MAE 4261: AIR-BREATHING ENGINES

1. MAE 4261: AIR-BREATHING ENGINES Review for Final Exam 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. READING: HILL AND PETERSON • Chapter 6: Non-Rotating Components • 6.2 and 6.3: Subsonic and supersonic inlets • What are flow patterns inside and outside of inlet • Under what circumstances does an inlet generate a force? • Why use multiple oblique shocks instead of single normal shock to decelerate flow? • 6.7: Exhaust nozzles • Sized to handle all of mass flow that is passing through engine • What is importance/relevance of variable geometry? • How is real mixing down between core stream and fan stream • 6.4: Combustors • Burning of primary air to ensure stable combustion and then mixing of remaining air to reduce turbine inlet temperature to suitable levels • How is combustion affected by altitude • What are design trades in primary combustor versus afterburner? • Chapter 7 and Chapter 8: Dynamic exchange of energy with moving blade rows • Euler energy equation • Velocity triangles • Implications for flow path and blade design (axial and radial directions) • Diffusion coefficient, Degree of reaction (50% versus impulse turbine), solidity, rotational stress • Chapter 8.7: Compressor and turbine matching, compressor and turbine maps

4. CROSS-SECTIONAL EXAMPLE: GE 90-115B • Why does this engine look the way that it does? • Identify inlet, fan, LPC and HPC compressor, combustor, HPT and LPT turbine, nozzle, etc. • How does temperature, pressure, density, specific heat, etc. vary axially through (and outside of) device? • Why are there more compressor stages than turbine stages? • What is bypass ratio of this engine? Why was it selected as such? Is this engine more appropriate for a commercial transport or a military aircraft – how do you know? • 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?

5. 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 Relative to CS Inertial

6. MOMENTUM EQUATION: NEWTONS 2nd LAW Inertial Relative to CS • 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

7. 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

8. 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)

9. 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

10. 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

11. 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

12. 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

13. 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

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

15. 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

16. 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

17. RAMJET RESULTS

18. RAMJET RESULTS

19. 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

20. TURBOJET RESULTS

21. 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

22. TURBOFAN RESULTS

23. TURBOFAN RESULTS