This section has so far treated failure arising from a single pin; however, it is possible that due to an overall reactivity accident or an overall flow failure, the whole core might almost simultaneously fail. The characteristics of the widespread failure would be very different. To obtain a widespread failure one must start with a hypothetical accident.

Section 5.4.4 treats suggested design bases and outlines the behavior following a loss of electrical power to the pumps associated with a failure to scram the reactor. The sequence of events in that case is as follows (remembering always that this is the supposed chronology of a hypothetical event):

(a) Widespread voiding due to either sodium boiling or fission gas release or both effects and consequent reactivity feedback.

(b) Prompt criticality resulting in widespread fuel failure and melting. A slight dispersion shuts the system down.

(c) Slumping of the core under gravity into a more reactive position.

(d) A second more violent superprompt criticality.

(e) Violent dispersion of the core.

The calculations leading to estimates of voiding times are the same as those previously described in Section 1.3. However the main difficulty in this analysis enters into the slumping calculation. Just how does molten fuel collapse? The time of collapse is all-important in defining the time scale in

which the slumping-induced reactivity feedback is added. This in turn de­fines the subsequent energy release.

Several fuel slumping models have been suggested in the past. One code, MELT II, allows the user to specify his own mode of fuel collapse for a single representative pin (31).

Another method used in the Fermi hazards report calculated the molten patterns in a homogeneous core following a loss of cooling. These molten regions, shown in Figs. 4.19-4.24, were then assumed to slump under gravity (32a).

In several cases, EBR-II and Fermi, the hypothetical case of a gravita-

tional slumping of the top third of the core onto a previously slumped and compacted bottom two-thirds was used as a design basis (32b).

Another suggested method is shown in Fig. 4.25 in which a representative fuel pin is modeled. The molten fuel distribution is assumed to run down as a collar in the equivalent channel of the pin and to successively grow as

more molten fuel is produced from the transient. The assumptions in this approach are that the core is voided and the void does not reenter while slumping is proceeding; there is no separated dripping of fuel; one rod is representative; the top of slumped collar is level with the top of the un­melted fuel; and there is apparently no hold-up of molten fuel by the surrounding unmolten material. The equations that define the configuration are those for conservation of mass and gravitational fall. The assumptions of this model are at least no worse than those of the others. However, they all suffer from one considerable defect: None of the core collapse models to date treat the combination of core voiding and fuel collapse and the inter­action between the two phenomena, especially inasmuch as sodium liquid reentry is liable to have a compacting effect on the molten fuel. In some cases (23b) this interaction is not present, since the void exists for a long enough time for the fuel to slump while the liquid sodium is out of the core, but generally this may not be true.

Another hypothetical event which can lead mechanically to a core disrup­tive accident is an uncontrolled core reactivity increase. In this case the sequence is as follows:

(a) Power increase leading to fuel melting and eventual melting of the cladding from the high fuel heat fluxes.

(b) Molten fuel and fission gas ejection and fuel slumping into the coolant channel.

(c) Widespread voiding throughout the core (notice that in this case the voiding comes after rather than before the cladding failure).

(d) Widespread fuel slumping in combination with voiding mechanics.

This case is very different from the loss of flow combined with loss of scram, since in the previous case the voiding initiated the cladding failure, whereas here the fuel fails into a subchannel which is still filled with sodium. This latter event is likely to be more chaotic, although it is much less likely because of the design of the reactivity control system and the plant pro­tective system.