Advanced propulsion systems 3 lectures

1
Advanced propulsion systems (3 lectures)

• Hypersonic propulsion background (Lecture 1)
• Why hypersonic propulsion?
• Whats different at hypersonic conditions?
• Real gas effects (non-constant CP, dissociation)
• Aircraft range
• How to compute thrust?
• Idealized compressible flow (Lecture 2)
• Isentropic, shock, friction (Fanno)
• Heat addition at constant area (Rayleigh), T, P
• Hypersonic propulsion applications (Lecture 3)
• Ramjet/scramjets
• Pulse detonation engines

2
Why use air even if youre going to space?

• Carry only fuel, not fuel O2, while in
  atmosphere
• 8x mass savings (H2-O2), 4x (hydrocarbons)
• Actually even more than this when the ln( ) term
  in the Brequet range equation is considered
• Use aerodynamic lifting body rather than
  ballistic trajectory
• Ballistic need Thrust/weight gt 1
• Lifting body, steady flight Lift (L) weight
  (mg) Thrust (T) Drag (D), Thrust/weight L/D
  gt 1 for any decent airfoil, even at hypersonic
  conditions

L
T
D
mg
3
Whats different about hypersonic propulsion?

• Stagnation temperature Tt - measure of total
  energy (thermal kinetic) of flow - is really
  large even before heat addition - materials
  problems
• T static temperature - T measured by a
  thermometer moving with the flow
• Tt temperature of the gas if it is decelerated
  adiabatically to M 0
• ? gas specific heat ratio Cp/Cv M Mach
  number u/(?RT)1/2
• Stagnation pressure - measure of usefulness of
  flow (ability to expand flow) is really large
  even before heat addition - structural problems
• P static pressure - P measured by a pressure
  gauge moving with the flow
• Pt pressure of the gas if it is decelerated
  reversibly and adiabatically to M 0
• Large Pt means no mechanical compressor needed at
  large M

4
Whats different about hypersonic propulsion?

• Why are Tt and Pt so important? Isentropic
  expansion to Pe Pa (optimal exit pressure
  yielding maximum thrust) yields
• but its difficult to add heat at high M
  without major loss of stagnation pressure

5
Whats different about hypersonic propulsion?

• High temperatures ? not constant, also molecular
  weight not constant - dissociation - use GASEQ
  (http//www.gaseq.co.uk) to compute stagnation
  conditions
• Example calculation standard atmosphere at
  100,000 ft
• T1 227K, P1 0.0108 atm, c1 302.7 m/s, h1
  70.79 kJ/kg
• (atmospheric data from http//www.digitaldutch.co
  m/atmoscalc/)
• Pick P2 gt P1, compress isentropically, note new
  T2 and h2
• 1st Law h1 u12/2 h2 u22/2 since u2 0,
  h2 h1 (M1c1)2/2 or M1 2(h2-h1)/c121/2
• Simple relations ok up to M 7
• Dissociation not as bad as might otherwise be
  expected at ultra high T, since P increases
  faster than T
• Problems
• Ionization not considered
• Stagnation temperature relation valid even if
  shocks, friction, etc. (only depends on 1st law)
  but stagnation pressure assumes isentropic flow
• Calculation assumed adiabatic deceleration -
  radiative loss (from surfaces and ions in gas)
  may be important

6
Whats different about hypersonic propulsion?
7
Breguet range equation

• Consider aircraft in level flight
• (Lift weight) at constant flight
• velocity u1 (thrust drag)
• Combine expressions for lift drag and integrate
  from time t 0 to t R/u1 (R range distance
  traveled), i.e. time required to reach
  destination, to obtain Breguet Range Equation

8
Rocket equation

• If acceleration (?u) rather than range in steady
  flight is desired neglecting drag (D) and
  gravitational pull (W), Force mass x
  acceleration or Thrust mvehicledu/dt
• Since flight velocity u1 is not constant, overall
  efficiency is not an appropriate performance
  parameter instead use specific impulse (Isp)
  thrust per unit weight (on earth) flow rate of
  fuel ( oxidant if two reactants carried), i.e.
  Thrust mdotfuelgearthIsp
• Integrate to obtain Rocket Equation
• Of course gravity and atmospheric drag will
  increase effective ?u requirement beyond that
  required strictly by orbital mechanics

9
Brequet range equation - comments

• Range (R) for aircraft depends on
• ?o (propulsion system) - dependd on u1 for
  airbreathing propulsion
• QR (fuel)
• L/D (lift to drag ratio of airframe)
• g (gravity)
• Fuel consumption (minitial/mfinal) minitial -
  mfinal fuel mass used (or fuel oxidizer, if
  not airbreathing)
• This range does not consider fuel needed for
  taxi, takeoff, climb, decent, landing, fuel
  reserve, etc.
• Note (irritating) ln( ) or exp( ) term in both
  Breguet and Rocket
• because you have to use more fuel at the
  beginning of the flight, since youre carrying
  fuel you wont use until the end of the flight -
  if not for this it would be easy to fly around
  the world without refueling and the Chinese would
  have sent skyrockets into orbit thousands of
  years ago!

