. | OF I ORNL P 1680 .. LE MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS - 1963 ORNL Pl- 1680 Conf-65V/03-)! CLASSIFICATION TIF APPLICAOLE)". PAGE NO. $M–70/29" ** OUTTOM OF FINST LINE OF TEXT. OR CHAPTER TITLE ---Del... Radio · . 10 7--- EXPERIMENTAL AND CALCULATED SYSTEM CRITICALITY 15. --- J. T. Tnomag** LEFT MARGIN- Oak Ridge National laboratory, United States RIGHT MARGIN o S.. DESIRED MAXIMUM : inii 30 1:::::;? :: LEGAL NOTICE This report was prepared as an account of Government sponsored work, Nolther the United States, nor the Commission, aor any person acting ca behalf of the Commission: A. Makes any warranty or representation, exprossed or implied, with respect to the accu- racy, completeness, or usefulness of the information contained in the report, or that the use of any information, apparatus, method, or procon disclosed in this report may not infringo privately owned rigata; or B. Assumor any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or procesu disclosed in this report, As used in the above, "person acting on behalf of the Commission" includes any em- ployee or contractor of the Commission, or employee of such contractor, to the extent that such omployee or contractor of the Commiosion, or employee of such contractor proparan, dinnominatos, or provides acco to, any information pursuant to his employment or contract with the Commission, or bir employment with such contractor. : D W EAR SCIENCE ABSTRACTS 35 in.. : 21 40 EXY *Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. ...**Including work done by J. 1. Mihalczo and E. B. Johnson of thei :... 1: Oak Ridge National Laboratory , **... r ?MAINING LINES Or: 'YPE.... home si mware 3.1 . END TYPINO -- . CLASSIFICATIO:! OF Auntirano wird . . . . . . . . . . . . . . !.! . !:., Introduction ! 1;1!:;!' poco . The fountainhead for specifications of the safe handling of f1boile mate- rials is the definition of their criticality. The framework for evaluating the degree of safety that has evolved over the past few years circumvents the natural.. starting point for safety analysis, criticality, by specifying factors and con- ! ditions to be applied to a given number of units producing a fictitious system which must be demonstrably subcritical. Such an approach can result in fertile ground for disputations between mutually interested parties, even within manage-1. ments of installations. Knowledge of systems criticality and of the magnitudes of factors affecting ! their criticality directly applied to problems in safety is a preferable, less controversal approach. During the past decade the United States has actively gupported an experimental program on systems criticality. The purpose of the program has been to produce information on systems that are as free from ex- üzeneous materials as possible, that are free from geometric complexities, and that may serve as a basis both fou: evaluating calculational techniques or models and for direct application to nuclear safety problems. Monte Carlo cal- culational techniques combined with the existing system criticality data can provide a necessary basis for a more l'avorably oriented delineation of safety evaluations. Date representative of the contributions of the Oak Ridge National Labora- tory Critical Facility are presented in the-f01.lowing along with results from three methods of calculation. The experiments are exclusively with uranium having two greatly differing values of su enrichment, a wide range of uranium density, and extensive variation in size und geometry of units used. In addition to the effect on array criticality of unit variation, other array effects ex- amined included array shape, degree os reflection and/or moderation, and combi- i nation of arrays with different neutron energy spectra. Typical Monte Carlo and neutron current calculations of these data are compared. -- - - Material this section. A general description of materiale is presented in the following. Specifio details necessary to characterize criticality are given with the experimental data for each series. The principle rode of assembly and control is stated; particular details of the apparatus are to be found in the oited references. 2.1 Fissile The physical forms of the fideile materials used were either metal or aqueous salt solutions. The Low 2550 enrichment \material was a fluoride solution ... ---------- -------------... . ...... ..... ... . . . .... C .. -. -- . . .... .. used exclusively at a single concentration near that which would produce the minimum critical volume measured in 0. single vessel. The material at a higher ontent was utilized both as a nitrate solution at various uranium con- centrations and as a metal. There was a negligible amount of excess fluoride ion in the fluoride solutions; the total nitrate in the nitrate solution cor- responded to an N: SYU ratio of 2.006. 'No other impurities of significant quantities were present in the fissile materials. The 1sotopic content of the uranium for the various physical fornis 18 given in Table I. .. .. .. .. .. .. .. . . . -- . .. - .. .... it! Pos 1:1 .' .. , ,- 2.2 ltydrogenous Hydrogenous materials were used as reflectors of and moderators in the i arzeye. Paraffin, in various thickne:8888 from 1.3 to 15.2 cm, and polyethylene, 25.2-cm thickness, were used as reflectors. Plexiglas, a methacrylate plastic, was used as a moderator in the arraye. The physical properties of these mate- cals are listed in Table II. 2.3 Iron A number of experiments with metal units were performed with the unite in iron containers. The containers were suitable lengths of 14.130-cm-ÓD pipe with a 0.655-cm-thick wall (5-in.-schedule 40 pipe), having 0.635-cm-thick end plates.... The density was 7.85 g/co.. 2.4 System Assembly The method of assembly for solution units was to space the proposed system : of units by hand including three, four, or five centrally located empty con- tainers, depending upon the total nwaber of units in the array, which could be ii Thailed remotely. Reactivity control and criticality were achieved by varying the common solution height in these central units. The spacing was adjusted ...to attain criticality when the control containers were indistinguishable from the hand-placed units. A system of 125 units 18 shown in Fig. 1; visible at the top of the array are five vent I:Ines from the control units in the centrali plane of the array. i. The two component metal absemblies were conducted on the Criticality Testing Unit (2); a double platform device in which the lower platform 18 vertically movable under the action of an air-actuated hydraulic system bringing : the parts of an assembly together. Control was by unit separation. The multiple component metal systems were conducted on the Split Table Apparatus (1), two tables in the same horizontal plane, one of which is move- able under the action of an air-hydraulic cylinder regulated by an electric motor drive providing variable closure speed, the other table is fixed. A suite, able portion of an array. was assembled on each of the tables and control was table separation. ... ..