NASA/TM-2001-209625

AFDD/TR-01-A-003

Devices that Alter the Tip Vortex of a Rotor

Kenneth W. McAlister and Chee Tung

Army/NASA Rotorcraft Division

Aeroflightdynamics Directorate (AMRDEC)

US Army Aviation and Missile Command

Ames Research Center, Moffett Field, CA

James T. Heineck

Experimental Physics Branch

Ames Research Center, Moffett Field, CA

National Aeronautics and

Space Administration

Ames Research Center

Moffett Field, California 94035-1000

February 2001

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Devices that Alter the Tip Vortex of a Rotor

Kenneth W. McAlister and Chee Tung

Army/NASA Rotorcraft Division

Aeroflightdynamics Directorate (AMRDEC)

US Army Aviation and Missile Command

Ames Research Center, Moffett Field, CA

James T. Heineck

Experimental Physics Branch

Ames Research Center, Moffett Field, CA

ABSTRACT

Small devices were attached near the tip of a hovering rotor blade in order to alter the structure and

trajectory of the trailing vortex. Stereo particle image velocimetry (PIV) images were used to quantify

the wake behind the rotor blade during the first revolution. A procedure for analyzing the 3D-velocity

field is presented that includes a method for accounting for vortex wander. The results show that a vortex

generator can alter the trajectory of the trailing vortex and that a major change in the size and intensity

of the trailing vortex can be achieved by introducing

a high level of turbulence into the core of the vortex.

NOMENCLATURE

a

A

C

G

M

N

r

rc

R

Re

U,U,W

Pc

Yi

VO

YrO

x,y,z

speed of sound, ms- 1

area enclosed by circulation path, m 2

chord length, m

thrust coefficient, thrust/plr_ _R 4

hover tip Mach number, R_a-1

number of points to be averaged

radial distance from vortex center, mm

vortex core radius, mm

radius of rotor tip path, m

hover tip Reynolds number, cR_v -1

velocity compontents, ms -1

vortex convection velocity, ms-1

vortex interior velocity, ms-1

circumferential velocity in x-y plane, ms -1

ve relative to convection velocity, ms-1

coordinates relative to rotor tip, mm

mean values of x, y, mm

x, y relative to basic blade vortex, mm

angle of position vector, deg

angle of if+ _Yvector, (leg

F

F,

O"

0.; z

f_

circulation, m2s - 1

circulation at particular value of r, m2s - 1

radial departure from mean location, mm

kinematic viscosity, m2s -1

standard deviation of vortex wander, mm

azimuthal angle measured from blade, deg

vorticity normal to x-y plane, s-1

rotational speed of rotor, RPM

ABBREVIATIONS

BERP

BVI

CCD

FFT

LDV

PIV

TG

VG

British Experimental Rotor Program

Blade-vortex interaction

Charged-coupled device

Fast Fourier transform

Laser Doppler velocimetry

Particle image velocimetry

Turbulence generator

Vortex generator

INTRODUCTION

Although the helicopter performs well in hover

and low speed forward flight, it lacks community acceptance in populated areas due to the noise that it

produces. A major source of helicopter noise comes

from the rotor blade as it cuts through its own wake.

This phenomenon is known as blade/vortex interaction (BVI) noise, and it occurs primarily when the

helicopter is descending. Applying a mitigating device that reduces rotor noise can be quite challenging

since the offending trailing vortices are shed from the

tips of the rotor blades where the centripetal acceleration is highest. In addition to the force that such a

device must withstand, consideration must be given

to rotor performance since any alterations to the tip
region,wherethedynamicpressureis highest, could

degrade the aerodynamic efficiency of the blade. Increasing the chord length and reducing the tip speed

of the rotor may seem like an obvious solution for

reducing BVI noise, however the added weight and

control loads may be offsetting.

Earlier studies have identified two important parameters governing BVI noise generation. The first

parameter is the miss distance between the rotor

blade and the trailing vortex. The second parameter is the size (or intensity) of the vortex. The miss

distance and the vortex core size can be simultaneously increased with a nonplanar tip configuration

(refs. 1,2), however, the shape of this blade limits

its application to hover and low speed flight. Another

approach to lowering BVI noise involves a momentary

change in blade pitch at just the right azimuth using

higher harmonic control (ref. 3), an active flap (ref.

