2008-ERF-Dual plane PIV paper 2

Turbulence Measurements in Blade Tip Vortices UsingDual-Plane Particle Image Velocimetry

Bradley Johnson∗ Manikandan Ramasamy† J. Gordon Leishman‡

Department of Aerospace EngineeringGlenn L. Martin Institute of Technology

University of Maryland, College Park, MD 20742

Abstract

The characteristics of the blade tip vortices generated bya hovering rotor were studied using dual-plane stereo-scopic digital particle image velocimetry (DPS-DPIV).The DPS-DPIV technique permitted the non-invasivemeasurement of the three components of the velocity field,as well as the nine-components of the velocity gradi-ent tensor. DPS-DPIV is based on coincident flow mea-surements made over two differentially-spaced laser sheetplanes, thus allowing for velocity gradient calculations tobe made also in the direction orthogonal to the measure-ment planes. A polarization–based technique employingbeam-splitting optical cubes and filters was used to givethe two laser sheets orthogonal polarizations, and to en-sure that the cameras imaged Mie scattered light fromonly one or the other laser sheet. The digital processingof the images used a deformation grid correlation algo-rithm, optimized for the high velocity gradient and small-scale turbulent flows found inside the vortices. Detailedturbulence measurements provided the fluctuating termsthat are involved in the Reynolds-averaged stress trans-port equations. The results have shown that an isotropicassumption of turbulence is invalid inside the tip vortices,and that stress should not be represented as a linear func-tion of strain. The measurement of all nine velocity gra-dients also allowed for precise measurements of the in-clination between the vortex axis and measurement plane,which were found to be almost orthogonal at all vortexwake ages.

∗ NDSEG Fellow. [email protected]† Assistant Research Scientist. [email protected]‡ Minta Martin Professor. [email protected]

Presented at the 34th European Rotorcraft Forum, September16–19, 2008, Arena and Convention Center, Liverpool, Eng-land. c©2008 by Johnson, Ramasamy & Leishman. All rightsreserved. Published by the Royal Aeronautical Society of GreatBritain with permission.

NomenclatureA rotor disk areac blade chordCT rotor thrust coefficient, = T/ρAΩ2R2

i, j, k unit directional vectors~n vector normal to measurement plane(s)p static pressurer, θ, z polar coordinate systemr0 initial core radius of the tip vortexrc core radius of the tip vortexR radius of bladeRi Richardson’s numberRev vortex Reynolds number, = Γv/ν

u, v, w velocities in Cartesian coordinatesu′, v′, w′ normalized RMS velocities (Cartesian)u′v′ normalized Reynolds stress in X ,Y planev′w′ normalized Reynolds stress in Y,Z planeu′w′ normalized Reynolds stress in X ,Z planeVr, Vθ radial and swirl velocities of the tip vortexV ′

r , V ′θ, V ′

z normalized RMS velocitiesVtip tip speed of bladex, y, z vortex coordinate system (Cartesian)X , Y, Z DPIV coordinate systemα Lamb’s constant, = 1.25643Γv total vortex circulation, = 2πrVθ

δ ratio of apparent to actual kinematic viscosityδi j Kronecker deltaθ inclination between~n and vortex axisθMP inclination between laser sheet and vortex axisν kinematic viscosityζ wake ageρ air densityσ strainψ azimuthal position of blade~ω vorticity vectorΩ rotational speed of the rotorτ stress2-C two-component3-C three-component

IntroductionDecades of research have been directed toward gaining anunderstanding of the complex vortical wake generated byrotor blades (e.g., Refs. 1–10), and assessing the effectsof the wake on vehicle performance, unsteady airloads,vibration, and noise levels. Much of the research hasbeen rightfully focused on better understanding the bladetip vortices, which are the dominant features of the rotorwake (e.g., Refs. 11–18). It is important to better under-stand and predict the physics that determine the formation,strength, and trajectories of these tip vortices so as to de-velop more consistent and reliable mathematical modelsthat describe the aerodynamics of the rotor. To this end, norotor wake model can be completely successful unless itis able to accurately represent the three-dimensional, tur-bulent flows that are present inside the vortices.

Predicting rotor wake developments using computa-tional fluid dynamics (CFD) based on N–S methods aresteadily on the rise. Direct numerical solution (DNS)of the N–S equations is presently unrealistic for ro-tor wake problems because of the high computationalexpense, and more effort has been focused in solv-ing the Reynolds-Averaged Navier–Stokes (RANS) equa-tions. RANS methods represent a time-average form ofthe N–S equations in which the flow velocity ui at a pointis represented as a combination of a mean component uiand a fluctuating component u′i, as given by the equation

ui = ui +u′i (1)

Using Eq. 1 results in the RANS equations, as given by

Dui

Dt=

∂

∂x j

[−

p δi j

ρ+ν

(∂ui

∂x j+

∂u j

∂xi

)−u′iu

′j

](2)

where D/Dt is the substantial derivative and uiv j is thecorrelation (or shear stress) term. The overbar in each caserepresents the time-averaged or mean values.

Time-averaging the N–S equations to form the RANSequations bypasses the need to explicitly compute thehigh-frequency, small-scale fluctuations caused by turbu-lent eddies in the flow (i.e., the u′i and u′j terms). However,this advantage is countered by the creation of an additionalunknown term, the Reynolds stress u′iu

′j. This term makes

the RANS equations unsolvable unless a closure model isused to rebalance the number of equations and unknowns.This so-called “correlation term” basically accounts forthe effect of velocity fluctuations created by the presenceof eddies of different length scales. All such turbulenceclosure models are based on actual flow measurements,so the model adopted must be consistent with the flowphysics to correctly model the contributions of the turbu-lence to the developing flow. The model must also con-sider any numerical stability limits inherent to the specific

discretization scheme being used. Because different tur-bulence models must be developed for different physicalproblems and types of flows, the models will understand-ably vary in complexity and in the number of equationsand coefficients used in the model (Refs. 19–23). Gen-erally, the closure coefficients and damping functions inthese models have been derived from experimental mea-surements on free shear or homogenous flows.