-- ..- . .. . . .. .. . demasmane..... .......... 11 . 1.1 . ,un . Table I: Weight Percent of Uranium Isotopes Present in the Hasile Materials. Uranium Isotope . U()0,F. : (92.670,(NO2) .. 234 - 0.03 4.97 Metal . 1.0 i . 93.2 : 0.2 : 5.6 ! le parce 235 236 - 1.0 92.6 0.5 5.9 - 0.05 94.95 i - - lit 11!.1, . 233 ----- --... . 307- 373. ------- . -- -- ...........-----------------...--.-.-- - - - -- - -... - - - - WCY ..... : "? MIPIRAID.. . Wise -. م . بلا - • . Table II. Physical Characteristics of Reflector and Moderator Materialo Material Chemical Form Density Paraffin : CHE 0.939 0.916 Polyethylene Plexiglas C5Hgºz 1.18 1. a. An exception to the paraffin density given 18 0.88 g/cc for the 1.3-cm-thick reflected experiments. ..- . . ......... ...... ' " "'1 ...1111.!!!! ਜਾਣ- ** ** Photo 1765 , --. . . ' " . Fig. 1. A View of a Critical System of 1125 F!-Units of Series III Experiments. Each unit contains 1.92 kis of 235U ag uranyl nitrate solution. . * ..... . * * . :: **. * * * ' • !, ••• • • ... - • ........... * * * . • • | . ***** . ” ' ' .. T . , - .. 3. Series I - U(93.2) Metal Discs? .. The neutron interaction was atulied between two and three component systems *** (2) utilizing uranium metal cylinders of varying thicknesses to determine the . critical spacing of identical pieces. The units were U(93.2) metal with a density of 18.7 g/cm3. The unit surface separation between the large, parallel, fiat surfaces of the cylinders as a function of their geometry and thickness 18 shown in Fig. 2. The insert on the figure gives the data for the oritical height of the individual cylinder diameters used in the experiments (3) and provides asymptotes for the curves shown. The asymptotic behavior 16 typical or unre. flected and unmoderated arrays limited to one or two dimensions. 4. Series II - U(93.2) Metal Cylinders For convenience in reference and description, everage dimensic.. masses of the units utilized in the arrays constructed in these experiments have i beer collected in Table III. The experimental results from assembling the units ! ....... into arroyo are grouped according to the effects investigated. The largest group : comprises regular three dimensional reflected and unreflected arrays. Other : ............ groupings are partial reflection, cubic and rectangular parallelepiped lattice . . cella, unit shape, array shapo, moderation and mixed arrays. 4.1 Regular Three Dimensional Arrays. Arrays having an equal number of units along the three directions of the i . array are referred to as regular arrays. Data obtained from regular arrays of ' 8, 27, and 644 unite, both unreflected and reflected by various thicknesses of paraffin are given in Tablo IV. Each entry represents a critical orray with the two noted exceptions. The array description, column 1, utilizes the letter and superscript of Table III to identify the average unit in the array, the sub- script is the total number of units in the array, and the numbers in parentheses are the number of unito along each of the three directions. The uniform paraffin reriector thickness (om) surrounding the array is given in column 2. The surface separation of units, equal in three directions, and the average uranium density appear in columns 3 and 4, respectively. Column 5 gives an indication of the array shape expressed as the ratio of the array height to the square root of 1to ......... base area. TO simplity reference to the critical arrays or Table IV and to reduce their recurring descriptions the following notation will be used! . . . I 2. mie oeries of experimento was conducted by J. T. Mihalcao (3). 2. v(93.2) designates uranium containing 93.2 wt% ESTU. 0 . - C 4 - 1 UD . DO TU . X år Arrays . SC 110 DU0 . OD . . LUC + I : ! 0 PC . D an L . 4. . LL be U II ON . U C . . . LO OT . A POR . L UU 7 U1 . > 1 LO . TDK NO . O 0 TO 111 11 to CL . . n YO 1 - 1 2. 12 * MI DO VO . OL O . . 11 0 IN 0 . 1 . CKN U 1 1 . U 0 LLI . .' : . TOD . 1 AO . C 1 .IT . U L Q O . U . U . S . 1 . . 1 1 [- I 1 E 17 - i 1. ... IS . Di 1 CU ROB A AMDALLA HADIAH IHMISM AMAH William PALMA BRATARE AUTHEVALIE! HEADER B OL . . . 1 ii'i' I . . SO 90 D 7 C - UU 1 0 : . 07 11 1 . . . 16 .: + 11 1 1 . 11 1 32 1 - - Ett T IN HET PENSIEDLER ARBED MARIAHEITENSPEE . THICKNESS OF EACN UNIT , cm. 1. Table III. Dimcnolons of Average U(93.2) Metal Unito Constituting Arrays Vranium density - 18.76 g/cm3 Height, h tinit Das notion Moss (kB of u) Diometer, a (cm) n/a 21.506 11.500 9.116 10.400 10.4844 10.507 10.489 10.458 10.4344 10.384 bene in staat 5.382 5.382 8.61 8.641 5.382 5.382 5.382 9.216 11.494 15.461 12.454 95 ooooooo 0.47 8.077 8.077 0.70 0.70 15.692 15.683 15.696 15.807 11.194 11.490 9.116 12.962 1.42 0.94 li..464 1...506 11.184 11..488 Buwono 0.94 ; 20.005 20.960 20.877 20.896 20.892 21.008 10.765 10.765 10.765 10.765 17.282 9.116 1.90 . : : 26.218 13.459 26.113 Eero 13.4591 1.27 1.17 UNL Su 5.225 5.254 5.245 1:..494 9.116 9.116 2.691 4.320 4.320 0.23 0.47 0.47 This unit consisted of one BJ mounted coaxially with and between two pie. 8. This wit consisted of ons A7 mounted coaxially is the and between two otio : en - - . .. i 7 * . th 19 T . i . . . i . r.. Table IV. Critical Conditions for Regular Three Dimensional Arrays with various Paraffin Reflectors . . . . Paraffin Reflector Thickness (cm) Average Uranium Density in Argay (g/cm) Surface Separation 0:2 Units (cm) Ratio of Array Height to ✓ Base Area . Array Description - - - AŽ (2x2x2) 0.47 0.48 - 14.709 13.563 7.825 5.350 4.995 .. Aầy (3x3x3) 0.229 1.981 3.416 3.696 2.007 2.992 5.872 3.258 :8.689 moooo 7.767 5.954 3.085 1.967 1.826 .-- AB (2x2x2) 24.632 .------.. 0.96 - 3.8 7.6. 0.602 2.362 3.970 4.308 4.865 12.037 7.248 4.503 7.096 15.2 ---.. "... -- a ny (3x3x3) - - 2.436 3.426 6.579 9.017 9.434 2.798 - 1.3 3.8 7.6 15.2 5.526 1.80 . 0.97 0.97 0.97 -- - - 1.686 - ... . . 3.952 4.693 - . . A Sur (4x4x4) B (2x2x2) 12.360 - . all ... 0.73 1.035 11.374 8.756 4.445 - 0.902 1.905 4.961 . . 0.75 0.79 0.82 0.82 . .-.. 2.845 . . . 15.2 1.823 . . . 1.3 . . 2.645 5.185 3.869 2.827 1.137 1.067 4.204 5.677 10.190 23.693 24.294 3.8 0.78 0.80 0.84 0.86 0.87 . . . . . 