Department of Mechanical EngineeringME 322 – Mechanical Engineering

Thermodynamics

Lecture 27

Gas Power GenerationThe Brayton Cycle

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

2

The Gas TurbineComparison of the schematic to the ‘real thing’

3

Gas Turbine Examples

4

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

5

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

6

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

7

Brayton Cycle PerformanceThermal Efficiency

,ASCnet t c

thin in

W W WQ Q

8

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

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

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

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

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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