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Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
Aerospace PropulsionAerospace PropulsionMEC 4280 / 4740MEC 4280 / 4740
Semester I2009/2010
Lectures (2-3)
Basic Thrust EquationsBasic Thrust Equations
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
2
Airbreather ThrustAirbreather Thrust
Airbreather ThrustFor thrust production by ramjet and turbojet; and by ducted fans, propellers and rotors driven by turbine or piston engine.
Newton Second Law for Moving FluidAssume one-dimensional (curvilinear or rectilinear), steady flow.From conservation of mass,
Curvilinear flow Rectilinear flow
constant AVm
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
3
Airbreather ThrustAirbreather Thrust
Apply Newton’s second law to the shown fluid element
Integrating over the control volume R shown, we obtainx
x
VmddVm
dVAVdt
dVAdxonacceleratimassdF
)(
)()(
xenteringleavingx VmVmF )()(
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
4
Airbreather ThrustAirbreather Thrust
Forces on a Fluid ElementConsider a differential fluid element within an airbreathing engine.Forces acting on the fluid element:
End faces
Side-wall forces
Substituting and rearranging
xbxfxsxex dFdFdFdFdF ,,,,
pdApdAdFdF snsxs sin)(sin,,
) ( pAVmnctionimpulse futhrust or Fx
dxdx
pAddx
dx
pAdpApAdF xe
)()(,
xx
xxbxf
FdpAVmd
pAdVmddFdFpdA
)()(,,
00
end-faceside-wall
frictionbody
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
5
Airbreather ThrustAirbreather Thrust
Forces on Finite Fluid ZoneSteady, one dimensional-flowThe total force acting on the fluid within the enclosure between 1 and 2
Thrust of the fluid acting on the interior of the engine body (between 2 and 3)
12 FFF
2323int pAVmpAVmFFT
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
6
Airbreather ThrustAirbreather Thrust
Total ThrustExternal forces on the exterior of the engine body (nacelle) is considered
Total thrust
3223extext AApAApAApdApT aaa maxmax
3223extint AAppAVmpAVmTTT a
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
7
Airbreather ThrustAirbreather Thrust
From momentum balance of the region between 1 and 2
Then,
From momentum balance of the region between 3 and 4
1 , mthroughputenginema
112222 VmVmAppa
aa ppAVmVmT 33133
333344 AppVmVm a
14 VmVmT a mm , 3
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
8
Airbreather ThrustAirbreather Thrust
Total Thrust
1 mthroughputenginema
333344 AppVmVm a
43 mmm
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
9
Airbreather ThrustAirbreather Thrust
Gross Thrust and Net ThrustThrust can be rewritten as
Or, net thrust = gross thrust – ram drag
Net thrust,
Gross (static) thrust,
Ram drag,
13
33 Vmm
AppVmT aa
1VmR aD
m
AppVmT aG
333
13
33 Vmm
AppVmT aaN
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
10
Airbreather ThrustAirbreather Thrust
Exhaust velocity (V3)
Characteristic velocity (V4)
m
AppVVc a
3334
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
11
Airbreather ThrustAirbreather Thrust
ExampleTG = 98 kN
c = 515 m/s (constant with altitude)ma ≈ m
Calculate for the flight conditions given in the following tableThroughput (ma)
Ram drag (RD)
Net thrust (TN)
Capture cross section of free-stream air (A)
..
.
