department of mechanical engineering me 322 mechanical ... · department of mechanical engineering...

Department of Mechanical Engineering

ME 322 – Mechanical Engineering

Thermodynamics

Lecture 27

Gas Power Generation

The 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 Turbine

Comparison 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 Performance

Thermal Efficiency

,ASCnet t c

th

in in

W W W

Q Q

8

4 1

,ASC

3 2

1th

h h

h 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

9

Cold Air Standard Thermal Efficiency

4 1 4 1

,cold ASC

3 2 3 2

1 1p

th

p

h h c T T

h h c T T

3 34 4

2 1 1 2

1 1T TT T

T T T T

Processes 3-4 and 1-2 are isentropic

1 4 14 1

3 2 2 3 2

/ 11 1

/ 1

T T TT T

T T T T T

1 / 1 /

3 3 2 2

4 4 1 1

k k k k

T P P T

T P P T

Cold Brayton Cycle Performance

10

1 4 1

,cold ASC

/ 11th

T T T

2 3 2/ 1T T T

1

2

1T

T

Substituting ...

Since process 1-2 is isentropic,

1 / 1

1 1 1,cold ASC

2 2 2

1 1 1

k k k

th

T P v

T P v

Cold Brayton Cycle Performance

11

Define ...

Finally ... we have several ways to write

the cold ASC thermal efficiency,

1,cold ASC

2

1 /

1 /1

2

1

11

2

1

1 1

1 1

th

k k

k k

k

k

T

T

PPR

P

vCR

v

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

12