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?

Answer 1

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

w_p = 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

w_T = h₃ - h₄ = 1436.5 kJ/kg  

Steam generator:

q_H = h₃ - h₂ = 3107 kJ/kg  

w_NET = w_T ? w_p = 1436.5 – 30.54 = 1406 kJ/kg  

? = w_NET/q_H = 1406 / 3107 = 0.45