Calculating Array Criticality Using Thomas's Limiting Surface Density Model

Abstract

Most calculations of array criticality are performed using Monte Carlo computer codes. The Limiting Surface Density model is a hand-calculation tool which provides a companion to such codes, where applicable. This paper describes the development of the tool and compares the results with an equivalent KENO Monte Carlo computer model. Thomas's Limiting Surface Density model is based on the experimental result that different cubical arrays of a given material (e.g. 4x4x4, 5x5x5, 6x6x6 etc.), with total number of array units N and with different array pitch and thus with different geometrical bucklings BN2, are critical with the same unit mass if the product NBN2 is the same for each array considered. Starting from this result, two simple expressions are derived. One of these relates the geometrical characteristics of the array to a parameter referred to as the "limiting surface density" ( a function of the total mass of the units of the array on a vertical projection over the area of one unit cell). The other relates the characteristics of the material of the array to the same parameter. These simple expressions are linear and a geometrical construction of these expressions will produce an intersection point which is the unit mass, for that material and that geometry, which will result in (cubical) array criticality. From this starting point, transformations to the linear expressions to cater for non-cubic arrays, different materials, different densities and different unit shapes can be performed. An estimate of array subcriticality can be made for arrays with unit masses less than the calculated critical size. The method finds its primary use in the criticality safety analysis of storage arrays and is demonstrated for a notional array arrangement. The result is compared to a KENO Monte Carlo calculation. Finally some shortcomings in the model and deficiencies in data are pointed out.