2006-ahs-flow field of micro-rotor

8/14/2019 2006-AHS-Flow Field of Micro-rotor

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FLOW FIELD OF A ROTATING-WING MICRO AIR VEHICLE

Manikandan Ramasamy J. Gordon Leishman Timothy E. Lee

Alfred Gessow Rotorcraft Center

Department of Aerospace Engineering

Glenn L. Martin Institute of Technology

University of Maryland

College Park, Maryland 20742

Abstract

An experiment was conducted to measure the hoveringperformance of a rotor typical of that used on a rotating-wing micro air vehicle. The rotor was shown to have rela-tively low hovering efficiency that can be traced, at least inpart, to its significant viscous wake and the relatively largeaerodynamic losses that are associated with the wake.

High-resolution flow visualization images have divulgedseveral interesting flow features that appear unique torotors operating at low Reynolds numbers. The vortexsheets trailing the rotor blades were found to be muchthicker and also more turbulent than their higher chordReynolds number counterparts. Similarly, the viscouscore sizes of the tip vortices were relatively large as afraction of blade chord compared to those measured athigher vortex Reynolds numbers. However, the tip vor-tices themselves were found to be laminar near their coreaxis with an outer turbulent region. Particle image ve-locimetry measurements have been made at various wakeages that have quantified the structure and strength of thewake flow, as well as the tip vortices. An analysis of

the vortex aging process has also been conducted, includ-ing the development of a new non-dimensional equiva-lent time scaling parameter to normalize the core growthof tip vortices generated at substantially different vortexReynolds numbers.

Nomenclature

A Rotor disk area

Ae Effective disk area

c Blade chord

Cd Drag coefficient

Cl Lift coefficientAssistant Research Scientist. [email protected] Minta Martin Professor. [email protected] Minta Martin Undergraduate Intern. [email protected]

Presented at the 62nd Annual Forum and Technology Display

of the American Helicopter Society International, Phoenix, AZ,

May 911, 2006. c2006 by M. Ramasamy, J. G. Leishman, &T. Lee, except where noted. Published by the AHS International

with permission.

CT Rotor thrust coefficient, = T/A2R2

DL Disk loading, = T/A or T/AeFM Figure of merit

PL Power loading, = T/P or W/Pr Radial distance

rc Core radius of the tip vortex

r Non-dimensional radial distance, = r/rcR Radius of the blade

Rev Vortex Reynolds number, = v/t Time

T Rotor thrust

Te Equivalent time

vh Hover induced velocity

vi Induced velocity

Vr Radial velocity

V Swirl velocity

W Vehicle weight

Lambs constant, = 1.25643 Circulation, = 2rVb Bound circulation

c Circulation at the core radiusv Circulation at large distances Ratio of apparent to actual viscosity Wake age Kinematic viscosityt Eddy or tubulent viscosityT Total kinematic viscosity, = +t Air density Rotor solidity Azimuthal position of blade Rotational speed of the rotor

IntroductionAerodynamic research on hover capable micro-air vehi-cles (MAVs) that have good flight endurance and can alsoperform desirable maneuvers has been gaining significantinterest from the research community over the past fewyears. This is because MAVs have potential advantagesfor performing critical military operations at low risk,such as surveillance over enemy territories, various covertoperations, or remote sensing in hazardous environments

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when airborne chemicals or biological agents exist. Whilevarious definitions of MAVs exist, generally speaking theyare defined as flight vehicles that have a maximum size di-mension that does not exceed 6 inches (15 cm).

Biomimetic (insect based) flapping as well as rotat-ing wings are two different concepts being considered forhovering types of MAVs. Both mechanisms have theirown relative advantages and disadvantages. Flapping-wing mechanisms are known to have relatively poor me-chanical efficiency, but there have been several hypothe-sis forwarded that claim that flapping wing concepts offerbetter aerodynamic efficiency compared to rotating wingswhen operated at extremely low chord Reynolds numbers,say below 50,000. Numerous attempts have been madethrough computational fluid dynamic simulations, as wellas experiments, to verify these hypothesis and to under-stand the basic physics of flapping wing flight (Refs. 1,2). This work, however, has resulted in only limited suc-cess. Computationally, one difficulty is tracking vortic-ity to long times. Experimentally, there are difficultiesin measuring accurately the low thrust generated and the

corresponding small power required, not to mention thedifficulties of both measuring and predicting the com-plex three-dimensional, highly unsteady, viscous domi-nated vortical flows that are present in this type of flowfield.

As a result, a comprehensive knowledge of flappingwing flight has not yet been established to fully explainthe aerodynamic performance of flapping-wing insects orbirds, or to prove the postulated gains in relative aero-dynamic efficiency of flapping-wing based MAVs overrotating-wing MAV concepts. Therefore, the present au-thors have been conducting a research program, fundedby the U.S. Army Research Office, to better understandthe fluid dynamics and relative performance merits of

rotating-wings versus flapping-wing MAVs. Initial workon the flow diagnostics of a flapping-wing concept is re-ported in Ref. 3, and the focus of the present paper is on arotating-wing concept.

