Re: fission question

From: Steven Sharp (sharp_at_cadence.com)
Date: 07/23/04 

Date: 23 Jul 2004 14:55:31 -0700

sbharris@ix.netcom.com (Steve Harris sbharris@ROMAN9.netcom.com) wrote in message news:<79cf0a8.0407221504.4276969@posting.google.com>...
>
> But take a look at the energy production rate. We can't figure the
> first release lasted longer than maybe 5 seconds, so you're running
> those 320 kJ out in 5 seconds, for a power of 64 kilowatts.

A lot of the power is produced in an initial spike, followed by a lower
plateau. However, looking at the graph of the plateau, 64 kilowatts
is pretty close to the graph at 1 second elapsed time.

> That's
> enough to melt the core if you let it keep up. The equalibrium temp is
> the one at which the core loses that much in IR radiation from its
> surface area of 0.022 m^2. So you need 2.9 megawatts/m^2, and
> Stefan-Bolzmann gives you 2676 K for that, way above the melting point
> of nickel. With outputs of 10's of kw, this is a meltdown situation at
> equilibrium.

Are you sure that radiation is the dominant heat loss mechanism from
the core in that timeframe? These cores were sitting inside
hemispherical hollows in metal reflectors. The thermal contact may not
have been great, but there would be some conduction into that larger
metallic mass, delaying meltdown.

In another posting I mentioned a Soviet accident that did reach
thermal equilibrium, lasting 6.5 days before being disassembled.
This involved a uranium core with copper reflector, stabilizing at
around 865 C and 480 watts. Those figures certainly support your
prediction of eventual meltdown for 10s of kw in a smaller core.

> I figured the total heat capacity of the sphere at around 800 J/K, so
> at a power output of 64 kw you're getting a temp increase of 80 C/sec,
> which is only +400 C over the course of the event, in worst case. Not
> *quite* enough to melt the plutonium, but getting very close (within
> another few seconds). I figure only 2 or 3 times the total energy of
> this though WOULD have melted the sphere, nickel can and all, which
> means that in both cases the prompt attentions of the operators
> probably did prevent meltdowns.

The nickel canning was only 5 mils thick, so it wouldn't have provided
much structural support.

Before melting, the plutonium would presumably have transitioned from
the delta to the epsilon phase. The NWFAQ says that the gallium alloy
is stabilized in delta phase up to at least 475 C. Normally the epsilon
phase is denser than the delta phase (which would have made the assembly
more reactive), but it's not clear to me what effect the gallium alloying
would have on this. The epsilon phase does have a significant positive
coefficient of expansion, which would tend to slow things down again
with further temperature increase. However, upon melting, liquid
plutonium is denser than solid plutonium. So the situation could have
gotten quite messy.

As an aside, Daghlian may have made the situation worse in the short
term by moving back in, since his body would have provided additional
neutron reflection and moderation.

> > "The Los Alamos National Laboratory archives include some data and comments
> > about a rerun performed 2 October 1945 to determine the radiation dose
> > received in the accident of 21 August 1945. The yield of the rerun was
> > about 6x10**15 fissions, but the prompt critical state was not reached.
> > The maximum reactivity of the system during this experiment was about
> > 60 cents above delayed criticality."
>
>
> Wow, that's cheap. :) Read, of course, the modern "percent" for
> "cents".

Actually, the "cent" is defined as "A unit of reactivity equal to
one-hundredth of the increment between delayed criticality and prompt
criticality (a dollar)." So yes, a percent, but of a particular change
in reactivity. So that was 60% of the way between delayed and prompt
criticality. The accidents themselves were estimated as 15 cents and
10 cents above prompt criticality (or 1.15 dollars and 1.10 dollars
above delayed criticality).

If you are interested in reading the Los Alamos report yourself, I
can send it to you. It is a 4M PDF file.

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