFRs, a research program to develop the evaluation methodology for the material relocation behavior in the CDA of SFRs has been conducted. This program consists of three developmental studies, namely the development of the analysis method of molten material discharge from the core region, the development of evaluation methodology of molten material penetration into sodium pool, and the development of the simulation tool of debris bed behavior. The analysis method of molten material discharge was developed based on the computer code SIMMER-III since this code is designed to simulate the multi-phase, multi-component fluid dynamics with phase changes involved in the discharge process. Several experiments simulating the molten material discharge through duct using simulant materials were utilized as the basis of validation study of the physical models in this code. It was shown that SIMMER-III with improved physical models could simulate the molten material discharge behavior, including the momentum exchange with duct wall and thermal interaction with coolant. In order to develop an evaluation methodology of molten material penetration into sodium pool, a series of experiments simulating jet penetration behavior into sodium pool in SFR thermal condition were performed. These experiments revealed that the molten jet was fragmented in significantly shorter penetration length than the prediction by existing correlation for light water reactor conditions, due to the direct contact and thermal interaction of molten materials with coolant. The fragmented core materials form a sediment debris bed in the lower plenum. It is necessary to remove decay heat safely from this debris bed to achieve IVR. A simulation code to analyze the behavior of debris bed with decay heat was developed based on SIMMER-III code by implementing physical models, which simulate the interaction among solid particles in the bed. The code was validated by several experiments on the fluidization of particle bed by two-phase flow. These evaluation methodologies will serve as a basis for advanced safety assessment technology of SFRs in the future.     

Development of multicomponent vaporization/condensation model for a reactor safety analysis code SIMMER-III: Theoretical modeling and basic verification

It is believed that the numerical simulation of thermal-hydraulic phenomena of multiphase, multicomponent flows in a reactor core is essential to investigate core disruptive accidents (CDAs) of liquid-metal fast reactors. A new multicomponent vaporization/condensation (V/C) model was developed to provide a generalized model for a fast reactor safety analysis code SIMMER-III, which analyzes relatively short-time-scale phenomena relevant to accident sequences of CDAs. The model characterizes the V/C process associated with phase transition through heat-transfer and mass-diffusion limited models to follow the time evolution of the reactor core under CDA conditions. The heat-transfer limited model describes the nonequilibrium phase-transition processes occurring at interfaces, while the mass-diffusion limited model is employed to represent effects of noncondensable gases and multicomponent mixture on V/C processes. Verification of the model and method employed in the multicomponent V/C model of SIMMER-III was performed successfully by analyzing a series of multicomponent phase-transition experiments.     

Analysis of gas–liquid metal two-phase flows using a reactor safety analysis code SIMMER-III

SIMMER-III, a safety analysis code for liquid-metal fast reactors (LMFRs), includes a momentum exchange model based on conventional correlations for ordinary gas–liquid flows, such as an air–water system. From the viewpoint of safety evaluation of core disruptive accidents (CDAs) in LMFRs, we need to confirm that the code can predict the two-phase flow behaviors with high liquid-to-gas density ratios formed during a CDA. In the present study, the momentum exchange model of SIMMER-III was assessed and improved using experimental data of two-phase flows containing liquid metal, on which fundamental information, such as bubble shapes, void fractions and velocity fields, has been lacking.

It was found that the original SIMMER-III can suitably represent high liquid-to-gas density ratio flows including ellipsoidal bubbles as seen in lower gas fluxes. In addition, the employment of Kataoka–Ishii’s correlation has improved the accuracy of SIMMER-III for gas–liquid metal flows with cap-shape bubbles as identified in higher gas fluxes. Moreover, a new procedure, in which an appropriate drag coefficient can be automatically selected according to bubble shape, was developed.

Through this work, the reliability and the precision of SIMMER-III have been much raised with regard to bubbly flows for various liquid-to-gas density ratios.     

