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Basics in the Thermodynamic Analyses
of theGas Turbine Power Plant
Prof. R. ShanthiniDept. of C&P EngineeringUniversity of PeradeniyaSri Lanka
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Comp-ressor
atmosphericair
Combustionchamber
fuel
Gasturbine
gasesto the stack
Gen
compressed air
hot gases
Gen stands for Electricity Generator
Compressorshaft
Turbineshaft
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atmospheric air
(WGT)out
fuel
Gen
compressed air
hot gases
Comp-ressor
Combustionchamber
Gasturbine
gasesto the stack
W stands for work flow rate and GT stands for Gas Turbine
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atmospheric air
(WGT)out
Comp-ressor
(QCC)in
Gen
compressed air
hot gasesCombustion
chamber
Gasturbine
gasesto the stack
Q stands for heat flow rate and CC stands for Combustion Chamber
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atmospheric air
(WGT)out
Comp-ressor
(WC)in
(QCC)in
1
2 3
4Gen
compressed air
hot gasesCombustion
chamber
Gasturbine
gasesto the stack
W stands for work flow rate and C stands for Compressor
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atmospheric air
(WGT)out
Comp-ressor
(QCC)in
1
2
4Gen
hot gases
compressed air 3
Combustionchamber
Gasturbine
gasesto the stack
(WC)in
![Page 7: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/7.jpg)
(WGT)out
3
4
+ (QGT)out
= m ( h – h )3 4g
+ m ( C – C ) / 23 42 2
g
hot gases
gasesto the stack
Gasturbine
m stands for mass flow rate of gas,
h stands for enthalpy,
C stands for speed of gas flow
g stands for gravitational acceleration, &
Z stands for height above reference level
Steady flow energy equationapplied to the flow across turbine:
g
+ m g ( Z – Z ) 3 4g r
r
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+ (QGT)out=
+ m ( C – C ) / 23 42 2
g
Assumptions: - Adiabatic condition prevails across the gas turbine- Kinetic energy changes are negligible compared to enthalpy changes
= m ( h – h )3 4g+
- (QGT)out 3
4
hot gases
gasesto the stack
Gasturbine
+ m g ( Z – Z ) 3 4g r
- Potential energy changes are ignored
(WGT)out
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(WGT)out
= 3
4
hot gases
gasesto the stack
Gasturbine
Assumptions: - Adiabatic condition prevails across the gas turbine- Kinetic energy changes are negligible compared to enthalpy changes- Potential energy changes are ignored
= m ( h – h )3 4g+
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(WGT)out
= m ( h – h )3 4g 3
4
hot gases
gasesto the stack
Gasturbine
Assumptions: - Adiabatic condition prevails across the gas turbine- Kinetic energy changes are negligible compared to enthalpy changes- Potential energy changes are ignored
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(WGT)out
= m ( h – h )3 4g
Assumption: - Gases flowing through the turbine behave as ideal gases
(WGT)out
= m C ( T – T )3 4g pg
3
4
hot gases
gasesto the stack
Gasturbine
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(WGT)out
3
= m C ( T – T )3 4g pg
T 4
T 3
Specific heat of gas at constant pressure
Mass flow rate of gas
4
Temperature at the outlet
Temperature at the inlet
Gasturbine
m ( h – h )3 4g=
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3
T 4
T 3 =
4
fixed
changes
fixed
free to choose, but we fix it at some value
= ?
(WGT)out
= m C ( T – T )3 4g pg
Gasturbine
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3
T 4
T 3 =
4
= ?
P 4 =
P 3 =
should be as small as possible
T 4
How small should T4 be ?
