1. MAE 5360: Hypersonic Airbreathing Engines
Brayton Cycle Analysis and Efficiency Summary
Mechanical and Aerospace Engineering Department
Florida Institute of Technology
D. R. Kirk

2. Outline
Review
General expression that relates the thrust of a propulsion system to the net changes in momentum, pressure forces, etc.
Efficiencies
Goal: Look at how efficiently the propulsion system converts one form of energy to another on its way to producing thrust
Overall Efficiency, hoverall
Thermal (Cycle) Efficiency, hthermal
Propulsive Efficiency, hpropulsive
Specific Impulse, Isp [s]
(Thrust) Specific Fuel Consumption, (T)SFC [lbm/hr lbf] or [kg/s N]
Implications of Propulsive Efficiency for Engine Design
Trends in Thermal and Propulsive Efficiency

3. Derivation of Thrust for Airbreathing Engine
Chemical
Energy
Thermal
Energy
Kinetic
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

4. 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, TSFC as function of design parameters
Aircraft engines (and all gas turbine engines) operate on a Brayton Cycle

5. Heat Engine: Propulsion Train
Chemical
Energy
Heat
(Thermal
Energy)
Mechanical
Power
Mech.
Power to
GasFlow
Thrust
Power
Combustion
Thermal
Mechanical
Propulsive
The overall efficiency for the propulsion chain is given by:

6. Concepts/Tools for Ideal Cycle Analysis
Ideal gas equation of state, p = rRT
One-dimensional gas dynamics
Concepts of stagnation and static quantities (temperature, pressure, etc.)
Relations between Mach number and thermodynamic properties
Thermodynamics of propulsion cycle
Make use of 1st and 2nd Laws of Thermodynamics
Behavior of useful quantities: energy, entropy, enthalpy
Relations between thermodynamic properties in a reversible (“lossless”) process
Isentropic = reversible + adiabatic
Properties of cycles (it is cyclic)
Air starts at atmospheric pressure and temperature and ends up at atmospheric pressure and temperature
Definition of ‘Open’ vs. ‘Closed’ Cycles

7. Stagnation Quantities
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

8. Isentropic Process

9. 1st Law of Thermodynamics
First law (conservation of energy) for a system: “chunk” of matter
of fixed identity
E0 = Q - W
Change in overall energy (E0 ) = Heat in - Work done
E0 = Thermal energy + kinetic energy ...
Neglecting changes in kinetic and potential energy
E = Q - W ; (Change in thermal energy)
On a per unit mass basis, the statement of the first law is thus:
e = q - w

10. 2nd Law of Thermodynamics
The second law defines entropy, s, by:
Where dqreversible is the increment of heat received in a reversible
process between two states
The second law also says that for any process the sum of the
entropy changes for the system plus the surroundings is equal
to, or greater than, zero
Equality only exists in a reversible (ideal) process

11. Representing Engines Processes in Thermodynamic Coordinates
First Law: E = Q - W, where E is the total energy of the parcel of air.
For a cyclic process E is zero (comes back to the same state)
Therefore: Q (Net heat in) = W (Net work done)
Want a diagram which represents the heat input or output.
A way to do this is provided by the Second Law
where ds is the change in entropy of a unit mass of the parcel and
dq is the heat input per unit mass
Thus, one variable should be the entropy , s

12. Steady Flow Energy Equation
For any device in steady flow
Heat input
Per unit mass flow rate: 2 1
Mass flow
Device
Shaft work
q is heat input/unit mass
wshaft is the shaft work / unit mass

13. Steady Flow Energy Equation
The form of the steady flow energy equation shows that enthalpy, h:
h = e + pv = e + p/r
Natural variable to use in fluid flow-energy transfer processes.
For an ideal gas with constant specific heat, dh = cpdT.
Changes in enthalpy are equivalent to changes in temperature.
To summarize, the useful natural variables in representing gas turbine engine processes are h,s (or T, s).
Represent thermodynamic cycle (Brayton) for gas turbine engine on a T,s diagram

14. Thermodynamic Cycles
Carnot Cycle
Non-Ideal Brayton
Cycle for turbojet,
turboshaft, turboprop,
ramjet

15. Ideal Brayton Cycle Model
1-2: Compression (accomplished with a compressor and fan in a turbomachine with spinning blade rows)
2-3: Combustor: Constant pressure heat addition
3-4: Expansion (accomplished with a turbine in a turbomachine with spinning blade rows)
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

16. Gas Turbine Engine Components
Inlet: Slows, or diffuses, the flow to the compressor
Fan/Compressor: (generally two, or three, compressors in series) does work on the air and raises its stagnation pressure and temperature
Combustor: Heat is added to the air at roughly constant pressure
Turbine: (generally two or three turbines in series) extracts work from the air to drive the compressor or for power (turboshaft and industrial gas turbines)
Afterburner: (on military engines) adds heat at constant pressure
Nozzle: Raises the velocity of the exiting mass flow
Exhaust gases reject heat to the atmosphere at constant pressure

17. Thermodynamic Characteristics of Components (Ideal Components)

18. Schematic of Conditions through a Turbojet Engine

19. Nominal Temperatures and Pressures for PW4000 Turbofan Engine

20. Review of Stagnation Condition Locations

21. 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

22. Propulsive Efficiency and Specific Thrust as a Function of Exhaust Velocity
Conflict

23. Commercial and Military Engine Comparison (Approximate same thrust and approximately correct relative sizes)
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 ↑
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 ↓
P&W 119 for F- 22, T~35,000 lbf, a ~ 0.3

24. Specific Impulse Comparison
PW4000 Turbofan
SSME
Space Shuttle Main Engine
T ~ 2,100,000 N (vacuum)
LH2 flow rate ~ 70 kg/s
LOX flow rate ~ 425 kg/s
Isp ~ 430 seconds
Airbus A , A , Boeing , /300, MD-11
T ~ 250,000 N
TSFC ~ 17 g/kN s ~ 1.7x10-5 kg/Ns
Fuel mass flow ~ 4.25 kg/s
Isp ~ 6,000 seconds