3, Atl'.vi 
 
 HL-m. .ASSIFIED 
 
 J 
 
 3 
 
 v 
 
 UNCLASSIFIED 
 
 BNL-1812 
 
 Subject Category: PHYSICS 
 
 UNITED STATES ATOMIC ENERGY COMMISSION 
 
 LIGHT WATER LATTICE STUDIES- PAPER 
 PRESENTED AT THE REACTOR INFORMATION 
 MEETING AT ANL, OCTOBER 7-9, 1953 
 
 By 
 
 H. Kouts 
 
 November 5, 1953 
 
 Brookhaven National Laboratory 
 Upton, New York 
 
 Technical Information Service, Oak Ridge, Tennessee 
 
Work performed under Contract No. AT-30-2-Gen-l6. 
 Date Declassified: October 27, 1955. 
 
 This report was prepared as a scientific account of Govern- 
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 ington 25, D. C. 
 
BNL-1812 
 
 LIGEE WATER LATTICE STUDIES - PAPER PRESENTED AT 
 THE REACTOR INFORMATION MEETING AT ANL, OCTOBER 7-9, 1953 
 
 By H. Kouts 
 
 The Brookhaven Reactor Physics Group is making a study of pile core 
 parameters for light water moderated, slightly enriched uranium rod assemblies. 
 This information is provided by measurements in a series of exponential assem- 
 blies which differ in uranium enrichment, moderator-to-fuel volume ratio, and 
 rod diameter. The enrichment range being explored varies from 1.3$ to 1$, the 
 rod diameters vary from .600" to .250", and the volume ratios lie in the range 
 from k-il to 1:1 (and in some cases are even smaller). The quantities being meas- 
 ured are f, e, p, B 2 , M 2 , and reflector savings (since the assemblies are reflec- 
 ted) . Similar measurements reported at the last Reactor Information Meeting were 
 done with .750" diameter rods with 1$ nominal enrichment. 
 
 I wish to discuss a few aspects of some of the more recent measurements. 
 Since the way we have been using to determine the Buckling is somewhat novel, a 
 fair-sized effort has been devoted to the two-fold job of improving the accuracy 
 of the results and exploring the validity of the method. We have been finding B 2 
 by measuring the vertical neutron relaxation length as a function of the loaded 
 diameter of the assembly, and fitting this observed relaxation length variation 
 to the usual expression, assuming buckling and reflector savings to have constant 
 values over the entire range of loading. The range of loadings used has been 
 quite large, ranging from about 20$ of the critical mass upwards, and a principal 
 criticism of the method used concerns the assumption that A does not vary over 
 this range. Therefore we have increased the total number of such loadings, taking 
 them at smaller loading differences and increasing the range up to a kg^f of about 
 •97- Thus we have been able to find separately the values of B 2 predicted by low 
 loadings and high loadings. We have also quite recently found it possible to make 
 moderately accurate radial traverses in some lattices. This allows finding the 
 buckling in the normal way by combining the information given by radial and axial 
 flux plots. Radial traverses have been made on only one lattice to date - the one 
 with 1.5:1 volume ratio, .600" diameter rods, and 1.15$ fuel enrichment. 
 
Figure 1 shows the results of B 2 measurements made so far with 1.15$ 
 metal. It is seen in every case that the buckling obtained from the higher load- 
 ings, the buckling obtained from lower loadings, and the buckling obtained from 
 all loadings all agree to within statistical error. Further, in the case of the 
 1.5:1 lattice, the value obtained from radial traverses agrees with that obtained 
 from axial measurements to within about 1$, and this difference is less than exper- 
 imental error allows. We intend to do radial traverses in several more lattices, 
 in order to generalize our results, but I think we can say at present that all 
 signs point to justification of our method of measurement. For instance, two-group 
 theory predicts that the reflector savings should decrease by about .15 cm. as the 
 loaded radius increases over the range we used with the 1.5:1 lattice. This should 
 make B as determined from the axial measurements alone about 3«5$ lower than that 
 obtained from radial and axial measurements. The difference is much less, and in 
 the opposite direction. The implication, of course, is that the fine points of 
 homogeneous pile theory are not to be trusted when one is calculating the proper- 
 ties of heterogeneous systems. 
 
 We have been measuring migration areas in two ways. The first method 
 used was reported at the last Reactor Information Meeting; it involves measurements 
 of buckling and themal utilization as boron is added to the moderated water. If 
 it is assumed that these are the only quantities influenced by the addition of boron 
 poisoning, then they are related linearly, and the migration area can be found from 
 a straight line fit to a plot of them. Chernick had pointed out that the assumption 
 that TJ is not influenced by the high boron content of the water is very question- 
 able. The mean neutron temperature must rise as the poison is added, and one will 
 have the usual decrease of T] which results. It does not stretch the imagination to 
 believe that an error of as much as 10-15$ in the estimated migration area can re- 
 sult from this source; that is - the value of M 2 so deduced may be that much too low. 
 
