- Email: [email protected]
Numerical investigation on LBE-water interaction for heavy liquid metal cooled fast reactors
Nuclear Engineering and Design xxx (xxxx) xxxx
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Numerical investigation on LBE-water interaction for heavy liquid metal cooled fast reactors ⁎
Xi Huanga, , Peng Chenb, Yuan Yina, Bo Panga, Yongchun Lia, Xing Gonga, Yangbin Denga a b
Advanced Nuclear Energy Research Team, College of Physics and Optoelectronic Engineering, Shenzhen University, 518060, PR China China Nuclear Power Technology Research Institute, Shenzhen 518031, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Coolant-coolant interaction SGTR Lead-cooled fast reactors
Pool type Reactor Pressure Vessels (RPVs) containing steam generators with high secondary coolant pressure are adopted for a number of heavy liquid metal reactor conceptual designs. The primary side heavy liquid metal, e.g., liquid Lead-Bismuth Eutectic (LBE) with low pressure and secondary water with high pressure can come into contact in the event of Steam Generator Tube Rupture (SGTR) scenarios. Due to the pressure wave propagation and resultant sloshing of liquid LBE, the vigorous interaction between water and melt LBE can threaten the structural integrity of the reactor internals. Moreover, Reactor Pressure Vessel (RPV) pressurization, reactivity feedback as a result of steam entrance into the core as well as primary system pollution are also key concerns for SGTR accidents. The article aims to evaluate the capability of the MC3D code for LBE–water interaction in the event of SGTR scenarios. MC3D is a multidimensional numerical tool developed by IRSN for multi-phase flow studies and assessments in nuclear safety. Its field of application is mainly on Fuel-Coolant Interaction (FCI), especially the stages of premix and explosion in case of severe accidents. In order to evaluate the capability of MC3D for the Coolant-Coolant Interaction (CCI) of Liquid metal cooled Fast Reactors (LFRs), simulation of a small-scale experiment investigating water jet plunging into a pool of molten lead-bismuth alloy is carried out. Afterwards, experiments on LIFUS5/Mod2 facility at ENEA studying LBE-water interaction in the event of SGTR, for which a series of experiments have been conducted including the injection of sub-cooled water into LBE from the bottom of the test vessel, is simulated with MC3D as well. The simulation results for both facilities are then compared with those of the tests. The results predicted with MC3D for LIFUS5/Mod2 is also compared against the simulation results with SIMMER. The comparison implies that MC3D is generally capable for the phenomena of CCI in the event of SGTR for LFRs. Nevertheless, the potential employment of MC3D for intensive investigation of the LBE-water interaction will still need further experimental studies and improvement of physical models.
1. Introduction The Lead-cooled Fast Reactors (LFRs) are proposed as Generation IV reactors. According to typical LFR designs, the reactor core is cooled by molten lead or lead-based alloys operated at relatively low pressure. Due to the high boiling point of the liquid metal coolant, which is up to 1743 °C (Smith and Cinotti, 2016), LFR’s core outlet coolant temperature is typically ranging between 500 °C and 600 °C. For some designs with advanced materials, the core outlet temperature can be over 800 °C, which makes it possible for hydrogen production. In order to increase the reactor performance and to simplify the reactor layout, LFRs are usually designed as the pool type, i.e. reactor core, primary pumps, steam generators (or the heat exchangers) and other main components are submerged in the liquid metal pool within the primary ⁎
vessel (Fazio et al., 2006; Cinotti et al., 2007). This implies that the interaction between the liquid metal in the pool and the secondary side coolant (water) may occur in the event of tube rupture of steam generator or heat exchanger. Water in steam generator or heat exchanger tubes is normally sub-cooled at high pressure. When it encounters the liquid metal after tube rupture, pressure wave will be created and propagated, which can challenge the integrity of the internals in the primary system (Pesetti et al., 2015). Moreover, sloshing, steam entrainment into the core inserting positive reactivity, and lead-water interface phenomena are important safety concerns of SGTR accidents of LFRs (Roelofs et al., 2019). Over the past few years, experimental researches and numerical simulations regarding Fuel-Coolant Interaction/Coolant-Coolant Interaction (CCI/FCI) scenarios of LFRs have been conducted by
Corresponding author. E-mail address: [email protected] (X. Huang).
https://doi.org/10.1016/j.nucengdes.2020.110567 Received 16 August 2019; Received in revised form 6 November 2019; Accepted 8 February 2020 0029-5493/ © 2020 Elsevier B.V. All rights reserved.
Please cite this article as: Xi Huang, et al., Nuclear Engineering and Design, https://doi.org/10.1016/j.nucengdes.2020.110567
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Nomenclature
THINS
Abbreviations
Greek symbols
ADS ANL CAS CCI CEA CONST DCH ENEA
αB, D Γ ρ υ Φ
FCI ICE IRSN JAEA KIT LBE LFR MC3D OECD NEA NTC RPV SGTR
Accelerator Driven Systems Argonne National Laboratory Chinese Academy of Sciences Coolant-Coolant Interaction Alternative Energies and Atomic Energy Commission CONSTant fragmentation rate model Direct Containment Heating Italian National Agency for New Technologies, Energy and Sustainable Economic Development Fuel-Coolant Interaction Implicit Continuous-fluid Eulerian Radioprotection and Nuclear Safety Institute Japan Atomic Energy Agency Karlsruhe Institute of Technology Lead-Bismuth Eutectic Liquid metal cooled Fast Reactor Multi Component 3D Organization for Economic Cooperation and Development Nuclear Energy Agency Neutronics and Thermal-hydraulics Coupled Simulation Program Reactor Pressure Vessel Steam Generator Tube Rupture
Thermal-Hydraulics of Innovative Nuclear Systems
Flow configuration threshold based on void fraction Mass transfers Density Velocity Heat flux
Roman letters
C D m l f Frd g H h j R t∗ t v
Cavity Diameter Melt (Liquid metal) Liquid Film Densimetric Froude number Acceleration due to gravity Height of depth Enthalpy Water jet Density ratio= ρmelt / ρwater Dimensionless time= tυj / Dj Time after jet collision on melt surface Vapor
simulation of the LFR is SAS4A developed by Argonne National Laboratory (ANL) (Gu et al., 2015). The CAS has developed neutronics and thermal hydraulics coupled code NTC, which can also be used in the SGTR simulation for LFRs (Wang et al., 2008). The MC3D (Multi Component 3D) code is developed by Radioprotection and Nuclear Safety Institute (IRSN) and Alternative Energies and Atomic Energy Commission (CEA) in France, and it is a multidimensional Eulerian code investigating multi-phase flow phenomena for the nuclear safety application. The physical models in the code are sufficient for various thermal hydraulic problems, from geologic media flows to the waves of detonation (Huang et al., 2010; Wang et al., 2010; Meignen and Janin, 2010; Raverdy et al., 2017). The code has also been used to simulate the premix between bismuth-tin-lead alloy and water after the injection of liquid metal into the water pool (Wang et al., 2010). In the study MC3D is applied for the prediction of free-falling liquid alloy jet plunging into water pool, according to the specific experimental condition. The preliminary simulation results agree well with the test data and this indicates the code potentially can be employed to study SGTR accident scenarios in LFRs. The article presents the application of the MC3D code for the investigation of LBE–water interaction, which can occur during SGTR of LBE cooled fast reactor. Simulation of JAEA small-scale experiments and LIFUS5/Mod2
various research institutions (Nakamura et al., 1999; Sibamoto et al., 2007; Wang, 2017; Del Nevo et al., 2016; Flad et al., 2010; Fukano, 2015; Gu et al., 2015; Wang et al., 2008; Guo et al., 2016; Cheng et al., 2015; Meignen et al., 2014). These studies have contributed important information in understanding the overall effect and the basics of transient of the accidents. Regarding experimental investigations, numerous small-scale facilities were established with visualization technology to study the transient and local phenomena during the CCI process between LBE and water. The Japanese Atomic Energy Agency (JAEA) (Nakamura et al., 1999; Sibamoto et al., 2007) has studied the plunge of water downwardly into the LBE pool and the injection of liquid LBE into water pool respectively. Chinese Academy of Sciences (CAS) also carried out small scale experiments studying hot LBE droplets interfacial fragmentation in water (Wang, 2017). Various large-scale experiments have also been performed to study LBE–water interaction during SGTR scenarios of LBE cooled fast reactor over the past few years. In THINS (Thermal Hydraulic of Innovative Nuclear System) Project (Pesetti et al., 2015), LIFUS5 facility was designed and established by ENEA to investigate LBE-water interaction under different operating conditions. Based on the operating experience on LIFUS5, LIFUS5/Mod2 has been established for the development and validation of physical models for computer codes used for SGTR simulation (Del Nevo et al., 2016). Karlsruhe Institute of Technology (KIT) also developed an experimental program of SGTR of LFRs with argon or water injection into the lead circulating environment. The facility was also used for the further validation of numerical simulation tools (Fukano, 2015). CAS has recently developed the KYLIN-II-S facility mainly to study the LBE-water interaction under different operating conditions and to support LBE-cooled Accelerator Driven Systems (ADS) reactor designs (Wang, 2017). Concerning simulation tools, the SIMMER-III code has been developed for the safety evaluation in advanced liquid metal cooled fast reactors and it is capable of simulating the coolant-coolant interaction considering the water evaporation. Accordingly, the code is the most commonly used one in the study of SGTR accident in LFRs (Pesetti et al., 2015). Another widely used simulation tool for the transient
Fig. 1. Two fields describing the liquid metal (The figure is reproduced by authors corresponding to the one in literature (Meignen et al., 2014)). 2
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Table 1 Experimental conditions for simulation.
