1. Unit 61: Engineering Thermodynamics
Lesson 16: The Gas Turbine Engine

2. Thermodynamic Cycles
Thermodynamic cycles can be subdivided into two broad categories: (a) power cycles which produce a net power output and (b) refrigeration and heat pump cycles which consume net power.
Thermodynamic power cycles can be categorised as gas and vapour cycles
In gas cycles the working fluid remains in the gas phase throughout the entire cycle
In vapour cycles, the working fluid exists in a vapour phase in one part of the cycle and a liquid in another part

3. Thermodynamic Cycles
The internal combustion engine and the gas turbine engine undergo a gas power cycle.
The two areas where gas turbine engines are used are electric power generation and aircraft propulsion
The ideal cycle for a gas turbine engine is called the Brayton Cycle.

4. Objective
The purpose of this lesson is to consider a Gas Turbine Engine.

5. The Gas Turbine Engine
The modern gas turbine engine has many applications for example it may be used as a power source for electrical generation or used to power ships or aircraft
The working cycle of the gas turbine engine is similar to that of the four-stroke piston engine.

6. The Gas Turbine Engine
In the gas turbine engine combustion occurs at a constant pressure, while in the piston engine it occurs at constant volume.
In both engines there is an induction, compression, combustion and exhaust phase
In piston engines there is a non-flow process where as in a gas turbine engine we have a continuous flow process.

7. The Gas Turbine Engine

8. The Gas Turbine Engine

9. The Gas Turbine Engine
In the gas turbine engine the lack of reciprocating parts gives smooth running and enable more energy to be released for a given engine size.
Combustion occurs at constant pressure with an increase in volume, therefore the peak pressures that occur in the piston engine are avoided. This allows the use of lightweight fabricated combustion chambers and lower octane fuels although the higher flame temperatures require special materials to ensure a long life for combustion chamber components

10. The Gas Turbine Engine
To ensure maximum thermal efficiency in the turbine, we require the highest temperature of combustion (heat in) to give the greatest expansion of the gases.
There is a limit to the temperature of combusted gases as they enter the turbine and this is dictated by the turbine of materials.
Additional cooling within the turbine helps to maximise the gas entry temperature to the turbine.

11. The Gas Turbine Engine

12. The Gas Turbine Engine
Within limits of the materials, the higher the turbine entry temperature the turbine thermal efficiency.
Although the closed gas turbine engine can be modelled reasonably accurately on the constant pressure cycle, in the practical cycle there will be thermodynamic and mechanical losses due to such things as…

13. The Gas Turbine Engine
The air not being pure but containing other gases and water vapour
Heat being transferred to the materials of the compressor, turbine and exhaust units (open cycle) so that they are not pure adiabatic or isentropic processes
Dynamic problems (in open gas turbines) such as turbulence and flame stability in the combustion chamber, whereby constant temperature and hence constant pressure cannot be maintained

14. The Gas Turbine Engine
Pressure losses as a result of the burnt air causing an increase in volume and hence a decrease in its density
Thermodynamic losses resulting from friction and play in mechanical mechanisms

15. The Gas Turbine Engine
The losses in the compressor and turbine units of a closed gas turbine engine can be catered for by comparing the real cycle with the ideal constant pressure through the use of isentropic efficiencies.
The open cycle gas turbine cannot be directly compared with the ideal constant pressure cycle because of the energy losses an d complications that arise as a result of the combustion process.

16. Isentropic Efficiency & the Real Cycle
In real cycles in the closed gas-turbine plant with respect to the compression and expansion processes, the real compression process will require a larger work input to the compressor than in the ideal isentropic case.
The efficiency of the compressor…
ηc = Ideal specific enthalpy change
Actual specific enthalpy change

17. Isentropic Efficiency & the Real Cycle
ηc = Ideal specific enthalpy change
Actual specific enthalpy change
ηc = (T’2 – T1)
(T2 – T1)
The difference between isentropic (ideal) compression and real compression is illustrated on the T – S diagram of the gas turbine constant pressure cycle
_______________

18. Isentropic Efficiency & the Real Cycle
T(k)
Isentropic expansion
Constant pressure lines 3 2 2’
Isentropic compression 4 4’ 1
Real expansion
Real compression
s (kJ/kg.K)

19. Brayton Cycle

20. Isentropic Efficiency & the Real Cycle
If the expansion process of the gas in a real constant pressure cycle takes place in a turbine, the friction effects and other disturbances will cause the gas to leave hotter than it would do in an ideal expansion,which of course means the temperature drop through the turbine (T3 – T4) would be less than the ideal case.

21. Isentropic Efficiency & the Real Cycle
In a similar manner to that of the compressor, the isentropic turbine efficiency, ηT, is the ratio of the actual work output (measured by enthalpy change) to the isentropic work output for the same pressure ratio and inlet temperature…
ηc = cp(T3 – T4)
cp(T3 – T’4)

22. Isentropic Efficiency & the Real Cycle
If cp for isentropic and real cases is approximately equal then…
ηc = (T3 – T4)
(T3 – T’4)

23. Isentropic Efficiency & the Real Cycle
Example: In a simple closed gas turbine engine consisting of a compressor, combustor, turbine and heat exchanger, the isentropic efficiency of the compressor is 85% and that of the turbine is 90%. The inlet air temperature to the compressor is 290K, the compression ratio is 5:1 and the maximum temperature of the air in the engine is 1000K. Assuming adiabatic compression and expansion, constant pressure addition and that the specific heat capacities for the air are also constant, determine (a) the specific work done one the compressor (b) the specific work output from the turbine and (c) the specific net work from the engine and (d) the cycle thermal efficiency

24. Isentropic Efficiency & the Real Cycle
We are told that the gas is air and the specific heat capacities are constant. Therefore using standard value, cp = kJ/kg.K; cv = kJ/kg K and so
γ = cp/cv = 1.005/0.718 = 1.4
T’2 = p2 (γ-1)/γ Thus T’2 = (290)(5)0.286
T P1
i.e. T’2 = K

25. Isentropic Efficiency & the Real Cycle
thus ηc = 0.85 = (485.5 – 290) (T2 – 290) Hence T2 = K Thus the actual specific work done on the compressor is given by… Wc = h2 – h1 = cp(T2 – T1) h1 = cp(T2 – T1) = 1.005(489.4 – 290) = 200 kJ/kg K

26. Isentropic Efficiency & the Real Cycle
for the turbine…
T’4 = p4 (γ-1)/γ Thus T’4 = (1000)(1/5)0.286
T P3
i.e T’4 = 631 K
thus ηt = 0.9 = (1000 – T4) which give T4 = K
(1000 – 631)
Thus the actual specific work output from the turbine,
WT = cp(T3 – T4) = 1.005(1000 – 667.9) = kJ/kg K

27. Isentropic Efficiency & the Real Cycle
Wnet = WT - Wc = kJ/kg K
The cycle thermal efficiency may be found using…
ηthermal = Wnet/Q1
and Q1 = cp(T3 – T2) = 1005( ) = kJ/kg K
thus ηthermal = 133.4/ = = 26%