Polytropic efficiency is a measure of the efficiency of a compressor. It is defined as the ratio of the actual work done by the compressor to the work that would be done if the compression process were isentropic (reversible and adiabatic). The polytropic efficiency of a compressor is always less than its isentropic efficiency.
Formula of Compressor polytropic efficiency
The polytropic efficiency of a compressor can be calculated using the following formula:
Po/Pi = (To/Ti)^(n/(n-1))
n/(n-1) = log(Po/Pi)/log(To/Ti)
η = (n/(n-1))/(k/(k-1))
η = log(Po/Pi)/log(To/Ti)/(k/(k-1))
where η is the polytropic efficiency, Pi and Ti are the inlet pressure and temperature, Po and To are the outlet pressure and temperature, and k is the specific heat ratio of the gas.
η : polytropic efficiency
Po : outlet pressure (psig)
Ti : inlet temperature (degF)
To : outlet temperature (degF)
n : compression ratio
k : specific heat ratio
Python code of Compressor polytropic efficiency
The following Python code is an example of calculating the polytropic efficiency of a compressor when gas introduced at 30 psig, 140 degF is compressed to 125 psig, 350 degF. (specific heat ratio k = 1.243).
Run Python code below : https://www.mycompiler.io/view/JMIFkEueEHW
import math
def compressorpolytropiceff(Pi, Po, Ti, To, k):
Pi : inlet Pressure (psig)
Po = Po + 14.696
Pi = Pi + 14.696
To = To + 460
Ti = Ti + 460
if k == 1 or Pi == 0 or Ti == 0: return -1
return math.log(Po/Pi)/math.log(To/Ti) / (k/(k-1)) * 100
polyeff = compressorpolytropiceff(30, 125, 140, 350, 1.243)
print("compressor polytropic efficiency = ", polyeff)
Po = Po + 14.696
Pi = Pi + 14.696
To = To + 460
Ti = Ti + 460
if k == 1 or Pi == 0 or Ti == 0: return -1
return math.log(Po/Pi)/math.log(To/Ti) / (k/(k-1)) * 100
polyeff = compressorpolytropiceff(30, 125, 140, 350, 1.243)
print("compressor polytropic efficiency = ", polyeff)
When run the code, you will receive the following results.
compressor polytropic efficiency = 74.2%
