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To estimate the status of the Fukushima Daiichi nuclear power plant’s reactor pressure vessel, it is important to understand the breakup and fragmentation behavior of a molten jet of core f...

In this chapter the applications of advanced multiphase lattice Boltzmann methods (LBMs) to enhance the understanding of the molten fuel–coolant interaction (FCI) during a severe accident are presented. Since the FCI is very complex due to the strong thermodynamic and hydrodynamic coupling, which means that it is difficult to understand all the mechanisms simultaneously. Here, the investigation on the FCI with multiphase LBMs is decoupled into two parts: melt jet breakup and boiling. Our original color-gradient and pseudopotential models are employed to study the melt jet breakup and boiling, respectively.

The aim of the present study is to clarify the flow structure of gas phase jet in pool scrubbing to improve the model written in the MELCOR code. Gas phase jet are injected into a water pool under various flow rates. At first, the gas flow structure were observed with a high-speed video camera in detail. Visualization was performed for each height along the flow direction inside the test section. The bubble size and aspect ratio were estimated from the observed images obtained. Secondly, from the comparisons between the flow model in the MELCOR code and the experimental data, bubble-aspect-ratio was found to be more flattened and widely distributed than the model. Thirdly, in order to understand the flow structure, void-fraction distribution and bubble velocity were measured by using a wire-mesh sensor (WMS) for various flow rate on each height inside the test section. The air-phase speed measured just above the nozzle had a larger value than the swarm velocity estimated in MELCOR. As the bubble rises, the rising speed became more similar to the predicted model. Finally, it is clarified by the comparisons of the visualization results and PIV-analysis results that the interface oscillation of globules leads to the increase of the amount of aerosol transferred from gas phase to liquid phase.

To better understand the fundamental interactions between melt jet and coolant during a core-disruptive accident at a sodium-cooled fast reactor, the jet breakup and droplet formation in immiscible liquid-liquid systems were studied experimentally. Experiments using two different pairs of test fluids were carried out at isothermal conditions. The observed jet breakup behavior was classified into characteristic regimes based on the classical Ohnesorge classification in liquid-gas systems. The variation in breakup length obtained in the present liquid-liquid system was similar to that in a liquid-gas system. The droplet size distribution in each breakup regime was analyzed using image processing and droplet formation via pinch-off, satellite formation, and entrainment was observed. The measured droplet size was compared with those available from melt jet experiments. Based on the observation and analysis results, the breakup regimes were organized on a dimensionless operating diagram, with the derived correlations representing the criteria for regime boundaries of a liquid-liquid system. Finally, the experimental data were extrapolated to the expected conditions of a sodium-cooled fast reactor. From this, it was implied that most of the hydrodynamic conditions during an accident would be close to the atomization regime, in which entrainment is the dominant process for droplet formation.

When boiling occurs in a liquid flow field, the phenomenon is known as forced-convection boiling. We numerically investigate such a boiling system on a cylinder in a flow at a saturated condition. To deal with the complicated liquid-vapor phase-change phenomenon, we develop a numerical scheme based on the pseudopotential lattice Boltzmann method (LBM). The collision stage is performed in the space of central moments (CMs) to enhance numerical stability for high Reynolds numbers. The adopted forcing scheme, consistent with the CMs-based LBM, leads to a concise yet robust algorithm. Furthermore, additional terms required to ensure thermodynamic consistency are derived in a CMs framework. The effectiveness of the present scheme is successfully tested against a series of boiling processes, including nucleation, growth, and departure of a vapor bubble for Reynolds numbers varying between 30 and 30000. Our CMs-based LBM can reproduce all the boiling regimes, i.e., nucleate boiling, transition boiling, and film boiling, without any artificial input such as initial vapor phase. We find that the typical boiling curve, also known as the Nukiyama curve, appears even though the focused system is not the pool boiling but the forced-convection system. Also, our simulations support experimental observations of intermittent direct solid-liquid contact even in the film-boiling regime. Finally, we provide quantitative comparison with the semi-empirical correlations for the forced-convection film boiling on a cylinder on the Nu-Ja diagram., 23 pages, 21 figures

