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From: (Jim Glass)
Subject: Re: Effects of external combustion on plug/aerospike nozzles
Date: Fri, 12 Jul 1996 15:04:19 GMT

In article <4rppse$>, (Paul F. Dietz) writes:
|> A question about these things...  since rocket exhaust is typically
|> fuel rich, what is the effect on the performance of a plug or
|> aerospike nozzles of reaction between the exhaust and the atmosphere?
|> Naively,  I would expect it to add energy to the jet, reducing the
|> rate at which the jet's gas pressure declines as it expands, thereby
|> increasing thrust.  What do calculations say?
|> 	Paul

I can't respond to the precise question. 

However, the addition of energy to the expanding flow is well-known;
it is termed "shifting combustion" and occurs even in conventional
bell nozzles.  Indeed, it DOES result in higher temperatures in the
exhaust as it expands--relative to a fixed-composition flow field,
usually called "frozen". The higher-temperature gas results in
higher pressures as you mention, yielding higher specific impulse
for shifting conditions than for frozen.

Real nozzle flows are neither fully frozen nor fully shifting, due
to the rate of reaction of the components.  The departure from pure
shifting is thought of as a loss (kinetic loss), but could just as
well be considered a gain (relative to frozen).

In the 60's there were some efforts to "tailor" the shape of the
nozzle in order to minimize kinetic losses (or force things toward
shifting).  Unfortunately, these usually resulted in fairly long
nozzles which adversely affected nozzle weight and increased drag

[Interestingly, Soviet nozzle designs have a 'different' look to
them than typical US designs.  US designs are 'truncated Rao optimum'
bells, usually designed by method-of-characteristics methods.  Soviet
nozzles, to US eyes, look more 'conical' (not comical) than ours.
Ours have that nice 'parabolic' look to them--less conical.
One would suppose the Russians are fully capable of running M-O-C
and CFD codes and thus their nozzles, if optimum, should look
'just like' ours.  Since they don't, I've always wondered if they
know something we do not.  In my experience, the US is better at
combustion engineering (minimal C-star losses) but has fairly substantial
losses in the nozzle (aerodynamic losses).  The Russians tend to
reverse this, throwing away huge gobs of energy due to incomplete
combustion and then using a very efficient expansion process to
get some of it back.  The bottom line is both design approaches 
appear to yield roughly the same Isp efficiency... One wonders 
what would happen if one were to mate a US combustor to a Russian

Jim Glass

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Subject: Re: Effects of external combustion on plug/aerospike nozzles
From: Henry Spencer <>
Date: Jul 17 1996

In article <4sgcflINNe96@HOBBES.NA.CS.YALE.EDU> yarvin-norman@CS.YALE.EDU (Norman Yarvin) writes:
>>...Interestingly, Soviet nozzle designs have a 'different' look to
>>them than typical US designs.  US designs are 'truncated Rao optimum'
>>bells, usually designed by method-of-characteristics methods.  Soviet
>>nozzles, to US eyes, look more 'conical' ...
>If the fuel is still burning as it enters the nozzle, one needs a more
>conical nozzle to deal with it properly.  (The more conical and the
>less bell-shaped the nozzle is, the more it will delay expansion; and
>delayed expansion seems to be what one needs to deal with delayed

This is unlikely to be the explanation, alas.  In almost any rocket
engine, some of the combustion is "delayed" in the sense that a slower
expansion would release more energy -- the exhaust products normally do
not have time to reach equilibrium.  Unfortunately, to a good first
approximation, reaction rates are zero after the nozzle throat. 

Why?  Well, as the gas accelerates, two things happen.  First, obviously,
it covers distance much more quickly -- the gas spends *much* less time in
the last 10% of the nozzle than in the first 10%.  Second, the conversion
of thermal energy to kinetic energy implies a rapid fall in temperature...
meaning that reaction rates, which are exponential with temperature, drop
*precipitously*.  The combined bottom line is that if you plot reaction
rate versus distance down the nozzle, you discover that there's a point --
the "Bray freezing point" -- where the reaction rate absolutely falls off
a cliff, plunges almost vertically downward.  To a fair approximation, the
exhaust composition is in equilibrium up to that point, and constant
afterward.  The Bray freezing point is necessarily in the immediate
vicinity of the nozzle throat, and you don't lose much by assuming that
it is in fact at the throat. 

(I oversimplify slightly, most seriously in assuming that there is one
Bray freezing point, when in fact each reaction has a slightly different
one... but that doesn't change the general picture much.)

Fiddling with the nozzle shape is not going to delay expansion enough to
see any major gains from better equilibrium.  The change of reaction rate
at the Bray freezing point is several orders of magnitude.  And no, there
is no magic way to move the Bray freezing point down the nozzle -- its
existence and approximate location are fundamental results of the basic
expansion process.

It *is* curious that the Russians seem to prefer less curved nozzles, but
I note that this might be the result of fairly mundane considerations like
manufacturing.  Greater curvatures are harder to make, and Russian engines
are built for mass production by a less sophisticated industrial base.
..the truly fundamental discoveries seldom        |       Henry Spencer
occur where we have decided to look.  --B. Forman  |

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