Computer modeling of steady state fission gas behavior in carbide fuels

A model for the simulation of long-term, steady-state fission gas behavior in carbide fuels is formulated. It is assumed that fission gas release occurs entirely through gas atom diffusion to grain boundaries and cracks. Fission gas bubbles are assumed to remain stationary and to grow as the net result of gas atom precipitation into the bubbles from the matrix solid and gas atom re-solution from the bubbles into the matrix. Furthermore, assuming that local gas atom redistribution process in the immediate neighborhood of a bubble is very rapid, the bubble size is assumed to correspond to the equilibrium size that maintains exact balance between the rate of gas atom re-solution and that of gas atom precipitation.The model also treats the effect of attachment between bubbles and second-phase precipitates; the experimentally observed faster growth rate of precipitate bubbles is simulated using a reduced re-solution parameter for precipitate bubbles. With the grain matrix assumed to be spherical, the model allows the computation of the radial distribution of the intragranular bubbles and the gas atom concentration in the matrix.The flux of gas atoms arriving at the grain boundary is computed. The continual growth of grain boundary bubbles, resulting from the accumulation of gas atoms on the grain boundary, leads to grain boundary interlinkage and all gas atoms that subsequently reach the grain boundary are assumed to be released. Similarly, all gas atoms generated following the interlinkage of intragranular bubbles are also assumed to be immediately released.Application of the model indicates that fission gas swelling is largely due to intragranular bubbles. Grain boundary bubbles, although very large in size, contribute little to fission gas swelling and the contribution from gas atoms in solid solution in the matrix is even less significant.Physical parameters entering the model were assigned numerical values that closely represent the physical characteristics of the irradiation samples. Careful comparisons between the results of sensitivity studies and the experimental data readily identify the re-solution parameter to have the strongest influence on the results predicted by the code and that the grain size, and not the temperature, is the dominant factor affecting gas release.When allowance is made for the uncertainties of the experimental data, the predicted fission gas swelling also correlates well with experiment. The spread in the fuel swelling data, however, indicates that fuel cracking, and not fission gas swelling alone, very often contributes significantly to the fuel external dimensional changes. The linear fission gas swelling rate prediceted by the model exhibits almost a linear variation with temperature. This result correlates well with the linear swelling rate obtained from experimental swelling data if immersion density data alone are used, in order to eliminate the sources of uncertainties associated with fuel cracking.     

An advanced model for grain face diffusion transport in irradiated UO2 fuel. Part 2: Model implementation and validation

The advanced model for intergranular diffusion transport in irradiated UO₂ fuel described in Part 1 is numerically realized. The important model parameters are specified and improvement of the model for the irradiation induced re-solution of gas atoms from the intergranular bubbles is carried out. Implementation of the model in the MFPR code and numerical treatment of various available data on gas release from irradiated fuel and grain face microstructure show a satisfactory agreement of the code predictions with experimental observations. In particular, the main model prediction concerning the onset of gas release from fuel at very low grain face bubble coverage, below the saturation value manifested by formation of bubble network on grain faces, was confirmed by calculations.     

The fission gas bubble distribution in a mixed oxide fast reactor fuel pin

The fission gas bubble distribution has been studied in a mixed oxide fast reactor fuel pin irradiated in DIDO MTR to 2.8% burn-up at centre and surface temperatures of 2000 and 1000°C. The intragranular fission gas bubbles are very small (<6 nm diameter) and this is a consequence of the high re-solution rate at fast reactor ratings. The bubbles nucleate heterogeneously and linear arrays of bubbles, due to nucleation on fission tracks, are observed up to irradiation temperatures of 1900°C. At 1980°C ~4% of the fission gas produced is present in intragranular bubbles. There is no definite evidence for gas bubble mobility or coalescence. Apart from any effects of columnar grain growth fission gas release in fast reactor fuel pins seems to occur predominantly by the diffusion of single gas atoms, at least up to irradiation temperatures of 2000°C.     

Re-solution effects and fission gas swelling in UO2

A fission gas swelling model is proposed which enables one to calculate swelling in the vicinity of grain boundary networks and in imperfection-free regions. The grain boundary swelling requires a knowledge of the gas accumulation and the reaction-rate at the boundary. The gas accumulation was calculated by deriving a modified form of Fick's second law wherein it was assumed that because of re-solution effects the in-pile diffusion coefficient can be described as a function of the gas concentration but is independent of the actual operating time. Reaction-rates for bubbles at grain boundaries were derived in the manner discussed by de Jong and Koehler in their treatment of vacancy clustering. The results indicate that there is a grain size of about 10⁻⁴ cm for which the swelling is a maximum, which increases somewhat with irradiation temperature and with depletion at a constant temperature. The results enable one to predict the swelling and the mean radii of both intergranular and intragranular bubbles. Mean bubble radii predicted using the re-solution swelling model are in reasonable agreement with radii obtained from electron micrographs of irradiated UO₂ fuel samples. It is argued that gas bubble migration is the predominant means by which gas atoms arrive at grain boundaries at irradiation temperatures above about 900°C.     