10
Brequet range equation - examples

• Fly around the world (g 9.8 m/s2) without
  refueling
• R 40,000 km
• Use hydrocarbon fuel (QR 4.5 x 107 J/kg),
• Good propulsion system (?o 0.25)
• Good airframe (L/D 20),
• Need minitial/mfinal 5.7 - aircraft has to be
  mostly fuel - mfuel/minitial (minitial -
  mfinal)/minitial 1 - mfinal/minitial 1 -
  1/5.7 0.825! - thats why no one flew around
  with world without refueling until 1986
• To get into orbit from the earths surface
• ?u 8000 m/s
• Use a good rocket propulsion system (e.g. Space
  Shuttle main engines, ISP 400 sec)
• Need minitial/mfinal 7.7 cant get this good a
  mass ratio in a single vehicle - need staging -
  thats why no one put an object into earth orbit
  until 1957

11
Thrust computation

• In airbreathing and rocket propulsion we need
  THRUST (force acting on vehicle)
• How much push can we get from a given amount of
  fuel?
• Well start by showing that thrust depends
  primarily on the difference between the engine
  inlet and exhaust gas velocity, then compute
  exhaust velocity for various types of flows
  (isentropic, with heat addition, with friction,
  etc.)

12
Thrust computation

• Control volume for thrust computation - in frame
  of reference moving with the engine

13
Thrust computation - steady flight

• Newtons 2nd law Force rate of change of
  momentum
• At takeoff u1 0 for rocket no inlet so u1 0
  always
• For hydrogen or hydrocarbon-air FAR ltlt 1
  typically 0.06 at stoichiometric

14
Thrust computation

• But how to compute exit velocity (ue) and exit
  pressure (Pe) as a function of ambient pressure
  (Pa), flight velocity (u1)? Need compressible
  flow analysis, coming next
• Also - one can obtain a given thrust with large
  (Pe - Pa)Ae and small mdota(1FAR)ue - u1 or
  vice versa - which is better, i.e. for given u1,
  Pa, mdota and FAR, what Pe will give most thrust?
  Differentiate thrust equation and set 0
• Momentum balance on exit (see next slide)
• Combine
• ? Optimal performance occurs for exit pressure
  ambient pressure

15
1D momentum balance - constant-area duct

• Coefficient of friction (Cf)

16
Thrust computation

• But wait - this just says Pe Pa is an extremum
  - is it min or max?
• but Pe Pa at the extremum cases so
• Maximum thrust if d2(Thrust)/d(Pe)2 lt 0 ? dAe/dPe
  lt 0 - we will show this is true for supersonic
  exit conditions
• Minimum thrust if d2(Thrust)/d(Pe)2 gt 0 ? dAe/dPe
  gt 0 - we will show this is would be true for
  subsonic exit conditions, but for subsonic, Pe
  Pa always since acoustic (pressure) waves can
  travel up the nozzle, equalizing the pressure to
  Pa, so its a moot point for subsonic exit
  velocities

17
Propulsive, thermal, overall efficiency

• Thermal efficiency (?th)
• Propulsive efficiency (?p)
• Overall efficiency (?o)
• this is the most important efficiency in
  determining aircraft performance (see Breguet
  range equation)

18
Propulsive, thermal, overall efficiency

• Note on propulsive efficiency
• ?p ? 1 as u1/ue ? 1 ? ue is only slightly larger
  than u1
• But then you need large mdota to get required
  Thrust mdota(ue - u1) - but this is how
  commercial turbofan engines work!
• In other words, the best propulsion system
  accelerates an infinite mass of air by an
  infinitesimal ?u
• Fundamentally this is because Thrust (ue - u1),
  but energy required to get that thrust (ue2 -
  u12)/2
• For hypersonic propulsion systems, u1 is large,
  ue - u1 ltlt u1, so propulsive efficiency usually
  high (I.e. close to 1)

19
References

• Archer, R. D. and Saarlas, M., An Introduction to
  Aerospace Propulsion, Prentice-Hall, 1996
• Hill, P. G. and Peterson, C. R., Mechanics and
  Thermodynamics of Propulsion, 2nd ed.,
  Addison-Wesley, 1992