chapter 8 Gas Power Cycle

8-1 The Analysis of a Cycle

8-1-1 The average temperature of a process

12

2

1

ss

TdsT

We define:

That is:

2

112 )( TdsssT

1

2

T

ss1 s2

T

8-1-2 The Analysis of a Cycle

1

2

T

ss1 s2

As to a cycle:

a

b

2121 ba

cycle TdsTdsw

)()( 122122 ssTssTwcycle

)(

)()(

122

121122

ssT

ssTssTcycle

T2

T1

2

12

T

TTcycle

2

11T

T

8-2 Otto Cycle8-2-1 N. A. Otto

Nicolaus August Otto the inventor of the four-stroke cycle was born on 14th June 1831 in Germany. In 1862 he began first experiments with four-strokes engines. The first four-stroke engines is shown. they correspond to the today's engines. He died on 26th January 1891 in Cologne

8-2-2 The Cycle - The Four StrokesIntake stroke:

The piston moves down the cylinder and the pressure will drop (negative pressure). The intake valve is opend. Because of the low pressure the air/fuel mixtures is sucked into the cylinder.

Compression stroke:

At Bottom Dead Center (BDC) the cylinder is at its maximum volume and the intake valve is closed. Now the piston moves backward the Top Dead Center (TDC) and compresses the air/fuel mixtures.

Near the end of the compression stroke, the ignition starts the combustion and the mixture burns very rapidly. The expanding gas creates a high pressures against the top of the piston.

Power stroke

The force drives the piston downward to crank shaft (the valves are closed). The volume is increased and the pressure is decreased. No more energy is added and because of this the internal energy of the gas is decreased as so as the temperature.

Exhaust stroke

At BDC the exhaust valve is opened and the piston moves up the cylinder. The pressure drops near the pressure outside the cylinder because of the opened exhaust valve. Exhaust gas leaves the cylinder. The volume is decreased.

The theory cycle

1

2

3

4

5

p

v

8-2-3 The Cycle - The Four Strokes

Adiabatic process

Theory efficiency of Otto cycle

)(

)(1

23

14

TTC

TTC

v

v

1

1

1

2

3

1

4

2

1

T

TTT

T

T

3

4

2

1

V

V

V

V

)1(

2

1

1

2

k

V

V

T

T

)1(

3

4

4

3

k

V

V

T

T

Then ：2

3

1

4

T

T

T

T

1

2

11

TT

k

k

p

p)1(

1

2

11

k

k )1(

11

ε compression ratio

8-3 Diesel Cycle8-2-1 Rudolf Diesel

Rudolf Diesel (1858 – 1913) was born in Paris in 1858. After graduation he was employed as a refrigerator engineer. However, his true love was in engine design. In 1893, he published a paper describing an engine with combustion within a cylinder, the internal combustion engine. In 1894, he filed for a patent for his new invention, the diesel engine. Diesel was almost killed by his engine when it exploded - however, his engine was the first that proved that fuel could be ignited without a spark. He operated his first successful engine in 1897.

                                                                                        

8-3-2 The Diesel Cycle

8-3-3 The Efficiency of Diesel Cycle

The theory cycle

1

2 3

4

5

p

v

Theory efficiency of Diesel cycle

23

141TTC

TTC

p

v

23

1

41 1

11

TT

TT

T

k

kk VPVP 2211

kk VPVP 3344

41 VV

32 PP

k

V

V

p

p

3

2

4

1

We define 2

3

V

V

k

p

p

1

4

1

4

1

4

1

p

p

T

T

Since process 1-4 has a constant volume

k

1

1

2

1

3

111

T

T

T

Tk

k

23

1

41 1

11

TT

T

TT

k

1

2

1

2

2

3

111

T

T

T

T

T

Tk

k

11

2

3

111

kk

k

T

Tk

11

111

kk

k

k

To increase efficiency:

1

2 3

4

5

p

v

The compression pressure should be higher

The volume increase should be smaller

Other internal combustion engine

8-4-1 The Equipments of Brayton Cycle

8-4 Brayton Cycle

Advantages

Gas turbine engines are smaller than their reciprocating counterparts of the same power

Gas turbine engines have a great power-to-weight ratio compared to reciprocating engines. That is, the amount of power you get out of the engine compared to the weight of the engine itself is very good.

                                                                                                                                                                

8-4-2 Brayton Cycle

T

s

1

2

3

4

Constant

pressure

p

v

1

2 3

4

adiabatic

8-4-3 Efficiency of Brayton Cycle

23

141TTC

TTC

p

p

k

k

p

p

T

T

T

T1

2

1

2

1

3

4

k

k

p

p

TT

TT1

2

1

23

14

k

k 1

11

8-4-3 The Optimum Compression Ratio

T

s

1

2

3

4

Tmaxthe compression ratio will be increased to get high efficiency

But the power ratio will decrease

3’

4’

If T3 is limited:

We have to compromise between high efficiency and high power ratio.

Usually in aerospace field the power ratio is more important

T

s

Tmax

T0

Obviously there must be an optimum compression ratio which makes the cycle has maximum power ratio

This ratio is denoted as: εmax

12

1

3max

k

k

T

T

k

k 1

11

3

11T

T

The efficiency depends on T3 basically

8-4-4 The methods to increase the efficiency

(1) Regenerative Brayton CycleT

s

T2

T1

T2

T1

Engine Characteristic

Type Twin-Spool, Augmented Turbofan

Application F-22 Advanced Tactical Fighter

Thrust 35,000 Pound Thrust Class

Engine Control Full-Authority Digital Electronic Control

Compression System

Twin Spool/Counter Rotating/Axial Flow/Low-Aspect Ratio     Three-Stage Fan     Six-Stage Compressor

Combustor Annular

TurbineAxial Flow/Counter Rotating• One-Stage, High-Pressure Turbine• One-Stage, Low-Pressure Turbine

Nozzle Two-dimensional Vectoring Convergent/Divergent

oil Combustion chamber

Air in

compressor

gas turbine

regenerator

(2) Isothermal compression and regenerative cycle

T

s

8-5 Jet EngineEngine Characteristic

Type Twin-Spool, Augmented Turbofan

Application F-22 Advanced Tactical Fighter

Thrust 35,000 Pound Thrust Class

Engine Control Full-Authority Digital Electronic Control

Compression System

Twin Spool/Counter Rotating/Axial Flow/Low-Aspect Ratio     Three-Stage Fan     Six-Stage Compressor

Combustor Annular

TurbineAxial Flow/Counter Rotating• One-Stage, High-Pressure Turbine• One-Stage, Low-Pressure Turbine

Nozzle Two-dimensional Vectoring Convergent/Divergent

T

s

1

2

3

4

5

6

1 2 3 4 5 6

The methods to increase the power ratio of jet engine

(1) After burning

After burner

T

s

1

2

3

4

5

6

7

(2) Increase T4

T

s

1

2

3

4’

5’

6’4

6

8-5 The Stirling Cycle

p

v

1

23

4

T

s

12

34

The End Of This Chapter

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