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S.1 The Basic Gas Turbine Cycle

The first working gas turbine was demonstrated in year 1903; and in 1939 the first jet engine was in the air.

Today gas turbines have many important

applications: • Electricity generation, • Jet propulsion (aircraft engines), • Marine propulsion.

Moreover, the gas turbines' strong position for

power generation is strengthened by their use in combined gas/steam cycles for electricity generation.

Application of gas turbines for jet propulsion

P1.1 Acknowledgements

Modified by Catharina Erlich, 2005, updated 2006 Author: Samuel Roy, KTH, 1998 Editor: Vitali Fedulov, KTH, 2005

P1.2 Literature

Cohen, H.; Rogers, GFC and Saravanamuttoo HIH 2001 “Gas Turbine Theory, 5th edition”, ISBN 0130158477-X

Moran M. J., Shapiro H. N., 1998; Fundamentals of engineering thermodynamics: SI version John Wiley & sons ltd, ISBN 0471979600

Weston, K, 1992 "Energy Conversion – The EBook", http://www.personal.utulsa.edu/~kenneth-weston/

P1.3 Prerequisites

It is expected that the reader:

• Has successfully passed at least one year of engineering studies at university level,

2

• Knows basic thermodynamics (at least 160 LU = 4 weeks of fulltime studies).

P1.4 LU and TU

Learning Units: 6 Teaching Units: 2

P1.5 First working gas turbine

The first working gas turbine was demonstrated in 1903 by Aegidius Elling.

With this, and the fact that a propeller-driven

aircraft has large limitations at high altitudes, Frank Whittle developed the first jet-engine, which was patented in 1930.

About the same time, without the knowledge

about Whittle's work, Dr. Hans von Ohain also invented a jet engine.

According to their calculations these new engines

should perform better at higher altitudes than the propeller engines.

The jet engine by Dr. von Ohain flew for the first

time in 1939 and the one by Sir Whittle in 1941.

Aegidius Elling (1861-1949), Norwegian engineer

1884 - first gas turbine patent,1903 - first operating gas

turbine, 1912 - presented a multi-shaft

engine with intercooling and reheat,

1923 - patented the multi-shaft engine.

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S.2 Educational Objectives

After this chapter the student should be able to:

Describe which components are included in the gas turbine and how it works,

Introduce the cycle in the state diagram,

Understand the influence of irreversibilities on the efficiency of different components,

Perform thermodynamic analysis of the real gas turbine cycle.

Exemplary gas turbines

S.3 Basic Gas Turbine Cycle in Comparison with Steam Cycle

Possibilities: • A gas turbine cycle installation is cheaper than a steam cycle installation. It

also occupies less space compared to the steam cycle, • Heat is delivered to the gas turbine at a relatively high temperature and low

pressure, • The gas turbine can be started in a few minutes, while a steam power plant

needs around 24 hours to start.

Limitations: • The gas turbine is very fuel sensitive and needs high-quality fuels such as

natural gas and light oil, • Even though the temperature of heat supply is very high in the gas turbine, the

efficiency of gas turbine is limited because of high exhaust temperatures.

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GE9H gas turbine MP36 steam turbine

P3.1 GE9H gas turbine

Number of compressor stages

18

Pressure ratio 23:1 Firing temperature 1430ºC

P3.2 MP36 steam turbine

Power out put 55 MW Pressure 87.2 bar Temp 510ºC

P3.3 High exhaust temperature

High exhaust temperature becomes an advantage when the exhaust gases are used to generate steam in a recovery boiler (in a combined gas/steam cycle).

S.4 Components of a Basic Gas Turbine Cycle

Ambient air is sucked in and pressure is raised in the compressor.

Fuel is injected into the compressed air in the combustion chamber, and combustion takes place, increasing the temperature of the gas.

Hot pressurized gas expands in the turbine, generating work.

Work required for pressurizing relatively

cold air (in the compressor) is smaller than work produced during expansion at higher temperatures (in the turbine). This

1.

2. 3.

4.

Fuel

Air

Compressor Turbine

CombustionChamber

G

Gas

5

is the basic reason why the gas turbine cycle generates net work.

P4.1 Compressor

A compressor consumes work to raise air pressure. Compressing a gas requires relatively more work (compared to liquid, for

example), as gases are compressible. Compression reduces gas volume and increases temperature.

The temperature at the compressor outlet depends on the compression efficiency and pressure ratio. The lower the efficiency and the higher the pressure ratio, the higher the temperature.

Temperatures over 300°C are common after compression in a gas turbine. In a gas turbine the compressor most often is an axial type, but sometimes it can

be a centrifugal type. If it is axial, the number of stages varies between 5 and 40. The corresponding

pressure ratio (i.e. outlet pressure/inlet pressure) varies between 4 and 35. A compressor always has a larger number of stages than the turbine. In a one-axis gas turbine (where the turbine and compressor are placed on the

same shaft) the compressor is run by the turbine. Typically it consumes ca. 60-70% of the turbine power.