The primary objective of the present work was to ex-amine the wake from a MAV-size, micro-rotor, and to un-dertake a baseline experiment that helps further the un-derstanding rotor behavior at low blade Reynolds num-bers. This experiment principally sets the groundwork forfurther research. The experiment was performed in twostages. First, the performance of the micro-rotor was mea-sured at various rotational speeds and blade pitch angles.This was followed by flow visualization and PIV measure-ments. The work reported in this paper describes the var-ious aerodynamic structures that are present in the flowfield and which contribute to the net aerodynamic perfor-mance of a micro-rotor.

Background

The efficiency of any hovering vehicle can be quantifiedin terms of effective power loading, which is defined as

the ratio of vehicle weight to power required to hover, i.e.,W/P = T/P = PL. The induced (ideal) power required tohover is given by P = T vh, where vh is the minimum av-erage induced velocity through the plane of the rotor disk(or normal to the effective stroke plane of wing flapping)to produce the thrust T. This means that the ideal powerloading will be inversely proportional to the induced ve-locity; this is a fundamental result that comes about basedon the solution to the momentum theory, which invokesthe principles of conservation of mass, momentum, andenergy in the flow.

Using the momentum theory, the average ideal (mini-mum) induced velocity can be written in terms of the ef-fective disk loading as

vh vi =

T

2Ae=

DL

2=

P

T= (PL)1 (1)

where DL is the effective disk loading, T/Ae. For a rotorAe =A and in the case of a flapping wing the effective diskarea Ae is based on the net swept area in the stroke plane

over one complete wing stroke. The power loading canalso be written in terms of the figure of merit FM(i.e., theaerodynamic efficiency) of the system as

PL =T

P=

2 FM

DL(2)

where the FMaccounts for all sources of non-ideal losses.This means that the best hovering efficiency (i.e, the max-imum power loading) is obtained when the effective diskloading is a minimum and also when the F M is a maxi-mum.

According to the results in Fig. 1, the power loading forhovering flight increases quickly with decreasing effective

disk loading (note the logarithmic scales). The best theo-retical hovering performance under the stated assumptionsis given by the FM= 1 line. It will be apparent that hov-ering concepts that have low effective disk loadings willalways require relatively low power per unit of thrust pro-duced (i.e., they will have high ideal power loading) andwill require less power (and consume less fuel or energy)to generate any given amount of thrust.

Therefore, the key to hovering efficiency for any type ofMAV concept (rotating-wing or flapping-wing) is alwaysto have a low effective disk loading, although it must alsohave good aerodynamic efficiency (i.e., a high FM). No-tice that insects and hummingbirds generally have very

low effective disk loadings and so have good hoveringefficiency, even although their effective FM values maynot always be that high. Measurements made on rotating-wings at similar disk loadings show similar hovering per-formance efficiency to that achieved by insects.

Because of the relatively low mechanical efficiency ofexisting flapping-wing MAV concepts, a proven conceptsuch as rotating-wing may be the best short-term solu-tion towards successfully developing a hovering-efficientMAV, but only if the rotor can be designed to have low

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Figure 1: Power loading versus effective disk loading

for biological and mechanical systems. Low effective

disk loading always leads to high hovering efficiency

(high power loading).

disk loading and also be given good aerodynamic effi-

ciency. While good aerodynamic efficiency requires thedesign of blade airfoil sections with low drag and highlift-to-drag ratios, a major source of performance loss fora rotor is contained within the structure of its blade wake,i.e., the induced losses.

Comprehensive rotor wake measurements have beencarried out to help understand the source of these lossesusing various scales of rotors, from model-scale to full-scale (Refs. 714). However, no detailed wake mea-surements have yet been performed on MAV-scale rotors,where the blade tip chord Reynolds numbers lie in therange of 10,000 to 50,000. This lack of data is not onlybecause of the experimental complexities associated with

measuring rotor flows at any scale, but also from the spe-cific measurement challenges that are unique at the MAV-scale level. This includes, but is not limited to, the phys-ical size of the flow structures that are present, which areoften too small to be sufficiently resolved with most typesof flow diagnostic methods.

The substantial difference in the operating chordReynolds numbers between a MAV-size rotor and evenmoderately larger scale rotors (say, 1/4 to 1/6 of full-scale) raises immediately several scaling issues that needto be addressed. Clearly, viscous forces are more impor-tant for determining the characteristics of the flow fieldat these low operating Reynolds numbers. Also, existingexperimental evidence suggests that the hover efficiencyof rotating-wing MAVs are much lower, with FM val-ues of no more than 0.5 when compared with their highReynolds number counterparts (Refs. 46). This clearlysuggests that the recovery of aerodynamic efficiency tolevels comparable to full-size rotors stems, in part, froman understanding and minimization of the various sourcesof losses in the rotor wake. This includes the vortex sheetstrailed from each blade, as well as the blade tip vorticesand their evolution at low vortex Reynolds numbers.

Experiment

Rotor Performance Measurements

The rotor blades for the micro-rotor were made of com-posite carbon fiber, and had circular arc, cambered airfoilsections. The radius of the blade was 86 mm, with a uni-form chord of 19 mm, giving a blade aspect ratio of 3.7.

The blades had no twist or taper. The rotor had a solidity,, of 0.14 with two blades attached.

