Page 123 - Advanced thermodynamics for engineers

5.4 EXAMPLES 109

Q2. Re-evaluate the parameters for the steam plant in Q1 based on t 0 ¼ 81.3 C if (a) The isentropic
efficiency of the turbine is 80%; (b) The isentropic efficiency of the feed pump is 70%; (c) If the
efficiency of the components is the combination of those given in (a) and (b).
Solution
(a) Turbine efficiency, h T ¼ 80%.
If the turbine efficiency is 80% then the work output of the turbine becomes

w T ¼ h ðw T Þ isen ¼ 0:80 598:2 ¼ 478:6kJ kg:
T
w net w T þ w P 478:6 2:0
Hence, the thermal efficiency of the cycle is h ¼ ¼ ¼ ¼ 0:194
th
The rational efficiency is q in h 4 h 2 2799 342:0
½w net Š actual ½w net Š actual 478:6 2:0
h ¼ ¼ ¼ ¼ 0:798:
R
b 4 b 2 b w net 597:2
The rational efficiency has been significantly reduced by the inefficiency of the turbine, and the
rational efficiency is approximately equal to the isentropic efficiency of the turbine.
(b) Feed pump efficiency, h P ¼ 70%.
The feed pump work becomes

ðw P Þ isen 2:0
w P ¼ ¼ ¼ 2:864 kJ=kg:
h P 0:7
h 0 ¼ h 1 þ dh 12 0 ¼ 340 þ 2:864 ¼ 342:9kJ=kg:
2
w net w T þ w P 598:2 2:864
The thermal efficiency of the cycle becomes h ¼ ¼ ¼ ¼ 0:242.
th
q in h 4 h 2 0 2799 342:9
The exergy at 2 may be evaluated approximately by assuming that the entropy does not change
0
significantly over the pumping process, i.e. s 20 ¼ s 1 :
Hence
b 2 ¼ h 2 T 0 s 2 a 0 ¼ 342:9 354:3 1:091 a 0 ¼ 43:6 a 0 kJ=kg:
0
0
0
The rational efficiency is
½w net Š actual ½w net Š actual 598:2 2:86
h ¼ ¼ ¼ ¼ 0:997
R
b 4 b 2 0 b w net 597:2
The reduction in thermal efficiency is small and the rational efficiency is almost 1. Hence, the
Rankine cycle is not much affected by inefficiencies in the feed pump.
(c) Turbine efficiency, h T ¼ 80%; feed pump efficiency, h P ¼ 70%.
w net w T þ w P 478:6 2:86
The thermal efficiency is h ¼ ¼ ¼ ¼ 0:194
th
q in h 4 h 2 0 2799 342:9
½w net Š actual ½w net Š actual 478:6 2:86
The rational efficiency is h ¼ ¼ ¼ ¼ 0:797
R
b 4 b 2 0 b w net 597:2
Q3. Steam turbine cycles
The steam plant in question Q2 is modified so that the steam is superheated before entering the
turbine so that the exit conditions from the turbine of the ideal cycle are dry saturated. Evaluate the