[american institute of aeronautics and astronautics 2nd aiaa "unmanned unlimited" conf....

Hover Performance of Rotor Blades at Low Reynolds Numbers forRotary Wing Micro Air Vehicles

Felipe Bohorquez∗, Darryll Pines†

Smart Structures Laboratory, Alfred Gessow Rotorcraft CenterDepartment of Aerospace Engineering, University of Maryland

College Park, MD 20742

Abstract

Rotary wing Micro Air Vehicles (MAV’s) are especiallywell suited for a broad range of missions that fixed wingMAV’s cannot accomplish. An efficient small-scalehovering rotor is required to make this configurationpractical. Experimental studies show that for a va-riety of rotors at low Reynolds numbers (Re<50,000),poor performance was consistently measured. The cur-rent investigation explores the influence of a series ofparameters such as airfoil shape and tip Reynolds num-ber on the rotor’s performance, as well as the differ-ent stall mechanisms present on different rotor blades.Figure of merit was measured experimentally, and sur-face flow visualization was implemented on the rotorblades with the use of fluorescent oil. A Blade Ele-ment Momentum Theory model of the rotor was usedto calculate the airfoil characteristics from the hovertests. The model also showed that the profile contri-butions to the total power requirements are consider-ably larger than for full-scale rotors, reducing the effectof any blade planform optimization. The ongoing re-search will bring some insight on the behavior of theflow over the rotor blade at low Re, establishing thebasis for an optimized rotor design.

Introduction

The concept of a small-scale flying machine capableof collecting or transmitting information for intelli-gence or surveillance use was first introduced in theearly nineties. Just until then, the miniaturizationand cost reduction of electronic components reachedthe point where a small affordable flying robot wasconceivable. Realizing the great potential of this newtype of vehicles, in 1996 DARPA started the MicroAir Vehicle (MAV) program. The program’s objec-

∗ Graduate Research Assistant† Associate Professor

tive was to develop a system with an endurance of60 min, no dimension larger than 6 in, and a grosstakeoff weight close to 100 gm. At the end of the sixyear program a series of successful fixed wing aircraft,such as the Black Widow (Aerovironment)1 and theMicrostar (Lockheed Martin) were developed. Theseprototypes achieved the weight and size requirementsset by DARPA, however their endurance was inferiorto 30 min. On the other hand, no successful hoveringMAVs have been developed. Existing prototypes suchas the LUMAV (Auburn University) and the hoveringentomopter MENTOR (SRI), lack the endurance tomake them practical, achieving flying times inferior to8 minutes.The objective of this paper is to explore the physicsbehind the poor performance of rotary-wing configura-tion MAVs, in order to determine some basic guidelinesfor small-scale rotor design.

Motivation

The Alfred Gessow Rotorcraft Center has developedover the last three years its own rotary-wing MAVcalled MICOR (MIcro COaxial Rotorcrat). The sec-ond generation of the battery powered vehicle has acoaxial configuration and a GTOW of 100 gm. Eachthree-bladed rotor has a diameter of 17.2 cm and asolidity of 0.118. MICOR can hover for 4 min whenpowered by three LIMnO2 3V batteries, each with acapacity of 430 mAh. An initial study on the vehicle’sperformance showed that two main factors directly in-fluence the vehicle’s endurance.First, the large current flow (about 3 A) required bythe two electric motors exceeds the batteries capabili-ties. The batteries used are designed to provide a max-imum current flow of 1 A. When forced to dischargeat higher current levels, the effective energy density ofthe batteries is reduced, shortening the flying time.The second factor, which is the source of the large

1American Institute of Aeronautics and Astronautics

2nd AIAA "Unmanned Unlimited" Systems, Technologies, and Operations — Aerospac15 - 18 September 2003, San Diego, California

AIAA 2003-6655

Copyright © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

amount of energy required, is the poor aerodynamicperformance of the rotors. The tight size constraintestablished by DARPA made the vehicles one order ofmagnitude smaller than previously developed systems,requiring them to operate under low Reynolds numberaerodynamic flow conditions (Re < 50,000).Reynolds number (Re) can be understood as the ra-tio of inertial to viscous forces in a fluid, hence forMAVs, viscous forces are dominant. The effects of Rereduction in airfoils has been widely studied, since it iscritical for sub-scale testing of models. However MAVsare below the documented range, and only over the lastdecade new research has been performed in that area.Because of the lack of performance data on small-scale rotors in the published literature, an experimen-tal study was completed.

