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Lecture Notes on Thermodynamics 2008Chapter 10 Steam Power Cycles

Prof. Man Y. Kim, Autumn 2008, ⓒmanykim@chonbuk.ac.kr, 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

QQ

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