UAS Propeller

8/11/2019 UAS Propeller

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American Institute of Aeronautics and Astronautics

1

Passively Varying Pitch Propeller for Small UAS

Stearns B. Heinzen 1 North Carolina State University/ AFRL SCEP, Raleigh, NC, 27695

Charles E. Hall, Jr. 2 and Ashok Gopalarathnam 3 North Carolina State University, Raleigh, NC, 27695

A novel design for a passively-varying pitch propeller to improve small UASperformance is examined. The proposed system uses propeller blades free to pivot on aradial axis and blade cross sections tailored for positive pitching moment to achieve stableand efficient operation over a large advance ratio range. Computational analysis of thepassively-varying propeller system indicates that large improvements can be gained,especially at high advance ratios, while sacrificing very little low speed performance. Aproperly designed propeller will enable a much expanded flight envelope and, with properlimits to rotation angle, good takeoff/ climb performance and automatic feathering in theengine off case. Experimental analysis to corroborate computational findings is currentlyunderway.

Nomenclature = blade mean aerodynamic chord

cr = local chordCd = local sectional drag coefficientCl = local sectional lift coefficient curve slope (dC l/d)CMo = zero lift pitching moment coefficientCM = pitching moment coefficient slope (dC m/d)dCm/dC l = pitching moment slope with C L (also S.M.)I = Mass inertia of blade about blade pivot or disk about motor shaft

J = Advance Ratio

2

M = pitching momentn = propeller rotations per secondq = dynamic pressurer = local element radiusR = propeller radiusRPM = rotations per minuteS = planform reference areaS.M. = static margin referenced to pitching axis and blade aerodynamic centerUTOT = total local velocity axial and rotationalU = freestream velocitywf = weighting functionxa.c. = section aerodynamic center location in chordwise directionXa.c. = propeller blade aerodynamic center in chordwise directionX rotation = blade pitching axis location in chordwise direction = local section angle of attack = local section pitch (twist) angle = blade rotation angle = propeller efficiency

1 Lecturer, Mechanical and Aerospace Engineering/ AFRL SCEP, [email protected], Member AIAA.2 Associate Professor, Mechanical and Aerospace Engineering, [email protected], Associate Fellow AIAA.3 Associate Professor, Mechanical and Aerospace Engineering, [email protected], Member AIAA.

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-62

Copyright 2010 by Stearns Heinzen, Charles E. Hall, and Ashok Gopalarathnam. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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= blade rotation = total to freestream velocity ratio = atmospheric density = torque, shaft or absorbed = local flow angle, corresponding to U TOT = angular velocity (disk)

I. Introduction N the past decade the flight hours flown by unmanned systems in the military arena have grown at anunprecedented rate; the next decade will see a similar pattern in the civilian realm. 1 Small unmanned aerial

systems (UASs) in the 5-350 lb range fall into a region where, although navigation, control, and many avionicssystems have become sophisticated, the propulsion systems largely utilize retrofitted R/C and ultralight equipment.Consequently, new high performance airframes often rely on relatively primitive propulsive technology. This trendis beginning to shift with the recent advances in small turboprop engines, fuel injected reciprocating engines, andimproved electric technologies. Although these systems are technologically advanced, they are often paired withstandard fixed pitch propellers. To fully realize the potential of these aircraft and the new generation of engines,

propellers which can efficiently transmit power over wide flight envelopes and a variety of power settings must bedeveloped.

This is done easily on large aircraft that employ variable-pitch constant speed propellers, allowing the aircraft an

expanded flight envelope without significant losses to propeller efficiency. However, the complexity and addedweight of this type of system prohibit use on a small aircraft. To gain the performance advantage of a variable-pitch propeller, while not exceeding the weight constraint of a small UAS, a system is envisioned that weighs onlymarginally more than a fixed pitch propeller but achieves many of the advantages of variable-pitch propellers.