Experimental Setup

Two main sets of experiments were performed: rotorperformance and surface flow visualization on the rotorblades. In this section the methods used are explained.

Rotor performance

The figure of merit (FM) of a rotor can be definedas the ratio between ideal power and actual power re-quired by the system at a specific thrust coefficient.The figure of merit is given by:

FM =C

3/2T

CP√

2(1)

Where thrust (CT ) and power (CP ) coefficients aregiven by:

CT =T

ρAΩ2R2(2)

CP =P

ρAΩ3R3=

τΩρAΩ3R3

(3)

Based on these equations the physical quantities thatneed to be experimentally measured are thrust T ,torque τ and rotational speed Ω. Density ρ, disk radiusR and area A are known.The test stand, shown in Fig. 1 is an instrumentedplatform where the MAV’s motor-transmission systemis mounted via a stem. The rotor is inverted so thatthe airflow goes from bottom to top. This avoids anyIn Ground Effect (IGE) and simplifies the thrust mea-surement (directed downwards). Thrust is measuredby a load cell, and torque is directly measured by atorque sensor placed at the base of the stand. Thrustand torque are decoupled by a set of spring steel mem-branes placed inside the body of the device. The rota-tional speed of the rotor system is measured by a hall

!"

Figure 1: Hover test stand.

sensor that is excited by an array of small permanentmagnets attached to the rotating shaft. All the datais acquired and processed by a data acquisition systemlinked to a computer running a customized MATLABcode.Four different rotors with a diameter of 17.17 cm anda solidity of 0.118 were tested. Three of the rotors haduntwisted blades and one had a linear twist distribu-tion of -10 deg. The airfoils used for the untwistedblade tests consisted of NACA 0012, a flat plate with0.37 mm thickness and blunt edges, and a 8% camberflat plate. For the twisted blades the 8% camber flatplate airfoil was also used. All the rotors have a rootcutout of 20% and an identical rectangular planformwith a chord of 1 cm.The NACA 0012 blades and both sets of 8% cam-ber flat plates were made from a molded multilayeredgraphite-epoxy composite material. Surface finishingis smooth, and airfoil shape is accurate along the bladespan. The 0.37 mm thickness flat plate blades weremade of laminated stainless steel.Each rotor was tested at collective pitch angles rang-ing from 0 deg to 18 deg in steps of 3 deg. For thetwisted rotor, collective pitch was measured at 75% ofthe blade radius. Rotational speed was varied from2500 RPM to 5000 RPM in steps of 500 RPM incre-ments.For each data point, 5 sec of data were acquired at asampling rate of 1000 samples per second. The meanvalue of the data is the one used for all calculations.


Surface flow visualization

Visualization of the flow state on the blades can beachieved using a series of methods, including shear sen-sitive liquid crystals, chemical sublimation and fluores-cent oil 2 The first two methods require shear forcesthat exceed the ones found in the tested rotors, hencethe fluorescent oil technique was used.A uniform layer of aviation oil, Aeroshell oil 100 SAE50, was sprayed with an airbrush on one of the bladesof the rotor, then the rotor was operated at the re-quired test condition until the flow patterns were es-tablished. The rotor was stopped, and a digital picturewas immediately taken under UV light. The oil glowsunder UV light with different intensities depending onthe thickness of the film. Where the flow is separated,recirculation exists and the oil accumulates. In theregions of attached flow the oil is washed away, leav-ing a thin oil deposit. The separated flow regions areidentified in the pictures by the brighter colors.Photographs where taken for the the flat plates, theuntwisted 8% curved plates and the NACA 0012 ateach collective pitch angle at 4,500 RPM. In Figs 4, 5and 6 photographs of the three sets of blades at 3 deg,9 deg, and 15 deg collective are shown.