Inside an automobile engine, there are a camshaft, a crankshaft, a chain sprocket, etc. that transmit driving force. There are many rotating parts installed there. For example, there are gears soaking in engine oil, and bubbles are generated by rotating gears which drag air into engine oil. That raises void fraction of the engine oil. The void fraction is the gas phase fraction per unit volume. In general, high void fraction causes decreasing performance of the engine oil, such as lubrication, cooling and pressure transmission. Although it is required to reduce void fraction and establish a defoaming technique, the processes of bubble generation have not been clarified. One of the reasons is difficulty to measure void fraction and other physical parameters in oil flow using a real engine. Therefore, the influence of rotating speed, number of teeth, and kinematic viscosity of test fluid on bubble generation behavior is not grasped in detail. In this study, the motivation is to understand the mechanism of bubble generation behavior around a rotating body. Detailed visualization was conducted around a rotating body soaking in fluid. The actual phenomena were reproduced by using silicone oil having the same kinematic viscosity of real engine oil. From the visualization using a high speed video camera, there are some characteristic phenomena such as dragging air, subdividing bubbles, and bubbles coalescence. By using observed images, we measured bubble diameter and bubble number density with image processing. Rotating speed, shapes of the rotating bodies, and kinematic viscosity of the test fluids affected on bubble generation behavior. In particular, as the rotating speed increased, the bubble diameter decreased and the bubble number density increased.

In this paper, the melt jet breakup behavior are numerically studied in 3D with nonorthogonal central-moment MRT color-gradient lattice Boltzmann method, which could significantly enhance the numerical stability and accuracy when applied to flows with very high Reynolds number. Firstly, the methodology to simulate immiscible two-phase flow is validated by conducting droplet oscillation tests. Then the ability of this model to accurately predict melt jet breakup in water is validated by simulating molten Wood's metal jet breakup experiments. Meanwhile, the breakup mechanisms are clarified. For the leading edge, the breakup of the side part is due to large eddies, the main part of the leading edge starts breakup owning to Rayleigh-Taylor instability. For the jet column, small droplets and filaments are stripping due to Kelvin-Helmholtz instability, segment breakup of the jet column is owning to Rayleigh-Taylor instability. Finally, the model is employed to simulate molten corium jet breakup in water. The hydrodynamic characteristics such as jet penetration depth, jet breakup length and fragment size are analyzed in detail. It is found that the simulation results are basically consistent with the dimensionless jet breakup length predicted by Epstein et al.‘s correlation when E 0 = 0.1 , but relatively shorter. RTI theory significantly overestimates mass median diameter while critical Weber number and KHI theories underestimate it.

We develop a lattice Boltzmann (LB) model for immiscible two-phase flow simulations with central moments (CMs). This successfully combines a three-dimensional nonorthogonal CM-based LB scheme [A. De Rosis, Phys. Rev. E 95, 013310 (2017)] with our previous color-gradient LB model [S. Saito, Y. Abe, and K. Koyama, Phys. Rev. E 96, 013317 (2017)]. Hydrodynamic melt-jet breakup simulations show that the proposed model is significantly more stable, even for flow with extremely high Reynolds numbers, up to $O(10^6)$. This enables us to investigate the phenomena expected under actual reactor conditions., Comment: 19 pages, 14 figures

A sodium-cooled fast reactor (SFR) is now under development in Japan. A shell-and-tube type once-through heat exchanger is to be installed to generate steam in the design. Low-pressure hot sodium flows in the shell side and high-pressure water, which heated to become steam, flows in the tube side. It has been anticipated that a pin hole is formed on the tube wall and high-pressure steam blows out from the hole. When a high-pressure steam flows out from the tube hole, a high-speed steam jet is formed in the sodium coolant. Fine sodium droplets are torn off from the sodium surface and entrained into the steam jet. Sodium-water chemical reaction causes an increase of entrained droplet temperature. The hot and high-speed sodium entrained droplets attack the wall of a neighboring tube and cause a wastage on the tube wall, which may lead to a failure propagation. In Japan Atomic Energy Agency (JAEA), an analysis code for the sodium-water reaction phenomenon, called SERAPHIM, has already been developed. Visualization data is required to validate the liquid entrainment model in this code. Since the flow velocity at the gas leakage is a sonic speed, it is extremely difficult to visualize the inside of the gas jet. Experiments have been carried out to visualize this phenomenon in the past; however, experimental data for model validation has not been entirely obtained due to the above-mentioned difficulty. Thus, the motivation of this study is to examine the possibility of visualization method and to clarify flow structure. To this end, we first performed the preliminary experiments using simple test facilities. Two types of test sections were used in the experiments: three-dimensional one and two-dimensional one. In the experiment using the three-dimensional one, we tried to visualize a more realistic phenomenon. Through this experiment, the whole gas-jet behavior was clearly captured. However, we found that the detailed droplet-entrainment behavior in a gas jet could not be obtained in this setup, especially at high-velocity conditions. Then, we carried out the experiments using the two-dimensional one. In these experiments, the flow structure of a gas jet was simplified. However, it was difficult to distinguish the liquid film formed on the wall surface of the test section from the entrained droplets. We considered that the liquid film is formed due to the nozzle outlet shape and improved the test section. By experiments with new test section, we succeeded in visualizing entrained droplets of relatively large diameter and calculated droplet diameter distribution. Then, we discussed the mechanism of entrained droplet behavior.

