The analytical approaches as well as the capabilities of three advanced analyses for predicting propeller aerodynamic performance are presented. It is shown that two of these analyses use a lifting line representation for the propeller blades, and the third uses a lifting surface representation

Bober, L. J.

English

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ADVANCED PROPELLER AERODYNAMIC ANALYSES
Lawrence J. Bober
National Aeronautics and Space Administration
Lewis Reasarch Center
SUMMARY
Three advanced analysis methods for predicting the aerodynamic performance
of propellers are presented. Two of these analyses are lifting-line methods,
and the third is a lifting-surface method. The approach used in each of the
methods is described, and the capabilities are presented.
INTRODUCTIO N
Increased concern over fuel cost and availability have fostered renewed
interest in propellers for aircraft propulsion because of the propeller's inher-
ent high efficiency compared with a turbofan. The quest for improved efficiency
and lower noise at high subsonic flight speeds at 30 000 feet or more has forced
propellers away from conventional designs toward the type shown in the previous
paper. The combination of high flight speed and high rotational speed has re-
suited in propellers with a large number of highly swept blades having signifi-
cant cascade effects in the inboard region of the blades. Carefully contoured
nacelles contribute to the already complex flow field associated with the pro-
peller. These radically different geometries and the complex flow fields they
cause cannot be adequately analyzed using conventional aerodynamic performance
analyses. To overcome the shortcomings of established approaches to propeller
performance predictions, advanced propeller aerodynamic analyses are being de-
veloped as part Of NASA's Advanced Turboprop Program.
This paper will discuss three advanced analyses currently under develop-
ment. Two are lifting-line analyses in which each blade is represented by a
single line of vorticity. The third is a lifting-surface analysis in which each
blade is represented as a solid surface. Although these analyses were developed
for the kinds of propellers described in the previous paper, they have features
that are applicable to both low and high-speed general-aviation propellers. Be-
fore discussing the advanced analyses, an established approach to propeller per-
formance prediction will be discussed.
ESTABLISHED APPROACH
In a velocity potential solution for the flow around a propeller, the non-
uniform spanwise loading on the blades causes a sheet of vorticity to extend
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downstreamto infinity as shownin figure i. This vortex wake is shownas a fi-
nite numberof filaments, but could more accurately be represented as an infi-
nite numberof vortex filaments. The vortex wake is important in propeller
performance prediction since it causes an induced velocity at the propeller,
thereby changing the local blade angle of attack.
The important features of this established approach are summarizedin fig-
ure i. Calculation of the induced flow in this approach is based on the work
done by Goldstein (ref. i) about 50 years ago. Becauseof the limited computing
capability at that time, Goldstein used a very simplified model so that he could
obtain an analytical solution for the induced velocity at the propeller due to
the wake. He assumedthat the shape of the wake was a rigid helix which was
known to correspond to a lightly loaded propeller with optimumdistribution of
loading. To visualize a rigid helical wake, consider a plane normal to the axis
of revolution of the propeller. The intersection of this plane with the rigid
helical wake is a straight line. Another feature of this wake shape is that the
pitch of the helix does not changewith axial location. (This wake is shownin
fig. I.) Goldstein published results for single rotation propellers (ref. I),
and Theodorsenobtained results for coaxial counterrotating propellers using an
electrical analogy (ref. 2). The induced velocities obtained from the Goldstein
and Theodorsen results are strictly correct only for straight propeller blades.
Also their original works contained no provisions for a nacelle since the vor-
ticity extended to the axis of the propeller. These results form the basis of a
procedure which has been refined over the years and has becomean established
approach to propeller performance analysis.
This procedure is implemented using a strip analysis in which the flow con-
ditions are determined at one radial location at a time. For each strip the
induced velocity is determined from Goldstein's or Theodorsen's results. The
effect of the nacelle is taken into account in an approximate mannerby assuming
that at each strip the induced velocity is the sameas for the entire propeller
operating at the samevelocity that exists at that strip. The total velocity is
then the vector sumof the induced velocity, the local velocity for the isolated
nacelle, and the rotational velocity. The flow velocity and the blade geometry
determine the local blade angle of attack, which allows the determination of the
lift and drag coefficients from isolated airfoil data. Sweepis taken into
account through the cosine rule (ref. 3). These forces are resolved into thrust
and torque componentsthat can be integrated radially to get the propeller
thrust, torque, power, and efficiency.
It is important to note that for any operating condition, the effect of the
wake is assumedto be the sameas for an optimally loaded propeller, even if
there is a nacelle and spinner present.
