Numerical study on melt drop collision and hydraulic fragmentation during FCI of a nuclear reactor severe accident

https://doi.org/10.1016/j.nucengdes.2020.110862Get rights and content

Highlights

  • Head-on collision of two UO2 melt drops in water pool was investigated at different Weber numbers.

  • Interfacial waves and wrinkles were observed on the melt film and finger structures presented at the rim of melt film.

  • The increase of fuel–coolant contact area was divided into the inducements by deformation and fragmentation.

  • Size distribution of melt children droplets was like an off-centered normal distribution.

  • An empirical model to calculate the contact area was developed.

Abstract

Melt drop collision is an important phenomenon in the circumstance of pressure wave propagation during fuel–coolant interaction (FCI). The deformation and fragmentation of melt drops can increase the contact area with coolant, and as a result will affect the heat transfer and melt oxidation. In this study, a numerical model was established by considering surface tension and validated with the experimental results that were obtained from water droplet collision in gaseous environment. Then, the head-on collision of two UO2 melt drops in water pool was investigated at different Weber numbers, and the melt morphology, contact area, and the number and size distribution of children droplets were analyzed. The results show that interfacial waves and wrinkles could be clearly observed on the melt film, and the finger structures presented at the rim of melt film and finally separated into children melt droplets. The increase of fuel–coolant contact area could be divided into the inducements by deformation and fragmentation. The melt deformation only had influence to the area increase at intermediate process but no effect to that at steady state. By contrast, the final fuel–coolant contact area was determined by the intensity of melt fragmentation. The size distribution of melt children droplets was like an off-centered normal distribution, where the maximum number of children droplets existed in the size range of 0.03 < D/D0 < 0.045, but the droplets in this size range contributed little to the fuel–coolant contact area. With the above analysis, an empirical model to calculate the contact area was developed. The model had a discrepancy of ±10% in the range of Wec = 290–1815 that the model was established in, but the discrepancies were about 13.3% and 19.3% for the cases of Wec at 2196 and 2612, respectively.

Introduction

Fuel-coolant interaction (FCI) is an important phenomenon in nuclear reactor severe accident, which occurs as melt relocates into the coolant in lower head or ex-vessel cavity. Violent hydraulic disturbance and energy transfer take place accompanying the FCI process that can be roughly divided into four phases: (I) initial premixing phase, (II) triggering phase, (III) detonation propagation phase, and (IV) hydrodynamic expansion phase, as shown in Fig. 1 (Corradini et al., 1988). Melt deformation and fragmentation during FCI can rapidly increase melt-coolant contact area and further affect heat transfer, melt oxidation and solidification. Moreover, as the fragments are cooled down, their size distribution will influence the porosity and coolability of the debris bed.

Melt fragmentation can be categorized into thermal fragmentation and hydraulic fragmentation according to the difference of their mechanisms. Thermal fragmentation mode is characterized by intensive coolant evaporation that destroys the integrity of melt drops, which mainly takes place in the triggering phase and early propagation phase of FCI. In contrast, hydraulic fragmentation mode is characterized by strong shear flow at the surface of melt drop and melt jet. Interface instabilities incurred by relative flow and density gradient are the dominant factors for melt hydraulic deformation and fragmentation. Hydraulic fragmentation mainly occurs in the premixing phase, late propagation phase and expansion phase. Compared with thermal fragmentation, the time scale of hydraulic fragmentation is relatively large, and it controls the global behavior of melt drop breakup.

