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Gas Turbine Cycles

N S SenanayakeSenior LecturerDept of Mechanical EngineeringThe Open University of Sri Lanka Lecture 02

Two shaft turbines

Low Pressure Turbine

High Pressure Turbine

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In a single shaft arrangement , the turbine is arranged to drive the compressor as well as to develop network.

It is sometimes more convenient to have two separate turbines . one to drive the compressor and other provides the power output

The first or high pressure (HP) turbine is known as the compressor turbine

The second or low pressure (LP)turbine is called the power turbine

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T-S diagram for two shaft turbine

3-4 Expansion in compressor turbine4-5 Expansion in power turbine

Gas Turbine Improvements

Modifications to the basic gas turbine thermodynamic cycle:

Regeneration (With Heat Exchanger)

Inter cooling

Reheating

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Note: The use of a regenerator is recommended only when the turbine exhaust temperature is higher than the compressor exit temperature.

Regenerative Gas Turbine cycle

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Temperature of the exhaust gas leaving the turbine is higher than the temperature of the air leaving the compressor.

The air leaving the compressor can be heated by the hot exhaust gases in a counter-flow heat exchanger (a regenerator or recuperator) – a process called regeneration

The thermal efficiency of the Brayton cycle increases due to regeneration since less fuel is used for the same work output.

Regenerative Gas Turbine cycle

Regeneration - Simple cycle with heat exchanger

8

)( 5353 TTcq p

35

1234

qqq

Since heat supplied is less than that of basic cycle, efficiency increases

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Effectiveness of the Regenerator

Assuming the regenerator is well insulated and changes in kinetic and potential energies are negligible, the actual and maximum heat transfers from the exhaust gases to the air can be expressed as follows.

enthalpyavailableMaxenthalpyinIncreaserregeneratoofessEffectiven .

25, hhq actregen

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Effectiveness of the Regenerator

Mass of fuel added to the combustion chamber is small compared to the air flow. We can neglect the difference in mass.

pg

pa

cTTcTT

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25

24

25

max,

,

hhhh

qq

regen

actregen

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Effectiveness of the Regenerator….

If a perfect heat exchanger is used then effectiveness = 1

Then T5 = T4 and also T6 = T2

But in reality this is not possible. Therefore concept of effectiveness/thermal ratio is used.

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Effect of Regenerator on Gas Turbine Efficiency

Efficiency of Regenerative cycle

/)1(

3

11 prTT

1

11

p

th

rFor simple cycle

Assume an ideal regenerator regen = 1 and constant specific heats

433 hhhhq xin

1243 hhhhwnet

43

12

43

12 11TTTT

hhhh

Same equation for the work ratio for basic cycle

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Regenerative cycle efficiency depends upon maximum and minimum temperatures (T1 and T3 )and pressure ratio.

Efficiency increases with increasing ‘t’ value or turbine inlet temperature T3 at constant cycle pressure ratio.

Also efficiency decreases with increasing pressure ratio for fixed ‘t’ value.

Whereas in simple cycle the efficiency increases with increasing pressure ratio.

tr

TT

r pp

1

1

3

/)1(

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Efficiency of Regenerative cycle…

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Thermal efficiency of Brayton cycle with regeneration depends on: Ratio of the minimum to

maximum temperatures Pressure ratio

Regeneration is most effective at lower pressure ratios and small minimum-to-maximum temperature ratios.

Factors Affecting Thermal Efficiency

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The addition of a heat exchanger only improves the cycle efficiency, but does not change the net work output.

The net work can be increased either by reducing the compressor work or by increasing the turbine work output

Heat exchanger

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Gas turbine regenerators are usually constructed as shell-and-tube type heat exchangers using very small diameter tubes, with the high pressure air inside the tubes and low pressure exhaust gas in multiple passes outside the tubes

Intercooling in compression

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The state 1 is the atmospheric condition

Ideally, it is possible to cool the air to the atmospheric temperature and in this case inter cooling is said to be complete inter cooling.

Inter cooling in compression…

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With inter cooling, Wc = Cp(T2 – T1) + Cp(T4 - T3)

Without inter cooling ,Wc = Cp(T2 – T1) + Cp(T2’ – T2)

Since pressure lines diverge with the increase of temperature

Cp(T4 - T3) < Cp(T2’ – T2)

This implies that total work of the compressor with inter cooling is reduced

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Therefore if the compression is carried out to high pressure (state 2 ) in two stages, 1 -2 and 3- 4 with the air cooled at constant pressure pi between the stages, a reduction of compressor work can be obtained. Net work is increased. Hence Work ratio is increased.Also when compression is done at lower temperatures, the work input to the compressor is reduced. Thus increases net work and hence increase the thermal efficiency

The back work ratio of a gas- turbine improves as a result of inter cooling and reheating. However, inter cooling and reheating decreases thermal efficiency unless they are accompanied with regeneration.

Inter cooling in compression…

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With isentropic compression and complete inter cooling the compression work is given by the following expression

)()( 3412 TTcTTcw ppcomp

/)1(

'2

3

4

/)1(

11

2

i

i

pp

TTand

pp

TT

Also we know that,

Intermediate pressure for min. compressor work

1'1/)1(

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/)1(

11

ip

ipcomp p

pTcppTcw

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The saving of work depends on the choice of the intermediate pressure pi.

By equating dW/dpi to zero the condition for minimum work can be proved to be; 

)( '21 pppi

ppi rppr

1

'2

pii

i rpp

pp

'2

1Therefore we can write

rpi = compression ratio at each stage

Intermediate pressure for min. compressor work..

Thus for minimum compressor work, each compression ratio and the work inputs between the two stages are equal.