The proposed system is comprised of a propeller designed to passively adjust to the incoming airflow such that itdoes not experience blade stall in low-velocity / highly-loaded thrust cases, and is not prone to overspeeding at highflight speeds. The propeller will incorporate blades that pivot freely on a radial axis and are aerodynamicallytailored to attain and maintain a pitch angle yielding favorable local blade angles of attack, matched to changinginflow conditions. This blade angle is achieved through the use of reflexed airfoils designed for a positive pitchingmoment, comparable to those used on many tailless flying wings (Figure 1). By setting the axis of rotation at a pointforward of the blade aerodynamic center, the blades will naturally adjust to a predetermined positive lift trimcondition; then, as inflow conditions change, the blade angle will automatically pivot to maintain the same anglewith respect to the incoming air.

Figure 1: Propeller with Reflexed Airfoil Section for positive C Mo

Blade loading in the thrust and drag directions has been well analyzed and documented. 2 The current work willfocus on the blade pitching moment, which plays an important role in this effort. To find the blade pitchingmoment, integration is performed from the blade root to the tip:

12 The variables in the integrand include blade chord, local velocity, and pitching moment; all of which are likely

functions of radial position. The moment coefficient can be further divided into its elementary linear parts.

12

I

(1)

(2)


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Cm0 is the zero- pitching moment of the local airfoil section, governed by the airfoil geometry; and C m is thelocal pitching moment variation with angle of attack, governed by the location of the axis of rotation relative to thelocal airfoil aerodynamic center. For simplicity we assume that the same airfoil is used throughout the propeller andthat the moments are taken about the pivot axis, which is held at a constant percent of chord. This results in constantCm0 and C m along the blade:

12

12

At the design condition, each element along the blade will be at an identical design . As the speed of theaircraft or engine rpm changes, the local angles of attack will change. Assuming a radially-constant axial inflow andnegligible induced changes to the inflow angle; non-dimensionalizing the blade pitching moment with respect tofreestream dynamic pressure, blade mean aerodynamic chord and blade reference area yields:

_ tan This relationship represents the propeller blade pitching moment coefficient for a fixed pitch propeller with static

distribution. To model a varying pitch propeller, another term, representing the rotation of the blade from itsdesign orientation, , is added:

_ tan where the local angle attack is represented by the term:

tan Equation 5 describes the pitching moment coefficient of the propeller blade as a function of the advance ratio.

Given the flight conditions and the basic properties of the propeller blade, the relationship between the pitchingmoment and the blade rotation, , can be calculated.

The case of interest in this investigation is a propeller blade mounted such that it is free to pivot about a radialaxis. The blade is mounted with the blade center of rotation forward of the blade aerodynamic center, thussatisfying static stability requirements. Based on equation 5, for a passively varying blade to trim (C M=0) at a

positive angle of attack (positive C L) C M0 must be positive for a negative C M, requiring a reflexed airfoil section.To find the trimmed pitch variation, the C M equation is set to zero and solved for in terms of advance ratio. Tofacilitate this the blade aerodynamic center can be found as with the neutral point for an aircraft configuration.However, because the tips of the propeller are traveling at velocities significantly higher than sections inboard, themean aerodynamic chord, , along with other planform constants must be redefined. This is accomplished throughthe use of a non-dimensional weighting function which captures the radial velocity variations (neglecting inducedvelocities):

1

Using the weighting function to redefine the and S of the propeller planform constants yields:

1 1

1

(3)

(4)

(5)

(7)

(6)

(8(a/b))


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Assuming a constant lift coefficient and defining an aerodynamic center for the propeller in the same fashion as for a3D wing 3,4.

. .. 1 . .1

This describes the effective aerodynamic center after incorporating the effects of radially varying velocities. Theorigin of aerodynamic center x-location is the same as that of the local x a.c. in the integrand. Using the definedaerodynamic center x-location the pitching moment is expressed in terms of the lift curve slope and the propeller

blade static margin:

. . Assuming that the lift coefficient along that blade is relatively constant at the design condition:

. .

. . . .

. . . . This gives the static pitching moment in terms of the redefined and under the assumptions previously stated.

The definition for static margin is the same as a conventional wing but incorporates the redefined planformconstants. Due to the inclusion of the weighting function it should be noted that the reference values and staticmargin are not constant for a given geometry, as they would be on a finite wing; rather, they vary with advance ratioacross the operating envelope.

