THEORY OF PROPULSION 1' Idealized Flow Machines

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THEORY OF PROPULSION1. Idealized Flow Machines

• P. M. SFORZA
• University of Florida

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An Idealized Flow Machine
Ve

• Steady, quasi-one-dimensional flow
• Entrance and exit stations are pressure matched
• No heat transfer across control volume
• Friction outside the flow machine is negligible
• Mass injected into the stream is negligible

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Quasi-1D conservation equations

• Conservation relations
• Mass
• Momentum
• Energy

Net force on the fluid
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zero heat addition Q0
because no heat is added to the flow
Force on the fluid
Power added Pgt0 thrust on machine
Power removed Plt0 drag on machine
Propulsive efficiency
Useful power Actual power
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Example of Q0 with Pgt0 Propellers
ATR-72
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The latest turboprop engine
http//defence.rolls-royce.com/most-powerful-turbo
prop-engines/
The Europrop International TP400-D6 (Rolls-Royce,
MTU, Snecma and ITP). Power range in excess of
11,000shp TP400-D6 is the most powerful Western
turboprop ever Applications Airbus Military
A400M TP400-D6 TP400-D6 fact sheet(pdf, 301kb)
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Fans and Turbines
Example of Q0 with Pgt0 Fans
Example of Q0 with Plt0 Turbines
GE 1.5 MW wind turbine farm in Gatun, Spain
Cincinnati Fan tube axial fan
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Turbopumps
Example of Q0 with Pgt0 Turbopumps Even though
Pratt Whitney Rocketdyne's SSME weighs
one-seventh as much as a locomotive engine, its
high-pressure fuel pump alone delivers as much
horsepower as 28 locomotives, while its
high-pressure oxidizer pump delivers the
equivalent horsepower for 11 more.
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Propeller Operation
The propeller is speed-limited F1/Vavg 1/Vo
Propeller region
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Propulsive efficiency
Propeller propulsive efficiency drops off slowly
with flight speed
Propulsive efficiency hpVo / Vavg constant
VeVoV
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constant Q with zero net power P0
Energy equation
waste heat
Thrust
Overall efficiency
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Example of Qgt0 with P0 the turbojet
Pratt Whitney J57 turbojet. World's first jet
engine to develop 10,000 lbs. thrust. It took the
F-100 to supersonic flight.
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Example of Qgt0 with P0 the ramjet
Marquardt RJ43-MA-20-B4 Ramjet powered the
unmanned 42 ft long D-21 (M3, 90kft) after
launching from an SR-71-like aircraft
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Jet is not speed-limited
The jet is not speed-limited - thrust is constant
with flight speed
F Vo/Vavg 1/(1Ve/Vo) here Ve/Vo2
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Specific fuel consumption
Heat generated by combustion of a fuel with
heating value HV
Specific fuel consumption lbs of fuel burned
per hour for each lb of thrust produced
Product of efficiencies
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the average velocity, Vavg
Prop
Jet
Thrust
Propulsive efficiency
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Specific fuel consumption
Specific fuel consumption for the jet sfc
3600V0
(hp)(hth)(hb)(778HV)
Hydrocarbon fuel, hth0.62
Hydrogen fuel, hth0.62
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Specific impulse comparison
Jet, LH2, hth0.62
Jet, HC, hth0.62
airbreathing jets
rockets
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Early problems with jet powered aircraft
Performance characteristics of early jet fighters
were different than those of propeller-driven
aircraft with reciprocating engines Differences
were due to the manner in which the thrust and
power of turbojet engines vary with speed.
Reciprocating engines generate the same amount
of power at takeoff as at high speeds, whereas
the turbojet at the same altitude has nearly the
same thrust at both high and low speeds.
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jet vs. propeller comparison
Acceleration of the jet on takeoff will be low
and takeoff distance long
For the same drag area, the jet would be much
faster than the propeller-driven aircraft.
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Ryan FR-1 hybrid jet-propeller fighter
Leading edge inlets
F1600 lbs
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The fanjet
The special case of combined heat and power
addition the fanjet
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The fanjet advantage
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Specific fuel consumption in the fanjet
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The fanjet advantage
(lbs fuel/hr)/hp
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Low bypass turbofan engine
Pratt Whitney's first F100 military engine flew
on July 27, 1972, on a twin-engine F-15 Eagle. It
also powered the F-16 Fighting Falcon.
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High bypass turbofan engine
GE's commercial engines of the 1970s built on the
technology of the TF39 military engine of the
1960s. By the 1980s, the CF6 family of engines
was powering wide-body aircraft, including the
Boeing 747 and 767
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The rocket
The special case of Ao0 the rocket
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Rocket engine equations
If A00 then m00 and the force on the fluid is
The energy equation may be rearranged to provide
an equation for the force as a function of the
heat addition
Waste heat
The propulsive efficiency
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The liquid-fueled rocket engine
Designed for the Boeing Delta IV family launch
vehicles, the Rocketdyne bell-nozzle RS-68 is a
LH2-LO2 booster engine
Thrust Level745,000 lbf Weight14,560 lb
Mixture Ratio6.06 Is410 sec
Chamber Pressure1410 psia
Expansion Ratio (E)21.5
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fuel efficiencies of propulsion systems
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Force field for airbreathing engines
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Force field acting on the control volume
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Force field acting on the structure
Airframe contribution
Engine contribution
F net thrust nacelle drag
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Thrust and drag components
Net thrust gross thrust
ram drag
Airframe drag
Additive, or inlet, drag
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Thrust components
For preliminary studies it is generally assumed
that wf/w0ltlt1 For airbreathing engines wf/w02
The gross thrust and ram drag become
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The nozzle as an energy transformer
A nozzle can transform internal energy to kinetic
energy. Consider a point on a streamline in the
exit plane, i.e., station 7
V7
7
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total pressure ratio across the engine
For a matched nozzle, i.e., one designed so that
p7p0