Development of multicomponent vaporization/condensation model for a reactor safety analysis code SIMMER-III: Extended verification using multi-bubble condensation experiment

Complex phenomena such as phase transitions and heat transfers in multiphase, multicomponent flows were modeled in the fluid-dynamics portion of SIMMER-III, which was developed to appropriately assess core disruptive accidents (CDAs) in liquid–metal fast reactors (LMFRs). A new multicomponent vaporization/condensation (V/C) model was developed and introduced to SIMMER-III by the authors. In the present study, a new series of multi-bubble condensation experiments was performed to demonstrate that SIMMER-III with the present V/C model is practically applicable to multicomponent, multiphase flow systems with phase transition. In the experiments, bubble diameters and void fractions were quantified from visualization images using original image-processing techniques. Comparing SIMMER-III predictions with experimental data, it was confirmed that SIMMER-III with the proposed V/C model could suitably represent the effects of noncondensable components on the condensation process in multi-bubble systems. This work has improved the reliability of SIMMER-III with regard to multicomponent phase-transition phenomena.     

Development of a three-dimensional CDA analysis code: SIMMER-IV and its first application to reactor case

For the transition phase analysis of core disruptive accidents, the development of a three-dimensional reactor safety analysis code, SIMMER-IV, has been carried out based on the technology of the two-dimensional SIMMER-III code. The world first application of SIMMER-IV to a small-sized sodium-cooled fast reactor has also been attempted to clarify event progression in the early stage of the transition phase. This SIMMER-IV calculation is compared to the two-dimensional case calculated by SIMMER-III, neglecting the presence of control rod guide tubes. The present analysis with the three-dimensional representation suggests that the conventional scenario leading to rather early high-mobility fuel pool formation is unrealistic and the degraded core tends to keep low mobility in the early stage of transition phase.     

3D Simulation of Solid-Melt Mixture Flow with Melt Solidification Using a Finite Volume Particle Method

Relocation and freezing of molten core materials mixed with solid phases are among the important thermal-hydraulic phenomena in core disruptive accidents of a liquid-metal-cooled reactor (LMR). To simulate such behavior of molten metal mixed with solid particles flowing onto cold structures, a computational framework was investigated using two moving particle methods, namely, the finite volume particle (FVP) method and the distinct element method (DEM). In FVP, the fluid movement and phase changes are modeled through neighboring fluid particle interactions. For mixed-flow calculations, FVP was coupled with DEM to represent interactions between solid particles and between solid particles and the wall. A 3D computer code developed for solid-liquid mixture flows was validated by a series of pure-and mixed-melt freezing experiments using a low-melting-point alloy. A comparison between the results of experiments and simulations demonstrates that the present computational framework based on FVP and DEM is applicable to numerical simulations of solid-liquid mixture flows with freezing process under solid particle influences.     

Experimental verification of the fast reactor safety analysis code SIMMER-III for transient bubble behavior with condensation

Experimental verification of a reactor safety analysis code, SIMMER-III, was undertaken for transient behaviors of large-scale bubbles with condensation. The present study aimed to verify the code for numerical simulations of relatively short-time-scale multi-phase, multi-component hydraulic problems. Among these, vaporization and condensation, or simultaneous heat and mass transfer, play important roles. In this study, a series of transient bubble behavior experiments dedicated to condensation phenomena with noncondensable gases was carried out. In the experiments, a pressurized mixture of noncondensable gas and steam was discharged as a large-scale single bubble into a cylindrical pool filled with stagnant subcooled water. The concentration of noncondensable gas was taken as an experimental parameter as was the species of noncondensable gas. The characteristics of transient behavior of large-scale bubbles with condensation observed in the experiments were estimated through experimental analyses using SIMMER-III. In the experiments with steam condensation, dispersion of the gas mixture discharged into the liquid pool was accompanied by vapor condensation at the bubble surface. SIMMER-III simulations suggested that the noncondensable gas had a less inhibiting effect on the condensation of large-scale bubbles. This is a different characteristic to that of the quasi-steady condensation of small-scale bubbles observed in our previous experiments.     

