1. Optimal Location of Multiple Bleed Points in Rankine Cycle
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
Sincere Efforts for Best Returns…..

2. n number of OFWHs require n+1 no of Pumps…..
A MATHEMATICAL MODEL A
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…

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

4. Contributions of Bleed Steamhs
TURBINE
The power developed by the bleed steam of ith heater before it is being extracted is given by yi
hbj

5. OPTIMIZATION METHODOLOGY (Contd..)
The work done by the bleeds of all feed water heaters is given by:

6. 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:

8. S A B D i
i-1 C T
T-S DIAGRAM FOR REGENERATION CYCLE

9. Therefore the thermal efficiency of the cycle is

10. Modified Heywood’s Model
Maximize:
Or Maximize:

11. Maximum Bleed Steam Power Model
Fundamentally, the steam is generated to produced Mechanical Power.
However, after expanding for a while, the scope for internal utilization of some steam for feed water heating looks lucrative.
To have a balance between above two statements.
Any optimal cycle should lead to:
Maximization of the combined power generated by all the bleed streams.

12. Therefore the work bone by bled steams can be written as

13. OPTIMIZATION MODEL Optimization problem can now be expressed as :
Maximising the function
Where hfi = f(p(i)) , hf(i+1) = f(p(i+1)) and hbi = f(pi, s)
And subjected to following constraints:
hfi , hf(i+1) , hbi >0

14. Artificial Intelligence Technique Applied to Optimization of OFWHs
P M V Subbarao
Professor
Mechanical Engineering Department
I I T Delhi
Best Blue Print for Carnotization of Rankine cycle…

15. OPTIMIZATION PROCEDURE
Suitable method to find the value of the variable that maximize the objective function.
The design variables and the constraints show that the system optimization is a non-linear programming problem.
For such problems, a Monte Carlo simulation technique has been found to be quite efficient.

16. Monte Carlo Method A Random Walk Method.
Solve a problem using statistical sampling
Name comes from Monaco’s gambling resort city

17. Example of Monte Carlo Method
Area of a square : 400 square units.
Area of Circle: square units.
D = 20 units
D = 20 units

18. Example of Monte Carlo Method
Generate 20 random number in the range 1 to 400.
Locate them inside circle or outside circle based on their value.
Count the points lying inside the circle.
Area = D2

19. Increasing Sample Size Reduces Error
Estimate
Error
1/(2n1/2) 10
100
1,000
10,000
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000

20. INPUT n, Tmax , Pmax, Pmin, max no. of generation
Flow Chart for optimisation
INPUT n, Tmax , Pmax, Pmin, max no. of generation
Go to 1 NO
YES
OUTPUT: efficiency,Popt
Calculate hbi, hfi
at each pressure Pi
and hboi, ht1, hc1, hc2.

21. Number of generation and Efficiency

22. RESULTS

23. RESULTS

24. RESULTS

25. Thermal Efficiency
Work output
Work output
Effect of no of feed water heaters on thermal efficiency and work output of a regeneration cycle

26. Closed Feed Water Heaters (Throttled Condensate)