l27 - the brayton cycle
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Department of Mechanical EngineeringME 322 – Mechanical Engineering
Thermodynamics
Lecture 27
Gas Power GenerationThe Brayton Cycle
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Gas Power Cycles• Much higher power output to weight ratio compared to
vapor power cycles– Well suited for mobile power plants– Smaller stationary power plants
• Commonly known as the gas turbine
Open cycle Closed cycle
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The Gas TurbineComparison of the schematic to the ‘real thing’
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Gas Turbine Examples
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The Air Standard Cycle (ASC) Analysis
• A fixed amount of air modeled as an ideal gas is the working fluid
• The combustion process is replaced by a heat transfer from an external source
• All processes are internally reversible
The Cold Air Standard Cycle Analysis
• All of the above plus … the heat capacity of the air is assumed to be constant
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The Brayton Cycle• 1-2: Reversible and adiabatic compression• 2-3: Constant pressure heat addition• 3-4: Reversible and adiabatic expansion• 4-1 Constant pressure heat rejection
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Brayton Cycle Analysis
2 1cW m h h
3 2inQ m h h
3 4tW m h h
4 1outQ m h h
cycle net t cW W W W
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Brayton Cycle PerformanceThermal Efficiency
,ASCnet t c
thin in
W W WQ Q
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4 1,ASC
3 2
1th
h hh h
3 2 4 1 4 1
3 2 3 2
1h h h h h h
h h h h
3 4 2 1 3 4 2 1
3 2 3 2
m h h m h h h h h h
m h h h h
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Cold Brayton Cycle Performance
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Cold Air Standard Thermal Efficiency
4 1 4 1,cold ASC
3 2 3 2
1 1 pth
p
h h c T Th h c T T
3 34 4
2 1 1 2
1 1T TT TT T T T
Processes 3-4 and 1-2 are isentropic
1 4 14 1
3 2 2 3 2
/ 11 1
/ 1T T TT T
T T T T T
1 / 1 /
3 3 2 2
4 4 1 1
k k k kT P P TT P P T
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Cold Brayton Cycle Performance
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1 4 1,cold ASC
/ 11th
T T T
2 3 2/ 1T T T 1
2
1 TT
Substituting ...
Since process 1-2 is isentropic,
1 / 1
1 1 1,cold ASC
2 2 2
1 1 1k k k
thT P vT P v
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Cold Brayton Cycle Performance
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Define ...
Finally ... we have several ways to write the cold ASC thermal efficiency,
1,cold ASC
2
1 /1 /1
2
111
2
1
1 1
1 1
th
k kk k
k
k
TT
P PRP
v CRv
2
1
pressure ratioP PRP
1
2
compression ratiov CRv
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Gas Turbine Irreversibilities
Isentropic efficiencies in the turbine and compressor
Isentropic efficiencies in the turbine and compressor and pressure drops
in the heat exchangers
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