1. Lecture 5 Shaft power cycles Aircraft engine performance
Cycle selection
Technology trends
Aircraft engine performance
Thrust and propulsion efficiency
Intakes and engine installation
Theory 5.1 and 5.2
Problem 3.1

2. Simple ideal cycle – max. efficiency
Maximum thermal efficiency when compressor exit temp. = max allowed turbine inlet temp.
T3 = 1500 => η = 81% efficiency attained at rc = 320
In practice titanium alloy compressor rotors withstand around 870 K and nickel alloys around 990 K
T3 = 990 K => η = 71% efficiency attained at rc = 75
T2 => Tmax

3. Simple real cycle – max. efficiency
Conservative assumptions (old technology)
Setting:
T3 = 1500 => η∞,c = 87%, η∞,t = 85%, 5% burner pressure drop and 99% mechanical efficiency => no power delivered at rc = 143 (far above allowable t2).
For real cycle maximum efficiency obtained for (with data above)
rc = 38 at which a cycle efficiency of η = 43.8% is obtained.

4. Curve is fairly flat around optimum
Lower pressure ratio may be taken with small perfor- mance penalty
Lower pressure ratio is cheaper to manufacture and maintain

5. Suitable compromise in this case is: Selecting a lower rc also
Reduces the number of required turbomachinery stages
Allows more efficient cooling (Tc low)
Between is current
state of the art.

6. GTX 100
π = 19.2
T3 = 1570 K

7. Technology improvements – permissible T3
T3 is increasing with 8 K/year
Originally the blades for high temperature were forged, but better creep performance could be obtained when the blades were cast
Direct crystals to form elongated in the direction of the span (Directionally Solidified blades)
A still better blade was obtained by casting each blade as a single crystal

8. Technology improvements – permissible T3
Originally the blades for high temperature were forged, but better creep performance could be obtained when the blades were cast
Direct crystals to form elongated in the direction of the span (Directionally Solidified blades)
A still better blade was obtained by casting each blade as a single crystal

9. Cycle Efficiency Optimal pressure ratio increase with t3.
Gain in efficiency becomes marginal as T3 increases

10. Specific output
Considerable increase in specific output with increasing t3.
Trend:
Increase T3 to increase specific output
Follow with rc to obtain high efficiency

11. Heat exchange cycle Recall: Heat exchanger useful when:
Optimum for r > 1 in real cycle.
Optimum rc increase with t3.
Gain in efficiency with t3 is greater than for simple cycle
Power output curves about the same
Cooling simplified – t2 low

12. Heat exchanger versus simple cycle
131
Heat exchanger cycle:
IRA (intercooled recuperated promises increased fuel efficiency).
More efficient cooling
Heavy and bulky

13. Which cycle has the highest ideal efficiency?
Theoretically the same!

14. What are the fundamentals of flight?
The performance of the jet engine
Aircraft aerodynamics
Covered by the Henrik Ekstrand material
Characteristics of the atmosphere

15. Aircraft propulsion – thrust generation
This is why high turbine inlet temperatures have lead to higher efficiencies (although the ideal cycle efficiency
does not depend on t3)

16. Jet engine – principles of thrust generation
In most operation the speed of sound is reached in the throat section => no further acceleration is possible.
A pressure surface with pressure pj will “stand” in the nozzle throat generating an additional thrust term called the “pressure thrust”

17. Efficiency considerations
How much of the power in the jet is transformed to thrust ?:

18. Efficiency considerations
ηp is at maximum when Cj=Ca but then the thrust is zero.
Make difference as small as possible, still obtaining the necessary thrust => classes of engines!!!

19. Further efficiency considerations
Note that:

20. How should we design the engine
Decrease T3 => Decrease jet velocity
Poor cycle efficiency
Poor specific output => high engine weight
What if we could:
Use high T3 and rc cycle and still obtain an average low Cj, optimized for the aircraft speed Ca !?