(WGT)out
= m C ( T – T )3 4g pg
Gasturbine
To get maximum work output from the turbine,
at the given P 3 P 4and
(P stands for pressure)
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3
T 4
T 3
4
P 4
P 3
(WGT)out
= m C ( T – T )3 4g pg
T
Specific Entropy (s)
3
4s
P3
P4
4
real flow
ideal flow
Gasturbine
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3
T 4s
P 3
4
T 4s 3
T = P ( 4
P 3 )
(-1)/
(WGT)out,ideal
= m C ( T – T ) 3 4sg pg
T 3
P 4
Gasturbine
(WGT)out
= m C ( T – T )3 4g pg
For the ideal flow (ideal gas at constant specific entropy):
Therefore,
where is the isentropic constant
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3
4
T =
(WGT)out
(WGT)out,ideal
m C ( T – T )3 4g pg
m C ( T – T )3 4sg pg
=
Turbine Efficiency
-=
T 3
T 3
T 4
T 4s -
Gasturbine
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3
4
TT4 = T3 ( T3 T4s– – )
T 4s 3 T = P ( 4 P 3 )
(-1)/
(WGT)out
(WGT)out,ideal
= T
= T m C ( T – T ) 3 4sg pg
Gasturbine
Governing equations:
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Let‘s do some Excel sheet calculations across the turbine
3
4
Gasturbine= 350 kg/s m g
C pg = 1.1 kJ/kg.s T 4
Data:
T 3
= 1200 K
P 4= 1 bar
T = 88%
γ = 1.3
(WGT)out
Determine
for P3 varying in the range of 2 to 15 bar
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300
400
500
600
700
800
900
1000
1100
1200
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Turbine Inlet Pressure P3 (in bar)
Tu
rbin
e O
utl
et T
emp
erat
ure
T4
(in
K)
at the specified efficiency
under ideal conditions
Turbine outlet temperature increaseswith decreasing turbine efficiency
= 88%T
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0
50
100
150
200
250
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Turbine Inlet Pressure P3 (in bar)
Tu
rbin
e W
ork
Ou
tpu
t
(WG
T )o
ut (
in M
W)
under ideal conditions
at the specified efficiency
= 88%T
Turbine work output decreaseswith decreasing turbine efficiency
![Page 22: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/22.jpg)
atmospheric air
gasesto the stack
(WGT)out
fuel
Gen
compressed air
hot gases
Comp-ressor
Combustionchamber
Gasturbine
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atmospheric air
gasesto the stack
(WGT)out
Comp-ressor
(WC)in
(QCC)in
1
23
4Gen
compressed air
hot gasesCombustion
chamber
Gasturbine
![Page 24: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/24.jpg)
atmospheric air
gasesto the stack
(WGT)out
Comp-ressor
(WC)in
(QCC)in
1
2
4Gen
3compressed air
hot gasesCombustion
chamber
Gasturbine
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atmosphericair
Comp-ressor
(WC)in
1
= (QC)out
+ m ( h – h )2 1a
+ m ( C – C ) / 22 12 2
a
2
compressed air
Subscript a stands for air
+ m g ( Z – Z ) 3 4a r
Steady flow energy equationapplied to the flow across compressor:
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atmosphericair
Comp-ressor
(WC)in
1
= (QC)out
+ m ( h – h )2 1a
+ m ( C – C ) / 22 12 2
a
2
compressed air
+ m g ( Z – Z ) 3 4a r
Assumptions: - Adiabatic condition prevails across the compressor- Kinetic energy changes are negligible compared to enthalpy changes- Potential energy changes are ignored
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atmosphericair
Comp-ressor
(WC)in
1
= + m ( h – h )2 1a
2
compressed air
Assumptions: - Adiabatic condition prevails across the compressor- Kinetic energy changes are negligible compared to enthalpy changes- Potential energy changes are ignored
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atmosphericair
Comp-ressor
(WC)in
1
= m ( h – h )2 1a
= m C ( T – T )2 1a pa
2
compressed air
Assumption: - Air flowing through the compressor behaves as an ideal gas
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1
2
T 1
T 2
(WC)in
= m C ( T – T )2 1a pa
T at the inlet
T at the outlet
Specific heat of air at constant pressure
Mass flow rate of air
Comp-ressor
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1
2
T 1
T 2
(WC)in
= m C ( T – T )2 1a pa
fixed
changes
fixed
free to choose, but we fix it at some value
=
= ?
