The Analysis of Propellers Including Interaction Effects

TL;DR: In this article, an analytical and experimental studies have been undertaken on propellers operating in the unsteady flow field produced by interaction effects due to the fuselage, wing, and nacelles.

Abstract: Analytical and experimental studies have been undertaken on propellers operating in the unsteady flow field produced by interaction effects due to the fuselage, wing, and nacelles Methods have been developed and verified experimentally for determining the velocity field in which a propeller operates as well as its aerodynamic and dynamic response to this unsteady environment Methods are presented for predicting the net thrust of a propeller-wing-body combination as well as the unsteady thrust and torque acting on the propeller Sample calculations as well as wind tunnel and flight test results are presented which illustrates the sensitivity of a propeller to flow field in which it is operating

Summary

AB~TRAC1

• Analytical and exper~mcntal stud~es have been undertaken on propellers operatinl!.
• In the unsteady flou field produ~cd by lnteraction effects due to the fuselage, w~ns. and nacellcb.
• Methorls have been developed and verified exper~mcntally for determ~n~nl!.
• The net thrust of a prrypeller-~~ng-bodv comb~nat~on as well as the unsteady tnrust and torque act~nl! on the propeller.
• Ls as well as wind ~unnel dn1 flight test results are presented WhlCh illustrates tne sensitivlty of a propeller to the flow field in WhlCh it is operatmg, also known as Saople calculat~c.

$OJ

• A propeller ~hich is poorly matched to its flo~ f1cld or eng1ne can be ~nefficlcnt ane subJect to exceSS1VC vlbratory strOesses.
• The study rf propeller aerodynam1cs and dynamlcs described here 1S div1ded mto three parts.
• The f1rst part deals with predict~ng the flo~ f1eld ~n ~hich the propeller 1S to operate.
• A nucer1cal ~ethod lS descr1bcd for calculat1ng the veloc1ty vector at any radlal and aZLCuthal 10cat10n.
• The third, and final section, examines the structural dynam1cs of the blades and presents methods for predic~ ing the1r normal u.odes.

PROGRAlI FOR PREDICTION OF PROPELLE~ FLOW FIELD

• Potential flow methods, at least for tractor propellrrs, will accurately predict the velocity field in whlch a propeller operates since the effect of viscosity ahead of a body is usually negliglble.
• Lett1ng ~(J) denote the veloc1ty potential assoc1ated ~ith Q(J) and N(I), the unit vector normal to the Ith panel and d1rected outwdrd.
• At any POl.nt can be detert:!ined by combining the free stream velocity aDd local w~ng induced velocity vector~ with the grJdient of ~ obtair.ed fro~ equdtions 2 and 5.
• The lifting Wlng is modeled slmply by a single horseshoe vortex placed along the quarter-chord lIne and trailing from the n/4 spanwlse station.
• It ~as then applIed to typical fuselage shapes ~ith a certain amount confIdence.

NETHOD FOR PREDICTING AERODYNANIC LOADS ON A PROPELLER

• Generally, both the magnitude and direction of the velocity field will be a functlon of blade POSItIon.
• The modern trend 1S to calculate the induced velocity v by applying the B10t-Savart relationship to the propeller's hel1cal ttai11ng vortex system.
• Even here, however, it is usually necessary to assume a shape to the wake beiore numerically 1ntegrat1ng the B1ot-Savart equat10ns.
• This method, used here, is much siI:lpler to apply by c~mpar1son to vortex lattice methods.
• The tansential conponent of w 1S related to the bound circulat10n through Prandtl's t1P loss factor F. Reference 1 shows that this closed fo~ approxination to Goldstein's y~ppa factor g1V~S predicted results very close to those obta1ned using l-appa.