The primary objective of the present work was to givebetter understanding of the turbulence production, trans-port, and diffusion in the rotor wake, and more specifi-cally, the blade tip vortices. This required velocity mea-surements of high spatial and temporal resolution, andwas accomplished using digital particle image velocime-try (DPIV). A dual-plane DPIV technique (DPS-DPIV)was developed to simultaneously measure the velocities,as well as the six in-plane velocity gradients and threeout-of-plane velocity gradients needed for measuring thecomplete turbulence field.

Description of the PresentExperiment

Two DPIV systems were used to measure the flow veloc-ity simultaneously in two parallel, adjacent planes, whichwere situated behind the blade of a one-bladed rotor sys-tem. The present study involved the use of a dual-planestereo digital particle image velocimetry (DPS-DPIV)system comprising of a pair of 4 mega-pixel CCD cam-eras and a single 2 mega-pixel CCD camera.The majorityof discussion in this paper is focused on the issues associ-ated with the DPS-DPIV concept, and the techniques usedto achieve these simultaneous, dual-plane flow measure-ments.

Rotor SystemA single bladed rotor operated in hover was used for themeasurements. The advantages of the single blade rotorinclude the ability to create and study a helicoidal vortexfilament without interference from other vortices gener-ated by other blades (Ref. 24), and the fact that a singlehelicoidal vortex is much more spatially and temporallystable than multiple vortices (Ref. 25). This allows forthe vortex structure to be studied to much older wake ageswithout the high levels of aperiodicity in the flow that isproduced when using multi-bladed rotors.

The single blade was of rectangular planform, un-twisted, with a radius of 406 mm (16 inches) and chordof 44.5 mm (1.752 inches), and was balanced with acounterweight. The blade airfoil section was the NACA2415 throughout. The rotor tip speed was 89.28 m/s(292.91 ft/s), giving a tip Mach number and chord

Reynolds number of 0.26 and 272,000, respectively. Thezero-lift angle of the NACA 2415 airfoil is approximately−2 at the tip Reynolds number. All the tests were madeat an effective blade loading coefficient of CT /σ ≈ 0.064using a collective pitch of 4.5 (measured from the chordline). The rotational frequency of the rotor was set to35 Hz (Ω = 70π rad/s).

DPS-DPIV Requirements and SetupDPS-DPIV differs from conventional DPIV because it canmeasure all nine components of the velocity gradient ten-sor, in addition to the three velocity components. The ve-locity gradient tensor can be written as

∇V =

∂u/∂x ∂u/∂y ∂u/∂z∂v/∂x ∂v/∂y ∂v/∂z∂w/∂x ∂w/∂y ∂w/∂z

(3)

A conventional, stereoscopic (3-component) DPIV sys-tem is capable of measuring three components of veloc-ity in a given plane (Refs. 26–29), but only six of thenine velocity gradient tensor components. Estimating allof the velocity gradients in the out-of-plane direction (i.e.,finding the ∂/∂z terms in Eq. 3) with DPIV requires themeasurement of three components of velocity in at leasttwo planes that are parallel to each other, and separatedby a small spatial distance in the z direction. An in-situ calibration procedure was used to determine the rela-tionships between the two-dimensional image planes andthree-dimensional object fields for both position mappingand 3-C velocity reconstruction (see later).

DPS-DPIV Imaging Arrangement

The optical setup of the current DPS-DPIV system isshown in Fig. 1. Two coupled DPIV systems are re-quired to simultaneously measure the flow velocities fromthe Mie scattering of the particles passing through bothlaser sheet planes. Three dual Nd-YAG lasers with 110mJ/pulse were used, the third laser being used to imagethe flow in regions where the blade cast a shadow fromthe other lasers, thereby preventing the need to mosaic theresulting images.

The DPS-DPIV system can be arranged as a combina-tion of two stereoscopic PIV systems, or as a combinationof one stereoscopic PIV system and one 2-component PIVsystem (Refs. 30, 31). While the former combination pro-vides all the three components of velocity in both of thetwo parallel planes, the latter provides all the three com-ponents of velocity in one plane and only the in-plane ve-locities (i.e., two components) in the other plane. The out-of-plane velocity is then calculated using the assumptionof mass conservation in the flow. This second method pro-vides several advantages over the dual-plane stereoscopic

(a) Schematic

(b) Three dual Nd-YAG lasers illuminating the flow

(c) Close-up of CCD cameras and beam splitting cubes

Figure 1: Schematic and photographs of the DPS-DPIV system as used for the rotor wake studies: (a)Schematic, (b) Lasers used to image the flow, (c) Close-up of cameras and beam splitting cubes.

setup, not least because of its simpler configuration andlower cost.

The present setup is shown in Fig. 1. The conventional2-C DPIV configuration (the 2 mega-pixel camera is la-beled as C2 in Fig. 1) is used to measure two compo-nents of flow velocity in one plane, while a stereo setup(a pair of 4 mega-pixel cameras labeled C1 and C3 inFig. 1) is used to measure the three flow velocity com-ponents in the second plane. The stereo cameras satisfiedthe Scheimpflug condition for DPIV imaging. Mass con-servation in the form of Eq. 4 was applied to estimatethe third component of velocity in the 2-C measurementplane (shown in green) by using the incompressible flowequation

w1 =−(

∆u1

∆x+

∆v1

∆y

)∆z+w2 (4)

The resulting velocity fields that are measured in the twoplanes (Fig. 2) can then be analyzed to determine all ninecomponents of the velocity gradient tensor in Eq. 3.

However, to maintain accuracy with these velocity gra-dient calculations several precautions have to be taken. Interms of the set up procedures, the two laser light sheetplanes must be both parallel and adjacent (ideally just asmall distance apart) to each other. Additionally, the twoNd-YAG lasers must be phase synchronized, not only witheach other, but also with both sets of cameras and pre-cisely to the rotational frequency of the rotor.

Figure 2: Typical instantaneous velocity fields mea-sured using DPS-DPIV. Interplane separation is exag-gerates; actual plane separation is much smaller thanvector-to-vector spacing within each plane.

Each laser pair (i.e., lasers 1 & 2 and lasers 3 & 4shown in Fig. 1) delivers two pulses of laser light witha pulse separation time of 2 µs. The first laser pulse fromthe green pair (laser 1) is synchronized with the first laserpulse from the blue pair (laser 3), and the same for the sec-ond laser pulse from each laser pair (lasers 2 & 4). Eachof the three cameras must then be synchronized with thelasers (i.e., the first particle pair image in each plane iscaptured upon the firing of lasers 1 & 3 and the secondimage in each plane is captured during the firing of lasers2 & 4).