The rotor was mounted in a test fixture with one loadcell to measure thrust, and another load cell was used tomeasure torque. The performance of the rotor was mea-sured at different combinations of rotor rpm and bladepitch angles. Tares were measured at different rpms withthe blades detached from the hub, and the tares weresubtracted from the measured thrust and torque with theblades attached.

The measurements were then converted to standardthrust and power coefficients, which are shown in Fig. 2.

The ideal power is given by CPideal = C3/2T /

2, and with a

figure of merit FM the predicted power is

CP =

1

FM

C

3/2T

2(3)

Notice that the measurements suggest a relatively lowaerodynamic efficiency, with an average figure of meritof about 0.5 describing the measurements.

A figure of merit plot versus blade loading coefficientis shown in Fig. 3. For reference purposes, FM curvespredicted on the basis of the equation

FM=

C3/2T

2

C3/2T

2+Cd0

8

(4)

are shown, which are marked simply to represent boundsrather than the actual predicted performance. An average

Figure 2: Power polar for the micro-rotor showing its

relatively low aerodynamic efficiency.

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Figure 3: Figure of merit curve for the micro-

rotor versus blade loading coefficient with theoretical

bounds shown.

Figure 4: Rotor figure of merit in terms of wake in-

duced loss and blade section efficiency.

sectional drag coefficient Cd0 = 0.03 was used (typical ofairfoil section drag coefficients at blade chord Reynoldsnumbers of 50,000), with induced power factors of 1.5 and2.0. The predicted results show reasonable bounds on themeasurements, and besides significant blade profile lossesalso suggest that relatively high induced losses are presentat the rotor compared to those obtained at higher Reynoldsnumber.

The problems associated with the design of an efficientrotating-wing MAV now becomes immediately apparent.

By plotting the rotor FM as a function of induced powerfactor (which is a measure of induced losses) and blade

section C3/2l /Cd (which is a measure of rotor efficiency),

as shown in Fig. 4, it will be apparent that reductions inboth induced losses and blade section losses are requiredto improve FM. Clearly with high induced losses (in-duced power factors > 1.5) then no amount of improve-

ment in airfoil section C3/2l /Cd can lead to increased val-

ues ofFM.

Flow Field Measurements

This experiment included flow visualization and two-component PIV measurements in the rotor wake. Thetwo-bladed rotor was placed on specially made rotorstand, as shown in Fig. 5, and was tested in a flow con-ditioned test cell. For these sets of experiments the rotorwas operated at a rotational frequency of 50 Hz with a tip

speed of 27.02 m/s. The operating tip Mach number andReynolds number based on chord were 0.082 and 34,200,respectively. The measured CT/ for the test conditionswas 0.0867.

For both the flow visualization and PIV measurements,the flow at the rotor was seeded with a thermally pro-duced mineral oil fog. The average size of the seedparticles were between 0.2 to 0.22 microns in diameter,which was small enough to minimize the particle track-ing errors for the vortex strengths found in these experi-ments (Ref. 15). For the PIV experiments, the entire testarea was uniformly seeded before each sequence of mea-surements. For the flow visulization, judicious adjustment

of the seeder was required to introduce concentrations offog at the locations needed to clearly identify specific flowstructures.

A laser light sheet from Nd:YAG pulsed laser sourcecapable of frequencies up to 15 Hz was used in synchro-nization with the rotor frequency to illuminate planes inthe flow field. A fully articulated optical arm was usedto locate the light sheet in the required region of focus.A 6.1 mega-pixel digital still camera was used to acquireall of the images. Digitizing the images relative to a cali-bration grid provided the required spatial locations of thevarious observed flow structures, such as the wake sheetsand the tip vortices. A schematic of the experimental setup is shown in Fig. 6.

The PIV system included dual Nd:YAG lasers that wereoperated in phase synchronization with the rotor, the opti-cal arm to transmit the laser light into the region of inter-rogation, a digital CCD camera with 1 mega-pixel reso-lution placed orthogonally to the laser light sheet, a high-speed digital frame grabber, and PIV analysis software.The laser could be fired at any blade phase angle, enablingPIV measurements to be made at any required wake age.

Figure 5: Photograph of the upper part of the rotor

test fixture.

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Figure 6: Schematic showing the experimental PIV set

up.

The two lasers were fired with a pulse separation time

of 15s; this corresponds to less than 0.1 of blade mo-tion. The interrogation region was focused to a particularregion of interest within the image using 50-by-50 nodeson either side. This corresponded to an interrogation sizeof 38-by-44 mm with 0.75-by-0.88 mm between adjacentnodes.

PIV Image Processing

Processing the acquired PIV images to obtain reliable ve-locity vectors at this scale was found to be relatively chal-lenging. The biggest advantage of PIV is its ability tomeasure the velocity field (over a plane) at a given instantof time rather than the point-by-point measurements typi-

cal of laser Doppler velocimetry. This advantage is gainedfor many flow conditions where the flow is not highlythree-dimensional and/or unsteady, such as an unidirec-tional flow, or a steady or periodic flow. However, for aflow that has substantial three-dimensional velocity gra-dients and/or is combined with large strain or rotationaleffects (e.g., for vortex flows, as in the present case), theprocessing of raw PIV images is more complicated.