4), or individual blade control (ref. 5). Reductions

in BVI noise have been achieved, but it is not certain

whether these improvements are the result of an increase in the miss distance, a decrease in the intensity

of the interacting vortex segment, or a combination

of both effects. There is also some concern that the

inputs needed for noise reduction may promote an

increase in vibration (ref. 5).

There have been numerous attempts to simply

reduce the intensity of the trailing vortex. An early

effort was aimed at reshaping the planform of the

blade near the tip such that the local flow swirling

around the streamwise edge of the blade would not

encounter a surface on the upper side on which to

reattach (or stagnate). This design was known as

the ogee tip and it did result in a significant reduction in the concentration of vorticity in the wake of

a model wing (ref. 6). The same design was applied

to the blades of a model rotor and was found to produce a similarly diffused tip vortex, however, there

was an unacceptable degregation in performance at

the higher thrust levels due to an early onset of stall

(ref. 7). Other attempts, such as tapering the planform or the thickness, sweeping the tip, or adopting a

major planform change (BERP), have all resulted in

only modest increases in the diffusion of the vortex,

with the conclusion that more intrusive devices need

to be considered (ref. 8).

Adding devices to the tip of the rotor is representative of the more agressive measures taken to reduce

BVI noise. The first known attempt originated as a

spoiler placed on the upper surface near the wing tip

of a full-scale transport (ref. 9). Although the maximum swirl velocity was reduced by a factor of 3, there

was little difference in the rolling moment experienced

by the aircraft following in the wake of the transport (ref. 10). Nevertheless, the dramatic increase in

core size was sufficient to attract its application to a

model rotor (ref. 11). The device, which functioned

as a spoiler, was placed at the quarter chord, normal to the upper surface, and measured 9% in height

and 12% in width relative to the chord of the rotor

blade. Tests revealed a substantial reduction in BVI

noise, however, a discouragingly high level of power

was consumed and there was a significant increase in

broadband noise (ref. 11).

One of the less intrusive additions to the tip of

the rotor blade was the subwing (ref. 12). This device took the form of a small wing with a chord length

about 20% that of the rotor blade. The subwing became an extension of the rotor blade and was intended

to force the circulation near the tip of the blade to

be shed as two co-rotating vortices, each having less

intensity than would occur without the subwing. Results from this test showed a slight reduction in torque

at moderate thrust levels and a modest reduction in

the swirl velocity of the vortex trailing from the rotor blade. A more recent test revealed that the two

vortices initially contract more rapidly than for the

blade-alone vortex, but then combine into a single

vortex (at around ¢ = 150 °, depending on the lift on

the subwing) and follow the same trajectory observed

for the blade-along vortex (ref. 13).

Recognizing the effectiveness of a spoiler in diffusing the trailing vortex, various devices have been

attached to the tip of a fixed wing at locations both

near and beyond the trailing edge (ref. 14). Once

again, several designs proved quite capable of diffusing the trailing vortex and each carried a certain measure of drag penalty. Since any device that causes an

increase in drag on a wing would be expected to be

even more objectionable when applied to the tip of

a rotor blade, the less intrusive among these spoilers

have been tested on a model rotor (ref. 15). Small angles and wedges were attached to the trailing edge of

the rotor blade, and a sizeable reduction in BVI noise

was observed. Although the results were encouraging, the seemingly inevitable increase in power led to

the suggestion that some means of actively deploying

these devices might be the only reasonable solution

(refs. 8, 11, 15, 16).

While avoidance, rather than forced diffusion,

may be the best approach for fixed-wing aircraft to

deal with the hazards of across-trail and in-trail vortex encounters (ref. 10), rotor blades engage relatively young vortices so that methods that even temporarily enlarge the trailing vortex could prove ,lseful.

