Speed of Sound at High Pressures

[rsterne]

When looking for information about the speed of sound at high pressures, I ran across the following website.... http://www.peacesoftware.de/einigewerte/einigewerte_e.html
It has calculators for Oxygen, Nitrogen, and Carbon Dioxide, which allow you to find the speed of sound at various combinations of temperature and pressure.... This is the only place I have ever found information on the speed of sound at high pressures.... I used the calculator to determine a bunch of data points, and then plotted them using Excel.... First for HPA at 20*C....



I extrapolated the data for air using the mix of Nitrogen and Oxygen in the atmosphere (78:21), but it ignores the other components in air.... However, it comes out to 1130 at 20*C which is just about right on, so I have no reason to believe it isn't pretty darn close at higher pressures.... Next for CO2....



There is very little "normal" for the chart on CO2.... Instead of the speed of sound increasing with pressure as happens with Nitrogen and Oxygen, it drops.... In all cases I plotted the speed of sound of the gaseous component, not the liquid.... The boiling curve spans pretty much the whole range where CO2 can exist as both liquid and gas, from -55*C to about 30*C.... As the temperature increases (increasing the pressure), the speed of sound drops....  In practical terms, we are really only interested in what happens between 0*C (freezing) and 40*C (103*F), and of particular importance is 20*C (room temperature, 68*F).... so I plotted those three temperatures at all pressures up to the maximum that would normally occur (without over filling the container)....

I then looked at what would be the typical pressure at the exit of the valve for the three temperatures over the bulk of the fill conditions for a tank containing CO2.... For the 0*C case, the pressure is about 500 psi, and the speed of sound is about 695 fps.... For the 20*C case, the pressure is about 800 psi, and the speed of sound is about 659 fps.... At 40*C, the pressure varies as the tank empties, starting at about 1500 psi but quickly dropping to 1300 at 90% full, then gradually dropping to about 1100 psi before dropping quickly again as the tank drops below 30% full.... It spends most of the time between 1100-1300 psi, and the corresponding speed of sound averages about 680 fps.... The average value I came up with for the speed of sound at the exit of the valve, while the valve is open, over the typical range of temperatures (0-40*C) is 680 fps.... I think that would be a good velocity to use for any calculation of sonic choking in the ports.... As the pressure drops, the speed of sound increases and the choking becomes less of an issue, so I think using 680 fps makes sense....

Bob

[PakProtector]

Thanks Bob...I can't help feeling the CO2 wackiness is related to its compressibility. Much food for thought; thanks for digging into it...
cheers,
Douglas

[rsterne]

It was NOT easy to find, I've been looking on and off for over 5 years.... Yes, the CO2 weirdness is because of the multiple states at various combinations of pressure and temperature.... I think using a value of 659 fps (800 psi @ 20*C) makes the most sense, as that's the lowest value we are likely to run into under "normal" circumstances.... and the value is under 700 fps except for some fill states at higher temperatures.... After all, for sonic choking, the lower the speed of sound the larger the ports must be.... 

Bob

[dougroundup]

CO2 wackiness = sublime and supercritical state of CO2 at pressures and temps?

[Gtownjake]

This is why I was a liberal arts major.
And why I just load it, cock it and pull the trigger. 

[rsterne]

CO2 acts nowhere near an ideal gas, so hence the weird velocities vs. temperature and pressure....

BTW, I recently found another document which confirmed the calculator I was using for Nitrogen, the speed of sound does, indeed, change at high pressures.... chart on the very last page of this PDF file....  http://www.bnl.gov/magnets/staff/gupta/cryogenic-data-handbook/Section6.pdf

According their data, 1110 fps @ NTP, 1460 fps @ 250 bar (3600 psi), both at 0*C.... very close agreement with my graph....

Bob

[vinenator]

Don't the calculations assume the atmosphere as a whole is composed of the gas in question?

so, the curve for "air" would be correct, but our atmosphere is not pure Nitrogen, Oxygen or CO2, so what do the other curves mean?

If we have an air rifle loaded up with Nitrogen and it is released at 2000psi, it is only pure Nitrogen behind the pellet and when the pellet exits the muzzle it is, for argument sake, travelling at 900fps, well below the speed of sound in air. the Nitrogen will be expelled behind the pellet at a much reduced pressure.

so how is this information useful? something that might influence ports or other orifice design? well above my pay grade until i know more.

[rsterne]

This information is to determine the speed of sound in the gas INSIDE the PCP, it is useless once the pellet exits the barrel.... Note that I couldn't find the data for "air", I made that graph by combining the data for Nitrogen and Oxygen in the ratio of 78:21.... This thread is useful in conjunction with the one on "Sonic Choking" of ports in a PCP.... http://www.gatewaytoairguns.org/GTA/index.php?topic=66737.0 .... Other than that, it is merely a curiosity....

Bob

[Gatorproof]

Bob and his new buddy are escspees from MIT experiential AG department.
If there is a test, I need to sit behind Bob so I can copy from his test paper, lol.

Cause I don't get it, lol.