This is further complicated by the aperiodic movementof the tip vortices; this requires individual PIV images tobe spatially orientated so that the center of any one vortex(i.e., the centroid of vorticity) in all of the images coin-cide with each other before phase-averaging to obtain the

mean velocity field. This correction for aperiodicity, how-ever, is based on the assumption that the inner region ofthe vortex flow rotates like a solid body, and so that allthe measurement points inside the vortex are displaced byequal amount and at the same velocity.

The following describes the procedure used in the cur-rent experiment for determining the velocities in the flowfield from the images acquired from the PIV system. Theraw images were first processed using a commerciallyavailable PIV analysis software, which yielded the ve-

locity vectors across the entire region of interest. Theprocessing was performed in such a way that the maxi-mum number of interpolated vectors allowed in each im-age (which has 50-by-50 nodes) was less than 10. Theinterrogation window was chosen such that the maximumdisplacement of the seed particles within the interrogationwindow was less that one-quarter of the window size. Itshould be noted that the vortex has nearly zero rotational(swirl) velocity at its center (axis of rotation), and hasmaximum swirl velocity at its core boundary. The corecenter, however, has a significant convection velocity. Be-cause the interrogation window size used was uniform (noadaptive grid has been developed yet) and is optimizedfor peak velocity measurements, the particle displacementnear the vortex center will be a very small fraction of thewindow size. This may not yield accurate results near thevortex core axis.

Furthermore, the combination of centrifugal and Cori-ollis forces affect the trajectories of seed particles awaynear the vortex core center (Ref. 15), which gives a clearseed void with a low concentration of seed particles, as

can be seen in Fig. 7. This further complicates the prob-lem of making measurements, because without enoughseed particles, the PIV analysis may not yield many ve-locity vectors in those regions. As a result, some of theinterpolated vectors obtained during data reduction comefrom this seed void region.

Determining the center of the vortex and estimating thecore radius at which the swirl velocity is a maximum, aretwo fundamental requirements for understanding the evo-lutional properties of tip vortices at any scale. Becausethe flow velocity vectors are measured through a spatiallydigitized grid over a given plane in the flow field, the prob-ability is relatively high that the grid lines will not passthrough either the center of the vortex or its core boundary.

Identifying the center of the vortex by estimating its cen-troid of vorticity is a procedure followed by many compu-tational fluid dynamic analysts (e.g., Ref. 16) as well as bysome experimentalists (e.g., Ref. 9). However, for the PIVmeasurements made in the current study it was found thatthe grid resolution at this small scale was not completelysufficient to accurately determine the centroid of vorticityby this approach. Therefore, the center of the vortex wasdefined as the mid-point of the peak swirl velocity thatexists on either side of the vortex flow.

This process brings in yet another complication of re-moving the local convection velocities of the tip vorticesthrough the wake flow. In the current experiment, this was

done by choosing equal number of points on either side ofthe vortex core, and averaging the tangential componentof velocity measured at these points. The velocity compo-nents associated with the rotation of the tip vortex is thencancelled, leaving only the convection velocity.

The next step was to increase the resolution of the gridto more accurately determine the tip vortex core bound-aries. This was done using Kriging, which is a standardtechnique followed to accurately interpolate the availabledata with less uncertainty. Kriging interpolates a value for

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each output cell by calculating a weighted average of thevalues at nearby points. Closer points are weighted moreheavily than more distant ones. The Kriging method ana-lyzes the statistical variation in values over different dis-tances and in different directions to determine the shapeand size of the point selection area as well as the set ofweighting factors that will produce the minimum error inthe interpolated estimate. The grid resolution was thenincreased by an order that resulted in the maximum dis-tance between adjacent nodes to be 0.05 mm, leaving themaximum possible uncertainty as less than 0.0125 mm.Once the vortex center was estimated, the procedure wasrepeated for multiple number of images that were obtainedat the same wake age. Upon identifying the center ofvorticity for all the images, the images were appropri-ately collocated so that the center of the tip vortices co-incided with each other. This allowed a determination ofthe phase-averaged flow properties.

Results

Flow Visualization

Flow visualization images were acquired at different wakeages by slipping the phase of the blade passage relative tothe plane occupied by the laser sheet. Figure 7 shows anexample of the concentrated vortices trailing from the tipsof blades. Because this was a two-bladed rotor system,every second tip vortex that appears in sequence on sameside of the image are 180 of wake age apart.

A closer view of the trailed vortex sheet that corre-sponds to the boxed region in Fig. 7 is shown in Fig. 8.This image clearly reveals the presence of more organizedtrailed eddies. These eddies identify regions of local con-

centrated vorticity that result from the merging of bound-ary layers from the upper and lower surfaces of the blade.In this case, the boundary layers are relatively thick be-cause of the low chord Reynolds numbers (< 50,000 atthe blade tip).

