Chapter 8. Production of Power from Heat

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(1)

Chapter 8.

Production of Power from Heat

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Introduction

Production of Power

Energy from the sun : Photovoltaic cells

Kinetic Energy from atmospheric wind : windmills

Fossil fuels, atomic fuels

- Chemical Energy  Heat  Power (Electrical Work) - Efficiencies are low (35 – 50 %)

Fuel cell

- Chemical Energy  Power (Electrical Work) - Greater efficiency (85 %)

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Use of Fossil Fuels

Steam Power Plant : Fossil fuel and nuclear

Internal combustion engines

Otto engines

Diesel engines

Gas turbine

Jet engines

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8.1 Steam Power Plant

Simple steam power plant

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Diagram of a real power plant

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Steam Plant…

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Carnot cycle

H C

H

T

T Q

W   

 1 1

 Efficiency increases as

T

H

increases T

C

decreases

T

S

1 2

4 3 T

H

T

C

Vaporization process in the boiler Reversible, adiabatic expansion of

saturated vapor into two-phase (turbine)

Condensation (condenser)

Isentropic compression (pump)

(9)

Rankine Cycle

In a Carnot cycle, several steps are almost impossible for practical reasons

23 : Steams with liquid content causes erosion problems in turbine blades

41 : Pumping of gas-liquid mixture is difficult

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Carnot vs. Rankine Cycles

Two major differences

Heating step 12 : Heating beyond vaporization

Cooling step 34 : Complete Condensation

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Rankine Cycle : alternative standard for power plant

Two modification from Carnot cycle

12 : Heating beyond vaporization

34 : Complete Condensation

T

S

2

1

3 4

Heating of subcooled liquid

(const P)

Vaporization at const T and P

Superheating of vapor well above the

saturation T

(Reversible, adiabatic) Expansion

(reduced moisture contents)

Condensation (Const P, const T) Pumping of sat.

liquid to boiler temperature

Real path due to irreversibility

(12)

Steam Power Plant

Turbine (Ch.7)

Pump (Ch.7)

Boiler and Condenser

Heat transfer process

S s

s

) H (

H )

isentropic (

W

W

 

) H H

( H

W

s

  

3

2

H ) H ( W

) isentropic (

W

S

s s

 

) H H

( H

W

s

  

1

4

H Q

, H m

Q      

(13)

Example 8.1

Steam generated in a power plant at a pressure of 8,600 kPa and a temperature of 500

o

C is fed to a turbine. Exhaust from the turbine enters a condenser at 10 kPa, where it is condensed to saturated liquid, which is then pumped to the boiler.

(a) The thermal efficiency of a Rankine cycle

(b) The thermal efficiency of a practical cycle if the turbine efficiency

and pump efficiency are both 0.75

(14)

Example 8.1

(a)

8,600 kPa

500 oC

H2 = 3391.6 kJ/kg

10 kPa

H3 = 2117.4 kJ/kg 10 kPa

Tsat= 45.83 oC H4 = 191.8 kJ/kg Isentropic pumping (process 4  1)

(H)S = 8.7 kJ/kg (Ex 7.10) H1 = H4 + (H)S = 200.5 kJ/kg

the turbine operate under the same condition as Ex. 7.6

   H

S

  1 , 274 . 2 kJ / kg

3966 .

1 0 . 191 , 3

5 . 1265 )

boiler (

Q

) Rankine (

W

kg / kJ 5 . 265 , 1 6

. 925 , 1 1 . 191 , 3 )

condenser (

Q ) boiler (

Q )

Rankine (

W or

kg / kJ 5 . 265 , 1 7

. 8 2 . 1274 )

pump (

W ) turbine (

W ) Rankine (

W

kg / kJ 1 . 191 , 3 5 . 200 6

. 391 , 3 H H

) boiler (

Q

kg / kJ 6 . 925 , 1 4

. 117 , 2 8 . 191 H

H ) condenser (

Q

S S S

1 2

3 4

(15)

Example 8.1

(b)   

 

2961 .