Although the concepts of vortex pairing and turbulent diffusion are not new, the present study examines

these ideas on a rotor and with a diagnostic technique

that provides a level of detail that was not previously

available.
Similarto thewakeofa fixed-wingaircraft,the

dominantfeatureofarotorwakeisthetrailingvortex

that isshedfromthetip of therotorblade.Experimentstypicallyfocusonthelocation,size,andintensity (ormagnitudeof vorticity)of thetrailingvortex

at variouswakeages.Thetrajectoryof the vortex

canbeaccuratelydeterminedfromflowvisualization

basedona triangulationtechniqueusinglaserlight

sheets(ref. 17). Whilethis techniqueis relatively

easyto apply,it doesnot provideany information

aboutthestructureof thevortex.Althoughtedious,

thestructureof thetrailingvortexcanbeobtained

usinglaserDopplervelocimetry(LDV).It is importantto notethatsmalldisturbancesinthefreestream

flowwillcausethevortexto wander,ormeander,over

a lateraldistancethat increaseswithdistancefrom

theblade.A pointmeasurement technique,suchas

LDV,will thereforerequiresomeprocedurefor conditionallyaveragingtheresults(ref. 18),especially

asthewakeagesor whenthefreestreamturbulence

levelis high.A planarmeasurement technique, such

asPIV,hastheadvantageofrequiringsubstantially

lesstimeto acquirethe3Dvelocityfield.Nevertheless,this datamustalsobeconditionallyaveraged

whenvortexwanderispresent(ref.19).

Thispapercontainsadiscussionofthetestsetup

anda methodfor obtainingthe3Dvelocityfieldin

thewakeoftherotoratspecificwakeages.Theprocedureforidentifyingseparatelythecentersofvorticity

andswirl,andhowtheyrelaterespectivelyto conditionalensembleaveragingandthevortexstructure,

will bepresented.Datawill beshownthat clearly

exposethedistinguishingfeaturesoftheflowandthe

effectivenessof bothvortexpairing(withsameand

oppositesense)andforcedturbulentdiffusiononthe

agingtrailingvortex.

TEST DESCRIPTION

Test Chamberand Stand-Theexperiment

wasperformedin the HoverTestChamberat the

NASAAmesResearchCenterundertheauthorityof

theU.S.ArmyAeroflightdynamicsDirectorate.The

chamberhasa baseof 26ft x 32ft anda heightof

28 ft. To minimize recirculation in the chamber and

to limit the influence of the floor on the flow, the collective pitch of the rotor blade was set to a negative

angle so that the wake would be directed upwards.

With the rotor acting like a pump, air was drawn into

the chamber through filters placed across two opposing rollup doors, then confined by an annular diffuser

located above the rotor, and finally exhausted to the

exterior through openings near the top of the chamber

(fig. 1).

The rotary-wing test stand that was used to drive

the rotor was configured with a single, 90-hp electric

motor and a 2.5:1 transmission. A flexible coupling

between the input shaft and the dummy balance was

instrumented to measure torque. An encoder with a

resolution of 4096 steps per revolution was attached

to the rotor shaft. The encoder signals were passed to

a variable delay circuit that enabled the PIV cameras

and Nd:YAG laser to be synchronized to any desired

rotor azimuth.

Rotor Blade and Hub- The rotor consists of

a single counter-weighted aluminum blade having a

rectangular planform, zero twist, 7.5 in. chord, and

a 45 in. radius (fig. 2). The outer 50 percent of the

blade conforms to a NACA 0012 profile (thickness at

the tip is 22.9 ram). Over the inner portion of the

blade radius the profile linearly thickens to a NACA

0020. The rotor hub consists of two steel sections

that are clamped together to hold the blade at a 0°

coning angle. The collective pitch angle was fixed

at -80 . When mounted on the test stand, the rotor

and hub were approximately 7.5 ft above the floor of

the test chamber. The solidity of this single-blade

configuration is 0.053.

Blade Attachments- One of the mechanical devices under study was designed to function as a vortex generator and the other as a turbulence generator

(figs. 2 and 3). The vortex generator has a NACA

0012 profile, rectangular planform with a rounded tip,

and measures 0.12c in chord and 0.10c in span (where

c refers to the chord length of the main element).