A dynamic intragranular fission gas behavior model

A model for the non-equilibrium behavior of intragranular fission gas in uranium oxide fuel is developed to study the fundamental phenomena that determine fission gas effects. The dynamic behavior of point defects and the variations in stoichiometry are explicitly represented in the model. The principle of distribution moment invariance is used to allow approximations that significantly reduce computational expense without sacrificing accuracy. A dynamic intragranular gas release and swelling (DIGRAS) computer code, that is based on the non-equilibrium model, was developed for both steady-state and transient applications. The code utilizes implicit multistep numerical integration methods, and is designed to give detailed information on all the physical processes that contribute to fission gas behavior.Simulations of steady-state irradiations indicate that the gas bubble re-solution process is very significant and results in very few large bubbles. The assumptions of equilibrium bubble sizes for normal steady-state irradiations in fast reactors appears to be adequate. On the contrary, a fully dynamic fission gas and point defect treatment was found necessary for transient simulations. The fuel stoichiometry was found to play an important role in determining bubble kinetics. This is mainly due to the strong dependence of point defect populations on stoichiometry. In fast transients, bubbles were found to be highly overpressurized, which suggests that a mechanistic plastic growth model is also needed.     

Reply to: “Comments on studies on diversion cross-Flow between two parallel communicating channels by a lateral slot — Part I” by J. Weisman

A model for the non-equilibrium behavior of intragranular fission gas in uranium oxide fuel is developed to study the fundamental phenomena that determine fission gas effects. The dynamic behavior of point defects and the variations in stoichiometry are explicitly represented in the model. The principle of distribution moment invariance is used to allow approximations that significantly reduce computational expense without sacrificing accuracy. A dynamic intragranular gas release and swelling (DIGRAS) computer code, that is based on the non-equilibrium model, was developed for both steady-state and transient applications. The code utilizes implicit multistep numerical integration methods, and is designed to give detailed information on all the physical processes that contribute to fission gas behavior.Simulations of steady-state irradiations indicate that the gas bubble re-solution process is very significant and results in very few large bubbles. The assumptions of equilibrium bubble sizes for normal steady-state irradiations in fast reactors appears to be adequate. On the contrary, a fully dynamic fission gas and point defect treatment was found necessary for transient simulations. The fuel stoichiometry was found to play an important role in determining bubble kinetics. This is mainly due to the strong dependence of point defect populations on stoichiometry. In fast transients, bubbles were found to be highly overpressurized, which suggests that a mechanistic plastic growth model is also needed.     

Molecular dynamics simulation of intragranular Xe bubble re-solution in UO2

The homogeneous re-solution of Xe fission gas bubbles in UO₂ is investigated by combined Monte Carlo and molecular dynamics simulations. Using a binary collision model, based on the Ziegler-Littmark-Biersack potential [J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Stopping and Ranges of Ions in Matter, vol. 1, Pergamon Press, New York, 1984], the recoil energy distribution of fission gas atoms is obtained. An extensive library of fission gas atom displacement cascades is then compiled using molecular dynamic simulations. It used for calculating recoil spectrum averaged quantities. The calculations yield a re-solution parameter for homogeneous re-solution and a displacement distribution of fission gas atoms around the fission gas bubbles. The results disagree considerably from past estimates. The importance of channeling and threshold energy for fission gas escape are discussed.     

Analysis of intergranular fission-gas bubble-size distributions in irradiated uranium-molybdenum alloy fuel

An analytical model for the nucleation and growth of intra and intergranular fission-gas bubbles is used to characterize fission-gas bubble development in low-enriched U-Mo alloy fuel irradiated in the advanced test reactor in Idaho as part of the Reduced Enrichment for Research and Test Reactor (RERTR) program. Fuel burnup was limited to less than ∼7.8 at.% U in order to capture the fuel-swelling stage prior to irradiation-induced recrystallization. The model couples the calculation of the time evolution of the average intergranular bubble radius and number density to the calculation of the intergranular bubble-size distribution based on differential growth rate and sputtering coalescence processes. Recent results on TEM analysis of intragranular bubbles in U-Mo were used to set the irradiation-induced diffusivity and re-solution rate in the bubble-swelling model. Using these values, good agreement was obtained for intergranular bubble distribution compared against measured post-irradiation examination (PIE) data using grain-boundary diffusion enhancement factors of 15-125, depending on the Mo concentration. This range of enhancement factors is consistent with values obtained in the literature.     