LOADS

• The prediction of unsteady aerodynam1C loads builds on the steady cnse.
• And body interference, the propell~r operates in a velocity field which varies both radially and c1rcumferentially.
• The approach taken here is to express the axial and tangential velocity components relat1ve to the propeller at a g1ven rad1US a~ the sum of harMon1cs of ~, the aZ1muth angl~.
• That is, (b) Combining VAN and Vrn vectorially, the Nth harmonIC or the velocity vector normal to the steady resultant velOCIty Vet sho~~ in figure 7 , can be ~Titten as, CombinIng equatIons 8 and 9 gives, (8) 0.0).

wc k .. 2V

• Here w is the ':1rcular frequency of th~ harmonic heaving notion which in th1s case is equal to the rotational speed of the propeller.
• Thus, equation 16 relates the amplitude and phase of che unsteady section left, L, to the heaving velocity h. ~!s the angle by which the lift force leads h. Substitut1ng V~1~ (equatlon 10) for h thus leads to the aMplitude a,d phase for the sect10nal unsteady lift on the propeller bJade.
• The computer program which accomplishes the foregolng 1S described 1n reference 1.
• Generally, the first narmonic is the predominant one.
• In the results to follow, only the first two harmonics are used although the program is capable of handl1ng up to eight.

RESULTS OF m~STEA.UY AIRLOAD CALCULATIONS

• And first solv1ng for the steady loads in order to get (~ + ai), the rcsults presented in figures 9 and 10 were obta1ned.
• ~CT' the increment in the thrust coefficient due to the unsteadiness is defined in accordance ~ith standard term-1nology as, (18) Three curves are sho~~ on the gr:ph.
• The fuselage is cut off behind the co~11ng and replaced by a smaller afterbody whi~h can be def1ned US1n3 fewer panels.
• Using draw1ngs of the p~opeller for the Cherokee 180 propeller supp11ed by the manufacturer and the calculated veloc1ty field.
• These results are typical of those to be found 1n the N~_CA reports sHch as re;t:.:ence 10.

PROPELLER BLADE D\~A}I1 CS

• The unsteady aerodynamIc.. forces just disc~ssed ~111 exc1te a d)nam1c response from the propeller blades.
• The obJect of trl.S study, which has been acco-npll.shed, \13S to develop a method for predictl.ng the normal modes of ~ibration for a propeller f"r the case where the bub is rigidly clamped.
• Sl.nce prope!ler blades ure very stiff in plane and torsionally the lO'Jcr modes of lohe coupled bending-bending and coupled bending-torsloon modes have approx~tely the same irequencies which are determined principally by the relatively soft flapwise (out of plane) bendlng stiffness.
• The relationsh~ps on which the co~puter program for deter~ining th~ nor~l nodes are based are too lengthy to be presented here.
• ~ith the hub clacped, the predicted frequencIes for the first codes for coupled bend1ng-bendln b and coupled bending-torslon are nearly equal and close to the frequency Measured for the cantilevered ~lade.

SL'!-:!-IAR"l

• A study of the aerodynaclcs and dYnamics of propellers for general aVlatlon aircrr.ft has resulted in the development of three computer progr.:.'!!.
• In addition, user's ~aduals are currentl~ belng prepared together with program listings 1n FORTR.
• ~riefly these programs B calculate the velocity field in the propeller plane for a wing-fusclagenacelle cocbinatio.l, e pr~dict the steady and unsteady propeller aerodyna~lc loaes, o predict the natural mode &hapes and freqLen~ies for the propeller up to th'! fust four nodes.
• A norr.~l ncdes app'~ach WIll probably be tried to accomplIsh thIS challenging task.

Figures

FIG. 3 VELOCITY DIAGfW1 FOR BlADE SECTION

FIG. 11 PREDICTED AZII11TI1AL DISTRlBlJTI'J:: OF AXIAL NlD TNlGF.rITIAL VELOCITIES Ii~ WE PRO~ELLER Pf.J\J:E

Table 1

FIG. 5 CCM?ARISON OF PREDICTED AND MFASURED POV~R COEFFICIENT AT 2000 R,P,M,

FIG. 1 PANELING OF BODY SURFACE

FIG. 14 CO"PNHSON OF AZIt~.AL DISTRIBlJTIo:JS OF AXIAL VELOCITY W THE PRC?ELLER PU..JJ!: OF A PIPER

FIG. 6 VIS'I OF PROPELLER LOOKING IN DlRECTI01J OF FLIGHT

FIG. 13 HAP';'O:HC CO:HENT OF TIiE TA'!S8JTIAL VELOCITY DlsTRrBUTrorl III TI1::: PROPC:LUR PUJ:E O?E;:IATWG W mE FLa.t FIELD CF