25.2 !!! · sot po operi . . -- Table IV. Continued --- ... ... Paraffin Reflector Thickness (cm) Surface Separation of Units (cm) Average Uranium Density in Array (g/cm3) Ratio of Array Height to Base Area .-. Array Description com (2x2x2)" 2.217 8.562 0.95 Lo Oni ob (2x2x2) 2.5 8.514 6.295 4.292 2.843 1.777 1.669 0.95 0.95 0.96 0.96 0.97 . 2.248 3.678 5.710 8.207 11.509 11.986 6.363 8.574 I't.764 3.8 7.6. 15.2 0.97 can (3x3x3)“: 0.96 3.827 2.683 1.187 0.776 0.744 0.96 0.97 18.720 0.98 19.147 D (2x2x2) Darassed..... 25.1.23 1.1.532 6.806 4.843 1.976 1.215 1.130 1.18 1.12 1.09 1.07 1.07 15. Day (3x3x3) ime OMA mo 16.378 8.1.94 1.L. a 29.606 211.498 24.991 2.980 2.025 0.817 0.532 0.520 1.10 1.09 1.06 1.05 2.05 15.2 Ann a. The letter and the superscript identify the average unit in the array de- , : scribed in Table III; the subscript 16 the number of units in the array; the numbers in parentheses are the hor:1zontal and vertical dimensions, respectives : : ly,' of the array expressed in number of units... . - . . . met - 8. Errors on all surface separations are + 0.013 cm for unreflected arrays and + 0.026 cm for reflected arrays. "... Array was subcritical with an apparent neutron source multiplication of ~ 3. å. Array was subcritical with an apparent neutron source multiplication of ~ - - - -. . ..! ; III . . , '';' l l lin!! (t; 8; 0; 1)." C!!!In where -- x 5 average unit in array described in Table III, In total number of units in the array, t paraffin reflector thickness, cm, 8 surface separation of units, cm, DI average uranium denuity in array, g of oms, and e ratio of array height to the square root of its base area. m.com ----- .! ! . . Comparison of arrays with equal numbers of units and the same reflector conditions reveals the expected Inverse relation between the average uranium density and the unit shape, the array shape and the mass of the unit. . - . 4.2. Partial Reflection The effect of a 15.2-cm-thick reflector on three sides of an array, "cor- | i brilli ner reflection," was investigated in two assemblies of units having averagë masses of 20.9 kg and a height-to-diameter ratio of 0.94. The results are given i logotiposo in Table V. The average densities of these two arrays may be compared to that of the critical array (2.5; 5.710; 4.292; 0.96) from Table IV and the inter- polated array, 07 (2.5; 11.53; 1.87; 0.96), which allows one to conclude that the thick reflector on three sides of the array was slightly less effective thani was one 2.5 cm thick completely surrounding the arrays. 4.3 Comparison of Array Patterns 4.3 Com Tight and twenty-seven unit arrays were employed to explore the effect of . changing the lattice cells in regular arrays from rectangular parallelepipeds to ! cubes. Pour arrays were constructed each with the units located at the corners of a cube. These arrays are described in Table VI where, for comparison, are aloo the dimensions of arraye of the same units located at the corners of rec- tangular parallelepipeds. The errays of A and Bl units in cubic pattern could not be made critical. As expeoted, arrays of CC and of co units were critical at substantially the same density in both patterns since the units were of appzoximately equal height and diameter. The uranium denoity in the array of de units at equal center spacing, however, was less than that in the array at equal surface spacing. The results suggest that, given a number of units, if the maximum achiev.. able density with equal center spacing 18 less than the critical density at equal surface spacing, the array at equal center spacing cannot be made critical. . . 3. This critical array is an interpolation between critical arrays of twenty sevenow units with 1.3 and 3.8-on-thick paraffin reflectors. ! ... : 12 Il Pin ! ! • Table V. Critical Conditions for Arrays Partially Enclosed in a Reflector Surface Separation of Units (cm) Average Uranium Density in Array (8/em>) Ratio of Array Height to ✓ mage Area Array Description Paraffin Reflector b . , : 0.96 ca (2x2x2) - chem (3x3x3) ö 5.398 1 0.013 4.538 20.542 10.541 + 0.013..* 2.028 ::. 097 . a. The letter and the superscript 1.dentify the average unit in the array de- scribed in Table III the subscript is the number of units in the array. 0. The dimensions of the base reflector were 76.2 x 76.2 x 15.2 cm and of the two sides were 76.2 x 45.7 x 15.2 cm. c. The dimensions of the base reflector were 106.7 x 206.7 x 15.2 cm and of the two sides were 106.7 x 76.2 x 15.2 cm. ,,.,.' Table VI. Comparison of Uranium Densities of Unreflected Cubic and Rectangular Parallelepiped Arrays i Average Uranium Center, Surface Spacing” (cm) Density Spacing In Array (cm) Horizontal Vertical (g/cm3) Array Description Ratio of Array Height to Babe Area Ratio of:.. Unit 1 Height to I Diameter 1.00 Aay (3x3x3) .... .. B (2x2x2) BASES . 0.47 6.127 i 6.877€ 2.007 7 .767 3.417 20.3348 11.5090 .. 2.007. 19.494 0 0.902 23.503 . 1.997 0.55 1.00 0.73 0.70 11.374 0.70 0.902 2.738 ..!'.';1!.*.!! op (2x2x2) 8.513 1.00 0.94 2.248 0.95 0.94 or w now or com 27.602 1.00 0.94 chany (3x3x3) cộn (2x2x2) 2.248 8.514 6.837 3.828 6.363 : 3.627 2.319 6.675 3.543 6.806 6.1.18 6363 4.269 3.543 0.94 0.96 1.00 1.13 15.778 - 1.17 *...**** 1.17 a. The letter and the superscript identify the average unit in the array de- scribed in Table III; the subscript is the number of units in the array. bo. The error on all spacing values io + 0.013 cm. 0. Array subcritical, maximum apparent source neutron multiplication ~ 70. d. Array subcritical, maximum apparent source neutron multiplication ~ 81. --- have wrowe, ani de canal..... : 4.4 Unit Shape A brief study was made to determine the effect on the critical dengity in 1,..., eight-unit arrays of changing the shape of the units. For one experiment, Bu units were constructed from three 5.2 kg cylinders arranged coaxially, with one of smaller diameter (9.1 cm) between two larger ones (11.5 cm). The critical density in both reflected and unreflected arrays of these irregularly shaped units was greater than that in arrays of regular B-units. In an unreflected array of c? units, formed with a piece of larger diameter, 11.5 cm, between two pieces 9.1 cm in diameter, the critical density was also larger than in the 'un reflected array of o2 units. The densities of arrays of ca and CS units when reflected by paraffin 15.2-cm-thick were approximately equal. In another experiment the units were the cº units of Table III, having a Magd of 21 kg and a height-to-diameter ratio of 1.90. The resulting critical densities of both the reflected and unreflected arrays were greater than those of arrays of more equilateral cylinders. The data are compared in Table VII. Figure 3 shows the average uranium density as a function of the surface-to- volume ratio of the units. In each case the change in geometry of the unit i i.! : :: ..opni.indeed value mi If the effect of array shape is neglected, these results indicate that reducing the kare of a unit in an array will require an increase in the array density to maintain criticality. . . . . . . . 