P4.2 Combustion chamber

The combustion chamber is the part of a gas turbine where fuel is supplied. The fuel is pressurized to make possible its injection into the combustion chamber.

A gas turbine requires special kinds of fuels: it can only burn combustible gases, such as natural gas or gas obtained from biomass/coal in the gasification process. It can also use liquid fuels with very low viscosity, such as light oil and diesel-like fuel (for example Jet A1).

Pressurized air and fuel are mixed in sequential steps, to control flame temperature. The sequential combustion avoids hot spots, where temperature is higher than 1500°C. The hot spots are the source of NOx production. During controlled combustion, temperature of the hot gases varies between 800°C and 1200°C.

Apart from the environmental concern (NOx emissions), turbine blades typically do not withstand temperatures higher than 1200°C.

There are several kinds of combustion chambers: silo, annular, can, and cannular.

P4.3 Turbine

Hot pressurized gas is allowed to expand in the turbine, which is forced to rotate and thus produces work.

After expansion, the gas is still hot. Exhaust temperatures vary between 400°C and 650°C (depends on the pressure ratio and the combustion temperature).

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In a one-axis turbine, most of the power produced is used to run the compressor. Only around 30-40% of the total power can be practically used (for example to produce electricity in a generator).

In an engine with free-power turbine, there are two turbines: one that only provides power to the compressor and one that produces the net power output. The exhaust from the compressor-turbine is lead to the second turbine on a separate shaft, where it is further expanded to the atmospheric pressure.

Axial turbines are mostly used. They contain up to 8 stages.

S.5 Representation of Flow Chart in a Real Gas Turbine

Starting device Shaft coupling Generator

P5.1 Starting device

Starting devices can be diesel engines or compressed air engines. The engine usually accelerates the compressor up to a relatively slow speed

(approximately 10-20% of the gas turbines’ rated speed)

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The compressor is now able to suck in and compress air. Fuel is supplied, combustion takes place and the turbine can start to produce mechanical power.

The engine aids the gas turbine in becoming self-sustaining and when the gas

turbine has reached this point, the starting engine is switched off.

P5.2 Shaft coupling

The gas turbine can drive a mechanical device or an electricity generator. In the first case, it can be a marine screw. Most often a reducer is needed to accommodate the high rotating velocity of a gas turbine.

P5.3 Generator

In the case of a land based machine, a generator, a pump a compressor or similar is attached to the shaft coupling.

S.6 T-s Diagram and Analysis of a Gas Turbine with Isentropic Expansion and Compression

The gas turbine is an open cycle, but is

illustrated as a closed cycle in a T-s diagram.

Both air and the combustion gas are

assumed to be ideal gases.

Process 1-2: Isentropic compression in the compressor.

Process 2-3: Isobaric heat supply in the

combustion chamber.

Process 3-4: Isentropic expansion in the turbine.

Process 4-1: Exhaust into the

atmosphere.

P6.1 Ideal gases

An ideal gas is a gas that obeys the ideal gas law:

8

RTpv =

where: p - pressure (Pa) v - specific volume (m3 /kg) R - specific gas constant (J/kg K) T - temperature (K)

Furthermore, the specific heat is assumed to be independent of pressure, but is heavily dependent on the gas temperature.

P6.2 Process 1-2: Isentropic compression in the compressor

Air is compressed isentropically to increase the pressure. As air is compressible, the pressure increase will cause a large increment in the air temperature. Compression requires a power input, which is obtained from the turbine.

The power input required is the mass flow of air through the compressor times the enthalpy increase:

( )12 hhmP airC −⋅= &

[kg/s · kJ/kg = kW ] Enthalpies for air at different temperatures can be found in tables. Note! Enthalpy

is independent of the pressure but dependent on the temperature.

The power can also be expressed as a function of specific heat (Note! Specific heat is temperature dependent and is taken as an average value between temperature T1 and T2)

( )1221, TTcmP PairC −⋅= −&

[kg/s · kJ/(kg·K) · K = kW ] In order to calculate the power needed by the compressor, it is thus necessary to

estimate the temperature after the compressor; this can be done knowing the pressure ratio of the compressor.

For an isentropic compression (temperatures in Kelvin):

C

C

PP

TT κ

κ 1

1

2

1

2

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

Where κC is the ratio of specific heats for compression, i.e. it is temperature dependent! At common room temperature κ = 1.4. The ratio of specific heat can be found in a diagram, see below (line x = 0 for pure air). The temperature on the x-axis is the average during the compression.