In severe accidents of nuclear power plants, large amounts of gas containing radioactive particles are generated. In the process of gas release into the atmosphere, it is needed to suppress the leakage of radioactive material. The gas is decontaminated by moving radioactive particles from the gas phase to the liquid phase. This effect of capturing particles is called pool scrubbing, and it has been verified great decontamination effect. Therefore, it is extremely important to analyze the effect in evaluating the influence to the environment. But study on its principle is not carried out sufficiently. And also we don’t have enough experimental date to analyze the effect. The purpose of this study is to clarify the gas-liquid two-phase flow behavior which is important in elucidating the mechanism of pool scrubbing. Particularly, this study focused on the behavior of bubble generation and breakup after being injected from the nozzle and the flow structure of rising bubbles in the still water. Furthermore, we evaluate the validity of the model used in the existing severe accidents analysis code such as the MELCOR by comparing the model with experimental data. We measure the gas phase jet injected from the upward nozzle inserted to a test water tank. Nozzle diameter, gas phase flow rate, liquid phase temperature, and water depth were used as parameters. Bubble behavior was observed via a high-speed camera. The bubble rising speed, bubble distribution and void fraction were measured by a wire mesh sensor. In previous studies, experiments using non-condensable gas in normal temperature water have been mainly conducted. In order to conduct the experiment under conditions that simulate actual equipment, steam which is a condensable gas was used in this study. Moreover, it is assumed that thermal stratification is formed in the pressure suppression pool during severe accidents. To reproduce this situation, thermal stratification is formed in the test water tank. For bubble behavior and flow phenomenon, the result of using non-condensable gas was compared with that using steam. We consider the influence of formation of a thermal stratification. As described above, the flow phenomenon in the pool scrubbing was visualized and measured. Finally, we discuss the validity of the analysis code by comparing the calculation formula and model in the analysis code with the experiment data.

Jet breakup and fragmentation are important phenomena to be well understood during a core-disruptive accident of sodium-cooled fast reactors. The three-dimensional two-phase lattice Boltzmann model developed previously by the authors is improved in numerical stability used to simulate the hydrodynamic process of melt jet breakup. Nonorthogonal central moments is successfully introduced into the model. Numerical simulations of FARO-TERMOS experiments demonstrate the enhancements in stability of the present model. The simulations with two types of grid resolutions show the effect of spatial resolution on the results.

As pool scrubbing plays an important role in fission product (FP) decontamination, a reliable model is needed. Despite the needs, mechanism of FP transfer from air-water from the swarm is not explained exactly which means that the evaluation of physical model used in pre-existing model couldn’t be done enough. Existing model for pool scrubbing is predicted in the MELCOR code. Inside the code, a simple model of bubbly jet divided in 3 regions is used: 1) Globule region where the gas including FP enter and collapse, 2) Swarm rise region where the bubble rises up stationary after the collapse is done and, 3) Entrainment region where the bubble pop out to the atmosphere. In each region, the decontamination factor (DF), the particle density ratio before and after each region, is calculated. On these region, flow and physical force inside the gas phase is predicted to be one of the driving force which cause the FP transfer. Therefore, our study aims at the particle behavior on the gas phase. As to understand the physical phenomenon individually, the study focuses on flow behavior and inner flow of a single rising bubble. As an approach, comparison of bubble containing aerosol and no aerosol has been done for each parameter of size, aspect ratio, velocity. Compared with existing equations, the rising speed of clean bubble condition and aspect ratio of CSI condition agreed well to the MELCOR code [1]. On the other hand, many difference were also measured in other condition. Application of parameters obtained from experiment were done against the MELCOR model. Calculation of velocity inside the oil droplet using the experimental parameters obtained from visualization measurement was done. The local gravitational sedimentation and centrifugal velocity took a higher value in clean bubble and OX50 condition compared to CSI condition. On the other hand, Brownian diffusion velocity had an opposite trend. PIV measurement were performed by a silicone oil to visualize the inner flow clearly and compared with the calculation. Seen from the results, the local diffusion velocity took a lower value compared to the calculation using the MELCOR model.