4.5 Array Shape The effect of changing the geometry of an array is similar to that observed for individual critical assemblies, i.e., a change in surface-to-volume ratio 16 accompanied by an inverse change in made to maintain criticality. The shape of " a critical system of unite may be altered in two ways, both requiring a com- pensating change in the array density. The array shape, x, may be changed either by assembling different numbers of units along ito three directions or : oy altering the nid of the units within an array. Examples of varying the array shape by altering the height-to-diameter ratio of the units are found in Table IV where any of the At or AC arrays may be compared to the corresponding A3 or Aarrays. In these comparative arrays ... there has been a gube tantial change in the values of hid and of r with only a slight change in array denoity and en insignificant change in total mass present (less than 17 & per unit). The c* units of Table III were used to explore the effect on the critical uranium density for values of r differing significantly from unity. The critical conditions for the various arrangemente are given in Table VIII with, for comparison, the critical densities interpolated from data of Table IV, in arrays having the same total number of units, were it possible ...... ..io...cm . . .. . . . . . . - ... 1:1;:18:11. AITORT f11 11:17 All!!! ilti t ipai '!J1A811: Lili i Table VII. Comparison of Critical Densities for Various Unit Shapes. Paraffin Reflector Thickness (cm) Array Description Average Uranium Density In Array (g/cm3). Surface Separation of Units (cm) Ratio of Unit Height to Diameter Ratio of Array Height to Base Area 1 - 0.70 - 0.902 7.823 ; 0.72 0.82 15.2 0.70 . -- -- 0.229 :.. love | 11.374 2.645 11.497 2.792 ! 8.524 1.669 -.- 0.85 0.90 • • N 2.248 0.95 15.2 a cor do com online 11.986 . Ina 0.97 ... : 15. 15.2 8.941 1.668 1.013 10.945 1.466 10.328 5: 10.002 ..013 1.90 1.90 1.77 15.2 1.42 a. The letter and superscript identify the average unit in the array described in Table III; the subscript is the number of units in the array. The irreg- ular shapes of the BJ and C5 units are also described in Table III. ..: b. The error in the separation of units in the unreflected arrays 18 + 0.013 cm; in the reflected arrays it is + 0.026 cm. 1 -. ..... • - ...... .- .... O? De smaramia .. . R i . . : o . .-1............ 1 NIPPO 11 Dr. . - UTIT 10 TI " P ' . S 39 124 . TI OUDULLULUU - "Y"TIT 1.. 1T M 1"- . IS ENJA 11 - WO 11 17 . To the Shape of Uniis on the Certical Densitions in Reflected and Ko . O 10t011 DO VI ADID NOONDONI DU 11 PPDI 310 Effect of the Shapelbil Units on the Critic Mrraus WUI Surface to volume Ratio of Units . .1 ITD. 1 H H ** * * . 1: 1 1 : PIST 10.0mm LIDE 1 . . ITIL ol IBLIOL . Q0 . 10 . 1 UNDIT UUDU 010 UITDU1102 DIIDID 11 LUDDD Inh. DIOT PIIIIII IDUDU 01001001 NITI DI 3 NITA ONDO 0011 IND 0 JU TODO DONUDA 1 TIT 1 OULUI LIMO LUI . 1 U ' 1 1 UNULUI TIT LE . DO1 LI 11 TIPO HUILEHTI HIM TY 1 1 1 1 0 LIST + .- Fiq3. 1. ur BATI RONDDD DU ILLUDOUITDA IIDU III LUN US tone 17 . le ME Se . Uraniura Deusin, iri Array (glemy) MILLIMETER :.. ☺ ... . . .. : MADE IN U. SA EUGENE DIETZGEN CO. NO. 341-M DIETZGEN GRAPH PAPER ; ... luni i Table VIII. Effect of Array Geometry on Critical Uranium Taole Valdo Densities in Unreflected Arrays of U(93.2) Metal Units i : Surface Separation of Unitab (cm) Ratio of Array Height to Baje Area. Average Uranium Density in Arrays of Identical Units (c/cm) Unequal Number Equal Number of Units in of Units in Three Three Dimensions Dimensions Array Description 0.35 .. : 12.232 :- 8.514 - .. 0.31 . . 12.400 7.83 . 0.64 -.. 5.212 4.97 .-..- . 2.91 6.008 5.38 ... . hoe het (2x4x1) Co (3x3x1') 06 (3x3x2) 06 (2x2x4) C16 (2x4+x2) 016 (4x4x1) 416 (2x2x4) AS (3X3X5) 2.0628 0.658 4.642 3.907 3.891 2.516 1.349 3.442 . 0.67 6.027 5.38 ... -------------- 1.526 . 10.059 5.38 0.24 1.05 9.442 10.50 . 0.99 5.313 5.70 as The letter and superscript identify the average unit in the array described ! in Table III; the subscript 18 the number of units in the array. D. The error on the separation values is + 0.013 cm. C. Interpolated values from Table IV. ä. . This array consisted of two clusters of tour units each with lateral surfaces in contact. This dimension to the horizontal separation between the two clusters . here to be more fe reason betweetened two faces .. -. - - .. - .- . . .... ******* cm------ ... . . . . . . - . . . . - -. . . ... ... ... . . - . - - . to arrange them with equal numbers in each dimension.' Arrays of AL and A? units, constructed to produce r values near unity, are also presented in Table VIII. The results indicate that the axray reactivity is more sensitive to changes in array shape than to changes in the shape of the unite themselves. 4.6 Array Moderation The effect of hydrogenous material, placed between adjacent units, on the critical dimensions of arrays was examined in assemblies of units having an average mass of 20.9 kg. Boxes of several sizes and wall thicknesses, fab- ricated from Plexiglas and described in Table IX, were mounted on the rode supporting the uraniwn unite. In each Instance the unit was centered in its container. The data for the critical configurations appear in Table X. : An investigation was made of the effect on reactivity of the thickness of : yárogenous material separating adjacent units. A system of eight ce unite, each in a pu box, assembled at an average density of 1.189 g/cms and surrounded by a 15.2-cm-thick paraffin reflector, was subcritical. The reactivity of their array increased as the thickness of the container walls separating units was increased until the total thickness of the Plexiglas was 4.9 cm. Further in- i crease reduced the reactivity. The detailed results of the experiments are shown in Fig. 4 where the reactivity of the array is expressed as a function of the Plexiglas thickness, including the walls of the pul boxes, separating the units. The uranium density as a function of the total thickness of Plexiglas between adjacent units in the eight unit arrays surrounded by reflectors of various thickness are given in Fig. 5. The points shown at 3 and 7 cm on the thick paraffin reflector curve were obtained from Fig. 4. The addition of a 15.2-cm-thick paraffin reflector to an unmoderated array reduced the critical density by a factor of about five; the insertion of a 4.8-cm-thick Plexiglas moderator around the units of an otherwise unreflected array reduced the criti- cal density by a factor of four. It is emphasized that this added moderator surrounded each unit and, consequently, introduced hydrogenous material into the reflector region. It may be observed, however, that simultaneous addition !....... of a thick reflector and optimum moderator reduced the critical density to only 1/8 that of the unreflected, unmoderated array. It 10 clear that the separate effects do not combine directly. 