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Lecture Notes on Thermodynamics 2008Chapter 10 Steam Power Cycles
Prof. Man Y. Kim, Autumn 2008, ⓒ[email protected], Aerospace Engineering, Chonbuk National University, Korea
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Carnot Cycle – Review
Comments on efficiency : , , 0 100%H th L th thLT T T
Reversible work done at the moving boundary :
w Pdv Ideal gas : and Pv RT 0vdu C dT
Assuming no changes in KE and PE : 0vRTq du w C dT dvv
Let’s integrate the above equation :
① → ② (Isothermal Heat Addition Process) :
② → ③ (Adiabatic Expansion Process) :
③ → ④ (Isothermal Heat Rejection Process) :
④ → ① (Adiabatic Compression Process) :
21 2
10 lnH H
vq q RTv
0 3
20 ln
L
H
Tv
T
C vdT RT v
343 4
3 40 ln lnL L L
vvq q RT RTv v
0 1
40 ln
H
L
Tv
T
C vdT RT v
From the Equations in adiabatic process :
0 3 3 31 4 2
2 4 2 1 4 1ln ln
H
L
Tv
T
C v v vv v vdT R RT v v v v v v
or
1 1 L
H
Lth
H
TT
We can find . Finally,2
13
4
ln
ln
HH H
L LL
vRTq Tv
vq TRTv
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Rankine Cycle – Ideal Steam Power Cycle• ideal, 4 steady-state process cycle
① Saturated liquid
③ Saturated or superheated vapor
① → ② : Pump – reversible adiabatic pumping (compression) process② → ③ : Boiler – constant pressure heat transfer③ → ④ : Turbine – reversible adiabatic expansion④ → ① : Condenser – constant pressure heat transfer
HQ
LQ
• Heat transferred to the working fluid ( ): area a-2-2’-3-b-a HQ• Heat transferred from the working fluid ( ): area a-1-4-b-a LQ• Thermal efficiency (neglecting changes in KE and PE)
3 4 2 1
3 2
1 2 2 3 4 12 2 3
netth
H
h h h hareawq areaa b a h h
• utilizing a phase change between vapor and liquid to maximize the difference in v during expansion and compression• idealized model for a steam power plant system
, ,th Rankine th Carnot • Temperature between 2-2’ is less than the temperature during evaporation
Expansion
Compression
3 2 4 1
3 2
h h h hh h
pumping process superheating the vapor
• Why Rankine than Carnot ?
pump,inw
turb,outw
• see Example 10–1
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Rankine Cycle – Efficiency
★ Effect of Exhaust Pressure Drop
T↓ in which heat is rejected → cycle efficiency↑ moisture content ↑ → erosion of the turbine blade
4 4P P
★ Effect of Superheating the Steam in the Boiler
w ↑ by area 3-3’-4’-4-3, qH ↑ by area 3-3’-b’-b-3 → cycle efficiency↑ Average T ↑ at which heat is transferred to the steam → cycle efficiency↑ quality ↑
★ Effect of Maximum Pressure of the Steam
If single cross-hating area = double cross-hatching area, average T ↑ at which heat is transferred to the steam → cycle efficiency↑ quality ↓
3 3P P
• see Example 10–3
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Real Steam Power Cycle – Losses Turbine Losses
major loss 3-4s : ideal isentropic turbine expansion process 3-4 : actual irreversible process in the turbine
flow of working fluid through the turbine blades and passages heat transfer to the surroundings Pump Losses
1-2s : ideal isentropic pump compression process 1-2 : actual irreversible process in the pump
irreversibility with the fluid flow of working fluid
Piping Losses a-b : entropy increase due to friction b-c : entropy decrease due to heat transfer
Condenser Losses Heat transfer by raising water to its saturation temperature
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Regenerative cycle : FWH (Feedwater Heater) → Average T at which heat is supplied has been increased
2-2’ : working fluid is heated while in the liquid phase, 2’-3 : vaporization process → The process 2-2’ cause the average T at which heat is supplied to be lower than in the Carnot cycle 1’-2’-3-4-1’ → Efficiency of Rankine cycle < corresponding Carnot cycle → In the regenerative cycle the working fluid enters the boiler at some state between 2-2’, and consequently the average T at which heat is supplied is higher
Open / Closed Feedwater Heater see Examples 10–4, 10–5, and 10–6
Reheative Rankine CycleRankine Cycle – Reheative and Regenerative Cycle
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Homework #10Solve the Problems 10–1C, 2C, 3, 5, 21