1 . .. .in - 2. . . . - TOFI ORNL P 3158. . , O . en . " . f . EEEFEEEE 1 11:25 1.4 LE - MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS - 1963 - alle ORNUP_3N? Cont-671102--/ - te y PHEN JUL 1 1963 240 . . & 10 . MASTER Bp. Art i . . DISCRETE ORDINATE TRANSPORT THEORY CALCULATIONS OF THE EFFECT .., OF HETEROGENEITIES ON REACTIVITY IN ZPR-3 ASSEMBLY 48 CHILI L'HICHS. #0197.00 MN_.65 G. E. Edison*, I. I. Bennett Oak Ridge National Laboratory Oak Ridge, Tennessee .... . .... .... ........... . LEGAL NOTICE This raport was prepared as an account of Government sponsored work. Neither the Unitert nor the Commission, nor any person acting on beball of the Commission: A. Makes any warranty er representation, expressed or implod, with respect to the arcy- racy, completeness, or usefulness of the information contained in this report, or that the u36 of any information, apparatus, method, or procons disclosed in this report may not infringe printoy owned righto; or B. Aorimos any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report. As used in the above, "person acting on behalf of the Commiosion" Includes any em- ployce or contractor of the Commission, or employee of such contractor, to the extent that auch employee or contractor of the Commission, or opployee of rch contractor propares, disseminates, or provides access to, any information pursuant to his employment or contract with the Commission, or his employment with suca contractor. For presentation at the American Nuclear Society Meeting, Chicago, Illinois, Novemher 5-9, 1967. *Presently at WARD, Westinghouse Electric Corp., Pittsburgh, Pa. LEGAL NOTICE DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED, This report wao prepared as an account of Govornment sponsored work, Nelther the United States, nor the Commission, nor any person acting on behalf of the Commission: A. Makea any warranty or representation, expressed or implied, with respoct to the accu- racy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or proceso disclosed in thio roport may not infringe privately owned rights; or ...B. Assumes any liabilities with respect to the use of, or for damages resulting from the ugo of any information, apparatus, method, or process disclosed in this report. As used in the above, "person acting on behalf of the Commission includes any om- ployee or contractor of the Commission, or employee of such contractor, to the extent that such employee or contractor of the Commission, or omployee of such contractor properos, with the Commission, or his employment with such contractor. . . : : " 21. . -"- ere T 24 i IT 24S . . N AZIS - DISCRETE ORDINATE TRANSPORT THEORY CALCULATIONS OF THE EFFECT OF HETEROGENEIT: IES ON REACTIVITY IN ZPR-3 ASSEMBLY 48 G. E. Edison*, L. L. Bennett · Oak Ridge National Laboratory Oak Ridge, Tennessee Previous work?,? has indicated that aprreciable reactivity effects, as large as Ak = 0.01 or 0.02, may result from heterogeneitics in ZPP : fast critical assemblies. The heterogeneities are caused by the configu- rations of fuel and diluent plates in the core drawers which make up a critical assembly. Corrections for heterogeneities have traditionally been • determined by performing unit cell transport calculations to obtain detailed flux distributions within and near fuel plates or other regions of interest. Cell calculations are of particular interest for ZPR-3 assembly 48 because this Pu-fueled assembly, with thin slabs of C, Na, depleted U, and stainless steel as diluents, has a soft flux spectrum similar to that expected in large fast power reactors. The simple design and composition of assembly 48 permit easy and accurate representation on the computer. Moreover, cal- culations which assume homogeneity of assembly 48 have been made by many organizations. Cell calculations on some earlier ZPR-3 assemblies with various plate configurations were made by Meneghetti' using a 3-group DSN transport ap- proach with up to 16 angles. He observed t’at the calculated multiplication constant k was strongly dependent upon the order of approximation in the angular quadrature. These results indicate that in order to approach an *Presently at WARD, Westinghouse Electric Corp., Pittsburgh, Pa. asymptotic flux distribution, it is necessary to use a high order of ap- proximation in the single Gaussian (SG) angular quadrature commonly employed in discrete ordinates calculations. However, it has been shown in a one-group non-iterative Tission source treatment that, by selecting an angular mesh distribution which is refined in the direction parallel to the slab inter- faces, asymptotic results may be obtained with a much lower order of approxi- mation. We have made multi-group iterative fission source discrete ordtiait intervals were employed with a double Gaussian angular quadrature (DG) and