There are several challenges with simultaneous mea-surements in spatially adjacent, parallel laser planes,mainly resulting from crosstalk between cameras.Crosstalk, which manifests as Mie scattering from bothilluminated laser planes, can occur because each camerahas a finite depth of field. If any camera images both laserplanes, not only will its planar velocity map be erroneousafter DPIV processing, but the comparison between thevelocity map in the first plane with that of the second plane(which is needed to calculate velocity gradients in the zdirection) would be meaningless. This problem is height-ened by the need to have the intensity of each laser setto high levels so that sufficient Mie scattering can be cap-tured by all of the cameras with approximately the samelevels of intensity.

Laser Polarization

To guarantee that each respective set of cameras only im-ages the flow in its designated laser plane, the special op-tical setup shown in Fig 1 was used. The purpose wasto split the polarizations of the two respective laser pairs(notice that lasers 1 & 2 are s-polarized and lasers 3 &4 are p-polarized), and then to use appropriate filters andbeam-splitting optical cubes placed in front of each cam-era to guarantee that they only imaged one type of polar-ized light. In the present setup, the center 2-C camera (C2)was tuned to the s-polarization of lasers 1 & 2, and thestereo cameras (C1 & C3) were tuned to the p-polarizedlight lasers from lasers 3 & 4.

Figure 1 shows how the Mie scattered blue (p-polarized) and green (s-polarized) light come from eachrespective laser sheet. One beam splitting cube in front ofthe 2-C camera initially images both sets of scattered im-ages, and allows the p-polarized blue light to pass throughdirectly but redirects the s-polarized green light to a sec-ond beam splitting cube. The second cube acts as 45 mir-ror by redirecting the s-polarized light into the camera. Alinear filter over the lens acts as a final buffer against anystray p-polarized light. Each stereo camera also has onebeam splitting cube placed in front of it. This redirectsthe s-polarized light into separate light dumps adjacent tothe cubes, and allows the p-polarized blue light to pass

Figure 3: Schematic of the timing circuit for the DPS-DPIV setup.

through to the camera lens. Each stereo camera has a lin-ear filter over the lens (oriented at a different angle thanthat of the 2-C camera) to act as a final buffer againstany s-polarized light. Final verification of the workingcondition of the optical setup was made before measure-ments were started to ensure that the cameras see only Miescattering from their designated lasers (i.e., to ensure thatthere was absolutely no image crosstalk).

Another challenge with DPS-DPIV involves the needfor coincident flow measurements in each image plane.Even after optically separating the two DPIV systems,care has to be taken to ensure that both systems are syn-chronized with each other so that the flow is measured co-incidently in each laser plane. This synchronization willguarantee that the turbulence measurements will be de-rived from exactly the same flow features. Figure 3 showsthe timing diagram of the DPS-DPIV experiment, whichtakes a 1/revolution pulse signal from the rotor, and usesthis signal to synchronize both Nd:YAG laser pairs witheach other and their respective imaging cameras.

DPS-DPIV Particle Image Processing

The digital processing of the acquired images from cam-eras used a deformation grid correlation algorithm (seeRef. 32), which is well-optimized for the high velocity

Figure 4: Schematic of the steps involved in the defor-mation grid correlation.

gradient flows found in blade tip vortices. The interroga-tion window size was chosen in such a way that the imagesfrom both the cameras were resolved to approximately thesame spatial resolution to allow for velocity gradient mea-surements in the out-of-plane direction.

The steps involved with this correlation algorithm areshown in Fig. 4. The procedure begins with the corre-lation of an interrogation window of a defined pixel size(say, 64-by-64), which is the first iteration. Once the meandisplacement of that region is estimated, the interrogationwindow of the displaced image is moved by integer pixelvalues for better correlation during the second iteration.The third iteration then moves the interrogation windowof the displaced image by sub-pixel values based on thedisplacement estimated from second iteration. Followingthis, the interrogation window is sheared twice (for integerand sub-pixel values) based on the velocity magnitudesfrom the neighboring nodes, before performing the fourthand fifth iteration, respectively.

Once the velocity is estimated after these five iterations,the window is split into four equal windows (of pixel size32× 32). These windows are moved by the average dis-placement estimated from the final iteration (using a pixelwindow size of 64× 64) before starting the first iterationat this resolution. This procedure can be continued untilthe resolution required to resolve the flow field is reached.The second interrogation window is deformed until theparticles remain at the same location after the correlation.

DPS-DPIV Calibration

DPS-DPIV imaging requires a calibration process to in-corporate the registration of the cameras and their map-ping from the object plane onto the image plane to correctfor distortions from variable magnification across the im-age. For the present system, the single camera and stereocamera pair were mapped in the usual way, followed bythe additional step mapping of the cameras to a single ref-erence frame. The latter was required to map the two in-

dependent DPIV grids onto a single grid for gradient cal-culation between corresponding nodes from the two ac-quired DPIV velocity vector maps.

A nonlinear mapping function was created from imagesof a dual-plane calibration target. This precision calibra-tion target was made from regular grid of white dots on ablack anodized background. The resulting mapping func-tion accounts for the distortion and provides the third out-of-plane velocity component. The calibration target wasmounted on a micrometer-controlled translation stage. Afiducial reference point on the target defined the origin forall the calibration images.

Post-Measurement Corrections

In addition to the challenges associated with DPIV imageacquisition and image processing (see Ref. 26 for exam-ple), there are several other post-measurement challengesthat can depreciate the accuracy of the mean and turbu-lent flow characteristics from a series of DPIV velocityvector maps. Two of these include: (1) The inherent ape-riodicity in the trajectory of the blade tip vortices; (2) theinclination of the measurement plane with respect to therotational axis of the vortex.

Aperiodicity Correction

Making the distinction between mean and turbulent ve-locities in the tip vortex is complicated by the fact thatthe wake general becomes more aperiodic at older ages.This is a natural behavior of convecting vortex filaments,which are known to develop various types of self- andmutually-induced instabilities that can be described as“wake modes” (Refs. 25, 33, 34). In successive instanta-neous DPIV vector maps this causes the spatial locationsof the tip vortices to change slightly from one rotor rev-olution to the next, and so the effect appears as an aperi-odicity effect (sometimes known as “wandering”) of thevortex center relative to a mean position. Unless this ape-riodicity effect is properly and accurately corrected for, itwill manifest as a bais in the measurements of the turbu-lent flow components based on Eq. 1.