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---
- -
----------
(NASA-CR-1S8111)
THE
ANAlYSIS
OF
PROPELLERS
879-16851
TNCLUCING
IN7ERAC~IOn
EFFECTS
(Pennsylvania
State
Univ.)
38
p
HC
A03jFI'I
A01 CSCL
02A
uncI
as
G1/07
14069
Tne
Analvsis
of
Propellers
Includ1nr
Interaction
Effects*
B. i-:. l-lcCormick
Professor
and Head
Departcent
of
AeTJSpaCe
Engineer1ng
The
Pennsylvanil'
State
Unlverslty
A.
S.
Aljabri
Graduate
Assistant
Department
of
Aerospace
Engineerlng
The
Pcnnsylvan13
State
Un1versity
s.
J.
Ju:nper
Graduate
Assis:ant
Departcent
of
Aeros~~L~
EngIneering
The
Pennsylvania
State
UnIversity
z.
N.
l-:artInovic
Graduate
Assistant
Department
of
Aerospace
EngineerIng
The
Pennsylvania
State
University
~ThlS
~ork
~a5
perfor~ed
under
N;SA
Grant
NSG
1308
I
\
I
;
)
----------~----~.--.------------------------------------------~----------~

· ,
AB~TRAC1
Analytical
and
exper~mcntal
stud~es
have
been
undertaken
on
propellers
operatinl!
in
the
unsteady
flou
field
produ~cd
by
lnter-
action
effects
due
to
the
fuselage,
w~ns.
and
nacellcb.
Methorls have been
developed
and
verified
exper~mcntally
for
determ~n~nl!
the
velocity
f~eld
~n
Wh1Ch
a
propeller
operates
as
well
as
its
aerodynaolc
and
dY:lam~c
r~
sponse
to
th~s
unsteadv
env~ronment.
Methods
are
presented
for
pred~ctinl!
the
net
thrust
of
a
prrypeller-~~ng-bodv
comb~nat~on
as
well
as
the
unsteady
tnrust
and
torque
act~nl!
on
the
propeller.
Saople
calculat~c:ls
as
well
as
wind
~unnel
dn1
flight
test
results
are
presented
WhlCh
illustrates
tne
sensitivlty
of
a
propeller
to
the
flow
field
in
WhlCh
it
is
operatmg.
$OJ
B.
H.
r-:cCorrlick
la

