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

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

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.

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

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 0.6-0.7 is current state of the art.

GTX 100 π = 19.2 T3 = 1570 K

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

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

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

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

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

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

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

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

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)

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”

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

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!!!

Further efficiency considerations Note that:

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 !?

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

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

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

Very high speed flight requires very high specific thrust First flight of an SR-71 was on Dec. 22, 1964. (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

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

The International Standard Atmosphere (ISA) Temperature drops with 6.5K per 1000 meters At 11000 m variation stops and T remains constant up to 20000 meters Pressure variation can be computed by simple integration of hydrostatic effects.

Hydrostatic integration....

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)

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

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

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

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.

SR71 – intake ram pressure ratio

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:

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):

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 = 1.400 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 = 1.0-0.075*(ma-1.0)^1.35 pirec_tot = pirec_subs*pirec_shock pi = piram*pirec_tot

Some examples of engine installation Buried in wing or fuselage.

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

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:

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

Theory 5.2 - Continuity in stagnation property form

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

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