"Maybe the laws of physics will change, but I'd be willing to bet that they won't."
There's absolutely nothing about the "laws of physics" that guarantees that this particular reactor design is going to be able to contain a full meltdown, because it's never happened before. Nobody knows.
"Concrete doesn't burn."
No one said it did. There's plenty of other stuff around that does burn readily, which is why the plant is currently on fire. A lot of that stuff is radioactive.
"Explosions don't just happen for no reason."
Indeed. But red-hot piles of radioactive waste are a good way of making explosions happen, particularly when there's lots of hydrogen gas floating around from the breakdown of the cooling water and the fuel. That's why there have been several explosions at the plant.
"Nuclear reactors don't hold enough fuel to form a critical mass. In order to become critical, they need a moderator (usually water) which thermalizes neutrons."
You're assuming an intact core. Criticality is a function of density, shape and temperature, in addition to mass. Melt the fuel rods, and the guarantees of that nice, well-moderated behavior are off.
In general, you're making lots of simplistic assumptions about a nicely behaved, engineered, controlled system. What they've got now is far messier. Moreover, a lot of the stuff that you're saying can't happen, is actually happening right now. The reality of the situation trumps your theories of the situation, however confident.
There's absolutely nothing about the "laws of physics" that guarantees that this particular reactor design is going to be able to contain a full meltdown, because it's never happened before. Nobody knows.
Physics isn't biology/medicine. The laws of physics are not discovered by running experiments to enumerate every possible combination or permutation of configurations.
You're assuming an intact core. Criticality is a function of density, shape and temperature, in addition to mass. Melt the fuel rods, and the guarantees of that nice, well-moderated behavior are off.
The optimal shape for criticality is a sphere - surface/volume is the key factor here. A wide, shallow puddle at the bottom of the containment chamber is the least dangerous shape.
Temperature affects things because higher density makes achieving criticality easier. I.e., the colder things get, the more likely criticality is to be achieved.
"Physics isn't biology/medicine. The laws of physics are not discovered by running experiments to enumerate every possible combination or permutation of configurations."
Wanna bet? Guess how we know most of what we know about criticality and neutron cross-sections? People like Louis Slotkin, who spent hundreds of hours poking at piles of radioactive material in the lab, to derive those mathematical models that you're leaning upon. Critical mass calculations, in particular, are so fiendishly complicated that the entire field of stochastic simulation (i.e. monte carlo methods) were invented to address them. So tell me again about the "laws of physics", and how they're not tested through pemutation.
"The optimal shape for criticality is a sphere....a wide, shallow puddle at the bottom of the containment chamber is the least dangerous shape."
Prove it. It's pretty amazing how everyone wants to cite "physics" to prove that there's no problem with a meltdown (in the face of overwhelming empirical evidence to the contrary), but nobody is doing much more than hand-waving allusions toward their undergrad physics textbook in defense of their assertions.
A sphere is definitely a shape where we have good calculations to model critical mass. Otherwise, we don't really know much that wasn't determined empirically. We know that criticality depends strongly on density. We've assumed that the structure of this reactor will prevent that density change from occurring. We don't actually know what will happen.
I can almost understand why a community of nerds is so strongly interested in maintaining the self-delusion that the world is a fully knowable, controllable place, but I don't understand how so many people can ignore so much real-world evidence for so long. If you're seriously telling yourself that a meltdown isn't a big deal, you need to go back and re-examine what you know about the situation, and why you think you know it.
So tell me again about the "laws of physics", and how they're not tested through pemutation.
Ok. You generally perform a sequence of experiments, construct a low entropy theory, and then apply that theory in the future. Kind of like what Louis Slotkin did.
He doesn't need to redo them on a train, a plane, in a car, at the bar. The fundamental principles discovered tend to be pretty solid.
Prove it.
Not that hard. Take a fixed volume, convolve it with the 1/r kernel of the neutron diffusion equation. If the volume of uranium is a sphere, you get the spot neutron density at the center is [(3V)^{2/3}]/2. If the volume is a disk of height dz, radius R, you find the the local density is 2(pi V dz)^{1/2}. The smaller dz gets, the smaller the local density of neutrons is, and the further from criticality you are.
(Computing the volume at someplace other than the center is left as an exercise for the reader. However, the maximum principle shows that it always goes down.)
Now plug this into the standard soliton machinery (i.e., use Duhamel's principle, L^p-L^q estimates, etc) and you'll always need a bigger source for a flat soliton than a spherical one.
