Steam at 1200 psi, 1000 degree F enters the first-stage turbine of a power plant

Question

Steam at 1200 psi, 1000 degree F enters the first-stage turbine of a power plant operating, on the Rankine cycle. The steam expands to 110 psi where some steam is extracted for feedwater heating. He remaining steam expands to the condenser operating at 110 psi with saturated liquid at the exit. Assume that the turbines have an isentropic 110 psi with saturated liquid at the exit. Assume that the turbines have an isentropic efficiency of 75% and that all pumps operate isentropically. Repeat the analysis of problem 1 above but replace the open feedwater healer with a closed feedwater heater operating at the same pressure and with a feedwater exit temperature of 325 degree F. For either of the above cycles, modify the cycle to include one stage of re-heat to 950 degree F at 110 psi (i.e. at the same pressure as the extraction for feedwater heating). Choose one type of feedwater heater and repeat the analysis from problem #1.

Explanation / Answer

1)   fx= 3X2-108=0

3x2=108

x2=36

x= -6 or 6

fy=3y2-147=0

3y2=147

y2=49

y= -7 or 7

that is (-6,-7), (-6,7),(6,-7),(6,7) are the critical points

fxy=0 , fxx=6x, fyy=6y

D:fxx fyy - (fxy )2 = 36xy

D(-6,-7)=36(-6)(-7)>0,fx<0 local maximum

D(6,7)=36(6)(7)>0,fx>0 local maximum

D(6,-7)= 36(6)(-7)<0 , fy<0 a saddle point

D(-6,7)= 36 (-6)(7) <0, fy<0 a saddle point

there fore

f(-6,-7)=1120 local maximum

f(6,7)=-1116 local minimum

f(6,-7)= 256 and f(-6,7)= -252 are saddle point

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