Molten UO2 Research Articles

Numerical study of the fuel rod melting and molten material migration behavior using the MPS method

The catastrophic consequences of nuclear reactor core meltdowns necessitate a comprehensive understanding of fuel rod behavior during severe accidents. This study employs the moving particle semi-implicit (MPS) method to simulate fuel rod melting and molten material migration, capturing complex phenomena such as phase changes, chemical reactions, and fluid dynamics. The developed MPS code integrates models for heat transfer, eutectic reactions, and surface tension, allowing for detailed three-dimensional simulations. Validation of the code is achieved through comparisons with analytical solutions and experimental data from the FROMA experiments. Simulations of Al–Zn substitute material rods show accurate temperature responses and phase transitions, highlighting the impact of radiation heat transfer and molten pool depth on melting behavior. Additional simulations of a single rod and a 2 × 2 rod bundle in a pressurized water reactor under extreme conditions reveal the significant role of atomic diffusion. Mass transfer between the cladding and fuel pellet expands the melting area and facilitates the formation of low-melting-point substances. The high-temperature behavior of the rod bundle demonstrates characteristic patterns, including the downward migration of molten zirconium and the dissolution of unmelted cladding. Analysis of molten UO2 migration within the rod bundle channel illustrates the influence of initial temperature and volume on migration dynamics and Zr cladding dissolution rates. This study offers valuable insights into understanding and mitigating the risks associated with core meltdowns, thereby enhancing nuclear reactor safety.

Numerical study on migration and solidification behavior of molten droplets on structure surface and in debris voids during debris bed melting process

The melt migration and solidification behavior on the surface of metal structure and in the debris voids is a key phenomenon of debris bed melting, which has an important impact on the assessment of reactor pressure vessel damage and melt leakage. In this study, the moving particle semi-implicit (MPS) method with high-order discretization scheme was coupled with a surface tension model that was established based on interface reconstruction. The migration and solidification behavior of UO2–ZrO2 and Fe–Zr melts on the metal structure surface and in the debris voids were investigated with the improved MPS method. The effects of temperature, velocity, contact angle and droplet diameter on the melt migration and solidification were analyzed. The results showed that the molten UO2–ZrO2 droplet on the metal structure surface presented three stages with solidification rate decreasing, while the solidification rate of molten Fe–Zr droplet had little change. The maximum spread factor and solidification rate increased with the increase of droplet falling velocity, but the spread factor was independent of the melt type at the same velocity. The high-temperature molten droplet penetrated the voids formed by the debris with diameter of 5 mm more easily compared to the voids formed by the debris with diameter of 3 mm. The influence of contact angle on the migration of molten droplet with initial velocity was small, and the maximum difference in droplet mass fraction was about 6%. Three groups of molten droplets with different diameters penetrated the voids, and the average increments of penetration mass fraction were 2.3%, 2.7% and 5.8%, respectively, with the increase of velocity. Near the bottom of the debris bed, the molten droplet without initial velocity solidified and blocked the flow channel, but the molten droplet with initial velocity of 0.5 m/s penetrated through the debris voids. The droplet with initial velocity of 0.5 m/s had a faster solidification rate in the voids compared to the droplet without initial velocity, and the droplet solidification mass fraction was 96.27% when the initial melt temperature was 1410 K.

Ab initio study of longitudinal and transverse dynamics, including fast sound, in molten UO2 and liquid Li–Pb alloys

The disparity between the masses of the two components in a binary liquid system can lead to the appearance of a peculiar phenomenon named “fast sound,” which was identified for the first time in Li4Pb several decades ago and later observed in other Li based alloys. However, the exact characteristics and nature of this phenomenon and the reasons behind its appearance have not totally been identified yet. In this work, we analyze the longitudinal and transverse current correlation functions of UO2, Li4Pb, and Li0.17Pb0.83, as obtained from ab initio molecular dynamics simulations. We find that fast sound appears to occur in the two former systems but not in the latter. Additionally, we discuss some of the properties of the liquid mixtures that may be related to the appearance (or absence) of the phenomenon, such as the composition, the polyhedral structure of the melt, and the type of bonding in the system.

