1. Lecture 6 Turbojet Turbofan Increasing thrust (afterburning)
Optimization
Cycle selection (mission dependency)
Indication of thrust
Convergent-divergent nozzles
Turbofan
Cycle optimization
Mixing
Increasing thrust (afterburning)
Turboprops
Problem 3.2

2. Optimization of the turbojet
Specific thrust is strongly dependent on T03
At constant pressure ratio an increase in T03 will cause some increase in SFC
Parameter variation is based on Example 3.1 data with polytropic efficiencies

3. Recall shaft power cycle behavior
For a given pressure ratio it is clear that ηcycle increases!
Opposite trend

4. Energy lost in jet increases faster than thrust
Energy lost in jet increases faster than thrust. The shaft power cycle does not experience the
loss in SFC due to decreasing propulsive efficiency.

5. High specific thrust is still attractive
High T3 => high specific thrust => small engine
Reduction in engine size => reduced drag which off-sets this effect
In particular for high speed flight

6. Optimization of the turbojet
Same trend in SFC as a function of pressure ratio, when compared with real shaft power cycle
Note that if pressure ratios where increased considerably above rc=25, SFC would start to increase again.
Which region of pressure ratios does the plot correspond to when you look
in the shaft power cycle diagram!

7. Cycle selection
High t3 => expensive alloys, complex (and expensive) cooling
High rc => many stages. Ultimately multi-spool configurations
Selection of cycle parameters depend on aircraft mission

8. Cycle selection Business jets:
Low cost (by low pressure ratios and cheap turbine material)
Fuel consumption less important
Range may be important (=>cheap turbojets have been supplanted by cheap turbofans/turboprops)

9. Lifting engines & long range subsonic
Lifting engines (VTOL)
Max. thrust per unit weight (compressor pressure ratio set by what could be achieved by one turbine rotor)
short life - but run only for short period of time
Thrust to weight > 20!!! Modern military engines have around 10.
high cost ok (military)
Long range subsonic
early - high pressure turbojet
Today high pressure ratio, high bypass ratio turbofans
The XJ99 (vertical engine above) operated at 1360 C, very short combustor (11.5 inch).
Counter-rotating shafts allowed the elimination of turbine stators!
9000 lb thrust for a weight around 440 lb (Thrust to weight = 20.5).

10. Indication of thrust
No direct method for measuring engine thrust during flight exists!!!
Indirect techniques exist

11. Theory 6.1 - Indication of thrust
P04 and T04 can be measured. Pa is known and the nozzle area is assumed to be fixed (assume choked operation and ηj =100%). The thrust is given by (sea level static): pc

12. Theory 6.1 - Indication of thrust
Continuity, the gas law and the first law give:
Which in introduced in the thrust expression yields: Tc

13. Theory 6.1 - Indication of thrust
But p04/p5 is the critical pressure ratio =>

14. Indication of thrust
In sea level static thrust can thus be directly related to the engine pressure ratio (EPR)!
When we have ram pressure ratio we have:
Thus we have an expression also for in flight thrust estimation

15. Velocity-Area relation for compressible flow
Combining the continuity and momentum equations in differential form for compressible flow gives (Appendix A – Eq. 9):
What does this tell us?

16. Convergent divergent nozzles
It can be shown:

17. So what was this…. ?

18. Lets undertake some back pressure variations
Pe is minutely below Po => small wind. Acceleration in convergent portion and deceleration in divergent
There will be some value of Pe at which the flow will just barely go sonic at the throat.
If Pe is reduced further the flow in the convergent portion will remain “frozen”

19. Lets undertake some back pressure variations
For values below Pe3 but higher than Pperfectly expanded a shock will stand in the divergent part
It will stand exactly in the exit when the pressure behind the normal shock at the design Mach number is equal to Pe
For lower pressures the shock will form an oblique shock pattern outside the nozzle which is reduced in strength until the isentropic pressure is attained.

20. When do we use convergent-divergent nozzles?
The critical pressure ratio can be estimated with:
For nozzle pressure ratios < 3 the losses incurred are greater in the convergent-divergent nozzles
Even at the isentropic condition!!!

