MAE 4261: AIR-BREATHING ENGINES

1. MAE 4261: AIR-BREATHING ENGINES Review for Exam 1 Exam 1: October 21, 2008 Mechanical and Aerospace Engineering Department Florida Institute of Technology D. R. Kirk

2. READING: HILL AND PETERSON • Chapter 1 • Can a jet or rocket engine exert thrust while discharging into a vacuum (with no atmosphere to “push against”)? YES • Could a rocket vehicle be propelled to a speed much higher than the speed at which the jet leaves the rocket nozzle? YES, See Homework 1, Problem 2 • Chapter 2: 2.1-2.3 and Chapter 3: 3.1-3.4 • If you need a review of mass, momentum and energy equations • Detailed review of thermodynamics is located online (Lecture 6) • Chapter 5: • 5.1 and 5.2: Review of overall concepts, thrust and efficiency definitions (See Lectures 4 and 5) • 5.3: Ramjet Engines (See Lectures 7 and 8) • Be familiar with trends shown in Figures 5.9 and 5.10 • 5.4: Turbojet Engines (See Lectures 9 and 10) • Be familiar with trends shown in Figures 5.19-5.22 • 5.5: Turbofan Engines (See Lecture 11) • Be familiar with trends shown in Figures 5.29-5.34

3. CROSS-SECTIONAL EXAMPLE: GE 90-115B • Why does this engine look the way that it does? • How does this engine push an airplane forward, i.e. how does it generate thrust? • What are major components and design parameters? • How can we characterize performance and compare with other engines?

4. CONSERVATION OF MASS • This is a single scalar equation • Velocity doted with normal unit vector results in a scalar • 1st Term: Rate of change of mass inside CV • If steady d/dt( ) = 0 • Velocity, density, etc. at any point in space do not change with time, but may vary from point to point • 2nd Term: Rate of convection of mass into and out of CV through bounding surface, S • 3rd Term (=0): Production or source terms

5. MOMENTUM EQUATION: NEWTONS 2nd LAW • This is a vector equation in 3 directions • 1st Term: Rate of change of momentum inside CV or Total (vector sum) of the momentum of all parts of the CV at any one instant of time • If steady d/dt( ) = 0 • Velocity, density, etc. at any point in space do not change with time, but may vary from point to point • 2nd Term: Rate of convection of momentum into and out of CV through bounding surface, S or Net rate of flow of momentum out of the control surface (outflow minus inflow) • 3rd Term: • Notice that sign on pressure, pressure always acts inward • Shear stress tensor, t, drag • Body forces, gravity, are volumetric phenomena • External forces, for example reaction force on an engine test stand • Application of a set of forces to a control volume has two possible consequences • Changing the total momentum instantaneously contained within the control volume, and/or • Changing the net flow rate of momentum leaving the control volume

6. HOW AN AIRCRAFT ENGINE WORKS Chemical Energy Kinetic Energy Thermal Energy • Flow through engine is conventionally called THRUST • Composed of net change in momentum of inlet and exit air • Fluid that passes around engine is conventionally called DRAG

7. NON-DIMENSIONAL THRUST EQUATION Result from control volume analysis employing conservation of mass and momentum equation Writing right side as a velocity ratio Introduce non-dimensional Mach number, M0 Speed of sound, a0 Non-dimensional or Specific Thrust Equation is only conservation of mass and momentum Starting point for all analyses (ramjet, turbojet, turbofan)

8. NOW INTRODUCE THERMODYNAMICS Non-Dimensional result from control volume analysis employing conservation of mass and momentum equation Goal is to tie this equation in with behavior of the engine, which is characterized thermodynamically Introduce V=Ma, which introduces Mach number and speed of sound, which depends on temperature For the ideal cycle analysis, assume that the specific heat ratio, g, and the gas constant R are remain unchanged throughout the engine Non-dimensional or Specific Thrust Equation now ties in mass, momentum and energy Starting point for all analyses (ramjet, turbojet, turbofan) Find Me and Te by accounting Tt and Pt through engine

9. MAJOR COMPONENTS: TURBOJET(LOW BYPASS RATIO TURBOFAN)

10. EXAMPLE OF COMMERCIAL ENGINE: HIGH BYPASS RATIO TURBOFAN

11. MAJOR GAS TURBINE ENGINE COMPONENTS • Inlet: • Continuously draw air into engine through inlet • Slows, or diffuses, to compressor • Compressor / Fan: • Compresses air • Generally two, or three, compressors in series • Raises stagnation temperature and pressure (enthalpy) of flow • Work is done on the air • Combustor: • Combustion or burning processes • Adds fuel to compressed air and burns it • Converts chemical to thermal energy • Process takes place at relatively constant pressure

12. MAJOR GAS TURBINE ENGINE COMPONENTS • Turbine: • Generally two or three turbines in series • Turbine powers, or drives, the compressor • Air is expanded through turbine (P & T ↓) • Work is done by the air on the blades • Use some of that work to drive compressor • Next: • Expand in a nozzle • Convert thermal to kinetic energy (turbojet) • Burning may occur in duct downstream of turbine (afterburner) • Expand through another turbine • Use this extracted work to drive a fan (turbofan) • Nozzle: • Flow is ejected back into the atmosphere, but with increased momentum • Raises velocity of exiting mass flow

