[AR] Re: Thrust augmentation?
- From: Norman Yarvin <yarvin@xxxxxxxxxxxx>
- To: arocket@xxxxxxxxxxxxx
- Date: Sat, 13 Feb 2021 05:09:08 -0500
On Fri, Feb 12, 2021 at 09:07:05AM -0500, Nels Anderson wrote:
On 2/11/21 4:59 PM, Henry Spencer wrote:
On Thu, 11 Feb 2021, Norman Yarvin wrote:
If ambient air is mixed into the exhaust as a working fluid, then it
will expand, conceivably generating additional thrust.
Still, to be realized, that thrust would have to actually exert
pressure somewhere, and the walls of that aluminum tube are parallel
to the flow, so that couldn't be where. (The bell-shaped portion is
the intake, not the exhaust.)
Other things being equal -- a big assumption -- suction in a
forward-facing intake bell is just as good as pressure in an
aft-facing nozzle bell.
Or how about simply increasing pressure at the original (w/o
augmentation tube) nozzle exit.
That's a different way of doing the accounting for thrust than I had
in mind, but it can work. Either you can integrate the pressure over
all exposed solid surfaces, or you can take any arbitrary volume which
includes the engine and integrate both pressure and momentum flow over
its boundary. To be precise, in both cases it's the integral of a
vector: not just pressure, but pressure multiplied by the unit vector
perpendicular to the surface. The former way is conceptually simpler,
and what I was invoking, but of course the two ways have to give the
same result. Only one of the three components of the result vector
(the one in the thrust direction) should end up nonzero, at least in
the usual situation where the rocket is cylindrically symmetrical.
Anyway, if you're using the second method, such that "pressure at the
exit" enters into the equation rather than just pressure on surfaces,
then you have to account for not just pressure but momentum flow. And
while a rise in pressure due to the air in the tube getting heated
does raise the pressure of the exhaust, it also probably lowers the
suction on the intake (Henry's point) as well as changing the flows,
putting the net effect at least at first glance into the "hmm, dunno"
category.
If you're just integrating pressure on surfaces, Henry's point looks
simpler: the surfaces on the inside of the bell are seeing lower
pressure and pulling the rocket forward. (Having the bell there,
though, restricts airflow somewhat, lowering the pressure on surfaces
on the rear of the rocket which are not part of the thrust augmenter
tube; since they're facing rearward, that would lower the thrust --
again making the net effect non-obvious.)
Anyway, about the original point that:
If ambient air is mixed into the exhaust as a working fluid, then it
will expand, conceivably generating additional thrust.
Although the ambient air will expand from heating, by the same token
the exhaust will contract from cooling. With PV=nRT being linear, one
might think the net effect would be zero, except that heat capacities
also enter into it. One could try to figure those out, but in any
case there's another effect, which is that the exhaust is probably
fuel-rich and will burn further in air, giving net expansion and
pressure rise, as we've been figuring.
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