Comp-ressor
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1
T 1
=
P 1
=
T 2 = ?
(WC)in
= m C ( T – T )2 1a pa
; P 2 = 2
should be as small as possible
T 2
How small should T2 be ?
at the given P 1 P 2and
Comp-ressor
To give minimum work input to the compressor,
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T
3
4s
P3=P2
4real flow
idealflow
(WC)in
= m C ( T – T )2 1a pa
1
T 1
P 1
T 2
P 2
2
1
2s2
P4=P1
Comp-ressor
Specific Entropy (s)
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1
T 2s 1
T = P ( 2
P 1 )
(-1)/
T 1
=
P 1
=
T 2s = ?
(WC)in,ideal
= m C ( T – T )2s 1a pa
P 2 = 2
(WC)in
= m C ( T – T )2 1a pa
Comp-ressor
For the ideal flow (ideal gas at constant specific entropy):
Therefore,
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1
C =
(WC)in,ideal
(WC)in
= T
2s
T 2
T 1
T 1
--
2 m C ( T – T )
2s 1a pa
m C ( T – T )2 1a pa
=
Compressorefficiency
Comp-ressor
![Page 35: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/35.jpg)
T 2s 1 T = P ( 2 P 1 )
(-1)/
1
2
CT2 = T1 ( T2s T1+ – )/
= C m C ( T – T ) 2s 1a pa /
Comp-ressor
in(WC) (WC)
in,ideal= C/
Governing equations:
![Page 36: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/36.jpg)
Let‘s do some Excel sheet calculations across the compressor
= 350 kg/s m a
T 2
Data:
T 1
= 300 K
P 1= 1 bar
C = 85%
γ = 1.4
Determine
for P2 varying in the range of 2 to 15 bar
1
2
Comp-ressor
(WC)in
C pa = 1.005 kJ/kg.s
![Page 37: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/37.jpg)
300
400
500
600
700
800
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Compressor Outlet Pressure P2 (in bar)
Co
mp
ress
or
Ou
tlet
Tem
per
atu
re T
2 (i
n K
)
at the specified efficiency
under ideal conditions
= 85%C
Compressor outlet temperature increaseswith decreasing compressor efficiency
![Page 38: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/38.jpg)
0
20
40
60
80
100
120
140
160
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Compressor Outlet Pressure P2 (in bar)
Co
mp
ress
or
Wo
rk I
np
ut
(WC)in
(in
MW
)
at the specified efficiency
under ideal conditions
= 85%C
Work input to the compressor increaseswith decreasing compressor efficiency
![Page 39: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/39.jpg)
atmospheric air
gasesto the stack
(WGT)out
fuel
Gen
compressed air
Comp-ressor
hot gases
(WC)in
Wnet
Combustionchamber
Gasturbine
![Page 40: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/40.jpg)
= (WC)in
(WGT)out
Wnet -
(WC)in,ideal
= (WGT)out,ideal-
Wnet,ideal
Net work output from the turbine is the power available for electricity generation
Net work output under ideal conditions is the maximum power available for electricity generation
![Page 41: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/41.jpg)
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Compressor outlet Pressure P2 (in bar) =
Turbine Inlet Pressure P3 (in bar)
Turbine work output (in MW)
Compressor work input (in MW)
Net work output from the Gas Turbine System (in MW)
= 85%C
T= 88%and
![Page 42: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/42.jpg)
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Compressor outlet Pressure P2 (in bar) =
Turbine Inlet Pressure P3 (in bar)
Net
Wo
rk O
utp
ut
fro
m t
he
Gas
Tu
rbin
e S
yste
m (
in M
W)
under ideal conditions
at the specified efficiencies
= 85%C
T= 88%and
![Page 43: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/43.jpg)
atmospheric air
gasesto the stack
(QCC)in
1
23
4Gen
compressed air
hot gases
WnetComp-ressor
Combustionchamber
Gasturbine
![Page 44: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/44.jpg)