The trailed vortex sheet rolls up into a concentrated vor-tex near the blade tip, as shown in Fig. 9. Notice thatthe inboard parts of the helical vortex sheets convect ax-ially below the rotor at a much faster rate compared tothe tip vortices. This is because they are well inside theslipstream boundary of the rotor wake, and so the vortexsheets take on increasing inclinations to their initial (al-most parallel) orientation to the rotor plane, as seen in

Fig. 10. It should be noted that the downstream vortexsheets are clearly much thicker and are also more turbulentthan would be obtained with a rotor operating at higherblade Reynolds numbers. The net effect is that the helicalvortex sheets are folded down on top of each other, ulti-mately occupying a substantial part of the vena contracta.

Even though the parts of the vortex sheets that roll upinto the tip vortices appear more turbulent, the flow nearthe core axis of the tip vortex is clearly laminar seeFig. 11. This is similar to that found with tip vortices

that trail from blades operating at higher vortex Reynoldsnumbers (Ref. 8). In this case, a tip vortex generally showsthree distinct regions: 1. An inner laminar region wherethere is no mixing interactions between adjacent layers offluid, 2. A transitional flow region where there are eddiesof several scales and, 3. An outer turbulent region wherethe flow is mostly turbulent but relatively free of any largereddies. This multi-region structure arises mainly becauseof a Richardson number effect (Ref. 17), which is a ro-tational stratification effect, and so the relative size ofthe three regions in the vortex flow depend on the vortexReynolds number v/.

PIV Measurements

Representative PIV results in the rotor wake that were ob-tained at 33 wake age are shown in Fig. 12. The resul-tant velocity vectors V +Vr shows the slipstream bound-ary from the rotor. The flow is well-organized and has ahigher velocity inside the wake slipstream boundary with

essentially a quiescent flow outside the boundary. Themean velocity field shown in this figure was obtained byphase-averaging 80 individual PIV vector fields withoutcorrecting for aperiodicity. As previously discussed, it isdifficult to apply aperiodicity corrections to larger regionsof the flow because the individual parts of the vortices (atdifferent wake ages) exhibit aperiodic displacements withslightly different magnitudes and frequencies. As a result,correcting the flow field based on the aperiodic propertiesat one point in the flow simply introduces a biased andincorrect correction at other locations

The vorticity contours, which are shown in the back-ground of these images identifies the presence of threestrong tip vortices. The tip vortex that is present closer

to the rotor blade (33 wake age) has not yet rolled upcompletely, resulting in relatively lower levels of vortic-ity. However, by a wake age of 213, the vortex clearlyshows strong vorticity at its core, which then diffuses ra-dially away from the core as wake age further increases.It is apparent from this image that the tip vortices moveradially inward and axially downward as their wake ageincreases. Also, from the axial location of the vorticesbelow the rotor plane, it can be observed that the axialconvection velocity of the tip vortex increases after thefirst blade passage. Of course, these are fundamental fea-tures common to the wake development on rotors at largerscale.

Figures 13(a) and (b) show the average velocity field ac-quired before and after correcting for the effects of aperi-odicity, respectively. On comparing the vorticity contourson the background of both figures, it is apparent that theensemble phased-averaged vector plot identifies the max-imum vorticity at the vortex axis. The results of simpleaveraged vector plot shows the presence of a tip vortex,however, the vorticity is not a maximum at its center.

The images in the left column of Figs. 14 and 15 showthe ensemble phase-averaged velocity vector field for six

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Rotor blade

Tip vortex = 0 deg

Tipvortices

Tip vortex = 180 deg

Turbulentvortexsheet

Rotor shaft

Figure 7: Flow visualization image acquired at 0 wake age showing the trailed blade tip vortices and the innervortex sheet.

Rotor blade

Tip

vorticesMerging

boundarylayers

(vortex sheet)

Figure 8: Closer view of the vortex sheets trailing from the rotor blade at 0 wake age.

wake ages. The swirl velocity and vorticity distributionswere determined by making a horizontal cut across thecenter of the vortex, which are shown in the middle and

right columns of these figures, respectively. The tan-gential velocity distribution was normalized using the tipspeed of the rotor. It can be seen from the vorticity con-tours that the maximum value of vorticity is near the vor-tex axis at all wake ages, as would be expected. This isconfirmed through the vorticity distribution plotted acrossthe vortex. Also, it is apparent that the peak value ofvorticity reduces (hence diffusing vorticity radially out-ward) with increasing wake age, again as would be ex-

pected based on known tip vortex behavior at higher vor-tex Reynolds numbers.

The classical swirl velocity signature of a tip vortex canbe seen in all of the measured velocity profiles. Compar-ing the swirl velocity profiles measured at 26 and 63of wake ages reveals that the peak swirl velocity initiallyincreases with increasing time. Such an observation hasbeen reported earlier using tip vortex measurements thatwere obtained from a sub-scale rotor (Ref. 18). However,the initially lower peak swirl velocity in the present case islikely attributed to the increased boundary layer thicknesson the blade at this low chord Reynolds number, which

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Tip vortex = 10 deg

Tipvortices

Tip vortex = 190 deg

Turbulentvortex sheet

Rotor shaft

Figure 9: Flow visualization image obtained at 10 of wake age showing the roll up of the vortices at the tip of theblade.