Fig. 2. Flow patterns used in MC3D (The figure is reproduced by authors corresponding to the one in literature (Meignen et al., 2014)).
Fluid parameters
Run 1
Run 3
Run 5
LBE initial temperature (K) LBE density (kg/m3) Water jet diameter (mm) Water initial temperature (K) Water density (kg/m3) Water injection speed (m/s) Densimertric Froude number
503 10,400 6 298 1000 7.5 9.6
778 10,050 6 298 1000 6.9 9.0
778 10,050 6 298 1000 4.7 6.1
tests is performed and the results are compared with tests and SIMMERIII simulation results. The capability of MC3D code to capture the key phenomena of the LBE–water interaction is discussed and highlighted. 2. Description of simulation tool The simulation of SGTR accidents in LFRs needs to consider the mass and heat transfers in liquid metal pool interacting with water/ steam. MC3D is developed for the study of thermal hydraulics of multiphase flow, particularly for the nuclear safety. The code is mainly used for the studies of molten Fuel-Coolant Interaction in nuclear reactors. Two separated models considering the premix process and explosion process were developed for FCI. Premix model addresses the fragmentation and dispersion of continuous liquid metal during FCI (Meignen and Janin, 2010). Based on the results of premix, Explosion model simulates a critical state that the melt-water mixture is further destabilized to produce an energetic steam explosion which may occur in the cases that melt is released to the water pool. The Premix model can also be used for the investigations of Direct Containment Heating (DCH) accidents. In the event of DCH, the reactor vessel might fail, and the melt will be ejected out of the pit, some of the corium may enter the compartments of containment. This may threaten the integrity of the containment by pressurization of its atmosphere. The fragmentation and dispersal of the corium melt out of the reactor pit has been investigated with Premix model (Meignen and Janin, 2010). Moreover, the cooling of corium debris beds and interaction between LBE and water can also be studied with MC3D (Wang et al., 2010; Raverdy et al., 2017). The code employs a local non-equilibrium model of different phases (coolant liquid, steam, liquid metal pool, non-condensable gas etc.). MC3D is developed on the basis of a Eulerian method. Each component in the code is described by mass, momentum and energy equations. These equations of balance are solved by semi-implicit ICE (Implicit Continuous-fluid Eulerian) method (Harlow and Amsden, 1968; Meignen, 2008). This method is characterized by 1. Use of the momentum balances to express velocities according to the local and neighboring pressures; 2. Integration of this expression in the energy and mass balance; 3. Combination of the equations to obtain a pressure system, and 4. Resolution of this system by a linearization with an iterative Newton-Raphson type method. The staggered grid is implemented in the code. For the purpose of modeling SGTR related phenomena in LFRs, the premix model is used.
Fig. 3. Schematic diagram of test facility (Reproduced by authors corresponding to the one in literature (Sibamoto et al., 2007)).
2.1. Flow patterns In the premix model of the MC3D code, liquid metal could be presented as either a continuous field, e.g. pools or jets, or a discrete field of drops, as described in Fig. 1. Transfers between these two fields are through the continuous liquid metal (JET) field breakup/fragmentation and drop field coalescence. The volume of fluid construction is used for the continuous liquid metal field in the code to describe the flow convection. The surface area of the droplets is calculated with the equation of interfacial area transport. Mean Sauter diameter which is also known as the surface-volume mean diameter is used in MC3D to describe the
Fig. 4. MC3D geometry model for small scale test facility.
3
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 5. Comparison between test results and MC3D simulations of LBE and water fraction distribution for JAEA small scale test facility (Experimental images are captured from literature (Nakamura et al., 1999)).
discrete droplet size. Other fluid fields considered in the code include the water; the vapor and non-condensable gases. These fluid fields can be described by liquid and gas phases. Fig. 2 shows the flow patterns used in the model, i.e., bubbles in continuous liquid and liquid drops in continuous gas. When the gas volume fraction is less than the limit of αB , it is considered that the liquid is continuous, and the gas is dispersed in the continuous liquid as bubbles. If the gas volume fraction is more than the limit of αD , the liquid is regarded in the form of drops dispersed in continuous gas. In case the gas volume fraction is between αB and αD , the flow patterns described above are coexisting and the mesh volume
is shared as shown in Fig. 2. 2.2. Major constitutive relations The limited knowledge about physical laws to close the numerical model is regarded as the major problem in FCI codes. For instance, the fragmentation of continuous melting metal is a complex phenomenon during FCI which involves different mechanisms and scales. Therefore, it has been a topic of intensive study for many years. In the present work the CONST (CONSTant fragmentation rate model) model in MC3D 4
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 6. Cavity configuration of the test and MC3D simulation during LBE-water interaction: (i) high melt temperature and (ii) low melt temperature. (Experimental images are captured from literature (Nakamura et al., 1999)).
Molten Fuel-Coolant interaction (FCI) research, the scattered liquid metal droplet diameter was studied based on the experimental data. It is revealed that the droplet diameter is dependent of complex factors, but it is not completely understood yet. In MC3D, the CONST model doesn’t give a law to predict the droplet size and it is defined by the users. Sensitivity analysis has been conducted on the effect of droplet diameter for CCI process, no obvious impact of the droplet size is detected in the transients of current work, this can be caused by the instantaneity of the transients simulated. However, an elaborate model for CCI issue is needed, this deserves intensive investigation.
is used to describe the transfer from continuous molten liquid metal to droplets. The model for primary fragmentation makes use of a correlation established from a theoretical work making the hypothesis of a vapor film surrounding the continuous melt. It is used for practical applications where the velocity of the continuous melt is not too large and the fragmentation rate of continuous melt is regarded constant (Meignen, 2008). Regarding the size of the melt droplets, in SERENA (Steam Explosion Resolution for Nuclear Application)-2 project (Hong et al., 2013), launched by OECD/NEA (Organization for Economic Cooperation and Development/Nuclear Energy Agency) for ex-vessel 5
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 8. Maximum penetration depth of experiments and MC3D results plotted against the densimetric Froude number Frd .
Fig. 9. LIFUS5/Mod2 facility with injection system (The figure is reproduced by authors corresponding to the one in literature (Pesetti et al., 2015)). Table 2 Boundary conditions of high pressure THINS tests selected for MC3D simulation (Pesetti et al., 2015).
Fig. 7. Cavity depth HC / Dj of experiments and MC3D results as a function of dimensionless time t ∗.
6
Boundary/initial conditions
T#1
T#4
LBE temperature [°C] Water pressure [bar] Water temperature [°C] Argon volume/LBE volume [%] Water injection penetration in reaction vessel [mm] Injector orifice diameter [mm]
400 40 240 30 120 4
400 40 240 30 120 4
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 10. Support structures in reaction vessel (Pesetti et al., 2014).
current version of MC3D can capture the key phenomena during the transient. This indicates the simulation tool can potentially be employed for intensive investigation of the interaction between liquid metal and water, although improvement is still foreseen in future.
2.3. Heat and mass transfer modeling MC3D employed several correlations for film boiling but all the correlations have limitations. The default correlation in the code is a composition of modified Epstein and Hauser’s forced convection film boiling correlation and Sakurai’s pool film boiling correlation (Meignen et al., 2014). For the FCI and CCI problem, it’s challenging that a part of the heat directly goes to the coolant and the rest goes into evaporate to create the void. Currently, in MC3D a simple approach is used for the heat flux going from the drop to water. If the water is saturated, all heat is used for vaporization. If it is sub-cooled and the temperature difference is over 10 °C, all heat goes into water phase if a minimum void fraction is given. Linear interpolation for the heat flux is used if it’s between the situations mentioned above. This model can avoid the modeling of heat flux between interface and water, which is quite complex. However, the arbitrary application of the model is not sufficient and experimental studies are still needed to validate or improve the model. For the film boiling, the heat going into water is used for boiling in the model and the mass transfer rate can be expressed by:
Γlv =
3. MC3D model and results for small scale experiment In the event of SGTR accidents of LFRs, water coolant can be injected into molten liquid metal pool. Water jet plunging into a pool of molten LBE alloy behavior has been studied in the small-scale experimental study conducted by JAEA with the high-frame-rate neutron radiography technique (Sibamoto et al., 2007). The layout of the test facility is reproduced according to the literature and is shown in Fig. 3, the top of the test section is open to atmosphere. The test results show that water jet penetration into heated LBE is limited by the buoyancy. The jet velocity and initial temperature of the melt have significant influences on the behavior of jet penetration. The molten LBE alloy (44.5% Pb − 55.5% Bi) is used in the experiments as the liquid metal material in the pool. In MC3D, the physical properties of the liquid metal can be defined by users, therefore all relevant LBE physical properties used for simulation are captured from literature (Fazio et al., 2015). The LBE alloy is heated by the furnace, the sub-cooled water jet is injected downwardly onto the surface of the melt via cylindrical nozzle at the centerline of the test section. In order to investigate the applicability of MC3D for the interaction between liquid metal and water, simulation was carried out in accordance with the test conditions. Fig. 4 shows the front view and top view of the nodalization for the simulation. Table 1 summarizes the test conditions of the 3 sets of experiments (Run 1 Run 3 and Run 5) which are selected for simulation. The melt initial temperature, the jet velocity are the test variables. The jet injection velocity is from 4.7 to 7.5 m/s, or 6.1 to 9.6 in densimetric Froude number, which can be described as
Φfilm·boiling h v (Tf ) − hl (Tl )
(1)
where Φfilm·boiling denotes the heat flux between particle and water. The vapor is generated at the saturation temperature. It’s assumed there is no differentiation between the vapor generated in the film and the vapor at the interface between bubbles and droplets. Then the evaporation/condensation rate for water droplets and bubbles is given in Eq. (2) if it’s boiling and is given in Eq. (3) when it’s condensing.
