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**Thermodynamic Analyses Gas Turbine Power Plant**

Basics in the Thermodynamic Analyses of the Gas Turbine Power Plant Prof. R. Shanthini Dept. of C&P Engineering University of Peradeniya Sri Lanka

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**fuel hot gases Gen gases to the stack atmospheric air Combustion**

chamber compressed air Comp- ressor Gas turbine Compressor shaft Turbine shaft Gen gases to the stack atmospheric air Gen stands for Electricity Generator

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**(WGT) fuel hot gases out Gen gases to the stack atmospheric air**

W stands for work flow rate and GT stands for Gas Turbine fuel hot gases Combustion chamber (WGT) out compressed air Comp- ressor Gas turbine Gen gases to the stack atmospheric air

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**(QCC) (WGT) in hot gases out Gen gases to the stack atmospheric air**

Q stands for heat flow rate and CC stands for Combustion Chamber (QCC) in hot gases Combustion chamber (WGT) out compressed air Comp- ressor Gas turbine Gen gases to the stack atmospheric air

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**(QCC) (WGT) (WC) in hot gases out Gen in gases to the stack**

W stands for work flow rate and C stands for Compressor (QCC) in hot gases Combustion chamber (WGT) out compressed air 3 2 Comp- ressor Gas turbine (WC) in Gen 4 1 gases to the stack atmospheric air

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**(QCC) (WGT) (WC) in hot gases out Gen in gases to the stack**

Combustion chamber (WGT) out compressed air 3 2 Comp- ressor Gas turbine (WC) in Gen 4 1 gases to the stack atmospheric air

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**+ (WGT) (QGT) = m ( h – h ) + m ( C – C ) / 2 + m g ( Z – Z )**

Steady flow energy equation applied to the flow across turbine: hot gases 3 + (WGT) out (QGT) out Gas turbine = m ( h – h ) 3 4 g + m ( C – C ) / 2 3 4 2 g + m g ( Z – Z ) 3 4 g r 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 4 g gases to the stack r

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**= + - (QGT) (WGT) (QGT) = m ( h – h ) + + m ( C – C ) / 2**

out hot gases = + (WGT) out (QGT) out 3 = m ( h – h ) 3 4 g + Gas turbine + m ( C – C ) / 2 3 4 2 g + m g ( Z – Z ) 3 4 g r Assumptions: - Adiabatic condition prevails across the gas turbine 4 gases to the stack - Kinetic energy changes are negligible compared to enthalpy changes - Potential energy changes are ignored

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**= (WGT) = m ( h – h ) + Assumptions: hot gases out 3 4 g**

turbine Assumptions: - Adiabatic condition prevails across the gas turbine 4 gases to the stack - Kinetic energy changes are negligible compared to enthalpy changes - Potential energy changes are ignored

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**= m ( h – h ) (WGT) Assumptions: hot gases out 3 4 g**

turbine Assumptions: - Adiabatic condition prevails across the gas turbine 4 gases to the stack - Kinetic energy changes are negligible compared to enthalpy changes - Potential energy changes are ignored

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**= m ( h – h ) (WGT) Assumption: = m C ( T – T ) (WGT) hot gases out 3**

4 g 3 Gas turbine Assumption: - Gases flowing through the turbine behave as ideal gases 4 (WGT) out = m C ( T – T ) 3 4 g pg gases to the stack

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**= m ( h – h ) (WGT) T = m C ( T – T ) T out 3 4 g 3 3 4 g pg**

Gas turbine Temperature at the outlet T 4 Temperature at the inlet 4 Specific heat of gas at constant pressure Mass flow rate of gas

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**= m C ( T – T ) (WGT) T = T = ? out 3 4 g pg 3 changes fixed fixed 4**

Gas turbine fixed fixed T 4 = ? 4 free to choose, but we fix it at some value

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**How small should T4 be ? = m C ( T – T ) (WGT) P = T = T = ? T P**

out = m C ( T – T ) 3 4 g pg P 3 = 3 T 3 = To get maximum work output from the turbine, Gas turbine at the given P 3 4 and (P stands for pressure) T 4 = ? T 4 should be as small as possible P 4 = How small should T4 be ? 4

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**(WGT) = m C ( T – T ) T P P3 T P P4 3 4 4s out 3 4 g pg 3 3 real flow**

Gas turbine real flow T P3 ideal flow 4 T 4 4s P 4 P4 4 Specific Entropy (s)

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**) ( T = m C ( T – T ) (WGT) P P = T T P (WGT) = m C ( T – T ) 3 out 3**