:
TIlE
AERODi1MHIC
AIm
Dn:M!lC
BEHAVIOR
of
pro-
pellers
for
gcncrdl
dV1alion
alrcraft
are
of
1cportance
to
the
operatlon
of
tnesc
a1rcraft.
A
propeller
~hich
is
poorly
matched
to
its
flo~
f1cld
or
eng1ne
can
be
~nefficlcnt
ane
subJect
to
exceSS1VC
vlbratory
strOesses.
The
study
rf
propeller
aerodynam1cs
and
dynamlcs
described
here
1S
div1ded
mto
three
parts.
The
f1rst
part
deals
with
predict~ng
the
flo~
f1eld
~n
~hich
the
propeller
1S
to
operate.
Here.
a
nucer1cal
~ethod
lS
descr1bcd
for
calculat1ng
the
veloc1ty
vector
at
any
radlal
and aZLCuthal
10cat10n
In
~he
propellcr
plane
as
a
function
of
wlng-fuse!age-nacclle
~eo
metry.
The
second
part
treats
botn
the
stcady
and
unsteady
nirloads
produced
by
the
propeller
blades
mov1ng
through
the
spatially
varying
velocity
field.
The
third,
and
final
section,
examines
the
structural
dynam1cs
of
the
blades
and
presents
methods
for
predic~
ing
the1r
normal
u.odes.
In
essence
thlS
paper
is
a
brief
sucmary
of
references
1.
2,
and
3.
For
more
details.
a
study
of
these
references
is
reco~~ended.
PROGRAlI
FOR
PREDICTION
OF
PROPELLE~
FLOW
FIELD
Potential
flow
methods,
at
least
for
tractor
propellrrs,
will
accurately
predict
the
velocity
field
in
whlch
a
propeller
operates
since
the
effect
of
viscosity
ahead
of
a body
is
usually
negliglble.
Ho~cver.
even
~ith
the
simpllflcatlons
afforded
by
potentlal
flo~,
the
calculations
for
a
fuselagc-wlng
conbination
can
prove
tedious.
Therefore,
part
of
thlS
study
investigated
the
accuracy
with
whic~l
one
needs
to
codel
the
cocplete
alrcraft
geo~etry
1n
order
to
obtain
a
sufficiently
preclse
velocity
field
at
the
propeller
p'ane.
!.L'!SR1CAL
l-10DEL
~e
s 5
Following
the
lead
of
references~
(5J
the
fuselage
surface
15
dlvided
into
a
~~unber
of
small
panels
as
lllustrated
In
a
\
1&
g~neral &~nse
ln
fi£ure
1.
Each
panel
15
\'J,')
JV)l
covered
"nth
a
const<lnt
dlc;tributed
source
strcngth
per
un1t
area
d~noted
by
0(1).
The
velocity
Induce~
by
the
Ith
panel
on
the
B.
W.
McCor~ick
surfnce
of
tl,at
pan~l
directed
(Jut1.:a
r
d and
noroal
to
the
panel
at
the
control
point
""ill
be
gl
ven by
Ib
.
''''
...,

\'
..
9..lli
.'
?
,.
-
(l)
For
an\'
other
panel,
sav
the
Jth
panel.
the
total
source
strpngth
over
the
panel
1S g1ven
by
Q(J)
..
e(J)
S(J)
(2)
In
order
to
calculate
the
velocity
induced
at
the
Ith
panel
by
Q(J),
Q(J)
1S
taKen
to
be
a
p01nt
source
located
on
the
Jth
panel
control
point.
Lett1ng
~(J)
denote
the
veloc1ty
potential
assoc1ated
~ith
Q(J)
and
N(I),
the
unit
vector
normal
to
the
Ith
panel
and
d1rected
outwdrd.
the
veloc1ty
induced
by
Q(J)
nor~~lly
out~ard
at
the
rth
panel
~1~
be
VN(I,J) -
grad
¢(J)
• N(I)
If
V
is
the
free-stream
velocity
vector
and
V~(I)
is
the
wing
induced
veloc1ty
vector
at
the
Ith
panel.
the
cocponents
of
these
vectors
normally
outward
at
the
Ith
panel
control
point
will
be
v •
HeI)
and,
V
(I)
• N(I)
w
Th~
norIllal
velocity
must
vanish
at
panel
I
1f
it
is
a
solid
bounda~y
or
nust
eq~al
the
specified
through
veloc1ty,
q.
norMal
across
tne
papel
if
it
1S
a
rela~ed
boundary
Wh1Ch
faodels a
regIon
of
through
flow.
SatisfYIng
the
approprIate
boundary
condItIon
on
panel
I,
it
follows
t~at
N
V •
N(I)
+ Vw(I) •
N(I)
+
a~I)
+ I VN(I.J)
J=l
(3)
- { 0
(~olid
bou~dary)
J 1
I)
- q
(relaxed
boundary)
(
(4)
For a
point
source
of
strength
Q.
:he
velocIty
potential
1a
gIven
by,
where r
is
the
~adial
dIstance
froc
the
source.
~~------------
(5)
B.
W.
HcCormick
2
-
•