II. Computational AnalysisDue to the difficulty in finding an analytic solution to a specific propeller without making a significant number

of simplifying assumptions, available propeller analysis codes were surveyed to serve as a base for a computationaltool. There are several available codes, based on the classic blade element formulation, which can be used toanalyze conceptual or existing propellers. Some of these codes assume linear aerodynamic coefficients with definedranges, others use airfoil data in the form of drag polars.

Two candidate codes were considered. The first is QPROP 5, developed by Mark Drela at MIT. This codeemploys an extension of the classic blade element/ vortex formulation 6. QPROP takes, as input, linear coefficientvalues for lift and drag with a defined linear range. Estimates for changes to the coefficients due to Reynolds andcompressibility effects are also included. The second code was developed at the Air Force Research Labs (AFRL)and uses a blade element model coupled with momentum calculation 7. Inflow is modeled as purely axial and can beset as radially uniform or varying. The AFRL code uses drag polars for the blade cross sections at various Reynoldsnumbers to determine aerodynamic performance along the blade. Results from the codes were compared to datacollected by AFRL at the NASA Basic Aerodynamics Research Tunnel (BART) and at the AFRL Vertical WindTunnel. Both codes match experimental data and each other fairly well. The correlation between the codes andexperiment is best for data at higher Reynolds Numbers and breaks down at lower Reynolds number, especially forRe on the order of 30k or less (Figure 2).

(9)

(10)


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Figure 2: Computational and Experimental Performance for Graupner 10x8 (left) and APC 18x14 (right)For pitching propeller analysis a code with the desired combination of functionality was assembled using QPROPas a base, modified to include pitching moment calculations and an outer loop to iterate blade rotation ( ). TheGraupner 10x8 propeller, tested by AFRL 7 in the NASA BART, was chosen as a first test case. Drag polars used inthe AFRL code analysis were used to extract the necessary linear aerodynamic coefficients. Assumed pitchingmoment characteristics were also applied corresponding to a C M0 of 0.06 and a dC M/dC L of -0.10, yielding a 2Dequilibrium lift coefficient of 0.6. This code was run in a variety of configurations; first, at a variety of fixed angles, yielding a family of curves, each similar to those in Figure 2. Then over a range of advance ratios with a outer loop to solve for equilibrium blade angles through a Newton iteration on pitching moment. Co-plotted thisshows the envelope expansion potential of the passively varying pitch propeller (Figure 3). Figure 4 shows the data

plotted with the experimental fixed pitch data and with the equilibrium angles. The analyses indicates that overthe specified range of advance ratios, 0-2, the blade rotates from an equilibrium of -0.25rad (-14 deg) to 0.42rad(24deg) (Figure 4). Throughout the rotation the passively-varying pitch propeller maintains efficiencies near the

peak of an appropriately matched fixed pitch propeller. Although, for this propeller, improvement in performance atlow advance ratios is less significant, the envelope at higher advance ratios extends in a near constant manner.

Figure 3: Graupner Propeller at Fixed (red) and Free-to-Rotate (blue)

J

P r o p e l l e r E f f i c i e n c y ( )

0 0.25 0.5 0.75 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1APC18x14E QpropAPC18x14E AFRLAPC18x14E VWT

J


0 0.25 0.5 0.75 10

0.1

0.2

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0.5

0.6

0.7

0.8

0.9

1GR10x8 Q propGR10x8 AFRLGR10x8 BART

J (V/nD)


0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-10 o = -15 o -5 o 0 o 5 o 10 o 15o

20 o


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Figure 4: Graupner Free-to-Rotate Compared to Fixed Pitch Computational and Experimental

Figure 3 indicates that as the propeller operates at lower advance ratios the benefits of varying pitch maydiminish, such that a propeller free to pivot in the positive direction (nose-up) may yield tangible benefits, while thefreedom to pivot to large negative angles adds little. Further, limiting nose down rotation allows the designer toachieve higher thrust levels, albeit at reduced efficiency, during low speed, high power flight, such as take off or

perching maneuvers.A further consideration is that of engine-propeller matching. As flight velocities increase, the increasing

dynamic pressure along the propeller blade increases the torque necessary from the driving shaft to maintain a givenengine RPM. This means that the dimensional loads on the engine shaft, increasing with flight speed, could slowthe engine and cause it to operate outside of a desired power band. Blade sweep was incorporated in thecomputational analysis to reduce RPM variability in a matched system by unloading blade C L at high advance ratios(high speeds) and increase blade C L at low advance ratios (low speeds). Sweep was defined by specifying a percent

blade chord to be held straight. The blade aerodynamic center, mean aerodynamic chord, and desired static marginvalues were then used to locate the pivot point. Using this process a second set of test propeller geometries wasdeveloped using a modified Eppler airfoil, an 18 disk diameter, and several sweeps.

