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L2 .A t' L W1 2. SSIFIED UNCLASSIFIED BNL1812 Subject Category: PHYSICS UNITED STATES ATOMIC ENERGY COMMISSION LIGHT WATER LATTICE STUDIES PAPER PRESENTED AT THE REACTOR INFORMATION MEETING AT ANL, OCTOBER 79, 1953 By H. Kouts A November 5, 1953 Brookhaven National Laboratory Upton, New York Technical Information Service, Oak Ridge, Tennessee Work performed under Contract No. AT302Gen16. Date Declassified: October 27, 1955. This report has been reproduced directly from the best available copy. Issuance of this document does not constitute authority for declassification of classified material of the same or similar content and title by the same authors. Printed in USA, Price 15 cents. Available from the Office of Technical Services, Department of Commerce, Wash ington 25, D. C. This report was prepared as a scientific account of Govern mentsponsored work and is made available without review or examination by the Government. Neither the United States, nor the Commission, nor any person acting on behalf of the Commis sion makes any warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any infor mation, apparatus, method, or process disclosed in this report may not infringe privately owned rights. The Commission assumes no liability with respect to the use of, or for damages resulting with respect to the use of any information, apparatus, method, or proc ess disclosed in this report. BNL1812 LIGHT WATER LATTICE STUDIES PAPER PRESENTED AT THE REACTOR INFORMATION MEETING AT AiL, OCTOBER 79, 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, moderatortofuel 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 4:1 to 1:1 (and in some cases are even smaller). The quantities being meas ured are f, E, p, B2, M2, 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 fairsized effort has been devoted to the twofold job of improving the accuracy of the results and exploring the validity of the method. We have been finding B2 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 keff of about .97. Thus we have been able to find separately the values of B2 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. 1 Figure 1 shows the results of B2 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, twogroup 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 B2 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 1 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 t7 which results. It does not stretch the imagination to believe that an error of as much as 1015% in the estimated migration area can re sult from this source; that is the value of M2 so deduced may be that much too low. As a result, we have been exploring a second method of finding M2, which still resembles the first in principle. This method is made possible by our being able to make measurements of f and B2 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 crosssection changes only from 10.2 to 9.3 barns. If a temperature effect inIl is important here, its effect would be to make the experi mental values of M2 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 M2 from 36 cm2 to 41 cm? as the volume ratio decreases from 4:1 to 1:1. The use of even 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 .4% 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 U238 in a fuel rod, and assume this is equal to the fraction of fission prod uced in the U238. This quantity is directly related to E 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 fastfissioning species like U238 and Th235, and thermallyfissioning species like U235. 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 E than we observe. Presumably our values of E 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 E may then change a little (probably upwards). A second source of possible error is the uncertainty in knowledge of V28 We assume it to be equal to v25. If it is 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, E can get quite large. The last two figures give values measured for volume ratios rang ing from 4:1 to .17:1, under a variety of conditions. The very tight packed lattice has a value of E 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 E 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 E. 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 E is negligible. 3 Such large values of E as are listed here are unique to the systems we have been studying. An interesting corollary is the relatively large fraction of U230 which is directly burned without being turned into thermally fissioning nuclides. For an C of 1.10, for instance, as exists at about a 1:1 volume ratio, fast fissions in the 28 make up 15% of the total fissions. 4 Lr I Q 05 z 0 O m in  , 0 1 0d r. so a o 51 , Sc + + +' +1 '0 % N L d44 ,,o C% o 1 i 0:C 0 rL 0 ef n 0 L 4U n4 U + + +' +' in + o 40 a' o L S.o N 0 (4~ 4 ~ Za o, OJ . 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