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Rankine Cycle
Ideal cycle for vapor power plants

Process 12
isentropic compression in a pump

process 23
constant pressure heat addition in a boiler

process 34
isentropic expansion in a turbine

process 41
constant pressure heat rejection in a condenser

internal irreversibilities?
NO!

Pump
 enters as  saturated liquid
 during: compressed isentropically; T increases, brought to operating pressure of boiler
 leaves as  compressed liquid

boiler
 enters as  compressed liquid
 during: heat exchanger, T increase, no P change
 leaves as  superheated vapor

turbine
 enters as  superheated vapor
 during  expands isentropically; T and P drop
 leaves as  saturated liquidvapor mix

condenser
 enters as  saturated liquidvapor mix
 during  Heat exchanger, reject heat to cooling medium, no P change
 dropleaves as  saturated liquid

steadyflow energy equation
(q_{in}q_{out}) + (w_{in}w_{out}) = h_{e}h_{i}

simple  Pump eq.
 (q=0)
 w_{pump,in}=h_{2}h_{1} = v(P_{2}P_{1})
 h_{1}=h_{f@P1} and v=v_{1}=v_{f@p1}

simple  boiler eq.
 (w = 0)
 q_{in}=h_{3}h_{2}

simple  turbine eq
 (q=0)
 w_{turb,out} = h_{3}h_{4}


thermal efficiency
n_{th}=w_{net}/q_{in} =1  q_{out}/q_{in}

w_{net}
w_{net} = q_{in}q_{out}=w_{turb,out}w_{pump,in}

simple  state 1
 saturated liquid
 Find h and v  given P, look @ Table A5 (saturated water)

simple  state 2
 compressed liquid
 Find h  apply conservation of energy eq.

simple  state 2 cons. of energy equation
 wpump,in = wturb,out
 h_{2}h_{1}=v(P_{2}P_{1})
 h_{2} = v(P_{2}P_{1})+h_{1}

simple  state 3
 superheated vapor
 Find h and s  given T and P, look @ Table A6 (superheated water)

simple  state 4
 saturated liquidvapor mix
 Find h  given P; apply quality equations
 get values from A5

quality equations
 x_{#} = x_{#}  s_{f} / s_{fg}
 h_{#} = h_{f}+x_{#}h_{fg}
 h_{#} = h_{f} + (s_{#}  s_{f} / s_{fg})h_{fg}

w_{turb,out} w/ efficiency
w_{turb,out} = n_{t}w_{s turb,out}

w_{pump,in} w/ efficiency
w_{pump,in} = w_{s, pump in} / n_{p}

linear interpolate
 y = y_{0} + (xx_{0})(y_{1}y_{0} / x_{1}x_{0})
 x  given
 0 and 1; table #'s

double linear interpolate
 Using ex. from hw
 1) Btwn two P's, linear interpolation for each T, get h_{a} and h_{b}
 2) Btwn two T's, linear interpolate with h_{a} and h_{b }for final h

net power
W*dot*_{net} = (mass flow rate)W_{net}

Increase efficiency
 increase T for superheated steam
 increase boiler pressure, at same T (but quality decreases)
 decrease T heat is rejected from condenser

reheat rankine cycle
two stage turbine to solve excessive moisture problem after increasing boiler pressure

reheat  q_{in}
q_{in} = q_{primary} + q_{reheat} = (h_{3}h_{2}) + (h_{5}h_{4})

reheat  w_{turb,out}
w_{turb,out} = w_{turb,I} + w_{turb,II} = (h_{3}h_{4})+(h_{5}h_{6})

P_{reheat}
= P_{5} = P_{4}

Find P_{reheat}
 T_{3} = T_{5}  to maintain heat
 find entropy at state 6  s_{6} = s_{f} + x_{6}s_{fg}
 use T_{5} and s_{5/6} , look @ Table A6 to find P

reheat  state 1
 saturated liquid
 find h and v = given P, look @ table A5

reheat  state 2
 compressed liquid
 apply conservation of energy eq. (use h_{1} and v_{1})

reheat  state 3
 superheated vapor
 find h_{3} and s_{3}, given P and T look @ Table A6

reheat  state 4
 saturated liquidvapor mix
 Calculate P_{4}, s_{4} (s_{3})
 Look @ Table A6

reheat state 5
 Superheated vapor
 Given T and s_{5}(s_{4}), look @ Table A6

reheat  state 6
 Saturated mixture
 Given P, look @ A5
 apply quality equations, h_{6} = h_{f} + x_{6}h_{fg}

Ideal Regen. Rankine cycle w/ open FWH
FHW  device that heats feedwater by regeneration

regeneration
transfer heat to the feedwater from the expanding steam, in counterflow exchanger built into the turbine

FWH  q_{in}
q_{in} = h_{5}h_{4}

FWH  q_{out}
q_{out} = (1y)(h_{7}h_{1})

FWH  w_{turb,out}
w_{turb,out }= (h_{5}h_{6}) + (1y)(h_{6}h_{7})

FWH  w_{pump,in}
w_{pump,in} = (1y)w_{pumpI,in} + w_{pumpII,in}

fraction of heat extracted
y = m_{6}/m_{5} (mass flow) = h_{3}h_{2} / h_{6}h_{2}

FWH  state 1
 saturated liquid
 Find h and v  given P, look @ Table A5

FWH  state 2
 compressed liquid
 apply conservation energy
 Find h

FWH  state 3
 saturated liquid
 find h and v, given P (same as 2 and 6), look @ Table A5

FWH  state 4
 compressed liquid
 apply conservation energy
 find h

FWH  state 5
 superheated vapor
 find h and s, given P and T, look @ Table A6

FWH  state 6
 saturated liquidvapor mix
 find h, given P, apply quality equation

FWH  state 7
 saturated liquidvapor mix
 find h, given P appy quality equation