Rotor blade Tip vortex = 73 deg

Tipvortices

Turbulentvortex sheet

Rotor shaft

Figure 10: Flow visualization image obtained at 73 wake age showing the higher axial convection velocities of thevortex sheets when compared to the convection velocity of the tip vortices.

could more significantly affect the initial development ofthe tip vortex. This can also be seen from Fig. 12, wherethe tip vortex at a wake age of 213 exhibits higher valuesof vorticity than at 33. The effects of viscous diffusioncan be seen from the swirl velocity profiles at older wake

ages, which thereafter exhibit a continuous reduction ofpeak swirl velocity with increasing wake age. This is ac-companied by an increase in the vortex core size (definedas the distance between two swirl velocity peaks), whichis consistent with conserved core circulation.

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Figure 11: Flow visualization image obtained at 90 of wake age showing the three-region flow structure inside thetip vortices.

Figure 12: PIV velocity vector plots obtained at 33 of wake age, also clearly showing the slipstream boundary.

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(b)(a)

Figure 13: PIV velocity vector plots obtained at 26 of wake age before and after correcting for the effects ofaperiodicity.

The circulation distribution in the tip vortices can be de-termined from the swirl velocity profiles given in Figs. 14and 15. Based on the assumption that the flow inside thevortex is closely axisymmetric, the circulation distributioncan be calculated using the expression

Rc= 2

V

R

r

c

(5)

The tip vortex strength, v, is related to maximum bound

circulation on the blade, b, and can be estimated fromRef. 6 using

vRc

=bRc

= k

CT

(6)

where k= 2 for a rotor blade with ideal twist and k= 3for an untwisted blade. For the current operating condi-tion of this rotor, the estimated value ofb/Rc is 0.256,which is consistent with the measurements ofv. It canbe observed from Fig. 16 that the total vortex circulationapproaches the value of bound circulation at large radialdistance away from the center of the vortex.

Tip Vortex Core Growth

The relative viscosity of the fluid plays a substantial rolein the evolution of all lift-generated tip vortices. This is es-pecially true in the case of MAV-size rotors, which alwayscreate tip vortices that have much lower vortex Reynoldsnumbers than achieved with even moderately larger rotors.The viscous spin-down and core growth behavior of thesetip vortices are often explained using Lamb-like models.

Figure 16: Measured circulation distribution across

the tip vortices at various wake ages.

Lamb and Oseen (Refs. 19, 20) derived an exact solutionto the NavierStokes equations to predict the core growthrate of laminar vortices, which is given by the simple ex-pression

rc(t) =

4t (7)

where is Lambs constant and is the kinematic viscos-

ity of the fluid. This result is based on the assumption thatthe flow inside the vortex is completely laminar, althoughthis is really not a correct assumption based on the flow vi-sualization results shown previously in Fig. 11. The term tis time, which represents in this case the real time elapsedsince the tip vortex was trailed from the blade. The useof real time to compare the growth properties of laminartip vortices at any vortex Reynolds number is entirely ap-propriate. This is because the transfer of momentum be-tween adjacent layers of fluid is only through molecular

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Figure 14: Velocity and vorticity distributions across the tip vortex for wake ages of 26, 63, and 83.

diffusion. This would mean that the time scale governingcore growth is only dependent on the fluid properties (i.e,the effective kinematic viscosity), which is independent of

vortex Reynolds number if the flow is completely laminar.For real vortices, the transfer momentum and vorticity

between adjacent layers of fluid due to turbulence yieldsthe concept of eddy viscosity, which can be viewed as ameasure of turbulence in any given flow field. The corre-sponding vortex core growth is then given by

rc(t,) =

4t (8)

where > 1 accounts for the increased eddy viscosity in

the vortex flow, on average. It is known that is a functionof vortex Reynolds number (Refs. 17, 21, 22); an increasein vortex Reynolds number results in an increase in turbu-

lence that, in turn, increases the average eddy viscosity inthe vortex flow and so increases the core growth rate.

Vortex models based on the LambOseen model can bemodified empirically to include the effects of turbulence,which then have different values of averge eddy viscosityat different vortex Reynolds numbers. This means that thetime scale (which is dependent on the total viscosity) willbe different at different vortex Reynolds numbers. There-fore, the comparison of vortex core growth measurements

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Figure 15: Velocity and vorticity distribution across the tip vortex for wake ages of 123, 163, and 263.

acquired at significantly different Reynolds numbers us-ing the same time scale is probably not appropriate, andthat the time scale must be normalized by an appropri-ate scaling parameter that must take into account vortex

Reynolds number effects.

This concept can be better explained by plotting thecore size of the tip vortices measured in the current exper-iment with the micro-rotor and comparing them to resultsmeasured from a sub-scale rotor operated at much highervortex Reynolds numbers, which are shown in Fig. 17. Itcan be seen from this figure that the tip vortex core mea-sured from the MAV-size rotor appears much higher at thesame wake age. Despite the fact that the vortex Reynolds

number of MAV-size rotor is about five times smaller thanthose even in the sub-scale measurements, when plottedversus wake age the value of appears to be twice thatof the sub-scale measurements. This would imply that the

tip vortices trailing the MAV-size rotor at the same agecontain on average twice the amount of turbulence com-pared to the vortices from the sub-scale rotor. This doesnot seem reasonable bearing in mind the much lower vor-tex Reynolds number at MAV-scale.