Investigation of cascade-induced re-solution from nanometer sized coherent precipitates in dilute Fe–Cu alloys

Molecular dynamics (MD) simulations have been used to investigate the re-solution of copper atoms from coherent, nanometer-sized copper precipitates in a body-centered cubic iron matrix. The molecular dynamics simulations used Finnis–Sinclair type interatomic potentials to describe the Fe–Cu system. Precipitate diameters of 1, 3 and 5 nm were studied, with primary knock-on atom (PKA) from 1 to 100 keV, although the majority of the cascade simulations and analysis of solute re-solution were performed for cascades of 10 or 20 keV. The simulation results provide an assessment of the re-solution on a per-atom basis as a function of precipitate size, cascade location and energy. Smaller sized precipitates, with a larger surface to volume ratio, experienced larger re-solution on a per-atom basis than larger precipitates. Re-solution was observed to occur predominantly in the initial ballistic stages of the cascades when atomic collisions occur at high kinetic energy. A minimum PKA energy of around 1 keV was required to produce re-solution, and the amount of re-solution appears to saturate for PKA energies above approximately 10 keV, indicating that the MD results are representative of the energy range of interest. A model for prompt, cascade induced solute atom re-solution has been derived, following the approach used to describe fission gas bubble re-solution, and the parameters for describing copper atom re-solution are provided.     

A description of stress driven bubble growth of helium implanted tungsten

Low energy (<100 keV) helium implantation of tungsten has been shown to result in the formation of unusual surface morphologies over a large temperature range (700-2100 °C). Simulation of these macroscopic phenomena requires a multiscale approach to modeling helium transport in both space and time. We present here a multiscale helium transport model by coupling spatially-resolved kinetic rate theory (KRT) with kinetic Monte Carlo (KMC) simulation to model helium bubble nucleation and growth. The KRT-based HEROS Code establishes defect concentrations as well as stable helium bubble nuclei as a function of implantation parameters and position from the implanted surface and the KMC-based Mc-HEROS Code models the growth of helium bubbles due to migration and coalescence. Temperature- and stress-gradients can act as driving forces, resulting in biased bubble migration. The Mc-HEROS Code was modified to simulate the impact of stress gradients on bubble migration and coalescence. In this work, we report on bubble growth and gas release of helium implanted tungsten W/O stress gradients. First, surface pore densities and size distributions are compared with available experimental results for stress-free helium implantation conditions. Next, the impact of stress gradients on helium bubble evolution is simulated. The influence of stress fields on bubble and surface pore evolution are compared with stress-free simulations. It is shown that near surface stress gradients accelerate helium bubbles towards the free surface, but do not increasing average bubble diameters significantly.     

Spaltgasfreisetzung in Keramischen Brennstoffen Bei Reaktor-Zyklen-Betrieb

Gas release kinetics have been calculated in terms of a bubble migration model; different release mechanisms are assumed to operate in various temperature ranges. It is assumed that fission gas is taken up by a bubble immediately after its formation and that the bubble becomes freed after passing the distance between the point of formation and a grain boundary (or, in the model, a zone boundary). The amount of gas released can be obtained by summing over all gas bubbles which can reach the grain boundary in the course of a specified time interval.In the operation of reactor cycles, one can use the assumption that the gas components from the different cycles do not mutually influence each other in respect of gas release; on the basis of this the total gas release can be calculated. The distribution of gas bubbles is calculated, so that for each cycle the position of the bubbles is known; this can then be used for the next cycle as the starting point for those gas bubbles which have not been released in the preceding cycle. If for each cycle start one represents the as yet unreleased gas in terms of a homogeneous gas distribution, this approximation offers computational simplifications but underestimates the gas release for low-temperature irradiation.     