The quarter-chord axis of the vortex generator passes

through the quarter-chord location of the main element. The turbulence generator consists of a flat rectangular section and measures 0.12c in length (with a

fixed alignment with the span of the main element)

and 0.10c in height (oriented normal to the surface

of the main element). The center of the turbulence

generator also passed through the quarter-chord axis

of the main element. Both generators were mounted

0.057c inboard from the tip of the main element. If

the vortex generator were to be rotated 900 , its projected area would appear to the oncoming flow the

same as the turbulence generator. The relative dimensions and placement of the turbulence generator

are similar to the spoiler employed in an earlier study

(ref. 11).

Test Conditions- The present test was performed at a constant rotor speed of 870 rpm (14.5

Hz), which corresponds to a tip speed of 341.7 ft/sec.

Based on an average ambient temperature of 65 ° F

and barometric pressure of 760 mm Hg (14.7 psi), the

Reynolds number (based on c) at the tip of the rotor blade was Re = 1.33 × 106 and the Mach number

was M = 0.30. Based on a collective pitch angle of

-80 , the equivalent two-blade thrust coefficient was

Ct = 0.005 (ref. 20). The vortex generator was.tested
at eightangle-of-attazk(relativeto thechordof the

mainelement)conditions:-15°, -10°, -5°, 0°, 5°,

10°, 15°, andunrestrained.Theturbulencegenerator

wastestedat a fixedorientationnormalto theupper surfaceof themainelementandparallelto the

leadingedgeoftheblade.

StereoscopicPig Concept-Thevelocityofa

fluidis inferredfromthemotionofdiscreteparticles

that aresuspendedintheflow.Athinsheetoflightis

usedto definetheplaneofinterest.Theparticleimagesthatarerecordedat twodifferentimesarethen

crosscorrelatedto yielddisplacement vectors(magnitudeanddirection).Thetimeintervalbetweenthe

twoimagesmustbeshortenoughthat theparticles

remainin the light sheet,yet longenoughthat the

particledisplacementsareperceptible.It isassumed

thattheparticlesaresmallenoughtoaccuratelytrack

theflow.

A singlecameraplacednormalto the sheetof

lightresultsin a two-dimensional arrayof velocity

vectors. If the flowhasa significanthird component(directednormalto the planeof the light

sheet),anerrordueto perspectivedevelopsin the

two-dimensional arraythat is zeroin thecenterand

increasestowardtheimageboundaries.Thisseeminglyundesirablesensitivityto out-of-planemotion

waslaterexploitedto derivethethirdcomponent of

velocity(ref. 21). In fact,sensitivityto theout-ofplanecomponentof velocityoverthe entireimage

planecanbeincreasedby intentionallyplacingthe

cameraat an obliqueangleto the light sheet.To

uniquelydeterminea threedimensional particledisplacementrequirestwocamerasthat areobliqueto

thelightsheet,eachofferingadifferentperspectiveof

theparticlemotionbetweenthetwoexposures(fig.

4). ThisprocedureisknownasStereoscopicPIVor

3D-PIV.

Thetechniquedemandsbothcriticalfocusand

maximumbrightnessof theparticleimage.Conventional lens mounts create a plane of focus in object

space that is parallel with both the image plane and

the lens plane. When the lens plane is oblique to

the object plane (as is the case for Stereoscopic PIV),

particles will be increasingly defocused as their distance from the centerline of the object plane increases.

The conventional corrective action would be to increase the depth of field by reducing the aperture of

the lens. Unfortunately, reducing the lens aperture

drastically reduces both the particle image intensity

and the image resolution. The problem is solved with

Scheimpfiug focusing (refs. 22 and 23). To keep the

object plane in focus when the lens plane is rotated

to an oblique orientation, the image plane (where the

camera sensor is placed) must also be rotated such

that all three planes (object, lens, and image) intersect along a common line (fig. 5).

Arrangement of Equipment- The cameras

were mounted in a forward-scatter position on a horizontal plane that passed 3 in. above the rotor disc

(fig. 6). The bisecting angle between the light sheet

and each camera was 360 , and the cameras were rotated so that the image areas were coincident. The

centerline dimensions of the image area were 14 in.

vertical and 18 in. horizontal. Due to perspective the

vertical dimension of the image ranged from 12 in.

(near side to the cameras) to 16 in. (far side}. The

lower, outboard corner of the image area was placed

so as to capture the trailing vortex over a maximum

range of wake ages (which was less than one revolution for this test).

