Pump with intake and compression using different pressure ratios

[goran d]

Lets say we got a larger cylinder-piston combo and a smaller one.
First we move the larger cylinder, filling in with vacuum. Then we pump in air, using the smaller cylinder, isothermally, with variable expansion ratio.
Here, we clearly have exp ratio > P_atm/P_final
We then compress the larger cylinder isothermally, this time
we have exp ratio = P_atm/P_final
Thus we have gained energy from the air, or so it seems?
This is because work of isothermal expansion is proportional to ln(exp ratio)

 

[jrmichler]

Any piston that compresses isothermally must do so at low speed. A practical reality of low speed operation is that mechanical friction losses and leakage losses become a larger percentage of the total work. There is a speed that minimizes both adiabatic losses and mechanical friction losses, for the best compression efficiency. At that speed, the compression cylinder is "large", thus expensive. The most economical compression design trades off adiabatic losses, friction losses, capital cost, and operating cost to get minimum net present operating cost.

For an example of the reverse situation, search Atkinson cycle engine. The Wikipedia hit is a good place to start.

Then study some thermodynamics until you understand that you are trying to invent, if not a perpetual motion machine, a cycle better than the Carnot cycle (search that term also).

Do all of that until you can discuss your cycle using the correct equations, and calculating the efficiency relative to both isothermal and adiabatic compression. Do this while recognizing that your design cannot do perfect isothermal or adiabatic compression. Include pressure - temperature - time curves for your cycle, isothermal compression, and adiabatic compression. Discuss the conditions necessary to get isothermal and adiabatic compression, with calculations.

If you spend sufficient time studying the above, show us your work and we can help you proceed further.

 

[goran d]

I do get net work with adiabatic compression, but only if the large cylinder is kept under environment temperature during the fill phase. If the heat is left to build up freely, negative work done.
It is relatively inefficient with 60L large cylinder and 1L small.
To make it efficient a gas container for keeping the inlet pressure high can be used, but it will have to be huge!
At one atmosphere its about 1.5KW with two alternating phase 1L small cylinders and one larger 60L one.
I guess it would need a 3-4 K drop in the large cylinder due to high volume (drop at the fill in phase), hopefully it still works then.

 

[jrmichler]

Do all of that until you can discuss your cycle using the correct equations, and calculating the efficiency relative to both isothermal and adiabatic compression. Do this while recognizing that your design cannot do perfect isothermal or adiabatic compression. Include pressure - temperature - time curves for your cycle, isothermal compression, and adiabatic compression. Discuss the conditions necessary to get isothermal and adiabatic compression, with calculations.

You still need to do this.

but only if the large cylinder is kept under environment temperature during the fill phase.

Then you have an energy flow that must be included in your calculations.

I do get net work with adiabatic compression

Wrong. See above for why it's wrong.

 

[goran d]

It seems that to get 10K drop in a 1L small cylinder it needs to have area of 6m^2.
About the large cylinder, to be able to do sufficient heat exchange area can be similar.
Note that "everything" is isothermal except the compression.
So it is outputting air hotter than the environment, while doing work.
But the heat is flowing in through a heat exchanger in the cylinders.
Technically that makes the efficiency negative even though its doing work since the heat is flowing from colder to hotter air.