In order to decrease the leakage and diffusion of Fission Products (FPs) in a severe accident (SA) of nuclear power plants, BWR have a suppression chamber filled with water to decontaminate the polluted air from the reactor vessel when emergency ventilation is done. It’s called pool scrubbing having a function of decontamination effect that transfer particles from gas to liquid phase by blowing gas containing FP into water. decontamination factor (DF) which is an index of decontamination performance evaluation of pool scrubbing is predicted and calculated by using a flow model in the existing analysis model such as MELCOR code. Evaluation of the DF by pool scrubbing is important in analyzing SA progress of nuclear power plants. For this reason, validation of flow model and decontamination model is important. It is necessary to validate whether the analysis result of each model matches the actual phenomenon. Despite of these needs, generic experimental data on gas-liquid two phase flow including aerosol is insufficient in confirming the validity of existing model. Therefore, the aim of this study is to investigate aerosol behavior in air jet and its relation to bubbly flow structure during pool scrubbing. This is to obtain the flow structure when air - aerosol released to the pool part and are obtained. Transition behavior of particles from the gas phase into the liquid phase was observed by high-speed camera. In addition, the effect of aerosol on void fraction in the pool was measured by wire mesh sensor from the nozzle exit to the water surface ware also observed. Ejecting air-aerosol from the nozzle to the pool part at various flow rates, visualization of bubble diameter, bubble aspect ratio, void fraction and the gas phase velocity were done by using image processing and a wire-mesh sensor. From these results, we compared the parameters by the presence or absence of aerosol. DF is also compared with the model used in the MELCOR code.

It is essential to understand the fundamental processes between melt jet and coolant during a postulated core-disruptive accident of a sodium-cooled fast reactor. In the present study, jet breakup and droplet formation in immiscible liquid-liquid system were studied numerically. A lattice Boltzmann two-phase model was modified in framework of three-dimensional 27-lattice to enhance the numerical stability. This model was applied to the conditions of jet breakup simulations. The present lattice Boltzmann simulations qualitatively reproduced the characteristic transitions of breakup regimes.

A three-dimensional color-fluid lattice Boltzmann model for immiscible two-phase flows is developed in the framework of a three-dimensional 27-velocity (D3Q27) lattice. The collision operator comprises the D3Q27 versions of three sub-operators: a multiple-relaxation-time (MRT) collision operator, a generalized Liu--Valocchi--Kang perturbation operator, and a Latva-Kokko--Rothman recoloring operator. A D3Q27 version of an enhanced equilibrium distribution function is also incorporated into this model to improve the Galilean invariance. Three types of numerical tests, namely, a static droplet, an oscillating droplet, and the Rayleigh--Taylor instability, show a good agreement with analytical solutions and numerical simulations. Following these numerical tests, this model is applied to liquid-jet-breakup simulations. The simulation conditions are matched to the conditions of the previous experiments. In this case, numerical stability is maintained throughout the simulation, although the kinematic viscosity for the continuous phase is set as low as $1.8\times10^{-4}$, in which case the corresponding Reynolds number is $3.4\times10^{3}$; the developed lattice Boltzmann model based on the D3Q27 lattice enables us to perform the simulation with parameters directly matched to the experiments. The jet's liquid column transitions from an asymmetrical to an axisymmetrical shape, and entrainment occurs from the side of the jet. The measured time history of the jet's leading-edge position shows a good agreement with the experiments. Finally, the reproducibility of the regime map for liquid-liquid systems is assessed. The present lattice Boltzmann simulations well reproduce the characteristics of predicted regimes, including varicose breakup, sinuous breakup, and atomization., Comment: 20 pages, 17 figures

