Specific heats at high pressure

I just got the book "Mechanics and Thermodynamics of Propulsion",
mostly on the recommendations found in the sci.space.tech archives. I
turned to Appendix 2 to find tables with specific heat vs temp for the
various gases that you find in a rocket engine (O2, CO2, CH4, H2, H2O,
that sort of thing). Hooray!

Imagine my disappointment when I noticed that the tables were
specifically for gases at low pressure -- 1 atm. That pressure
doesn't come up very often in simulations of rocket engines and
hypervelocity guns.

I've looked on the web, but have not found a reference for specific
heats of these gases at high pressures. I'm mostly interested in the
100 - 1000 atm range.

Am I just being stupid or unread? Is there some bog-standard
adjustment that I'm supposed to make to these specific heats to
account for pressure? Or did some guy in 1886 prove that specific
heats are completely independent of pressure?

On 10 Jul 2003 16:48:01 -0700, in sci.space.tech
(Iain McClatchie) wrote:

I just got the book "Mechanics and Thermodynamics of Propulsion",
mostly on the recommendations found in the sci.space.tech archives. I
turned to Appendix 2 to find tables with specific heat vs temp for the
various gases that you find in a rocket engine (O2, CO2, CH4, H2, H2O,
that sort of thing). Hooray!

Imagine my disappointment when I noticed that the tables were
specifically for gases at low pressure -- 1 atm. That pressure
doesn't come up very often in simulations of rocket engines and
hypervelocity guns.

I've looked on the web, but have not found a reference for specific
heats of these gases at high pressures. I'm mostly interested in the
100 - 1000 atm range.

Am I just being stupid or unread? Is there some bog-standard
adjustment that I'm supposed to make to these specific heats to
account for pressure? Or did some guy in 1886 prove that specific
heats are completely independent of pressure?

How accurate are you trying to be? In my copy of NASA SP-3045,
Compressed Gas Handbook, the variation of the Cp of air as a function
of pressure is small at higher temps. Data eyeballed off graph:

T (F) Cp @ 0psia (Btu/Lbm) Cp @ 15,000psia (Btu/Lbm)
500 0.248 0.289
1000 0.265 0.288
2000 0.283 0.2835
3000 0.295 0.301
4000 0.3045 0.3065

FWIW, this data is courtesy of the Cornell University, Engineering
Experiment Bulletin No.30. Where the data included for other gases
also came from.

Ed How accurate are you trying to be?

Probably more accurate than neccessary. I'm writing a simulator for
a travelling charge gun burning high-pressure CH4-O2. This first
simulator is terribly crude -- I've cut the gas slug behind the projectile
into a stack of disk-shaped homogenous gas masses, I'm assuming completely
uniform axial gas motion, and the burn rate model is a a*(1-f)*e^(b*f)
limited exponential. So all this is highly inaccurate. On the other hand,
I've read papers from the 1950s that suggest that guns less than 100
caliber lengths lose just a few percent to drag losses, and I'm just trying
to get some rough estimates of muzzle velocity versus barrel size and
pressure (i.e. cost). Since I don't have any idea how much Cp changes over
pressure, I don't know if it's an ignorable effect or if it dominates lots
of other effects. And if I can just write a Cp(pressure, temp, species)
function from a bunch of accurate tables and never have to worry about that
again, that'd be great.

Actually, I'm so thermodynamically retarded that I'm going to have to
prove to myself that the second law of thermodynamics still holds with
these varying specific heats. Even just that isn't clear to me yet.

Eventually I may try a Navier-Stokes integration. My current ignition
scheme is to use electronically triggered gunpowder charges funnelled
through little nozzles to inject hot gas into the cold CH4-O2 mix. I
expect there are probably some very serious problems with this idea
near the end of the launch, where the gunpowder product jet is moving
slower than the CH4-O2 behind the projectile. Maybe that next
simulation will show some of these problems, maybe not.

Ed In my copy of NASA SP-3045, Compressed Gas Handbook,

Compressed Air and Gas Handbook, John P. Rollins Ed.?

Ed the variation of the Cp of air as a function of pressure is small
Ed at higher temps. Data eyeballed off graph:

T (F) Cp @ 0psia (Btu/Lbm) Cp @ 15,000psia (Btu/Lbm)
500 0.248 0.289
1000 0.265 0.288
2000 0.283 0.2835
3000 0.295 0.301
4000 0.3045 0.3065

Hmmm. at 1000F there's a 10% diff. That'll show up.

FWIW, this data is courtesy of the Cornell University, Engineering
Experiment Bulletin No.30. Where the data included for other gases
also came from.

Couldn't find that one the web. I don't suppose there is a web
reference for all this data?

On 11 Jul 2003 17:28:32 -0700, in sci.space.tech
(Iain McClatchie) wrote:


Ed In my copy of NASA SP-3045, Compressed Gas Handbook,

Compressed Air and Gas Handbook, John P. Rollins Ed.?

No, this is a NASA publication, edited by John S. Kumkle, Samuel D.
Wilson and Richard A. Cota, John F. Kennedy Space Center
Library of Congress Catalog Card no. 68-62085


Couldn't find that one the web. Go to your local technical library, not everything is available on the web. The web may be the first place to look, but certainly not the only.

(Iain McClatchie) wrote in message . com...
I've looked on the web, but have not found a reference for specific
heats of these gases at high pressures. I'm mostly interested in the
100 - 1000 atm range.

Programs like propep can calculate the specific heats in this pressure range.