Adiabatic Pneumatic Cylinder Model

Once upon a time, Ether asked:

For fast-acting pistons (as in previous years) I wonder if adiabatic behavior would be a better model.

I’d hunch that in general adiabatic behavior is more realistic. And so, I modeled it.

adiabatic_cylinder_model.pdf (475.7 KB)

I totally agree that an adiabatic solution makes far more sense than a constant pressure or even constant temperature solution, especially for a fast process such as a launcher. I haven’t followed through your math yet, but I’m concerned with a few of your assumptions.

  1. the open system … is the air contained within a pneumatic cylinder, plus the air in the hose leading up to it
  2. The cylinder itself is considered to have a mass M and sees the cylinder pressure, a resistive force Fload, and atmospheric pressure.
  3. No heat transfer; _Qin = 0
  4. Mass transfer into the system has negligible velocity (v) and head height (gz), leaving only enthalpy h(T).

Here are the issues I noticed with these assumptions:

  1. is a definition and OK by itself, but impacts assumptions 3 and 4 below.
  2. The constant Fload is a good first approximation, and probably OK if the cylinder is directly moving the load in a relatively constant orientation. However, if the load is moving on a rotating arm or other non-linear transfer, this will cause the net load force to change along the stroke.
  3. As heat-carrying mass [air not at zero kelvins] is entering, heat is entering as well.
  4. Does not make sense because the boundary of the system is a relatively small tube; the air will be moving at a decent speed. Perhaps later in the math you added something so that the head (pressure) is applied at a large diameter (the tank) and you applied Bernoulli’s equation across a small air mass. Even then, the implicit assumption of an infinitely large tank will break down at some point.
  1. Yep.
  2. Never said Fload is constant. This is for a numeric DE solver so Fload can be anything (infact, in my sim, it is an expression box, so wide open to be used in such practical ways)
  3. I suppose this isn’t “adiabatic” by the definition I just looked up. I do model incoming air as transferring heat, though, but there’s no Q from conduction/convection/etc. The entire pneumatic system is adiabatic (no mass entry/exit), but this isn’t particularly helpful as the different portions are at different states.
  4. Adding a term to account for velocity wouldn’t be hard - will revise and see how that fares.
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