Why does nuclear fuel not form a critical mass in the course of a meltdown? A BWR reactor core may contain up to 146 tons of uranium.  Why does it not form a critical mass when molten?  Are there any estimates of the critical mass of the resulting zirconium alloy, steel, concrete and uranium oxide mixture?
 A: 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.
A: 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.  
A: But it does have a critical mass. Otherwise it would not become critical.
What you avoid in a well designed power reactor is 'prompt' criticality where an active core becomes supercritical on prompt neutrons only. Normally a critical reactor is stable on a fraction of prompt neutrons (neutrons released at the instant of fission) and delayed neutrons (netrons released on average several seconds after the incident neutron). This is fundamental to the operation of a power reactor as it allows the control system to manage the neutron flux.
A reactor that becomes supercritical on prompt neutrons only will increase in power at a rate only controlled by the fission rate and increase in fractions of a second to very high power. This is how a nuclear weapon operates.
A reactor that becomes supercritical on delayed neutrons will increase power much slower and can be controlled.
A: 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.
A: Several things are required to cause a nuclear explosion. It is not just about mass... In terms of a melt down, perhaps heat is the real issue, because it expands the gap between atoms and this diminishes the target cross section for a neutron to strike, thus lengthening the mean neutron pathway.
Other issues include isotope purity of the fissile mass... Also impurity from decay products like Xenon 135. In a nuclear melt down like Chernobyl for example there was very high Xenon poisoning before the steam/hydrogen explosion which destroyed containment buildings.
Geometry of a critical mass is a further consideration, but given the two points above once it is too hot and contaminated Geometry is the least consideration.
Compression of the critical mass is another and this is related to heat. If the mass were squashed tight or frozen the chances of explosion would be higher. In a nuclear warhead too much Alpha activity raises the temperature and degrades the bomb. With heat in a reactor melt down there is virtually no compression.
Having an effective reflector would increase the chances of a nuclear explosion, but nuclear reactors are not normally configured to reflect neutrons back into the pile. In any case in a melt down the confinement vessel is usually ruptured.
Even if you somehow overcame all this there still has to be sufficient neutron flux and this is totally unlikely. In terms of Neutron Flux one has to ensure that 35-40% of neutrons do not escape the mass to obtain an explosion. 
A: A thermal reactor requires a moderator to be in a critical state.  A BWR (and a PWR) use water $H_2O$ as the moderator.  Other thermal reactors use graphite-the old N reactor at Hanford- or heavy water $D_2O$- the CANDU and the old Savannah River production reactors- as a moderator.  If the core melts and slumps into a mass of $UO_2$, cladding metal, and control rod materials, the fuel/water is no longer in a critical configuration; the water is on top and acts as a reflector, not interspersed among the fuel.
A fast reactor does not require a moderator to be critical. The fuel is of a higher enrichment than that of a thermal reactor because the fission cross section is lower at higher neutron energies.  It is possible for a melted mass of fast reactor fuel to go critical and result in a minor nuclear excursion (called "work energy" release in the jargon of reactors).
The safety issue for reactors is removing the decay heat; the energy released from the radioactive decay of radionuclides that build up from the fission process  during operation.  At shutdown, the decay heat is about 5% of full power; that is 150 MW for a 3000 MW (thermal power) reactor, a significant level.
A nuclear reactor cannot explode like a nuclear weapon. For a thermal reactor the prompt neutron generation lifetime is too long. For a fast reactor (and a thermal reactor) there is no mechanism for creating and maintaining a super prompt critical assembly sufficiently long for significant release of energy from fission. You have to really work hard to assemble the correct material to create a nuclear weapon; you need to create a system that is super prompt critical using fast neutrons and remains so sufficiently long for the chain reaction to produce enough energy before pressure causes dis-assembly into a non-critical configuration. By super prompt critical is meant super critical on the prompt neutrons alone without having to wait for the delayed neutrons to contribute.  In operation, reactors are critical but not prompt critical; delayed neutrons are required for criticality.
A: My guess would be that the moderator (normally the water, graphite already would have caused the accident) is missing and that is still vital in a compacted mass. The uranium oxide is not enriched to military grade, but I can't speak for MOx-elements.
Should be difficult to say without some decent figures about leftover UO_2, mass, previous distribution.
A: I seriously doubt that any realistic reactor will contain 146 TONS of Uranium at any one time.
Even if it did, it'd be so spaced out as to preclude the creation of a supercritical mass (i.e. a mass that leads to a nuclear explosion).
Of course any operational reactor WILL be critical, if it weren't there'd be no chain reaction going on, no sustained fision reaction, no energy output.
A: if the pressure vessel contained a supper critical mass long enough it could go boom like a nuclear bomb but its more likely to blow the containment before then and lose mass 
its about a self compounding reaction that quickly builds on its self if they lost all ability to moderate the reaction a critical mass could be reached much quicker but it still comes down to the containment being intact at the last moment unlikely but some advocates have spoken out about this remote possibility
japan was close to this outcome they had a fizzle type explosion that was more or less a dirty bomb if their containment was stronger they would have likely had a nuclear bomb of some size  