Camera Specifications- Images were acquired

with 8-bit charged-coupled device (CCD), crosscorrelation cameras having a sensor array of 1008

(horizontal) × 1018 (vertical) pixels. Each pixel

measures 9 #m on a side. The cameras can operate in a double-exposure mode and acquire two noninterlaced, full-frame images in a single frame interval.

The time interval between images is variable between

2 ps and 30 ms. These are non standard video cameras that can be externally triggered and driven at

any frequency up to 15 Hz in double-exposure mode.

A computer interface provides control over gain, contrast, black level, and trigger mode. Both cameras

used 55-mm fl.2 lenses. The lenses were remotely

translated to focus on the centerline of the image area

and the sensor (located inside the camera body) was

rotated about its centerline to satisfy the Scheimpflug

condition.

Laser and Sheet Optics- A Nd:YAG laser was

frequency doubled to provide a beam having a wavelength of 532 nm, a pulse width of 9 ns, and power of

350 mJ. The laser model used has a beam diameter

of 9 mm and a divergence of 0.50 mrad. All optical

elements have damage thresholds exceeding 1 J/cm 2.

A laser-light sheet was formed using lenses that thin

the beam in one direction and expand the beam in

the orthogonal direction. The thickness (horizontal

direction in this test) of the light sheet was controlled

by two cylindrical lenses, the focal length of one was

f = +200 mm and the other f = -200 mm. By adjusting the distance between these two lenses, the beam

waist (_, 1 mm thick) could be positioned in the region imaged by the cameras. The vertical expansion

of the light sheet was controlled by a single f = -75

mm cylindrical lens. The distance between the sheet

forming optics and the imaged area was about 25 ft.

System Alignment- The rotor blade was positioned at the 0° reference azimuth and a calibrated

laser level (sweeping type) was used to establish the

vertical plane passing across the trailing edge of the
blade.Thelaser-lightsheetwasadjustedto becoincidentwith thelaserlevel.A calibrationtargetwas

placedagainsthe trailingedge,thentranslatedto

coincidewith theareaviewedby the cameras,and

finallyleveledto within +0.01 ° with a digital inclinometer. The location of the blade tip relative to

a point on the calibration target was measured to

within +1/32 in. The alignment of the target was

considered to be satisfactory when the surface of the

target was evenly grazed by the light sheet. Using

only white light to illuminate both sides of the target, the cameras were focused and calibration images

were recorded.

PIV Software- This experiment was performed

using the Integrated Design Tools (IDT) WinVu v5.10

software (ref. 24). This software functions as both a

data acquisition interface and an image-processing interface. This has the advantage of providing a fully

integrated calibration procedure that allows for acquisition, quality assurance and data reduction. The calibration yields all the optical parameters required for

accurate reconstruction of three-component velocityvector fields. A calibration was performed before and

after each series of runs.

Images are processed by first covering the region

of interest with an interrogation grid. The intersections of the vertical and horizontal grid lines define

the centers of each interrogation window. The interrogation window is the smaller region in the reference

and delayed images that are cross-correlated using all

optimized Fourier transform. When the camera calibrations are applied, the grid in each camera view

covers the exact same area in the flow field.

The size of the interrogation window is based

on the particle density and the maximum instantaneous displacement of the particles. Typically the

window size ranges from 8 to 64 pixels on a side.

Each interrogation window yields one vector. The

cross-correlation of the interrogation window in the

reference image with that of the delayed image yields

a correlation map. The location of the correlation

peak in space determines the local displacement in

both magnitude and direction.

WinVu incorporates quality-assurance tests in

the vector calculations. The processing begins with

a first-pass correlation between the reference image

and delayed image to determine the maximum displacement range. For the second pass the software

enlarges the interrogation area in the delayed image.

The amount of the enlargement is based on the maximum displacement range determined in the first pass.

Since the Fourier transform requires both interrogation areas to be identical, the software "adds zeros" to

the interrogation area of the reference image to match

the size of the delayed image area. This technique

maximizes the probability of correlating all the particles found in the reference image interrogation area to

those found in the delayed image, thereby maximizing

the statistical accuracy.

