Japan Earthquake: nuclear plants

zapperzero

the pressure inside the blast's fireball is much lower than atmospheric - so water could boil at a much lower temp than the usual hundred celsius. Dunno if anyone's tried anything like this, but it sure would make a fun little experiment.

MadderDoc

OK, thanks, I'll give it another go, at least now I know there's supposed to be a method.

Thanks for your efforts, it does not seem to me far off, so I'll go with that. But that's just the water from the combustion. The initial 14400 cubic meters of hydrogen would have come mixed with some air, the nitrogen of which would add to the final volume of combustion products. Air is appr. 80 % nitrogen and 20 % oxygen. So for the complete combustion of 14400 cubic meters of hydrogen we'd need to mix it well, with 2.5 times as much air, for a total of 50000 cubic meter of fuel mixture inside the building.

(Btw, this seems a tight fit for the size of the building, it seems not much more than 1 ton of hydrogen can be realistically imagined to have been combusting inside it)

Anyways, after the combustion of the 50000 cubic meters of fuel mixture, we end up with that volume minus the volume of oxygen consumed = about 43000 cubic meters of combustion gases. (14400 cubic meters of steam mixed with 28800 cubic meters of nitrogen). That would be a sphere roughly 22 meters in radius. But the mushroom cloud is bigger than that. Air, we can entrain some air! However, not too much, entraining air means our cloud looses buoyancy, without which there can be no Rayleigh-Taylor instability, hence no mushroom cloud.

MadderDoc

Heh. In the old days we had cars with which to do that kind of experiment :-) One learned quickly to protect the hand with a piece of cloth when releasing the lid to depressurise the hot radiator and to do it gently. More excitingly, one could make a swift twist to the lid and jump back. Whoosh!

Joffan

50000 ≈ 37^3 - a bit oversize I'd say but close enough. Hydrogen can still explode even when 50% by volume though.

Don't forget the explosion energy will heat & expand the gases significantly (well, pressurize them first, then expand them). Hydrogen burning in air is up to about 2300K ~ 8x volume at atmospheric, less the decrease from oxygen consumption, -> ~7x, by my rough calculation.

MadderDoc

Fair enough, but I don't think we can assume the temperature of a dark non-glowing cloud to be 2300K or anywhere near it.

MadderDoc

In a funny way the video of the Unit 3 explosion indicates the possible behaviour of combustion gases from a hydrogen explosion by its kind exposure to our view of the fire phenomenon in the SE corner -- and the ensuing development of a knob of the condensed steam from that combustion, at the downwind side of the stem of the mushroom cloud.

Unfortunately Internet has been thoroughly cleaned of the best videos of the explosion, but if you can get your hands on one still, and it has more than the first dozen of seconds after the blast, this knob of steam from the explosion in the SE corner can be followed, as it travels downwind along with the mushroom. It stays low, and appears to have little tendency to rise, rather it just slowly grows and thins out by entraining air, and gradually disperses, much like the behaviour of the clouds we saw going with the wind from unit 1.

Image above is the last frame from this Unit 3 explosion animation

r-j

What is the source of the hydrogen that is believed to have caused the explosions?

Most Curious

Short answer; Zircaloy cladding of the fuel rods in a steam or water atmosphere and very high temperatures releases a lot of hydrogen.

Joffan

No, well, that's full of dust and rubble too by the time we see it, don't forget. The 2300K burn temperature is (1) a maximum and (2) quickly diluted and reduced as the gas expands. It won't have transmitted more than a small fraction of that heat into the debris.

And anyone who knows more about the physics of explosions should jump in and correct me, incidentally, since I'm definitely no expert.

zapperzero

I did not mean to be chiding you, sorry. It is simply that you know the size of the building, so you can get a fair estimate of how fast the ball grows because of also knowing at what intervals the frames are taken.

zapperzero

'Zackly. I don't know if you can get the same effect when you blow the roof off a depressurized equipment hall.

zapperzero

Dunno about that... I just stated the volume of steam at normal temp. That figure implies a rather low partial pressure (iow the air is pre-mixed :).

Also, initially there would have been, oh, however many meters of hydrogen-air mix the building can fit :).

MadderDoc

Re - by the time we see it - 'it' being the mushroom cloud, when that would be that we see it. In the initial development of the vertically projected cloud, its upper edge would represent the front of ejected debris. The material to produce the mushroom cloud is of course there too. As the cloud progresses upwards, the debris slows down to eventually, except for the fine dust, start falling back to the ground. It is at this stage the mushroom can be most clearly seen, as it is emerging out of the top of the eruption cloud, steadfastly continuing its buoyancy driven travel upwards.

To illustrate, here's an animation of 17 frames, one for each of the first 17 seconds of the explosion. Images are heavily color enhanced to allow better distinction between the different cloud formations.

SteveElbows

I see the reactor 3 TIP room investigation was a bit of a failure, due to door etc debris.

http://www.tepco.co.jp/en/nu/fukushi...20524_06-e.pdf

Given that a human was able to visually inspect one part of the room, I am less than impressed about a lack of photo of this area. It makes me curious about the nature of any debris inside the room.

MadderDoc

I think you are speaking in the context of a shortlived pressure drop below ambient, that would be present in connection with a detonation. But it takes time to nucleate water, that's why it works well to jump back from the radiator in the case of the car. I think to get some steam out of the effect in a pool in depressurised hall, you'd need more than a brief underpressure pulse, something like the permanent decrease of the pressure above the water in the car radiator. Also, you must lower the pressure, such that the new saturation temperature is lower than the temperature of the water. In the case of the pool we are probably looking at a body of water at about 50 deg C, so that is quite some pressure drop that must be maintained.

The theoretical mass of steam that can be produced by the depressuring can be fairly easily estimated. It is directly proportional to the difference between the initial temperature and the boiling temperature at the new lower pressure, and directly proportional to the amount of water present. The proportionality factor is about 0.002K^-1.

Mass(steam)=0.002*(Twater-Tsat)*Mass(water)

Example: You have a pressurised PCV filled with saturated steam and 4000 m3 of liquid water at 150 deg C. Swiftly release the containment lid and jump back a mile. Don't try this at home.

Mass(steam)=0.002*(150-100)*4000 = 400 tons

MadderDoc

Weird to see that the door and apparently the door frame has not been blown away, but has been blown inward, into what they call the labyrinth. The implied pressure differential that should have existed to produce that effect is intriguing.

zapperzero

Yes.

How much time? We have about a second, second and a half to work with, no?

That's what I meant, when I said this should be experimented upon. But are you sure about the pool water temp? Could easily have been more.

I'm reasonably sure that the RPV didn't have that much water in it, in the event :). Anyways, this gives me a saturation temp of 60.something degrees celsius at 0.2 atm absolute. At 7.5 m^3/kg that's... a lot of steam, should the pool boil over. I am not sure how fast it nucleates, though. It should still be reasonably clean at this point, unless crud was thrown in by the earthquake.