4 g pg 3 P 3 For the ideal flow (ideal gas at constant specific entropy): Gas turbine T 4s 3 = P ( 4 ) (-1)/ T 4s where is the isentropic constant P 4 4 Therefore, (WGT) out,ideal = m C ( T – T ) 3 4s g pg

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**- (WGT) = m C ( T – T ) = T = Turbine Efficiency out out,ideal T 3 4**

Gas turbine m C ( T – T ) 3 4 g pg 4s = 4 - = T 3 4 4s

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**( ) = ( T – ) P = T 4s 4 3 = (WGT) = m C ( T – T )**

Governing equations: 3 T 4s 3 = P ( 4 ) (-1)/ Gas turbine T 4 = 3 ( T 4s – ) 4 (WGT) out out,ideal = T = T m C ( T – T ) 3 4s g pg

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**Let‘s do some Excel sheet calculations across the turbine**

3 Data: Determine Gas turbine = 350 kg/s m g T 4 C pg = 1.1 kJ/kg.s T 3 = 1200 K (WGT) out 4 P 4 = 1 bar γ = 1.3 for P3 varying in the range of 2 to 15 bar T = 88%

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** Turbine outlet temperature increases**

with decreasing turbine efficiency = 88% T

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** Turbine work output decreases with decreasing turbine efficiency**

= 88% T

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**(WGT) fuel hot gases out Gen gases to the stack atmospheric air**

Combustion chamber (WGT) out compressed air Comp- ressor Gas turbine Gen gases to the stack atmospheric air

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**(QCC) (WGT) (WC) in hot gases out Gen in gases to the stack**

Combustion chamber (WGT) out compressed air 3 2 Comp- ressor Gas turbine (WC) in Gen 4 1 gases to the stack atmospheric air

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**(QCC) (WGT) (WC) in hot gases out Gen in gases to the stack**

Combustion chamber (WGT) out compressed air 3 2 Comp- ressor Gas turbine (WC) in Gen 4 1 gases to the stack atmospheric air

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**(WC) (QC) + m ( h – h ) + m ( C – C ) / 2 + m g ( Z – Z ) =**

Steady flow energy equation applied to the flow across compressor: compressed air 2 Subscript a stands for air Comp- ressor (WC) = (QC) out + m ( h – h ) 2 1 a in 1 + m ( C – C ) / 2 2 1 a atmospheric air + m g ( Z – Z ) 3 4 a r

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**Assumptions: (WC) (QC) + m ( h – h ) + m ( C – C ) / 2 + m g ( Z – Z )**

- Adiabatic condition prevails across the compressor compressed air - Kinetic energy changes are negligible compared to enthalpy changes 2 - Potential energy changes are ignored Comp- ressor (WC) = (QC) out + m ( h – h ) 2 1 a in 1 + m ( C – C ) / 2 2 1 a atmospheric air + m g ( Z – Z ) 3 4 a r

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**Assumptions: (WC) + m ( h – h ) =**

- Adiabatic condition prevails across the compressor compressed air - Kinetic energy changes are negligible compared to enthalpy changes 2 - Potential energy changes are ignored Comp- ressor (WC) = + m ( h – h ) 2 1 a in 1 atmospheric air

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**Assumption: (WC) m ( h – h ) = m C ( T – T ) =**

- Air flowing through the compressor behaves as an ideal gas compressed air 2 Comp- ressor (WC) = m ( h – h ) 2 1 a in 1 = m C ( T – T ) 2 1 a pa atmospheric air

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**T = m C ( T – T ) (WC) T 2 in 2 1 a pa T at the inlet T at the outlet**

Comp- ressor T at the inlet 1 T at the outlet T 1 Specific heat of air at constant pressure Mass flow rate of air

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**T = ? (WC) = m C ( T – T ) T = 2 in 2 1 a pa fixed changes 1 fixed**

= ? 2 (WC) in = m C ( T – T ) 2 1 a pa Comp- ressor fixed 1 changes T 1 = fixed free to choose, but we fix it at some value

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**How small should T2 be ? T = ? ; P = (WC) = m C ( T – T ) T = T P**

= ? ; P 2 = 2 (WC) in = m C ( T – T ) 2 1 a pa Comp- ressor To give minimum work input to the compressor, 1 at the given P 1 2 and T 1 = T 2 should be as small as possible P 1 = How small should T2 be ?

