2 40 points A supercritical reheatregeneration cycle is prop

2. (40 points) A supercritical reheat-regeneration cycle is proposed to operate as shown in the T-s diagram in Fig. with two reheat stages and two open feedwater heaters. Saturated liquid exits each of two OF WHs. Determine the maximum possible cycle efficiency. It is mandatory to present the schematic of the cycle marking all the states the cycle with numbers. Hint: Pay attention that there is a state that is omitted on the diagram! Introduce it to the diagram and assign number 12 to it. T6 Ts 600 °C MPa 350 °C 5) 4 MPa 0.2 MPa 0.01 MPa. Answer: Solution:

Solution

solution:

1)here we are dealing with supercritical rankine cycle means it is operating above pressure of 240 bar with two reheatre and two open feed water heater,

2)here pump work is given by

Wp=[(30-4)10/10+(4-.2)10/10+(.2-.01)10/10]=26+3.8+.19=29.99 kj/kg

3)here one stage of feed water pump is absent after point 3,hence it is added and name as 12

4)here from that let enthalpy at various ponts are

h1=hf1=191.8 kj/kg

h2=h1+.19=191.99 kj/kg

h3=hf3=504.7 kj/kg

h12=h3+3.8=508.5 kj/kg

h4=hf4=1087.4kj/kg

h5=h4+26=1113.4 kj/kg

4)here from table of supercritical steam enthalphy at temparature and pressure are

h8=3673.5 kj/kg

h10=3173.89 kj/kg

h11=hg1=2584.6 kj/kg

5)here by equating entropy at 6 -7 and 8-9 we get superheating temperature as follows

s6=sg+cpln(Tsup/Tsat)

6.237=6.069+2.299ln(Tsup/250.33)

Tsup=269.3 c

h6=hg6+cp(Tsup-Tsat)=2843.93 kj/kg

in same way

s8=s9

T9=134.45 c

h9=2735.43 kj/kg

6)as we know all enthlpy for knowing feed water bleeded mass as from energy balance equation as follows

m7+h7+(1-m7)h12=h4

m7=.2478 kg/kg steam

m9h9+(1-m9)h2=h3

m9=.09246 kg/kg of dstteam

7)total turbine work is

Wt=(h6-h7)+(1-m7)(h8-h9)+(1-m7-m9)(h10-h11)=1697.25 kj/kg

Wp=29.99 kj/kg

W=Wt-Wp=1667.26 kj/kg

8)supplied heat

Q=(h6-h5)+(1-m7)(h4-h12)+(1-m7-m9)(h3-h2)=2975.12 kj/kg

8)hence efficioency is

n=W/Q=1667.26/2975.47=.5604=56.04%