To extract accurate mean flow velocities, the positionsof the vortices first have to be co-located such that the cen-ter of each vortex image is aligned with one another. Thisguarantees that the individual mean velocities at a pointin the flow are calculated based on locations with respectto a defined tip vortex “center” and not based on its un-adjusted location with respect to the image boundaries.The helicity-based aperiodicity bias correction procedurewas used in the present study, as discussed in detail inRef. 26. Mean and turbulence measurements were madefrom 1,000 instantaneous velocity vector maps, colocat-ing them such that the point of maximum helicity (i.e., the

value of ωz ·w) coincided in each of the instantaneous vec-tor maps before the phase-averaging occurred. Only af-ter applying the conditional helicity phase-averaging tech-nique can accurate mean vortex flow properties be esti-mated.

Measurement Plane Inclination

One further challenge to estimating vortex propertieswithin finite measurement plane(s) is the need to ensurethat the measurement planes (as determined by the ori-entation of the laser light sheets) is normal to the rota-tional axis of the vortex flow. If the measurement planeis inclined with respect to the vortex axis by more than afew degrees, the planar velocity maps the vortex proper-ties will be in error.

Historically (as in the works of Refs. 26, 35, 36), themeasurement plane has been aligned parallel to the meanaerodynamic center line of the blade (usually taken as the1/4-chord). The measurements are then performed underthe assumption that the rotational axis of the tip vortexremains perpendicular to the 1/4-chord line, regardless ofthe vortex wake age.

To confirm this assumption, however, the orientation ofthe three-dimensional vorticity vector at the center of thevortex can be calculated. This requires the velocity gradi-ents in all three flow directions to calculate the curl of thevelocity field. Here, the dual-plane technique is especiallyuseful in that all nine velocity gradients in the vortex flowcan be measured.

The measurement plane itself provides the referenceaxes from which the velocity gradients are calculated. Thevorticity vector can be written as

~ω = ωx i+ωy j +ωz k (5)

where i, j, and k are unit vectors along the x, y, and z axesof the measurement plane, and ωx, ωy, and ωz are the threecomponents of vorticity, respectively, as given by the curlof the velocity field, i.e.,

ωx = ∂w/∂y−∂v/∂z

ωy = ∂x/∂z−∂w/∂x

ωz = ∂y/∂x−∂u/∂u (6)

To find the angle θ between the vorticty vector and theunit normal vector of the measurement plane, ~n, the dotproduct of the two vectors must be calculated. Here, ~n =0i + 0 j + 1k, so that

θ = cos−1(

~ω ·~n|~ω|

)(7)

For a perfectly aligned measurement plane, the normalvector and the vorticity vector should be aligned, i.e., θ =

Wake age, ζ ωx ωy ωz Measurement plane inclination, θMP(degrees) (1/s) (1/s) (1/s) (degrees)

4 1907 3864 55212 8615 2236 5868 57122 8430 502 4138 54180 8760 1463 125 36361 88

Table 1: Inclination of the Measurement plane with respect to the vortex axis at 4 different wake ages.

0. This corresponds to an 90 angle between the mea-surement plane and the vortex axis, i.e., θMP = 90−θ.

This calculation was performed at four different wakeages, and the results are given in Table 1. For the dual-plane flow experiments, the two laser light sheets (i.e., thetwo measurement planes) were aligned parallel to the 1/4-chord line of the blade. With this particular setup, theangles θMP were found to be between 84 and 90.

These results verify that the laser alignment with theblade 1/4-chord provides a good basis to ensure that thevortex axis is normal with the measurement plane, at leastin hovering flight. Because of this fact, no correction pro-cedure was needed in the present work to account for theinclination of the measurement plane.

Results and Discussion

The results of the current study are discussed in the fol-lowing categories: (1) Mean flow characteristics and ve-locity gradients of the tip vortices; (2) turbulence char-acteristics of the tip vortices. The coordinates (and thesign convention) used in the presentation of the results isshown in Fig. 5.

Figure 5: Schematic showing the coordinates systemsused for the present experiments.

Mean Tip Vortex Flow CharacteristicsAfter correcting for wake aperiodicity, the DPS-DPIV ve-locity vector maps were phase-averaged to determine themean flow characteristics of the tip vortices. The deter-mination of accurate mean vortex measurements not onlyprovides an ability to compare vortex characteristics atdifferent wake ages, but is also a prerequisite to accurateturbulent measurements based on Eq. 1.

The mean swirl and axial velocity distributions areshown in Figs. 6(a) and 6(b), respectively, and were de-termined from the measured data by making horizontalslicing cuts across the vortex flow. The classical signatureof the swirl velocity distribution can be seen here, withthe peak swirl velocity continuously decreasing with anincrease in wake age.

In the case of the mean axial velocity, the measurementsat the earliest wake age of 2 showed an axial velocitydeficit of 75% of the blade tip speed. This flow componentrapidly reduced to about 45% of tip speed at a wake ageof 4. However, further reduction in velocity proved to bemuch more gradual, and the peak axial velocity remainednear 30% of the tip speed even after 60 of wake age. Suchhigh values of axial velocity deficit at the centerline of thetip vortices have been previously reported in Ref. 26.

From the swirl velocity profiles, the viscous core ra-dius of the vortex can be estimated. This parameter isusually assumed to be the distance between the center ofthe vortex (in this case, the point of maximum helicity)and the radial location at which the maximum swirl ve-locity occurs. This location is obtained again by slicingcuts across the center of the vortex. The core sizes mea-sured with the DPS-DPIV system at various wake ages areshown in Fig. 6(c), along with complementary measure-ments made using 3-C laser Doppler velocimetry (LDV).The length scales were normalized using blade chord. Theplot also shows the core growth estimated from Squires’core growth model (Ref. 37) as extended by Bhagwat andLeishman (Ref. 38), which is given by

rc(ζ) =√

r20 +4ανδ(ζ/Ω) (8)

When δ = 1, the Bhagwat–Leishman model reduces tothe classical laminar Lamb–Oseen model. Increasing thevalue of δ basically means that the average turbulence

(a) Swirl velocity

(b) Axial velocity

(c) Vortex core growth

Figure 6: Normalized swirl and axial velocity distribu-tion at various wake ages, and vortex core growth: (a)swirl velocity, (b) axial velocity, (c) core growth.

levels of the flow inside the tip vortex are increased (seelater), which produces more mixing, faster radial diffu-sion of vorticity, and will result in a higher average coregrowth rate with time. It can be seen that the present mea-surements follow closely the δ = 8 curve, which is alsoconsistent with the LDV measurements.

