Where to begin? Well, anyway, here goes...
So, you have a bunch of fissionable material ...
The fuel in a LWR is not "fissionable", it is fissile. It undergoes fission by absorption of a thermal neutron. Fissionable material is typically classified as something that requires a high-energy neutron to induce fission.
...sitting there fissioning away,
Other than spontaneous fission and perhaps a very small amount of subcritical neutron multiplication, there is no credible evidence of ongoing criticality in any of these reactors.
... and no longer contained within its stainless steel fuel housings
Fuel in a LWR is not contained in stainless steel. The cladding of fuel rods is zircalloy.
~ at a low rate of course ~ but it's still fissioning.
See comment above.
You take tons of water, with the requisite inclusion of some Deuterium and a small amount of Tritum, and you pump it into this mass in an attempt to cool it, and you get a surprising increase in temperature!
Far too little deuterium and tritium and in far too dilute a form to be significant for any fusion-type reactions. You need a plutonium trigger fission bomb to have sufficient energy to initiate any kind of fusion reaction. Try as you might, you are not going to get a fission detonation from any kind of LWR core, no matter how badly you damage it.
That's basically what you do in a few milliseconds in your typical friendly neighborhood hydrogen bomb.
Silly descriptors (friendly neighborhood) aside, you need far more to make a thermonuclear explosion than just bringing together uranium, plutonium, deuterium, and tritium. And the reactions in a thermonuclear detonation occur on a time scale of nanoseconds, not milliseconds. If it were milliseconds, there would be a yield comparable to chemical explosives. It is the release of a lot of energy over a very short time scale that makes for a big bang.
The first thing you need is a plutonium fission bomb. You don't have that in a LWR. Plutonium is preferred (weapons-grade, not reactor fuel grade, there is a BIG difference) because it has a higher reproduction factor than uranium. You need specially-designed tampers and "pushers", you need specially-machined radiation channels for directing the energy from the fission weapon (primary x-rays), you need a significant quantity of thermonuclear fuel, either liquid deuterium (as in Ivy Mike) or lithium deuteride. You need a pure plutonium (again, weapons-grade, not reactor fuel grade) embedded in the thermonuclear fuel. Happenstance in a damaged LWR core isn't going to produce these things, and certainly not in the form needed to initiate any kind of significant thermonuclear activity.
Thank you for sharing your knowledge. Would you please sum up the risks and options for recovering a safe state in these damaged reactors?
I love it ~ you did the perfect job on deriving the correct answer (from the perspective of the hot nukes school of thought).
I'm sure the fella's at Fukushima are going to be so happy to hear it's just their imagination.
So, regarding the "zircalloy" containers ~ when they're all busted up and this stuff is just lying about being fissile, why are you pouring water on it? Like I asked, did anybody ever try this trick out before?
Can't we assume some criticality based on temperatures going up under circumstances of massive water infusion?