Sizing Air Tank: Estimating Polytropic Efficiency 2

[erk1313]

Problem: Starting with an air compressor with a known free air displacement, how long would it take to fill a 5 gallon air tank to 95psig? See below for more detail.

Method: Use (PV^n = constant) to convert free air displacement (in standard atmosphere units SCFM) into resulting pressure built up in the fixed volume of the tank. Because the free air displacement changes based on the outlet pressure (see manufacturer's

http://www.eng-tips.com/threadminder.cfm?pid=391

chart), take small iterative steps until the final pressure is reached.
P = Patm*Vatm^n/V^n
Vatm = Vinitial + Vcompressor; The resulting air volume in the tank, but expressed as (SCF) standard atmosph. pressure and temperature.

Question: In using (PV^n = constant), how would I estimate the polytropic efficiency so I am not stuck assuming adiabatic expansion (n=1.4) (all heat generated is absorbed as increased gas temperature) or isothermal expansion (n=1) (all heat generated is removed so that the gas is kept at a constant temperature). Looking over manufacturer's pages, I typically see the assumption of isothermal expansion (n=1) being made when estimating fill time. Is this because inefficiency is already built into their free air displacement spec?

Knowns (assume STP conditions):
Air Tank Volume: V = 5 Gal = 0.67CF
Flow Rate: Vatm ~ 0.6SCFM (See manufacturer's table for Free Air Displacement chart) or approximate with best-fit line (Q = 1.117*Poutlet^-0.169)
Pressure (1atm): Patm = 14.7psia
Target Pressure: Pf = 95psig = 109.7psia
Compressor: Oil-lubed, reciprocating compressor
Specific Heat of Air: k = 1.4

Notes:
-Other threads mention taking an assumption of 85% isothermal efficiency for reciprocating compressors, but how would this figure into the polytropic exponent ?
(thread1036-238662)
-The following thread mentions a way to calculate the polytropic exponent , but I am unclear at how to conduct this (or may be missing information from the manufacturer) (no discharge temperature or motor rpm).
thread391-151370 (6 April 06 post)

 

[racookpe1978]

1/16 inch ID tube is your flow restriction point n that setup. Also, that small a tube over a 36 inch length will effectively cool the newly compressed air back to ambient very effectively.

 

[erk1313]

BTW: To share a little about the project, the air bladder is our partner's proprietary design but it requires a large volume of air to go from full deflation (such as CPR mode) to full inflation (about 8CF @ 1psig). Hence the large high pressure air tanks. My guess is that bedroom air mattresses never fully deflate, and the kind that do fully deflate take several minutes to blow up. Actual operating pressure is less than 1psig and is regulated via PPC valve. Function is to evenly distribute pressure to prevent bed sores. I agree that the bladder could be improved by minimizing the required air volume, but that's for further down the road.
Thank you for the contributions. I now feel much better about my assumptions and will be able to size air compressors more accurately.

 

[erk1313]

Interestingly, after measuring the actual flow from the output of the compressor (using McM #41945K56, I get much lower flow than the rate provided by the factory:

Plugging this measured flow rate into the predicted ADIABATIC equation (green line), I get similar results to using the manuf. spec flow with ISOTHERMAL equation (black line). Perhaps this reinforces that manufacturers back calculate the FAD using an isothermal assumption but the true output is adiabatic?