4.7 Mixed Arrayo A brief but important exploration was conducted to determine the effect on array reactivity of varying the geometry or mase of a single unit in a : i - . --- . . *** --:-- - .... .. Tablo IX. Dimensions of Containers for Unito in Moderated Arrays Wall Inickness (om) Container Designation Outside Dimensions (cm) Baso Height Material : .. Plexiglas 12.01 . .... . the Plexiglas 0.64 0.64 1.27 14.8 12.9 x 12.9 15.6 x 15.6 17.9 x 17.9 21.4 x 21.4 ...... ... Plexiglas 27.2 .. not on .. . Plexiglas 2.38 20.7 ... o Iron* 0.66 14.1 diam. 13.2 ! : *5-in. Schedule 40 Iron pipe provided with end plates of thickness equal to the pipe wali. ... - - 75. - . . .. . . ! - --------. --- --- --------...... . --- --. - --.. - ... - .. -- .. ----- . ...... ------- ..... .. .. PT1":.00 pollini Tablo X. Critical Conditions for Moderated Arrays of 20.9 kg Unite Paraffin Reflector . Thickness (cm) Sw.face Separation" of Unitab Average Uranium Density in Array (g/cm3) Description of Array Ratio of Array Height to Base Area (62- 5.810 1.532 0.95 0.97 15.2 1828) 0.95 . os 1.3 7.6 12.573 ... 5.635 4.270 1.549 1.482 3.670 0.97 15.2 0. -- .... .. 4.082 12.662 4.239 5.875 12.929 6.619 8.611 14.503 16:31 16.289 Ponpolg ... 0.96 -..- 2.673 0.96 : rop allery 1.226 -. -.. 2.110 ro².ph) (032-rP27 . 0.97 0.97 0.97 0.97 15.2 0.986 2:..- . . com 1.000 . . ::: -.- . . . 6.884 0.95 - . ... (-81) (02-st-ple 3.239 5.169 - - . . o 4.732 0.96 . - - . The first letter and superscript identify the average unit in the array de- scribed in Table III; the second letter and superscript identify the con- tainer (Table IX) in which each unit was centered; the subscript 18 the number of units, in the array. . The error in the separation of the units in the unreflected arrays in + 0.013.,cm; in the roflected arrays it 16 + 0.026 cm. .. .. .. .. . - . . . - 11:. !II.11.11 لا مسسان سس ہنسن 21 . UNCLASSIFIED ORNL-OWG 64-4292 MAXIMUM AT ~ 4.9 cm . REACTIVITY (arbitrary units) · 1 5 9 fi 2 : 3 4 TOTAL THICKNESS O 6 7 8 AS BETWEEN UNITS (cm) :... Figt The Effect on Reactivity of tanging the lo Thickness of Planxiglan Between the 2.09 kg Metal wists of a Paraffin Reflected sights unit array . :. .: :.:. DO 22 INCLASSIFIED ORNL-OWG 64-4296 . - URANIUI! DENSITY liv ARRAY (g/cm') - 1.3-cm-THICK PARAFFIN REFLECTOR WUNREFLECTED ARRAYS :- -- FROM FIG. 15.2-cm-THICK PARAFFIN REFLECTOR oo 3 2 8 9 . 10 . TOTAL THICKNESS OF PLEXIGLAS BETWEEN UNITS (cm) Rothe Effect of Plaxiales as a modercitor Fort i and Paraffin ao. a ictecctor on the Critical Drinity .. .................17 - ..., :01. an 'Egluto.cout Arany of 20,9 key.seminte pohod...pono......com.v9** **. d o.com temamo. Savopumper pro poser ?, ?.., L ." In die € Page 21 Pov 22 01.11 riske Lithium critical array and of combining portions of different critical arrays. In one experiment the central unit of the critical array chn (0; 6.363; 3.8273 0.96) was replaced by a DC unit without a change in the lattice cell volume. The substitution of a unit having both a larger mass and a greater kete produced an in array reactivity increase in excess of 1.5 dollars. In the second experiment, the central unit of the critical array Ban (0; 4.204; 5.185; 0.78) was replaced by a B* unit and the cell volume maintained. Although the uranium content of the B* unit was 124 g more than that of the B' unit, its karp was less and the replacement, resulted in a decrease of about 5 cents in the array reactivity. . . Additional experiments used parts of critical eight-unit systems to 111ustrate the effect of multiple component replacement. In these experimento il one half each of two different critical arrays were brought together along a common center line until their cell boundaries coincided. The units of one of the critical arrays were right circular cylinders of aqueous uranyi nitrate solution contained in 0.64-cm-thick Plexiglas vessels 20.32 cm in outside diameter and 19.05 cm in outside height. 'Each unit' contained 2.06) kg of uranium enriched to 92.6 wt% 2350 at an H:-30 atomic ratio of 59. ALTAMIL.NO Three assemblies of mixed units were attempted. In one, four ol units of T. the critical array c (0; 2.248; 8.514; 0.95) were assembled with four of units ! .. of the critical array Da (0; 3.542; 6.806; 1.18). In another, four of the solution units at their critical spacing were mated with four units of the cri- tical array of one units; the composite array is shown in Fig. 6. In a third, four of the solution units were combined with one half the critical array Co (0; 1.466; 10.002; 1.77). Tach of the composite arrays was more than one dollar subcritical. The array of solution units and C units was made critical by reducing the spacing between the c units from 2.248 to 1.689 cm. . 5. Series III - U(92.690,(NO2), Aqueous Solutions The units utilized in this series of experiments are described in Table XI! I for convenience. The volume of solution present in each of the units was care- fully adjusted to 5.000 liters by weighing to + 0.5 8. The 2393 content of the uranium was 92.6 wt%. The data describing regular three dimensional arrays are presented in *** Table XII. A majority of the experiments was performed with the full units of solution having an H:?5%u ratio of 59. A limited number of experiments was performed with more dilute solutions. - . 4. See section 5 for a complete description of critical conditions of arrays of these units. Pi!!!:,:..AI1919 ... -----... - ----- -oramot . Nowed. * 60 NCHES . - min. 39'. :.'.- a F .. ........... eminteaias. m . . . . . .. · .. . - Fig. - - - "... ---.. . . . . . . . . - ..- .-.- :. of voz (NO ), Solution. Metal Units and Four 2.1-kg U(92.6) Units composite Array of Four 20.9-kg U(93.2), . Photo 70801 Cowan www.o. ... - und miniinisen minden . .. eatv. .. - KA 1 DAU Prelimilior ilinii Table XI. Description of Five Liter Unite Constituting Arrays - -- Containers: 0.64-cm-thick Plexiglas Cylinders 20.32 cm OD and 19.05 cm Outside Height. -- .. - Unit Designation Concentration 8 U per Liter Aqueous Solution . . Specific Atomic Ratio G:cavity H:2590 Uraniumi Mass, kg 415 1.555 59 2.074 -- 279 279 . 