1. Optimal Location of Multiple FWHs in Rankine Cycle
P M V Subbarao
Professor
Mechanical Engineering Department
A Truly Concurrent Model for PGS ……

2. Rankine Cycle with Double Closed Feed Water Heaters

3. Rankine Cycle with two OFWHs :Generalized Notations for Variable Cardinal Points –

4. Development of Constant  Model – Step 1

5. Analysis of mixing in HP-OFWH
Constant pressure mixing process
Conservation of energy:

6. Analysis of mixing in LP-OFWH
Constant pressure mixing process
Conservation of energy:

7. Development of Constant  Model – Step 2

8. Cost to Benefit Ratio for Rankine Cycle with Two OFWHs

9. Approximate Solutions to Optimal Locations for Two OFWHs

10. Approximate Solutions to Optimal Locations for Two OFWHs
For a given steam conditions,  and  are known and constant.
 The condition for maximum efficiency is:

11. Exact Iterative Solutions to Optimal Locations for Two OFWHs – Method - 1
Generate two random number for pb1 and pb2, in the viscinity of corresponding approximate optimal locations.
Calculate values of , , 1 and 2.
Compute efficiency of cycle.
Repeat step 1 to 3 for several combinations of pb1 and pb2.
Select the highest the locations corresponding to highest cycle efficiency as optimal locations

12. Exact Iterative Solutions to Optimal Locations for Two OFWHs – Method - 2
Generate two random number for pb1 and pb2, in the range (pL,pA).
Calculate values of , , 1 and 2.
Compute efficiency of cycle.
Repeat step 1 to 3 for several combinations of pb1 and pb2.
Select the highest the locations corresponding to highest cycle efficiency as optimal locations

13. Rankine Cycle with Double Closed Feed Water Heaters1 2 3 4 5 12 6 9 10 7 11 8

14. Optimal Selection of two CFWHs1 2 3 4 5 6 7 8 9 10 11 12 f

15. Exact Iterative Solutions to Optimal Locations for Two OFWHs
Generate two random number for p2 and p3, in the viscinity of corresponding approximate optimal locations based on OFWHs.
Calculate values of enthalpy at all the cardinal points..
Compute efficiency of cycle.
Repeat step 1 to 3 for several combinations of p2 and p3. T s 1 2 3 4 5 6 7 8 9 10 11 12
Select the highest the locations corresponding to highest cycle efficiency as optimal locations

16. Exact Iterative Solutions to Optimal Locations for Two OFWHs
Generate two random number for p2 and p3, in the range (p1,p4).
Calculate values of enthalpy at all the cardinal points..
Compute efficiency of cycle.
Repeat step 1 to 3 for several combinations of p2 and p3.
Select the highest the locations corresponding to highest cycle efficiency as optimal locations T s 1 2 3 4 5 6 7 8 9 10 11 12

17. Structure of Modern Rankine Cycle Power Plant

18. Rankine Cycle with N number of OFWHs
Turbine B SG
Yj-11,hbj-1
yj, hbj
Yj-2,hbj-2 C
OFWH
OFWH
OFWH C
1 ,hf (j)
1- yj
hf (j-1)
1- yj – yj-1
hf (j-2)
1- yj – yj-1- yj-2
hf (j-3)
n number of OFWHs require n+1 no of Pumps…..
The presence of pumps is subtle…

19. ANALYSIS OF ‘ith’ FEED WATER HEATER
Mass entering the turbine is
STEAM IN
STEAM TURBINE
Mass of steam leaving the turbine is
STEAM OUT
y(i-1)
hb(i-1)
yi,
hbi
y1,
hb1
mie , hfi
mi,i, hf(i-1)

20. Analysis of ‘ith’ Feed Water Heater
Mass balance of the heater at inlet and exit is given by:
yi , hbi
hfi
h f i-1
ith heater
Energy balance of the feed heater gives:

21. Recursive Formula for ith FWHs

22. Cost to Benefit ratio for Rankine Cycle with n OFWHsD i
i-1 C T
Therefore the thermal efficiency of the cycle is

23. Objective Function For Optimization
Maximize:

24. HP CFWHs – one OFWH (deaerator) – LP CFWHs
Sequence of FWHs
HP CFWHs – one OFWH (deaerator) – LP CFWHs

25. Thermodynamic Analysis of Modern Power Plant

26. Train of Shell & Tube HXs.