Reassessment of Computational Tools for the Modeling of Heat Transfer in a Molten UO2 Pool in Natural Convection

Abstract This work, performed within the European sodium fast reactor safety measures assessment and research tools (ESFR-SMART) H2020 European project, is part of a larger framework intending to reassess the modeling of heat transfer in molten pools on SCARABEE available experimental results. This paper presents simulation results of the in-pile Bain Fondu (BF1) test, performed within the SCARABEE-N program, using accident source term evaluation code (ASTEC), Sn method implicit multifiel multiphase Eulerien recriticality (SIMMER) III, and SIMMER V simulation tools as well as comparison with its available experimental data. This program was performed in the 1980s in the frame of the Safety Assessment studies of Superphenix sodium-cooled reactor. This test was dedicated to verify the stability of a pure molten UO2 pool under decay heat conditions within natural convection and the long-term resilience of the peripheral fuel crust. The pool was generated in a stainless steel crucible by a progressive heating of a fuel pellet stack through six successive power plateaus. For the benchmark purposes, only the molten pool behavior k the last power plateau, where the pool was the largest and the fuel temperatures the highest, was investigated. Experimental data such as the axial profile of radial heat fluxes and heat transfer from the pool to the surrounding interassembly coolant as well as the axial profile of the peripheral fuel crust thickness were used for the reassessment of the simulation tools. In addition, other variables of interest not measured during the test, such as the radial and axial velocities in the pool, were also benchmarked. Finally, a critical analysis of the correlations and models used in the different simulation tools for the BF1 test modeling is also provided in the paper.

Thermophysical properties of liquid (U, Zr)O2 by molecular dynamics

ABSTRACT In-depth understanding of nuclear fuel behaviour under operation is critical to anticipate and prevent severe accidents. Loss-of-cooling events can lead to core meltdown, and formation of U–Zr–O liquids (the basic components of corium lavas), formed of molten fuel and cladding. To improve the knowledge on those liquid mixtures, we evaluate the ability of existing interatomic potentials (CRG and Yakub) for solid-phase (U, Zr)O to accurately reproduce density and heat capacity of molten UO and ZrO and their binary mixes within molecular dynamics simulations. Facing their limits, we determine a new set of parameters for the CRG potential through optimisation on a single experimental density point for ZrO (d=0.070 atoms/Å at T=2900 K). The proposed fitted potential shows good agreement during validation with experimental data when applied at high temperatures.

Fragmentation characteristics of molten materials jet dropped into liquid sodium pool

The nuclear reactor is locally melted to form molten corium under instantaneous total blockage accidents in fuel subassembly of Sodium-cooled Fast Reactor (SFR). Molten Fuel-Coolant Interaction (MFCI) will result in violent interphase heat transfer and intensive fragmentation of molten core materials, which significantly affects the formation and cooling of core debris bed. Due to approximate ambient Weber Number (Wea) with molten metallic uranium, kilogram quantities of molten copper are used as fuel simulant to drop into liquid sodium pool to study the fragmentation characteristics during MFCI. Considering the influence of instantaneous solidification at the contact interface on fragmentation, initial temperature of molten copper is decreased to obtain the instantaneous contact interface temperature (Ti) less than the melting point (Tmp) of copper. Furthermore, hydrodynamic fragmentation is independently examined through experiments with molten aluminum jet under different initial temperatures of molten aluminum jet. The Ti between molten aluminum jet and liquid sodium is varied within the range of Tmp of aluminum and boiling point (Tbp) of liquid sodium. According to the present results, nucleate boiling of liquid sodium is proved to occur during molten copper-liquid sodium interaction and thermodynamic effects are much more predominant than hydrodynamic effects to cause finer fragmentation. The fragmentation of same molten material generally increases consistently with Ti. Due to considerable energy release capability of molten copper, molten state can be potentially maintained at the contact interface to cause adequate fragmentation under the same thermal conditions. Instantaneous solidification originating from contact interface greatly increases the criteria of fragmentation. Due to poorer thermal attributes, molten UO2 is provided with smaller variation rate of Ti under the approximate Ti, which suggests longer duration for violent sodium boiling to stimulate fragmentation. As the temperature of liquid sodium increases, interfacial instability is enhanced to fracture the solid crust with reduced thickness, contributing to fragmentation. The fragmentation caused by transition boiling seems to be more significant than that of nucleate boiling. Furthermore, the fragmentation mechanism of molten materials jet discharged into sodium pool is further discussed in the present study.