Γlv =
Γlv =
Φbubbles + Φfilm·boiling + Φdroplets h v, sat − hl (Tl )
(2)
Φbubbles + Φfilm·boiling + Φdroplets h v (Tv ) − hl, sat
(3)
Frd =
In the event of SGTR in LFRs, the presence of large scale LBE pool will need the modification of flow configurations, e.g. consideration of dispersed water drops or bubbles inside continuous melting as well as the heat transfer models. Nevertheless, the attempts in the present work show that the simulation results of LBE-water interaction with MC3D are generally in agreement with the test data, the application of the
υj RgDj
(4)
Fig. 5 shows the test results and the MC3D simulation results of LBE and water fraction distribution after the plunging of water jet into the melt pool. The time after the jet arrival at the melt surface is indicated in a dimensionless form: 7
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 11. Water and vapor bubble in reaction tank calculated by SIMMER-III (Pesetti et al., 2015) and MC3D code.
t∗ =
tυj Dj
to boil at the interface between water and melt. Then water flow in the cavity becomes deflected, water is accumulated in the cavity, jet becomes disintegrated and the cavity surface becomes unstable. These phenomena occur at different dimensionless time for different test conditions. For the test of Run 1, with relatively low melt temperature of 503 K, an arched cavity was formed after the entry of water jet. The cavity surface remained smooth at the beginning and the jet maintained its integral structure as it reached the bottom region of the arched cavity.
(5)
The time is made nondimensional considering the impact velocity and the initial jet diameter. This particular way of making the time and the diameter nondimensional is often used for inertial driven impact (Rioboo et al., 2002). The images on the left of Fig. 5 show the transient of jet impingement at the surface of the liquid metal pool. The following images show the cavity formation resulted by the water jet, which starts 8
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Then the neck of the cavity became narrow. The water was continuously accumulated in the cavity and the cavity area was closed later. The cavity depth was maximized, and then vigorous evaporation started with boiling over the melt-water interface. So far, MC3D can present the water cavity development in correspondence with the process described above. Afterwards, as the LBE-water interaction continued, the cavity area was enlarged, the substantial amount of water and vapor in the cavity was expelled upwards. At this stage, the MC3D results could still generally exhibit the similar trend, but the volume fraction distribution deviated from the experimental images gradually. In Run 3 and Run 5, with the jet velocity of 6.9 m/s and 4.7 m/s respectively and the higher melt liquid metal temperature of 778 K, both showed considerable instability due to the bulk boiling of water in the cavity at the early stage, which was not highlighted in Run 1. This phenomenon could be reproduced by the MC3D simulation as indicated in Fig. 5. However, the simulation results also deviated from those of experiments to a considerable degree at the late stage. It can be inferred from the experiment and simulation results that for the cases with higher melt temperature (Run 3 and Run 5), after the closure of the cavity area, the liquid metal surrounding the cavity was accelerated in both lateral and vertical directions due to boiling. The boiling resulted in a more irregular shapes of cavity surface compared to the cases with a lower melt temperature. The bottom part of the cavity tended to break and detach from the upper part. The typical cavity configuration was illustrated and demonstrated with experimental/simulation results in Fig. 6, on the basis of the cavity configuration discussed in the work of Sibamoto et al. (2007). The cases with a lower melt temperature exhibit different behavior. Since the melt temperature is lower, the boiling is less intense. The surface of the interface between melt and water is relatively smooth. The lower portion of the cavity presents a shape of an elongated tear drop. Both two modes of water cavity development described above can be captured with MC3D, as shown in Fig. 6. It’s noteworthy that at the late stage, almost for all the simulated cases, the volume fraction calculated with the code started to deviate from the tests results during the vigorous mixing between water and melt. Regarding the penetration depth, the maximum jet penetration depth under non-boiling steady state can be given assuming the pressure balance between stagnated jet and the melt pool at the interface, which can be expressed as:
Fig. 12. Experimental and calculated pressure change of the test T#1 and T#4 (Pesetti et al., 2015).
Fig. 13. MC3D prediction of pressure change at center and at reaction vessel wall during the first 0.2 s after water injection.
1 2 ρ υj = (ρm − ρj ) gHC 2 j
(6)
Or given with densimetric Froude number
υj2 HC R ⎞ Frd2 = = 0.5 ⎛ Dj 2(R − 1) gDj ⎝ R − 1⎠
(7)
Eq. (7) gives the maximum possible depth under a steady state with a stable jet reaching the interface without creating the water pool in the cavity which may lead to energy dissipation due to slip flow and gas entrapment (Nakamura et al., 1999). Assuming that in case of water to water impingement, the cavity to jet diameter ratio is constant as suggested by Oguz et al. (1996), then the dimensionless cavity depth HC / Dj will be proportional to Frd2 , as indicated in Eq. (7). On the other hand, Saito (1988) reported a linear correlation of Frd as shown in Eq. (8) to predict HC / Dj based on their test data. Similarly, Park (1998) give a correlation according to the experimental results as expressed in Eq. (9).
Fig. 14. Mechanical energy in the cover gas region calculated with SIMMER-III code and cover gas total energy change calculated by MC3D.
9
HC = 2.1Frd Dj
(8)
HC = 1.45Frd Dj
(9)
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 15. MC3D simulation of LBE volume fraction change of Test T#1/ T#4 with longer time scale.
which can jeopardize the structural integrity of the internals. Additionally, the rupture of SG tubes can also threaten the integrity of the neighboring tubes, this can worsen the consequences of the accidental scenarios. To investigate this issue, ENEA C.R. Brasimone performed a series of experiments on the LIFUS5/Mod2 facility (Del Nevo et al., 2016). The layout of the facility is presented in Fig. 9. LIFUS5/Mod2 facility is mainly comprised of two main components, i.e., the reaction vessel, where the interactions between LBE and water take place, the gas pressurized water storage tank. The water injection orifice at the end of injection line is 120 mm above the internal bottom of the reaction vessel. The diameter of the injection orifice is 4 mm. During the experiments, high pressure water is ejected from the orifice and interacts with LBE in the reaction vessel filled with argon. In order to evaluate the applicability of MC3D for SGTR events of LFRs, the geometry model is established, and simulation is conducted in
Fig. 7 presents the dimensionless cavity depth HC / Dj as a function of dimensionless time t∗ for the 3 selected tests and the corresponding MC3D simulation results. In Fig. 8, both calculated and tested results of the maximum cavity depth are plotted. The maximum depths predicted by Eq. (7) and correlations of Saito et al. and Park et al. as expressed in Eq. (8) and Eq. (9) are plotted as well for comparison. It’s demonstrated that the cavity penetration behavior and the depths simulated by MC3D are in accordance with the test results.
4. Preliminary application of MC3D for the LIFUS5/Mod2 facility In contrast to water jet plunging into liquid metal downwardly, the rupture of SG tubes is more likely to take place under the level of liquid metal in the event of SGTR in LFRs, high pressure secondary coolant water is ejected into the melt and goes upwards. This results in pressure wave propagation and pressurization of non-condensable cover gas, 10
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
This fact also indicates that the simulation tool MC3D, although exhibits deviations to a degree compared to the test and SIMMER-III results, is capable for the phenomena of SGTR accidents in LFRs. Fig. 15 demonstrates the LBE volume fraction change in Test T#1/ T#4 with longer time scale simulated with MC3D. It can be inferred from the images that, due to the instant phase change of the water in the vessel, the interaction between water and LBE is vigorous at the beginning of the transient. This is also suggested by the pressure time trends in Fig. 12. Thereafter, as a result of pressure increase in the reaction vessel, the water injection rate decreases quickly in the simulation and the volume fraction distribution is stabilized. This is in accordance with the pressure trend recorded in the tests and simulations. Nevertheless, it should not be overlooked that the melt LBE is thrust to the top region of the calculation domain during the transient as shown in the simulation results. This phenomenon can challenge the structural integrity of the components and therefore deserves further investigation in the future.