Velocity Gradients

The corrected mean flow measurements allow for accuratemeasurements of all nine velocity gradients in the threeflow directions. Figure 7 shows the nine gradients mea-sured at a wake age of 12. The solid circles marked oneach plot represents the average core size of the tip vor-tex, as estimated by the procedures described previously.The value of the ninth gradient ∂w/∂z was obtained usingthe continuity equation given in Eq. 4. To avoid confu-sion, the gradients of velocity in the plane of measurement(i.e., ∂/∂x and ∂/∂y) will be referred to the in-plane gra-dients, and the gradients of velocity orthogonally betweenthe two planes of measurement (∂/∂z)will be referred tothe out-of-plane gradients (refer to Fig. 5 for visual de-scription).

Notice that not only do all these gradients have differ-ent orders of magnitude, but their distributions throughoutthe vortex flow are also different. The presence of thelobed-patterns shown in Fig. 7 are a result of analyzingrotational coherent flow structures in terms of a Cartesiancoordinate system. When examining the gradients, boththe ∂u/∂y and ∂v/∂x components were found to have thehighest magnitudes, with both of the components reachinga maximum magnitude near the vortex center, albeit withopposite signs. The in-plane gradients of the axial veloc-ity, ∂w/∂x and ∂w/∂y also were observed to have largemagnitudes near the vortex axis, which can be expectedbecause of the steep rise in the axial velocity deficit withinthe predominantly viscous vortex core. The two lobes ofopposite signs in the distribution pattern of these w gra-dients is an artifact of the fact that the velocity deficit in-creases moving radially inwards towards the center of thevortex, and decreases moving radially outwards.

The other in-plane velocity gradients (i.e., ∂u/∂x and∂v/∂y terms) were observed to exhibit a four-lobed pat-tern, with the lobes oriented at approximately 45 withrespect to the x-y coordinate axes. Specifically, the ∂u/∂xcomponent showed negative lobes at 45 and 225, andpositive lobes at 135 and 315. The pattern developed inthe ∂v/∂y gradient is offset from that in ∂u/∂x by 90. Asa result, when calculating the out-of-plane gradient ∂w/∂z(whose magnitude is the sum of ∂v/∂y and ∂u/∂x based onEq. 4), the positive lobes in ∂u/∂x are added to the neg-ative lobes in the ∂u/∂x, and vice-versa. These regionstend to cancel each other out, and results in the magnitudeof ∂w/∂z being an order of magnitude lower than for theother gradients.

The final two gradients are the out-of-plane gradientsof the in-plane velocities (i.e., ∂u/∂z and ∂v/∂z). As ex-pected, a two-lobed pattern was observed in each gradi-ent as a result of the turbulent diffusion of vorticity in thestreamwise, or out-of-plane direction. Based on the co-ordinate system followed in this work , the ∂u/∂z term is

Distance from the vortex center, Y/R

Distancefromthevortexcenter,X/R

-0.01 -0.005 0 0.005 0.01-0.01

-0.005

0

0.005

0.01dudx: -6.556 -4.635 -2.714 -0.793 1.128 3.050 4.971

(a) ∂u/∂xDistance from the vortex center, Y/R


-0.01 -0.005 0 0.005 0.01-0.01

-0.005

0

0.005

0.01dudy: -2.000 1.000 4.000 7.000 10.000 13.000 16.000

(b) ∂u/∂yDistance from the vortex center, Y/R


-0.01 -0.005 0 0.005 0.01-0.01

-0.005

0

0.005

0.01

dudz: -0.369 -0.228 -0.087 0.053 0.194 0.334 0.475

(c) ∂u/∂z



-0.01 -0.005 0 0.005 0.01-0.01

-0.005

0

0.005

0.01dvdx: -15.000 -12.000 -9.000 -6.000 -3.000 0.000

(d) ∂v/∂x



-0.01 -0.005 0 0.005 0.01-0.01

-0.005

0

0.005

0.01dvdy: -6.500 -4.500 -2.500 -0.500 1.500 3.500 5.500

(e) ∂v/∂yDistance from the vortex center, Y/R


-0.01 -0.005 0 0.005 0.01-0.01

-0.005

0

0.005

0.01dvdz: -1.20 -0.80 -0.40 0.00 0.40 0.80 1.20

(f) ∂v/∂z

Distance from the vortex center, X/R

Distancefromthevortexcenter,Y/R

-0.01 -0.005 0 0.005 0.01-0.01

-0.005

0

0.005

0.01dwdx: -7.000 -4.000 -1.000 2.000 5.000 8.000

(g) ∂w/∂xDistance from the vortex center, X/R


-0.01 -0.005 0 0.005 0.01-0.01

-0.005

0

0.005

0.01dwdy: -9.000 -6.000 -3.000 0.000 3.000 6.000

(h) ∂w/∂yDistance from the vortex center, Y/R


-0.01 -0.005 0 0.005 0.01-0.01

-0.005

0

0.005

0.01dwdz: -2.500 -0.500 1.500 3.500

(i) ∂w/∂z

Figure 7: DPS-DPIV measurements of the nine velocity gradients inside the tip vortex core at a wake age of 12.

negative on the lobe aligned with the positive y-axis, andpositive on the lobe aligned with the negative y-axis. Thisis consistent with a clockwise rotating vortex, as presentin the current measurements. In polar coordinates, thismeans the out-of-plane swirl velocity gradient, ∂Vθ/∂z,will be negative at all points inside the vortex core, in-dicating a reduction in the swirl flow of the tip vortices.This gradient can be expected to be positive on the upperblade surface when the tip vortex is undergoing its roll-up.