Molten uranium dioxide structure and dynamics.

Uranium dioxide (UO2) is the major nuclear fuel component of fission power reactors. A key concern during severe accidents is the melting and leakage of radioactive UO2 as it corrodes through its zirconium cladding and steel containment. Yet, the very high temperatures (>3140 kelvin) and chemical reactivity of molten UO2 have prevented structural studies. In this work, we combine laser heating, sample levitation, and synchrotron x-rays to obtain pair distribution function measurements of hot solid and molten UO2. The hot solid shows a substantial increase in oxygen disorder around the lambda transition (2670 K) but negligible U-O coordination change. On melting, the average U-O coordination drops from 8 to 6.7 ± 0.5. Molecular dynamics models refined to this structure predict higher U-U mobility than 8-coordinated melts.

VULCANO VB-U7 experiment on interaction between oxidic corium and hematite-containing concrete

In a severe accident, the core of a reactor melts and forms corium, a mixture that includes molten UO2 and ZrO2. If the reactor pressure vessel fails, corium can interact with concrete.This paper describes the VB-U7 experiment, which was performed in the VULCANO facility in Cadarache, France, in co-operation between CEA and VTT. This test aims at studying the interaction of more than 50kg of prototypic oxidic corium with EPR sacrificial ferro-siliceous concrete. The experimental configuration, the measured data and post examination and analysis results are presented.This test showed that EPR-type ferro-siliceous sacrificial concrete was anisotropically ablated by oxidic corium. This behavior is similar to that of other silica-rich concretes previously tested in CCI and VULCANO facilities. The corium temperature decreased to the value corresponding to about 50vol% solid fraction when the concrete test section broke, leading to significant spreading.

Potential for Steam Explosions Considering Droplet Solidification and Crust Stability

It is well known that under certain circumstances a mixture of coarse, hot (molten) drops in water that forms from pouring a hot melt into water explodes. This so-called “steam explosion” is generally believed to involve fine fragmentation of the melt drops induced by steam bubble collapse and concomitant water vaporization on a timescale that is short compared with the steam pressure relief time. Motivated by a previously published idea that rapid solidification would render uranium oxide (UO2)-containing (corium) melt drops stiff and resistant to the fragmentation induced by steam bubble collapse that is requisite for an explosion, here we combine solidification theory with an available theory of the stability of thin, submerged crusts subject to acceleration to predict the “cutoff time” beyond which melt drop fragmentation is suppressed by crust cover rigidity. Illustrative calculations show that the cutoff time for corium melt drops in water is a fraction of a second and probably shorter than the time it takes to form the coarse-premixture configuration of melt drops in water that is a prerequisite for an explosion, while the opposite is true for the molten aluminum oxide (Al2O3)–water system for which the window of opportunity for an explosion is predicted to be several seconds. These theoretical findings are consistent with previous experiments that revealed molten UO2 or corium pours into water to be nonexplosive and produced steam explosions upon pouring molten Al2O3 into water.