 As a result, we have been exploring a second method of finding M 2 , which 
 still resembles the first in principle. This method is made possible by our being 
 able to make measurements of f and B in lattices which differ only in the enrich- 
 ment of the metal used. So far we have looked at only 1.3$ and 1.15$ enrichments, 
 but the results are already quite interesting. It should be noted first that the 
 change of neutron temperature with this small enrichment variation should be small, 
 because the mean uranium cross-section changes only from 10.2 to 9-3 barns. If a 
 temperature effect in Tj is important here, its effect would be to make the experi- 
 mental values of M 2 greater than the actual values. Thus migration areas by boron 
 poisonings are lower limits; migration areas by fuel enrichment variation are upper 
 limits. The measured values obtained the latter way should be greater than those 
 found the former way. This does seem to be the trend. 
 
 Figure 2 shows values of M2 found by the two methods. Considerable scat- 
 ter exists in both cases; the two procedures are extremely sensitive to normal er- 
 rors in thermal utilization measurement. For instance, a 1$ error in f for one of 
 the 3:1 lattice measurements would push that value in line with those of the other 
 two lattices. By the same token, of course, errors may exist in the other values. 
 
 2 - 
 
We have used for all these analyses measured values of f . If for the 
 measurements with changing enrichment we use values of f based on simple diffusion 
 theory, the result of the analysis is a monatonic variation of M 2 from 36 cm 2 to 
 kl cm 2 as the volume ratio decreases from ^:1 to 1:1. The use of evert such a sim- 
 ple minded calculation is probably not too bad, because only the ratio of f for 
 the two enrichments in involved in the analysis, and the change in f is between .kfy 
 and 1$. For better analysis we are redoing some f measurements, and waiting for a 
 set of P3 calculations which Fleck is about to have done on the N. Y. U. Univac. 
 
 The fast effect measurements we have been doing are carried out in a more 
 or less standard way. We measure the fraction of fission product activity produced 
 by U 2 38 in a fuel rod, and assume this is equal to the fraction of fissions' prod- 
 uced in the U 2 3o. This quantity is directly related to € through the upper part of 
 the neutron fission cycle. 
 
 The assumption of equality of ratios of fissions and fission product ac- 
 tivities is pretty standard for this type of measurement, but it has never been 
 systematically checked. There is reason to suspect a slight error from this source. 
 We have observed in a set of delayed neutron studies now being carried out some 
 differences between the relative yields of delayed neutrons from fast-fissioning 
 species like u238 and Th 2 35^ and thermally-fissioning species like U 2 35. Presum- 
 ably the fission product yield must differ in these cases. Moreover, all the cal- 
 culations I know of for lattices we have measured predict slightly higher values 
 of € than we observe. Presumably our values of € are then a little too low. Soon 
 we expect data on the relation between the fission rates and fission product ac- 
 tivities ; our values of £ may then change a little (probably upwards). 
 
 A second source of possible error is the uncertainity in knowledge of J/ 28* 
 We assume it to be equal to ^25- ^ i* ^ s different, our deduced values of e will 
 be different. Of course, the calculated values would then change by the same factor. 
 
 For tight packed lattices such as must be used with light water, € can 
 get quite large. The last two figures give values measured for volume ratios rang- 
 ing from k:l to .17:1, under a variety of conditions. The very tight packed lattice 
 has a value of 6 closely equal to that measured some time ago in the Snell experi- 
 ment; there it was found to be 1.21. 
 
 The measurements made at varying rod loadings and relaxation lengths were 
 intended to show what errors, if any, were introduced in the experiment by fast 
 leakage of neutrons from the exponential assembly. Calculation set an upper limit 
 of about .1$ in€- 1 for this difference between the measured € and that for an in- 
 finite lattice. As can be seen, variation of the radius and the relaxation length 
 simultaneously produced no observable change in €. Variation of the relaxation 
 length alone by boron poisoning also produced no obvious change. Since either a 
 change of loaded radius or relaxation length changes the leakage, we conclude that 
 within the ranges we used, such an effect on € is negligible. 
 
Such large values of € as are listed here are unique to the systems we 
 have been studying. An interesting corollary is the relatively large fraction 
 f u^3° which is directly burned without being turned into thermally fissioning 
 nuclides. For an € of 1.10, for instance, as exists at about a 1:1 volume ratio, 
 fast fissions in the 28 make up Vyfa of the total fissions. 
 
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UNIVERSITY OF FLORIDA 
 
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