TRACE simulation of sodium boiling in pin bundle experiments under loss-of-flow conditions

In the framework of PSI's FAST code system, the thermal–hydraulic code TRACE is being extended for representation of sodium two-phase flow. As the currently available version (v.5) is limited to the simulation of only single-phase sodium flow, its applicability range is not enough to study the behavior of a Generation IV sodium-cooled fast reactor (SFR) during transients in which boiling is anticipated. The work reported here concerns the extension of the non-homogeneous, non-equilibrium two-fluid models, which are available in TRACE for steam-water, to sodium two-phase flow simulation. The conventional correlations for ordinary gas–liquid flows are used as basis, with optional correlations specific to liquid metal where necessary. A number of new models for representation of the constitutive equations specific to sodium, with a particular emphasis on the interfacial transfer mechanisms, have been implemented and compared with the original closure models.A first assessment of the extended TRACE version has been carried out, by using the code to model experiments that simulate a loss-of-flow (LOF) accident in a SFR. One- and two-dimensional representations of the test section have been considered. Comparison of the 1D model predictions, with both experiment and SIMMER-III code predictions, confirm the ability of the extended TRACE code to predict the principal sodium boiling phenomena. Two-dimensional representation of the test section, however, has been found necessary for providing more detailed comparisons with the experimental data and thereby studying, in greater detail, the influence of the physical models on the calculated results.The paper thus presents a first-of-its-kind application of TRACE to two-phase sodium flow. It shows the capability of the extended code to predict sodium boiling onset, flow regimes, pressure evolution, dryout, etc. Although the numerical results are in good agreement with the experimental data, the physical models should be further improved. Other integral experiments are planned to be simulated, in order to further develop and validate the two-phase sodium flow modeling.     

COSINE多相场子通道分析程序的开发与评估

COSINE多相场子通道分析程序基于两流体三相子通道守恒方程,在气液两相的基础上,单独考虑了液滴相的行为,并通过考虑通道间的交混,提高了对压水堆压力容器内的热工水力学现象分析能力及大破口事故的计算能力。本研究介绍了程序的基本模型及求解方法,选取代表性算例及实验工况进行建模计算,验证多相场子通道程序的计算能力。计算结果表明：程序可以对多通道热工水力现象进行模拟计算,计算结果与理论分析相符,程序可以精确模拟堆芯交混及再淹没工况,计算结果与实验数据具有良好的一致性,COSINE多相场子通道程序具备对压力容器内热工水力工况的计算能力。     

Comparison of two models for a pebble bed modular reactor core coupled to a Brayton cycle

The pebble bed modular reactor (PBMR) plant is a promising concept for inherently safe nuclear power generation. This paper presents two dynamic models for the core of a high temperature reactor (HTR) power plant with a helium gas turbine. Both the PBMR and its power conversion unit (PCU) based on a three-shaft, closed cycle, recuperative, inter-cooled Brayton cycle have been modeled with the network simulation code Flownex.One model utilizes a core simulation already incorporated in the Flownex software package, and the other a core simulation based on multi-dimensional neutronics and thermal-hydraulics. The reactor core modeled in Flownex is a simplified model, based on a zero-dimensional point-kinetics approach, whereas the other model represents a state-of-the-art approach for the solution of the neutron diffusion equations coupled to a thermal-hydraulic part describing realistic fuel temperatures during fast transients. Both reactor models were integrated into a complete cycle, which includes a PCU modeled in Flownex.Flownex is a thermal-hydraulic network analysis code that can calculate both steady-state and transient flows. An interesting feature of the code is its ability to allow the integration of an external program into Flownex by means of a so called memory map file.The total plant models are compared with each other by calculating representative transient cases demonstrating that the coupling with external models works sufficiently. To demonstrate the features of the external program a hypothetical fast increase of reactivity was simulated.     