Experimental Results

In this section rotor thrust and power coefficients arecalculated from the experimental measurements to ob-tain the FM at each test point.

Rotor tests

The plots of Figure of merit vs. thrust coefficient attwo representative rotational speeds (2500 and 4500RPM) are shown in Figs 2, 3. It can be observedthat the general shape of the curves is similar to theones found in full-scale helicopters, however the over-all magnitudes are smaller, considering that full-scalerotors have maximum FM between 0.65 and 0.8.As expected, the rotor that uses flat plate airfoilsachieves the lowest performance, with maximum FMsof the order of 0.3. Following the flat plates are theNACA 0012 blades. By using these streamlined airfoilsa large increase in performance was expected, how-ever maximum FMs of only 0.37 were attained. Fi-nally the 8% cambered blades gave the best efficiency.Maximum FMs of 0.55 for the untwisted and twistedrotors were respectively measured. These results are25% larger than the ones presented Bohorquez et al.3,however note that the rotor diameter and leading edgeshape of the rotor blades are different in these two setsof tests.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.005 0.01 0.015 0.02CT

FM

Twisted 8%

Untwisted 8%

Flat Plates

NACA 0012

Figure 2: FM vs CT at 2500 RPM.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.005 0.01 0.015 0.02CT

FM

Twisted 8%

Untwisted 8%

Flat Plates

NACA 0012

Figure 3: FM vs CT at 4500 RPM.

The relative magnitude of all the curves is the same atall rotational speeds. However as speed is decreased,maximum FM values, and the range of thrust coeffi-cients the rotors can reach are reduced.From the plots it can be seen that for thrust coefficientsbelow 0.008, the NACA 0012 blades have the highestFM. The characteristics of MICOR require the rotorsto operate at thrust coefficients close to 0.014, valuesthat these blades cannot even reach. Above thrustcoefficients of 0.008 only the 8% cambered blades havea positive FM slope, and are the only ones that canreach the thrust values required for MICOR.At lower rotational speeds, for the most part the 8%camber twisted and untwisted blades have a very sim-ilar behavior. As the rotational speed is augmented,the performance of the untwisted blades slightly ex-ceeds that of the twisted blades. However the twistedblades can reach higher thrust coefficients.

Surface flow visualization

The flow visualization pictures taken reveal differentboundary layer behaviors and stall mechanisms for thedifferent airfoils.Figure 4 shows the oil patterns observed for the flatplate blades. First it is important to point out thatthe flat plates used have blunt edges, so the flow is dis-


turbed at the leading edge (LE). Because of this, it isexpected that separation occurs very early. For all thecollective angles tested, three distinct regions formedon the surface of the airfoil. At low and moderate col-lective angles, a region of separated flow is observedstarting from the LE. The flow eventually reattachesat different chord positions, forming a dark colored tri-angle, where a thinner oil layer exists. This region ishighlighted in Figs. 4a and 4b. At higher collectiveangles reattachment only occurs at smaller isolated re-gions shown in Fig. 4c. The brighter area outside thetriangles seems to be fully separated flow.The oil needs a minimum level of shear stress to re-spond to the boundary layer behavior. It seems thatthe threshold is reached over the outer 50% of the bladewhere the dynamic pressure is higher. Thus, only theoutermost radial sections of should be considered inthe present analysis. Oil accumulation on the innerregions of the blades does not necessarily mean thatfull separation took place.Figure 5 shows that in the 8% cambered blades threedistinct regions can be identified. The first one is avery narrow area close to the LE that has oil accumu-lation, it might be possible that flow conditions simi-lar to the ones found in the flat plate blades are alsopresent in this case. The leading edge might have smallimperfections that introduce disturbance in the flow,producing early separation. Since the airfoil is a circu-lar arc, the suction peak should be located close to themid-chord, at a considerable distance from the leadingedge. This allows for favorable pressure gradients inthe boundary layer for a large portion of the chord.The flow quickly reattaches forming the second regiondenoted by the triangles in Figs. 5a, 5b and 5c. Theattached flow region continues to grow as the collec-tive pitch is increased, reaching its maximum size at15 deg, where it extends up to half chord near to theblade tip. In the surroundings of the midchord, theboundary layer is facing an adverse pressure gradientwhich produces separation, forming a third region cov-ered with an oil layer.The NACA 0012 blades present a more complex be-havior than the other two cases. The NACA 0012 is astreamlined symmetric airfoil that has its suction peakclose to the LE. This means that the boundary layerwill encounter adverse pressure gradients at a shortchordwise position. Hence, it is expected to observeseparation or transition of the boundary layer fromlaminar to turbulent at a short distance from the LE.From Fig. 6a, it is clear that there are two distinctregions. Starting from the LE and up to 15% of thechord, the surface of the airfoil is completely clear ofoil. The rest of airfoil is covered in a uniform thinoil layer. This second region might have an attached

