Following fuel ejection sodium vaporization may occur due to the high heat transfer rates. The heat input into the channel may be calculated by using the previously calculated ejection rates with a calculated heat transfer rate, so that the final heat input is effectively of the form:

qlqо = [1 — exp(— Ґ//.ЖЛ — P2- 6P)H (4.38)

The first term in this equation accounts for the delay time in attaining full mass flow. This heat input is used in conjunction with the voiding model described in Section 1.3 (24) to account for growth of the bubble and the rise of channel pressure (up to 1000 psia). In Eq. (4.38), ta is the time constant for the fuel mass flow rate. Figure 4.17a shows the typical results which are produced. The size of the bubble is very small when the maximum pressure is attained; so condensation of the bubble does not have much effect on the maximum pressure value. However the maximum pres­sure is very dependent on the following parameters.

(a) The delay time expressed by [1 — exp(— t/ta)] which represents that rate of ejection of molten fuel.

(b)

The heat transfer rate and therefore the fuel fragmentation repre­sented by Я in Eq. (4.38).

(c) The efficiency of the heat transfer process, which is a measure of the fuel fragmentation or possible vapor blanketing of the fuel during its ejection or the number of subchannels to which the voiding extends.

Most of the calculations performed to date assume 100% efficiency in transferring heat from the molten fuel to the sodium. However the amount of work energy which is derived from this heat energy is dependent on the model used to describe the voiding.

The ratio of work energy to original molten fuel thermal energy is defined as a reaction efficiency, and theoretical models for the molten fuel-sodium interaction may be checked for adequacy by comparing calculated efficien­cies with values obtained from experiment.

Figure 4.17b shows the transient that resulted when uranium dioxide fueled pins were subjected to a high power transient in the TREAT facility piston autoclave. Sodium temperatures and pressure pulses were measured and correlated with the amount of fuel that was ejected from the fuel pins. The work energy was calculated from the motion of the piston as shown in the figure (23a).

The surprising result was a reaction efficiency of between 0.0015 and 0.018% and it seemed that the bond gas might be producing the pressure

interaction. Subsequent experiments with evacuated fuel pins showed that the gas might be blanketing the interaction as the reaction efficiency rose to 0.15%. How­ever the efficiency was still very low.

In laboratory experiments in which molten fuel (U02) was dropped into sodium, efficiencies of less than 0.01% have resulted although efficiencies of between 0.4 and 1.0% have been achieved with water injected into molten salt. The model described in Section 1.3 (24) is a pessimistic one, in that it results in a reaction efficiency in the neighborhood of 1-5%.

The voiding calculations should be linked to the fuel ejection calculations to provide a more accurate estimation of the channel backpressures. The voiding of a subchannel is very rapid and the complete subchannel may be voided in as little as 10 msec. The radial extent of that voiding occurs with about 80% of the speed of the axial voiding. This voiding is so rapid that the assumption that a jet of molten fuel might affect the neighboring pins depends on whether that jet transfers any of its heat to the coolant. If it does, then the coolant is likely to vaporize and failure could propagate by vapor blanketing rather than by jet impingement.

Once the void extends into the upper blanket region, the condensation
rate becomes very high and the pressure is reduced and the void-liquid interface begins to reenter in about 0.6 sec.

While the sodium is being voided from the channel, condensation takes place on all the pin surfaces and the film left on the pin surfaces increases. Eventually however when the film has built up, in about 0.15 sec, the reverse occurs and the film dries out, so that when the sodium reenters, it may arrive back in a channel in which the fuel cladding has failed following dry-out.

The exact course of the voiding of a subchannel depends on the assump­tion of the fuel behavior within that subchannel. It is possible to postulate fuel failure while the liquid is out of the channel, such that when the sodium tries to reenter, it is prevented from doing so by the high heat ratings present in the molten fuel. Thus the void increases again, starting a chugging motion that has been postulated as an extreme form of heat removal. It has also been suggested that some of the fuel material which is ejected into the channel may be carried out of the channel by the vapor-liquid interface in the form of solid frozen particles. Such a condition, if it occurred widely, could cause a reactivity decrease.