Molten salt related extensions of the SIMMER-III code and its application for a burner reactor

Molten salt reactors (MSRs) can be used as effective burners of plutonium (Pu) and minor actinides (MAs) from light water reactor (LWR) spent fuel. In this paper a study was made to examine the thermal hydraulic behaviour of the conceptual design of the molten salt advanced reactor transmuter (MOSART) [Ignatiev, V., Feynberg, O., Myasnikov, A., Zakirov, R., 2003a. Neutronic properties and possible fuel cycle of a molten salt transmuter. Proceedings of the 2003 ANS/ENS International Winter Meeting (GLOBAL 2003), Hyatt Regency, New Orleans, LA, USA 16–20 November 2003]. The molten salt fuel is a ternary NaF–LiF–BeF₂ system fuelled with ca. 1 mol% typical compositions of transuranium-trifluorides (PuF₃, etc.) from light water reactor spent fuel. The MOSART reactor core does not contain graphite structure elements to guide the flow, so the neutron spectrum is rather hard in order to improve the burning performance. Without those structure elements in the core, the molten salt in core flows freely and the flow pattern could be potentially complicated and may affect significantly the fuel temperature distribution in the core. Therefore, some optimizations of the salt flow pattern may be needed. Here, the main attention has been paid to the fluid dynamic simulations of the MOSART core with the code SIMMER-III [Kondo, Sa., Morita, K., Tobita, Y., Shirakawa, K., 1992. SIMMER-III: an advanced computer program for LMFBR severe accident analysis. Proceedings of the ANP’ 92, Tokyo, Japan; Kondo, Sa., Tobita, Y., Morita, K., Brear, D.J., Kamiyama, K., Yamano, H., Fujita, S., Maschek, W., Fischer, E.A., Kiefhaber, E., Buckel, G., Hesselschwerdt, E., Flad, M., Costa, P., Pigny, S., 1999. Current status and validation of the SIMMER-III LMFR safety analysis code. Proceedings of the ICONE-7, Tokyo, Japan], which was originally developed for the safety assessment of sodium-cooled fast reactors and recently extended by the authors for the thermo-hydraulic and neutronic models so as to describe the molten salt reactors. For the adaptation to molten salt reactor, a complete equation of state (EOS) for this liquid fuel had to be developed and implemented into the SIMMER-III code. Through those simulations it was concluded that the thermal hydraulic behaviour appeared to be very important in molten salt reactors concerning design, operation and safety. A flow distribution plate design was found effective to optimize the flow pattern in the core region. Further investigations are under way to obtain optimal flow fields without exceeding design limits.     

Addressing the heavy liquid metal – Water interaction issue in LBE system

The interaction between heavy liquid metal (HLM) and water is a safety concern for the preliminary designs of lead fast reactor (i.e. LFR) and of subcritical transmutation system prototypes (i.e. XT-ADS). Current pool-type configurations have steam generators (SG) inside the reactor vessel. This implies that the primary to secondary leak (e.g. steam generator tube rupture) shall be considered as a postulated initiating event. The issue is addressed for CIRCE facility in ICE (Integral Circulation Experiment) configuration. CIRCE facility is a large pool system aimed at studying key operating principles of Lead Bismuth Eutectic (and Lead) systems. The configuration ICE was carried out to perform integral experiments, simulating the coupling between a high-performance heat source (electrically heated fuel bundle) and the heat exchanger, which was representative of the preliminary design of the XT-ADS heat exchanger. A Failure Mode and Effect Analysis (FMEA) is applied in order to get a complete picture of all the failure modes pertaining to this system, to determine their effects and to classify them according to their severity. The outcome of the analysis has identified as major hazard, relative to the CIRCE facility in the ICE configuration, the risk related to the LBE/water reaction, although with a very low probability, with the potential for a suddenly and dangerous pressurization (beyond the failure threshold) within the main vessel. A SIMMER-III code model of the system has been setup to provide deterministic results of the scenario. The results are supported by means of a LBE/water interaction experiment executed in LIFUS5 facility. LIFUS5 is a separate effect test facility dedicated to the investigation of LBE/water interaction. SIMMER-III code pre-test and post-test analyses are performed to define the boundary conditions of the experiment and to demonstrate the reliability of the code in simulating the phenomena of interest. The activity contributes to solving the safety issue raised for the operation of CIRCE facility and it provides a sample approach for addressing the safety studies needed in the development of the lead fast reactor and of the subcritical transmutation system.     