turbulent boundary layer. Looking at the CP and CTvs. collective plots (Figs. 8 and 9) it is clear thatabove 6 deg collective the slope of the plots changes.This change should also be noticeable at the level ofthe airfoil. In fact, in Fig. 6b it can be observed thatthere are three regions on the blade. It seems that alaminar separation bubble that extends for about 40%of the chord has formed. Inside the bubble there is arecirculating flow that allows extensive oil accumula-tion. Usually the bubble is closed by the reattachmentof a turbulent boundary layer. The third region hasa thinner oil layer than the one found in the bubble,producing a darker shade of gray (dotted lines). Athigher collective pitch angles (Fig. 6c) the length ofthe bubble is reduced to around 10% of the chord, andmoves closer to the LE. This is a typical Boundarylayer behavior at low Re for streamlined airfoils4. Itis not clear how the size and location of the bubbleaffects the pressure distribution of the airfoil, howeverfrom Figs. 8 and 9, it seems that the main effects ofthe laminar separation bubble is to increase the profiledrag of the airfoil.

BEMT Implementation

While simple momentum theory can be used as a firstapproximation to estimate the efficiency of rotors, amore elaborate aerodynamic theory is needed to incor-porate blade geometry, sectional orientation and twistcondition. Momentum theory and blade element the-ory where combined to incorporate the effects of dragand twist on rotor performance. Using the mathemat-ical model and equations presented Bohorquez et al.3

a numerical implementation of the BEMT model wasused to predict and understand the behavior of thetested rotors.Usually the airfoil characteristics (lift-curve slope anddrag coefficient for each angle of attack) are known,and the model is set such that the collective pitch isvaried until a required thrust coefficient is obtained5.However, in the current work this is not the case, andthe airfoil characteristics are not known. The modelwas implemented in a different way. Instead, BEMTwas used in conjunction with rotor experimental datato estimate the airfoil lift and drag characteristics.

Iteration algorithm

The algorithm requires as inputs the experimentalthrust and power coefficients and the physical param-eters of the rotor such as collective pitch, taper andtwist distribution, number of blades, solidity etc. Aninitial guess of the CL vs. α and CD vs. α functions


Tip

LE

b, 9 deg

SF

AF

SF

AF

LE

Tip

a, 3 deg c,15 deg

LE

Tip

AF

SF

AF

Figure 4: Flow visualization, flat plate

SF

LE

Tip

c,15 deg

AF

SF

LE

Tip

b, 9 deg

AF

SFSF

LE

Tip

a, 3 deg

AF

SFSF

Figure 5: Flow visualization, 8% camber plate

SB

Tip

LE

c,15 deg

AFTAF

Tip

LE

b, 9 deg

LSB

AF

TAF

LE

AF

Tip

a, 3 deg

TAF

Figure 6: Flow visualization, NACA 0012

Input data:•Rotor parameters solidity, # blades, twist dist. collective•Experimental CP and CT•Initial guess of CL

and CD vs. α

Calculation of inflow distribution and induced angle

of attack of the blades sections

BEMT CT is calculated

CL vs. α is modified

BEMT CT exp. CT BEMT CT = exp. CT

Calculation of inflow distribution and induced angle

of attack of the blades sections

BEMT CP is calculated

BEMT CP exp. CP BEMT CP = exp. CP

CD vs. α is modified

Output: CL and CD vs. aInflow dist, k vs CT, CPi, CPo

Figure 7: Block diagram of BEMT algorithm.