ADVANCEDANALYSES
Curved Lifting-Line Analysis
The important features of this analysis are shownin figure 2. The wake is
represented by a finite numberof helical vortex filaments instead of the con-
376
tinuous sheet of vorticity used by Goldstein. Each filament has constant pitch,
but its location relative to another is arbitrary as shown in figure 2. At any
point on the blade, the induced flow due to each wake filament and the lifting
line is calculated using the law of Biot-Savart (ref. 3). The total induced
flow at any point is then the sum from all these vortices. This analysis is
currently restricted to single-rotation propellers. The propeller blades are
represented by curved lifting lines of arbitrary shape. The nacelle is re-
stricted to being an infinite cylinder since the wakes cannot contract radially.
The strengths of the wake vortex filaments are related to the spanwise var-
iation of lift on the blade. Thus it is necessary to solve for the blade and
wake vortex strengths simultaneously. An important aspect of the solution pro-
cedure is the placement of the bound vortex at the quarter chord line and the
requirement that the flow be tangent to the mean camber line at the three-
quarter chord line. Thus no isolated airfoil data are needed since the lift at
any radius can be determined from the vortex strength at the same radius. How-
ever, this approach cannot predict the blade drag. This analysis has been de-
veloped by Sullivan (ref. 4) at Purdue University under a grant from NASA Lewis
Research Center.
An interesting application of this analysis is shown in figure 3, which
shows the effect of proplets on propeller performance. A proplet is an aerody-
namic device at the tip of the propeller blade similar to winglets, which have
been shown to increase the lift-to-drag ratio of wings. If the proplet is prop-
erly integrated into the tip flow field, an improvement in performance as shown
in figure 3 can be obtained. The plot shows the predicted efficiency as a func-
tion of power coefficient for a propeller with and without proplets. The re-
suits show an increase in efficiency due to the proplets of about i percent at
low power and about 3 percent at high power.
The development of this analysis is continuing both at Purdue and at
Lewis. Radially varying inflow velocities will be included to better account
for the nacelle. A drag prediction procedure using isolated airfoil data will
be implemented so that the effect of blade drag can be included.
Propeller Nacelle Interaction Analysis
The second advanced lifting-line analysis has more extensive capabilities,
which are summarized in figure 4. This analysis was developed by United Tech-
nologies Research Center (ref. 5) under contract to Lewis. The wake is repre-
sented by a finite number of vortex filaments that are located on stream sur-
faces so that they conform to the shape of the nacelle. The pitch of these
filaments is not constant, and they can contract in both the axial and radial
directions. This capability is clearly shown in figure 4 just downstream of the
propeller where the wake filaments are displaced radially because of the in-
creasing nacelle diameter. This analysis is capable of analyzing both single
and coaxial counterrotating propellers. The blades are represented by lifting
lines and can have any arbitrary shape. The nacelle can be any axisymmetric
shape.
377
The solution procedure in this analysis is as follows. First an inviscid
solution for the nacelle alone is obtained. The results are used to locate the
wake vortex filaments along stream surfaces and to determine the radially vary-
ing inflow for the propeller. The induced flow at the propeller due to each
wake filament is calculated using the law of Biot-Savart (ref. 3). The total
induced velocity at any radial location on a blade is obtained by summingthe
induced flow from the individual wake filaments and from the lifting lines. The
blade lift and drag are determined from two-dimensional airfoil and cascade
data. An iteration procedure is required to insure that the wake vortex
strengths are consistent with the spanwise load distribution on the blade. A
final optional step is to use the blade forces in a circumferentially averaged,
viscous, compressible flow calculation.
For a propeller operating at high flight speed or high rotational speed,
portions of the blades may be moving at supersonic speeds relative to the un-
disturbed flow. Whenthis occurs someadditional effects (shown in fig. 5) must
be considered. In a supersonic flow a disturbance in the flow is felt only in a
conical region downstreamof the disturbance knownas the region of influence.
For the propeller shownin figure 5 only the shaded portion of the upper right
hand blade is affected by what happens at the tip of the upper left hand blade.
Thus, when the induced velocity due to the wake is calculated, it is necessary
to limit the region over which each wake filament has an effect. A second con-
sideration is that, when the tip is supersonic, the flow becomeshighly three-
dimensional near the tip due to the tip Machcone. This effect is taken into
account by applying a correction to the lift determined from isolated airfoil
data.