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
12
Airbreather ThrustAirbreather Thrust
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
13
Airbreather ThrustAirbreather Thrust
Airbreather PerformanceThrust Power = P = T V1
Propulsive Efficiency, p
eexpenditurenergy of rate
power usefulp
1,
4
1 nV
V
nVV
V
VVm
VVVm
VmVm
TV
ap
1
2
1
22
)(
)(
14
12
12
421
1142
1212
421
1
14Vm
T
Forward speed parameter
1
2p
)1(22
421 Vm
P
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
14
Airbreather ThrustAirbreather Thrust
Thermal Efficiency, th
f
ff
th
HVVV
AFR
HVmVVm
21
powerheat available
expeditureenergy of rate
21
24
21
242
1
)(
.)(
Air/fuel ratioFuel lower
heating value
f
a
mm
AFR
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
15
Airbreather ThrustAirbreather Thrust
Performance Presentation p = P = 0, and T is a maximum at zero forward speed, V1 = 0
Maximum thrust, Tmax =
p = 1 and T = P = 0 at = 1 (i.e. highest propulsive efficiency is obtained with the least increase in jet speed above free stream speed.)Higher propulsive efficiency is obtained by increasing mass flow and reducing jet speed. It is better to move a large mass of air more slowly than to move a small mass of air more rapidly. When > 1, the airbreather act in the windmill, wind turbine, braking regimeMaximum power Pmax = at = ½, that is at V1 = ½ V4 . At which T = ½ Tmax
244
1 Vm
4Vm
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
16
Rocket ThrustRocket Thrust
Derivation of Rocket ThrustDerived from air-breathing thrust equation with no captured airflow
Derived directly from the momentum balance of non-air-breather
02 amm
3334 )( AppVmVmT a
m
AppVVmTc a
3334 )(/
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
17
Rocket ThrustRocket Thrust
Ideal Rocket PerformanceThrust Variation with Altitude
Design Altitude
333 )( AppVmT a
43
3
3
/ VVmTc
VmT
pp
dd
d
a
Pressure imbalance thrustMomentum thrust
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
18
Rocket ThrustRocket Thrust
Specific Impulse, Isp
Thrust per unit propellant weight flow rate
Thrust Specific Fuel Consumption, tsfc
Burn Time,
(s) // psp gcWTI
cgITm
ITW
/1/1/tsfc
/1/tsfc
sppm
sppw
T
W
W
WITIWWW o
o
pspspppp //
spo
o
p )1,1( IT
W
W
W
Lift-off weight/thrust ratioPropellant/liftoff
weight ratio
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
19
Rocket ThrustRocket Thrust
Total Impulse, I
Propulsive Efficiency
psp0 psp0WIdtWITdt
I
4122
21
24
412
1421
1
1p
//1,1
2
1
2
2
)(
VVnn
n
VV
VV
VVmTV
TV
14
Vm
T 21
2
p22
421 Vm
P
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
20
Rocket ThrustRocket Thrust
Variation of Rocket Performance with Forward SpeedForward speed parameter is not restricted to be < 1Thrust is independent of Power has no maximum and increases linearly with Propulsive efficiency has a maximum of 1 at = 1
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
21
Turbofan ThrustTurbofan Thrust
Pratt & Whitney PW4084 Pratt & Whitney PW4084 turbofan which propels turbofan which propels the Boeing 777 (84,000 lb the Boeing 777 (84,000 lb thrust)thrust)
It is better to move a large mass of air more slowly than to move a small mass of air more rapidly
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
22
Turbofan ThrustTurbofan Thrust
Fundamentals
Bypass Ratio (BPR)
Jet Speed and Propulsive EfficiencyRate of kinetic energy loss in core jet exhaust =Rate of kinetic energy gain in fan bypass =
mm
BPR F
)( 2242
1FVVm
)( 21
221 VVm FF
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
23
Turbofan ThrustTurbofan Thrust
From the mechanical efficiency of the fan-turbine drive
Then
Solving for VF
)()( 21
2224 VVmVVm FFDF
FF
DF
FD
F
FF
VVVV
VVVV
mm
BPR
/,/
//1
141
222
22
21
2
224
D
D
F
F
BPRBPR
VV
222
4
.
1and1then As p FBPR ,
F
F
F
F
VV
VV
1
2
)/(1
)/(2
1
1p
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
24
Turbofan ThrustTurbofan Thrust
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
25
Turbofan ThrustTurbofan Thrust
Core engine thrust (no fan)
Turbofan thrust
)1(4
14 V
VVmT
))(1(
))((
4
1
44
1
VV
VV
BPRVm
VVmmT
F
FFF
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
26
Turbofan ThrustTurbofan Thrust
Takeoff performance (V1 = 0)
Ideally, when D = 1
Generally,
040
2
04
)1(,
VV
BPRTT
BPRVV FF
D
DF
BPRTT
BPRVV FF
1,
11
004
4
1
40
)1(V
V
V
VBPR
T
T FF
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
27
Turbofan ThrustTurbofan Thrust
D = 1)
BPRT
T
BPRV
V FF
1,
1
1
004
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
28
Turbofan ThrustTurbofan Thrust
D = 1)
)//(1
)//(2
1
2,)1(
4
4p
4
1
40 VV
VV
V
V
V
VBPR
T
T
F
F
F
FFF
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
29
Turbofan ThrustTurbofan Thrust
ExamplesE 2-4-1Compare p of a fanjet with BPR = 5 and D = 0.9 with that of a core jet at its maximum power condition ( = 0.5).
E 2-4-2A simple turbojet has constant throughput of 100 kg/s and a constant exhaust of 500 m/s. If it is fitted with a fan to provide a BPR of 1:1, compare the following engine parameters with and without the fan at flight speeds V1 of 150 knots and zero
exhaust jet speed (V4 or VF), thrust (T or TF), propulsive efficiency p .
1 knot = 0.514 m/s
Aerospace Propulsion (MEC 4280/4740)Dr. Raed Kafafy
30
Assignment #1Due Date: Monday, January 12, 2009
Quiz #1Monday, January 12, 2009