How to predict the exit temperature of an air compressor?

[Lnewqban]

I'm asking these questions to have a better theoretical understanding of the process.

That is excellent!

I recommend that you study centrifugal compressors, as their internal compression process is much less brutal than the one happening in reciprocating machines.

Please, see:
https://lindbergprocess.com/2020/01/centrifugal-vs-reciprocating/

 

[MysticDream]

I recommend that you study centrifugal compressors, as their internal compression process is much less brutal than the one happening in reciprocating machines.

I've studied them a bit but will more. Thanks.

 

[MysticDream]

In my judgment, if you really want to understand all this fundamentally, you need to learn about Newtonian fluid mechanics and heat transfer. This is covered in the best book I know of, Transport Phenomena, by Bird, Stewart, and Lightfoot. Transport phenomena include momentum transfer (Newtonian fluid mechanics), heat transfer (conduction and convection), and mass transfer (diffusion). Both fluid dynamics and heat transfer are part of the picture on the microscope in a cylinder of gas undergoing and adiabatic reversible expansion or compression.

I've bought the pdf and there is a ton to info to cover which may take a long time. Is it possible for you to narrow the last question down for me? I know I should have to work for it, as I'm sure you have, but any help would be appreciated. I'm wanting to get a general idea of what an approximate reversible process would look like with the velocity of a piston in a cylinder and what the scale looks like as it increases. For example, would it be "near" reversible with a piston peak velocity at 1 m/s and then if doubled in speed it becomes 50% irreversible?

 

[BillMcC]

That I don’t know. I should have clarified that I’m assuming the process is adiabatic with no heat exchanger. I’m trying to understand the interaction between only the piston and gas which I suspect depends on it’s speed and how it’s driven. Would a faster moving piston (higher rpm) naturally do more work on the gas because of the nature of a constant angular velocity crank acting on a volume of gas? Because it has to maintain a speed or torque to overcome its final delivery pressure, it seems it would do far more work on the gas than is necessary during its initial compression for each cycle. I’d imagine a truly reversible adiabatic process varying in driving torque or speed throughout one cycle, perhaps slowing down during the initial compression or at least decreasing in torque. It seems the only way for that to be possible mechanically is to have a very slow moving piston. A truly reversible process would make a compressor most efficient because the mass flow rate for the target pressure would be the highest. The temperature would not raise as much due to excess work being done during an irreversible process.

When it is a piston-type compressor, the head of the compressor usually has some provision for dissipating heat. The lines leaving the compressor sometimes have fins. Most piston compressors are two-stage compressors: One large cylinder compresses the incoming air to some percentage of the final second-stage piston pressure, which keeps changing as the reservoir, the compressor storage tank raises in pressure.