Reflector extrapolated thickness

Plutonium Concentration Acid Molarity Reflector Critical Thickness of Infinite Slab of Solution Plus System (cm) Material Buckling (m- ) Effective Extrapolation Length (cm)... 

Before discussing the analogous treatment of other geometries, some of the physical consequences of the addition of the reflector will be considered. The results which follow are developed for the special case of the sphere, but similar relations can be obtained for the cylinder and the rectangular-block reactors. We begin with a study of the reflected-sphere system in which the extrapolated thickness (Ri — Ro) of the reflector is small compared to both the core radius Rq and the diffusion length in the reflector Lr, (Admittedly the diffusion theory postulated... 

In many cases of interest Dc Dr thus, the addition of a reflector of extrapolated thickness — / o to a bare spherical reactor allows the... 

Experiments with varying refiector thicknesses and materials were also performed in a 90° sector around haif the core length. Extrapolating the results linearly to a full reflector, It was found that doubling the above nickel reflector thickness to 4 In. would be only 1.3 times as effective. Further results are given in Table t. 

Criticality was first achieved on July 21, 1961,.with Pu(NO,) solution in a 14-in. diam sthinless steel spKere reflected with a -in. layer of paraffin. Since thenCriti-cality data halve been obtained for the bare sphere (frdin extrapolation only), for the spherd nominally reflected (with -in. of paraffin and 1-in. of paraffin), and witha4-in. thick concrete reflector. One of the experimental assemblies is shown in Fig. 1. Plutonium solutions with aCid molarities in the rpnge of 1.2 to 6, with plutonium concentrations of 33 to 300 g Pu/f have been studied. 

For purposes of calculation the Plexiglas walls of the cylinders employed in the experiments were treated as HjO and were mixed in with the solution, giving a concentration of 349 g/U (92.6% U-23S) per liter. The homogenized units were approximated by spheres having a radius of 11.25 cm. The reflectors were all assumed to be HjO, and the effect of thickness was calculated from experimental data expressed as albedos. The material buckling of a unit was calculated to be 0.0306 cm" which, with bare and water reflected extrapolation distances of 2.6 and 5.8 cm, is consistent with experimental data for similar solutions. ... 

Results of the measurements with the 11.5- and 15.2-in.-diam spheres are given in Table I. Critical e]q>eri-ments with the 14-in.-diam sphere were previously reported . Minimum critical volumes for the plutonium nitrate solution containing 4.6 wt% Pu-240. when bare and water reflected, were determined from interpolation of the data to be about 22 and 11 t, respectively, for a Pu concentration of 175 25 g Pu/f. A concrete reflector was found to be somewhat more effective than water on the 14-in. sphere, but slightly less effective on the 11.5-in. sphere where the concentration Pu was greater. Neutron-flux measurements made in the 11.5-in. and the 15.2-in. sphere were used to determine extrapolation lengths and, hence, critical bucklings for the solutions. A typical flux plot is shown in Fig. 1. The effect of a stainless-steel shell on criticality was also evaluated in several experiments by the addition of extra shells that permitted a subsequent extrapolation to zero shell thickness. 

For the purposes of the present calculation we assume that the equivalent spherical system is one which has the same core volume as the actual geometry and a spherical-shell reflector 17.8 cm thick. On this basis the radius of the spherical core is 72 = 31.93 cm, and for convenience we take the extrapolated outer radius of the reflector to be jS = 50 cm. It is important to note that the simplification proposed here, and in particular the selection of the equivalent system, is not to be construed as necessarily representing a good approximation. Its only function is to clarify the presentation. 

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