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Regenerative Cycle And Its Process

 In the practical regenerative cycle, the feedwater enters the boiler at the temperature between 4 and 4' and It is heated by steam extracted from intermediate stages of the turbine. The flow diagram of the regenerative cycle with the saturated steam at the inlet to the turbine, and the corresponding T-s diagram. For every kg of steam entering the turbine, let m1 kg steam be extracted from an intermediate stage of the turbine where the pressure is p2, and it is used to heat up feed water ((1-m1)kg at state 8) by mixing in heater 1. The remaining (1-m1)kg of steam then expands in the turbine  from pressure p2 ( state 2 ) to pressure p3 ( state 3 ) when m2 kg of steam is extracted for heating feed water in heater 2. So (1- m1 - m2)kg of steam then expands in the remaining stages of the turbine to pressure p4, gets condensed into water in the condenser, and then pumped to heater 2, where it mixes with m2 kg of steam extracted at pressure p3. Then (1-m1) kg of water is pumped into heater 1 where it mixes with m1 kg of steam extracted pressure p2. The resulting 1kg of steam is then pumped to the boiler where heat from an external source is supplied. Heaters 1 and 2 thus operate at pressure p2 and p3 respectively. The amounts of steam m1 and m2 extracted from the turbine are such that the exit from each of heaters, the state is saturated liquid at the respective pressures. The heat and work transfer quantities of the cycle as follows: 


 regenerative cycle flow diagram with two feed waters

Wt = 1(h1-h2) + (1-m1) (h2-h3) + (1- m1-m2) (h3 - h4)  kJ/kg.

Wp = Wp1 + Wp2 + Wp3

      = (1-m1-m2)(h6-h5) + (1 -m1) (h8-h7) + 1 ( h10-h9) kJ / kg 

Q1 = 1(h1 - h10) kJ / kg 

Q2 = (1 - m1 - m2) (h4 - h5) kJ / kg 

Cycle efficiency N = (Q1 -Q2) / Q1 = (Wt - Wp) / Q1

Steam Rate = 3600 / ( Wt - Wp )   kg / kWh

In the Rankine cycle operating at the given pressures, p1 and p4, the heat addition would have been from state 6 to state 1. By using two stages of regenerative feed water heating, feedwater enters the boiler at state 10, instead of state 6, and heat addition is, therefore, from state 10 to state 1. There fore, 

(Tm1) with regeneration =( h1 - h10 ) / (s1 -s10) 

and 

(Tm1) without regeneration = (h1 - h6) / (s1 - s6) 

Since (Tm1)  with regeneration > (Tm1)without regeneration. 

The efficiency of the regenerative cycle will be higher than that of the Rankine cycle. 

The energy balance for heater 2 gives, 

m1h2 + ( 1- m1) h8 = 1h9

m1 = (h9 -h8) / (h2 - h8)                                                              *

The energy balance for heater 1 gives 

m2h3 + (1 - m1- m2 ) h6 = (1- m1) h7 

m2 = (1- m1) ((h7-h6) / (h3-h6))                                                  #

from the equations * and #  

(1-m1) (h9-h8) = m1(h2-h9)

(1-m1-m2) (h7-h6) = m2(h3-h7)

Energy gain of the feed water = Energy given off  by vapor in condensation.

Heaters have been assumed to be adequately insulated, and there is no heat gain from, or heat loss to, the surroundings.

                            regenerative cycle on t-s plot with decreasing mass fluid

                                    regenerative cycle on t-s plot for unit mass fluid.


Path 1-2-3-4 represents the states of decreasing mass of fluid.

For 1kg of steam, the states would be represented by the path 1-2'-3'-4'. 

Wt = (h1-h2) + (1-m1) (h2-h3) + (1-m1-m2) (h3-h4)

     = (h1-h2) + (h2' - h3') + (h3' + h4') 

where  (1-m1) (h2-h3) = 1(h2' - h3') 

        (1 - m1 - m2) (h3 -h4) = 1( h3" - h4')

 The cycle 1-2-2'-3'-3''-4'-5-6-7-8-9-10-1 represents 1kg of working fluid. The heat released by steam condensing from 2 to 2' is utilised in heating up the water from 8 to 9/ 

1(h2 -h2') = (h9 -h8)

Similarly, 

1(h3' -h3") = 1(h7 -h6)

Wt = (h1-h4')-(h2-h2')-(h3-h3")

     = (h1-h4') - (h9-h8) - (h7-h6)

                                               Regenerative cycle on h- s diagram 




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