On Sun, 26 Jan 2003, Randall Clague wrote:
> I'm also a little fishy about getting all the benefit of LOX/LH2 by
> adding LOX to a monatomic hydrogen engine. IIRC, LOX/LH2 is run fuel
> rich to exhaust a lot of atomic hydrogen and drive the molecular
> weight through the floor, since exhaust velocity wants to go up as the
> inverse square root of the molecular weight.
It's not quite that simple...
First, a minor correction: the excess of hydrogen gives you molecular
hydrogen, not atomic hydrogen, in the exhaust. Atomic hydrogen forms in
significant quantities only at very high temperatures.
Now, Isp is proportional to sqrt(temperature/molecularweight), yes, but in
a chemical rocket, those two variables are not independent! After a
simplifying assumption or two, temperature/molecularweight is just
energyrelease/mass in funny units. (Hill&Peterson2 shows this, although
it fails to notice the implications.) There is no way you can raise
energyrelease/mass by adding non-reacting mass.
However, nozzle efficiency also matters, and in most cases that is a
strong function of gas properties. Diatomic molecules like H2 have fewer
places to hide energy, keeping it away from a conversion process (heat to
kinetic energy) which has to be fairly rapid, than triatomic ones like
H2O. So an excess of H2 is good for nozzle efficiency, and since hydrogen
is so light, even quite a substantial excess of H2 weighs little and thus
doesn't hurt energyrelease/mass very much.
Also, one of the simplifying assumptions I mentioned tends to break down
in a low-pressure LOX/LH2 chamber. Dissociation (H2O -> H2 + O2) prevents
the combustion from going to completion, and the expansion through the
nozzle is rapid enough that recombination in the nozzle doesn't clean up
the excess completely. Roughly speaking, the effect of this is to set an
upper limit on chamber temperature which is independent of mixture ratio,
over a limited range... which decouples temperature from molecular weight,
within that range. So in a dissociation-limited engine, you do have some
freedom to manipulate the two variables independently, and engine
performance pushes you toward mixture ratios which lower molecular weight.
Henry Spencer
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