Combustor Gas turbine Air inlet Exhaust a n on n Heat recove

Combustor Gas turbine Air inlet Exhaust -a n on n Heat recovery Steam generator Turbine Vapor cycle i 11 Condenser Pump I 10 Cooling A combined gas turbine vapor power plant has a net heat rate transfer in combustor, Qin 100 Mw. Air enters the compressor of the gas turbine at 100 kPa, 300K, and is compressed to 1200kpa. The isentropic efficiency of the compressor is 8496. The condition at the inletto the turbine is 1200 kPa, 1400 K. Alr expands through the turbine, which has an isentropic efficiency of 88%, to a pressure of 100kpa. The air then passes through interconnecting heat-recovery steam generator and is finally discharged at 400 K. Steam enters the turbine of the vapor power cycle at 8 Mpa, 400 °C, and expands to condenser pressure of 8 kPa. Water enters the pump as saturated liquid at 8 kParThe turbine and pump of the vapor cycle have isentropic efficiency of 90 and 80% respectively. (a) Determine the mass flowrates of air and the team, each in kg/s the net power developed by gas turbine and vapor power cycle, each in MW; and thermal efficiency. (b) For gas turbine only, using the same conditions and discharging combustion products at state 4, determine the mass flow rate of air in kg/s; the net power developed by gas turbine in Mw; and thermal efficiency.

Solution

solution:

1)here for brayton cycle following ags turbine powerplant we have as following for compresor

T2/T1=(P2/P1)^(k-1/k)

k=1.4

here we get that

t2=610.18 K

but efficiency relation for compressor

nc=T2-T1/T2\'-t1

T2\'=669.26 k

where for turbine it is given by

T3/T4=(P3/P4)^.4/1.4

T4=688.32 k

where from efficiency we write

nt=T3-T4\'/T3-T4

T4\'=773.72 k

where for combustor

Qs\'=ma\'Cp(T3-T2\')

ma\'=136.1673 kg/s

2)where for combined cycle

T5=400 K

hence heat rejected is

Qr=ma\'Cp(T4\'-T5)

Qr=51143.10 kw

for vapor steam power plant

Pb=80 bar

Pc=.08 bar

where for saturation at Pc=.08 bar

T9=314.53 k

h9f=173.9 kj/kg

where pump work=wp=Pb-Pc/10*.8=h9-h6=9.99 kj/kg

h6=183.99 kj/kg and temperature as T6=315.2 k

here for combustor

Qr=mw*Cpw(T7-T6)

51143.10=mw*4.5737*(673-315.2) at mean temp cp=4.5737

mw\'=31.25 kg/s

where pump work

Wp=mw*wp=312.20kw

here T7=673 k

h7=3138.89 kj/kg

and sf7=6.3604=sf8=.593+x(7.637)

x=.7558

h8=173.9+x(2403.2)

h8=1990.23 kj/kg

here turbine work=mw(h7-h8)=wt2

wt2=32305.78 kw

net power=wt2-Wp=31993.58 kw

4)here for turbine cycle

wt=maCp(T3-T4\')=85705.25 kw

wc=mcp(T2\'-T1) =50532.54 kw

net power in gas turbine cycle=wt-wc=35172.70 kw

6)net power=wt2+wt=31993.58+35172.70=67166.28 kw

Qs=100000 kw

efficiency=wt/Qs=.6716 =67.16% for combined cycle with regeneration

5)for alone vapor power plant where Qs=Qr=100000kw

Qr=mw\'*Cpw(T7-T6)

same condition flow rate would be

mw\'=61.10 kg/s

here then pump work=610.46 kw

wt=70183.126 kw

hence net power=69572.60kw

and efficiency=wn/Qs=69572.66/100000=.6957