accordance with a set of experiment (T#1 and T#4) in THINS project as shown in Table 2 (Pesetti et al., 2015). The geometry data of LIFUS5/ Mod2 facility for modeling is summarized from the literature (Pesetti et al., 2014). It’s noteworthy that a support frame with four horizontal cruciform levels is welded coaxially to reaction vessel flange as indicated in Fig. 10, where the thermocouples are installed. This structure constitutes an obstacle that can break the water jet flowing upwards into the liquid metal pool. Accordingly, in the geometry model of MC3D the structure in the central area which can hinder the water jet is approximated in the nodalization. In the study of Pesetti et al. (2015), Post-test simulations were carried out with SIMMER-III model. Fig. 11 shows the simulation results of SIMMER-III steam bubble formation and growth in the reaction vessel for T#1 test. The MC3D results performed in the current work for the same case are presented as well for comparison. The LBE volume fraction between 0 and 1 is described in blue and in red respectively. As shown in Fig. 11, MC3D simulation of the volume fraction gives a similar trend as that of SIMMER-III and that the vapor bubble reaches the cover gas region at about 0.15 s after the water enters reaction vessel. Experimental data and SIMMER-III/MC3D calculated pressure change of the tests T#1 and T#4 are shown in Fig. 12. The measured data and SIMMER-III results are captured from the literature (Pesetti et al., 2015). The experimental results and simulated pressure change are differentiated by colors and line types. Tests T#1 and T#4 were performed by imposing almost the same boundary and initial conditions. However, the experimental pressure time trends measured in the reaction tank differed by almost 10 bars at about 1.5 s after the injection started, which can be discovered in the literature (Pesetti et al., 2015). This can be attributed to the different timing at which the cap rupture occurs because of the uncertainty about the cap rupture dynamics and the consequent different injection line pressurization. The computed pressure with both simulation tools increases faster than the measured value. This is mainly resulted by the lower depressurization simulated along the injection line with SIMMERIII and MC3D model. Two phase phenomena occur along the water injection line. The vaporization of water in the injection line has significant impact on the pressure drop as well as the pressurization process in reaction vessel. This also leads to the higher pressure slope in the reaction vessel calculated with both codes compared to the measured value. In the work of Pesetti et al. (2015), the injection system is modeled and the Lockhart–Martinelli two-phase pressure drop multiplier is introduced later into SIMMERIII in order to improve the simulation results, as indicated in Fig. 12, that the pressure change is getting closer to the test results after the application of the pressure drop multiplier. In contrast to SIMMERIII geometry model, injection system is not modeled with MC3D and two-phase pressure drop multiplier is also not considered. Therefore, the pressure boundary is given at the bottom of the injection pipe in MC3D calculation domain. Nevertheless, the pressure change in reaction vessel calculated with MC3D is in principle consistent with the result of SIMMERIII before the Lockhart–Martinelli multiplier has been introduced, as shown in Fig. 12. Fig. 13 gives pressure change at the center and at reaction vessel wall during the first 0.2 s after water injection predicted by MC3D. It’s important to note that the pressure at the vessel center exhibits a spike at the very beginning. The height of the spike decreases as pressure collection point moves away from the injection point. The pressure spike is created after the instant contact between water and LBE. This is also observed in the experimental results of LIFUS5/Mod2. However, experimental results presented in Fig. 12 are roughly captured from literature. As a result, the phenomenon of instant pressure change is not shown. More information can be found in the work of Pesetti et al. (2015) Fig. 14 shows a similar trend of mechanical energy in the cover gas region calculated by SIMMER-III code and cover gas total energy change calculated by MC3D. Both simulation tools can capture the wavy energy increase in the cover gas region as a result of energy propagation.
5. Concluding remarks The article discussed the significance of heavy liquid metal-water interaction which may occur in the event of SGTR of LFRs and summarized the information of experimental researches and numerical studies regarding this safety issue over the past few years. The application of MC3D code for the investigation of LBE–water interaction is presented. Simulation of JAEA small-scale experiments and LIFUS5/ Mod2 tests is performed and the results are compared with experimental and SIMMER-III simulation results. It’s concluded that the simulation results with MC3D are in good agreement with the experimental data, the application of MC3D can capture the key phenomena during the transient. For the cases of water jet plunging into LBE pool, critical phenomena including the creation of water cavity around the water-LBE interface, the generation of the bubbles due to boiling, dispersion of the water can be reproduced with MC3D code. The volume fraction evolution, cavity depths were consistent with experimental images especially at the early stage of the transients. Regarding the cases of water injection from the bottom of the LBE vessel, which is more likely to take place in the event of SGTR in LFRs, the simulation of LIFUS5/Mod2 with MC3D is carried out in the current work and the results are compared with that of SIMMERIII. The comparison also implies that MC3D is capable for the phenomena of SGTR accidents in LFRs. Nevertheless, the potential employment of MC3D for intensive investigation of the interaction between LBE and water will need the modification of the flow configurations e.g., consideration of dispersed water drops and bubbles inside continuous melt, as well as interface heat transfer models. Further experimental studies and development of pertinent physical models are still foreseen in the future. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References Sci. Technol. Nucl. Install. 2015, 1–14. https://doi.org/10.1155/2015/964327. RGN (4), 30–39. https://doi.org/10.1051/rgn/20074030. Del Nevo, A., Ciampichetti, A., Tarantino, M., Burgazzi, L., Forgione, N., 2016. Addressing the heavy liquid metal–Water interaction issue in LBE system. Prog. Nucl. Energy 89, 204–212. Fazio, C., Alamo, A., Henry, J., Almazouzi, A., Gomez-Briceno, D., Soler, L., … Stieglitz, R., 2006. European research on heavy liquid metal technology for advanced reactor systems. In Pacific Basin Nuclear Conference 2006. Australian Nuclear Association, p. 188. Fazio, C., Sobolev, V.P., Aerts, A., Gavrilov, S., Lambrinou, K., Schuurmans, P., Gosse, S., 2015. Handbook on Lead-Bismuth Eutectic Alloy and Lead Properties, Materials
11
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Int. J. Multiph. Flow 22 (S1) 130 130. Park, H.S., 1998. Study on energetic fuel-coolant interaction in the coolant injection mode of contact. In Proc. 6th Int. Conf. Nuclear Engineering (ICONE-6), San-Diego, May 10, 1998. Pesetti, A., Del Nevo, A., Forgione, N., 2015. Experimental investigation and SIMMER-III code modelling of LBE–water interaction in LIFUS5/Mod2 facility. Nucl. Eng. Des. 290, 119–126. Pesetti, A., Forgione, N., Del Nevo, A., 2014, July. Water/Pb-bi interaction experiments in LIFUS5/MOD2 facility modelled by simmer code. In 2014 22nd International Conference on Nuclear Engineering. American Society of Mechanical Engineers. Raverdy, B., Meignen, R., Piar, L., Picchi, S., Janin, T., 2017. Capabilities of MC3D to investigate the coolability of corium debris beds. Nucl. Eng. Des. 319, 48–60. Rioboo, R., Marengo, M., Tropea, C., 2002. Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 33 (1), 112–124. Roelofs, F., Gerschenfeld, A., Tarantino, M., Van Tichelen, K., Pointer, W.D., 2019. Thermal-hydraulic challenges in liquid-metal-cooled reactors. In: Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors. Woodhead Publishing, pp. 17–43. Saito, M., 1988. Experimental study on penetration behaviors of water jet into freon-11 and liquid nitrogen. In ANS-Proc. 25th Natl. Heat Transfer Conf., pp. 173–183. Sibamoto, Y., Kukita, Y., Nakamura, H., 2007. Small-scale experiment on subcooled water jet injection into molten alloy by using fluid temperature-phase coupled measurement and visualization. J. Nucl. Sci. Technol. 44 (8), 1059–1069. Smith, C.F., Cinotti, L., 2016. Lead-cooled fast reactor. In: Handbook of Generation IV Nuclear Reactors. Woodhead Publishing, pp. 119–155. Wang, G., 2017. A review of research progress in heat exchanger tube rupture accident of heavy liquid metal cooled reactors. Ann. Nucl. Energy 109, 1–8. Wang, X., Li, T.S., Huang, X., Yang, Y.H., 2010, January. Analysis of fuel coolant interaction in PWR with experiment and computer code. In 18th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, pp. 491–496. Wang, S., Flad, M., Maschek, W., Agostini, P., Pellini, D., Bandini, G., Morita, K., 2008. Evaluation of a steam generator tube rupture accident in an accelerator driven system with lead cooling. Prog. Nucl. Energy 50 (2–6), 363–369.
Compatibility, Thermal-Hydraulics and Technologies-2015 Edition (No. NEA–7268). Organisation for Economic Co-Operation and Development. Flad, M., Wang, S., Maschek, W., 2010, January. Simulation of a steam generator tube rupture accident in a lead-cooled accelerator driven system. In 18th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, pp. 241–249. Fukano, Y., 2015. SAS4A analysis on hypothetical total instantaneous flow blockage in SFRs based on in-pile experiments. Ann. Nucl. Energy 77, 376–392. Gu, Z., Wang, G., Bai, Y., Song, Y., Zhao, Z., 2015. Preliminary investigation on the primary heat exchanger lower head rupture accident of forced circulation LBE-cooled fast reactor. Ann. Nucl. Energy 81, 84–90. Guo, L., Li, R., Wang, S., Flad, M., Maschek, W., Rineiski, A., 2016. Numerical investigation of SIMMER code for fuel-coolant interaction. Int. J. Hydrogen Energy 41 (17), 7227–7232. Harlow, F.H., Amsden, A.A., 1968. Numerical calculation of almost incompressible flow. J. Comput. Phys. 3 (1), 80–93. Hong, S.W., Piluso, P., Leskovar, M., 2013. Status of the OECD-SERENA project for the resolution of ex-vessel steam explosion risks. J. Energy Power Eng. 7 (3), 423. Huang, X., Wang, X., Yang, Y.H., 2010, January. Computational analysis of pressure loading and impulse distribution in the reactor cavity during the process of ex-vessel steam explosion. In 18th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, pp. 497–504. Meignen, R., 2008. Description of the Physical Models of the PREMIXING Application. IRSN, France. Sci. Technol. Nucl. Install. 2010, 1–13. https://doi.org/10.1155/2010/289792. Meignen, R., Picchi, S., Lamome, J., Raverdy, B., Escobar, S.C., Nicaise, G., 2014. The challenge of modeling fuel–coolant interaction: part i-premixing. Nucl. Eng. Des. 280, 511–527. Nakamura, H., Sibamoto, Y., Anoda, Y., Kukita, Y., Mishima, K., Hibiki, T., 1999. Visualization of simulated molten-fuel behavior in a pressure vessel lower head using high-frame-rate neutron radiography. Nucl. Technol. 125 (2), 213–224. Oguz, H.N., Prosperetti, A., Kolaini, A.R., 1996. Air entrapment by a falling water mass.
