In thermodynamics, an isentropic process is an ideal thermodynamic process that is adiabatic and reversible. In this system, the transfer of work is friction less and there is no net transfer of heat or mass.
Formula of Isentropic efficiency of steam turbine
The isentropic efficiency is the ratio of actual power to the isentropic power and this isentropic efficiency of a steam turbine can be calculated using the following formula:
η = (hi - ho) / (hi - hos)
Here,
hi : enthalpy of the steam at the inlet of the turbine (btu/lb)
ho : enthalpy of the steam at the outlet of the turbine (btu/lb)
hos : isentropic enthalpy of the steam at the outlet of the turbine (btu/lb)
Python code
The following is a Python example that calculates the isentropic efficiency of a steam turbine when superheated steam at 600 psig, 700 degF operates the turbine and is extracted at 60 psig, 350 degF.
from pyXSteam.XSteam import XSteam
steamTable = XSteam(XSteam.UNIT_SYSTEM_FLS) # ft/lb/sec/°F/psi/btu
def isentropicefficiency(Pi, Ti, Po, To):
hi = steamTable.h_pt(Pi+14.696, Ti)
ho = steamTable.h_pt(Po+14.696, To)
si = steamTable.s_ph(Pi+14.696, hi)
hos= steamTable.h_ps(Po+14.696, si)
return (hi - ho) / (hi - hos) * 100
hi = steamTable.h_pt(Pi+14.696, Ti)
ho = steamTable.h_pt(Po+14.696, To)
si = steamTable.s_ph(Pi+14.696, hi)
hos= steamTable.h_ps(Po+14.696, si)
return (hi - ho) / (hi - hos) * 100
# from 600 psig + 700 degF to 60 psig + 350 degF
When run the code, you get the results below.
hi : enthalpy of steam Pi, Ti (btu/lb) = 1350.1
si : entropy of steam Pi, Ti (btu/lb-F) = 1.584
ho : enthalpy of steam Pi, Ti (btu/lb) = 1205.5
so : entropy of steam Po, To (btu/lb-F) = 1.657
hos : isentropic enthalpy of steam Po, si (btu/lb) = 1149.6
isentropicefficiency = (1350.1 - 1205.5) / (1350.1 - 1149.6) * 100 = 71.1
isentropicefficiency = 72.1
print("isentropicefficiency = ", isentropicefficiency(600, 700, 60, 350))