13. ENGINE STATION NUMBERING CONVENTION

14. ENGINE STATION NUMBERING CONVENTION 2.0-2.5: Low Pressure Compressor 0: Far Upstream 1: Inlet 3: Combustor 4: Turbine 2.5+: High Pressure Compressor 5-6: Nozzle 7 8 One of most important parameters is TT4: Turbine Inlet Temperature Performance of gas turbine engine ↑ with increasing TT4 ↑

15. TYPICAL PRESSURE DISTRIBUTION THROUGH ENGINE

16. AIRCRAFT ENGINE BASICS • All aircraft engines are HEAT ENGINES • Utilize thermal energy derived from combustion of fossil fuels to produce mechanical energy in the form of kinetic energy of an exhaust jet • Momentum excess of exhaust jet over incoming airflow produces thrust • Remember: Thrust is a Force and Force = Time Rate Change of Momentum • In studying these devices we will employ two types of modeling • Thermodynamic (Cycle Analysis) • Thermal → mechanical energy from thermal is studied using thermodynamics • Change in thermodynamic state of air as it passes through engine is studied • Physical configuration (geometry) of engine NOT important, but rather processes are important • Fluid Mechanic • Relate changes in pressure, temperature and velocity of air to physical characteristics of engine

17. INTRODUCTION TO CYCLE ANALYSIS • Cycle Analysis → What determines engine characteristics? • Cycle analysis is study of thermodynamic behavior of air as it flows through engine without regard for mechanical means used to affect its motion • Characterize components by effects they produce • Actual engine behavior is determined by geometry; cycle analysis is sometimes characterized as representing a “rubber engine” • Main purpose is to determine which characteristics to choose for components of an engine to best satisfy a particular need • Express T, h, Isp as function of design parameters

18. STAGNATION QUANTITIES DEFINED • Quantities used in describing engine performance are the stagnation pressure, enthalpy and temperature • Stagnation enthalpy, ht , enthalpy state if stream is decelerated adiabatically to zero velocity Ideal gas Stagnation temperature Speed of sound Total to static temperature ratio in terms of Mach number

19. FOR REVERSIBLE + ADIABATIC = ISENTROPIC PROCESS

20. THERMODYNAMIC PROCESSES IN THE ENGINE • How should we represent thermodynamic process in engine? • It is cyclic • Air starts at atmospheric pressure and temperature and ends up at atmospheric pressure and temperature • Definition of ‘Open’ vs. ‘Closed’ Cycles • Consider a parcel of air taken round a cycle with heat addition and rejection • Need to consider thermodynamics of propulsion cycle • To do this we make use of First and Second Laws of Thermodynamics

21. THERMODYANMICS: BRAYTON CYCLE MODEL • 1-2: Inlet, Compressor and/or Fan: Adiabatic compression with spinning blade rows • 2-3: Combustor: Constant pressure heat addition • 3-4: Turbine and Nozzle: Adiabatic expansion • Take work out of flow to drive compressor • Remaining work to accelerate fluid for jet propulsion • Thermal efficiency of Brayton Cycle, hth=1-T1/T2 • Function of temperature or pressure ratio across inlet and compressor

22. P-V DIAGRAM REPRESENTATION • Thermal efficiency of Brayton Cycle, hth=1-T1/T3 • Function of temperature or pressure ratio across inlet and compressor

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

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

25. 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 hprop ↓ GE CFM56 for Boeing 737 T~30,000 lbf, a ~ 5 • 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 hprop ↑ P&W 119 for F- 22, T~35,000 lbf, a ~ 0.3

26. 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

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

28. ENGINE AND OVERALL AIRPLANE PERFORMANCE • Most MAE 4261 lectures focused on characterizing propulsion system • Also look at behavior of entire airplane • Which parameters from engine performance feed directly into overall airplane performance (Thrust, Isp, TSFC, etc.) • How fast can airplane fly? • How far can airplane fly on a single tank of fuel (range)? • How long can airplane stay in air on a single tank of fuel (endurance)? • Tie in MAE 4261 with aerodynamics and structures

29. 3 TYPES OF AIR-BREATHING ENGINES • Apply cycle analysis to control volume result for conservation of mass, momentum and energy • Consider 3 engine types • Ramjets • Turbojets • Turbofans

30. 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 Cycle analysis employing general form of mass, momentum and energy Energy (1st Law) balance across burner

31. RAMJET RESULTS

32. RAMJET RESULTS

33. 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 (1st Law) balance across burner

34. TURBOJET RESULTS

35. TURBOFAN SUMMARY Two streams: Core and Fan Flow Turbine power = compressor + fan power Exhaust streams have same velocity: U6=U8 Maximum power, tc selected to maximize tf

36. TURBOFAN RESULTS

37. TURBOFAN RESULTS