The relative importance of someof these effects is shownin figure 6 where
predicted power coefficient is shownas a function of advance ratio. The dif-
ferent curves were obtained using the samecomputer program but with different
options for each curve to isolate certain effects. The configuration analyzed
was an eight bladed propeller with 30o of tip sweep(denoted as SRI in the
previous paper). The curve labeled "rigid wake" was obtained using a rigid hel-
ical wake without the high-speed effects and is essentially the sameas the re-
suits that would be obtained with the established approach. For the curve
labeled "wake model," the wake filaments were distorted by the nacelle. (The
high-speed effects again were not included.) The difference between the two
curves is solely due to the different assumedwake shapes. The curve labeled
"wake model and high-speed effects" includes the distorted wake and the high-
speed effects described in figure 5. The difference between this curve and the
"wake model" curve is solely due to the high-speed effects. As expected the
largest difference between these two curves occurs at the lowest advance ratio,
which corresponds to the highest tip speed. The high-speed effects cause the
largest changes to the shape of the curves. From comparisons not shownhere, it
was found that the shape of the wake model and high speed effects curve agrees
with the experimental results, indicating the treatment of these effects in the
analysis is qualitatively correct.
Shownin figure 7 are results from the circumferentially averaged, viscous,
compressible flow calculation for the configuration shown in figure 6. Each
curve in figure 7 represents the radial distribution of circumferentially aver-
378
aged swirl velocity at that axial location. The uniform spacing of the curves
aheadof the propeller indicates no swirl is present in the flow. The distorted
curves in the vicinity of the blades indicate that swirl is being introduced
into the flow. The uniform spacing of the curves downstreamof the blades indi-
cates that the swirl persists in the flow. These results from the viscous cal-
culation are used to check fluid velocities between the blades and downstreamof
the propeller. If the velocities are too high, large losses due to shock waves
can occur. These results also give the pressure and viscous drag on the nacelle
in the presence of the propeller. United Technologies Research Center will be
doing modifications and applications of this analysis under a follow-on contract.
Lifting-Surface Analysis
The key features of the three-dimensional, compressible lifting-surface
analysis are shownin figure 8. Also shownare partial front and side views of
the grid on which the flow calculations are performed. The grid actually ex-
tends much further in the radial direction than is shown. The nacelle is re-
quired to be axisymmetric so that the flow between each two adjacent blades is
the same. Thus it is only necessary to solve for the flow between two blades.
The flow is required to be tangent to all solid surfaces and beyond the blade
tips is assumedto be periodic. The equations of motion in finite-difference
form, are solved at discrete points in the grid. The equations that are solved
are the three-dimensional, unsteady, Euler equations, which govern the inviscid
flow of a compressible fluid and can accurately represent the pressure variation
caused by shock waves and the work done by the propeller on the fluid. The
equations are solved by marching in time using an implicit finite-difference
method until a steady state is reached. Nowakemodeling or two-dimensional
airfoil data are required. Viscous effects, however, are not included. This
analysis was developed by Kutler of NASAAmesResearch Center and Chausseeof
Nielsen Engineering and Research and is described in reference 6.
Results from this lifting surface analysis are shownin figure 9 for an
eight bladed propeller having 30° of sweepat the blade tips. The plots show
the distribution of static pressure coefficient on the suction and pressure
surfaces of the blades at three spanwise locations from near the hub to near the
tip. The most significant feature of these results is the predicted shock wave
along the entire span of the blade. At the conditions for which these results
were obtained, experimental data also indicate compressibility losses. The de-
tailed spanwise and chordwise distribution of loading predicted by this code is
important for improved propeller designs from acoustic and structural stand-
points. Developmentof this code is continuing at Lewis.
FUTUREPLANS
The development of these advanced analyses will continue. Initial compar-
isons of the analytical results from all these advancedmethods with performance
data have shownqualitative agreement (ref. 7). However, performance data can-
not substantiate the details of the flow as predicted by the analyses. Thus an
experimental program is planned for the Lewis 8x6 foot wind tunnel in 1980 to
379
provide detailed data for verifying these analyses. A laser velocimeter system
(fig. i0) will be used to make these measurementssince this type of system does
not introduce hardware which might disturb the flow. This experimental program
will define the details of the flow around the blades and upstream and down-
stream of the propeller. These results will pinpoint any deficiencies in the
analyses so that quantitative, as well as qualitative, agreementcan be obtained.
CONCLUDINGREMARKS
Three advanced analyses for predicting propeller aerodynamic performance
have been presented. The analytical approaches as well as the capabilities of
these analyses have been described. Two of these analyses use a lifting-line
representation for the propeller blades, and the third uses a lifting-surface
representation. The detailed flow-field measurementsto be made in the near fu-
ture will provide data for validating the analyses, making them available as
analytical tools for designing improved propellers.
REFERENCES
I. Goldstein, S.: On the Vortex Theory of Screw Propellers. Proc. Roy. Soc.,
(London), vol. 123, no. 792, Apr. 6, 1929, pp. 440-465.
