1. Gas Turbine Cycles for Aircraft Propulsion
CHAPTER 3
Gas Turbine Cycles
for Aircraft Propulsion

2. Gas Turbine Cycles for Aircraft Propulsion
Aircraft GT Cycles differ from Shaft Power Cycles in that the useful power output in the former is produced wholly or in part as a result of expansion in a propelling nozzle wholly in Turbojet and Turbofan engines and partly in Turboprop engines.
A second distinquishing feature is the need to consider the effect of forward speed and altitude on the performance of an aircraft engine.
Chapter Shaft Power Cycles

3. Gas Turbine Cycles for Aircraft Propulsion 3.1 Criteria Of Performance
For simplicity assume that
mass flow ṁ is constant
(i.e the fuel flow is
negligible).
The net thrust is then;
ṁ a Va Vj
FIG.3.1 Schematic Diagram of a Propulsive Duct
F = ṁj Vj - ṁa Va - ṁf Vf + Aj (Pj-Pa)
F = ṁ a (Vj - Va ) + Aj (Pj-Pa) ( 3.1 )
Chapter Shaft Power Cycles

4. Criteria Of Performance
When the exhaust gasses are expanded completely to Pa in the propulsive duct i.e Pj = Pa ;
then;
F = ṁ a (Vj-Va) ( 3.2 )
From this equation , it is clear that the required thrust can be obtained by designing the engine to poduce :
either a high velocity jet of small mass flow
or a low velocity jet of high mass flow.
Chapter Shaft Power Cycles

5. Criteria Of Performance
The most efficient combination of these two variables is povided by the following analysis;
Chapter Shaft Power Cycles

6. Criteria Of Performance
From eqns. (3. 2) , (3.3);
a) F is max when Va = 0 ηp = 0
b) ηp is max when Vj =Va F = 0
We may conclude that;
although Vj must be greater than Va,
the difference (Vj-Va) should not be too great.
Chapter Shaft Power Cycles

7. Criteria Of Performance
As a result a family of propulsion units are developed.
FAMILY of PROPULSION ENGINES
1. Piston Engine
2. Turboprop
3. Turbofan
4. Turbojet
5. Ramjet
From 1 to 5 Vj increases and m decreases,
for a fixed Va, F increases and ηp decreases
Chapter Shaft Power Cycles

8. Chapter2 Shaft Power Cycles
Propulsion Engines
Piston Engine Turboprop Turbofan
Turbojet Ramjet
Chapter Shaft Power Cycles

9. Criteria Of Performance
Taken in the order shown :
Propulsive jets of decreasing mass flowrate and increasing jet velocity
therefore suitable for aircraft of
increasing design cruising speed.
Chapter Shaft Power Cycles

10. Chapter2 Shaft Power Cycles
Fig 3.2 Flight Regimes
Ram-jet
Turbojet
Chapter Shaft Power Cycles

11. Criteria Of Performance
Propulsion efficiency is a measure of the effectiveness with which the propulsive duct is being used for propelling the aircraft.
Efficiency of energy conversion
( 3.4 )
Chapter Shaft Power Cycles

12. Criteria Of Performance
From the above definitions;
( 3.6 )
Efficiency of an aircraft power plant is inextricably linked to the aircraft speed.
For aircraft engines,
Specific fuel consumption =
sfc = Fuel Consumption/Thrust [kg/hN]
is a better concept than efficiency to define performance.
Chapter Shaft Power Cycles

13. Criteria Of Performance
Since Qnet,p = const for a given fuel, then
for aircraft plants ; ηo = f (Va/sfc ).
for shaft power units ; ηo = f (1/sfc ).
Another important performance parameter is specific thrust, Fs ;
Fs thrust per unit mass flow of air [N.s/kg].
Chapter Shaft Power Cycles

14. Criteria Of Performance
This ( Fs ) provides an indication of the relative size of engines producing the same thrust, because the dimensions of the engine are primarily determined by the airflow requirements.
Note that;
sfc = ηo / Fs ( 3.8 )
Chapter Shaft Power Cycles