2 0 . 188 , 3

0 . 944 )

boiler (

Q

) Rankine (

W

kg / kJ 2 . 188 , 3 4 . 203 6

. 391 , 3 H H

) boiler (

Q

kg / kJ 4 . 203 6

. 11 8 . 191 H

H H

kg / kJ 0 . 944 75

. 11 6 . 955 )

pump (

W ) turbine (

W ) Rankine (

W

kg / kJ 75 . 75 11

. 0

676 . ) 8 pump (

H W H

, 10 . 7 Ex From

kg / kJ 0 . 436 , 2 6 . 955 6

. 391 , 3 H H

H

kg / kJ 6 . 955 2

. 274 , 1 75 . 0 ) turbine (

W H

H , 6 . 7 Ex From

S

1 2 4

1

S S

S

S S

2 3

S S

 

 

(16)

The Regenerative Cycles

Higher efficiencies

Increased Boiler Temperature  Increased Boiler Pressure  Increased cost for construction

Lower condenser temperature  Lower condenser pressure  practical condensation controlled by ambient temp

Most modern power plants operate on a modification of the Rankine cycle that incorporates feed water heaters

Water from the condenser is first heated by steam extracted from the turbine

In Rankine cycle, water from the condenser is pumped directly back to the boiler

(17)

The Regenerative Cycles

Stagewise preheating the feed water can improve efficiencies

Simple steam power plant

steam power plant by regenerative cycle

(18)

Example 8.2

Determine the thermal efficiency of the power plant in

Figure, assuming turbine and pump efficiency of 0.75.

(19)

Example 8.2 – Section I

From energy balance

 

kg / kJ 4 . 240 )

5 . 320 (

75 . 0

H H

WS S

) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H

H ) liq . sat ( H H

) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H

kg / kJ 5 . 971 )

liq . sat ( H

H ) liq . sat ( H H

kg / kJ 2 . 151 , 3

4 . 240 6

. 391 , 3 H

balance Energy

Basis

(20)

Example 8.2 – Section II

From energy balance

 

S

S H H

W    

) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H

H ) liq . sat ( H H

) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H

kg / kJ 5 . 971 )

liq . sat ( H

H ) liq . sat ( H H

 

H S 2

. 151 , 3 H

balance Energy

(21)

Example 8.2

To get the thermal efficiency of whole process,

 Complete the calculation on turbine (section I – V)

 

3276 .

6 0 . 418 , 2

4 . 792 )

boiler (

Q

) Rankine (

W

kJ 6 . 418 , 2 0 . 973 6

. 391 , 3 H )

boiler (

Q

kJ 4 . 792 6

. 11 0

. 804 )

pump (

W )

turbine (

W )

Rankine (

W

kg / kJ 6 . 75 11

. 0

676 . ) 8 pump (

H W H

, 10 . 7 Ex From

) V I tion (sec turbine

for kJ 0 . 804 W

S

S S

S

S S

S

 

 

 

(22)

8.2 Internal – Combustion Engines

Characteristics of Steam Power Plant

Steam is an inert medium  heat is transferred from a burning fuel

Large heat transfer surfaces

- Absorption of heat by the steam at a high T in the boiler, and rejection of heat from the steam at a relatively low T in the condenser

- Thick walls to withstand high T, P impose a limit on heat absorption.

Complicated structure

Characteristics of Internal-Combustion Engines

Combustion are carried out within engine

- The combustion products serve as the working medium, acting on a piston in a cylinder - High temperatures are internal, and do not involve heat-transfer surfaces

Complex thermodynamic analysis

No working fluid undergoes a cyclic process

(23)

The Otto Engine

No working fluid undergoes cyclic process

An imaginary cyclic engine with air as working fluid

- The combustion step is replaced by the addition to the air of an equivalent amount of heat

Equivalent in performance to actual internal-combustion engine

The most common internal-combustion engine

 The Otto engine

- Used in automobiles

(24)

Otto Engine Cycle

Air / fuel mixture fed into the engine Air / fuel mixture are

compressed by the piston

Combustion of fuel : So rapid so that the volume remains const.

Adiabatic expansion

Valve opened and exhaust gas vented

Piston pushes remaining exhaust

gases

(25)

Idealized Otto Cycle

Increasing the compression ratio is to increase the efficiency of engine. (Proof ?)

Using idealized Otto engine

Two adiabatic & two const V steps

The working fluid is air (ideal gas with constant Cp)

Reversible adiabatic compression Sufficient heat is absorbed by the air at

constant volume (P and T increase)

Reversible adiabatic expansion

Cooling at constant volume

(26)

Thermodynamic Analysis of Otto Engine

Increasing the compression ratio is to increase the efficiency of engine. (Proof ?)