Turbulence Characteristics

A detailed analysis was performed on the measured turbu-lence characteristics to help understand the evolutionarybehavior of the tip vortices. In the present work, 1,000velocity vector maps were used to estimate the fluctuatingvelocity components, which is needed to ensure statisti-cal convergence of the measurements (Ref. 26). Noticethat all of the first- and second-order velocity fluctuations

were normalized by Vtip and Vtip2, respectively, and the

length scale was normalized by the blade radius, R. Thecoordinate axes in each figure are referenced to the phase-averaged center of the vortex, which was defined to as thepoint of maximum helicity measured at each wake age—see Ref. 26.

Turbulence Intensities

Figure 8 shows the distribution of normalized turbulenceintensities u′, and v′ from ζ = 4 to 30 of wake age. Thewake age ζ = 0 corresponds to the point at which thevortex leaves the trailing-edge of the blade, not its 1/4-chord. Turbulence measurements made around and on topof the blade surface (i.e., for ζ < 0), thereby capturing theformation of the vortex were also made, and are reportedin Ref. 18.

It can be seen from Fig. 8 that the u′ and v′ componentsare biased along x- and y-axes, respectively. This resultis further detailed in Fig. 9(a), which show the values ofu′, and v′ at a wake age of ζ = 15 that were obtainedfrom making four equally spaced slicing cuts through thecenter of the vortex. While the u′ component is the high-est along the 0–180 slicing cut (which is a cut along thex-axis of the measurement plane), its magnitude is notice-ably smaller along the oblique 45–225 and 135–315 cuts,and the smallest along the 90–270 cut (which is the cutalong the y-axis of the measurement plane). Conversly, v′has the highest magnitude along the 90–270 cut, and thelowest magnitude along the 0–180 cut.

This bias of Cartesian velocity fluctuations along theirrespective axes correlates extremely well with previ-ous turbulence measurements made on a micro-rotor(Ref. 26), as well as those made behind a fixed-wing(Refs. 39, 40). Despite this bias, it should be noted thatboth the u′ and v′ fluctuations reach a maximum magni-tude of approximately equal value at the center of the vor-tex, and gradually decrease moving away from the vortexcenter.

To gain a further perspective into why the turbulent ve-locity fluctuations were biased along their respective axesin a Cartesian coordinate system analysis, the results weretransformed into polar coordinates. A representative ex-ample is presented in Fig. 9(b), which now shows the tur-bulent fluctuation terms V ′

r and V ′θ

at ζ = 15 along thesame slicing cuts as those presented in the Cartesian anal-ysis in Fig. 9(a).

In contrast to the Cartesian analysis presented in Figs. 8and 9(a), in polar coordinates, there is an axisymmetricdistribution about the center of the vortex. This can beseen clearly in Fig. 9(b), which shows that the magnitudesof V ′

r , and V ′θ

are relatively constant along each slicing cut.This axis-symmetric distribution is shown further in thecomplete velocity contour map at ζ = 15 in polar coor-

dinates, shown in Fig. 10(a). Unlike Fig. 8, which clearlyshows biased lobes of u′ and v′ along the Cartesian axes,the contours of Fig. 10(a) are circular, and centered aroundthe vortex.

However, it is apparent the magnitude of the V ′r compo-

nent is noticeably larger than that of the V ′θ

component in-side the vortex core. This is seen in both the velocity con-tour plots of Fig. 10(a) and in the one-dimensional slicingcuts through the vortex center in Fig. 10(b). While bothfluctuating terms reach their maximum at the vortex cen-ter (as also seen in the Cartesian case in Fig. 9(a)), the V ′

rcomponent is larger than V ′

θat all points inside the vortex

core. This was the case for all wake ages measured. Thisobservation is of particular significance in understandingthe evolutionary characteristics of vortices, and has beenpreviously hypothesized by Chow et al. (Ref. 40) as anexplanation of the Cartesian bias observed in the turbu-lence components.

Employing this analysis to explain the anisotropy be-tween V ′

r , and V ′θ

requires an examination of the turbu-lence production terms for V ′

r and V ′θ

transport. The trans-port equations can be written as

V ′r(prod) =−2

[V ′2

r∂Vr

∂r+V ′

z V ′r

∂Vr

∂z− Vθ

rV ′

r V ′θ

](9)

V ′θ(prod) =−2

[V ′2

θ

∂Vr

∂r+V ′

z V ′θ

∂Vθ

∂z+

∂Vθ

∂rV ′

r V ′θ

](10)

In comparing the two equations, it can be seen that thesecond term in each equation is the streamwise, or out-of-plane gradient. As previously discussed, this term is rel-atively small and becomes even smaller when multipliedby the shear stress term V ′

z V ′r . The first term in each of

the preceeding equations is also relatively small. This isbecause the radial velocity within the vortex is very small,making the out-of-plane gradient even smaller. However,the presence of a normal stress term (which is significantlylarger than the shear stresses) does tend to compensate forthe small gradients found in the radial velocity.

The last term in both of the preceding equations in-volves the shear stress term V ′

r V ′θ

and the swirl velocitygradients. Inside the vortex cores, the components Vθ/r,and ∂Vθ/∂r are similar in both sign and magnitude. This isbecause the swirl velocity rises from zero to a peak swirlvelocity in a linear fashion within the viscous core region.It should be noted that this observation is consistent withthe assumption of solid-body rotation, which serves to bea good first-order assumption to describe the mean veloc-ity and the velocity gradients within the vortex core. No-tice that the assumption of pure solid-body rotation inher-ently implies that the second-order correlation term V ′

rV ′θ

has to be zero. However, both the present results and thosecited in Ref. 40 have measured non-zero, and predomi-nantly negative values of V ′

r V ′θ

within the vortex flow. A



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.020.020 0.060 0.100 0.140u

__,



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.020.020 0.060 0.100 0.140v

__,

(a) ζ = 4



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.020.020 0.060 0.100 0.140u,

__



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.020.020 0.060 0.100 0.140v,

__

(b) ζ = 7



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.020.020 0.060 0.100 0.140u ,

__



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.020.020 0.060 0.100 0.140v ,

__

(c) ζ = 15

Figure 8: In-plane measurements of turbulence right behind the blade over 4 to 15 wake age. Every fourth vectorhas been plotted to prevent saturating the image.