2. Theodorsen, Theodore: Theory of Propellers. McGraw-Hill Book Co., Inc.,
1948.
3. Kuethe, Arnold M and Schetzer, J. D.: Foundations of Aerodynamics. John
Wiley & Sons, Inc., 1950.
4. Sullivan, J. P.: The Effect of Blade Sweepon Propeller Performance AIAA
Paper 77-716, June 1977.
5. Egolf, T. A.; et al.: An Analysis for High SpeedPropeller-Nacelle Aero-
dynamic Performance Prediction. Vol. i - Theory and Initial Application.
Vol. 2 - User's Manual for the ComputerProgram. R79-912949-19, United
Technologies Research Center.
6. Chaussee,D. S.: Computation of Three-Dimensional Flow Through Prop Fans.
NEAR-TR-169,Nielsen Engineering and Research, Inc., 1979.
7. Bober, L. J. and Mitchell, G. A.: Summaryof AdvancedMethods for Predicting
High Speed Propeller Performance. AIAA Paper 80-0225, Jan. 1980; also NASA
TM81409, 1980.
380
ESTABLISHEDAPPROACH
MODEL
WAKE - RIGID HELICAL VORTEX SHEET
SINGLE OR COUNTER ROTATION
BLADES - STRAIGHT LIFTING LINE
NACELLE- NONE
SOLUTIONTECHNIQUE
STRIP ANALYSIS
Figure I
CS-79-4089
MODEL
CURVEDLIFTINGLINEANALYSIS
WAKE - RIGID HELICAL VORTEX FILAMENTS
SINGLE ROTATION
BLADES - CURVED LIFTING LINE
NACELLE- INFINITE CYLINDER
SOLUTIONTECHNIQUE
SIMULTANEOUS SOLUTION FOR BLADE
AND WAKE VORTEX STRENGTHS
Figure .2
CS-79-4088
381
EFFICIENCY
CURVEDLIFTING LINE RESULTS
•94[--_\/-PROPELIFRALONE
I _"_ ,-PROPELLERWITH
.90 L_ _,._PLET
•86-- "-"__ PROP LLER H PR P
•82
i I i I
I.R02 .04 .06 .06 .10g
POWERCOEFF CS-79-4087
Figure 3
PROPELLERNACELLEINTERACTIONANALYSIS
MODEL
WAKE- VORTEXFILAMENTSALONG
STREAMSURFACES
SINGLEOR COUNTER
ROTATION
BLADES- CURVEDLIFTINGLINE
NACELLE- ARBITRARYGEOMETRY
SOLUTIONTECHNIQUE
INVISClDNACELLESOLUTIONTO
LOCATEWAKEFILAMENTS
INDUCEDANGLEOF ATTACKDUE
TO WAKE
BLADEFORCESUSEDIN
ClRCUMFERENTIALLYAVERAGED
VISCOUSFLOW
Figure 4
382
CS-79-4090
HIGHSPEEDEFFECTS
PROPELLER NACELLE INTERACTION ANALYSIS
• :i !•
SUPERSONIC FLOW REGIONS OF INFLUENCE
SUPERSONIC TIP CORRECTION
CS-79-3788
Figure 5
EFFECTOFLIFTINGLINEREFINEMENTS
PROPELLERNACELLE INTERACTION ANALYSIS
POWER
COEFF
2.4
1.6
WAKE MODEL + HIGH
SPEED EFFECTS7
I
-- I
I
_ /
RIGID WAKE -/ '"_,,
8
III _.
WAKE MODEL-" "_
I I I
2.4 2.8 3.2 3.6
ADVANCE RATIO
Figure 6
Moo =0.80
CS-79-4182
383
PROPELLERINDUCEDSWIRLVELOCITIES
PROPELLERNACELLEINTERACTIONANALYSIS
Figure 7
8 BLADES
Moo- O.80
CS-79-3888
3-DCOMPRESSIBLELIFTINGSURFACEANALYSIS
ENTIREFLOWFIELDSOLUTION
3-D EULEREOUATIONS
IMPLICIT FINITEDIFFERENCEMETHOD
CS-79-4124
Figure 8
384
3-DCOMPRESSIBLEIFTINGSURFACERESULTS
STATIC
PRESSURE
COEFF
Moo = 0.8, MTI P -- 1. 15
!
I
F
-SONIC
q,#
HUB MEAN
Figure 9
F
_SUCTION
L •., _u,
..-"PRESSURE
,., SURFACE
1#% # |
TIP
CS-79-2179
LASER VELOCIMETER MEASUREMENTS
Figure 10
CS-7q-37O7
385



Advanced propeller aerodynamic analysis

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