1. MAE 4261: AIR-BREATHING ENGINES Exam 2 Review Exam 2: November 18 th, 2008 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

2. EXAM 2 TOPICS Turbofans –Section 5.5 –Figure 5.23, 5.29, 5.30, 5.31, 5.32, 5.33, 5.34 Non-rotating components –Inlets: Section 6.1- (first half of) 6.3 –Nozzles: Section 6.7 –Combustors (burners): Section 6.4-6.5 Figures 6.21, 6.22, 6.23, 6.24, 6.26 Energy exchange with moving blade rows –Section 7.1-7.2 Axial compressors –Section 7.3-7.7 –Figures 7.7, 7.8, 7.11, 7.12, 7.27, 7.32, 7.33

3. BYPASS RATIO: TURBOFAN ENGINES Bypass Air Core Air Bypass Ratio, B,  : Ratio of bypass air flow rate to core flow rate Example: Bypass ratio of 6:1 means that air volume flowing through fan and bypassing core engine is six times air volume flowing through core

4. TRENDS TO HIGHER BYPASS RATIO 1958: Boeing 707, United States' first commercial jet airliner 1995: Boeing 777, FAA Certified PW4000-112: T=100,000 lbf,  ~ 6 Similar to PWJT4A: T=17,000 lbf,  ~ 1

5. EFFICIENCY SUMMARY Overall Efficiency –What you get / What you pay for –Propulsive Power / Fuel Power –Propulsive Power = TUo –Fuel Power = (fuel mass flow rate) x (fuel energy per unit mass) Thermal Efficiency –Rate of production of propulsive kinetic energy / fuel power –This is cycle efficiency Propulsive Efficiency –Propulsive Power / Rate of production of propulsive kinetic energy, or –Power to airplane / Power in Jet

6. PROPULSIVE EFFICIENCY AND SPECIFIC THRUST AS A FUNCTION OF EXHAUST VELOCITY Conflict

7. COMMERCIAL AND MILITARY ENGINES (APPROX. SAME THRUST, APPROX. CORRECT RELATIVE SIZES) Demand high T/W Fly at high speed Engine has small inlet area (low drag, low radar cross- section) Engine has high specific thrust Ue/Uo ↑ and  prop ↓ P&W 119 for F- 22, T~35,000 lbf,  ~ 0.3 Demand higher efficiency Fly at lower speed (subsonic, M ∞ ~ 0.85) Engine has large inlet area Engine has lower specific thrust Ue/Uo → 1 and  prop ↑ GE CFM56 for Boeing 737 T~30,000 lbf,  ~ 5

8. CRUISE FUEL CONSUMPTION vs. BYPASS RATIO

9. SUMMARY OF IN-CLASS EXAMPLES

10. RAMJETS Thrust performance depends solely on total temperature rise across burner Relies completely on “ram” compression of air (slowing down high speed flow) Ramjet develops no static thrust Energy (1 st Law) balance across burner Cycle analysis employing general form of mass, momentum and energy

11. TURBOJET SUMMARY Cycle analysis employing general form of mass, momentum and energy Turbine power = compressor power How do we tie in fuel flow, fuel energy? Energy (1 st Law) balance across burner

12. TURBOJET TRENDS: IN-CLASS EXAMPLE

14. TURBOJET TRENDS: HOMEWORK #3, PART 1 T t4 = 1600 K,  c = 25, T 0 = 220 K

15. TURBOJET TRENDS: HOMEWORK #3, PART 2a T t4 = 1400 K, T 0 = 220 K, M 0 = 0.85 and 1.2

16. TURBOJET TRENDS: HOMEWORK #3, PART 2b T t4 = 1400 K and 1800 K, T 0 = 220 K, M 0 = 0.85

17. TURBOFAN SUMMARY Two streams: Core and Fan Flow Turbine power = compressor + fan power Exhaust streams have same velocity: U 6 =U 8 Maximum power,  c selected to maximize  f

18. TURBOFAN TRENDS: IN-CLASS EXAMPLE

20. INLETS

21. OVERVIEW: INLETS AND DIFFUSERS Purpose: 1.Capture incoming stream tube (mass flow) 2.Condition flow for entrance into compressor (and/or fan) over full flight range At cruise, slow down flow to 0.4 < M 2 < 0.7 At take-off, accelerate flow to 0.4 < M 2 < 0.7 Remain as insensitive as possible to angle of attack, cross-flow, etc. Requirements 1.Bring inlet flow to engine with high possible stagnation pressure Measured by inlet pressure recovery,  d = P t2 /P t1 2.Provide required engine mass flow May be limited by choking of inlet 3.Provide compressor (and/or fan) with uniform flow