21. Propulsion engines – families
The turbofan:
BPR 0+-10

22. Propulsion engines – families
The turboprop:
BPR typically
around 25-30
BPR range is taken from Hill and Peterson: “Mechanics and Thermodynamics of propulsion”

23. High speed flight requires high specific thrust
RM12 engine powering the Swedish GRIPEN fighter –
Military turbofan (low bpr)

24. Very high speed flight requires very high specific thrust
First flight of an SR-71 was on Dec. 22, (Mach 3+ or more than three times the speed of sound) and at altitudes of over 85,000 feet.
SR-71s are powered by two Pratt and Whitney J-58 axial-flow turbojets with afterburners, each producing 32,500 pounds of thrust. Studies have shown that less than 20 percent of the total thrust used to fly at Mach 3 is produced by the basic engine itself. The balance of the total thrust is produced by the unique design of the engine inlet and "moveable spike" system at the front of the engine nacelles and by the ejector nozzles at the exhaust which burn air compressed in the engine bypass system.
The J58 engine was developed in the late 1950s by Pratt and Whitney Aircraft Division of United Aircraft Corporation to meet a U.S. Navy requirement. It was designed to operate for extended speeds of Mach 3.0+ and at altitudes of more than 80,000 ft. The J58 was the first engine designed to operate for extended periods using its afterburner, and it was the first engine to be flight qualified at Mach 3 for the Air Force.
Variable intake optimize aerodynamic
performance of “shock-compression”
system

25. The International Standard Atmosphere (ISA)
Approximation to conditions averaged over location and season
Deviations largest at sea level
Deviations largest in temperature

26. The International Standard Atmosphere (ISA)
Temperature drops with 6.5K per 1000 meters
At m variation stops and T remains constant up to meters
Pressure variation can be computed by simple integration of hydrostatic effects.

27. Hydrostatic integration....

28. Intakes
Adiabatic duct used to recover kinetic energy in air at minimal pressure loss, i.e. we have
Another example of the first law for open systems with no heat or work
exchange (same idea as for the nozzle)

29. Intake efficiencies The available stagnation temperature is:
T´01is the stagnation temperature that would have been necessary to achieve P01 under isentropic conditions, i.e.:
Some algebra gives (as well as definition of Mach number and a relation for cp):
ηi will depend on installation but we will assume a value of 0.93 for all calculations

30. Intakes Design criteria: Minimize inlet compressor inlet distortion
Distortion may lead to surge => flame out or mechanical damages

31. Functionality Static conditions, very low aircraft speeds
Intake acts as a nozzle
Cruise – normal forward speeds
Intake performs as diffuser
Supersonic operation
System of shock waves followed by a subsonic diffusion section

32. Supersonic intakes Pressure recovery factor is used: where:
A rough rule of thumb published by the Department of Defense is:
To obtain the overall pressure recovery the DOD expression must be multiplied with the subsonic (friction) loss recovery factor.

33. SR71 – intake ram pressure ratio

34. SR71 – intake ram pressure ratio
The ram pressure rise is estimated using the following expression:
where the second factor in the left hand expression is obtained from:
Includes both shock and viscous losses
the first factor is obtained from:

35. SR71 – intake ram pressure ratio
The subsonic part is calculated from from our “universal” assumption of ηi=0.93, i.e:
The shock pressure recovery factor is estimated by the crude formula stated by the Department of Defence (assuming a cruise Mach number of 3.0):

36. SR71 – intake ram pressure ratio
and thus the pressure recovery factor is:
The pressure ratio over the intake can finally be estimated to:
This is a very crude approximation methodology, but it gives a demonstration of the considerable pressure ratio that a successfully designed inlet may give. It also illustrates why the ram jet engine provides a thermodynamically attractive cycle at very high speeds.
ma = 3.0 mas = 1.0 gama = etai = 0.93
piram = (1.0+((gama-1.0)/2.0)*ma^2)^(gama/(gama-1.0))
pirec_subs = ((1.0+etai*((gama-1.0)/2.0)*mas^2)/(1.0+((gama-1.0)/2.0)*mas^2))^(gama/(gama-1.0)) pirec_shock = *(ma-1.0)^1.35
pirec_tot = pirec_subs*pirec_shock pi = piram*pirec_tot

37. Some examples of engine installation
Buried in wing or fuselage.

38. Engine installation examples
Wing mounted pod installation (attached to the wing by pylons):
Third engine buried in the tail fuselage

39. Theory 5.1 – Stagnation pressure for isentropic compression
We have already introduced the stagnation temperature as:
and shown that (revision task):
The specific heat ratio γ is defined:
The Mach number is defined as:

40. Theory 5.1 – Stagnation pressure for isentropic compression
Thus:
but we have: which directly gives:

41. Theory 5.2 - Continuity in stagnation property form

42. Theory 5.2 - Continuity in stagnation property form
Thus:
extremely powerful.

43. Learning goals
Have an understanding for the propulsive efficiency concept and how it:
relates to the total efficiency
relates to the different jet engine types available
Have a quantitative understanding of how real cycle effects impact cycle efficiency and choice of design conditions
Have a basic understanding of how intakes work and know how engines can be integrated in aircraft