A Er 710 Propeller 2

7/29/2019 A Er 710 Propeller 2

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Introduction

Propellers

Internal Combustion Engines

Gas Turbine Engines

Chemical Rockets

Non-Chemical Space Propulsion Systems

AER 710 Aerospace Propulsion


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C-130

Nieuport N.28C-1


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Introduction to the Propeller

The rotating blade of a propeller sharessimilar characteristics to a wing passingthrough the air

A propeller blade generates thrust Fthroughan aerodynamic lift force component,demands an engine torque Qto overcomeaerodynamic drag, and will stall if the local

resultant angle of attack of the bladeexceedsmax

Additional factors: trailing vortex generation,tip losses, compressibility


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Martin MB-2


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DH-98 Mosquito


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Forces acting on wing airfoil section (above) and propeller blade section (below)


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For evaluation of propeller performance, one canapply a simple analytical approach using theprinciple of linear momentum conservation, andtreating the propeller as an actuator disk wherethere is a step increase in pressure

Actuator Disk Theory


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)VV(VA)VV(mF 033303

Thrust generated by disk:

)pp(AF 121

Alternatively:

2

11

2

00

2

1

2

1VpVp

Bernoullis eq. applied from upstream to front of disk:


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2332222

1

2

1VpVp

Similarly, downstream of disk:

)VV)(VV()VV(pp 03032

0

2

31221

21

Noting po = p3 , and V2 = V1, via subtraction one gets:

A3V3= A1V1

Conservation of mass, incompressible flow:

)VV(VA)pp(AF0333121

Substituting from earlier:


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)VV)(VV()VV(VA

App

0303033

1

3

122

1

which gives the simple result:

and

2

03

1

VVV

wVV 01

Define propeller-induced velocity w such that:

wVV 203

w)wV(A)VwV)(wV(A)VV(VAF 0100010311 22

and so for thrust,


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2

01

2

0

2

001

2

0

2

3 22

2

1

2

1

2

1)wV(wA]V)wV)[(wV(AVmVmP

Ideal power required:

)wV(FP 0

or

Since power from a piston or turboprop engine is relativelyconstant at a given altitude, one can expect the thrust to

drop as the airplane picks up airspeed, according to this

correlation.

022 012

1 Fw)VA(w)A(

If one wishes to find was a function ofF, from earlier:


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1

2

0

0 2

2

1

2 A

FV

Vw

giving

1

23

2 A

F

wFPP

/

o

ooo,indo

Ideal static power (Vo= 0):

0

0

0

1

1

Vw)wV(F

FVi,pr

Ideal propeller propulsive efficiency:

1

11

2

qA

Fi,pr

or via substitution (qis dynamic pressure):


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i,pr

S

prP

FV

Actual propeller propulsive efficiency, in terms of useful

(thrust) power and engine shaft powerPS:

SP)()wV(FP factorcorrection0

Correction factor, less than 1, for ideal power estimate:

Variable-pitch propeller better able to approach theideal power requirement, as compared to a fixed-pitch

propeller, in accommodating different flight speeds

and altitudes.


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Momentum-Blade Element

Theory

Logically, the next level of analysis would

look at a given propeller blades

aerodynamic performance from hub toblade tip

one can discretize the blade into a finite

number of elements, while applyingmomentum conservation principles


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Schematic diagram of a three-bladed propeller, and framework for discretizing an individual blade for analysis


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)sin(D)cos(LFii ddd

Increment of thrust:

22

V)r(VR

Resultant velocity:


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)]cos(D)sin(L[rFrQ iiQ dddd

Increment of torque:

rcCVL E d21d

2

Increment of lift:

rcCVD dE d2

1

d

2

Increment of drag:

22)V)cos(w())sin(wr(V iiE

Overall resultant velocity:


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)

V

w(sin

R

i

1

Induced angle of attack:

)(a)(CC ioi

Airfoil lift coefficient:

min,dd CC

Airfoil drag coefficient:

C < C,min

2)CC(kCC min,min,dd C,min < C < C,m

)(kCC max,dd max 1 >max


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cosr)(caV

B

cosLF ioR d2dd2

Via substitutions, increment of thrust:

where Bis number of blades.

cosw)coswV(Aw)wV(AF d2d2d 0

Borrowing from actuator disk theory:

cosV)cosVV()rr( RiRi d22

088

2 )(cosr

Bca)

cosr

Bca

cosV

V( oi

o

R

i

Equating the above relations, one arrives at:


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R

Bc

R

RcB refrefref

2areadisk

areablade

Overall propeller solidity:

r

Bcx

R

Bc

Local solidity:

x = r/R

R

V

)R))(/((

V

nd

VJ

p

22

Advance ratio:

where nisthe prop shaft rotation speed (rps).