Validation Studies of a Computational Model for Molten Material Freezing

Validation studies are described of a computational model for the freezing of molten core materials under core disruptive accident conditions of fast breeder reactors. A series of out-of-pile experiments named SIMBATH, performed at Forschungszentrum Karlsruhe in Germany, has already been analyzed with the SIMMER-II code. In the current study, TRAN simulation tests in the SIMBATH facility are analyzed by SIMMER-II for its modeling validation of molten material freezing. The original TRAN experiments were performed at Sandia National Laboratories to examine the freezing behavior of molten UO2 injected into an annular channel. In the TRAN simulation experiments of the SIMBATH series, similar freezing phenomena are investigated for molten thermite, a mixture of Al2O3 and iron, instead of UO2.Two typical TRAN simulation tests are analyzed that aim at clarification of the applicability of the code to the freezing process during the experiments. The distribution of molten materials that are deposited in the test section according to the experimental measurements and in calculations by SIMMER-II is compared. These studies confirm that the conduction-limited freezing model combined with the rudimentary bulk freezing (particle-jamming) model of SIMMER-II could be used to reproduce the TRAN simulation experiments satisfactorily. This finding encourages the extrapolation of the results of previous validation research for SIMMER-II based on other SIMBATH tests to reactor case analyses. The calculations by SIMMER-II suggest that further improvements of the model, such as freezing on a convex surface of pin cladding and the scraping of crusts, make possible more accurate simulation of freezing phenomena.

Laboratory Measurement of the Heat Capacity of Urania up to 8000 K: I. Experiment

The heat capacity C[sub p] of UO[sub 2] was measured in a laboratory experiment where sintered 0.5- to 1-mm-diam microspheres were heated by four tetrahedrally oriented laser beams in an inert-gas-filled autoclave at pressures up to [approximately]1000 bar. The sample, suspended by a tungsten needle, was heated to 8000 K during pulses of a few milliseconds duration. The experimental technique, the instrumentation, and the analytical method used to deduce C[sub p] from the experimental pulse-heating curves are described. Between the melting point T[sub m] and [approximately]4000 K, the heat capacity decreases to a value close to that given by the Neumann-Kopp rule for a triatomic, harmonic lattice, i.e., 9R. Near 5000 K, however, the heat capacity again increases, and it appears to saturate at a value [approximately]30% higher by 8000 K. The new results are compared with published C[sub p] values for molten UO[sub 2] (and other relevant materials) and are briefly discussed in light of the established temperature dependence of C[sub p] at T [lt] T[sub m] and the high-energy electronic structure of UO[sub 2].

Melting attack of solid plates by a high temperature liquid jet — effect of crust formation

When a molten UO 2 jet impinges on a steel structure in a reactor vessel during a severe accident, the erosion rate of the steel by the molten UO 2 jet is expected to be limited considerably by a UO 2 crust layer forming on a molten steel substrate at the jet/steel plate interface. A series of simulation experiments was performed to study the melting behavior of solid plates by high temperature liquid jets and the effects of crust forming at jet/structure interface. In the first series of experiments, salt (NaCl) was selected as the jet material and tin (Sn) as the solid structure. The experiments were conducted with varying the jet diameter (10 ∼ 30 mm) and jet temperature (900 ∼ 1100° C). The jets were accelerated to a range of 3 ∼ 5 m/s at the nozzle outlet by gravitational force and impinged perpendicularly to the solid plate underneath. Furthermore, to check the effects of the thermo-physical properties on the erosion behaviors, preliminary experiments were performed by using a molten Al 2O 3 jet (∼ 2200°C) impinging on stainless steel plate at room temperature. The erosion rates obtained in the present experiments were far less than the values predicted by an analytical solution that neglects the existence of a crust layer and its thermal effects. With the inclusion of the crust behavior in the model, the experimental results were predicted fairly well. From the present experiments, a Nusselt number of the turbulent heat transfer, which takes into account simultaneous melting and freezing in the impingement region of a molten jet, is correlated by a Reynolds number and a Prandtl number as follows: Nu m = 0.0033 RePr. In conclusion, the existence of a crust layer plays an important role in the erosion process of a solid plate by the molten fuel jet with high melting point as in a reactor situation.

