Investigations revealed that if the initial thermal neutron flux value is on the order of, or higher than, Ф0 = 1013 cm_2-s_1, passive zone development is then followed by a regularity of the type described in (8.3)

I « A/Pa (8.35)

not only at l << r1, but also at l < 0.3 r1, with an accuracy no worse than 20 %. If gas thermal diffusivity, a, in this instance is assumed to equal its value at the initial moment in time, the proportionality factor, Ah will then fluctuate within limits of a few units. So, for a cell with planar layers (see Fig. 8.12), A/ = 3.24 for Ar and Ai = 2.75 for He. Here, expression (8.35) describes the l(t) dependence derived from an accurate calculation all the way up to l« 0.25d, with an error no higher than 6 %. For a cylindrical cell, Al = 4.61 for Ar and Al = 3.04 for He, with this same accuracy.

Calculations of different excitation alternatives demonstrated that at l < 0.3r1, the Al factor is most highly dependent upon cell geometry (planar or cylindrical), and to a lesser extent, upon the shape and intensity of the exciting neutron pulse, uranium layer thickness, and gas mixture thermophysical properties, despite the fact that mixture characteristics are partially taken into account by the thermal diffusivity in correlation (8.35). This Al factor behavior is explained by the fact that passive region development is determined not only by heat removal to the cell wall, but also by the gas motion, during which the occurrence of thermal and

Fig. 8.15 Dependence of the active region’s outer boundary upon pumping power rise time:

(1) D0 = 0.1; (2) D0 = 0.5; 3.) D0 = 1

gas-dynamic processes is dependent upon the power and spatial distribution of the energy release sources in the gas at any given moment in time.

The regularity noted makes it possible for the initial stage of passive zone development in cells with identical geometries to establish the approximate rela­tionship between their dimensions and the thermal diffusivities of the gases filling the cells

/,~l

If two identical cells irradiated by identical neutron pulses are filled with mixtures that have identical compositions, but different initial densities, it then follows from the latter correlations that

(8.36)

Here, the determination of thermal diffusivity is used, a = kg/cvp.

The calculation results for the moment in time at which the fluence reaches 3 • 1013 cm~2 are presented in Fig. 8.15 for a cylindrical cell with r1 = 1 cm, filled with helium at different pressures, and irradiated by an exponentially rising neutron flux (8.34). Because the moment in time, t, and the fluence, ф, are linked by the formula t = т1п(1 + фФ0т), the т value at given Ф0 and ф corresponds to specified t value. The data in Fig. 8.15 confirm the existence of approximate dependence

(8.36) for the values of I < 0.3r1.