This problem can be further understood by plotting thetip vortex measurements from the micro-rotor in terms ofequivalent peak swirl velocity and equivalent downstreamdistance using an Iversen-type correlation curve (Ref. 22),

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Figure 17: Comparison of the measurements of tip

vortex core size at different Reynolds number with in-

creasing wake age.

Figure 18: Iversen-type of correlation function used to

consolidate all tip vortex measurements.

as shown in Fig. 18. Tip vortex measurements acquiredat different vortex Reynolds numbers (both rotating- andfixed-wings) have been plotted along with Iversens solu-tion. It is apparent from the figure that the measurementsfrom the micro-rotor correlates well with the Iversenmodel. This suggests that the growth characteristics of thetip vortices trailed from the micro-rotor should be substan-tially similar to that generated by any type of tip vortex. Asubstantially higher value of (growth rate) suggested byFig. 17, therefore, cannot be physical.

The viscous core size and growth rate of the vortex atany given time depends at least on four parameters: 1. Theinitial core size as it leaves the blade, 2. The total viscos-ity of the fluid (kinematic plus eddy, +t), 3. Time orwake age and, 4. The strain (stretching or squeezing) ex-

Figure 19: Variation of the tip vortex core growth ver-

sus normalized time for the sub-scale rotor measure-

ments.

Figure 20: Variation of the tip vortex core growth

with normalized time for the MAV-size rotor measure-

ments.

perienced by the filament as it convects in the flow. Theinitial core size, r0, takes into account the thickness of theboundary layer on the blade (which also rolls up into thetip vortices) and the total viscosity addresses the effectsof scaling (vortex Reynolds number, v/). Using dimen-sional analysis, an equivalent time parameter can be de-fined as

Te =t

c2/v=

/

c2/v=

R

c

vRc

(9)

with the assumption that any strain effects on the vor-

tex flow are negligible. This equivalent time parametercan also be derived from the non-dimensional similarityvariable used in the RamasamyLeishman vortex model(Ref. 17), which is an exact solution to the NavierStokesequations for a vortex flow.

Using this equivalent time concept, the measured coregrowth of the tip vortex is compared in Figs. 19 and20 with measurements from the larger sub-scale rotor.Clearly, the initial core radius of the MAV-size rotor ismuch higher. This is expected and, as mentioned earlier,

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Figure 21: Normalized circulation of the tip vortices

from the MAV-size rotor relative to Iversens solution.

is partly a result of the relatively thick boundary layers onthe blade that determine the initial structure of the tip vor-tices. Upon comparing the results in the two figures, it isapparent that when plotted in terms of equivalent time Te,the core growth of the MAV-size rotor is nearly identicalto that of the sub-scale rotor. Even though the growth rateof tip vortices is much smaller than that was predicted ear-lier based on Fig. 17, it is higher despite the lower vortexReynolds number.

A further analysis of the micro-rotor tip vortex mea-surements is obtained by plotting the ratio of core circula-tion to the total vortex circulation as a function of vortexReynolds number (as obtained from the Iversens exactsolution to the NS equations (Ref. 22) see the resultsin Fig. 21. A larger value for this ratio (0.707 for laminarflow) would mean that the vortex will diffuse its containedvorticity more slowly. It is apparent that the value of this

ratio for the micro-rotor measurements is smaller whencompared with the Iversens solution at the measured vor-tex Reynolds number (10,000). This may be because ofthe observed increase in boundary layer thickness on theblade (because of the lower chord Reynolds number), al-though further work must be done to examined this hy-pothesis.

Conclusions

The performance of a small rotor typical of application toa rotating-wing micro-air vehicle has been measured. This

was accompanied by flow visualization and PIV measure-ments in the wake of the rotor. It has been shown thatthe wakes generated by the rotor blades are thicker andmore more turbulent than compared to the wakes gener-ated by rotors operating at higher chord Reynolds num-ber. A closer examination of the vortex sheets revealeda more organized series of discrete eddies along the bladespan. The tip vortex structure also showed some importantdifferences from that expected on rotors operated largerchord Reynolds numbers. The following specific conclu-

sions have been drawn from this study:

1. The hover performance of a MAV will directly de-pend on its effective disk loading and its aerody-namic efficiency (FM). Decreasing the effective diskloading increases the power loading and attemptingto raise the FMby reducing both induced and profilelosses are the primary requirements for developingany form of efficient hovering MAV.

2. The maximum FM values measured for this smallrotor were found to be substantially lower (no morethan 0.5) than for rotors operated higher chordReynolds number (which often approach 0.8). Theincreased boundary layer thicknesses on the bladesand the more turbulent wake trailed from the blades(both of which increase losses), seem to play an im-portant role in reducing the F M of rotating-wingsthat are operated at low chord Reynolds numbers.

3. Viscous effects, which are relatively more importantat low Reynolds numbers, appears to affect the initial

formation and roll-up of the blade tip vortices, whichdo not reach their full circulation until some distancedistance downstream of the blade. This roll-up is fol-lowed by diffusion of vorticity, which results in an in-creased tip vortex core size and a reduced peak swirlvelocity with increasing wake age.