For the unswept blade, with the rotation point set at 10% chord, it can be seen that the overall C L does notsignificantly change with advance ratio (Figure 5). The inboard section unloads and the outboard loads as J isincreased, which, given higher flight speeds, will increase the load on the motor. However, by sweeping the blade

back we can change in this behavior. In the case of the blades swept using 50% and 80% as unswept chord lines, wecan see that as advance ratio increases and the inboard unloads, the outboards loads at a much lower rate. From theengine propeller matching perspective this allows the designer to tailor the propeller to unload at higher speeds sothat the motor does not become bogged down, and operate at RPMs below its power band.

The performance result from blade sweep is due to the changing ratio of freestream and rotational velocities; thisdrives aerodynamic center and mean aerodynamic chord, but also affects the lift distribution along the blade. Asadvance ratio increases, the weighting function in equations 8a and 8b begins to weight the inboard section of the

blade more heavily. As this happens, the lift distribution begins to skew towards the propeller tips (Figure 5). Fora swept blade the changes to equation 8a, 8b, and 9 have the effect of moving the blade aerodynamic center forward,reducing static margin, but this effect is overpowered by the increased loading on the propellers tips, which, due tothe sweep, have a large x a.c.. The combination of higher C L loading at the tips, and the higher x a.c. of the tips, causethe blade as a whole to rotate nose down, unloading the blade at higher advance ratios.

J (V/nD)


B l a d e R o t a t i o n (

- r a d i a n s )

0 0.5 1 1.5 20

0.1

0.2

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0.5

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0.9

1

-0.2

-0.1

0

0.1

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0.5

Stock Fixed Pitch GR10x8

GR 10x8 Free to Rotate C Mo=0.04, C M=0.08

GR 10x8 BART Data

Blade Angle Offset - Free to Rotate


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Figure 5: Local Blade AOA Variation w/ J Effects of Sweep

III. Dynamic Simulation

Having evaluated the static equilibrium behavior of the propeller a dynamic model was built to examine the behavior of the 80%c rotation point (Figure 5) propeller with changing flow conditions and engine power inputs.The equation of motion for the blade is a 2 nd order equation with nonlinear terms. The disk equation of motion is 1 st order with nonlinear terms for motor torque and torque load:

0

Inertias of the disk and blades were estimated using a solid model of a candidate propeller, the damping termswere assumed to correspond to constant mechanical damping in the system and thus not dependent on flowconditions. Input torque, , was modeled using two simplified models corresponding to electric and internal

combustion motors:

_ 1 _ 1 Given the size of the propellers being investigated, the motor model coefficients were set for powers of about 2hpand maximum speeds ( ), of 7.5-8.0 kRPM.

r/R

( d e g )

0 0 .25 0 .5 0 .75 1-2

0

2

4

6

8

J=0.52 50%cJ=0.79 50%cJ=1.05 50%c

r/R

( d e g )

0 0 .25 0 .5 0 .7 5 1-2

0

2

4

6

8

J=0.52 80%cJ=0.79 80%cJ=1.05 80%c

r/R

( d e g )

0 0 .25 0 .5 0 .75 1-2

0

2

4

6

8

J=0.52 10%cJ=0.79 10%cJ=1.05 10%c


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The simulation velocity profile is user defined to investigate responses to a variety of inputs. For the followingcases the velocity profile was kept constant as shown in Figure 6. This profile was chosen to demonstrate thesystem response to ramping and a step inputs in velocity.

Figure 6: Candidate Velocity Profile

The first case, Figure 7, was run with the pitch angle held constant to demonstrate the expected performance ofthe candidate propeller geometry if the blades were not allowed to rotate. The plots show the initial angularacceleration to an equilibrium RPM and then, as velocity is ramped from 40 to 160 fps, the increase in propeller rpmand corresponding decrease in absorbed torque as the propeller unloads. A new equilibrium is established after theramp and then a step in the input velocity results in a further increase in RPM indicating that the propeller has begunwind-milling (Load < 0).