The software then counts the number of particle images (each composed of several contiguous pixels) in the interrogation window. Ten particle pairs

are required to contribute to a correlation map. The

centroid of each particle is calculated, thus yielding

sub-pixel accuracy of their position. A second-order

curve fit is determined from the ten displacements.

This curve fit yields a single vector, at the precise grid

point location, whose error is reduced by a factor of

0.3 (l/v@-, where N = 10 particles) over the straight

fast Fourier transform (FFT) of the same area (ref.

24).

If there are not enough particles in a given interrogation region, the program will automatically enlarge the interrogation area of the reference image. If

there are ten or more particles in this enlarged area,

then the correlation proceeds in the same manner described above. The data for this grid point is considered to be a recalculation. If ten particles are not

counted, the software will expand the interrogation

area incrementally. It will repeat this process until

the interrogation area expands to a limit of 64x64

pixels. If the ten-particle threshold is not met for the

largest area, then velocity values are interpolated for

that grid point using a second-order curve fit based on

nearest-neighbor values. This vector is also counted

as a recalculation. The software tracks the number of

these recalculations and displays that number after

each camera view is processed. If the number of recalculations is less than 1% of the total vectors, then

the data are considered reliable.

Calibration Procedure- The stereoscopic images recorded by the cameras that are oblique to the

object field must subsequently be corrected for both

magnification and perspective. One method by which

this can be accomplished results from recording the

images of a flat rectangular target (with precisely

known dimensions) that is placed in the field of view

of both cameras. The target used in this test consisted of a double sided print containing three rectangles (the largest measuring about 217 mm on a side)

and a background dot pattern that simulated a particle field (fig. 7).

A reliable method for assessing the accuracy of

the velocity measurements obtained from test data

is to evaluate the displacements recorded for known

target translations (ref. 25). Consecutive translations of the target over orthogonal distances of 0.200

in. resulted in an in-plane standard deviation of 0.3%

(horizontal) and 0.5% (vertical), and an out-of-plane

standard deviation of 1.2%. Since actual particle dis-
placementswillnormallybesubstantiallysmaller,the

probableerrorshouldbeincreasedbyseveraltimes.

Therefore,in the worstcase,the out-of-planecomponentisestimatedto beaccurateto withinabout

3%.

Particle Seeding-Properseedingof theflow

iscriticalto accuratePIV measurements. Theseed

particlesmustbeevenlydistributedandofsufficient

densitytodefinetheflowwithoutalteringits physical

properties.Theparticlesmustalsobesmallenough

that theyaccuratelyfollowtheflow(especiallychallenging in accelerating flows), yet large enough that

they scatter a sufficient amount of light to be detected. It is usually convenient to have remote control

over the delivery of the seed material into the flow.

The particle generator used in this test employs an inert gas to atomize a non-toxic, pharmaceutical-grade

mineral oil. The mist is vaporized and then condensed

before being released into the flow. The particle size

is estimated to be less than 0.5 tim. The particle generator was located near the floor of the hover chamber

so that the particles would mix with the air entering

into the chamber before being drawn into the wake of

the rotor.

Data Acquisition- The CCD cameras were

connected to separate frame-grabber cards installed

in a PC workstation. Using WinVu software, images

were acquired and immediately processed in order to

evaluate the quality of the raw images and the adequacy of the inter-pulse time delay. Good image correlations depend on such issues as background light

contamination, particle image brightness, contrast,

focus, beam alignment, and light pulse separation.

Prior to taking data, fine focusing and beam

alignment were performed using a seeded jet. Focusing was accomplished by translating the camera

lenses while observing the real-time image displays.

The gain and black levels were adjusted to maximize

the contrast and brightness of the particle images.

The two laser sheets were judged to be coplanar when

both laser pulses were recorded as a single image and

the resulting particle images appeared as doublets.