1.373 1.395 - - pag 63.3 1.083 440 0.316 I'tindirildi 2. Content of each unit was 5.000 + (3 x 10") liters determined by weighing ·to + 0.5 8. isa116HUMI - - - - coco. 29:55 Lii- . - . . - . - - . . - - - .-. . . - . . -.- . - . .--.- page Jug AAL 241,00 - ܚܚܚܚܚܗ.- Ilarrillos 1.0111! tillo1YPalla ..' . . . . lio ilegal de resort Ph:. : . Triinu till halt 10 most birto ! IloIl culonan 11 Table XII. Critical Conditions for Regular Three Dimensional Arrays of U(92.6)0,(NO2), -Five Liter Solution Units with various Paraffin Reflectors. i Para plin Reflector Thickness (cm) Surface Separation : Average Uranium Density in Array (g/cm3) Ratio of Array Height to Base Area of unitab Array Description., (cm) F (2x2x2) 1.43 1.3 3.8 0.214 0.167 0.108 0.092 0.087 7.6 25.2 óóóóó o o ó ó po (3x3x3) 0.114 0.006 1.3 15.2 0.055 0.072 10.67 14.40 0.052 : 0.96 .............. FZL (4x4x4) P125 (54585) erine (2x2x2) PS, (3x3x3) Sony (2x2x2) 1.43 8.72. 0.144 0.060 0.94 0.96 ........ o 6.40 0.077 0.95 . o 0 0.0€ 0.040 · 0.94 0 Fin (3x3x3) 2.41 0.029 0.95 Faze (3x3x3) 6.41 0.107 0.95 a. The Letter and the superscript identify the average unit in the array de- scribed in Table XI; the subscript 16 the number of units in the array; the numbers in parentheses are the horizontal and vertical dimensions, respec- tively, of the array expressed in number of units. 10. The uncertainty in the values of the separation 18 + 0.13 cm. The separation was 16.91 cm where one face of the array was reflected by Plexiglas 15.2-cra-thick. d. The array was reflected on the bottom by 15.2-cm-thick paraffin. 8. Array suboritical kere ~0.6. f. Five control units in center tier are units and remaining 22 units are fa. 21. ä olis ... ga ... di ripror; isl ...! ! :1.! 1 iii The behavior of the arrays parallels that of Individual critical units with respect to variations in concentration. Each of the critical arrays Feat :(0; 1.43; 0.214; 0.94 ) and to 10; 1.43; 0.144; 0.94) contained solutions of different uranium concentration although they had the same lattice volume, and the same total volume, within the uncertainty of the measured separation dis- tance. The total mass present, however, differed by about 33%. The H: 350 ratio of the solution constituting these arrays was within a range including the concentration at which the minimum critical volume of an unreflected indi- vidual unit occurs. Within this range only slight variation in the critical volume is observed, although the variation of critical mass 18 comparable to the difference observed in the arrays. The specific reactivity of an unit in arrays is, nevertheless, smaller than that of an fol unit. This observation was verified by comparing the critical array Porn (0; 6.41; 0.107; 0.95) to mann (0; 6.48; 0.114; 0.95) where it is shown that a decrease in spacing was "144. required when five of the units in the latter array were replaced by you. units. . . The specific reactivity of a unit in an array 18 further reduced by de- creasing its uranium concentration as shown by the eight and twenty-seven unit arrays of units. 5.1 Some Planar Arrays Several other experiments were performed with two dimensional arrays of · Bolution at a concentration of 415 g o:f uranium per liter. Nineteen units arranged in a single tier with their centers in a triangular pattern were cri. ! tical, unreflected, at a unit surface separation of 1.35 cm. It was observed that 16 units in a single tier, in contact, arranged in a square pattern, and unreflected were subcritical with an apparent source neutron multiplication of approximately 6. Four units in a single tier, square pattern, with a surface separation of 3.94 cm were critical when surrounded by a 15.2-cm-thick paraffin reflector at the cell boundaries. 6. Series IV - U(4.9)0F. Aqueous Solution? The experiments reported in this section were performed with uranyl fluoride solution in which the <330 content of the uranium was 4.9 wt%. The concentra- . .*** tion, as in the series with V(92.6) solutions, was chosen to be as near that i estimated to result in a minimum critical volume for an unreflected individual unit as solubility permite. Aluminum cylinders 2461 cm-ID by 152.4 cm in height, having a wall and a bottom thickness of 0.32 and 0.64-om," respectively, ... - ... -- .... ... .. ... 1 . ... ... ... 5. This series of experiments was conducted by B. B. Johnson (4,5). los indikio pia!!!!") .. .. .. .. . . - . ..1 lililori - ---- ---- .. .- -- -- - - were used as solution containers. The effect of unit variation on the criti. cality of arrays was studied by filling the cylinders to different heights. ". A description of the everage units used in the arrays assembled is given in Table XIII. The physical properties of the polyethylene, used as a reflector, i ! and of the Plexiglas, used as a moderator, are given in section 2.2. The critical conditions for unreflected two dimensional, or planar, arrays are given in Table XIV. Although only planar arrays were assembled, significant; ! variation of unit hid ratio, of array pattern, and of array shape are presented. I Figure 7 16 a photograph of the critical array L. (0; 14.75; 0.276; 0.98). The container dimensions prohibited construction of arrays completely burrounded by a reflector at the cell boundaries. In one experiment, however, a 15.2-cm-thick polyethylene" reflector was placed, at the cell boundaries, on the lateral surfaces of a 3 x 3 x I. square array. The unit surface separation was 11.94 cm and criticality was achieved when the solution height in three " control cylinders, constituting a center row, was 132.6 cm. The remaining six cylinders had a solution height of 142.2 cm, the Ivy unit of Tablo XIII. In another experiment, the thickness of Plexiglas for optimum array moder- ation of these units was determined.. An array of nine L' units, in a square pattern, spaced at 15.46 cm with a 15.2-cm-thick polyethylene reflector on the four lateral array boundaries was subcritical in the absence of a moderator. Variations in the thicknesses of Plexiglas centered between the units produced i critical arrays with different solution heights in the three control cylinders. The results are shown in Fig. 8 where the control cylinder solution heights, normalized to the height with 1.3-cm thickness, are given as a function of the Plexiglas thickness between adjacent units. The loved minimal portion of the curve shows that 1.5-cm-thick Plexiglas produces optimum moderation of the array: of these units. 