atmospheric air
gasesto the stack
(QCC)in
1
23
4Gen
compressed air
hot gases
WnetComp-ressor
Combustionchamber
Gasturbine
![Page 45: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/45.jpg)
(QCC)in,ideal
= m ( h – h ) 3 2a
Assumptions: - Kinetic energy changes are negligible
- Potential energy changes are ignored
- Fuel flow rate is negligible compared to the air flow rate
2 3compressed air
hot gasesCombustionchamber
fuel
![Page 46: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/46.jpg)
2 3compressed air
hot gasesCombustionchamber
fuel
= m C ( T – T )3 2a pa
Assumption: - Air flowing through the compressor behaves as an ideal gas
(QCC)in,ideal
= m ( h – h ) 3 2a
![Page 47: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/47.jpg)
(QCC)in
2 3compressed air
hot gasesCombustionchamber
fuel
= m C ( T – T )3 2a pa
is the compressor efficiency
(QCC)in,ideal
= CC/
CC
CC/
![Page 48: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/48.jpg)
Let‘s do some Excel sheet calculations across the combustion chamber
2 3compressed air
hot gasesCombustionchamber
fuel
= 350 kg/s m a
CC = 80%
C pa = 1.005 kJ/kg.s
P 2
P 3
=
Determine
(QCC)in
![Page 49: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/49.jpg)
= 80%CC
0
50
100
150
200
250
300
350
400
450
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Compressor outlet Pressure P2 (in bar) = Turbine Inlet
Pressure P3 (in bar)
Heat input at the specified efficiency (in MW)
Heat input inder ideal conditions (in MW)
= 80%CC
![Page 50: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/50.jpg)
atmospheric air
(QCC)in
1
2
compressed air
Comp-ressor
Combustionchamber
gasesto the stack
3
4Gen
hot gases
WnetGas
turbine
= th
Wnet
(QCC) in
Thermal efficiency
![Page 51: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/51.jpg)
= 80%CC
0
50
100150
200
250
300
350400
450
500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Compressor outlet Pressure P2 (in bar) = Turbine Inlet
Pressure P3 (in bar)
Heat input at the specifiedefficiency (in MW)
Net work output from the GasTurbine System (in MW)
![Page 52: Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant](https://reader030.vdocument.in/reader030/viewer/2022012908/56814320550346895daf88f0/html5/thumbnails/52.jpg)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Compressor outlet Pressure P2 (in bar) = Turbine Inlet
Pressure P3 (in bar)
Overall Thermal Efficiency underideal conditions
Overall Thermal Efficiency at thespecified unit efficiencies
C
CC = 80%
= 85%
T= 88%
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atmospheric air
gasesto the stack
(QCC)in
1
23
4Gen
compressed air
hot gases
Wnet
Heat Loss?
Comp-ressor
Combustionchamber
Gasturbine
= -(QCC)in Wnet
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0
50
100
150
200
250
300
350
400
450
500
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Compressor outlet Pressure P2 (in bar) = Turbine Inlet Pressure P3 (in bar)
Heat input at the specified efficiency (in MW)
Heat loss at the specified unit efficiencies (in MW)
Net work output from the Gas Turbine System (in MW)
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atmospheric air
gasesto the atmospherethrough the stack
(QCC)in
1
23
4Gen
compressed air
hot gases
Wnet
Heat Loss
Comp-ressor
Combustionchamber
Gasturbine
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Heat is lost with the turbine exhaust gases to the atmosphere through the stack
Should not we make good use of all that heat
that is not only getting wasted
but also pollute the environment in many ways?