Figure 7: Fixed Pitch Simulation with Velocity Ramp and Step - Electric Motor Model

The simulation was then run with the blades free to rotate with both the electric and internal combustion motormodels. In both cases, as the propeller disk accelerates, the blades pitch down in response to the reducing advanceratio until they reach equilibrium, at a of approximately -0.1 radian. Then, as the velocity ramps to 160, bladeangles increase as they adjust to the changing inflow conditions. The velocity step at 8s causes small transient whichis quickly damped, before returning to nearly the equilibrium RPM and load from before the step. Over the entiretransition, from an inflow of 40 fps to 200 fps, the equilibrium load absorbed by the propeller and RPM change verylittle, and the blade angle adjusts from -0.1 radians to just over 0.2 radians (Figure 8, Figure 9).


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Figure 8: Varying Pitch Simulation with Velocity Ramp and Step - Electric Motor Model

Figure 9: Varying Pitch Simulation with Velocity Ramp and Step - IC Motor Model


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Thrust output from the simulations shows that at low flight speeds the varying propeller thrust levels are a littleunder those of the fixed pitch propeller. This indicates that either, pitching moment characteristics of the propellershould be adjusted to result in a somewhat higher equilibrium pitch angles, or, that pitch angle rotations for thisgeometry should be limited to positive angles, forcing higher angles, and therefore higher loading at low advanceratios. At higher flight speeds the benefits of the varying pitch propeller becomes apparent as the fixed pitch

propeller thrust goes down and eventually negative at high speeds. The varying pitch propeller, at relativelyconstant torque and RPM, produces relatively constant power output and therefore positive, although reducing,thrust as velocity increases.

Figure 10: Thrust Performance - Varying Pitch (green) and Fixed (blue)

IV. Experimental ValidationTo correlate computational predictions with experiment, a test article is currently in design and construction.

The propeller will have an overall diameter 18 and a relatively large chord to facilitate placement of the axis ofrotation. The propeller is designed with the primary goal of wind tunnel testing in the North Carolina StateUniversity (NCSU) Subsonic Tunnel. There exists the potential to subsequently test the propeller in flight on avehicle currently in the construction phase at NCSU.

ConclusionAn analysis of a propeller with free-to-pitch blades was conducted using classic blade element methods. The

study shows the potential to significantly expand the efficient envelope of propeller performance as compared to thefixed pitch propellers currently used on most small unmanned systems. This improvement will allow small aircraftto fly over expanded envelopes, more efficiently, without sacrificing on-design performance. An analysis of thethrust output of varying pitch vs. constant configuration indicates that, depending on the airframe, motor, andmission it may be beneficial to limit blade rotations to some minimum angle, to allow the propulsion system toattain higher thrust levels at low speeds.


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AcknowledgmentsThe authors would like to thank the Air Force Research Laboratory, Dayton OH for their sponsorship during

much of this work. They would also like to thank Jason Bishop at NCSU for his assistance in the design, modeling,and calibration of the NCSU propeller load cell.

References

1Unmanned Aircraft Systems Roadmap 2005-2030 , Office of the Secretary of Defense, 2005.2 Weick, Fred, Aircraft Propeller Design, McGraw-Hill Book Company, Inc, New York, 1930.3 Etkin, Bernard, Dynamics of Flight Stability and Control, 2 nd Edition, John Wiley and Sons, Inc, New York,1982.4 Kuethe, Arnold, and Chow, Chuen-Yen, Foundations of Aerodynamics: Bases of Aerodynamic Design, JohnWiley and Sons, New York, 1986.5 QPROP Propeller/ Windmill Analysis and Design, Software Package, Ver1.22, MIT, Cambridge, MA 2007.6Drela, Mark, QPROP Formulation, http://web.mit.edu/drela/Public/web/qprop, MIT, Cambridge, MA(unpublished)

7 Ol, M, Zeune, C; and Logan, M, Analytical Experimental Comparison for Small Electric Unmanned AirVehicle Propellers, AIAA Applied Aerodynamics Conference , AFRL, 2008.

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UAS Propeller