On Wed, Jan 29, 2020 at 11:30:20AM -0600, Jim Davis wrote:
On Tue, Jan 28, 2020 at 07:57:14PM -0600, Jim Davis wrote:
On 1/28/2020 2:16 PM, Norman Yarvin wrote:
The thing is, if the pressure were higher after expansion, wouldn't
that have to mean it was higher before expansion, too?
Yes, Indeed it would. Constant volume heat addition will result in a
higher pressure and a higher temperature than the same amount of heat
being added at constant pressure. The difference is that the constant
volume heat addition results in a lower entropy increase than the
corresponding constant pressure heat addition. This means the Humphrey
cycle rejects less heat which means more of the heat added is doing work
which means the cycle is more efficient.
And if you
pumped up your conventional engine to that same higher pressure,
wouldn't it have the same efficiency?
Indeed, it might have higher efficiency. But we're comparing cycles
with the same pressure ratio.
That's what I'm arguing against; it seems like the wrong comparison.
That "pressure ratio" is the compression ratio, and the compression
stage isn't a process that actually exists in a rocket engine; it's
just a theoretical part of those cycles.
But that doesn't negate the thermodynamic advantages of constant
volume heat addition.
The ratio that exists in a
rocket engine is the expansion ratio; that seems like the proper
standard of comparison. When you're actually building a combustion
chamber, it is of no consequence that the 'official' high pressure is
the one before combustion: you still have to design it to deal with
the much higher pressure after combustion.
Sure, there are enormous challenges to be overcome to arrange constant
volume heat addition to get the thermodynamic advantages. But
designing more robust combustion chambers is way down the list.
(Pump-fed rocket engines do involve compression, of course, but the
pumps are normally pumping liquids, which thermodynamically falls not
into the "heat engine" category but almost purely into the "doing
work" category, since liquids have minimal compressibility. And since
they are denser than gases, not nearly as much power is required in
the first place, compared to what is required to run a compressor in a
jet engine of the same thrust.)
But it doesn't follow that it is a trivial matter to raise the
combustion pressure in a rocket engine. Given a set of propellant
turbopumps that raise the propellants to a given pressure (or a set of
propellant tanks that can be pressurized to a given pressure) it is
still thermodynamically advantageous to add heat (burn the
propellants) at constant volume rather than constant pressure.
The
challenges to arrange constant volume heat addition are certainly
enormous but the thermodynamic advantages are attractive enough that
interest in PDEs and such has never died out.