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.020.020 0.060 0.100 0.140u,

__



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.020.020 0.060 0.100 0.140v,

__

(d) ζ = 30

Figure 8: (Cont’d) In-plane measurements of turbulence for 30 of wake age. Only every fourth vector has beenplotted here to prevent saturating the image.

270°

90°

180° 0°

45°135°

315°

x

y

225°

(a) Schematic of vortex cuts (left), and turbulence fluctuations across the vortex core at a wake age of 15 in terms of a Cartesiancoordinate system.

270°

90°

180° 0°

45°135°

315°

rθθ

225°

(b) Schematic of vortex cuts (left), and turbulence fluctuations across the vortex core at a wake age of 15 in terms of a polar coordinatesystem.

Figure 9: Distribution of turbulence fluctuations across slicing cuts through the vortex core at a wake age of 15

non-zero, negative value of V ′rV ′

θwill increase the produc-

tion of V ′r and reduce V ′

θbecause of the sign difference be-

tween the last terms of Eq. 9 and Eq. 10. Consequentlythis will result in the V ′

r component being greater than V ′θ,

leading to an anisotropic distribution of turbulence withinthe vortex flow. Converting this anisotropy from polar toCartesian coordinate terms will then produce the intensity

bias observed in the u′ and v′ components, as shown pre-viously in Fig. 8.

Reynolds Stresses

Figure 11 shows the distribution of Reynolds shear stress(u′v′) and the associated strain (∂u/∂y+∂v/∂x) measured



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.020.020 0.080 0.140V

,__r



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.020.020 0.080 0.140V

,__θ

(a) Complete velocity contour map of turbulent fluctuation intensities in polar coordinates, V ′r (left) and V ′

θ(middle), across the

ζ = 15 vortex

270°

90°

180° 0°

45°135°

315°

rθθ

225°

(b) Anisotropy between V ′r (left) and V ′

θ(right) across vortex core

Figure 10: Distribution of turbulence fluctuations across the vortex core at a wake age of 15 in polar coordinates

from ζ = 4 to ζ = 15. The reason for showing shearstress and strain together is because of the basic assump-tion made in linear eddy viscosity-based turbulence mod-els that stress is represented as a linear function of strain.However, even a cursory examination of the contours inFig. 11 clearly suggests that this assumption is invalid,as has already been shown for curved streamline flows(Refs. 41, 42).

Figure 11 shows that the shear stress and strain quicklyform sharp, four-lobbed patterns as early as ζ = 4. Theselobes, whose magnitudes alternate in sign, are alignedalong the Cartesian coordinate axes for strain, and at 45

with respect to the coordinate axes for the shear stress.The contours also suggest significantly high levels ofshear stress inside the vortex sheet at early wake ages,which can be expected based on results of the instanta-neous turbulence activity shown in Ref. 18.

The present system also allow for the measurement ofthe v′w′ component of the Reynolds shear stress and itsassociated strain. These results are plotted in Fig. 12 forζ = 60. Unlike the u′v′ term, the v′w′ term has only twolobes. However, the alignment of the lobes are still 45

offset from the coordinate axes. The associated strain alsoshows only two lobes, which are aligned with the x-axis.This suggests that the orientation of all the shear stressdistributions are again at a 45 offset from the shear straindistribution. This conclusion has also been drawn byRef. 40 based on experiments with vortices generated by afixed-wing, and also in Ref. 26 based on vortex flows frommicro-rotor with much smaller vortex Reynolds numbers.Therefore, the modeling assumption that stress is a linearfunction of strain in clearly invalid for vortex flows.



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.02 -0.005 -0.002 0.002 0.005u’v’___



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.02-6000 -2000 2000 6000Strain rate:

(a) ζ = 4



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.02 -0.005 -0.002 0.002 0.005u’v’___



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.02-6000 -2000 2000 6000Strain rate:

(b) ζ = 7



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.02 -0.005 -0.002 0.002 0.005u’v’___



-0.01 0 0.01 0.02 0.03

-0.02

-0.01

0

0.01

0.02-6000 -2000 2000 6000Strain rate:

(c) ζ = 15

Figure 11: In-plane measurements of Reynolds stress and strain behind the blade over 4 to 15 of wake age.



-0.00500.005

-0.005

0

0.005

VW: -0.004 -0.002 0.000 0.002v’w’___

(a) v′w′ at ζ = 60Distance from the vortex center, X/R


-0.00500.005

-0.005

0

0.005

Strain rate: -6000 -3600 -1200 1200 3600 6000

Figure 12: Reynolds stress (v′w′) and strain rate –( ∂v∂z + ∂w

∂y ) at 60 wake age showing an anisotropy in the distribu-tions.

Turbulent Transport and Vortex Evolution

One effective way to correlate the core growth of the tipvortex (see Fig. 6(c)) and the production of turbulence isthrough comparisons of the distributions of the eddy vis-cosity across the core. Any growth of the vortex core de-pends on the diffusion of momentum from one layer inthe fluid to an adjacent layer. This process depends onthe eddy viscosity, which in turn is a function of the shearstress (i.e., Boussinesq’s assumption—see Ref. 43).

Figure 13 shows the measured Reynolds shear stressu′v′ in the tip vortex for three wake ages. It is clear thatthe peak value of the shear stress decreases with wakeage, and is distributed further away from the vortex cen-ter. While the peak values of shear stress move radiallyfurther away from the core at the older ages, the area un-der the curves still remain approximately constant. Thismeans that average eddy viscosity is also approximatelyconstant, which is the basic assumption made in the coregrowth model of Bhagwat and Leishman.

The existence of the eddy viscosity is the basic fluidmechanics phenomenon that will sustain the growth rateof the vortex cores. In the Ramasamy–Leishman (R–L)turbulence model (Ref. 44), a Richardson number (Ri)concept is used to describe the distribution of eddy vis-cosity. The Ri is the ratio of turbulence produced or con-sumed as a result of centrifugal force to turbulence pro-duced from shear (Ref. 41), and is given by

Ri =(

2Vθ

r2∂(Vθr)

∂r

)/(r

∂(Vθ/r)∂r

)2

(11)

Turbulence produced from shear is usually very low at thecenter of the vortex (pure solid body rotation does not pro-duce any turbulence at all because there is no shear). Con-sequently, the value of Ri is high near the center of the vor-

tex, much larger than the threshold value that allows forthe sustainment of turbulence—see Fig. 14. Therefore, noturbulence is produced near the center of a vortex, a resultsuggested by flow visualization of a vortex flow as shownin Fig. 15.