Yes, I'm skipping a few steps. You can find them in Cazenave's book on solitons (that's where I learned it) and most likely any book on nuclear engineering (but with much less of a mathematical bent). No, it's not the "undergrad physics textbook" you seem to think I'm referring to.
It's pretty amazing how everyone wants to cite "physics" to prove that there's no problem with a meltdown (in the face of overwhelming empirical evidence to the contrary), but nobody is doing much more than hand-waving allusions toward their undergrad physics textbook in defense of their assertions.
What is the "overwhelming empirical evidence" that criticality will be achieved?
The physical principles behind criticality calculations are not fiendishly complicated. The computations are computationally intensive, yes (Slotin was around in a time where experiments were cheaper and easier than simulations), and (maybe -- I don't know) the exact nature of physical materials involved was not well known, and needed to be measured.
Prove it.
Why don't you prove it? It's not other people's job to do all the work for you. It is provable that a sphere is the optimal shape. If somebody on the internet suggests that you're wrong, you don't win the argument by saying it's their responsibility to do all the hard work of convincing you you're right. You're still the one who is wrong.
It's a shame that cperciva's nonsense is being modded up.
> "Nuclear reactors don't hold enough fuel to form a critical mass."
Come on. Each reactor core holds over 100 tons of uranium, of which about 3-5 tons is U-235. Critical mass under perfect conditions is 50 kilograms. Conditions are not perfect for forming a critical mass, but you've got 100 times as much U-235 as is strictly necessary, and there is no fucking way of knowing what will happen when an entire reactor core melts and flows together, because no one has ever been stupid enough to try it. Chernobyl experienced a criticality event, and there is absolutely no guarantee that Fukushima will not.
Moreover, each reactor has a spent fuel pool with five times as much fuel in it as the reactor itself has. And no containment vessel. And no water being supplied. And when the water boils away from those pools, and that fuel melts and flows together...
Each reactor core holds over 100 tons of uranium, of which about 3-5 tons is U-235. Critical mass under perfect conditions is 50 kilograms.
Critical masses don't work that way: the additional U-238 absorbs neutrons making more difficult to achieve criticality. In fact, even an infinite amount of unmoderated natural uranium cannot sustain a chain reaction. See the figure 3.1 in [1] for more information about unmoderated critical masses for enriched uranium.
Chernobyl used UNENRICHED uranium, containing only .7% of U235, and went kablooey. Which you just said can't happen, so I suppose Chernobyl didn't actually happen. /thread
This thread has brought out the worst aspects of Hacker News - reasonably bright people who feel compelled to opine, in their usual arrogant "I am always right" manner, about subjects where they have no clue.
Please read carefully before making absurd accusations. I said: "even an infinite amount of unmoderated natural uranium cannot sustain a chain reaction". The nuclear excursion at Chernobyl occurred in a graphite-moderated reactor core.
I don't claim any special expertise in nuclear power but, as you don't seem to know the importance of moderation in criticality, I think you should refrain from accusing others of cluelessness in this topic.
Criticality is a function of density, shape and temperature, in addition to mass. Melt the fuel rods, and the guarantees of that nice, well-moderated behavior are off.
It is impossible for the uranium in a nuclear power plant to become critical in the absence of a moderator. Even if it's shaped into a sphere and supercooled. Add heat, and it gets further away from criticality (mostly due to doppler broadening; partly due to thermal expansion). Change the shape, and it gets further away from criticality (because there's more surface area to lose neutrons).
There's absolutely nothing about the "laws of physics" that guarantees that this particular reactor design is going to be able to contain a full meltdown, because it's never happened before. Nobody knows.
"Concrete doesn't burn."
No one said it did. There's plenty of other stuff around that does burn readily, which is why the plant is currently on fire. A lot of that stuff is radioactive.
"Explosions don't just happen for no reason."
Indeed. But red-hot piles of radioactive waste are a good way of making explosions happen, particularly when there's lots of hydrogen gas floating around from the breakdown of the cooling water and the fuel. That's why there have been several explosions at the plant.
"Nuclear reactors don't hold enough fuel to form a critical mass. In order to become critical, they need a moderator (usually water) which thermalizes neutrons."
You're assuming an intact core. Criticality is a function of density, shape and temperature, in addition to mass. Melt the fuel rods, and the guarantees of that nice, well-moderated behavior are off.
In general, you're making lots of simplistic assumptions about a nicely behaved, engineered, controlled system. What they've got now is far messier. Moreover, a lot of the stuff that you're saying can't happen, is actually happening right now. The reality of the situation trumps your theories of the situation, however confident.