4. The properties of blade tip vortices that are measuredat vastly different vortex Reynolds numbers must beproperly analyzed on the same equivalent time scale.It was shown than by using an equivalent time param-eter to compare the vortex core sizes the growth rateof the tip vortices is similar to that found at highervortex Reynolds numbers.

Acknowledgments

This research was supported, in part, by the Multi-University Research Initiative under Grant ARMYW911NF0410176. Gary Anderson is the technical moni-tor. The authors wish to acknowledge the contributions ofJayant Sirohi and Moble Benedict in helping to measurethe performance of the micro-rotor.

References

1Ellington, C. P., and Usherwood, J. R., Lift andDrag Characteristics of Rotary and Flapping Wings,Fixed and Flapping Wing Aerodynamics for Micro-AirVehicle Applications, Edited by Thomas A. Mueller,Vol. 195 of AIAA Progress in Aeronautics and Astronau-tics, Chap. 12, AIAA, Reston, VA, 2001, pp. 231248.

2Tarascio, M., Ramasamy, M., Chopra, I., and Leish-man, J. G., Flow Visualization of MAV Scaled Insect

14


15/15

Based Flapping Wings in Hover, Journal of Aircraft,Vol. 42, (2), March 2005, pp. 355360.

3Ramasamy, M., Leishman, J. G., and Beerinder Singh.,Wake Structure Diagnostics of a Flapping Wing MAV,2005 SAE Transactions Journal of Aerospace, Vol. 114(1), February 2006, pp. 907919.

4

Laitone, E. V., Aerodynamic Lift at Reynolds NumberBelow 7104, AIAA Journal, Vol. 34, (9), September1996, pp. 19411942.

5Laitone, E. V., Wind Tunnel Tests of Wings atReynolds Number Below 70,000, Experiments in Flu-ids, Vol. 23, 1997, pp. 405409.

6Leishman, J. G., Principles of Helicopter Aerodynam-ics, 2nd Edition, Cambridge University Press, New York,NY, 2006.

7Martin, P. B., Pugliese, G., and Leishman, J. G., HighResolution Trailing Vortex Measurements in the Wake ofa Hovering Rotor, Journal of the American Helicopter

Society, Vol. 49, (1), January 2003, pp. 3952.8Ramasamy, M., and Leishman, J. G., Interdepen-

dence of Diffusion and Straining of Helicopter Blade TipVortices, Journal of Aircraft, Vol. 41, (5), SeptemberOctober 2004, pp. 10141024.

9McAlister, K., Rotor Wake Development During theFirst Rotor Revolution, Journal of the American Heli-copter Society, Vol. 49, (4), October 2004, pp. 371390.

10Heineck, J. T., Yamauchi, G. K., Wadcock, A. J., andLourenco, L., Application of Three-Component PIV toa Hovering Rotor Wake, American Helicopter Society

56th Annual National Forum, Virginia Beach, VA, May24, 2000.

11Yu., Y. H., and Tung, C., The HART-II Test: Ro-tor Wakes and Aeroacoustics with Higher Harmonic PitchControl (HHC) Inputs, American Helicopter Society 58th

Annual National Forum, Montreal, Canada, June 1113,2002.

12Cook, C. V., The Structure of the Rotor Blade Tip Vor-tex, Paper 3, Aerodynamics of Rotary Wings, AGARDCP-111, September 1315, 1972.

13Kraft, C. C., Flight Measurements of the VelocityDistribution and Persistence of the Trailing Vortices of an

Airplane, NACA TN 3377, 1955.

14Boatwright, D. W., Three-Dimensional Measure-ments of the Velocity in the Near Flow Field of a Full-Scale Hovering Rotor, Mississippi State University Re-port EIRS-ASE-74-4, 1974.

15Leishman, J. G., On Seed Particle Dynamics inTip Vortex Flows, Journal of Aircraft, Vol. 33, (4),July/August 1996, pp. 823825.

16Duraisamy, K., and Baeder, J., Studies on Tip VortexFormation, Evolution and Control, Ph.D. Dissertation,University of Maryland, April 2005.

17Ramasamy, M., and Leishman, J. G., A GeneralizedModel For Transitional Blade Tip Vortices, Journal of theAmerican Helicopter Society, Vol. 51, (1). January 2006,pp. 92103.

18Leishman, J. G., Baker, Andrew., and Coyne, Alan.,Measurements of Rotor tip Vortices Using Three-Component Laser Doppler Velocimeter, American He-licopter Society International Aeromechanics SpecialistsConference, Bridgeport, CT, October 1113, 1995.

19Lamb, H., Hydrodynamics, 6th ed., Cambridge Uni-versity Press, Cambridge, 1932.

20Oseen, C. W., Uber Wirbelbewegung in einer reiben-den Flussigkeit, Arkiv f or Matematik, Astronomi ochFysik., Vol. 7, (14), 1911, pp. 1421.

21Squire, H. B., The Growth of a Vortex in TurbulentFlow, Aeronautical Quarterly, Vol. 16, August 1965,pp. 302306.

22Iversen, J. D., Correlation of Turbulent Trailing Vor-tex Decay Data, Journal of Aircraft, Vol. 13, (5), May1976, pp. 338342.

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2006-ahs-flow field of micro-rotor

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