is also needed.There are three main iterations in the algorithm. Oneto find the CL vs. α curve, another to find the CD vs.α curve, and a third one for the inflow calculations.Lift coefficient iteration: Using the initial guess of theairfoil’s CL vs. α function, the rotor thrust coeffi-cient (CT ) is calculated for each collective pitch set-ting. These values are compared with the experimen-tal ones, and depending on the sign of the error the CLvs. α curve is modified until there is a good agreementbetween the calculated and the experimental values.Drag coefficient iteration: The drag coefficient itera-tion has to be performed after the CL vs. α curve has

been found. This is required because the power co-efficient has an induced component that will directlydepend on the lift characteristics of the airfoil. Again,an initial guess of the CD vs. α curve is given. Foreach collective, the calculated power coefficients (CP )are compared with the experimental ones. The CD vs.α plot is modified until good agreement between thecalculated and the experimental values is obtained.Inflow calculation iteration: Every time the inflow dis-tribution is calculated, an initial guess of the lift-curveslope (Clα) for each blade element is required. Foreach section the inflow is calculated and the inducedangle of attack is obtained. (α = θ− λ

r ). The induced


0

0.005

0.01

0.015

0.02

0.025

0 3 6 9 12 15 18

collective, deg

CT

Exp. NACA 0012Exp. Flat plates Exp 8% plate untwistedExp 8% plate twisted

Figure 8: Experimental CT vs. collective pitch forrotor with NACA 0012 blades

0

0.001

0.002

0.003

0.004

0.005

0 3 6 9 12 15 18

collective, deg

CP

NACA 0012Flat Platescambered untwistedcambered twisted

Figure 9: Experimental CP vs. collective pitch forrotor with NACA 0012 blades

angle of attack is used as an input in a table look-upsubroutine that interpolates the CL vs. α vector. TheClα value is updated and the cycle continues until thedifference in Clα between two consecutive iterations isnegligible. This inflow calculation occurs in each of thelift coefficient iterations.Figure 7 shows a block diagram of the algorithm withthe inputs and outputs and the iterative processes in-volved. By implementing this simple algorithm it ispossible to calculate an approximation of the airfoilcharacteristics by using just the hover rotor tests.A simple numerical error analysis was performed todetermine an ideal number of elements to use. Theblade span was initially divided into 10 elements andthe BEMT power and thrust coefficients were calcu-lated. The number of elements was then increased insteps of 5, until the difference between two consecutiveruns was below 0.5%. A minimum of fifty elements was

required to meet the error criteria.

BEMT Results

In this section the experimental results obtained at4,500 RPM (tip Re ∼= 27,000) are used to calculate thesectional characteristics of the airfoils used in the dif-ferent rotors. This particular set of tests was used sinceit is close to MICOR’s hovering operating conditions.To check the BEMT predictions, wind tunnel measure-ments can be compared with the airfoil characteristicsobtained with the BEMT model. One of the assump-tions of the model is that 2D airfoil characteristics arekept constant over the blade span. This is not truesince the Re varies along the rotor radius. The innersections of the blade will have lower Clα and CLmaxand higher drag coefficients. The consequence of thisis that the BEMT calculations will predict the air-foil characteristics of an “average” location which isaround 75% of the blade span (Re = 20,000). Windtunnel test values for the lift and drag coefficients ofthe NACA 0012 airfoil6 at Re = 4,000 are presented inFigs. 10 and 11. Figures 12 and 13 show the predictedNACA 0012 CL vs. α and CD vs. α plots respec-tively. It can be observed that the general shape of thecurves is similar to the ones found experimentally inwind tunnel measurements, highly nonlinear and withtwo changes in slope before stall.Figures 12 and 13 show the calculated airfoil charac-teristics of the flat plate blades. Results can be com-pared with wind tunnel measurements7 at Re = 42,000in Figs 10 and 11. The wind tunnel measurementswere performed using a flat plate airfoil with roundedleading edge and sharp trailing edge, and with a thick-ness to chord ratio of 0.37. The flat plates tested inthe rotor had the same thickness to chord ratio, buthad square leading and trailing edges. Since there isa difference in the airfoil geometry and in the Re, 2D-experimental data gives only an idea of what the airfoilproperties should be. For the flat plates, again, the cal-culated CL and CD vs. α functions exhibit a similarbehavior than the wind tunnel measurements.For the 8% camber plates, the airfoil characteristicswere obtained from the untwisted blade tests. Figures12 and 13 show the BEMT results. The plots are com-pared with wind tunnel tests6 of a thin 10% cambercircular arc airfoil at a Re and 4,000. Due to airfoilgeometry and Re differences only a qualitative com-parison between the wind tunnel and the BEMT datais possible. The lift coefficient plot has typical low Recharacteristics, highly nonlinear and with a low maxi-mum lift coefficient. The BEMT results are below thewind tunnel experimental values.