15. ISA (InternationalStandard Atm.)
When estimating the cycle performance
at altitude one needs to know
the variation of ambient pressure
and temperature with altitude.
ISA (InternationalStandard Atm.)
corresponds to middling lattitudes
Ta decrease by 3.2 K per 500 m
up to m.
After m Ta = const
up to m.
Then Ta starts increasing slowly Z
(m) Ta
(K)
Chapter Shaft Power Cycles

16. Criteria Of Performance
For high-subsonic or supersonic aircraft it is more appropriate to use Mach number rather than V (m/s) for aircraft speed, because "DRAG" is more a function of Ma.
Inrease in Mach number with altitude is experienced
for a given Va
Chapter Shaft Power Cycles

17. Criteria Of Performance
Mach Number vs.
Flight Velocity
Va (m/s)
Chapter Shaft Power Cycles

18. 3.2 Intake & Propelling Nozzle Efficiencies
FIG 3.4 Simple Turbojet Engine
Chapter Shaft Power Cycles

19. Intake & Propelling Nozzle Efficiencies
The turbine produces just sufficient work to drive the compressor and remaining part of the expansion is carried out in the propelling nozzle.
Because of the significant effect of forward speed, the intake must be considered as a seperate component.
In studying the performance of aircraft propulsion cycles it is necessary to describe the losses in the two additional components ; i.e.
INTAKE
PROPELLING NOZZLE
Chapter Shaft Power Cycles

20. Chapter2 Shaft Power Cycles
3.2.1 Intakes
The intake is a simple adiabatic duct.
Since Q = W = 0 ,
the stagnation temperature is constant,
although
there will be a loss of stagnation pressure
due friction and due to shock waves
at supersonic flight speeds.
Chapter Shaft Power Cycles

21. Chapter2 Shaft Power Cycles
Intakes
Under static conditions or at very low forward speeds ;
intake acts as a nozzle
in which the air accelerates from zero velocity
or from low Va to V1 at the compressor inlet .
At cruise speeds, however,
the intake performs as a diffuser
with the air decelerating from Va to V1
and the static pressure rising from Pa to P1.
Chapter Shaft Power Cycles

22. Chapter2 Shaft Power Cycles
Intakes
Inlet isentropic efficiency, “ηi “ defined in terms of temperature rise.
The isentropic efficiency for the inlet ;
( 3.9 )
here;
T01' = Temperature which would have been reached
after an isentropic Ram compression to P01.
Chapter Shaft Power Cycles

23. Chapter2 Shaft Power Cycles
Intakes V
Fig 3.5 Intake Losses V V V V
Chapter Shaft Power Cycles

24. Chapter2 Shaft Power Cycles
Intakes
P01 - Pa = Ram Pressure Rise
RAM efficiency , ηr
is defined in terms of pressure rise
(pressure rise / inlet dynamic head ).
Chapter Shaft Power Cycles

25. Chapter2 Shaft Power Cycles
Intakes
The isentropic efficiency for the INLET ;
( 3.9 )
Chapter Shaft Power Cycles

26. Chapter2 Shaft Power Cycles
Intakes
The intake presure ratio;
( 3.10.a )
Chapter Shaft Power Cycles

27. Chapter2 Shaft Power Cycles
Intakes
Noting M= V / (gRT )1/2 and R = Cp( g- 1 )
( 3.10.b )
The stagnation temperature;
( 3.10.c )
Chapter Shaft Power Cycles

28. Chapter2 Shaft Power Cycles
Intakes
RAM efficiency is defined as;
For supersonic inlets it is more usual to quote values of stagnation pressure ratio P01 / P0a as a function of Mach number.
Chapter Shaft Power Cycles

29. Chapter2 Shaft Power Cycles
Propelling Nozzles
Chapter Shaft Power Cycles

30. Chapter2 Shaft Power Cycles
Propelling Nozzles
Propelling nozzle is the remaining part of the engine after the last turbine stage.
The question is immediately arises, as to whether a simple convergent nozzle is adequate or whether a convergent - divergent nozzle should be employed.
It can be shown that for an isentropic expansion, the thrust produced is maximum when complete expansion to Pa occurs in the nozzle.
Chapter Shaft Power Cycles