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**T = m C ( T – T ) (WC) P P3=P2 T P4=P1 P 3 2 4 2s 4s 1 2 in 2 1 a pa 2**

Comp- ressor T P3=P2 2 4 2s real flow 4s T 1 P4=P1 P 1 1 1 ideal flow Specific Entropy (s)

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**) ( T = ? (WC) = m C ( T – T ) P = T = P T = (WC) = m C ( T – T )**

2s = ? (WC) in = m C ( T – T ) 2 1 a pa P 2 = For the ideal flow (ideal gas at constant specific entropy): 2 Comp- ressor T 2s 1 = P ( 2 ) (-1)/ 1 Therefore, T 1 = (WC) in,ideal = m C ( T – T ) 2s 1 a pa P 1 =

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**- (WC) = m C ( T – T ) = T = Compressor efficiency in,ideal in C 2s**

1 a pa 2 = Comp- ressor = T 2s 2 1 - 1

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**( ) / / / T = ( T + – ) P = T 2 1 2s (WC) = = m C ( T – T )**

Governing equations: 2 T 2s 1 = P ( 2 ) (-1)/ Comp- ressor C T 2 = 1 ( T 2s + – ) / 1 in (WC) in,ideal = C / = C m C ( T – T ) 2s 1 a pa /

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**Let‘s do some Excel sheet calculations across the compressor**

1 2 Comp- ressor Data: = 350 kg/s m a Determine C pa = kJ/kg.s T 2 T 1 = 300 K (WC) in P 1 = 1 bar γ = 1.4 for P2 varying in the range of 2 to 15 bar C = 85%

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** = 85% Compressor outlet temperature increases**

with decreasing compressor efficiency = 85% C

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** = 85% Work input to the compressor increases**

with decreasing compressor efficiency = 85% C

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**(WGT) W (WC) fuel hot gases out net Gen in gases to the atmospheric**

Combustion chamber (WGT) out compressed air Comp- ressor Gas turbine W net (WC) in Gen gases to the stack atmospheric air

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**- - = (WC) (WGT) W (WC) = (WGT) W in out net in,ideal out,ideal**

Net work output from the turbine is the power available for electricity generation (WC) in,ideal = (WGT) out,ideal - W net,ideal Net work output under ideal conditions is the maximum power available for electricity generation

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= 85% C T = 88% and

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= 85% C T = 88% and

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**(QCC) W in hot gases net Gen gases to the atmospheric stack air**

Combustion chamber compressed air 3 2 Comp- ressor Gas turbine W net Gen 4 1 gases to the stack atmospheric air

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**(QCC) W in hot gases net Gen gases to the atmospheric stack air**

Combustion chamber compressed air 3 2 Comp- ressor Gas turbine W net Gen 4 1 gases to the stack atmospheric air

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**(QCC) = m ( h – h ) Assumptions: compressed air hot gases fuel**

2 3 compressed air hot gases Combustion chamber fuel (QCC) in,ideal = m ( h – h ) 3 2 a Assumptions: - Kinetic energy changes are negligible - Potential energy changes are ignored - Fuel flow rate is negligible compared to the air flow rate

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**(QCC) = m ( h – h ) = m C ( T – T ) Assumption: compressed air**

2 3 compressed air hot gases Combustion chamber fuel (QCC) in,ideal = m ( h – h ) 3 2 a = m C ( T – T ) 3 2 a pa Assumption: - Air flowing through the compressor behaves as an ideal gas

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**/ / = (QCC) (QCC) = m C ( T – T ) compressed air hot gases fuel**

2 3 compressed air hot gases Combustion chamber fuel / CC (QCC) in = (QCC) in,ideal / CC = m C ( T – T ) 3 2 a pa CC is the compressor efficiency

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2 3 compressed air hot gases Combustion chamber fuel Let‘s do some Excel sheet calculations across the combustion chamber = 350 kg/s m a Determine C pa = kJ/kg.s CC = 80% (QCC) in P 2 3 =

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= 80% CC = 80% CC

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** (QCC) W W (QCC) = in hot net Thermal efficiency Gen net gases to the**

atmospheric air (QCC) in 1 2 compressed Comp- ressor Combustion chamber gases to the stack 3 4 Gen hot W net Gas turbine Thermal efficiency W net th = (QCC) in

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= 80% CC

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C CC = 80% = 85% T = 88%

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**= - Heat Loss? (QCC) W (QCC) W in hot gases net Gen in net gases**

Combustion chamber compressed air 3 2 Comp- ressor Gas turbine W net Heat Loss? Gen 4 = (QCC) in W net 1 gases to the stack atmospheric air

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**Heat Loss (QCC) W in hot gases net Gen gases to the atmosphere**

Combustion chamber compressed air 3 2 Comp- ressor Gas turbine W net Gen 4 Heat Loss 1 gases to the atmosphere through the stack atmospheric air

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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?

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