Turbulence production can be calculated by finding theproduct of strain rate and Reynolds shear stress. The meanstrain for a given vortex is defined, so the production de-pends largely on the shear stress. Because it can be seenin Fig. 13 that the shear stress is minimum at the vortexcenter, the intermittency function given in the R–L turbu-lence model is, therefore, fully consistent with the find-ings made in the present set of measurements.

In addition to the radial core growth of the vortex, theaxial velocity inside the vortex is also dependent upon theReynolds stresses. This can be better understood from ex-amining the momentum equation in the z direction, whichis given by the equation

u∂u∂z

+ v∂v∂z

+w∂w∂z

= −1ρ

∂p∂z

+ν∇2w− ∂u′w′

∂x

−∂v′w′

∂y− ∂w′2

∂z(12)

The pressure gradient in Eq. 12, which is positive duringthe tip vortex roll up (resulting in increased axial veloc-ity deficit as the wake age increases), can be assumed tobe negligible at older wake ages. Similarly, the effectsof molecular viscosity alone can be considered negligi-ble compared to the effects of the turbulent (eddy) viscos-ity. This leaves the gradients of the stress terms (i.e., u′w′,v′w′, and w′2) to play a role in defining the axial momen-tum at any wake age. This is especially important at thecenter of the vortex flow, where the axial velocity deficitreaches a maximum.

Figure 13: Reynolds stress (u′v′) distribution at threewake ages.

Figure 14: The variation of the Richardson numberacross the vortex suggests that turbulence productionwill be suppressed in the central core region. Measure-ments made at ζ = 4, 15, 30 and 45.

The results in Fig. 12(b) suggests that the gradi-ent ∂v′w′/∂y is relatively high inside the vortex core.Such high gradients directly transfer momentum from thestreamwise direction to the cross flow direction therebyresulting in the reduction of the peak axial velocity, asshown in Fig. 6(b).

ConclusionsComprehensive measurements in the wake of a hover-ing rotor were performed using dual-plane digital particleimage velocimetry (DPS-DPIV). The measurements dis-cussed in this paper have concentrated on the vortex wakesystem behind the blade, and examined the tip vortex evo-lution from as early as ζ = 2 to about 270 of wake age.The DPS-DPIV technique allowed for the measurementof all three flow velocities and also all nine-componentsof the velocity gradient tensor, a capability not possible

Figure 15: Flow visualization of a fully developedblade tip vortex: 1. Inner zone free of large turbulenteddies, 2. A transitional region with eddies of differentscales, and 3. An outer, potential flow region.

with conventional DPIV systems. The method was basedon coincident flow measurements made over two differen-tially spaced laser sheet planes. A polarization-based ap-proach was used in which the two laser sheets were givenorthogonal polarizations, with filters and beam-splittingoptical cubes placed so that the imaging cameras saw Miescattering from only one or other of the laser sheets. Thedigital processing of the acquired images was based on adeformation grid correlation algorithm optimized for thehigh velocity gradient and turbulent flows found in bladetip vortices.

The following are the specific conclusions drawn fromthis study:

1. Dual plane DPIV uniquely provides the capability ofmeasuring the orientation of the measurement planewith the vortex axis, based on its ability to deduct thethree-dimensional orientation of the vorticity vectorat the center of the vortex from the nine measuredvelocity gradients. For hover applications, the align-ment of the laser light sheet(s) with the 1/4-chord lineof the blade provides a reasonably high level of ac-curacy in terms of the measurement plane’s inclina-tion with the vortex rotational axis. At all wake ages,the measurement plane was within 6 of being com-pletely orthogonal with the tip vortex rotational axis.

2. Mean flow measurements inside the tip vorticesshowed that the radial diffusion of vorticity from tur-bulence generation was about eight times higher thanthat obtained using a laminar flow assumption. Themeasured peak axial velocity deficit (corrected foraperiodicity bias effects by a helicity-based method)was found to be about 75% of the tip speed at theearliest wake age behind the blade. This remained ashigh as 40% as late as 60 wake age.

3. Turbulence intensity measurements inside the tipvorticies clearly showed anisotropy in the flow.

Specifically, the Vr′ component was found to be

greater in magnitude than the Vθ

′ at all points in-side the vortex in both the near- and far-wake. Thisanisotropy in the flow, in turn, biases the Cartesianvelocity fluctuations u′ and v′ along the x and y axes,respectively.

4. While the assumption of solid body rotation in-side the vortex core is a reasonable assumption forfirst principles based modeling of the flow veloc-ity inside tip vortices, it falls short in predictingthe second-order velocity fluctuations that are usedin the Reynolds-averaged stress transport equations.Specifically, the solid body assumption of a zeroV ′

rV ′θ

was found to be inconsistent with the non-zerovalues obtained by the high-fidelity measurementsinside a vortex flow.

5. Good correlation was found in the Reynolds shearstress distributions and strain rates between thepresent measurements and previous measurementsmade of the vortex flow generated by a fixed-wing.This suggests that the turbulence pattern will proba-bly be essentially the same for all lift-generated tipvortices, regardless of the operating Reynolds num-ber or the type of lifting surface from which theywere generated.

6. The measured results confirm that shear stresses can-not be written as a linear function of strain, as as-sumed in existing linear eddy viscosity based turbu-lence models. Further work should be done to de-velop more appropriate turbulence models if the goalis to improve predictions of the rotor wake.

AcknowledgmentsThis research was partly supported by the Army Re-search Office (ARO) under grant W911NF0610394 andpartly under the Multi-University Research Initiative un-der Grant W911NF0410176. Dr. Thomas Doligalski wasthe technical monitor for both contracts. The authorswould like to thank Drs. Christopher Cadou and Ken-neth Yu for loaning the additional lasers needed for thiswork. Our appreciation also extends to Joseph Ramsey,who aided in the processing of the DPIV data and in theanalysis of the flow measurements.

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2008-ERF-Dual plane PIV paper 2