0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 2 4 6 8 10 12αααα, deg

CL

Flat plate, Sherman, Re = 42,000

10% camber plate, Sunada Re = 4,000

NACA 0012, Sunada Re = 4,000

Figure 10: Wind tunnel results, CL vs α.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 2 4 6 8 10 12αααα, deg

CD

NACA 0012, Sunada Re = 4,000

Flat plate, Sherman Re = 4,000

10% camber plate, Sunada Re = 4,000

Figure 11: Wind tunnel results, CD vs α.

Special care needs to be taken when comparing airfoilcharacteristics from different wind tunnel tests. Aero-dynamic forces might be obtained by direct measure-ment using a sensitive strain gauge balance, or by in-tegration of pressures measured in the wake. Differenttechniques will give different results. Even if similarexperimental techniques are used, wind tunnel turbu-lence levels might differ, also affecting the measure-ments 4. At very low Re the boundary layer behav-ior is very sensitive to disturbances, so small differ-ences of the contour or roughness of the model testedmight produce considerably different results. It is ex-pected that the airfoil characteristics obtained fromthe BEMT model differ in magnitude from wind tun-nel tests, however results should be able to give a goodidea of the airfoil behavior.

Discussion

In the tests performed, the tip Re of the blades changesfrom 30,000 at 5,000 RPM to 19,500 at 2500 RPM.For such low Re there is a degree of uncertainty inthe value of the zero lift drag coefficient, CDo, and in

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8 10 12

αααα, deg

CL

Flat plates

NACA 00128% camber

Figure 12: BEMT results, CL vs α.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 2 4 6 8 10 12αααα, deg

CD

8% camber

NACA 0012

Flat Plates

Figure 13: BEMT results, CD vs α.

the induced losses of the rotary system. Experimentalstudies suggest that CDo at low Re for conventionalNACA series airfoils may range from 0.05 to 0.0084 atRe = 1× 104 and 3× 105, respectively, and for curvedplates may range from 0.17 to 0.08 at Re = 1×104 and6×104, respectively6,8,9. The actual value depends onthe viscous drag effects, geometry and surface rough-ness of the manufactured airfoils.In general the sectional drag coefficient below stall isapproximated as

CD(α) = CDo + d1α+ d2α2 (4)

Where d1 and d2 are empirically determined coeffi-cients. Typical values for full-scale helicopter airfoilsare CDo=0.01, d1=0.025 and d2=0.65. For the BEMTresults, at low angles of attack (< 5) , the drag coeffi-cient behavior can be also be approximated using Eq.(4). For the NACA 0012 blades CDo is 0.025 d1=0and d2=1.5, and for the 8% camber flat plate CDo is0.0525 d1=0 and d2=1.5. The large difference in themagnitude of the second order coefficients with respectto the typical full-scale values explains why at low Re,considering a drag coefficient independent of the angle


of attack is not a good assumption.BEMT provides the tools to make a more refined anal-ysis. The induced power factor can be obtained forevery thrust coefficient, and the profile power calcu-lations consider the variation of drag coefficient withangle of attack.Using the airfoil characteristics obtained from the 8%camber plates, the BEMT model was used to calcu-late the profile and induced power contributions tothe total power required by the rotor. The model wasalso used to predict the performance of the twistedbladed rotor. Figure 14 shows the experimental andthe numerical results. BEMT predicts a maximum in-crease in FM of 2% when -10 deg linear twist is used.This differs from the experimental results shown in Fig.3, which shows practically no difference with the un-twisted blade results. The difference between the ex-