The correct inter-pulse delay can best be determined under actual test conditions. Images are acquired and correlated to determine the maxinmm particle displacement. This displacement corresponds to

the maximum particle velocity and the pulse separation should be adjusted to produce a + 3 pixel

range, regardless of the window size. Pixel displacements that are too small will limit the dynamic range

whereas displacements that are too large will decrease

the probability of correlation (ref. 26). Because of

the high in-plane particle displacements, caused by

the high circumferential velocity of the trailing vortex from the rotor at different wake ages, the optimum

pulse separations varied from 30 to 50 its (Table 1). It

should be noted that if the thickness of the light sheet

is 1 mm and the minimum delay between laser pulses

is 30 #s, the highest out-of-plane velocity (w) that can

be detected is 33 m/s. Since the tip of the rotor blade

is moving at 104 m/s, portions of the flow in tile near

wake may be in error. If this condition were to occur

at a calculation node, an interpolated value based on

values at neighboring nodes would result. Therefore,

at any point in the flow where w reaches 33 m/s, it

may be assumed that the correct value may actually

be much higher. Once image quality was assured, 50

image pairs were acquired per wake age. Data for each

wake age required about 200 megabytes of storage.

Table 1: Pulse Delay Times (ps)

Config

Basic

Free VG

0° VG

+5 ° VG

-50 VG

+10 ° VG

-10 ° VG

+15 0 VG

-150 VG

900 TG

Wake Age

20 10 ° 300 60 ° 100 ° 1500 210 ° 2800

30 30 30 30 30 30 30 35

30 30 30 30 30 30 30 30

30 30 30 30 30 35 35 35

30 30 30 30 30 35 35 35

30 30 30 30 30 35 35 35

30 30 30 30 30 35 35 35

30 30 30 30 30 35 35 35

30 30 30 30 30 30 30 30

30 30 30 30 30 35 35 35

30 30 30 30 40 45 50 50

Post-Test Data Processing- After completion

of the test, the data was processed on a PC workstation using ProVision software, which is a more advanced release that replaces WinVu. To obtain good

resolution of the primary vortex, a calculation mesh

having 99 nodes (horizontal) by 91 nodes (vertical)

was constructed over the region of significant interest in the flow field (fig. 8). The area covered by

the mesh resulted in an average of 8.5 pixels between

nodes in both directions. The interrogation window

was set at 20 pixels on a side, which gave about a

59% overlap. The total physical area measured about

386 mm (with horizontal increment of 3.9 ram) by 237

mm (with vertical increment of 2.6 ram).

A single file for each wake age includes a flag for

every velocity measurement that indicates the nature

of that vector (such as valid, invalid, interpolated,

recalculated, or not calculated). Reduced dala files

containing the coordinates of each calculation node

and the three components of velocity (in terms of displacement) were stored in ASCII format (about 32

megabytes in size) and then transferred to a mainframe computer for analysis.

The velocity components were first converted
fromdisplacement units to velocityunitsbasedon

thepulsedurationfor that particularmeasurement.

Thephysicalcoordinatesweretransformedsothat

x = y = 0 would correspond to the tip of the rotor

blade (fig. 9). The sequence for extracting the characteristics of the trailing vortex (fig. 10) for each case

begins with a calculation of the vorticity field, wz, for

every image pair. Vorticity can either be calculated

by differentiation or integration according to:

Ov Ou

_ - Ox Oy (1)

or

_ = A-lr = A-l _(g,g).d(2, y-') (2)

where the direction of integration is such that tile

enclosed area, A, is on the left of the integration path.

In this study the vorticity was calculated using the

integration (or circulation box) method.

When more than one vorticity center is present in

the field of view, a single image pair must be processed

to determine where the field should be partitioned so

that statistics are built on only one vortex. A simple two-part partition is usually sufficient to separate

the two vortices. However, when a vortex generator

is installed on the rotor blade, a small (but potentially intense) satellite vortex develops along side of

the main vortex. In this case it is necessary to focus

the interrogation on a more restricted region of the

flow field. In such cases the statement "account for

wander: focus" will appear in the figure for this data.

After calculating the vorticity distribution over

the entire image, a search was performed to discover

the zone of greatest vorticity concentration based on

values exceeding 50% of the maximum (fig. ll shows

an example of the search). The center of vorticity

for a given image was defined to be at the average

of these selected locations. The resulting centers of

vorticity (one for each image) formed a set for which

the mean value (_, _) and the standard deviation (or)

could be calculated. Any image with a vortex center (x, y) that deviated from the mean (g, _) by more

than 1.5_ was purged from the set. The 50% threshold criterion prevents the center of vorticity for an

image from being determined by a single, and possibly erroneous, measurement. The standard deviation

criterion prevents an atypical departure, albeit a legitimate image, from being factored into the average.