Using idealized Otto engine

) (

A D

V

DA

C T T

Q  

) T T

( C

Q

BC

V C

B

   

 

D A

C B

D A

V

B C

V D

A V

DA BC DA

DA net

T T

T 1 T

T T

C

T T

C T

T C

Q Q Q

Q W

 

 

 

(27)

Otto Engine - Analysis

The Compression ratio, r ≡ V

C

/V

D

r increases : efficiency increases

The thermal efficiency increases rapidly at low value of r, but more slowly at higher value of r

 

T T

CA

T T

DB

 1

nRT PV 

const PV 

1

1

1

 

 

 

r

 

 

 

D C

V r V

Derive yourself! (Page 304)

(28)

Diesel Engine

Difference from Otto Engine

Compression is high, combustion is initiated spontaneously

High compression ratio, high efficiency

(29)

Efficiency in Diesel – Example 8.3

The thermal efficiency of Diesel cycle

The compression ratio, r (≡ V

C

/V

D

)

The expansion ratio, r

e

(≡ V

B

/V

A

)

) T T

( C

Q

DA

P A

D

) T T

( C

Q

BC

V C

B

 

 

 

D A

C B

D A

P

B C

V

DA BC DA

BC DA

T T

T T

1 1 T

T C

T T

1 C

Q 1 Q Q

Q Q

RT PV

V / V r

V / V r

V T V

T

V T V

T

A B e

D C

1 C C 1

D D

1 B B 1

A A

 

 

 

 

 

 

r / 1 r / 1

) r / 1 ( ) r / 1 ( 1 1

r / r 1

) r / 1 )(

r / r ( )

r / 1 ( 1 1

e e

e

1 e

1 e

Derive yourself!

(Page 306)

(30)

The Gas-Turbine Engine

Otto & Diesel engines

Direct use of the energy of high T and P gases, acting on a piston within a cylinder

However, turbines are more efficient than reciprocating engines

Gas Turbine Engine

Advantage of high T and P for internal combustion engine

Advantage of using turbine rather than reciprocating engine

(31)

Gas-Turbine Engine

The gas turbine is driven by high-T gases from a combustion chamber

The entering air is compressed before combustion

The centrifugal compressor operates on the same shaft as the turbine

Part of the work of the turbine serves to drive the compressor

(32)

Brayton Cycle

Brayton cycle

The idealization of the gas-turbine engine

The working fluid is taken as air, ideal gas with const Cp

Reversible adiabatic compression Heat QBC is added at

constant P

(replacing combustion) Reversible adiabatic

expansion (Isentropic)

Cooling at constant pressure

(33)

Thermodynamic Analysis of Brayton Engine

) T T

( C

Q

BC

P C

B

) T T

( C H

H

W

AB

B

A

P B

A

B C

A D

BC AB CD

BC net

T T

T 1 T

Q W W

Q W

 

 

) T T

( C

Q

DA

P A

D

) T T

( C

W

CD

P C

D



 





 





 



/ ) 1 (

A B /

) 1 (

C D C

D

/ ) 1 (

A B A

B

P P P

P T

T

P and P T

T

 

 

 

/ ) 1 (

B A

P

1 P

(34)

8.3 Jet Engines, Rocket Engines

Previous power cycles

High T, P gas expands in a turbine (steam power plant or gas turbine) or in the cylinders with reciprocating pistons (Otto or Diesel engine)

 The power become available through a rotating shaft!

Turbojet (or jet) engine

A nozzle for expanding the hot gases

The power is available as kinetic energy in the jet of exhaust gases leaving the nozzle

(35)

Turbojet engine (or jet engine)

Turbojet engine (or jet engine)

Compression by an axial-flow compressor

Combustion of the fuel with air

The hot gases pass through a turbine

- The expansion provides enough power to drive the compressor - The remainder of the expansion accomplished in the nozzle

- The velocity of exhaust gases increases  Provide a force on the engine in the forward direction

For adiabatic and reversible compression and expansion

- The jet engine cycle is identical to the ideal gas turbine cycle (Brayton cycle)

(36)

Rocket engine

Rocket engine

Difference from a jet engine  The oxidizing agent is carried with the engine (not surrounding air for burning the fuel)

Can operate in a vacuum such as in outer space

The combustion and expansion steps

- Same as an ideal jet engine

(37)

Homework

Recommend Problems

8.1, 8.2, 8.4, 8.5

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