Henry, thanks for the thoughtful reply.

HS Provided you can arrange for both to be gases at the time, there is some
HS merit to this... although there is also some risk of explosion.

I know that premixed LOX/liquid hydrocarbon is an explosive. But premixed
gas-phase O2/CH4 is reputed to be fairly tame. Certainly if you dilute it
with 4 parts N2 and run it at 1 atm it's pretty reasonable.

The danger, I think, is that liquid injection can allow a substantial mass
of propellant to build up in the combustion chamber. With gas phase
injection the amount that can build up is two orders of magnitude smaller.

HS Note that the function of a flameholder is partly to induce turbulence,
HS which somewhat defeats your intent.

Mmmm. My intent is actually to figure out something amateurs can fool with
at less risk to their heads. In any case, you are right, and the
flameholder turbulence would be supplied by a wire grid. That turbulence
would be nothing like the turbulence in the usual combustion chamber design.

HS Gaseous fuel mixes burn much faster if you stir some of the combustion
HS products back into the incoming mix; it's thought that they catalyze
HS otherwise-slow steps in the combustion process.

I didn't know this. I know that one other thing flameholders do is provide
streams of mixture below flame speed, so that the flame always has a chance
to burn back down the flow and doesn't get blown off.

For this design, I actually don't want the flame speed to be very high,
because higher flame speed = higher flow rate = more acceleration through
the flame = less efficiency. But flame speeds below 20 m/s don't actually
involve a lot of pressure drop, and there is quite a way to go between
16 cm/s for CH4/air at STP, and 20 m/s. (That 20 m/s is a pretty weak limit,
btw. Pressure drop builds slowly with velocity.)

There is another design point that I had initially considered. If the
injected gas is higher density (pressure and cold), the flame speed should
increase. At some point (turbopumps required), the flame speed should get
to the point that the combustion products are supersonic. Note that the
flame is subsonic -- this is not a detonation. In any case, since the
post-flame flow is supersonic, you can go directly to a diverging nozzle
and eliminate the combustion chamber altogether. It sure *looks* simple!

The problem with this design point is that it's apparently not very
efficient to accelerate gas by adding heat. So you apparently want to
minimize the flow velocity when burning, and then accelerate the gas.
This inefficiency shows up in my equations as a pressure drop across the
flame.

This is why I suspect that accelerating boiling two-phase is not an
efficient process (either in the cooling jacket, or in the combustion
chamber). It's probably better to keep the fluid under enough pressure
to keep it a liquid, then drop the pressure across an injector, where the
fluid flashes to vapor.

Do you know if the H2 in the SSME / RL10 / etc boils before it gets to
the injector face? The SSME has a very low injector pressure drop -- 5%
or so -- it would be awfully impressive to heat the H2 to within a few
percent of boiling but not over. I guess you could heat into into two
phase, and that's a pretty wide heat capacity target, but then you'd have
to deal with variable volumetric flows from various ratios of the two
phases.

Ooh you can really see how injector design gets so sensitive to operating
conditions.

HS People have run RL10s on methane and propane without difficulty, using
HS the same basic injection strategy (gaseous fuel, liquid oxidizer).

Ah, but with methane the liquid volume ratio is completely different.
Did they get good Isp out of the RL10 running LOX/CH4?