lect5 lec 5 aircraft proplusion
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lec 5 aircraft proplusionTRANSCRIPT
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Recap: Lecture 4, 13th January 2015, 0830-0925 hrs.
Ideal cycle for jet engines
Without and with afterburning
The generalised thrust equation
Momentum and pressure thrust
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The thrust equation
(Reaction) Control surface
Thrust producer
u, Pa
u
u
Ai Ae
ue
2 1
x
y
Ae, Pe
amem
sm
fm
2
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The thrust equation
The reaction to the thrust, , is transmitted to the support. The engine thrust is thus the vector summation of all forces on the internal and external surfaces of the engine.
Therefore,
Considering the components of force and the momentum flux in the x-direction only,
CS
dAnuuF ).(
CS
xx dAnuuF ).(
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The thrust equation
The pressure and velocity can be assumed to be constant over the entire control surface, except over the exhaust area, Ae.
The net pressure force acting on this control volume is (PaPe)Ae.
The only other force acting on the control volume is the reaction to the thrust, .
Adding up the forces in the x-direction,
eeax APPF )(
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The thrust equation
The mass flow that enters the capture area, Ai, is
Similarly, the mass flow crossing the exhaust area Ae, is,
Also,
Or,
Continuity equation for the CV gives,
ia uAm
eeee Aum
fae mmm
ieeef uAAum
)( is,Which
g,Rearrangin
0)(
ies
eeeefs
fseeee
AAum
AuuAmm
uAmmAAuAu
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The thrust equation
From the momentum balance across the CV,
This is the net outward flux of x-momentum.
This equation reduces to
From the force balance equation, we have,
uAAuumuAAuumumdAnuu iaeseeCS
x )()().(
umumdAnuu aeeCS
x
).(
eaeaee APPumum )(
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The thrust equation
If we define fuel-air ratio,
This is the generalised thrust equation for air-breathing engines.
The term (PePa)Ae is not zero only if the exhaust jet is supersonic and the nozzle does not expand the exhaust jet to ambient pressure.
However if Pa Pe, it can be substantial contribution.
eaeea APPuufm )()1(
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Engine performance parameters
The engine performance is described by different efficiency definitions, thrust and the fuel consumption.
The efficiency definitions that we shall now be discussing are applicable to an engine with a single propellant stream (turbojets or ramjets).
For other types of jet engines (turbofan, turboprop) the equations need to be appropriately modified.
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Engine performance parameters
Propulsion efficiency: The ratio of thrust power to the rate of production of propellant kinetic energy.
If we assume that f1 and the pressure thrust term is negligible,
2/)2/)(1( 22 uufmu
ea
P
e
e
e
eP
uu
uu
uu
uuu
/1
/2
2/2/
)(22
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Engine performance parameters
Thermal efficiency: The ratio of the rate of production of propellant kinetic energy to the total energy consumption rate
For a turboprop or turboshaft engine, the output is largely shaft power. In this case,
fuel. theofreaction ofheat theis , where,
2/)2/)(1(2/)2/)(1( 2222
R
R
e
Rf
eath
Q
fQ
uuf
Qm
uufm
engine. theofoutput power shaft theis , where, sRf
sth P
Qm
P
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Engine performance parameters
Overall efficiency: The product of thermal efficiency and propulsion efficiency.
In the case of aircraft that generate thrust using propellers,
thpo
.efficiencypropeller theis Where, pr
thpro
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Engine performance parameters
Thrust specific fuel consumption, TSFC
For turbine engines that produce shaft power, brake specific fuel consumption, BSFC
For engine (like turboprop) that produce both, equivalent brake specific fuel consumption,
uufmmm
TSFCea
ff
)1(
s
f
P
mBSFC
uP
m
P
mEBSFC
s
f
es
f
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PT6: Turboprop Engine
500 to 2,000 shaft horsepower class Multi- stage axial and single-stage centrifugal
compressor Reverse flow combustor Single-stage compressor turbine Independent free power turbine with shrouded
blades Forward facing output for fast hot section
refurbishment Epicyclic speed reduction gearbox
Source: http://www.pwc.ca/en/engines/pt6a 13
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Ideal cycle for jet engines
s
T
2
4
5
3
a
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Ideal turbojet cycle (without afterburning) on a T-s diagram
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Ideal cycle for jet engines
For cycle analysis we shall take up each component and determine the exit conditions based on known inlet parameters.
Intake: Ambient pressure, temperature and Mach number are known, Pa, Ta and M
Intake exit stagnation temperature and pressure are determined from the isentropic relations:
)1/(
0202
2
022
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a
a
a
T
TPP
MTT
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Ideal cycle for jet engines
Compressor: Let the known compressor pressure ratio be denoted as
Combustion chamber: From energy balance,
Hence, we can determine the fuel-air ratio.
/)1(
0203
0203
c
c
TT
PP
030403
0304
0304
//
1/,
TTTcQ
TTfor
fQhh
pR
R
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Ideal cycle for jet engines
Turbine: Since the turbine produces work to drive the compressor, Wturbine = Wcompressor
0304
)1/(
04
050405
02030405
02030504
02030504
chamber, combustion idealan For
Hence,
)1/()(
)())(1(,
)()(
PP
T
TPP
fTTTT
TTTTfor
TTcmTTcm papt
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Ideal cycle for jet engines
Nozzle: With no afterburner, T06=T05, P06=P05
Thrust, TSFC and efficiencies can now be determined using the formulae derived earlier.
/)1(06060607
707
2
/12
Since,
2
energy, kineticexit nozzle theTherefore,
PPTcu
hh
hhu
ape
e
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Ideal cycle for jet engines
Thrust,
Propulsion efficiency,
Thermal efficiency,
uufmAPP
APPuufm
ea
eae
eaeea
)1(
,negligible is )( If
)()1(
uufmmm
TSFCea
ff
)1(
2/)2/)(1( 22 uufmu
ea
P
R
eth
fQ
uuf 2/)2/)(1( 22
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