7. Calculational Methods A review of the various methods of computing the criticality of arrays 18 not required in order to reveal that those methods limited to the neutronics to individual subcritical units and relying on geometric proportioning of leakage neutrons are inadequate to cope with reflection, moderation and other array 1:04. modifications. For this reason the application of Monte Carlo codes, or methods treating the neutronics of system criticality rather than of subcritical units, are preferred. Tho Monte Carlo codes and an analytic code have been applied to a representative group of experiments from the series in this paper. - -- - ----- - roc -. - ... - - war . Lt -. • ATT Ir aripy portion www.in. men med enero 1:1,%:11 10" A11911 . m XIII. Description of Units Constituting Arrays : with U14.980,7, Solutions Aluminum Containers: 24.1 cm Inside Diameter; 0.32 cm Lateral wall thickness; 0.64-cm-thick bottom; 152.4 cm high Solution: :0(4.990 F.; sy.com : U(4.9)0 Fai sp.gr. 2.0001; 901.38 8 of U pey Ister H:2350 - 496.6 . . - bla - - - Solution Height (cm) Unit : Designation Volume of Solution (11ters) Vraniwa Mags (kg) Ratio .. 61.0 27.826 .--... .... 25.082 ..... 122.0 5.06 55.652 50.164 ...... 142.2 .. 5.90 ...::: 64.867 .. ... 58.4701 : . 10 --- - - -- - -- .- - --- --- - --- -.-- :- . Ilir 1.111 illar DOST......! !Table XIV. Critical Conditions for Unreflected Planar Arrays of U(4.9)0,F, Solution Vilts Ratio, Average Uranium Density in Array (8/cc) Unit Surface Separgtion (cm) 6 " Array Array Description Array Pattern Height to Vbase Area Tri. :1.89 0.649 0.96 - - - - or to - 8q. 1.32 0.593 0.80 .-- So 3.62 0.492 0.57 . --.-. Sa. 5.24 0.422 . 0.44 Tri. 1.37 0.689 2.27 .. 4.44 0.538 - ... 1.76 - - it to the who want to who not - Tri. .13.23 0.297 0.88 . . 4.85 0.452 1.43 . .. Sa. 9.16 0.333 0.97 . Sa. 12.42 0.270 0.72 ... . . . Tri. 1.47 0.684 2.63 to view TrL. 2.00 -... .. 5.11 14.75 0.524 0.276 Thi. " si Sq. Sa. 5.61 0.429 0.98 1.62 1.08 . . Sa. he 20.44 0.310 . - . 8q. 14.12 0.80 . . - - - a. The letter and superscript identify the average unit in the array described in Table XIII. The subscript is the number of units in the array. B. The uncertainty in the separation values to + 0.08 cm. - 301 . SAV :. : inn - - -- - - - - - - T: --- - - - roma ---- --- Photo 71552 -. . . --- . m ...- ... . “Fig. 7. A View of the Unreflected Nindteen-Unit] Array of U(5)0 F, Solution in a Triangular O Pattern. Each unit contains-58.5 kg of U. Bon T um ...3.. **166.... - en La L :" · -. - : -??. !.... 11 V . A . فنانانمسیون نفل سنننلننضم م. المملے، . - 1 * L 1 LU 1 i 1 E . ,!1! 2 1 1 1 111 1 . 0 1 . Vlinders of Vamping the implem ntia ween: 58:15 R isolution Units balap Reflected Ninehuu Aray # Hil 1 . betwe 1 1 1 . It! r TIL . Uli 10 1 1 0 . Il ( G . 1 . 1 1 .. . . I 1 - . . . . U OND .NL ALINA . ITS 10 . . . LI . ih itib ni TIT > : dii. NIIN w w 11 11 . totitor + ht LUN Ir. 22 IL XIranet M . THI KUI 00 é 0 1 0 0 i 20DDD UDIU DIRI DIONI UPDIURNO. 08m0000001 NILITO 1 €000AMRO III INITI DODDI. UDOVUTO 00 U ODINI11 LULU ON DO POI ... ... The Effect on Critical Solution Height wi Threc Control Cylinders of varying Varrying them the colores the Thickamion of Plexiglas Between 58.5 kg u Solutwin Nice-Chaint areal .. . mereka membeliny awarimi .. wüa? I pasya Page 3266 Fen8 .;!is, 1:1 Pildi.nl - - . . . . . . i . - - - - One of the Monte Carlo codes 1.6 GEMO, a neutronics code written for ..... the IBM 7090 computer. The GEM program Input is a simple description of the lui... material, unit, cell, and reflector. The system is divided in two by a neutronically important surface separating a 'core' from a 'reflector' which may not necessarily correspond to the true core-reflector boundary. In the program neutron tracking 18 done by stages, where a stage begins with the page : sage of a preselected number of neutrons into the core and terminates when all of the decendents of those neutrons reenter the core. The calculation provides the ratio of the neutron population, at the boundary, at the end of a stage to the population at the beginning. This ratio, together with neutron accountinga made at the boundaries during tracking, provides estimates of kore and other properties such as spectra and fluxes. The second code 16 the 05R, a general purpose Monte Carlo neutron trans- port program written for the IDM 70so and the CDC 1604A computers (6). Unlike 'GEM, 'the geometric input here is complex requiring the specification of all surfaces in the array. The program calculates the fission distribution from a batch of a preselected number of neutrons with a specified distribution in space. The resulting distribution is then assigned to the succeeding batch of neutrons and a new distribution calculated. This procedure is repeated for the desired number of batches. The multiplication factor is obtained by calculating the ratio of the number of neutrons produced in each batch to the number of source. neutrons, 1.e., kofe for each generation and then averaging it over all the batches. In this method a matrix of probabilities that a neutron in one region will cause a flssion in another region is used to determine when the effects of ! the assumed initial source distribution have disappeared. Only subsequent patches are used in computing the multiplication factor. The output of OSR is, In addition to the k n, a history of all the collisions from which the spectra, fauxes, and other measurable quantities may be obtained. In the application of the program to the experiments considered here, a simpler treatment utilizing monoenergetic neutrons and assuming isotropic scattering has been used. Mihalczo (9) has shown that when only the multiplication factors are to be calculated this treatment is reliable for a single material in unreflected, complicated geometry The third code is an analytic program prepared by Clark (7) for an IBM 704 computer and has been described as a pratical method for computing neutron inter- action in groups of fissionable units. The approximations made to simplify the calculations sufficiently characterize it and are the following. "A one-group . immer ó. Private communication from A. J. Rockwell and P. J. Hemminge of the United Kingdom Atomic Energy Authority, Health and Safety Branch. See (10) also. i t; : :. spacial distribution of neutrono le assumed to satiafy the wave equation. The unit and cell are replaced by a sphere and by a cube, respectively, of the same volumes retaining thereby the uranium density of the experimental array. In the calculation of reflected arrayo the reflector 16 assigned the actual dimensions of the experiment and an albedo. The value of the albedo 