Page 120 - Advanced thermodynamics for engineers

106 CHAPTER 5 RATIONAL EFFICIENCY OF POWER PLANT

If the turbine and feed pump of the cycle are not isentropic then the work output will be less than
that of the ideal Rankine cycle and it is possible to define the efficiency ratio as
h cycle
Efficiency ratio ¼ (5.27)
h Rankine
Substituting from Eqns (5.23) and (5.26) gives
w net h 3 h 2 w net
Efficiency ratio ¼ $ ¼
h 3 h 2 b 3 b 2 b 3 b 2 (5.28)
¼ rational efficiency; h R

This means that a steam turbine which operates on a reversible Rankine cycle will have a rational
efficiency of 100% because the condenser temperature is T 0 . If there are any irreversibilities then the
rational efficiency will be less than 100%. Rational efficiency shows the scope for improving the
device within the constraints of, say, peak pressure and temperature. If the rational efficiency is low
then the efficiency can be improved significantly, whereas if it is high then not much improvement is
possible.
It has to be remembered that these definitions of rational efficiency for a steam plant cycle
are based on the dead-state temperature being made equal to the condenser temperature. If
another temperature is chosen then the rational efficiency will be reduced as shown in
Eqn (5.22). It will be shown that this results in a rational efficiency of unity for an ideal (internally
reversible) Rankine cycle, and such an approach can be used to indicate how far an actual
(irreversible) steam plant cycle falls short of the yardstick set by the reversible one. However, this
approach also masks the ‘cost’ of external irreversibilities between the working fluid in
the condenser and the true dead state of environmental conditions. These effects are discussed in the
examples.
When the term rational efficiency is applied to an air-standard cycle it is never possible to achieve a
value of unity because the temperature at which energy is rejected is not constant. This will also be
considered in the examples by reference to the Joule cycle for a gas turbine.

5.4 EXAMPLES
5.4.1 STEAM TURBINE CYCLES
Q1. A steam turbine operates on a basic Rankine cycle with a maximum pressure of 20 bar and a
condenser pressure of 0.5 bar. Evaluate the thermal efficiency of the plant. Calculate the
maximum net work available from the cycle, and evaluate the rational efficiency of the cycle.
Solution
The T–s diagram for the Rankine cycle is shown in Fig 5.4. The parameters for the state points on
cycle 1-2-3-4-6-1 will now be evaluated.
Conditions at 4
p 4 ¼ 20 bar; x 4 ¼ 1

t s ¼ 212:4 C; h g ¼ 2799 kJ=kg; s g ¼ 6:340 kJ=kg K