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Equations of State for Gas Gun Applications

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Equations of State for Gas Gun Applications

Unread postAuthor: DYI » Tue Dec 17, 2013 1:00 am

As usual, I'm up to something, and I've hit a bit of a stumbling block;

Most of the "real gas" equations of state currently in use have been developed with various chemical industries in mind and are thus more oriented toward modeling significantly non-spherical and interacting molecules and mixtures, with correspondingly little attention paid toward high pressure - high temperature behaviour. In the regimes I'm interested in the repulsive term is a larger contributor to the overall compressibility than the attractive term (although both are significant). This inquiry is mostly directed toward high pressure performance at ~room temperature. High temperature effects are a different issue I'll be looking into later.

The Carnahan-Starling (CS) hard spheres equation of state appeared a promising candidate for the repulsive term, but in all of my test cases performed poorly compared to a simple Van der Waals (VDW) style repulsive term. This leads me to question the reason its accuracy appears to be held in such high regard - regardless of exact choice for the reduced number density term, the shape of the curve is just not a good fit - alter the reduced number density to fit at one point, and it gets even worse elsewhere. The most egregious errors I've seen from it so far appear using argon (a gas for which a hard spheres repulsive term should be quite accurate), but they are relatively severe for air, nitrogen, and helium as well, regardless of choice of attractive term (I've been playing with RK, SRK, Peng-Robinson, and ESD attractive terms).

Just in case it's relevant, I've been taking my P-V-T data from the NIST thermodynamic property papers for helium, nitrogen, and air, and a Contrails paper for argon. I could construct tabular equations of state based on results from these papers (they are highly comprehensive, with thousands of data points) and an interpolation algorithm, but I'd rather not if I can avoid it (the digital copies are scans of the originals). Can anyone offer insight on more appropriate equations of state for gas gun purposes, or even on the apparent poor performance of the CS repulsive term compared to the supposedly less accurate VDW term? The second one is bugging me more than the first at this point.
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Re: Equations of State for Gas Gun Applications

Unread postAuthor: ramses » Tue Dec 17, 2013 1:37 pm

If you have a set of data, is there a reason you can't just do a spline fit? I have fit high dimensional tabular data using a small neural network.
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Re: Equations of State for Gas Gun Applications

Unread postAuthor: DYI » Wed Dec 18, 2013 12:43 am

The issue is with moving the set of data from a scan of a typewritten page into a format where it can be worked with. That will require a script employing text recognition, which would be a project in itself. I'll do it if it's the only option, but I was hoping to find an EoS which more readily matched the available data to get around that hassle.

Due to the process of generating an equation of state in the form of P(ρ,I) from one in the form of P(ρ,T) and specific heat capacity data, the result which I actually use in my project will be tabular anyway. For speed, I'll likely be using a simple bilinear interpolation algorithm for pulling data from that table, but this is all largely irrelevant to the problem at hand. I'm quite capable of doing all kinds of fascinating things with the data, but I have to get it / generate it first.
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Re: Equations of State for Gas Gun Applications

Unread postAuthor: jackssmirkingrevenge » Wed Dec 18, 2013 9:18 am

Reading stuff like this makes me wish I paid more attention to thermodynamics at school :-/
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