12
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Numerical investigation on LBE-water interaction for heavy liquid metal cooled fast reactors ⁎
Xi Huanga, , Peng Chenb, Yuan Yina, Bo Panga, Yongchun Lia, Xing Gonga, Yangbin Denga a b
Advanced Nuclear Energy Research Team, College of Physics and Optoelectronic Engineering, Shenzhen University, 518060, PR China China Nuclear Power Technology Research Institute, Shenzhen 518031, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Coolant-coolant interaction SGTR Lead-cooled fast reactors
Pool type Reactor Pressure Vessels (RPVs) containing steam generators with high secondary coolant pressure are adopted for a number of heavy liquid metal reactor conceptual designs. The primary side heavy liquid metal, e.g., liquid Lead-Bismuth Eutectic (LBE) with low pressure and secondary water with high pressure can come into contact in the event of Steam Generator Tube Rupture (SGTR) scenarios. Due to the pressure wave propagation and resultant sloshing of liquid LBE, the vigorous interaction between water and melt LBE can threaten the structural integrity of the reactor internals. Moreover, Reactor Pressure Vessel (RPV) pressurization, reactivity feedback as a result of steam entrance into the core as well as primary system pollution are also key concerns for SGTR accidents. The article aims to evaluate the capability of the MC3D code for LBE–water interaction in the event of SGTR scenarios. MC3D is a multidimensional numerical tool developed by IRSN for multi-phase flow studies and assessments in nuclear safety. Its field of application is mainly on Fuel-Coolant Interaction (FCI), especially the stages of premix and explosion in case of severe accidents. In order to evaluate the capability of MC3D for the Coolant-Coolant Interaction (CCI) of Liquid metal cooled Fast Reactors (LFRs), simulation of a small-scale experiment investigating water jet plunging into a pool of molten lead-bismuth alloy is carried out. Afterwards, experiments on LIFUS5/Mod2 facility at ENEA studying LBE-water interaction in the event of SGTR, for which a series of experiments have been conducted including the injection of sub-cooled water into LBE from the bottom of the test vessel, is simulated with MC3D as well. The simulation results for both facilities are then compared with those of the tests. The results predicted with MC3D for LIFUS5/Mod2 is also compared against the simulation results with SIMMER. The comparison implies that MC3D is generally capable for the phenomena of CCI in the event of SGTR for LFRs. Nevertheless, the potential employment of MC3D for intensive investigation of the LBE-water interaction will still need further experimental studies and improvement of physical models.
1. Introduction The Lead-cooled Fast Reactors (LFRs) are proposed as Generation IV reactors. According to typical LFR designs, the reactor core is cooled by molten lead or lead-based alloys operated at relatively low pressure. Due to the high boiling point of the liquid metal coolant, which is up to 1743 °C (Smith and Cinotti, 2016), LFR’s core outlet coolant temperature is typically ranging between 500 °C and 600 °C. For some designs with advanced materials, the core outlet temperature can be over 800 °C, which makes it possible for hydrogen production. In order to increase the reactor performance and to simplify the reactor layout, LFRs are usually designed as the pool type, i.e. reactor core, primary pumps, steam generators (or the heat exchangers) and other main components are submerged in the liquid metal pool within the primary ⁎
vessel (Fazio et al., 2006; Cinotti et al., 2007). This implies that the interaction between the liquid metal in the pool and the secondary side coolant (water) may occur in the event of tube rupture of steam generator or heat exchanger. Water in steam generator or heat exchanger tubes is normally sub-cooled at high pressure. When it encounters the liquid metal after tube rupture, pressure wave will be created and propagated, which can challenge the integrity of the internals in the primary system (Pesetti et al., 2015). Moreover, sloshing, steam entrainment into the core inserting positive reactivity, and lead-water interface phenomena are important safety concerns of SGTR accidents of LFRs (Roelofs et al., 2019). Over the past few years, experimental researches and numerical simulations regarding Fuel-Coolant Interaction/Coolant-Coolant Interaction (CCI/FCI) scenarios of LFRs have been conducted by
Corresponding author. E-mail address: [email protected] (X. Huang).
https://doi.org/10.1016/j.nucengdes.2020.110567 Received 16 August 2019; Received in revised form 6 November 2019; Accepted 8 February 2020 0029-5493/ © 2020 Elsevier B.V. All rights reserved.
Please cite this article as: Xi Huang, et al., Nuclear Engineering and Design, https://doi.org/10.1016/j.nucengdes.2020.110567
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Nomenclature
THINS
Abbreviations
Greek symbols
ADS ANL CAS CCI CEA CONST DCH ENEA
αB, D Γ ρ υ Φ
FCI ICE IRSN JAEA KIT LBE LFR MC3D OECD NEA NTC RPV SGTR
Accelerator Driven Systems Argonne National Laboratory Chinese Academy of Sciences Coolant-Coolant Interaction Alternative Energies and Atomic Energy Commission CONSTant fragmentation rate model Direct Containment Heating Italian National Agency for New Technologies, Energy and Sustainable Economic Development Fuel-Coolant Interaction Implicit Continuous-fluid Eulerian Radioprotection and Nuclear Safety Institute Japan Atomic Energy Agency Karlsruhe Institute of Technology Lead-Bismuth Eutectic Liquid metal cooled Fast Reactor Multi Component 3D Organization for Economic Cooperation and Development Nuclear Energy Agency Neutronics and Thermal-hydraulics Coupled Simulation Program Reactor Pressure Vessel Steam Generator Tube Rupture
Thermal-Hydraulics of Innovative Nuclear Systems
Flow configuration threshold based on void fraction Mass transfers Density Velocity Heat flux
Roman letters
C D m l f Frd g H h j R t∗ t v
Cavity Diameter Melt (Liquid metal) Liquid Film Densimetric Froude number Acceleration due to gravity Height of depth Enthalpy Water jet Density ratio= ρmelt / ρwater Dimensionless time= tυj / Dj Time after jet collision on melt surface Vapor
simulation of the LFR is SAS4A developed by Argonne National Laboratory (ANL) (Gu et al., 2015). The CAS has developed neutronics and thermal hydraulics coupled code NTC, which can also be used in the SGTR simulation for LFRs (Wang et al., 2008). The MC3D (Multi Component 3D) code is developed by Radioprotection and Nuclear Safety Institute (IRSN) and Alternative Energies and Atomic Energy Commission (CEA) in France, and it is a multidimensional Eulerian code investigating multi-phase flow phenomena for the nuclear safety application. The physical models in the code are sufficient for various thermal hydraulic problems, from geologic media flows to the waves of detonation (Huang et al., 2010; Wang et al., 2010; Meignen and Janin, 2010; Raverdy et al., 2017). The code has also been used to simulate the premix between bismuth-tin-lead alloy and water after the injection of liquid metal into the water pool (Wang et al., 2010). In the study MC3D is applied for the prediction of free-falling liquid alloy jet plunging into water pool, according to the specific experimental condition. The preliminary simulation results agree well with the test data and this indicates the code potentially can be employed to study SGTR accident scenarios in LFRs. The article presents the application of the MC3D code for the investigation of LBE–water interaction, which can occur during SGTR of LBE cooled fast reactor. Simulation of JAEA small-scale experiments and LIFUS5/Mod2
various research institutions (Nakamura et al., 1999; Sibamoto et al., 2007; Wang, 2017; Del Nevo et al., 2016; Flad et al., 2010; Fukano, 2015; Gu et al., 2015; Wang et al., 2008; Guo et al., 2016; Cheng et al., 2015; Meignen et al., 2014). These studies have contributed important information in understanding the overall effect and the basics of transient of the accidents. Regarding experimental investigations, numerous small-scale facilities were established with visualization technology to study the transient and local phenomena during the CCI process between LBE and water. The Japanese Atomic Energy Agency (JAEA) (Nakamura et al., 1999; Sibamoto et al., 2007) has studied the plunge of water downwardly into the LBE pool and the injection of liquid LBE into water pool respectively. Chinese Academy of Sciences (CAS) also carried out small scale experiments studying hot LBE droplets interfacial fragmentation in water (Wang, 2017). Various large-scale experiments have also been performed to study LBE–water interaction during SGTR scenarios of LBE cooled fast reactor over the past few years. In THINS (Thermal Hydraulic of Innovative Nuclear System) Project (Pesetti et al., 2015), LIFUS5 facility was designed and established by ENEA to investigate LBE-water interaction under different operating conditions. Based on the operating experience on LIFUS5, LIFUS5/Mod2 has been established for the development and validation of physical models for computer codes used for SGTR simulation (Del Nevo et al., 2016). Karlsruhe Institute of Technology (KIT) also developed an experimental program of SGTR of LFRs with argon or water injection into the lead circulating environment. The facility was also used for the further validation of numerical simulation tools (Fukano, 2015). CAS has recently developed the KYLIN-II-S facility mainly to study the LBE-water interaction under different operating conditions and to support LBE-cooled Accelerator Driven Systems (ADS) reactor designs (Wang, 2017). Concerning simulation tools, the SIMMER-III code has been developed for the safety evaluation in advanced liquid metal cooled fast reactors and it is capable of simulating the coolant-coolant interaction considering the water evaporation. Accordingly, the code is the most commonly used one in the study of SGTR accident in LFRs (Pesetti et al., 2015). Another widely used simulation tool for the transient
Fig. 1. Two fields describing the liquid metal (The figure is reproduced by authors corresponding to the one in literature (Meignen et al., 2014)). 2
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Table 1 Experimental conditions for simulation.
Fig. 2. Flow patterns used in MC3D (The figure is reproduced by authors corresponding to the one in literature (Meignen et al., 2014)).