22. EFFECT OF MASS FLOW ON THRUST VARIATION Mass flow into compressor = mass flow entering engine Re-write to eliminate density and velocity Connect to stagnation conditions at station 2 Connect to ambient conditions Resulting expression for thrust –Shows dependence on atmospheric pressure and cross-sectional area at compressor or fan entrance –Valid for any gas turbine

23. NON-DIMENSIONAL THRUST FOR A 2 AND P 0 Thrust at fixed altitude is nearly constant up to Mach 1 Thrust then increases rapidly, need A 2 to get smaller

24. OPERATIONAL OVERVIEW High Thrust Low Speed, M 0 ~ 0 High Mass Flow Stream Tube Accelerates Low Thrust High Speed, M 0 ~ 0.8 Low Mass Flow Stream Tube Decelerates Aerodynamic force is always favorable for thrust production

25. NORMAL SHOCK TOTAL PRESSURE LOSSES As M 1 ↑ p 02 /p 01 ↓ very rapidly Total pressure is indicator of how much useful work can be done by a flow –Higher p 0 → more useful work extracted from flow Loss of total pressure are measure of efficiency of flow process Example: Supersonic Propulsion System Engine thrust increases with higher incoming total pressure which enables higher pressure increase across compressor Modern compressors desire entrance Mach numbers of around 0.5 to 0.8, so flow must be decelerated from supersonic flight speed Process is accomplished much more efficiently (less total pressure loss) by using series of multiple oblique shocks, rather than a single normal shock wave

26. NOZZLES

27. OVERVIEW: NOZZLES Subsonic Aircraft: Usually a fixed area convergent nozzle is adequate –Can be more complex for noise suppression Supersonic Aircraft: More complex, variable-area, convergent-divergent device Two Primary Functions: 1.Provide required throat area to match mass flow and exit conditions 2.Efficiently expand high pressure, high temperature gases to atmospheric pressure (convert thermal energy → kinetic energy)

28. KEY EQUATIONS FOR NOZZLE DESIGN Nozzle area ratio as a function of engine parameters Once nozzle area is set, operating point of engine depends only on  t A 7 is the throat area, how do we find the exit area of the nozzle? Found from compressible channel flow relations, recall that M 7 =1 Set by jet stagnation pressure and ambient Compare with Equation 3.15 Compare with Section 6.7 H&P

29. COMBUSTORS

30. MAJOR COMBUSTOR COMPONENTS Key Questions: –Why is combustor configured this way? –What sets overall length, volume and geometry of device? Compressor Turbine Air Fuel Combustion Products

31. WHY IS THIS RELEVANT? Most mixtures will NOT burn so far away from stoichiometric –Often called Flammability Limit –Highly pressure dependent Increased pressure, increased flammability limit –Requirements for combustion, roughly  > 0.8 Gas turbine can NOT operate at (or even near) stoichiometric levels –Temperatures (adiabatic flame temperatures) associated with stoichiometric combustion are way too hot for turbine –Fixed T t4 implies roughly  < 0.5 What do we do? –Burn (keep combustion going) near  =1 with some of ingested air –Then mix very hot gases with remaining air to lower temperature for turbine

32. SOLUTION: BURNING REGIONS Air Compressor Turbine  ~ 1.0 T>2000 K  ~0.3 Primary Zone

33. RELATIVE LENGTH OF AFTERBURNER Why is AB so much longer than primary combustor? –Pressure is so low in AB that they need to be very long (and heavy) –Reaction rate ~ p n (n~2 for mixed gas collision rate) J79 (F4, F104, B58) Combustor Afterburner

34. AXIAL COMPRESSORS

35. WHERE IN THE ENGINE? PW2000 Fan Compressor

36. 2 SPOOL DEVICE: PW2000 High Pressure Compressor (  high ) Low Pressure Compressor (  low ) High and Low Pressure Turbines

37. REVIEW: PRESSURE DISTRIBUTION Rotor –Adds swirl to flow –Adds kinetic energy to flow with ½  v 2 –Increases total energy carried in flow by increasing angular momentum Stator –Removes swirl from flow –Not a moving blade → cannot add any net energy to flow –Converts kinetic energy associated with swirl to internal energy by raising static pressure of flow –NGV adds no energy. Adds swirl in direction of rotor motion to lower Mach number of flow relative to rotor blades (improves aerodynamics)

38. AXIAL COMPRESSOR ENERGY EXCHANGE Rotor –Adds swirl to flow –Adds kinetic energy to flow with ½  v 2 –Increases total energy carried in flow by increasing angular momentum Stator –Removes swirl from flow –Not a moving blade → cannot add any net energy to flow –Converts kinetic energy associated with swirl to internal energy by raising static pressure of flow –NGV adds no energy. Adds swirl in direction of rotor motion to lower Mach number of flow relative to rotor blades (improves aerodynamics) Centerline 

39. EXAMPLES OF BLADE TWIST