Aerospace Propulsion Lec 2 5 Thrust

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


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


3


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 )()(


4


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


5


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


6


Total ThrustExternal forces on the exterior of the engine body (nacelle) is considered

Total thrust

3223extext AApAApAApdApT aaa maxmax

3223extint AAppAVmpAVmTTT a


7


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


8


Total Thrust

1 mthroughputenginema

333344 AppVmVm a

43 mmm


9


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


10


Exhaust velocity (V3)

Characteristic velocity (V4)

m

AppVVc a

3334


11


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)

..

.


12



13


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


14


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


15


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


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 )(/


17


Ideal Rocket PerformanceThrust Variation with Altitude

Design Altitude

333 )( AppVmT a

43

3

3

/ VVmTc

VmT

pp

dd

d

a

Pressure imbalance thrustMomentum thrust


18


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


19


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


20


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


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


22


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


23


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


24



25


Core engine thrust (no fan)

Turbofan thrust

)1(4

14 V

VVmT

))(1(

))((

4

1

44

1

VV

VV

BPRVm

VVmmT

F

FFF


26


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


27


D = 1)

BPRT

T

BPRV

V FF

1,

1

1

004


28


D = 1)

)//(1

)//(2

1

2,)1(

4

4p

4

1

40 VV

VV

V

V

V

VBPR

T

T

F

F

F

FFF


29


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


30

Assignment #1Due Date: Monday, January 12, 2009

Quiz #1Monday, January 12, 2009

Documents

Aerospace Propulsion Lec 2 5 Thrust