Estimation of sonic velocity in molten UO 2 by an internal pressure approach

The internal pressure approach reported earlier, interrelates the critical temperature T c, the sonic velocity C, the molar heat capacity C p and the density ρ to facilitate the computation of one of these parameters which is more difficult to determine experimentally. This paper discusses the variation in the sonic velocity computed for molten UO 2 over the range 3120 (T m) to 6000 K by employing different sets of data on C p and ρ as a function of temperature and also of different values of T c reported in the literature.

Melting of a horizontal substrate placed under a heavier and miscible pool

The melting of a horizontal substrate under a heavier miscible pool is studied. This phenomenon has applications in nuclear reactor safety where, in the event of a hypothetical core disruptive accident, molten UO2 may come in contact with and melt the core structural material. Knowing that the growth and geometry of the melt layer is governed by Taylor instability, a model based on the hydrodynamics and heat transfer of the melt layer is used to obtain a relation for the melting rate and heat flux. The analysis includes the radial flow of the melt, is not restricted to uniform melt layers, and considers the uneven shape of the melting solid. A heat flux correlation that depends on the relevant melt properties and reveals the dependence of the heat flux on the pool-to-melt density ratio and the temperature difference across the melt layer is obtained. The results are compared with the available experimental data.

The heat capacity and enthalpy of condensed UO 2: Critical review and assessment

Having established the role of the heat capacity, C p ( T), of condensed UO 2 in various FBR accident scenarios, e.g. HCDA and PAHR, and having noted the unsatisfactory state of present knowledge concerning this basic thermophysical property of the fuel, all existing enthalpy and heat capacity data are collated and assessed, and certain recommendations made. The conventional method of obtaining C p ( T) by analytical differentiation of some adopted fit to this enthalpy data is then critically examined. The attendant problems are illustrated both for solid UO 2, where the contribution to C p ( T) from the weak, sigmoidal, enthalpy structure (which is just discernible in the data of Hein and Flagella) is missed and for molten UO 2, where not even the direction of the trend of C p ( T) with T can be definitively established, resulting, upon extrapolation to 5000 K, in C p values which can differ by as much as 60 J mol −1K −1. Some recent progress towards a more acceptable, “model-independent” approach, known as quasi-local linear regression (QLLR), is then reviewed and applied to enthalpy data of UO 2 on both sides of its melting point, T m . In the case of solid UO 2, a pronounced heat capacity peak, extending over about 100 K and centred on 2610 K., is revealed, whose magnitude and location is very similar to that found in other fluorite structured materials near 0.8 T m wherein it indicates a (Bredig) transition to a state characterised by giant ionic conductivities. Whilst it is impossible to establish any definite T-dependence for the C p (QLLR) values in molten UO 2, the tendency to slightly decrease appears to marginally outweigh the converse, in qualitative accord with the dependence advocated by Hoch and Vernardakis. In the post-transitional region T t < T< T m the opposite holds, as is necessary for consistency between the independently established T-dependences of the thermal conductivity and diffusivity, which requires that C p ( T) increases with T faster than the density decreases. Attention is then drawn to some interesting comparisons which exist between the behaviour of UO 2 and other (non-actinide) fluorites near their melting points, which suggest the existence, in UO 2 of a significant degree of (i) cation disorder in the post-transitional region, 0.8 T m < T < T m and (ii) electronic disorder in the melt. The review concludes with an extended, retrospective overview of the present situation regarding the heat capacity of condensed UO 2, and identifies some specific experimental goals in connection with the current experimental programme of the Joint Research Centre, Karlsruhe, Fed. Rep. Germany.

An approach for the prediction of temperature dependence of sonic velocity: Application to liquid alkali metals and molten UO 2

The method of internal pressure has been used to calculate sonic velocity in liquid alkali metals and in molten UO 2. A comparison of the predicted values of sonic velocity as a function of temperature with experimental values available in the literature for liquid alkali metals, shows a reasonable agreement. In the case of molten UO 2, experimental values of sonic velocity are available in the literature only in a narrow range of temperature (3133 to 3203 K). In molten UO 2, sonic velocity as a function of temperature has been predicted from melting point to about 6000 K, using the present approach. The versatility of the method has also been demonstrated in the case of liquid Ar, Kr, Xe, N 2 and O 2.

