Array, fissile units

Failure to allow for neutron transmission through concrete between tiers or layers of arrayed fissile units. Calculations reported by Thomas and by Welfare have indicated that as much as an 6-in.-thick layer of concrete is not a general isolator. 

VII. Neutron Interaction between Fissile Units in an Array. 94... 

VII. NEUTRON INTERACTION BETWEEN FISSILE UNITS IN AN ARRAY... 

BOUDIN, X., et. al., Rule relating to the mixing of planar arrays of fissile units . Physics and Methods in Criticality Safety (Proc. Top. Mtg Nashville, TN), American Nuclear Society, LaGrange Park, IL (1993) 102-111. 

Unmoderated lattices with a density of 0.06 would require 146 5 units for criticality, while those with a density of 0.023 would require 250 a 30 units. In lattices in which the fissile units are separated by 1 in. of Plexiglas approximately 27 units would be required for a critical array with a lattice density of 0.06 and about 75 units for a density of 0.023. Distributing Foamglas (containing 2% boron) throughout a moderated array increased the critical number of fissile units by a factor of 6, while Styrofoam had a small effect. 

If the number of fissile units required for high subcrltical multiplications in a specific lattice type is known as a function of the lattice density, and if a good estimate of the critical number of fissile units for one lattice density Is available, the critical number of fissile units for other densities of that lattice type may be predicted. The number of fissile units required to produce a given inverse multiplication for the unmoderated and moderated arrays as a function of lattice density Is shown in Figs. 1 and 2. (See figures on next page). 

Interaction In Reflected Arrays, H, K. Clark (DuP- SR). A simple technique for rapidly computing the interaction between fissile units or between a fissile unit and a reflector has been preVlpusly described, and is now extended to the general case of reflected arrays such as are often encountered in nuclear safety problems. The technique is illustrated by calculating the critical spacing of 20-kg enriched uranium spheres in a 2x2 X. 2 array enclosed by a concentric hydrogenous reflector as a function of the effective radius of the reflector.. 

Fig. 1. Ratio of surface density to critical slab thickness as function U concentration in fissile units for water reflected planar arrays of cylinders.

To safely ship and store large numbers of fissile units, the critical reflected array size must be determined for each mass, spacing, and internal moderation of the subcritical unit imder consideration. 

G (Geometry) this parameter involves the shape of the fissile unif. The most reactive shape for an individual fissile unit is a sphere for cylindrical objects, the most reactive shape is an aspect ratio (height/diameter ratio) of about 1 (buckling equations give the optimum as 0.924 for bare cylinders). For arrays of imits, the optimum H/D can be situation-dependent. 

An indication of the interaction of multiple fissile units— usually either a single unit, a lattice arrangement (i.e., of fuel pins), or an array of the basic units. 

This summary. reports two critical experimonts with cubic arrays of individually subcritical units of fissile materials Intended to further establish bases for regulations governing their transport and storage. Preliminary experiments in this program were reported most recent by Gilley and Thomas and by Mibalczo and Lynn. ... 

H. C. Paxton, has noted an empirical relationship between the critical volume per unit base area, or surface density, of an air-spaced plane array of discrete units of fissile material and the critical thickness of a uniform slab of the same material. It has been proposed that this relationship be used to establish safe spacing criteria by limiting stored units to some maximum fraction critical and the surface density to some fraction of the critical, uniform slab thickness. The fraction critical is defined as the ratio of the mass of a single unit to the bare critical mass of the same fissile material in a similar shape. In a more recent study, Gutman noted the complex behavior of arrays of metal units but suggested less conservative criteria than Paxton, for application to solution systems. 

Figure 1 illustrates the marked effect of the density of the fissile material in the stored units on the ratio of the surface density (ta) of the array to the critical thickness (tc) of the reflected slab for units at 0.3 fraction critical. Other calculations,-not illustrated here, for tall cylinders of enriched uranyl fluoride solution with, fraction critical values ranging from 0.035 to 0.8, show. that the surface density does not approach the critical, reflected slab thickness until the fraction critical falls below 0.1. 

The mockup for Curve C was identical to that of Curve A except for the unit shape. Instead of the solid cylinder, a hollow cylinder (H/D = 1) of equal mass with a 1469-cm central cylindrical void (this void never contains water) was used in the 6x6x3 array. As can be seen, there are several differences between Curves A and C, the most important of which is that the array of solid cylinders is more reactive when dry, but the array of hollow cylinders is more reactive when both are optimumly moderated. This reversing will cause considerable difficulty in choosing an appropriate array unit to be used in calculations needed to demonstrate the criticality safety of an actual plant array consisting of numerous forms of fissile material. 

This paper presents Monte Carlo calculations by both the GEM 4 and KENO codes for critical arrays of 2, 3, and 4 kg plutonium metal pieces and critical arrays of lOL and 3L Dow type shipping containers of fissile solutions, These calculations indicate that the assumption of a water reflector, as specified for Class n and ro shipments in Federal and IAEA Regulations would result in a critical array of metal units three times larger than one reflected by concrete. Care, then, must be exercised when shipments that meet regulations are to be stored within concrete enclosures. 