Mitigative measures against the event of a core disruptive accident (CDA) are of the importance from the viewpoint of safety of a sodium-cooled fast reactor (SFR). If the CDA occurs, the so-called post-accident heat removal must be surely achieved. The present study focuses on the scenario that the molten materials are injected into the lower plenum as jets. The jet breakup behavior during the CDA will be very complicated. Therefore, a specialized study on the fundamental process during the jet breakup is believed to be an effective approach. The aim of this paper is to understand the fundamental process of hydrodynamic interaction of jet breakup and droplet formation Using the immiscible liquid-liquid system, water and silicon oil as the test fluids, visualization via high-speed videography was performed. From the visualization results, the breakup length and droplet diameter were measured by image processing. The experimental data were scaled with ambient Weber number. When the Weber number was smaller than 1, the droplet diameter was close to the nozzle diameter, and distribution of droplet size was not observed. When the Weber number exceeded 1, the breakup length became longer and the generated droplet diameter possessed a distribution with two peaks due to satellite droplet formation. In both cases, the droplet formed at the leading edge of jet. In case that Weber number is around 100, the droplets were formed by entrainment of interfacial wave at jet side. From the mass median diameter data, we can see that the increase of the Weber number caused the decrease of median diameter and the increase of the width of the distribution.

For the safety design of a Fast Breeder Reactor (FBR), if a Core Disruptive Accident (CDA) occurred hypothetically, it is required to suppress the rapid energy release due to a prompt criticality. Even if the rapid energy release does not occur, there is a possibility that a large amount of fuel melts. Therefore it is important to achieve Post Accident Heat Removal (PAHR). In order to achieve PAHR, it is strongly required that the molten material which is released from a core region gets cool and solidifies in the sodium coolant in a reactor vessel by breaking up. It is considered that the molten fuel is injected into the coolant like a jet. Furthermore, in the actual FBR, the interfacial temperature between the molten fuel jet and the coolant is considered to be lower than the melting point of the molten material. Thus for PAHR in CDA, it is important to understand the interaction between the jet and the coolant in such a condition and to estimate the molten jet behavior quantitatively. In order to estimate quantitatively the effects of the solidification on the molten jet behavior, we carried out the experiment in which a simulant material was injected into a simulant coolant. In the experiment, we used low melting point alloy (Bi -Sn) and water as the simulant molten material and the simulant coolant respectively. In the experiments, we chose the temperature range including the condition that the interfacial temperature was lower than the melting point of the molten material. The jet breakup and the fragmentation behavior of the molten material jet were observed with a high speed video camera. Then the jet breakup length is estimated form the results. We changed the initial interfacial temperature condition by adjusting temperature of the molten material and the coolant. We also changed the jet velocity by adjusting the height of the nozzle tip from the water surface. From the experiment, we found that the jet breakup behavior depends greatly on the interfacial temperature and the injection velocity and that the solidification of a molten material jet and the growth of unstable jet surface, which results from the relative velocity of the jet to the coolant, are in a competitive relation for the jet breakup. We also found that when the molten material jet breaks up into fragments, the breakup length is independent of the initial interfacial temperature and the initial injection velocity.

Mitigative measures against a Core Disruptive Accident (CDA) are important from the viewpoints of safety of a Fast Breeder Reactor (FBR). If a CDA occurs, Post Accident Heat Removal (PAHR) must be surely achieved. In the PAHR, molten materials are likely to be injected into the coolant like a jet and they must satisfy two requests simultaneously: fast ejection and stable cooling after quenched. In order to estimate the quench behavior of the molten jet, it is important to understand how the jet breaks up. The objective of this study is to clarify that the influence of hydrodynamic interaction between a jet and the surrounding fluid on jet breakup. Previous works have clarified that one cause of the jet breakup is provoked by fragmentation at the side of a jet. However, there are few detailed results describing the correlation between jet breakup and hydrodynamic interaction at the leading-edge region of a jet. Additionally, air entrainment with a jet is always observed in our past experiments using simulants, but its influence has not been discussed yet. In this study, jet injection experiments in liquid-liquid system were conducted for investigating the interaction a jet and an ambient fluid, and the effect of air entrainment on jet breakup behavior. Both simulant core materials and coolants were transparent liquids for visualization. The stored simulant core material was injected into a tank filled with the simulant coolant. In order to realize the condition without air entrainment, the air remaining within the nozzle was removed using a syringe. The jet breakup behavior was observed with a high speed video camera. A normal backlight system and a Laser Induced Fluorescence (LIF) system were employed for visualization. The inner velocity distribution of a jet was measured by Particle Image Velocimetry (PIV). As a result, in the experiments without air entrainment the jet breakup lengths were described by Epstein’s equation. In addition, a pair of vortices was observed at the leading-edge region. The vortices were generated at the leading edge and the leading edge rolled up by the vortices returned toward a jet core. Thus, it was very likely that the vortices at the leading edge region promoted jet breakup.