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.022CT

FM

BEMT twisted blades prediction

BEMT untwisted blades

Exp. twisted blades

Exp untwisted blades

Figure 14: FM vs. CT for 8% cambered plate

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

0.005 0.01 0.015 0.02CT

CP

Twisted blades total CPTwisted blades Induced CPTwisted blades profile CPUntwisted blades total CPUnwisted blades Induced CPUntwisted blades profile CP

Figure 15: CT vs. CP for 8% cambered plates.

perimental and the predicted increase in FM might bea consequence of experimental error, especially in themeasurement of the collective pitch of the rotor. It is

possible that the centrifugal forces as well as the airfoilpitching moments, modify the twist distribution elas-tically deforming the blades. Even a small variation inthe collective pitch or in the twist distribution has asignificant influence on the performance of the rotor.The use of twist and/or taper in the rotor blades ishighly beneficial in full-scale rotors, however at low Retheir effect seems to be largely reduced. The idea be-hind twisting the blades is to reduce the induced powerrequired by the rotor by making the inflow distributionmore uniform. As shown by Leishman5, the minimumpossible induced power would be achieved by having auniform inflow. Tapering the blades does not changethe physical orientation of the airfoil, however by re-ducing the blade area the inflow is also reduced, andthe induced angle of attack of each blade section canbe controlled. An optimum hovering rotor minimizesthe profile and the induced power, and profile lossesare minimum when all the blade sections of the rotorwork at the highest lift to drag ratio. In a full-scale he-licopter, usually 30% of the power is consumed by theprofile losses and 70% by the induced losses. In Fig. 15the BEMT calculated power coefficients for the twistedand untwisted blades with the induced and profile con-tributions are shown. At these low Re the profile draghas a larger influence over the total power required bythe rotor. At the range of thrust coefficients encoun-tered by MICOR the contribution of profile power goesup to 50%. This is the reason why the reduction in in-duced power does not have a large impact on the rotorperformance. In fact, the increase in FM obtainedwhen twisted blades are used is due to the simulta-neous reduction of the profile and the induced power(Fig.15).The BEMT calculations of the induced power factorare presented in Fig. 16. As can be observed thereis a reduction in κ by twisting the blades. In fact theinduced power factor of the twisted blades is below theone for the NACA 0012 and flat plate blades.From the lift to drag ratio plot obtained from the airfoilcharacteristics calculated with the BEMT model (Fig.17), it can be observed that the NACA 0012 and theflat plate airfoils have a very flat and uniform behavior.The 8% camber airfoil has a slightly higher maximumlift to drag ratio, and presents larger slope changes.In all three cases the maximum lift to drag ration isrelatively low when compared to the ones that are ob-tained at higher Re. This means that optimization ofthe induced angle of attack of the blades will not pro-duce large performance changes. The use of twist and/ or taper in rotor blades will have a marginal benefi-cial effect as long the lift to drag ratio characteristicsof the airfoil have a typical low Re behavior.From the surface flow visualization experiments it is


clear that enhancing the lift and drag characteristics ofthe different airfoils at low Re is not a simple task. Forthe streamlined airfoils like the NACA 0012 where lam-inar separation bubbles are found, the use of boundarylayer trips, also known as turbulators, is an option.The function of the boundary layer trips is to causetransition from laminar to turbulent avoiding the de-velopment of a bubble. This approach can improve theairfoil characteristics, but its implementation is diffi-cult considering that the position of the bubble changesdepending on the radial position and operating condi-tions of the rotor. The same approach can be usedfor airfoils like the 8% circular arc, not to avoid theformation of a laminar separation bubble but to delayseparation.Airfoil design becomes the critical parameter for a bet-ter rotor performance at the low Re encountered byrotary-wing MAVs. The design of airfoils that avoidor delay separation over a larger chord fraction canpotentially enhance their lift to drag ratio characteris-tics. This would increase the impact on performanceof blade planform optimization.

