5.1 A HISTORY AND A MIXING ANALYSIS

A potential explosion when molten reactor fuel mixes with its vaporizable coolant is an example of a more general phenomena. Outside the nuclear industry other highly destructive thermal detonations involve iron + water [186,187]; aluminum + water [188]; liquefied natural gas + seawater [189], soda ash + water [190]; coal tar + water [191]; and glass + water [192]. However, the sparseness of reports indicates that such explosions are far from frequent events. Indeed, if they were other than rare, the corresponding industrial processes would now have been discontinued. Moreover, many technical recordings show molten lava from on-land or subsea volcanoes mixing passively with seawater, and the last documented detonation was at Krakatau in August 1883. This rarity in usually passive industrial and natural processes clearly indicates that special conditions are necessary for a detonation.

Though true scientific investigation began in the nineteenth century [186], the physical processes underlying an explosive interaction only became partially understood after 1960 [193]. Even now, however, knowledge of some aspects remains incomplete. From pioneering

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experiments with aluminum and water in 1970 Laker and Lennon [194] suggest that the formation of a “macro-mixture” is a necessary precur­sor for an explosive interaction. Then a localized disturbance, such as the partial collapse of a coolant vapor film around the molten metal, triggers a propagating detonation.1 They (correctly) conjecture that the shock wave would escalate in intensity by finely fragmenting the melt to achieve the rapid heat transfer rate[72] [73] [74] for the detonation timescale of around 1 ms. Finally, though hydrogen production is recorded, later experiments by Robinson and Fry [192] prove the oxidation of alumi­num to have been irrelevant. The necessity of first creating a particular coarse-mixture morphology of the two liquids is confirmed by subse­quent experiments with kilogram quantities of molten metals or ceramics. Available evidence establishes that a potentially explosive coarse mixture has a sponge-like structure with a cell size of around 10 mm. Figure 5.1 depicts part of a typical untriggered coarse mixture

Figure 5.1 A Coarse Mixture Formed in Aluminum-Water Experiments

recovered from an aluminum-water experiment at AEEW. The follow­ing simplified fluid dynamics analysis confirms the necessity for first creating an appropriate coarse mixture over a timescale significantly longer than the 1 ms of a detonation.

If a one-step division process over t seconds transforms a contigu­ous mass M into identical spheres each separated by their own diameter d, then the work done against the surrounding liquid drag forces is of order [195]

with

p—coolant density.

The thermal energy change of the initially molten corium is

Ec ‘ MCPDT with Cp ‘ 500 J/kg (5.2)

where AT is the temperature difference in the corium prior to and then after a postulated interaction. Computer simulations of Severe Accidents suggest that a fast reactor provides the extreme molten corium tempera­ture of 5000 K, so it is assumed here that

25009 AT <4000 tC (5.3)

with:

Psodium ‘ 800 kg/m3 and Pwater ‘ 1000 kg/m3 (5.4)

As described in Section 5.7 the diameter of a fragmented corium particle must be below about 250 mm for its energy to be transferred over the 1 ms timescale of a detonation. Over this restricted size-range experiments provide the approximate mass mean diameter

d ‘ 100 mm

Granted the total elapsed time of an MFCI event as 1 ms, the above equations give

3.75M<Ef1/Ec <6.0M water coolant

(5.6)

4.70M<Ef1/Ec<7.50M sodium coolant

Hypothetically, if the entire 100 tonne fuel inventory of a PWR were to be involved, it follows that

3.8 x 105<Ef1 /Ec <6.0 x 105 in a PWR (5.7)

and similarly for a 20 tonne fast reactor fuel load

0.94 x 105<EFi/Ec <1.5 x 105 in a fast reactor (5.8)

6 pD3 pf

for a fuel density pf ‘ 104 kg/m3

On the other hand, consider a two-stage process in which a contiguous mass M is first mixed into spheres of diameter D in 1s, and then finely fragmented into spheres of diameter d in t second. The approximate number N of larger spheres is evidently

and their mixing energy requirement is obtained from equation (5.1) as EM ‘ ^4^^)M2 with D ‘ 10 mm (5.10)

Similarly the energy E for finely fragmenting just one sphere of diameter D in t second is

Equations (5.9)—(5.11) yield the two-stage fragmentation energy as

.2 -1

and from equation (5.2)

For the range of temperature differences in equation (5.3) and a total PWR fuel inventory of 100 tonne, equation (5.13) evaluates for a 1 ms detonation as

3.8 x 10_3<Ef2/Ec< 6.0 x 10“3 in a PWR (5.14)

and for a 20 tonne fast reactor fuel inventory

0.93 x 10_2<Ef2/Ec<1.5 x 10“3 in a fast reactor (5.15)

Though the above are merely “scoping calculations,” the orders of magnitude involved indicate that an explosive MFCI with a one-step fine fragmentation process for a sizeable portion of a reactor fuel load is impossible. However, an experimentally consistent two-stage process could involve just a plausibly small fraction of the fuel’s thermal energy, so MFCIs cause concern in water and fast reactor safety assessment [59]. Significantly, the coarse-mixing energy term in equation (5.13) is totally dominant which possibly explains the natural rarity of detonatable morphologies.