Abstract
Analysis of the experimental data on release of gas from uranium dioxide shows that for a definite degree of burnup the output of gaseous fission products reaches the maximum possible steady value corresponding to the minimum rate of swelling [1-3]. When this state is reached, the microstructure of uranium dioxide (grain size and open porosity) becomes insensitive to the temperature of irradiation, since the yield of fission products no longer changes with increasing irradiation temperature [1]. This makes it possible to characterize such a structure as a limiting structure [4]. One type of limiting structure is the well-known columnar structure [3, 5, 6]. The experimental data are limited and they do not make it possible to obtain a relation between the limiting open porosity and the limiting grain size. Due to the large number of reactor investigations which are required, it is useful to establish an analytical relation between the limiting values of open porosity and grain size. In [7] a model was developed for determining the gas permeability of porous materials. In this model the open porosity near grains of the material was treated as a collection of elementary capillaries of variable cross section. Under the conditions of operation of a fuel cell exposed to radial thermal gradients, through radial boundary microchannels (capillaries, passing along grain boundaries [3, 6]) form in the uranium dioxide pellets. This makes it possible to represent the microstructure of the uranium dioxide pellets as a system of radially oriented cylinders whose diameter is equal to the diameter of spherical grains. We represent the open boundary porosity near cylindrical grains as through capillaries surrounding these grains. The volume of each capillary is equal to the volume of the open porosity near the radial chain of grains. This model corresponds most closely to the columnar structure of uranium dioxide with extended grains in the form of regular hexahedral prisms [3, 5, 6]. We shall consider the laminar flow regime of gaseous fission products through a porous uranium dioxide pellet with uniform grains and we assume that the pellet is irradiated up to the corresponding degree of burnup. Under conditions of laminar flow of gas through a porous material the gas permeability of the material is determined uniquely by the permeability, which according to Darcy's law for laminar gas flow through a cylindrical capillary near a cylindrical grain [7] is
Published Version
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