Tests on Models of Nuclear Reactor Elements - Studies of Diffusion

Abstract

To estimate the distribution of temperature in the proposed nuclear reactor, one must determine a coefficient of eddy diffusivity and devise a suitable method of computing the heat transfer. Measurements of diffusion in a model of a blanket element for the proposed reactor indicated a gross eddy diffusion coefficient of about 0.002 (? .0005) ft{sup 2}/sec. Thus, the apparent eddy diffusion for the test conditions is about 200 times the molecular diffusivity of water and about. twice that of the liquid sodium. Even approximate methods of applying this result require an elaborate calculation if the primary characteristics of the flow system are to be taken into account. The dispersion of dye in flowing water provided an indication of the diffusion in the model tests. The presence and arrangement of the rods, the effect on the flow?of the spiral wire spacers, and the existence of a comparatively large area on which a laminar sub-layer develops made it impossible to get simple turbulence criteria like those obtained downstream from a screen. Although the results are consequently somewhat unsystematic, they do establish reliably the approximate magnitude of the coefficient of eddy diffusivity. The data were obtained from both line and sectional traverses, the two results being approximately equal. Preliminary data were also obtained for a core element for which {epsilon} ~ 0.003, only slightly less than for the blanket element. Determination of the diffusion coefficient makes it possible to compute the temperature for an array of spatially variable heat sources, as occur in any element. Because of the extreme complexity of the problem, two alternative simplifying assumptions are proposed., In one, the heat sources are assumed to be concentrated along their axes. In the other, the heat is assumed to pass to the fluid immediately at the surface of each circular rod and then to diffuse as though no other rods were present. In each case the effect of the rods on the pattern of diffusion is taken into account only by the afore-mentioned ratio between the local and the apparent diffusivities. The calculations involve a doubly infinite summation to account for the rods and for the so\id walls of the container which are assumed to be insulated. An effect of the rods is to make the local diffusivity much more than the apparent diffusivity, which was observed. In a calculation based on an analogy with heat transfer, the former was found to be 5.3 times the latter