Consider an ideal Rankine cycle using water with a high-pressure side of the cyc
ID: 2086643 • Letter: C
Question
Consider an ideal Rankine cycle using water with a high-pressure side of the cycle at a supercritical pressure. Such a
cycle has a potential advantage of minimizing local temperature differences between the fluids in the steam
generator, such as the instance in which the high-temperature energy source is the hot exhaust gas from a gas-
turbine engine. Calculate the thermal efficiency of the cycle if the state entering the turbine is 30 MPa, 550°C, and
the condenser pressure is 5 kPa. What is the steam quality at the turbine exit?
Explanation / Answer
For the efficiency we need the net work and steam generator heat transfer.
C.V. Pump. For this high exit pressure
from table at State 1:
s1 = 0.4764 kJ/kg K,
h1 = 137.82 kJ/kg
Entropy .:
s2 = s1 => h2 = 168.36 kJ/kg
wp = h2 - h1 = 30.54 kJ/kg
C.V. Turbine. Assume reversible and adiabatic.
Entropy :
s4 = s3 = 6.0342 = 0.4764 + x4 x 7.9187
x4 = 0.70186 => Very low for a turbine exhaust
h4 = 137.79 + x4 × 2423.66 = 1838.86 ,
h3 = 3275.36 kJ/kg
wT = h3 - h4 = 1436.5 kJ/kg
Steam generator:
qH = h3 - h2 = 3107 kJ/kg
wNET = wT ? wp = 1436.5 – 30.54 = 1406 kJ/kg
? = wNET/qH = 1406 / 3107 = 0.45