Stirlingengineforum.com

I'm designing a kind of modified Stirling engine and I really need information on what kind of pressure can generally be expected inside the displacer chamber during the Hot or expansion cycle.

I'm not talking about actual pressure but potential pressure.

That is; if the displacer chamber did not have a piston but instead was simply a sealed chamber or cylinder without any outlet and the hot end of the chamber was heated in the usual way and then the displacer was moved so as to heat up the air in the chamber and the air expanded...

Though in this case, it would have nowhere to expand to...

Assuming that the thing was constructed with sturdy enough material that it didn't blow apart or rupture a seal or something...

How many PSI would be generated.

Is there some kind of ratio between cylinder size, temperature differential and potential PSI generated ?

Any information or links to sources of such information would be greatly appreciated.

This is all theoretical at the moment. My only alternative is to experiment by making various size displacer chambers and attaching some sort of pressure gage, but it would be nice to have some kind of ball park figures to start out with...

If the pressures can get extremely high, like enough to blow the thing apart without a piston to push out of the way to relieve the pressure... I don't want to have it blow up in my face while I'm experimenting with it, if it can be avoided.

Thanks !

Tom

To easily get an estimate for the pressure inside a sealed can that is heated a few assumptions need to be made:
1) There is no temperature gradient across the inside of the can. That is, all of the air inside of the can is at the same temperature.
2) The gas inside of the can obeys the ideal gas law. (http://en.wikipedia.org/wiki/Ideal_gas_law).

If you assume both of these than the pressure inside of the can will be P=(nRT)/V. If you use n = density*volume/(molar mass of air). The density of dry air is about 1.2041 kg/m^3 (http://en.wikipedia.org/wiki/Density_of_air) and the molar mass of air (assuming you're using air inside of your Stirling engine) is approximately 28.97g/mol. The volumes cancel in the ideal gas equation and you get:

P = (density/molar mass)RT

As long as the volume of the gas remains constant the pressure will not depend on the volume.

These calculations would give you a rough estimate of the maximum pressure that could be created inside a can that is being heated. If you wanted to assume that the temperature inside the can was not the same throughout the can or that one side of the can could lose heat the equation would become more difficult.

Also, the values for density and molar mass are metric so if you want psi you will either have to use metric and convert later or look up there equivalents in other units.

Thanks, but I don't think the information is applicable -- in that all the air inside the can is NOT the same temperature. At least not for any length of time that I could possibly calculate but is going rapidly from cold to hot and back with the movement of the displacer.

I'm interested in the peak pressure that might develop when air inside a displacer chamber goes from cold to hot.

Hopefully with some relationshipd given between air volume and temperature differential -- using plain old air rather than Nitrogen or Helium etc.

I guess this has not been investigated.

I'll try attaching a small air tank... like an old propane tank to the displacer chamber with some kind of reed (or leaf) valve or check valve in between and put a pressure guage on the tank. I think in that way I can build pressure in the tank slowly and get some idea of how high it might go.

Perhaps I'll start out by attaching a balloon. That way the worst that could happen is the balloon breaks - - though that won't give an accurate pressure reading... It would be a start and give me some idea of how much air expansion is going on.

I read on some DOE (Department of Energy) PDF I downloaded which tested Stirling engines and listed PSI ratings of from about 400 PSI to several thousand, which seemed like awfuly high numbers !

It didn't seem to give clear information though - - as to if they were using pre-pressurized gas (Nitrogen or Helium) in the engines they were testing or if this was pressure that developed from zero in the displacer chamber.

It is very common and widely accepted to use an isothermal analysis in first order analyzes. I agree with CanadaPhysics. The easiest, most conservative way is to assume that the cylinder is at some static pressure before heating, calculate the mass of the air, and calculate volume of the air. Then assume all of the air goes to the high temperature. Using the same volume and mass, calculate the new pressure of the air. This will give you a rough order of magnitude estimate that you can use for prototypes.

Here is a nice online ideal gas law calculator I found: http://www.extremescience.com/ideal-gas-law.htm