chapter 8 gas power cycle 8-1 the analysis of a cycle 8-1-1 the average temperature of a process we...
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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
Thank You
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