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

Rankine Cycle with Double Closed Feed Water Heaters

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

Development of Constant  Model – Step 1

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

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

Development of Constant  Model – Step 2

Cost to Benefit Ratio for Rankine Cycle with Two OFWHs

Approximate Solutions to Optimal Locations for Two OFWHs

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

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

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

Rankine Cycle with Double Closed Feed Water Heaters 1 2 3 4 5 12 6 9 10 7 11 8

Optimal Selection of two CFWHs 1 2 3 4 5 6 7 8 9 10 11 12 f

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

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

Structure of Modern Rankine Cycle Power Plant

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…

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)

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:

Recursive Formula for ith FWHs

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

Objective Function For Optimization Maximize:

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

Thermodynamic Analysis of Modern Power Plant

Train of Shell & Tube HXs.