Fluid parameters
Run 1
Run 3
Run 5
LBE initial temperature (K) LBE density (kg/m3) Water jet diameter (mm) Water initial temperature (K) Water density (kg/m3) Water injection speed (m/s) Densimertric Froude number
503 10,400 6 298 1000 7.5 9.6
778 10,050 6 298 1000 6.9 9.0
778 10,050 6 298 1000 4.7 6.1
tests is performed and the results are compared with tests and SIMMERIII simulation results. The capability of MC3D code to capture the key phenomena of the LBE–water interaction is discussed and highlighted. 2. Description of simulation tool The simulation of SGTR accidents in LFRs needs to consider the mass and heat transfers in liquid metal pool interacting with water/ steam. MC3D is developed for the study of thermal hydraulics of multiphase flow, particularly for the nuclear safety. The code is mainly used for the studies of molten Fuel-Coolant Interaction in nuclear reactors. Two separated models considering the premix process and explosion process were developed for FCI. Premix model addresses the fragmentation and dispersion of continuous liquid metal during FCI (Meignen and Janin, 2010). Based on the results of premix, Explosion model simulates a critical state that the melt-water mixture is further destabilized to produce an energetic steam explosion which may occur in the cases that melt is released to the water pool. The Premix model can also be used for the investigations of Direct Containment Heating (DCH) accidents. In the event of DCH, the reactor vessel might fail, and the melt will be ejected out of the pit, some of the corium may enter the compartments of containment. This may threaten the integrity of the containment by pressurization of its atmosphere. The fragmentation and dispersal of the corium melt out of the reactor pit has been investigated with Premix model (Meignen and Janin, 2010). Moreover, the cooling of corium debris beds and interaction between LBE and water can also be studied with MC3D (Wang et al., 2010; Raverdy et al., 2017). The code employs a local non-equilibrium model of different phases (coolant liquid, steam, liquid metal pool, non-condensable gas etc.). MC3D is developed on the basis of a Eulerian method. Each component in the code is described by mass, momentum and energy equations. These equations of balance are solved by semi-implicit ICE (Implicit Continuous-fluid Eulerian) method (Harlow and Amsden, 1968; Meignen, 2008). This method is characterized by 1. Use of the momentum balances to express velocities according to the local and neighboring pressures; 2. Integration of this expression in the energy and mass balance; 3. Combination of the equations to obtain a pressure system, and 4. Resolution of this system by a linearization with an iterative Newton-Raphson type method. The staggered grid is implemented in the code. For the purpose of modeling SGTR related phenomena in LFRs, the premix model is used.
Fig. 3. Schematic diagram of test facility (Reproduced by authors corresponding to the one in literature (Sibamoto et al., 2007)).
2.1. Flow patterns In the premix model of the MC3D code, liquid metal could be presented as either a continuous field, e.g. pools or jets, or a discrete field of drops, as described in Fig. 1. Transfers between these two fields are through the continuous liquid metal (JET) field breakup/fragmentation and drop field coalescence. The volume of fluid construction is used for the continuous liquid metal field in the code to describe the flow convection. The surface area of the droplets is calculated with the equation of interfacial area transport. Mean Sauter diameter which is also known as the surface-volume mean diameter is used in MC3D to describe the
Fig. 4. MC3D geometry model for small scale test facility.
3
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 5. Comparison between test results and MC3D simulations of LBE and water fraction distribution for JAEA small scale test facility (Experimental images are captured from literature (Nakamura et al., 1999)).
discrete droplet size. Other fluid fields considered in the code include the water; the vapor and non-condensable gases. These fluid fields can be described by liquid and gas phases. Fig. 2 shows the flow patterns used in the model, i.e., bubbles in continuous liquid and liquid drops in continuous gas. When the gas volume fraction is less than the limit of αB , it is considered that the liquid is continuous, and the gas is dispersed in the continuous liquid as bubbles. If the gas volume fraction is more than the limit of αD , the liquid is regarded in the form of drops dispersed in continuous gas. In case the gas volume fraction is between αB and αD , the flow patterns described above are coexisting and the mesh volume
is shared as shown in Fig. 2. 2.2. Major constitutive relations The limited knowledge about physical laws to close the numerical model is regarded as the major problem in FCI codes. For instance, the fragmentation of continuous melting metal is a complex phenomenon during FCI which involves different mechanisms and scales. Therefore, it has been a topic of intensive study for many years. In the present work the CONST (CONSTant fragmentation rate model) model in MC3D 4
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 6. Cavity configuration of the test and MC3D simulation during LBE-water interaction: (i) high melt temperature and (ii) low melt temperature. (Experimental images are captured from literature (Nakamura et al., 1999)).
Molten Fuel-Coolant interaction (FCI) research, the scattered liquid metal droplet diameter was studied based on the experimental data. It is revealed that the droplet diameter is dependent of complex factors, but it is not completely understood yet. In MC3D, the CONST model doesn’t give a law to predict the droplet size and it is defined by the users. Sensitivity analysis has been conducted on the effect of droplet diameter for CCI process, no obvious impact of the droplet size is detected in the transients of current work, this can be caused by the instantaneity of the transients simulated. However, an elaborate model for CCI issue is needed, this deserves intensive investigation.
is used to describe the transfer from continuous molten liquid metal to droplets. The model for primary fragmentation makes use of a correlation established from a theoretical work making the hypothesis of a vapor film surrounding the continuous melt. It is used for practical applications where the velocity of the continuous melt is not too large and the fragmentation rate of continuous melt is regarded constant (Meignen, 2008). Regarding the size of the melt droplets, in SERENA (Steam Explosion Resolution for Nuclear Application)-2 project (Hong et al., 2013), launched by OECD/NEA (Organization for Economic Cooperation and Development/Nuclear Energy Agency) for ex-vessel 5
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 8. Maximum penetration depth of experiments and MC3D results plotted against the densimetric Froude number Frd .
Fig. 9. LIFUS5/Mod2 facility with injection system (The figure is reproduced by authors corresponding to the one in literature (Pesetti et al., 2015)). Table 2 Boundary conditions of high pressure THINS tests selected for MC3D simulation (Pesetti et al., 2015).
Fig. 7. Cavity depth HC / Dj of experiments and MC3D results as a function of dimensionless time t ∗.
6
Boundary/initial conditions
T#1
T#4
LBE temperature [°C] Water pressure [bar] Water temperature [°C] Argon volume/LBE volume [%] Water injection penetration in reaction vessel [mm] Injector orifice diameter [mm]
400 40 240 30 120 4
400 40 240 30 120 4
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 10. Support structures in reaction vessel (Pesetti et al., 2014).
current version of MC3D can capture the key phenomena during the transient. This indicates the simulation tool can potentially be employed for intensive investigation of the interaction between liquid metal and water, although improvement is still foreseen in future.
2.3. Heat and mass transfer modeling MC3D employed several correlations for film boiling but all the correlations have limitations. The default correlation in the code is a composition of modified Epstein and Hauser’s forced convection film boiling correlation and Sakurai’s pool film boiling correlation (Meignen et al., 2014). For the FCI and CCI problem, it’s challenging that a part of the heat directly goes to the coolant and the rest goes into evaporate to create the void. Currently, in MC3D a simple approach is used for the heat flux going from the drop to water. If the water is saturated, all heat is used for vaporization. If it is sub-cooled and the temperature difference is over 10 °C, all heat goes into water phase if a minimum void fraction is given. Linear interpolation for the heat flux is used if it’s between the situations mentioned above. This model can avoid the modeling of heat flux between interface and water, which is quite complex. However, the arbitrary application of the model is not sufficient and experimental studies are still needed to validate or improve the model. For the film boiling, the heat going into water is used for boiling in the model and the mass transfer rate can be expressed by:
Γlv =
3. MC3D model and results for small scale experiment In the event of SGTR accidents of LFRs, water coolant can be injected into molten liquid metal pool. Water jet plunging into a pool of molten LBE alloy behavior has been studied in the small-scale experimental study conducted by JAEA with the high-frame-rate neutron radiography technique (Sibamoto et al., 2007). The layout of the test facility is reproduced according to the literature and is shown in Fig. 3, the top of the test section is open to atmosphere. The test results show that water jet penetration into heated LBE is limited by the buoyancy. The jet velocity and initial temperature of the melt have significant influences on the behavior of jet penetration. The molten LBE alloy (44.5% Pb − 55.5% Bi) is used in the experiments as the liquid metal material in the pool. In MC3D, the physical properties of the liquid metal can be defined by users, therefore all relevant LBE physical properties used for simulation are captured from literature (Fazio et al., 2015). The LBE alloy is heated by the furnace, the sub-cooled water jet is injected downwardly onto the surface of the melt via cylindrical nozzle at the centerline of the test section. In order to investigate the applicability of MC3D for the interaction between liquid metal and water, simulation was carried out in accordance with the test conditions. Fig. 4 shows the front view and top view of the nodalization for the simulation. Table 1 summarizes the test conditions of the 3 sets of experiments (Run 1 Run 3 and Run 5) which are selected for simulation. The melt initial temperature, the jet velocity are the test variables. The jet injection velocity is from 4.7 to 7.5 m/s, or 6.1 to 9.6 in densimetric Froude number, which can be described as
Φfilm·boiling h v (Tf ) − hl (Tl )
(1)
where Φfilm·boiling denotes the heat flux between particle and water. The vapor is generated at the saturation temperature. It’s assumed there is no differentiation between the vapor generated in the film and the vapor at the interface between bubbles and droplets. Then the evaporation/condensation rate for water droplets and bubbles is given in Eq. (2) if it’s boiling and is given in Eq. (3) when it’s condensing.