Nozzle pressure recovery
Turbine work
removal Combustor
pressure recovery
Compressor work input Inlet pressure
recovery
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Conditions for maximum thrust
The gross thrust
Taking the first derivative and seeking the
stationary point yields
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From momentum conservation
So either p7p0 or A doesnt vary with p
Finally we find
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Isentropic flow with simple area change
dA/dpgt0
dA/dplt0
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Conditions for maximum thrust (cont.)
We consider the 2nd derivative to seek a maximum
For a matched nozzle, p7p0
lt0, for M7gt1Fgmaximum 0, for M1 Fgsaddle pt.
Note that for subsonic exit flow p7p0 so
Fgw7V7/g and therefore there is no stationary
point
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Mach angle and the zone of silence
m
Sound source moving supersonically
sound waves
Sound source moving sonically
sound waves
Mach angle marcsin(1/M)
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Nozzle types and related exit conditions
Mach lines
No real Mach lines
mlt90o
m90o
M7gt1 M71
M7lt1
Exit must be pressure matched because pressure is
felt everywhere
Exit flow can support pressure mismatch because
external pressure information cant get inside
nozzle
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interpretation of maximum thrust
Thrust loss pressure too low
Thrust loss - high pressure contribution lost
Correct length pressure matched
Pressure along nozzle wall
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Net thrust as a function of exit velocity
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Maximum thrust
Saddle point
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Exit flow subsonic
Exit flow supersonic
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Pratt Whitney J58 jet engine for the SR-71

• Fuel flow rate is 8000gal/hr of JP-7 (F/O0.034)
  with T-O Fg34,000lbs _at_200kts.M71 and
  TET1580FTt,7
• VeffgFg/wf(1O/F) 2400fps
• Net thrust FnFg-m0V029400lbs
• Sfcwf/Fn153600/294001.84/hr
• A0m0/r0V017.4 ft2 (D14.7ft)
• PusefulFnV014750 hp (11MW)
• T7Tt,71-(g7 -1)M72/2-1 2040R(0.86) 1750R
  (use g71.33)
• V7a7(g7RT7)1/22000fps
• FgA7p7(1g7M72)-p0 and m7(rVA)7 then
  A7m(1g)(RT/g)1/27/p0 Fg/p0 and A77.36ft2
  (D73.1ft)
• p7(Fg/A7p0)/(1g7M72)1.37p0

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The German A-4 Rocket (V-2)
The V-2 burned about 8000kg of propellant (LOX
and Alcohol, O/F1.3) in 65s with Ve 2000m/s
with a matched nozzle. Find a FmVe
(8000kg/65s)(2000m/s)246kN (or 55.3klbs), b
P on the pad and at V02km/s is given by PV0F 0
(on the pad) and 2250kN/s (2.25MW or 660,000hp)
at 2km/s, c IspF/mg 246kN/(8000kg/65s)(9.81m/s
2)203s, dhoFV0/mDQFV0/wfhbHFV0/(mg/1O/F
)hbHV(492MNm/s)/123kg/s(1)(27.2MJ/kg)/(11.3)
33.8
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Range dependence on sfc and structural weight
fraction
W2Wspp (all fuel used)
Note the structural weight fraction is
WFWspp/W1
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Range dependence on sfc and structural weight
fraction
General aviation airplanes
Most commercial airplanes