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Optimal Location of Multiple Bleed Points in Rankine Cycle

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…. A MATHEMATICAL MODEL. A. Turbine. B. SG. Y j-11, h bj-1. y j, h bj. Y j-2, h bj-2. C. OFWH. OFWH. OFWH. C.

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Optimal Location of Multiple Bleed Points in Rankine Cycle

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  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. A MATHEMATICAL MODEL A Turbine B SG Yj-11,hbj-1 yj, hbj Yj-2,hbj-2 C OFWH OFWH OFWH C 1- yj hf (j-1) 1 ,hf (j) 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 Steam The power developed by the bleed steam of ith heater before it is being extracted is given by hs TURBINE 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 yi , hbi ith heater hfi h f i-1 Mass balance of the heater at inlet and exit is given by: • Energy balance of the feed heater gives:

  7. A D T i i-1 B C 0 S T-S DIAGRAM FOR REGENERATION CYCLE

  8. Therefore the thermal efficiency of the cycle is

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

  10. 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.

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

  12. 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

  13. 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…

  14. 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.

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

  16. D = 20 units D = 20 units Example of Monte Carlo Method Area of a square : 400 square units. Area of Circle: 314.15 square units.

  17. 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

  18. Increasing Sample Size Reduces Error

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

  20. Number of generation and Efficiency

  21. RESULTS

  22. RESULTS

  23. RESULTS

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

  25. Closed Feed Water Heaters (Throttled Condensate)

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