31. Chapter2 Shaft Power Cycles
Propelling Nozzles
The pressure thrust arising from an incomplete expansion does not entirely compansate for the loss of momentum thrust due to smaller jet velocity.
But this is no longer true when friction is taken into account because the theoretical jet velocity is not achieved.
For values of P04/Pa ( nozzle pressure ratio ) up to 3
Fconv-div thrust = F simple conv.
Converging-diverging nozzle at off-design condition 
 Shock wave in the divergent section
loss in stagnation pressure.
Chapter Shaft Power Cycles

32. Chapter2 Shaft Power Cycles
Propelling Nozzles
With simple convergent nozzles;
a) It easy to employ a variable area nozzle,
b) It is easy to employ a thrust reverser,
c) It is easy to employ a noise suppressor
( i.e. increase the surface area of the jet stream ).
The thrust developed by a propulsive nozzle;
F = ṁ Vj + (Pj -Pa) Aj
Chapter Shaft Power Cycles

33. Chapter2 Shaft Power Cycles
Propelling Nozzles
For a given m to determine the nozzle exit area that yields maximum thrust, differentiate the above eqn.
dF = ṁ dVj + AjdPj + Pj dAj - PadAj
but ṁ = AV = rjAjVj
dF = Aj (dPj + r jVj dVj) + (Pj -Pa) dAj
Chapter Shaft Power Cycles

34. Chapter2 Shaft Power Cycles
Propelling Nozzles
since momentum equation;
dP + rVdV = 0 --> dF = Aj [0] + (Pj -Pa) dAj
solve for dF / dAj
dF / dAj = Pj - Pa for max thrust (Pj -Pa) =0
Therefore; the nozzle area ratio must be chosen so that the pressure ratio Pj / Po = Pa / Po
This design criterion is based on planar flow.
Chapter Shaft Power Cycles

35. Chapter2 Shaft Power Cycles
Propelling Nozzles
This design criterion is based on planar flow.
If a similar equation is derived for a conical nozzle , it is seen that some under expansion is desirable.
Then the thrust gain is about 2% higher than Pe=Pa.
Variable exit / throat area ratio is essential to avoid shock losses over as much of the operating range as possible, and the additional mechanical complexity has to be accepted.
Chapter Shaft Power Cycles

36. Variable Area, Thrust Reversal and Noise Suppression
Chapter Shaft Power Cycles

37. Chapter2 Shaft Power Cycles
Propelling Nozzles
The main limitations on the design of convergent divergent nozzles are :
a) The exit diameter must be within the overall diameter of the engine, otherwise the additional thrust is offset by the increased external drag.
b) In spite of the weight penalty; the included angle of divergence must be kept below about 30o, because the loss in thrust associated with the divergence of the jet increases sharply at greater angles.
Chapter Shaft Power Cycles

38. Chapter2 Shaft Power Cycles
Propelling Nozzles
In order to allow nozzle losses two approaches are commonly used;
i) Isentropic efficiency :
From definition of hj;
( 3.12 )
Chapter Shaft Power Cycles

39. Nozzle Loss for Unchoked FlowsV
Chapter Shaft Power Cycles

40. Nozzle Loss for Choked FlowsV V
Chapter Shaft Power Cycles

41. Chapter2 Shaft Power Cycles
Propelling Nozzles
ii) Specific thrust coefficient :
Kf = actual thrust / Isentropic thrust
For adiabatic flow with w =0 ;
For critical pressure ratio M5 = 1 ( T5 = Tc );
( 3.13 )
Chapter Shaft Power Cycles

42. Chapter2 Shaft Power Cycles
Propelling Nozzles
For adiabatic flow with w =0 ;
For critical pressure ratio M5 = 1 ( T5 = Tc );
( 3.13 )
Chapter Shaft Power Cycles

43. Chapter2 Shaft Power Cycles
Propelling Nozzles
For choked flow;
Then;
Chapter Shaft Power Cycles

44. Chapter2 Shaft Power Cycles
Propelling Nozzles
thus critical pressure ratio is;
(3.14)
Chapter Shaft Power Cycles

45. Chapter2 Shaft Power Cycles
Propelling Nozzles
For a given mass flow m;
( 3.15 )
Chapter Shaft Power Cycles