The compressor work can further be reduced by increasing the number of stages and intercoolers. However, the additional complexity and cost make more than two or three stages uneconomical.

pii

i rpp

pp

'2

1

Therefore, w12 = w34

Intermediate pressure for min. compressor work..

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Intercooling is mostly used with regeneration.

During intercooling the compressor final exit temperature is reduced.

Therefore, more heat must be supplied in the heat addition process to achieve the maximum temperature of the cycle. Regeneration can make up part of the required heat transfer.

Inter cooling with regeneration

Summary of equations - Intercooling in compression

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)( '21 pppi

)()( 341214 TTcTTcww ppcomp

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341265

TTcTTcTTcTTc

inputheatworkNet

p

ppp

45

341265

TTTTTTTT

Example 1 – Two shaft plant

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Air is drawn in a gas turbine unit at 15°C and 1.01 bar and pressure ratio is 7 :1. The compressor is driven by the HP turbine and LP turbine drives a separate power shaft. The isentropic efficiencies of compressor, and the HP and LP turbines are 0.82, 0.85 and 0.85 respectively. If the maximum cycle temperature is 610oC, Calculate:(i) The pressure and temperature of the gases are entering the power

turbine.(ii) The net power developed by the unit per kg/s, mass flow.(iii) The work ratio(iv) The thermal efficiency of the unit.

Neglect the mass of fuel and assume the following For compression process Cpa = 1.005 kJ/kgK γ = 1.4For combustion and expansion process Cpg = 1.15kJ/kgK and γ = 1.333

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In a gas turbine plant, air is compressed from 1.01 bar and 15°C through a pressure ratio of 4:1. It is then heated to 650°C in a combustion chamber and expanded back to original pressure of 1.01 bar.

Calculate the cycle efficiency and the specific power output if a perfect heat exchanger is employed. The isentropic efficiencies of the turbine and compressor are 0.85 and 0.8 respectively.

Example 2 – Regeneration with perfect HE

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In a gas turbine installation air is supplied at 1bar, 25°C into compressor. The pressure after compression is 7.2 bar. The gas leaves the combustion chamber at 1100°C. A heat exchanger having effectiveness of 0.8 is fitted at exit of turbine for heating the air before its inlet into combustion chamber. Isentropic efficiency of the compressor and turbine are 0.8 and 0.85 respectively. The heat transfer rate to the combustion chamber is 1.48MW

The adiabatic index is 1.4 for air and 1.33 for the gas produced by combustion. The specific heat Cp is 1.005 kJ/kgK for air and 1.15kJ/kgK for the gas. Determine the following.

mass flow rate net power output thermal efficiency of the cycle

Example 3 – Regeneration with non perfect HE

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In a gas turbine plant working on the Brayton cycle the air at inlet is at 27ºC, 0.1 MPa. Compression is divided into two stage , each of pressure ratio 2.5 and efficiency 80% with inter cooling to 27ºC.The maximum temperature of the cycle is 800ºC. Turbine isentropic efficiency is 80%.

FindThe cycle efficiencyThe turbine exhaust temperature

Example 4 – Inter cooling

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The air supplied to a gas turbine plant is 10 kg/s. The pressure ratio is 6 and pressure at the inlet of the compressor is 1 bar. The compressor is two stage and provided with perfect intercooler. The inlet temperature is 300K and maximum temperature of the cycle is limited to 1073K.

Isentropic efficiency of compressor stage is 80% and turbine stage is 85%. A regenerator having effectiveness of 0.7. is included. Neglecting the mass of fuel determine the power output and the thermal efficiency of the plant.

Example 5 – Inter cooling and regeneration

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The air in a gas turbine plant is taken in LP compressor at 293K and 1.05 bar and after compression it is passed through intercooler where its temperature is reduced to 300K. The cooled air is further compressed in HP unit and then passed in the combustion chamber where its temperature is increased to 750°C by burning the fuel. The combustion products expand in HP turbine which runs the compressor and further expansion is continued in LP turbine which runs the alternator. The gases coming out from LP turbine are used for heating the incoming air from HP compressor and then expanded to atmosphere pressure.

Example 6 – Inter cooling and regeneration with two shafts

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Pressure ratio of each compressor - 2. Isentropic efficiency of each turbine and compressor - 82% Effectiveness of Heat exchanger- 0.72Air flow – 16 kg/sCalorific value of fuel – 42000 kJ/kgCp for air – 1.005 kJ/kg KCp for gas - 1.12 kJ/kg K γ for air - 1.4 γ for gas – 1.33

Neglecting the mechanical, pressure and heat losses of the system, determine the following

The power output Specific fuel consumption Thermal efficiency

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(i) Why are the back work ratios relatively high in gas turbine plants compared to that of steam power plant?

(ii) In a gas turbine plant compression is carried out in two stages with perfect intercooling and expansion in one stage turbine. If the maximum temperature (Tmax) and minimum temperature (Tmin ) in the cycle remain constant, show that for maximum specific output of the plant, the optimum overall pressure ratio is given by

Inter cooling - Optimum pressure ratio for maximum specific work output

Example 7

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Where γ = adiabatic index ηT = Isentropic efficiency of the turbine ηC = Isentropic efficiency of the turbine

 

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(iii) In a Brayton cycle gas turbine power plant the minimum and maximum temperature of the cycle are 300K and 1200K. The compression is carried out in two stages of equal pressure ratio with inter cooling of the working fluid to the minimum temperature of the cycle after the first stage of compression. The entire expansion is carried out in one stage only. The isentropic efficiency of both compressors is 0.8 and that of the turbine is 0.9.

Determine the overall pressure ratio that would give the maximum work per kg working fluid . Take γ = 1.4.