with a modified single Gaussian quadrature (MSG), as well as with the usual SG quadrature. The calculated ceil flux distributions were used to calculate the effect of heterogeneities on reactivity in assembly 48. The discrete ordinates Sy code ANISN' was used to make 47-group slab cell calculations. The cross section set was basically the 99-group ORNL GAM-II° set except that ENLF/B 239 Pu data were used. A P, expansion was used for anisotropic elastic scattering cross sections. The upper 46 groups of the cell calculations corresponded to the top 46 groups of GAM-II, having a lower energy boundary of 150 kev. Group 47 represented a "sink" group condensed from the lower 53 groups of GAM-II. Thus, heterogeneity corrections were obtained only above 150 kev. A flux advantage factor, 5/ 7, was cal- culated in each of the 46 groups for each moterial in the core drawer. Ad- vantage factors for the Pu fuel plate are presented in Table I for three of the 47 energy groups. The results obtained with the different angular quadratures are compared on a basis of solutions having equal numbers of discrete angles: The more rapid convergence of the DG and MSS quadratures is evident, particularly in the high energy groups where the fuel plate is optically thin. " "..: " A ".' : .-... Ni ; '"" ," . : . , . . . , :: 3 Flux advantage factors obtained from the cell calculations were used în GAM-II to generate 23-group cross sections which, in turn, were used in . isomogeneous diffusion theory calculations for the overall assembly. A spatial synthesis diffusion code, MERC, was used to calculate k in R-Z geometry. A 2-dimensional 23-group diffusion calculation without heterogeneity corrections was also made with the EXTERMINATOR-2 code to serve as a ref- proncs fcil. Table II lists the results of these calculations which in- dicate a heterogeneity effect (above 150 kev) of about Ak = 0.013. A smaller effect is expected at neutron energies below 150 kev. ... .. . . . . . in Table I. Calculated Fast Flux Advantage Factors, Pu Fuel Plate of ZPR-3 Assembly 48 Core Drawer cell Group 7 7.40 to 8.18 Mev Group 27 1.00 to 1.10 Mev Group 41 0.24 to 0.27 Mev Sg S46 Sgg SG D G MSG SG DG MSG SG DG MAG 1.0787 1.1563 1.2052 1.0290 1.0525 1.0657 1.0022 1.0042 1.0057 1.2501 2.2728 1.2884 1.0491 ' 1.0800 1.0839 1.0038 1.0044 1.0041 1.22.19 2.2900 1.2897 1.0677 1.0837 1.0838 1.0044 1.0039 1.0041 1.2676 1.2894 1.0785 1.0835 1.0041 1.0040 L. . N E T . .. ... . 7 A WATOTT PET W . Table II. Calculated Multiplication Constant for ZPR-3 Assembly 48 Homogeneous* With Sy Cell Corrections With Sy Cell Corrections With 326 Cell Corrections With Sg Cell Corrections SG 0.9941 0.9980 1.0012 1.0046 1.0063 DG 0.9941 1.0015 1.0067 1.0069 1.0069 MSG 0.9942 1.0043 1.0071 1.0069 All values in the table were obtained with the MERC code. A 2-dimensional homogeneous EXTERMINATOR calculation gave a value of 0.9853. REFERENCES J. K. Long et al, "Fast Neutron Power Reactor Studies with ZPR-III," 1. Proc. of the Second United Nations International Conf. on the Peaceful Uses of Atomic Energy, Geneva, v. 12., p. 119, (1958). 2. D. Meneghetti, ''Theoretical Analyses of ZPR-III Fast Critical Assemblies," Proc. of the Seminar on the Physics of Fast and Inter- mediate Reactors, IAEA, V: Citão . i., p. 457, (Aug. 1961). 3. A. M. Broomfield et al, "ZPR-3 Assembly 48: Studies of a Dilute Plutonium Fueled Assembly," International Conference "International Conference on Fast Critical Experiments and Their Analysis, Argonne National Laboratory, (October 10-13, 1966). 4. W. G. Davey, "Intercomparison of Calculations for a Dilute Plutonium- Fueled Fast Critical Assembly (ZPR-3 Assembly 48)," International Conference on Fast Critical Experiments and Their Analysis, Argonne National Laboratory, (October 10-13, 1966). 5. D. Meneghetti, "Discrete Ordinate Quadratures for Thin Slab Cells," Nuclear Science and Engineering, 14, p. 295 (1962). 6. J. B. Sykes, "Approximate Intergration of the Equation of Transfer," Monthly Notices Royal Astr. Soc., 111, 377, (1951). 7. W. W. Engüe, Jic. "A Users Manual for ANISN," USAEC Report K-1693, . (March 30, 1967). W W M W . A .. !!Y -7,'13 i. - - i. 8. G. D. Joanou, J. S. Dudek, "GAM-II, A B, Code for the Calculation of Slowing Down Spectrun and Associated Multigroup Constants," GA-4265 (1963). 9. P. Greebler, P. Aline, B. Hutchins, "Evaluation and Compilation of 239 Pu Cross Section Data for the ENDF/B Files," GEAP-5272 (Draft, October 1966). 10.: T. . Keriin et al, "The MERC-1 Equilibrium Reactor Code," USAEC Report ORNL-TM-847, (April 22, 1964). 21. T. B. Fowler, M. L. Tobias, D. R. Vondy, "EXTERMINATOR-2: A FORTRAN IV Code for Solving Multigroup Neutron Diffusion Equations in Two Dimensions," USAEC Report ORNL-4078, (April, 1967). . END 15. . V. 'n - - DATE FILMED 11 / 6 / 67 . . tot . . i ;.' ' . * II } - >