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P6.3 Process 2-3: Isobaric heat supply in the combustion chamber

The pressurized (and heated) air enters the combustion chamber where fuel (most commonly natural gas or light oil) is supplied Combustion takes place, and increases the gas temperature to 800-1200°C (the higher the temperature the better the efficiency of the turbine) The fuel flow depends on the temperature desired in the turbine inlet (t3), the temperature after the compressor (t2) and on the fuel used and its heating value (denoted LHV or Hi). The heat supplied in the combustion chamber is:

LHVmQ fuelFUEL ⋅= && An important definition is the specific fuel consumption, β, which is defined as:

10

air

fuel

mm&

&=β

[kgfuel / kgair] For the simple gas turbine, β ≈ 0.01 – 0.03, depending on fuel, temperature after the compressor and the combustion temperature. The higher the temperature t3, the higher is β. The gas flow after the combustion, i.e. the flow entering the turbine is:

airfuelairgas mmmm &&&& ⋅+=+= )1( β The specific fuel consumption, and thus the fuel flow can be found through a heat balance on the combustion chamber knowing the temperatures t3 and t2:

32 )1( hmLHVmhm airfuelair ⋅⋅+=⋅+⋅ &&& β [1] However, as there is not only air in point 3, rather a combustion gas, the enthalpy in 3 is dependent on the fuel and the fuel flow. The higher the fuel flow, the higher is the enthalpy in 3. The enthalpy in 3 can be estimated knowing the gas content, x, for the gas. The gas content is the inverse of the excess air factor. Gas content is thus a measure of how much of the incoming air has reacted. If all the air supplied for combustion would react, the gas content in the resulting gas would be x = 1, i.e. the resulting gas consists solely of combustion gases and no air. For gas turbines x = 0.20-0.40 depending on the fuel, temperature out from the compressor and on the combustion temperature. This means that a large part of the air flow does not react in the gas turbine. The gas content is related to the specific fuel consumption according to:

( )β

β+

⋅+=1

1 fx [2]

where f is the stoichiometric air to fuel ratio (kg air/kg fuel). For light oil, f = 14.52, based on a typical composition. For methane (90-95% in natural gas), f equals 17.16. The enthalpy h3 is expressed as a function of the enthalpy for air and the gas content and includes a factor that makes up for the increased enthalpy, the DH-value:

h3 = h3,AIR + x⋅ DHt3 [3]

The DH-value is the (enthalpy) difference between the enthalpy of the gases with x=1 and the enthalpy of the gases with x = 0 (pure air).

The enthalpy for air and combustion gases are found in a gas-enthalpy table

Setting equation [2] into [3], the enthalpy for gases is fully expressed as a function of the specific fuel consumption, i.e.

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( ) 3,33 11 tAIR DHfhh ⋅

+⋅++=

ββ

[4]

Combining [4] into [1] and solving for β (the only unknown), following expression is obtained:

3,3

2,3

)1( tAIR

AIR

DHfhLHVhh

⋅+−−−

=β

P6.3.1 f equals 17.16 for methane

Example: calculation of stoichiometric air to fuel ratio of methane For methane (CH4) combusted in oxygen, the balanced complete reaction is:

CH4 + 2O2 CO2 + 2H2O i.e. for each mol of methane, 2 mol of oxygen is required. As nitrogen is part of air (79% N2 and 21% O2 is technical air), the combustion reaction in air can be written:

CH4 + (2O2 + 2*3.76 N2) CO2 + 2H2O + 2*3.76 N2 Molar mass for CH4 is 16 kg/kmol, for O2 32 kg/kmol and for N2 28 kg/kmol. Air/fuel ratio (kg/kg): (2*O2 + 2*3.76 N2 ) / CH4 = (2*32 + 2*3.76*28) / 16 = 17,16 [kg air / kg CH4]

P6.4 Process 3-4: Isentropic expansion in the turbine

The hot pressurized gas expands isentropically in the turbine, causing decrease in pressure and temperature.

The total power (a large part of this will go to compressor work) that the turbine produces is:

( )43 hhmP gasT −⋅= & [kg/s · kJ/kg = kW ]

The enthalpies are dependent on both temperature and gas content according to:

h3 = h3,AIR + x⋅ DHt3

h4 = h4,AIR + x⋅ DHt4 Enthalpies for air and DH-values at different temperatures can be found in tables.

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The power can also be expressed as a function of specific heat (Note! Specific heat is temperature dependent AND dependent on the gas content and is taken as an average value between temperature T3 and T4)

( )4343, TTcmP PgasT −⋅= −& [kg/s · kJ/(kg·K) · K = kW ]

In order to calculate the power produced by the turbine it is thus necessary to estimate the temperature after the turbine; this can be done knowing the pressure ratio of the turbine. For an open ideal gas turbine without pressure losses:

1

2

4

3

pp

pp

=

For an isentropic expansion (temperatures in [K]):

T

T

pp

TT κ

κ 1

1

2

4

3

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

Where κT is the ratio of specific heat for the expansion, and is dependent both on the temperature AND the gas content x. The ratio of specific heat can be found in a diagram, see below:

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P6.5 Process 4-1: Exhaust in the atmosphere

In the open gas turbine the exhaust is let out in the atmosphere. Typical temperatures are 400°C- 650°C.