18 that of an infinite slab, having the thickness of the reflector used, on an infinite slab core of. fissionable material with the same composition as the units. The emitted and incident neutron currents in the array are treated as though they were uniform over the entire surface of each unit. The angular distribution of emitted neutrons is assumed proportional to the cosine of the angle between the direction of emission and the normal to the emitting surface element. The extent of the array considered in the calculation 18 limited to those units, which, either by complete or partial shadowing, intercept all emergent neutrons. A boundary condiltion employed is that the incoming neutron current for an unreflected isolated unit is zero in order to express the total transport cross section in terms of an extrapolation distance which is con- sistent with the unreflected critical size and material buckling of an indivi- dual unit having the same composition as a unit in the array. The program computes the maximum eigenvalue of a set of homogeneous equations for the neutron currents as a function of the spacing and of the reflector albedo. A display of typical results from the application of these codes to the experiments of these series 18 presented in Table XV. The group of experi- ments represents a wide variation in both unit and array properties. 1 ! ! -- - - --- - 8. :. Conclusions Regular three dimensional arrays may be characterized as low density in- dividual critical systems. The similarity 18 apparent when the data are expressed graphically as total mase ve. the average uranium density in the array. It is immediately evident, when the data are examined in this manner, that the effect of a reflector on an array depends êtrongly on the energy of the leakage neutrons. Although this observation is not surprising, the magni- tude of the factors by which the reflector reduces the critical number of units and the range of these factors 16 important to the handling of fibrile materials The factors observed in these experiments were about 13 for the metal unite, 9 ! for the U(93) solution units and less than 3 for the U(4.9) solution units. This enhanced reflector effect, compared to that occurring for individual cri- tical units, can be associated with the relatively high neutron leakage through the area between the units in an array The effect of partial reflection by a thick reflector, on the other hand, 18 rolatively small, and appears to not" violate the usual factors of safety. . - - - - -.- 1:11. Lil'!!' Table XV. Comparison of Three Codes for Calculation of Multiplication Factor for Some Critical Systems 027 0.975 1.102 - - 1.11!!,111 . . . ::. H. K. Clark Array Description . GEM 05R [7,8] AGM (0; 3.952; 4.693; 0.61) 1.005 0.971 Any 10; 2.007; 7.767; 0.55) 1.004 (0:0,902; 11.374; 0.731 012 BZ (0;0.229; 11.497; 0.85) 1.038 1.010 Ban (15.2; 4.204; 5.185; 0.78) 1.013 ca (0; 2.248; 8.514; 0.95) 1.019 0.959 (15.2; 11.986; 1.669; 0.97) 1.017 (0; 6.363; 3.827; 0.96) 1.023 0.995 0.987 (15.2; 19.147; 0.744; 0.98) 1.027 1.079 CO (0; 1.516; 10.059; 0.2435 . 1.018 0.993 ca to; 3.891; 6.027; 0.672° 1.023 (ca-st)g (0; 3.239; 6.884; 0.95). 1.029 (02-8-p?)g (0; 5.169; 4.731; 0.96) . 1.031 Day (0; 8.494; 2.980; 1.10) 1.017 0.991 Dan (3.8; 19.606; 0.817; 1.06) 0.972 Faro (0; 1.43; 0.214; 0.944). 1.006 F7 (15:2; 8.99; 0.087; 0.96) 1.022 1.051 (O; 10.67; 0.072; 0.96) 1.052 LG (0; 20.44; 0.310; 1.08) 1.001. - - (15.2; 11.94; 0.282; 1.4034 1.001 a. Program utilized monoenergetic neutrons and isotropic scattering. Units were arranged as (4x4x1). c. Units were arranged as (2x4x2). The reflector is on the 4 lateral surfaces of the array and the solut height in the three control cylinders, constituting a center row, 18 132.6 cm. --------- 1.014 .. .. .. lon ... .--- - .... - - --- ----- - - --- - Unit shape has less effect on array reactivity than does array shape. Large changes in the reactivity of unreflected arrays may be accomplished by .altering the unit shape, but these reactivity changes are greatly diminished by the addition of a reflector. The observed effect of array moderation by hydrogeneous materials 18 due to a combination of neutron energy degradation, neutron scattering and leakage, and neutron absorption. An upper limit of the factors by which the critical number of units in an unmoderated array is reduced 18 that observed for the metal systems. The factor was about 4 in the absence of a reflector and about 2 with a reflector. The data from the mixed arrays appear to be a demonstration of the con- trapositive of the result derived by Thomas and Scriven (11) for pairs of dissimilar containers of f1boile materials in air. In a mixed critical array consisting of equal portions of two other regular critical arrays, each com- posed of identical units, the separation of adjacent unlike units is less than the geometric mean of the separations of the like units - a result in keeping with the concept of arrays as individual Low density systems. The good agreement between the results of experiments and of calculatione siggests that calculational techniques may have reached a stage where the reliability of their results is suitable for application to safety evaluation problems. -. -.. E -.-.-.--... ----- ' --- ... -- . -.-. -- - - .-. -- .. - - . .-.- - - .. - - - ... - - - - ... .. . - - - . ... . . . . . . . .. . . . . . -. . . -. - . . - - Pilli TYPIN, . - - - 1.1..1!..!.,111!:, ·lis nila? Nijl: - - - - . -- - ROERENCES : 1146 - () Neutron Physics Division Annual Progress Report for Period 8p l, 1961, 1 ng ORNL-3193 p. 168-173. (2) MIHALCZO, J. T., Trans. Am. Nucl. Soc. 6 (1963) 60. MIHALCZO, J. T., Nucl. Sci. Ing. 20 (1964) 60-65. 141 JOHNSON, E. B., Neutron Physics Division Annual Progress Report for Period Ending Sept. 1, 1965, ORNL-3858. JOHNSON, E. B., and CRONIN, D. F., Trans. Am. Nucl. Soc. 1 (1964) 301. (6) COVEYOU, R. R., et al., A General-Purpose Monte Carlo Neutron Transport 965). 11:1 17.';fonte 17? CLARK, H. K., Nucl. Sci. Eng. 15 (1963) 20. (8) CLARK, H. K., Nucl. Sci. Eng. 20 (1964) 307. (9) MIHALCZO, J. T., Trans. Am. Nucl. Soc. 8 (1965) 201. (10) WOODCOCK, E. R., et al., Session 6 in the International Conference on the Applications of Computing Methods to Reactor Problems, Argonne Natiora 1 Laboratory, May 17-19, 1965. (11) THOMAS, A. F., and SCRIVEN, R. A., in Technology, Engineering and Safety, Progress in Nuclear Energy Series IV VOL. 3, Pergamon Press, London 1960, 253-291. ---- --- .......-- --- Rill19 17p'lilii "1.4.!1.'m111331 1. - END DATE FILMED 12/ 0 / 65 * . . • . I' .' .A . . -- -- i. - -- - -- .. --- - - :. :. :.::.: : 1 .