Question

ard Rankine cycle utilises water as the working fluid. The boiler runs at a pressure of 7000 kPa and the condenser at a ...


A straightforward Rankine cycle utilises water as the working fluid. The boiler runs at a pressure of 7000 kPa and the condenser at a pressure of 50 kPa. The temperature at the turbine's entry is 450 degrees celcius. The turbine is isentropically efficient at 90%, pressure and pump losses are low, and water exiting the condenser is subcooled to 6.32 degrees celcius. The boiler has been designed to operate at a mass flow rate of 20 kg/s. Determine:

a) The rate of heat addition in the boiler b) The amount of energy needed to run the pumps
c) The cycle's net power output and thermal efficiency

Answer

Given:P1=7000 KPaP2=50 KPaT1=450 Cη=0.9T3=6.32°Cm=20 Kg/s

Properties are obtained from steam table:AT P1=7000 KPa and T1=450°Ch1=3287.78 KJ/Kgs1=6.6354 KJ/Kg.KAt P2=50 KPa:Ts=81.317°C       vf=0.00102993 m3/Kg     vg=3.2400 m3/Kghf=340.54 KJ/Kg      hg=2645.2 KJ/Kg    hfg=2304.7 KJ/Kgsf=1.0912 KJ/Kg.K      sg=7.5930 KJ/Kg.K     sfg=6.5018 KJ/Kgs2=s1=6.6354 KJ/Kg  (process 1-2 isentropic expansion)s2=sf+x*sfg6.6354=1.0912=x*6.5018x=0.8527h2=hf+x*hfgh2=340.54+0.8527*2304.7h2=2305.8 KJ/KgIsentropic efficiency of turbine:ηT=h1-h2'h1-h20.9=3287.78-h2'3287.78-2305.8h2'=2403.99 KJ/Kgh3=hf-C*(Ts-6.32)h3=340.54-4.186*(81.317-6.32)h3=26.60 KJ/Kgs3=sf-4.186*ln(81.317+273)(6.32+273)s3=1.0912-4.186*ln354.317279.32s3=0.09562 KJ/Kg.KFor process 3-4: isentropic compressions4=s3=0.09562At P4=7000 KPaTs4=285.829°Chf=1267.7 KJ/Kg     hg=2772.6 KJ/Kg     hg=1505.0 KJ/Kgsf=3.1224 KJ/Kg.K      sg=5.8148 KJ/Kg.K     sfg=2.6924 KJ/Kg.Ks4=sf-C*lnTs4T40.09562=3.1224-4.186*ln(285.829+273)T4T4=271.177 K =-1.82°Ch4=hf-C*(Ts4-T4)h4=1267.7-4.186*(285.829+1.82)h4=63.59 KJ/Kga) Rate of heat addition to boiler:Qa=m*(h1-h4)Qa=20*(3287.78-63.59)Qa=64483.8 KWb) Energy needed to run pumps:Wp=m*(h4-h3)Wp=20*(63.59-26.60)Wp=739.8 KWc)Net power output:Wnet=m*[(h1-h2')-Wp]Wnet=20*[(3287.78-2403.99)-739.8]Wnet=2879.8 KWThermal efficiency:η=WnetQa =2879.864483.8η=0.044 =4.4%

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