21. Supersonic flight
Ram pressure ratio => Exit pressure ratio is increased (EPR)
Pressure ratio for high Mach numbers (2-3) is often 10-20
Variable exit/throat area has to be allowed for
Divergence angle less than 30°.
Exit diameter less than engine diameter to not incur additional drag
Noise suppression and thrust reversing will be harder to implement

22. Thrust reversing
On icy, wet or snow covered runways the efficiency of the aircraft brakes may be reduced
Reversing the aircraft engine gas stream may allow for efficient braking

23. Thrust reversing

24. Thrust reversing

25. The turbofan engine
Improve ηp by reducing the mean jet velocity (in comparison with turbojet)
Reduce noise (in comparison with turbojet)
Example homework
Fan is driven by LP turbine
If fan and bypass streams are mixed additional equations are necessary

26. The turbofan engine

27. FPR (Fan Pressure Ratio) and specific thrust
For military aircraft engines mixers are used
Fan exit pressure and turbine exit pressure must be similar for efficient mixing => FPR and EPR are similar
EPR sets thrust =>
FPR sets thrust

28. Optimization of the turbofan
Four available variables:
FPR = Fan Pressure Ratio
BPR = Bypass Ratio
TIT = Turbine inlet temperature (T4)
OPR = Overall pressure ratio
For a fixed OPR and BPR one obtains:
Fig 3.26
We now get OPR,BPR and T4 as well as FPR=F(T4) because we have optima in thrust and SFC.
Select globally best SFC => FPR and T4 given for every OPR, BPR.
Increased T7 => more energy extraction needed before the optimal velocity is obtained

29. Optimization of turbofan
Perform operation for a “grid” of OPR and BPR.
Select the globally best point!
Optimization should be computerized
Installation losses and weight estimation
Life Cycle Cost
Engine must complete mission!!!
Take-off
Top of climb
Cruise (most important)

30. Mixing
For afterburning turbofans => only one reheat system. More oxygen is made available (compared to an unmixed core flow)
Subsonic transport – small but valuable reduction in SFC
An energy balance gives:

31. Mixing – obtaining p07 A momentum balance gives:
M6 (turbine design criteria), T06, P06 are known which gives P6. A6 is obtained from the “X-function”:
With p6=p2 we get M2 (p02 is known). mc, Rc, M2, p02 and T02 gives A2 from the X-function. Cc from continuity.
mC7+A7P7 is now obtained from the momentum balance.
A7=A6+A2 and m =ρC7A7 = (P7/RmT7)C7A7

32. Mixing
T07 is known but both P7 and P07 are unknown. Guess M7 => T7 from T07 and C7 from Mach number definition. Continuity => p7.
Check that momentum equation is satisfied. If not improve guess of M7.
Pooh….

33. Increasing thrust
Re-design to allow for increased mass flow or increased T3.
Temporary increase of thrust (augmentation)
Take-off, acceleration from subsonic to supersonic, combat maneuvering
Methods for augmentation
Liquid injection
Afterburning

34. Liquid injection
Spray water methanol (lowers freezing point of water and burns) mixture in compressor during take-off and climb
Equivalent drop in compressor temperature => less compressor work => more thrust
Secondary effect: thrust increases since mass flow increases
Partly outdated method

35. Afterburning Burn additional fuel in the jet pipe
No rotating parts => maximum allowable temperature is higher. Typically around 2000 K
Accept penalty in SFC
Poor “cycle” (better at high speed – for fixed momentum drag an increase in gross thurst => considerably greater incerease in net thrust)
Concordes acceleration from subsonic to supersonic => reduction in fuel consumption in spite of short term increase in fuel flow.
For mixed turbofans, provisions for burning even more fuel exist (low inlet temperature and little oxygen consumed in air). Even worse cycle in that case though! Why ?!

36. Afterburning
Speed of sound in the nozzle exit => variable area nozzle required!
Aim is to maintain gas generator at same condition => variable area necessary to pass the same mass flow at a much lower density.

37. Turboprop Jet and propeller deliver combined propulsion
Most designs operate with nozzle unchoked and cruise (optimally) around M=0.6.
Turboprops have lost market share for commuting and airlines to turbofan-powered aircraft
SAAB-Fairchild 340
aircraft.

38. Common cores Same core High pressure core common to different engines
Cut development cost
Even from civil to military is possible
Same core

39. Learning goals
Be able to explain why an increase in T3 may still be attractive in turbojet cycles, although the SFC is increased
Be able to relate this increase to performance gains of turbofan engines by considering the propulsive efficiency and designing for higher BPR
Be able suggest suitable engine cycle parameters (pressure ratio and T3 for different missions)
Be informed about how the delivered engine thrust is indicated
Be familiar with
convergent-divergent nozzles, thrust reversing, mixing, thrust augmentation (ways of increasing thrust)