Some experimental studies on melt fragmentation behavior have been carried out using the simulant materials. Chen et al., 1997, Chen et al., 1999 compared the fragmentation behaviors of molten tin and steel drops, which were forced to explode in a sustained pressure field. The fragment sizes of tin and steel melt showed different distributions. Ciccarelli and Frost (1994) investigated the fragmentation process of a single molten metal drop immersed in water pool during vapor explosion. Hansson et al. (2009) observed vapor bubble dynamics and fine fragmentation process of a tin melt drop at temperature of 1000 °C during vapor explosion. Through simultaneously analyzing X-ray radiography and high-speed photography, the results showed that an instability induced deformation and disintegration, like swelling, occurred before droplet fine fragmentation, which differed from the droplet distortion and melt finger structures observed in Ciccarelli and Frost’s experiment. Park et al. (2005) observed small-scale stratified explosion at the local region of droplet, triggered by an external shock pulse of about 1.0 MPa, and then the explosion propagated along the melt surface, disintegrating approximately 20% of the mass of melt drop. Kim et al. (1983) investigated the hydraulic fragmentation of gallium drop in water flow over a wide range of Weber number (30-3519). Gallium drops broke up into large daughter droplets at low Weber number and into smaller fragments at high Weber number, and formed fragment cloud at even higher Weber number. Uršic et al. (2014) investigated hydraulic fine fragmentation process of partly solidified melt droplets during vapor explosion. A modified Weber number was proposed by replacing surface tension with a crust stiffness as the stabilizing force. Haraldsson et al. (2001) investigated the effect of surface solidification on melt drop fragmentation in liquid–liquid media. Experiments were carried out with different melt materials, melt temperatures and coolant temperatures.

On the numerical simulations of melt fine fragmentation, Duan et al. (2003) investigated the critical Weber number of a melt drop breakup under different melt-coolant density ratios. Escobar et al. (2015) study showed that the breakup of a liquid drop in liquid pool occurred at Weber number over 30, which was higher than that in gaseous environment. Gelfand, 1996, Nomura et al., 2001 investigated drop breakup modes at Weber number over than the critical value. Burger et al. (1984) calculated drop fragmentation behavior using two different hydraulic modes, one of which was based on Taylor instability and deformation breakup and the other one described the fragmentation by the stripping effect of capillary waves produced by shear flow. The models could calculate the mass of disintegration and evaluate the actual size of fragments. Escobar et al. (2013) studied melt fragmentation process during FCI through the numerical simulation with MC3D and obtained droplet size distribution. Zhou et al. (2013) investigated the dimensionless breakup time of a melt drop under sudden accelerations at high Weber number. The results indicated that the hydraulic flattening of the droplet played a dominant role in fragmentation. In the modeling of melt drop fragmentation with vapor generation, the fragmentation process was divided into several stages and the high-pressure spots and breakup of filaments, which were difficult to be observed in experiment, were produced by numerical simulations. Li et al., 2019, Li et al., 2020, Li et al., 2020, Li et al., 2020 modeled the deformation and fragmentation behaviors of a melt drop with and without steam film using the moving particle semi-implicit method and obtained the changes of fragment number, size distribution and contact interface as the change of Weber number.

Melt drop collision is a frequent phenomenon in the circumstance of pressure wave propagation during FCI. The deformation and fragmentation of melt drops during collision are different from that of above-mentioned single drops. When the melt drops collide at a low velocity, they may coalesce to form one big drop. In this condition, the fuel–coolant contact area may decrease. By contrast, the melt drop collision at large velocities will result in melt fragmentation and the increase of contact area. Moreover, if the collision occurred between different melt materials, such as uranium dioxide and zirconia, the mass diffusion and eutectic reaction between these two melt types will be affected as the change of their contact area. The intensity of melt drop collision has significant effect on the fuel–coolant contact area and the melt-melt contact area at the condition of different material types. At present, an accurate theoretical model to describe the melt drop collision and fragmentation process, including the parameters of contact area and fragment amount, is necessary and important for the development of integrate programs for FCI analysis.