Swelling and gas release in oxide fuels during fast temperature transients

A previously reported intergranular swelling and gas release model for oxide fuels has been modified to predict fission gas behavior during fast temperature transients. Under steady state or slowly varying conditions it has been assumed in the previous model that the pressure caused by the fission gas within the gas bubbles is in equilibrium with the surface tension of the bubbles. During a fast transient, however, net vacancy migration to the bubbles may be insufficient to maintain this equilibrium. In order to ascertain the net vacancy flow, it is necessary to model the point defect behavior in the fuel. Knowing the net flow of vacancies to the bubble and the bubble size, the bubble diffusivity can be determined and the long range migration of the gas out of the fuel can be calculated. The model has also been modified to allow release of all the gas on the grain boundaries during a fast temperature transient.The gas release predicted by the revised model shows good agreement to fast transient gas release data from an EBR-II TREAT H-3 (Transient Reactor Test Facility) test. Agreement has also been obtained between predictions using the model and gas release data obtained by Argonne National Laboratory from out-of-reactor transient heating experiments on irradiated UO₂. It was found necessary to increase the gas bubble diffusivity used in the model by a factor of thirty during the transient to provide agreement between calculations and measurements. Other workers have also found that such an increase is necessary for agreement and attribute the increased diffusivity to yielding at the bubble surface due to the increased pressure.     

The growth of gas-bubbles by coalescence in solids during continuous gas generation

In order to get some insight into the mode of gas bubble growth during the high temperature irradiation of solids, we have calculated the distributions of bubbles grown by coalescence. The calculations are based on Gruber's coalescence model for annealing which we have extended to the case of an irradiation induced gas generation. The dominant assumption is that the continuously generated inert gas atoms go into new bubbles distributed around small radii. The results show that the bubble growth rate is markedly increased by the irradiation induced gas generation and that the calculated bubble distribution profile exhibits a double peak as often observed experimentally.     

文丘里式气泡发生器气泡碎化特性研究

熔盐堆在运行过程中须不断地去除氙等气体裂变产物。熔盐堆除气系统中气泡发生器的作用是通过向回路中注入一定量的直径为0.5 mm的小气泡,在扩散作用下吸收熔盐中的氙,最终气泡被分离出来,达到除氙的目的。在橡树岭国家实验室设计的基础上,本文为钍基熔盐研究堆设计气泡发生器,并在专门建造的水回路中对其工作特性进行了可视化研究。利用高速摄像系统跟踪气泡的运动和碎化过程,分析气液相流速对碎化后气泡尺寸的影响。结果表明：在实验条件下,当气体流量一定时,气泡尺寸随液体流量的增大而减小;当液体流量一定时,气泡尺寸随气体流量的增加而增大。     

Radiation re-solution of fission gas in uranium dioxide and carbide

Calculations have been performed to estimate the removal rate of fission gas atoms from bubbles due to collisions with energetic fission fragments and recoil cascades. The efficiency of this process was found to be higher than estimated earlier, but is still too low to be responsible for the experimental observations of fission gas bubble destruction during irradiation of oxide fuel. An irradiation experiment to investigate the interaction of fission spikes with free surfaces has enabled a simple theory to be developed which can explain the shrinkage of bubbles and pores by the surface relaxation of a shock wave produced by the passage of a fission fragment. This mechanism occurs in oxides but not carbides because of the faster dispersion of the fission fragment energy and provides the major reason for the difference in gas bubble distributions in oxide and carbide fuel. This process, however, does not remove gas atoms from the bubbles. Since high levels of apparently diffusive fission gas release are observed in oxides, the “effective solubility” of the fission gases required for this release must be sought in phenomena other than the fission spike.     

Fission gas swelling and long-range migration at low temperatures

Fission gas behavior at temperatures below ~ 1100°C is assumed to consist of gas bubble nucleation and coalescence through random motion of the bubbles and then complete bubble destruction by subsequent fission events. A model is proposed describing the gas behavior based on a modified form of Van der Waals gas law for very small bubbles. A bubble is assumed to move inversely to the cube of its radius. Long range migration of gas bubbles to grain boundaries is also predicted and the swelling due to gas motion in the grain boundaries is calculated.     

Modeling of fission gas swelling in LWR UO2 fuel under irradiation

An understanding of the behavior of fission gas in uranium dioxide (UO₂) fuel is necessary for the prediction of the performance of fuel rods under irradiation. A mechanistic model for matrix swelling by the fission gas in LWR UO₂ fuel is presented. The model takes into account intragranular and intergranular fission gas bubbles behavior as a function of irradiation time, temperature, fission rate and burn-up. The intragranular bubbles are assumed to be nucleated along the track of fission fragments, which play the dual role of creator and destroyer of intragranular bubbles. The intergranular bubble nuclei is produced until such time that a gas atom is more likely to be captured by an existing nucleus than to meet another gas atom and form a new nucleus. The capability of this model was validated by a comparison with the measured data of fission gas behavior such as intragranular bubble size, bubble density and total fuel swelling. It was found that the calculated intragranular bubble size and density are in reasonable agreement with the measured results in a broad range of average fuel burn-ups 6–83 GW d/tU. Especially, the model correctly predicts the fuel swelling up to a burn-up of about 70 GW d/tU.