Γlv =
Γlv =
Φbubbles + Φfilm·boiling + Φdroplets h v, sat − hl (Tl )
(2)
Φbubbles + Φfilm·boiling + Φdroplets h v (Tv ) − hl, sat
(3)
Frd =
In the event of SGTR in LFRs, the presence of large scale LBE pool will need the modification of flow configurations, e.g. consideration of dispersed water drops or bubbles inside continuous melting as well as the heat transfer models. Nevertheless, the attempts in the present work show that the simulation results of LBE-water interaction with MC3D are generally in agreement with the test data, the application of the
υj RgDj
(4)
Fig. 5 shows the test results and the MC3D simulation results of LBE and water fraction distribution after the plunging of water jet into the melt pool. The time after the jet arrival at the melt surface is indicated in a dimensionless form: 7
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 11. Water and vapor bubble in reaction tank calculated by SIMMER-III (Pesetti et al., 2015) and MC3D code.
t∗ =
tυj Dj
to boil at the interface between water and melt. Then water flow in the cavity becomes deflected, water is accumulated in the cavity, jet becomes disintegrated and the cavity surface becomes unstable. These phenomena occur at different dimensionless time for different test conditions. For the test of Run 1, with relatively low melt temperature of 503 K, an arched cavity was formed after the entry of water jet. The cavity surface remained smooth at the beginning and the jet maintained its integral structure as it reached the bottom region of the arched cavity.
(5)
The time is made nondimensional considering the impact velocity and the initial jet diameter. This particular way of making the time and the diameter nondimensional is often used for inertial driven impact (Rioboo et al., 2002). The images on the left of Fig. 5 show the transient of jet impingement at the surface of the liquid metal pool. The following images show the cavity formation resulted by the water jet, which starts 8
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Then the neck of the cavity became narrow. The water was continuously accumulated in the cavity and the cavity area was closed later. The cavity depth was maximized, and then vigorous evaporation started with boiling over the melt-water interface. So far, MC3D can present the water cavity development in correspondence with the process described above. Afterwards, as the LBE-water interaction continued, the cavity area was enlarged, the substantial amount of water and vapor in the cavity was expelled upwards. At this stage, the MC3D results could still generally exhibit the similar trend, but the volume fraction distribution deviated from the experimental images gradually. In Run 3 and Run 5, with the jet velocity of 6.9 m/s and 4.7 m/s respectively and the higher melt liquid metal temperature of 778 K, both showed considerable instability due to the bulk boiling of water in the cavity at the early stage, which was not highlighted in Run 1. This phenomenon could be reproduced by the MC3D simulation as indicated in Fig. 5. However, the simulation results also deviated from those of experiments to a considerable degree at the late stage. It can be inferred from the experiment and simulation results that for the cases with higher melt temperature (Run 3 and Run 5), after the closure of the cavity area, the liquid metal surrounding the cavity was accelerated in both lateral and vertical directions due to boiling. The boiling resulted in a more irregular shapes of cavity surface compared to the cases with a lower melt temperature. The bottom part of the cavity tended to break and detach from the upper part. The typical cavity configuration was illustrated and demonstrated with experimental/simulation results in Fig. 6, on the basis of the cavity configuration discussed in the work of Sibamoto et al. (2007). The cases with a lower melt temperature exhibit different behavior. Since the melt temperature is lower, the boiling is less intense. The surface of the interface between melt and water is relatively smooth. The lower portion of the cavity presents a shape of an elongated tear drop. Both two modes of water cavity development described above can be captured with MC3D, as shown in Fig. 6. It’s noteworthy that at the late stage, almost for all the simulated cases, the volume fraction calculated with the code started to deviate from the tests results during the vigorous mixing between water and melt. Regarding the penetration depth, the maximum jet penetration depth under non-boiling steady state can be given assuming the pressure balance between stagnated jet and the melt pool at the interface, which can be expressed as:
Fig. 12. Experimental and calculated pressure change of the test T#1 and T#4 (Pesetti et al., 2015).
Fig. 13. MC3D prediction of pressure change at center and at reaction vessel wall during the first 0.2 s after water injection.
1 2 ρ υj = (ρm − ρj ) gHC 2 j
(6)
Or given with densimetric Froude number
υj2 HC R ⎞ Frd2 = = 0.5 ⎛ Dj 2(R − 1) gDj ⎝ R − 1⎠
(7)
Eq. (7) gives the maximum possible depth under a steady state with a stable jet reaching the interface without creating the water pool in the cavity which may lead to energy dissipation due to slip flow and gas entrapment (Nakamura et al., 1999). Assuming that in case of water to water impingement, the cavity to jet diameter ratio is constant as suggested by Oguz et al. (1996), then the dimensionless cavity depth HC / Dj will be proportional to Frd2 , as indicated in Eq. (7). On the other hand, Saito (1988) reported a linear correlation of Frd as shown in Eq. (8) to predict HC / Dj based on their test data. Similarly, Park (1998) give a correlation according to the experimental results as expressed in Eq. (9).
Fig. 14. Mechanical energy in the cover gas region calculated with SIMMER-III code and cover gas total energy change calculated by MC3D.
9
HC = 2.1Frd Dj
(8)
HC = 1.45Frd Dj
(9)
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Fig. 15. MC3D simulation of LBE volume fraction change of Test T#1/ T#4 with longer time scale.
which can jeopardize the structural integrity of the internals. Additionally, the rupture of SG tubes can also threaten the integrity of the neighboring tubes, this can worsen the consequences of the accidental scenarios. To investigate this issue, ENEA C.R. Brasimone performed a series of experiments on the LIFUS5/Mod2 facility (Del Nevo et al., 2016). The layout of the facility is presented in Fig. 9. LIFUS5/Mod2 facility is mainly comprised of two main components, i.e., the reaction vessel, where the interactions between LBE and water take place, the gas pressurized water storage tank. The water injection orifice at the end of injection line is 120 mm above the internal bottom of the reaction vessel. The diameter of the injection orifice is 4 mm. During the experiments, high pressure water is ejected from the orifice and interacts with LBE in the reaction vessel filled with argon. In order to evaluate the applicability of MC3D for SGTR events of LFRs, the geometry model is established, and simulation is conducted in
Fig. 7 presents the dimensionless cavity depth HC / Dj as a function of dimensionless time t∗ for the 3 selected tests and the corresponding MC3D simulation results. In Fig. 8, both calculated and tested results of the maximum cavity depth are plotted. The maximum depths predicted by Eq. (7) and correlations of Saito et al. and Park et al. as expressed in Eq. (8) and Eq. (9) are plotted as well for comparison. It’s demonstrated that the cavity penetration behavior and the depths simulated by MC3D are in accordance with the test results.
4. Preliminary application of MC3D for the LIFUS5/Mod2 facility In contrast to water jet plunging into liquid metal downwardly, the rupture of SG tubes is more likely to take place under the level of liquid metal in the event of SGTR in LFRs, high pressure secondary coolant water is ejected into the melt and goes upwards. This results in pressure wave propagation and pressurization of non-condensable cover gas, 10
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
This fact also indicates that the simulation tool MC3D, although exhibits deviations to a degree compared to the test and SIMMER-III results, is capable for the phenomena of SGTR accidents in LFRs. Fig. 15 demonstrates the LBE volume fraction change in Test T#1/ T#4 with longer time scale simulated with MC3D. It can be inferred from the images that, due to the instant phase change of the water in the vessel, the interaction between water and LBE is vigorous at the beginning of the transient. This is also suggested by the pressure time trends in Fig. 12. Thereafter, as a result of pressure increase in the reaction vessel, the water injection rate decreases quickly in the simulation and the volume fraction distribution is stabilized. This is in accordance with the pressure trend recorded in the tests and simulations. Nevertheless, it should not be overlooked that the melt LBE is thrust to the top region of the calculation domain during the transient as shown in the simulation results. This phenomenon can challenge the structural integrity of the components and therefore deserves further investigation in the future.