The early studies on droplet collision were to investigate raindrop formation, focusing on the stability of collision (Adam et al., 1968, Park, 1970, Brazier-Smith et al., 1972, Brenn et al., 2001). In 1990, Ashgriz and Poo (1990) identified three collision configurations and developed theoretical models, which greatly promoted the research of droplet collision. Qian and Law (1997) depicted the schematic of various regimes according to the collision Weber numbers and the impact parameters through a series of experiments. Owing to the limitations of experimental work on the observation of the details in droplet collision, such as the children droplet size, expansion area, and the velocity field, many researchers conducted numerical simulations. Pan and Suga (2005) conducted numerical investigation for the collision of tetradecane and water droplets, respectively, and obtained detailed time-resolved dynamic simulation results. Dai and Schmidt (2005) studied the effect of viscosity on head-on droplet collision and analyzed the relationship of the dissipated energy and maximum deformation with the Reynolds number. Nikolopoulos et al. (2009) calculated geometrical characteristics of the ligaments produced in the collision of tetradecane droplets in gaseous environment, and the details of velocity and pressure fields in the deformed droplets were obtained. Moreover, Hu et al. (2017) investigated the collision of two alumina droplets that have large density and surface tension compared to alkanes. Regarding to the melt drop collision in FCI, Thakre and Ma (2015) modeled hydrodynamic deformation and coalescence processes of melt drops in a water pool using the VOF method. The results indicated that initial Weber number significantly affected drop deformation, and the deformation rate increased with the increase of Weber number. Most of the above-mentioned studies focus on the liquid droplet collisions at low and moderate Weber numbers in gaseous environment. The variation of contact area with the ambient fluid and the size distribution of fragments are not investigated. However, to facilitate FCI analysis with integrate programs, it is necessary to analyze the mechanisms of melt drop collision and develop theoretical models for fuel–coolant contact area calculation.

In this paper, we modeled hydraulic fragmentation behavior during the collision of two melt drops, and validated the numerical models with the experiment of water droplet collision in air environment. Then, the collision of uranium dioxide (UO2) droplets in water pool was simulated to investigate the changes of melt superficial area, fragment amount and size distribution under different Weber numbers. The mechanism of melt superficial area increase was studied by ascribing the inducements to the deformation and fragmentation, respectively. A correlation to calculate the melt-coolant contact area was proposed, which can be applied to the FCI analysis programs.

Section snippets

Numerical method

The governing equations are the incompressible, variable-density Navier-Stokes equations with surface tensiontρ+·ρu=0ρtu+u·u=-p+·2μD+σκδsnwhere ρ is the fluid density, u is the velocity vector, p is the pressure and μ is the dynamic viscosity; D is the deformation tensor defined as dij=(ui/xj+uj/xi)/2in index notation; δs is the interface Dirac function, n is the interface normal vector, σ is the surface tension coefficient and κ is the interface curvature.

A volume-of-fluid (VOF)

Validations of numerical modeling

During FCI, the melt drop collision and fragmentation are very energetic at high Weber numbers. Pan et al. (2009) have conducted collision experiment of water droplets in air environment at high weber numbers and the morphology of droplet deformation and fragmentation was observed. Two cases with Weber numbers at 442.3 and 805.2 were simulated in the present study, in which the Weber number Wed is defined as ρdD0Ur2/σ with ρd being the density of droplets, D0 the initial droplet diameter, Ur

Analysis conditions

The collision and fragmentation of two UO2 melt drops in water pool were investigated under head-on conditions. The initial diameter (D0) of melt drop was set at 10 mm, because the past studies have pointed out that debris size is usually about 0.1–10 mm. The density and viscosity of UO2 melt are 8770 kg/m3 and 0.02631 kg/(m·s), respectively. Surface tension coefficient of UO2 melt in water environment is about 0.55 N/m. The ambient pressure in water pool is 0.1 MPa. The melt drops contacted

Conclusions

Hydraulic melt deformation and fragmentation during melt drop collision was numerically investigated. The numerical models were validated by simulating the collision of water droplets in gaseous environment. Then, the head-on collision of two UO2 melt drops in water pool was simulated. The deformation morphology, fuel–coolant contact area and the number and size distribution of melt children droplets were obtained at the cases with different Weber numbers. An empirical model to calculate the

CRediT authorship contribution statement

Gen Li: Methodology, Funding acquisition, Writing - original draft, Writing - review & editing. Panpan Wen: Validation, Investigation, Writing - original draft. Yupeng Li: Validation, Methodology. Jinshi Wang: Formal analysis, Visualization. Weixiong Chen: Formal analysis, Visualization. Junjie Yan: Conceptualization.

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.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11975180), Natural Science Foundation of Shaanxi Province, China (Grant No. 2020JM-038), and National Key R&D Program of China (2019YFB1900704).

References (35)

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