[AR] Re: Orions and PDEs (was Re: More MAX delays.)
- From: Norman Yarvin <yarvin@xxxxxxxxxxxx>
- To: arocket@xxxxxxxxxxxxx
- Date: Fri, 31 Jan 2020 03:04:48 -0500
On Fri, Jan 31, 2020 at 12:48:18AM -0500, Henry Spencer wrote:
On Thu, 30 Jan 2020, Norman Yarvin wrote:
You're completely missing the point. For a given amount of heat
addition the constant volume process has a higher pressure rise, a
higher temperature rise, and (most importantly) a lower entropy
increase. This means that more of the energy is available to
accelerate the fluid and less has to be rejected as heat.
I thought you'd agreed that (in a rocket) you can get all those
benefits equally well just from upping the pressure...
Remember that upping the pressure costs energy -- it doesn't happen free,
indeed the cost can be quite significant. (It's not an accident that the
high-pressure engines use topping cycles so that the propellant burned to
power the pumps isn't then thrown away at low velocity -- you can't afford
that, there's too much of it.)
A large part of the reason for that, though, is that the process of
pumping is quite inefficient. To power the pumps you normally burn a
far off-stoichiometric mix so that your turbines don't melt, and then
both turbines and pumps have major inefficiencies, and then a lot of
the pump energy gets wasted in fluid friction. Yet as long as all the
propellant ends up in the combustion chamber, all of this inefficiency
doesn't matter: the exhaust from the off-stoichometric mix goes into
the chamber and finishes burning, and almost all the waste heat ends
up in the chamber where it makes the chamber hotter just as it would
if the combustion had occurred there.
So provided you use a topping cycle, the only energy you really lose
by upping the pressure is the actual pressurization energy (P*V).
Forcing a liter of kerosene into a 300 bar chamber takes 30
kilojoules, and burning it provides about as many megajoules. Even
though you also have to inject about twice the volume of LOX, that's
not a big energy loss. Maybe it gets up to half a percent, if you
also allow for the combustion energy being lower due to the fact that
even the main chamber combustion is somewhat fuel-rich. (And yes, if
you want the number to look worse, run it for liquid hydrogen.) For a
half percent energy loss, the Isp loss is a quarter of a percent,
because exhaust velocity goes as the square root of energy.
Besides, even setting that aside, such an equivalence would be rather
strange. Disregarding the (important) issue of nozzle efficiency, more
energy to accelerate fluid gives higher Isp.
Quite true (including the part I snipped), but this discussion
centered on nozzle efficiency, with two competing expressions being
given for the two cycles, one of which was the usual nozzle efficiency
and the other the nozzle efficiency after you boosted the chamber
pressure via constant volume combustion (but referenced to the
pre-boost chamber pressure). So disregarding nozzle efficiency in the
present context is a bit strange.
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