accordance with a set of experiment (T#1 and T#4) in THINS project as shown in Table 2 (Pesetti et al., 2015). The geometry data of LIFUS5/ Mod2 facility for modeling is summarized from the literature (Pesetti et al., 2014). It’s noteworthy that a support frame with four horizontal cruciform levels is welded coaxially to reaction vessel flange as indicated in Fig. 10, where the thermocouples are installed. This structure constitutes an obstacle that can break the water jet flowing upwards into the liquid metal pool. Accordingly, in the geometry model of MC3D the structure in the central area which can hinder the water jet is approximated in the nodalization. In the study of Pesetti et al. (2015), Post-test simulations were carried out with SIMMER-III model. Fig. 11 shows the simulation results of SIMMER-III steam bubble formation and growth in the reaction vessel for T#1 test. The MC3D results performed in the current work for the same case are presented as well for comparison. The LBE volume fraction between 0 and 1 is described in blue and in red respectively. As shown in Fig. 11, MC3D simulation of the volume fraction gives a similar trend as that of SIMMER-III and that the vapor bubble reaches the cover gas region at about 0.15 s after the water enters reaction vessel. Experimental data and SIMMER-III/MC3D calculated pressure change of the tests T#1 and T#4 are shown in Fig. 12. The measured data and SIMMER-III results are captured from the literature (Pesetti et al., 2015). The experimental results and simulated pressure change are differentiated by colors and line types. Tests T#1 and T#4 were performed by imposing almost the same boundary and initial conditions. However, the experimental pressure time trends measured in the reaction tank differed by almost 10 bars at about 1.5 s after the injection started, which can be discovered in the literature (Pesetti et al., 2015). This can be attributed to the different timing at which the cap rupture occurs because of the uncertainty about the cap rupture dynamics and the consequent different injection line pressurization. The computed pressure with both simulation tools increases faster than the measured value. This is mainly resulted by the lower depressurization simulated along the injection line with SIMMERIII and MC3D model. Two phase phenomena occur along the water injection line. The vaporization of water in the injection line has significant impact on the pressure drop as well as the pressurization process in reaction vessel. This also leads to the higher pressure slope in the reaction vessel calculated with both codes compared to the measured value. In the work of Pesetti et al. (2015), the injection system is modeled and the Lockhart–Martinelli two-phase pressure drop multiplier is introduced later into SIMMERIII in order to improve the simulation results, as indicated in Fig. 12, that the pressure change is getting closer to the test results after the application of the pressure drop multiplier. In contrast to SIMMERIII geometry model, injection system is not modeled with MC3D and two-phase pressure drop multiplier is also not considered. Therefore, the pressure boundary is given at the bottom of the injection pipe in MC3D calculation domain. Nevertheless, the pressure change in reaction vessel calculated with MC3D is in principle consistent with the result of SIMMERIII before the Lockhart–Martinelli multiplier has been introduced, as shown in Fig. 12. Fig. 13 gives pressure change at the center and at reaction vessel wall during the first 0.2 s after water injection predicted by MC3D. It’s important to note that the pressure at the vessel center exhibits a spike at the very beginning. The height of the spike decreases as pressure collection point moves away from the injection point. The pressure spike is created after the instant contact between water and LBE. This is also observed in the experimental results of LIFUS5/Mod2. However, experimental results presented in Fig. 12 are roughly captured from literature. As a result, the phenomenon of instant pressure change is not shown. More information can be found in the work of Pesetti et al. (2015) Fig. 14 shows a similar trend of mechanical energy in the cover gas region calculated by SIMMER-III code and cover gas total energy change calculated by MC3D. Both simulation tools can capture the wavy energy increase in the cover gas region as a result of energy propagation.
5. Concluding remarks The article discussed the significance of heavy liquid metal-water interaction which may occur in the event of SGTR of LFRs and summarized the information of experimental researches and numerical studies regarding this safety issue over the past few years. The application of MC3D code for the investigation of LBE–water interaction is presented. Simulation of JAEA small-scale experiments and LIFUS5/ Mod2 tests is performed and the results are compared with experimental and SIMMER-III simulation results. It’s concluded that the simulation results with MC3D are in good agreement with the experimental data, the application of MC3D can capture the key phenomena during the transient. For the cases of water jet plunging into LBE pool, critical phenomena including the creation of water cavity around the water-LBE interface, the generation of the bubbles due to boiling, dispersion of the water can be reproduced with MC3D code. The volume fraction evolution, cavity depths were consistent with experimental images especially at the early stage of the transients. Regarding the cases of water injection from the bottom of the LBE vessel, which is more likely to take place in the event of SGTR in LFRs, the simulation of LIFUS5/Mod2 with MC3D is carried out in the current work and the results are compared with that of SIMMERIII. The comparison also implies that MC3D is capable for the phenomena of SGTR accidents in LFRs. Nevertheless, the potential employment of MC3D for intensive investigation of the interaction between LBE and water will need the modification of the flow configurations e.g., consideration of dispersed water drops and bubbles inside continuous melt, as well as interface heat transfer models. Further experimental studies and development of pertinent physical models are still foreseen in the future. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References Sci. Technol. Nucl. Install. 2015, 1–14. https://doi.org/10.1155/2015/964327. RGN (4), 30–39. https://doi.org/10.1051/rgn/20074030. Del Nevo, A., Ciampichetti, A., Tarantino, M., Burgazzi, L., Forgione, N., 2016. Addressing the heavy liquid metal–Water interaction issue in LBE system. Prog. Nucl. Energy 89, 204–212. Fazio, C., Alamo, A., Henry, J., Almazouzi, A., Gomez-Briceno, D., Soler, L., … Stieglitz, R., 2006. European research on heavy liquid metal technology for advanced reactor systems. In Pacific Basin Nuclear Conference 2006. Australian Nuclear Association, p. 188. Fazio, C., Sobolev, V.P., Aerts, A., Gavrilov, S., Lambrinou, K., Schuurmans, P., Gosse, S., 2015. Handbook on Lead-Bismuth Eutectic Alloy and Lead Properties, Materials
11
Nuclear Engineering and Design xxx (xxxx) xxxx
X. Huang, et al.
Int. J. Multiph. Flow 22 (S1) 130 130. Park, H.S., 1998. Study on energetic fuel-coolant interaction in the coolant injection mode of contact. In Proc. 6th Int. Conf. Nuclear Engineering (ICONE-6), San-Diego, May 10, 1998. Pesetti, A., Del Nevo, A., Forgione, N., 2015. Experimental investigation and SIMMER-III code modelling of LBE–water interaction in LIFUS5/Mod2 facility. Nucl. Eng. Des. 290, 119–126. Pesetti, A., Forgione, N., Del Nevo, A., 2014, July. Water/Pb-bi interaction experiments in LIFUS5/MOD2 facility modelled by simmer code. In 2014 22nd International Conference on Nuclear Engineering. American Society of Mechanical Engineers. Raverdy, B., Meignen, R., Piar, L., Picchi, S., Janin, T., 2017. Capabilities of MC3D to investigate the coolability of corium debris beds. Nucl. Eng. Des. 319, 48–60. Rioboo, R., Marengo, M., Tropea, C., 2002. Time evolution of liquid drop impact onto solid, dry surfaces. Exp. Fluids 33 (1), 112–124. Roelofs, F., Gerschenfeld, A., Tarantino, M., Van Tichelen, K., Pointer, W.D., 2019. Thermal-hydraulic challenges in liquid-metal-cooled reactors. In: Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors. Woodhead Publishing, pp. 17–43. Saito, M., 1988. Experimental study on penetration behaviors of water jet into freon-11 and liquid nitrogen. In ANS-Proc. 25th Natl. Heat Transfer Conf., pp. 173–183. Sibamoto, Y., Kukita, Y., Nakamura, H., 2007. Small-scale experiment on subcooled water jet injection into molten alloy by using fluid temperature-phase coupled measurement and visualization. J. Nucl. Sci. Technol. 44 (8), 1059–1069. Smith, C.F., Cinotti, L., 2016. Lead-cooled fast reactor. In: Handbook of Generation IV Nuclear Reactors. Woodhead Publishing, pp. 119–155. Wang, G., 2017. A review of research progress in heat exchanger tube rupture accident of heavy liquid metal cooled reactors. Ann. Nucl. Energy 109, 1–8. Wang, X., Li, T.S., Huang, X., Yang, Y.H., 2010, January. Analysis of fuel coolant interaction in PWR with experiment and computer code. In 18th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, pp. 491–496. Wang, S., Flad, M., Maschek, W., Agostini, P., Pellini, D., Bandini, G., Morita, K., 2008. Evaluation of a steam generator tube rupture accident in an accelerator driven system with lead cooling. Prog. Nucl. Energy 50 (2–6), 363–369.
Compatibility, Thermal-Hydraulics and Technologies-2015 Edition (No. NEA–7268). Organisation for Economic Co-Operation and Development. Flad, M., Wang, S., Maschek, W., 2010, January. Simulation of a steam generator tube rupture accident in a lead-cooled accelerator driven system. In 18th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, pp. 241–249. Fukano, Y., 2015. SAS4A analysis on hypothetical total instantaneous flow blockage in SFRs based on in-pile experiments. Ann. Nucl. Energy 77, 376–392. Gu, Z., Wang, G., Bai, Y., Song, Y., Zhao, Z., 2015. Preliminary investigation on the primary heat exchanger lower head rupture accident of forced circulation LBE-cooled fast reactor. Ann. Nucl. Energy 81, 84–90. Guo, L., Li, R., Wang, S., Flad, M., Maschek, W., Rineiski, A., 2016. Numerical investigation of SIMMER code for fuel-coolant interaction. Int. J. Hydrogen Energy 41 (17), 7227–7232. Harlow, F.H., Amsden, A.A., 1968. Numerical calculation of almost incompressible flow. J. Comput. Phys. 3 (1), 80–93. Hong, S.W., Piluso, P., Leskovar, M., 2013. Status of the OECD-SERENA project for the resolution of ex-vessel steam explosion risks. J. Energy Power Eng. 7 (3), 423. Huang, X., Wang, X., Yang, Y.H., 2010, January. Computational analysis of pressure loading and impulse distribution in the reactor cavity during the process of ex-vessel steam explosion. In 18th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, pp. 497–504. Meignen, R., 2008. Description of the Physical Models of the PREMIXING Application. IRSN, France. Sci. Technol. Nucl. Install. 2010, 1–13. https://doi.org/10.1155/2010/289792. Meignen, R., Picchi, S., Lamome, J., Raverdy, B., Escobar, S.C., Nicaise, G., 2014. The challenge of modeling fuel–coolant interaction: part i-premixing. Nucl. Eng. Des. 280, 511–527. Nakamura, H., Sibamoto, Y., Anoda, Y., Kukita, Y., Mishima, K., Hibiki, T., 1999. Visualization of simulated molten-fuel behavior in a pressure vessel lower head using high-frame-rate neutron radiography. Nucl. Technol. 125 (2), 213–224. Oguz, H.N., Prosperetti, A., Kolaini, A.R., 1996. Air entrapment by a falling water mass.
12