Figures 1 and 2 illustrate the results of an attempt to correlate the surface density at which the array is critical with the surface-to-volume ratio of the. identical units comprising it. The results for semi-reflected uranium spheres agree very well with values ujxin which this concept was based in 1957. These plots are useful since conditions represented by points underneath the curve are safe (non-critical). One has only to measure the dimensions of a storage unit, calculate its surface-to-volume ratio, weigh it or know its density, and employ these curves to obtain the allowable spacing. Extension of this method would seem to be indicated for other fissile material for example, oxides, alloys, or aqueous solutions. The application of this method is discussed.

Tliis approach is limited to the extent that for the smallest data spread the fissile systems of the units should be well moderated (small water -gaps for under-moderated systems can result in k values greater than k ,). However, fuel elements or containers of fuel elements vdiich consist of sliE tly undermpderated lattices can be included by making the limiting curve someiAat more restrictive. A number of different infinite arrays... 

The use of noncubic storage arrays for fissile material is highly desirable since it could result in a better utilization of floor space as well as provide easier access to all material, Therefore, five useful large arrays were investigated calculationally square based, vertical racks, rows, planar, and an array of arrays. These arrays show that consideration of optimum moderation will produce results that can be tolerated easily. The l sic array unit in the investigation was a 20-kg uranium metal cylinder (H/D 1), enriched to 93.2 wt% in U and centered in a 20-in. cubic cell to simulate 20-in. birdcage spacing. 

The body of information on the criticality of sub-critical components of fissile materials arranged in reflected critical arrays has grown sufficiently in the past ten years to warrant examination of. density techniques and understanding of concepts employed. in nuclear criticality safety. Monte Carlo calculations of experimental data have permitted valid extensions of these limited data. Correlations of the data have been effected and have resulted in an analytic expression relating the total number of units, N, in an array, the edge dimension,... 

In those relations, u(m) is a limiting surface density (g - crii ) m is the unreflected critical mass in the geometry of the unit n is N c is a constant characterizing the geometry ot center spaced units and equals 0.55 C2 is a constant dependent on the type of fissile material and is Influenced by the unit shape, by (he array shape, and by the array reflector material. 

It may be said that the density methods can give complementary interpretations of criticality. The two constants, one for geometry and the other for fissile material as spherical units in arrays, are sufficient to represent criticality as... 

C. L. SCHUSKE and HUGH C. PAXTON, History of Fissile Array Measurements in the United States, to be published in Nucl. Technol. (1976). 

For a single array, neutron interaction was investigated for planar arrays of cylindrical units of highly enriched UOxF, and for IXlriNQi), solutions and for water- and concrete-reflected cubic arrays of spherical 11(93.2) metal units. Figurb la contains results of unit interaction of the three fissile materials. These data show that the safe-curve" for unit interaction recommended by TIO-7016 (Ref. S) cannot be applied generally to reflect cubic arrays of large numbers of units. 

Neutron interaction corves for the nine-cubic-array systems are presented in Fig. lb. For comparison, the interaction between taro square planar arrays of lK>2(NOa)2 cylinders is also shown. Although the interaction curves for the nine-array system were obtained for U(93.2) metal, they are applicable to 46 different fissile materials. Due to the generic nature of reflected arrays, the uranium metal units in the cubic arrays may be replaced by equivalent units of other fissile materials... 

A tabulation of minimum critical values, including mass, volume, dimension, concentration, and enrichment, starts the second lecture, which continues with the Influence of density and dilution Of fissile material. The balance of toe session is devoted to interaction between subcrltical units, the criticality of arrays, array moderar tion and reflection effects, and the effective isolation of units by neutron-absorbing materials. 

The Laboratory s neutron absorber for lining fissile-material storage containers is strong and pliable at room temperatures and will survive even the severe conditions of a fire without losing its neutron-absorption properties. It costs less to produce than commercially available materials and is easily adaptable fm numy uses. Safe for use in fissye-matetial storage vaults, the absorber preserves enhanced criticality safety in storage arrays, even for unusually massive units. 

If only the core material is considered, then the k-effec-tive (k-inflnity) of the infinite array would be the same for the same H/ ratio no matter what the core density or shape. However, with the addition of the drum walls another effect occurs. As the material densities increase, or as the H/D of the flssile material comes closer to 1.0, less neutron leakage occurs and the k-effective of the unit increases. In addition, because of the reduced neutron leakage, a smaller fraction of the neutrons is available for absorption in the iron drum walls. This also increases k-effective. It is this latter effect that makes simplified k-inflnity calculations tKHicon-servative if rignifleant densifleation of the fissile materia) in the waste can occur and is not taken into account. 

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