The radial distribution of capture rate and effective cross section in fuel rods of radii R, forming a light water reactor (LWR) lattice, is derived with routine cell calculations. Any internal radial subrange (r1,r2) is treated through the assessment of absorption in the two corresponding annular absorbers (r1,R) and (r2,R). The lattice of the latter absorbers, whose pitch is exactly the original LWR lattice pitch, is equivalenced to a lattice of solid cylindrical rods. Thus, for example, to obtain a tenfold radial distribution, ten routine cell calculations are required.
In determining the radius s of a cylinder equivalent to the annulus (r,R), the neutron escape from the annulus is first preserved by making the s rod have a circumference of 2R[1 - (0.5 - (1/)cos-1(r/R))G], where G is the "sticking" probability in the annulus for neutrons entering it from within. The radius s is then the result of making the solid rod and the annulus have the same average chord. In addition, a lattice is assigned to the s rods such that the original Dancoff factor is preserved. Finally, a Bell factor is determined for the s rod such that the actual grayness of the annulus (r,R) is preserved.
A special program for transport-related probabilities is invoked in obtaining the sticking and Dancoff probabilities just described, as well as the Bell factor.
Application of the theory was conducted with the ELCOS system BOXER cell code. Three benchmarks were considered. The first was the one suggested by Tellier et al. for a fuel pin of a typical pressurized water reactor cell. The second was almost identical to the first, except that the fuel was saturated with hydrogen to generate a flatter radial distribution than in the first benchmark. The third benchmark was based on detailed space-energy calculations for a boiling water reactor rod, performed in 1978.
All three benchmark testings resulted in satisfactory comparisons. Hence, the present theory may provide a practical, routine way of obtaining the in-rod distribution of absorption and cross section, calling just for a repeated use of straightforward cell calculations.