Evaluation of recriticality behavior in the material-relocation phase for Japan sodium-cooled fast reactor

As the most promising concept of sodium-cooled fast reactors, the Japan Atomic Energy Agency has selected the advanced loop-type fast reactor, so-called Japan sodium-cooled fast reactor (JSFR). Through the evaluation of event progressions during hypothetical core-disruptive accident (CDA) under the design extension condition, a CDA scenario for JSFR has been evaluated. It has already been demonstrated that in-vessel retention (IVR) against CDA could be achieved by taking adequate design measures under best estimate conditions.

The whole sequence of CDA scenario for JSFR was categorized into four phases according to the progress of core-disruption status. In the third phase, so-called material-relocation phase, the accident events would progress in the subcritical state. However, if the uncertainties about the molten state of core remnant and their discharge behavior outward from core are conservatively superposed, the disrupted core may lead up to recriticality.

In the present study, the factors leading to recriticality in the material-relocation phase were investigated using the phenomenological diagrams, and the recriticality behaviors were evaluated through parametric analyses using SIMMER-III/IV codes. The results of parametric analyses suggested that a significant mechanical energy leading to the boundary failure of reactor vessel would not be released even assuming recriticality due to the uncertainties about molten state and discharge behavior. Through the present evaluation of the hypothetical recriticality event, the CDA scenario for JSFR could obtain further robustness from the viewpoint of achieving IVR.     

Study on flow characteristics in gas-molten metal mixture pool

As part of basic research on the flow characteristics of a two-phase mixture pool under severe accident of fast breeder reactor (FBR), visualization and measurement of nitrogen gas-molten lead/bismuth two-phase flow in a rectangular pool were performed by using the neutron radiography technique. Measurements of drag coefficient of a single bubble and bubble shape regime showed that the relationship between the shape, size and the rising velocity of a single isolated nitrogen bubble in the molten lead/bismuth was not much different from that for an ordinary one. Appropriate correlation for drift velocity and drag coefficient between phases were recommended based on the drift flux correlation of measured pool void fraction. One- and two-dimensional analyses were performed by using a next generation computational code for safety analysis of severe accident of FBRs, SIMMER-III with various drag coefficient models. It was revealed that Kataoka–Ishii’s equation was suitable basically for estimation of drift velocity, namely, drag force between phases.     

Development of a thermal–hydraulic analysis code for the Pebble Bed Water-cooled Reactor

The Pebble Bed Water-cooled Reactor (PBWR) is a water-moderated water-cooled pebble bed reactor in which millions of tristructural-isotropic (TRISO) coated micro-fuel elements (MFE) pile in each assembly. Light water is used as coolant that flows from bottom to top in the assembly while the moderator water flows in the reverse direction out of the assembly.Steady-state thermal–hydraullic analysis code for the PBWR will provide a set of thermal hydraulic parameters of the primary loop so that heat transported out of the core can match with the heat generated by the core for a safe operation of the reactor. The key parameters of the core including the void fraction, pressure drop, heat transfer coefficients, the temperature distribution and the Departure from Nucleate Boiling Ratio (DNBR) is calculated for the core in normal operation. The code can calculate for liquid region, water-steam two phase region and superheated steam region. The results show that the maximum fuel temperature is much lower than the design limitation and the flow distribution can meet the cooling requirement in the reactor core. As a new type of nuclear reactor, the main design features with a sufficient safety margin were also put forward in this paper.     