Future Work

In order to determine an optimal type airfoil to use inMICOR’s rotor blades, a systematic testing of differentairfoil shapes, especially designed for low Re regimes,is going to be performed. A more detailed study ofcambered plates airfoils where the influence of param-eters like thickness, camber and surface roughness hasalready started. Finally, a CFD study of the rotorstested in this paper is being implemented and resultswill be published soon.

Summary and Conclusions

In summary, the experimental measurement of thepower and thrust coefficient of four different small-scale rotors was performed. Their FMs were calculatedfor a range of thrust coefficients and rotational speeds.Aerodynamic performance of the rotors was poor yield-ing a maximum FM of 0.55 for a set 8% camber blades.A BEMT model of the rotor was implemented, and air-foil characteristics were obtained from the rotor tests.The BEMT model showed that at the range of thrustcoefficients encountered by MICOR, the profile dragaccounts for up to 50% of the losses as opposed to 30%in full-scale helicopters. This fact considerably reducesthe beneficial effects obtained when twisted blades areused. Surface flow visualization experiments were per-formed on the different sets of blades, showing differ-ent boundary layer behaviors and stall mechanisms. In

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Figure 16: Induced power coefficient.

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Figure 17: Airfoil lift to drag ratio comparison.

general just a fraction of the blade area shows evidenceof attached flow, explaining the large profile drag andthe low lift to drag ratios that the airfoils can achieve.The development of customized airfoils for small-scalerotary wing vehicles, that can achieve large lift to dragratios at low Re, seems to be the path to follow inorder to make practical this MAV configuration.

References

1 J. Grasmeyer, Keenon M., Development of theBlack Widow Micro Air vehicle, (AeroVironment,Inc., Simi Valley, CA), AIAA Paper 2001-0127,AIAA, Aerospace Sciences Meeting and Exhibit,39th, Reno, NV, Jan. 8-11, 2001.

2 Leishman, J.G., Martin, P.B., Pugliese, G.J., ”Sur-face and Wake flow Characteristics of Hovering He-licopter Rotor”, Proc. of 9th International Sym-posium on Flow Visualization (eds.: Carlomagno


G.M., Grant I.), Edinburgh, August 2000, paperNo. 189, p. 7.

3 Bohorquez F., Samuel, P.,Sirohi, J., Pines, D.,Rudd, L., Perel. R. , ”Design Analysis and HoverPerformance of a Rotary Wing Micro Air Vehicle”,AHS Journal, Vol. 48, (2), April 2003, p. 80.

4 Lovson, M.V., “Aerodynamics of Aerofoils at LowReynolds Numbers,” proceedings fourteenth Un-manned Air Vehicle Systems International Confer-ence, paper 35, Bristol, UK, 12-14 April, 1999.

5 Leishman, J.G., “Principles of Helicopters Aerody-namics”, Cambridge University Press, New York,NY, 2000, pp. 69-70.

6 Sunada, S., Sakaguchi, A., and Kawachi, K., “Air-foil Section Characteristics at a Low ReynoldsNumber,” Journal of Fluids Engineering, Vol 119,March 1997, pp. 129-135.

7 A. Sherman, “Interference of Wing and Fuselagefrom Tests of 30 Combinations with Triangular andElliptical Fuselages in the NACA Variable-DensityTunnel,” NACA TN 1272, 1947.

8 Sunada, S., “Comparison of Wings Characteristicsat an Ultralow Reynolds Number,” Journal of Air-craft, Vol 39, (2), March-April 2000.

9 Azuma, A., Okamoto M., and Yasuda K., “Aero-dynamic Charateristics of Wings at Low ReynoldsNumber,” Fixed and Flapping Wing Aerodynam-ics for Micro Air Vehicle Applications, Progress inAstronautics and Aeronautics, AIAA Reston, Vir-gunia, edited by Thomas J. Mueller, Volume 195,2001,pp 341- 391.


[american institute of aeronautics and astronautics 2nd aiaa "unmanned unlimited" conf....

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