Why does nuclear fuel not form a critical mass in the course of a meltdown?

If you read Wikipedia page about corium, they say that critical mass can be achieved locally.

But if you are concerned about a critical mass allowing a nuclear explosion, the difficulty in nuclear weapon design, as told here, is to achieve the criticality fast enough. If you do not achieve criticality fast enough, your material heats and its interaction with neutrons decreases, slowing the chain reaction down. And that is with pure ²³⁵U. So basically what happens if criticality happens in a melting nuclear reactor is the release of a lot of heat and radiation, but not in an explosive manner as in an atomic bomb.

The probable answer is that to make a bomb one needs a very special design and very pure U235, in a sphere. So even if a critical mass forms in meltdown, a reactor does not have the geometry and purity for a nuclear bomb. No mushrooms.

But it may continue to heat, acting as a reactor, and the problem is in conveying the heat away without building up steam and hydrogen in order to avoid a chemical explosion.

A nuclear engineer should answer whether the amalgam of all the metals does not allow criticallity. Their plans to first cool the melted reactors and then encase them in sand and cement would imply that they do not expect the melted core to be critical. The fact that with the control rods in place the reactor is no longer critical by design, just has residual radioactivity, argues from conservation of mass that even in melt when the metals will be mixed the same will hold true.

One of the questions often being answered is “why don’t meltdowns go supercritical?” ie. “Why don’t they create a nuclear explosion?” A good understanding of why they don’t provides a good framework to understand why corium should not be critical, and why subcritical can be fairly bad.

Critical mass is more a description of neutron flux than actual mass of material. Perhaps a better term would be critical concentration, but I think “critical mass” sounds better; don’t you? In the supercritical mass the fuel can act as moderator and neutron generator. Fission produces mostly fast neutrons which are not absorbed at high probability by fuel nuclei, but if you have enough fuel nuclei this problem is obviated. Some nuclei will absorb fast neutrons and give off slow neutrons, and a gamma ray. Some of the first reactor designs were slurry reactors where finely ground moderator and fuel were mixed together. I suppose if a slurry reactor melted down the corium would be critical. Modern reactors use fuel rods and both solid and liquid moderators.

The fuel in the rods has both an internal and a surface neutron flux. The perfect nuclear reactor would have surface flux where all the fast neutrons escaping the fuel rod were reflected back as slow neutrons. This would allow the fuel to “burn” most efficiently. By arraigning the fuel rods and moderators in an optimal configuration the closest to perfect flux is achieved. If you remove the moderator the fuel is not critical by itself. If you change the arrangement the fuel should go subcritical also. If it were not for the fact that much more fuel is present for the minimal critical configuration it would be so statistically unlikely to even have local areas of critical flux that it would really be impossible. With the overabundance of fuel it is only highly improbable that a local slurry reactor zone could form in the corium blob.

Subcritical neutron flux does not mean that fission has stopped; it only means that fission will eventually drop to the level expected with only spontaneous fission. Depending on how subcritical the reactor is this could take a while.