Note
Go to the end to download the full example code.
Rankine cycle (with units)#
Calculate the efficiency of a Rankine vapor power cycle using a pure fluid model for water. Includes the units of quantities in the calculations.
Requires: Cantera >= 3.0.0, pint
***************** State 1 ******************
water:
temperature 300 K
pressure 3528.2 Pa
density 996.59 kg/m^3
mean mol. weight 18.016 kg/kmol
vapor fraction 0
phase of matter liquid-gas-mix
1 kg 1 kmol
--------------- ---------------
enthalpy -1.5858e+07 -2.857e+08 J
internal energy -1.5858e+07 -2.857e+08 J
entropy 3913.2 70500 J/K
Gibbs function -1.7032e+07 -3.0685e+08 J
heat capacity c_p 4181.3 75330 J/K
heat capacity c_v 4131 74425 J/K
***************** State 2 ******************
water:
temperature 300.14 K
pressure 8e+05 Pa
density 996.91 kg/m^3
mean mol. weight 18.016 kg/kmol
vapor fraction 0
phase of matter liquid
1 kg 1 kmol
--------------- ---------------
enthalpy -1.5857e+07 -2.8568e+08 J
internal energy -1.5858e+07 -2.8569e+08 J
entropy 3915 70532 J/K
Gibbs function -1.7032e+07 -3.0685e+08 J
heat capacity c_p 4178.6 75282 J/K
heat capacity c_v 4127.9 74368 J/K
***************** State 3 ******************
water:
temperature 443.62 K
pressure 8e+05 Pa
density 4.1587 kg/m^3
mean mol. weight 18.016 kg/kmol
vapor fraction 1
phase of matter liquid-gas-mix
1 kg 1 kmol
--------------- ---------------
enthalpy -1.3202e+07 -2.3784e+08 J
internal energy -1.3394e+07 -2.4131e+08 J
entropy 10183 1.8346e+05 J/K
Gibbs function -1.7719e+07 -3.1922e+08 J
heat capacity c_p 2464.4 44399 J/K
heat capacity c_v 1764.5 31790 J/K
***************** State 4 ******************
water:
temperature 300 K
pressure 3528.2 Pa
density 0.030558 kg/m^3
mean mol. weight 18.016 kg/kmol
vapor fraction 0.83516
phase of matter liquid-gas-mix
1 kg 1 kmol
--------------- ---------------
enthalpy -1.3822e+07 -2.4902e+08 J
internal energy -1.3938e+07 -2.511e+08 J
entropy 10700 1.9277e+05 J/K
Gibbs function -1.7032e+07 -3.0685e+08 J
heat capacity c_p inf inf J/K
heat capacity c_v nan nan J/K
efficiency = 0.23320852221836424 dimensionless
import cantera.with_units as ctu
# parameters
eta_pump = 0.6 * ctu.units.dimensionless # pump isentropic efficiency
eta_turbine = 0.8 * ctu.units.dimensionless # turbine isentropic efficiency
p_max = 116.03 * ctu.units.psi # maximum pressure
def pump(fluid, p_final, eta):
"""Adiabatically pump a fluid to pressure p_final, using
a pump with isentropic efficiency eta."""
h0 = fluid.h
s0 = fluid.s
fluid.SP = s0, p_final
h1s = fluid.h
isentropic_work = h1s - h0
actual_work = isentropic_work / eta
h1 = h0 + actual_work
fluid.HP = h1, p_final
return actual_work
def expand(fluid, p_final, eta):
"""Adiabatically expand a fluid to pressure p_final, using
a turbine with isentropic efficiency eta."""
h0 = fluid.h
s0 = fluid.s
fluid.SP =s0, p_final
h1s = fluid.h
isentropic_work = h0 - h1s
actual_work = isentropic_work * eta
h1 = h0 - actual_work
fluid.HP = h1, p_final
return actual_work
def print_state(n, fluid):
print('\n***************** State {0} ******************'.format(n))
print(fluid.report())
if __name__ == '__main__':
# create an object representing water
w = ctu.Water()
# start with saturated liquid water at 80.33 degrees Fahrenheit
w.TQ = ctu.Q_(80.33, "degF"), 0.0 * ctu.units.dimensionless
h1 = w.h
p1 = w.P
print_state(1, w)
# pump it adiabatically to p_max
pump_work = pump(w, p_max, eta_pump)
h2 = w.h
print_state(2, w)
# heat it at constant pressure until it reaches the saturated vapor state
# at this pressure
w.PQ = p_max, 1.0 * ctu.units.dimensionless
h3 = w.h
heat_added = h3 - h2
print_state(3, w)
# expand back to p1
turbine_work = expand(w, p1, eta_turbine)
print_state(4, w)
# efficiency
eff = (turbine_work - pump_work)/heat_added
print('efficiency = ', eff)
Total running time of the script: (0 minutes 0.232 seconds)