Electronic excitations in molten UO 2

New calculations are presented for the free energy of the charge-transfer reaction 2 U 4+ → U 3+ + U 5+ in molten UO 2. The theoretical basis of the calculations is the same as that of previous work by Gillan. Three topics are studied: 1. (1) the effect on the results of using an improved oxygen-oxygen potential 2. (2) the influence on the free energy of allowing for a high concentration of uranium ions with modified charge 3. (3) the calculation of the entropy of the reaction. We find that the improvement of the potentials has no significant effect on the estimate for the free energy. The free energy decreases as the concentration of modified uraniums increases, but the effect is too small to be of any practical importance. These conclusions provide a justification for assumptions made in the previous work and confirm the prediction that the free energy of charge transfer is lower in the liquid than in the solid by about 1.7 eV. The entropy of the reaction is estimated to have the small negative value of − 1/ k B (−2 cal mol −1 K −1), which is similar to a previous estimate by MacInnes and Martin.

A Fuel Freezing Model for Liquid-Metal Fast Breeder Reactor Hypothetical Core Disruptive Accidents

A proposed fuel freezing mechanism for molten UO2 fuel penetrating a steel channel was investigated in the course of liquid-metal-cooled fast breeder reactor hypothetical core disruptive accident safety studies. The fuel crust deposited on an underlying melting steel wall was analyzed as being subjected to two stresses, one due to the pressure difference between the flowing fuel and the stagnant molten steel layer, and the other resulting from the temperature variation through the crust thickness. Analyses based on the proposed freezing mechanism and comparisons with fuel freezing experiments confirmed that fuel freezing occurs in three modes. For initially low steel wall temperatures, the fuel crust was stable and grew to occlude the channel. At high steel wall temperatures (above 1070 K), instantaneous wall melting leading to steel entrainment was calculated to occur with final penetration depending on the refreezing of the entrained steel. Between these two extremes, the stress developed within the crust at the steel melting front exceeds the critical buckling value, the crust ruptures, and steel is injected into the fuel flow. Freezing is dominated by the fuel/steel mixture. The theoretical penetration distances and freezing times were in good agreement with the experimental results with no more than 20% error involved.

Fuel Foaming and Collapse During Light Water Reactor Core Meltdown Accidents

Fuel melting in severe core damage accidents will lead to the rapid release of fission gas from the fuel matrix and the volatilization of low boiling point metallic inclusions, which can be expected to significantly influence molten fuel dynamics. A quantitative analysis of UO2 foaming potential is based on an assessment of the time characteristics for bubble growth, surface escape, film thinning, and bubble coalescence. Analysis indicates that although the potential exists for early molten UO2 foaming, such foams are basically unstable and tend to collapse, thereby releasing volatilized fission products from the molten fuel debris. Release of such fission products will impact radiological source term evaluation and can result in up to a 40% reduction in the residual decay heat within the core debris. This reduction in core debris heat level will influence the timing and meltdown sequence for such accidents and can impact the heat load requirements of residual heat removal systems or other engineered melt mitigation devices.

Estimation of the free energy of charge transfer in molten UO2

Abstract The free energy change associated with the charge transfer reaction 2U4-→U3+ + U5+ in molten UO2 is estimated and it is argued that this will play an important role in determining the thermodynamic and transport properties of the melt. The calculations are based on the assumption that modification of its charge affects only the Coulomb interaction of a uranium ion with the other ions in the system, the short-range interactions being unchanged. It is shown that the required free energy may be expressed in terms of the average electric potential at the ion, which in turn depends on the radial distribution functions describing correlations with the other ions. The hypernetted chain approximation is used to calculate these radial distribution functions. This approximation is demonstrated to be accurate by testing it on an analogue charge-transfer reaction in molten alkali halides, for which experimental data are available. It is found that the free energy of the reaction in molten UO2 is about 1·7 eV...