Re: shootin down that recon satellite
- From: "andrew.higgins@xxxxxxxxx" <andrew.higgins@xxxxxxxxx>
- Date: Fri, 29 Feb 2008 23:51:40 -0800 (PST)
On Feb 15, 2:18 pm, John Doe <j...@xxxxxxx> wrote:
And since re-entry is capable of vapourizing metal, is it really
realistic to think that a fuel would not melt quickly and also be
destroyed ?
Allow me to lay out a scenario that is consistent with fundamental
heat transfer relations and reentry physics:
The tank begins reentry nearly full of frozen hydrazine. As it
reenters, it experiences intense aerodynamic heating for a period of
say, 3-5 minutes. During this time, most of the heat transferred to
the tank and its contents remains concentrated near the surface, since
there is not sufficient time for the heat to conduct into the center
of the frozen hydrazine ball. (You can estimate this depth of
penetration by sqrt(alpha*time), where alpha is the thermal
diffusivity of frozen hydrazine or the beryllium tank or whatever the
reentry body is made of. Since alpha is of the order 10^-5 m2/s and
time is 300 s, the depth of heat penetration is only a few centimeters
at most. Look up Fourier number for complete explanation.)
Now, the tank has to dissipate an enormous amount of energy during
reentry, so the heat transfer will be intense. On orbit, 500 kg of
hydrazine at 8 km/s has a whopping 16e9 J of energy (or 16000 MJ).
Essentially, all the energy has to be dissipated into heat. However,
only a tiny fraction of that energy goes into the reentry body; most
of it goes into heating up the air. A very approximate dimensional
analysis says that that the fraction energy that ends up in the body
is given by the skin friction coefficient, Cf, which for hypersonic
reentry is usually in the range 0.001 to 0.005. So, somewhere
between 16 and 80 MJ of heat is going to go into the tank. This is
enough heat to melt about 40 to 200 kg of hydrazine (heat of fusion =
394 kJ/kg), but not enough to melt the entire mass. Since, as I
explained above, the heat will not have time to conduct into the
center of the frozen hydrazine and remains concentrated at the edge,
it is likely that rather than uniformly melt the hydrazine, it will
melt and then significantly heat the hydrazine near the periphery of
the tank. Indeed, some of the hydrazine may boil.
Recall that this maximum heating is occur with the tank is still very
high up (say, 30-100 km) where atmospheric pressure is very low (1 kPa
down to 1 Pa). If we assume that the fuel lines leading to the tank
were ruptured, then this is the same pressure inside the tank. If the
rupture fuel line were pointing forward, the tank might see a higher
stagnation pressure (also called pitot/dynamic/ram pressure), but the
more likely scenario is the tank internal pressure is close to the
ambient pressure at the altitude. At this low pressure, the hydrazine
would boil easily, but the resulting vapors are at extremely low
density. The hydrazine vapors are free to expand out the ruptured
fuel line, so there is no build up in pressure. At this low of
pressure/density, explosion of the hydrazine vapors is unlikely. It
is possible that reentry heating may create a hot spot in the fuel
line, for example, that could ignite the hydrazine and flash back into
the tank. However, and this is a key point, even if the hydrazine
ignites and burns, it is unlikely to rupture the tank. Confined gas
explosions typically generate an overpressure 10 times the initial
pressure (so, say 10 kPa), while the tank is designed to be
pressurized to several bar, at least. Frozen/liquid hydrazine is very
insensitive and will not detonate.
So, now we have a robust tank that has survived reentry and any
possible ignition and explosion events in the hydrazine vapors. As it
continues to decelerate through the lower atmosphere and encounters
higher pressure air, the heating tapers off. What is the temperature
of the tank at this point? Probably very near the melt point of
hydrazine (1 C), since there is still several hundred kg's of frozen
hydrazine in the tank, acting as an enormous heat sink. The
temperature is certainly not greater than the boiling point of
hydrazine (100 C), as any greater temperature (in the beryllium tank
liner, for example) would immediately be soaked up by the phase change
of the boiling hydrazine (heat of vaporization = 1300 kJ/kg at 1 atm)
There is no possible ignition mechanism at this point.
Finally, the intact tank hits the ground, still more than half full of
frozen hydrazine.
This scenario is consistent with, and derives from, basic conservation
laws, heat transfer relations, and reentry physics. While much more
sophisticated analysis can be done (indeed, has been done and will be
done!), I doubt the numbers here are off my more than a factor of 10.
If you heat hydrazine sufficiently, won't it ignite and burn ? Or must
it absolutely be mixed with its catalyst to ignite ?
Hydrazine vapors can explode, either pure (with difficulty) or mixed
with air (very easily). Liquid/solid hydrazine is very stable and
does not detonate.
--
Andrew J. Higgins Mechanical Engineering Dept.
Associate Professor McGill University
Shock Wave Physics Group Montreal, Quebec CANADA
http://people.mcgill.ca/andrew.higgins/
.
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