Simulation of melt jet breakup and debris bed formation in water pools with IKEJET/IKEMIX

The objective of the development of the code system KESS is simulating the processes of core melting, relocation of core material to the lower head of the reactor pressure vessel (RPV) and its further heatup, modelling of fission product release and coolability of the core material. In the scope of the code development, IKEJET and IKEMIX were designed as key models for the breakup of a molten jet falling into a water pool, cooling of fragments and the formation of particulate debris beds. Calculations were performed with these codes, simulating FARO corium quenching experiments at saturated (L-28) and subcooled (L-31) conditions, as well as PREMIX experiments, e.g. PM-16. With the assumption of a reduced interfacial friction between water and steam as compared to usually applied laws, the melt breakup, energy release from the melt and pressurisation of the vessel observed in the experiments are reproduced with a reasonable accuracy. The model is further applied to reactor conditions, calculating the relocation of a mass of corium of 30 t into the lower plenum, its fragmentation and the formation of a particle bed.     

Simulation of MCCI with the TOLBIAC-ICB code based on the phase segregation model

In the event of a severe accident in a pressurized water reactor, corium, a mixture of molten materials issued from the fuel, cladding and structural elements, appears in the reactor core. In some circumstances, corium is likely to melt through the reactor pressure vessel and spread over the concrete basemat of the reactor pit. Molten core concrete interaction (MCCI) then occurs. The main question that has to be addressed in this scenario is whether and when the corium will make its way through the basemat. For some years, CEA is developing a numerical code named TOLBIAC-ICB in order to simulate molten core concrete interaction in reactor case. The general approach used in this code is based on the phase segregation model developed by CEA. The solid phase is supposed to be located at the corium pool boundaries as a solid crust composed of refractory oxides, whereas the corium pool contains no solid. The interfacial temperature between the crust and the pool is the liquidus temperature calculated with the composition of the pool. The interaction between thermalhydraulics (mass and energy balances) and physico-chemistry (liquidus temperature, crust composition, chemical reaction) is modelled through a coupling between TOLBIAC-ICB and the GEMINI code for the determination of the physico-chemistry variables. The main purpose of this paper is to present the modelling used in TOLBIAC-ICB and some validation calculations using the data of experiments available in the literature.     

Experimental investigation of solid–liquid mixtures freezing behavior in flow channels

The penetration and freezing of hot-core material mixtures through flow channels during core disruptive accidents (CDAs) within a sodium-cooled fast reactor is one of the major concerns confronting safety designers of the next-generation reactors. The main objective of this study is to investigate those fundamental characteristics of penetration and solidification involved in channeling molten metal and solid particle mixtures over cold structures. In this study, a low-melting-point alloy (viz., Bi–Sn–In alloy) and mixtures with solid particles (of copper and bronze) were used as a simulant melt, while L-shape metal (of stainless steel and brass) and stainless steel fuel pin bundle were used as cooling structures. Two series of basic experiments were performed to study the effect solid particles have on penetration and cooling behavior under various thermal conditions of melt by varying solid particle volume fraction, structure temperature and structural geometry. Melt flows and distributions were recorded using a digital video camera and subsequently analyzed. The melt penetration length into the flow channel and the proportion of melt adhesion on structural surfaces were measured. Results indicate that penetration length becomes shorter for molten-metal/solid particle mixtures (mixed melts) compared with pure molten metal (pure melt) as well as decreases with increasing solid particles volume fraction of the melt. The present study will contribute to a better understanding of the basic thermal-hydraulic phenomena of melt freezing in the presence of solid particles and to provide an experimental database for validation and improvement of the models of fast reactor safety analysis codes.