S.7 Power Output and Thermal Efficiency

The net power output of the gas turbine is (kW or MW):

CTGT PPP −=

Including efficiencies in the work transfer from turbine to compressor (mechanical, ηM), and for the axis in the generator (generator, ηG) the electrical net power output is:

GCmTGTel PPP ηη ⋅−⋅= )(

The electrical efficiency of the cycle is:

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fuelQGTelP

GT &=η

T-s diagram

S.8 The effect of irreversibility in turbine and compressor

In a real gas turbine, irreversibility is present during compression and expansion, i.e. the entropy increases.

In order to quantify the losses, isentropic or polytropic efficiencies of the compressor respective turbine can be introduced.

The temperature increase in the compressor with an isentropic efficiency will be larger than in the ideal case (isentropic). This means that the compressor work is larger in the real case than in the ideal.

The temperature decrease in the turbine with an isentropic efficiency will be smaller than in the ideal case (isentropic). This means that the turbine provides less work in the real case than in the ideal.

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Compression Expansion

P8.1 Polytropic compression and expansion

polytropic compression polytropic expansion

P8.2 The temperature increase in a compressor with an isentropic efficiency

It is assumed that the air is an ideal gas. The temperature difference between the compressor outlet and inlet is:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=−

−

1

1

1

2112

C

C

ppTTT

SC

κκ

η

where the temperature T1 is in [K] and ηSC is the isentropic efficiency of the compressor

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The ratio of specific heat is found as an average between temperatures T1 and T2.

P8.3 The temperature decrease in a turbine with an isentropic efficiency

It is assumed that the air is an ideal gas. The temperature difference between the turbine inlet and outlet is:

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅=− −

T

T

pp

TTT ST

κκη 1

4

3

34311

where the temperature T3 is in [K] and ηST is the isentropic efficiency of the turbine

The ratio of specific heat is found as an average between temperatures T3 and T4 for the present gas content.

P8.4 The temperature increase in a compressor with an isentropic efficiency

It is assumed that the air is an ideal gas. The temperature difference between the compressor outlet and inlet is:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=−

−

1

1

1

2112

C

C

ppTTT

SC

κκ

η

where the temperature T1 is in [K].

The ratio of specific heat is found as an average between temperatures T1 and T2.

P8.5 The temperature decrease in a turbine with an isentropic efficiency

It is assumed that the air is an ideal gas. The temperature difference between the turbine inlet and outlet is:

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⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅=− −

T

T

pp

TTT STκκη 1

4

3

34311

where the temperature T3 is in [K].

The ratio of specific heat is found as an average between temperatures T3 and T4 for the present gas content.

S.9 The Effect of Pressure Loss during Combustion

In a real gas turbine, there are pressure losses in the combustion chamber.

The pressure of the gas entering the turbine

is less than the pressure of air exiting the compressor.

1

2

4

3

pp

pp

<

The pressure loss results in the temperature

difference over the turbine becoming smaller (as the pressure ratio decreases), and thus the work output is smaller for a certain fuel supply.

Thus, the efficiency of the gas turbine

decreases due to combustion pressure loss.

S.10 Closed Gas Turbine

A closed gas turbine working with air or another gas can be used in combination with a solid fuel as external firing.

Instead of a combustion chamber, there is a heat exchanger, where the working

media obtains heat via heat exchange with a boiler or similar.

The closed gas turbine has much lower efficiency than the direct fired gas turbine and furthermore is more expensive and complex.

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Boiler

1

2

34

5

6

7

8

G

S.11 Summary

A basic gas turbine consists of a compressor, combustion chamber and turbine.

The compressor work is high and constitutes about 60-70% of the total turbine power.

The specific fuel consumption, β, and gas content, x, are used for analyzing the combustion and turbine expansion.

The net power output for a gas turbine is turbine work minus compressor work.

Isentropic efficiencies for compressor respective turbine illustrate the irreversibility prevailing, resulting in an entropy increase.

In real gas turbine there are pressure losses in the combustion chamber,resulting in a decreased gas turbine efficiency.

This you must know

P11.1 This you must know

The function of the components in a gas turbine cycle

How to illustrate the cycle in a T-s diagram with losses included

How turbine pressure ratio is related to the compressor pressure ratio

The definitions of specific fuel consumption and gas content

How to make a heat balance on the combustion chamber

Thermodynamic analysis of the whole gas turbine with different losses included