J

R

V

Nondimensional velocity ratio:


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)x

(tan)r

V(tan

11

Also:

TR xVrcosV VT = R

088

22

2 )(Vx

Va)

Vx

Va

x(

T

Ro

i

T

Ro

i

Substituting from earlier:

})](Vx

Va)

Vx

Va

x[()

Vx

Va

x({

/

T

Ro

T

Ro

T

Ro

i

21

2

2

222882

1

Applicable solution for induced angle of attack via the

above quadratic eq. gives:


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42dn

FCT

Propeller thrust coefficient:

53dn

PC SP

Propeller power coefficient:

QPS

r)]sin(C)cos(C[BcVF idiE d2

1d

2

Incremental thrust no. of blades:

r)]cos(C)sin(C[BcVrP idiES d2

1d

2

Incremental power no. of blades:


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)xJ(r

rVVV RE222

2

22

22222

FR

CT 42

2

4

Note:

Thrust coefficient:

x)]sin(C)cos(C)[xJ(FRCidi

x

T

h

d8d4

22

1

2

42

2

SP PR

C53

3

4

Power coefficient:

x)]cos(C)sin(C)[xJ(xPR

C idx

iSP

h

d8

d4

1

222

2

53

3


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Momentum-Blade Element

Theory (Summary)

The above equations forCT and CP canbe integrated from the hub station (x= xh)

to the blade tip (x= 1) using a numericalapproach as one moves along the blade ofvaryingand c, calculating the variouspertinent parameters (C

, Cd

,i

, etc.) inconjunction


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Thrust

Power


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Propeller Propulsive Efficiency

Define as useful thrust power over overall

shaft power:

S

pr

P

FV

JC

C

dnC

VdnC

P

T

P

T

pr

53

42

Also, via substitution:

A variable pitch propeller will have better efficiency over the

course of the flight mission, relative to a fixed pitch prop.


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Chart illustrating propeller propulsive efficiency for an example propeller


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Compressibility Tip Loss

Depending on the blade airfoil sectiondesign, drag divergence (compressibility)

effects will become evident when the

propeller blades resultant tip speed VR,tipexceeds a local flow Mach numberMatipofaround 0.85 (critical value, Macr)

As a result, one would not typically becruising at much greater than a flight Mach

numberMa of around 0.6


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22)(

Maa

ndMa

tip

)1.0

(100

15 crtipalminpr,nopr

MaMa

Dommasch correlation:

Blade tip Mach number:

Modern high-speed blades may be thinner, and swept

or curved along the blade length, to mitigate the

issues with compressibility and compression wave

development at higher local flow Mach numbers


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Activity Factor

Activity factor (AF) is a design parameterassociated with the propeller blades

geometry. The more slender the blade

(larger radius, smaller chord), the lowerthe AF value:

xxd

cAF

hx p

d16

100000 31

pd

cAF 1563

Typically see higher AF props on turboprop engines.


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Blade Number

One has the option of setting the numberof blades, B, for a given application. Whileone has a minimum of 2 blades to choose

from, one can presently go as high asaround 8 blades on the high-performance

end for an unducted propeller

On occasion, one also sees the use of twocontra-rotating rows of blades, to get more

thrust delivery from one engine


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Photo of Fairey Gannett carrier-borne anti-submarine/AEW aircraft,employing two contra-rotating rows of 4 propeller blades each on a co-axialshaft setup, powered by a 3000-hp Armstrong Siddeley Twin Mambaturboprop engine


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Airbus A400M Atlas


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Helicopter Rotors

helicopter rotors (main and tail) share anumber of similarities with airplane

propellers

analysis done above for propellers can beapplied to rotors

orientation of the rotor disk will be

somewhat different from that of thepropeller, with respect to the resultant

incoming air flow

Main helo rotor produces lift + thrust


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- rotor blade will advance into the air flow when

in forward flight, and then retreat during the

other half of the rotational cycle

CH-47


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- tail rotor primarily controls yaw forces and

moments [primarily main-rotor-induced

torque] on the helicopter, if only having one

main rotor- a tandem-rotor helicopter, with two contra-

rotating main rotors, would not need a tail

rotor


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HH-65 Dolphin

- ducted tail fan is an alternative to the conventional

tail rotor


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NOTAR

No Tail Rotor (Using Coanda Effect)


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The amount of lift generated by a main rotor is controlled

by two means: a) the engine throttle setting for desired

level of main rotor rotational speed, and b) collectivepitch setting, which sets the angle of incidence of the

main rotor blades collectively to produce the desired

uniform lifting force on the vehicle (e.g., higher lift

required, a higher blade incidence angle setting isneeded, for the same rotor rotational speed)

Rotation of the vehicles body in pitch or roll or some

combination thereof is largely via the cyclicpitch settingof the main rotor, whereby the individual main rotor

blades will have their incidence vary as they complete a

given revolution about the vehicle, depending on the

desired direction of the rotational moment


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Operations of swashplate (item #2, 4 above) for cyclic control


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The schematic diagram illustrates a conventional main rotor mast(rotorhead), with the hub above the mast connecting the rotor blades to the driveshaft in a fully articulated design (hinged); a swashplate approach is being used tocontrol the effective main rotor disk deflection and tilt direction thereof


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Fully articulated, a.k.a., hinged (horiz. + vert.) rotor head above

(vs. rigid, a.k.a., hingeless)


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From: Flight International 1986


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Bell UH-1C Iroquois (Huey)


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Rotor mast, Bell UH-1 Iroquois


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Hybrid Aircraft Designs

In order to improve range performanceover a conventional helicopter, one will

see tilt-wing and tilt-rotor designs for

V/STOL (vertical/short takeoff & landing)applications

Tilt-rotor V-22 Osprey


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Tilt-wing Canadair CL-84

A Er 710 Propeller 2

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