The threshold and purging criteria both have the effect of reducing the degree of wander in the data (fig.

12). When the acceptance threshold is 100% (the vorticity center in each image is determined by a single

point), 47 points are retained and 3 points are discarded because they exceeded the standard deviation

criterion. When the acceptance threshold is 50% (the

vorticity center in each image is determined by an aggregate of points), a distinct population of 44 points

results (some of which are coincident). The quantity

(f that appears in this figure, as well as many others,

represents the degree to which the vortex wanders for

a given set of images, and is calculated by taking the

square root of the sum of the squares of the x and y

offsets from the mean.

The images must be averaged to smooth out

small irregularities in the flow. However, whenever

there are large features in the flow, such as a trailing

vortex, and the vortex appears in different positions

from image to image (vortex wander), important details of the structure tend to be smeared out if a simple average of the images is performed. The remedy

is to perform the average after artificially aligning the

images based on a recurring feature of the flow, which

in this case is the center of vorticity. This process, in

contrast to a simple average, is referred to as conditional ensemble averaging, the condition here being

the alignment of all the images in the set based on

their centers of vorticity. The image with a vortex

center closest to the mean location that was established for the set of images was selected as the "anchor". The indices of each image matrix were then

adjusted according to the offset of each vortex center from the vortex center in the anchor image. All

data in the anchor image were retained. However,

some portion of all other images with adjusted indices

that fall outside the boundaries of the anchored image

were necessarily discarded. Hence, as a consequence

of vortex wander, the population contributing to the

conditional average was greatest over the interior of

the matrix.

For reasons that will become clear in the following discussion, emphasis will be placed on the swirling

nature of a vortex flow. To extract information about

the geometry of the vortex, the center of the vortex

was assumed to be at the center of swirl (which is not

necessarily at the center of vorticity that is accreted

from the rotor wake as a spiraling sheet with varying

vorticity). Using the center of vorticity as a starting point, the surrounding locations are interrogated

to determine the best node for which the sum of the

dot products of two unit vectors is a minimum over

a neighborhood of locations surrounding the candidate node. One of the unit vectors is defined by the

coordinates of the neighboring node relative to the

candidate node. The other unit vector is defined by

the velocity vector at the neighboring node. Denoting

the angles of these two unit vectors by c_ and fl (fig.

13), then the node nearest the center of swirl is found

when the following expression is a minimum:
N

Icos( -/3)t/N (3)

where N is the total number of neighboring points

considered. Relative to the center of swirl for a pure

vortex in a stationary flow, a and/3 will be orthogonal

for all neighboring points and the sum will be exactly

zero. For most real flows the sum will not be precisely

zero, and the procedure works best when the neighborhood under consideration does not extend beyond

about one or two core diameters (which is normally

sufficient to cover a majority of the vorticity in a single trailing vortex). After locating the center of swirl,

the size of the vortex core can be estimated. This is

accomplished by dividing the neighborhood into annular zones and then determining the average swirl

(or circumferential) velocity for each zone:

N

Idel/N (4)

r_--.1

where N is the number of nodes within a given annular zone. The mean diameter for the zone having

the highest average swirl velocity becomes the estimated diameter for the vortex core. This procedure

appears to work well even though the flow is not axisymmetric. The swirl velocity, ge, is defined by the

cross product of the unit position vector (relative to

the center of swirl) associated with a node and the

inplane velocity vector ff + _. This relation can be

expressed as:

=

H

v0 = I(ff+ if)sin(a-/3)1 (5)

where it is understood that ve is orthogonal to _'.

The ultimate method for calculating the size of

the vortex core requires that the space surrounding

the center of swirl again be divided into annular zones.

This time a larger array of bins is constructed that

contains the average swirl velocity and the associated

mean radius of each annulus. This array is then fit

with a least-squares spline subject to the condition

that the resulting curve have only one inflection along

its inner extent (nominally set to twice the estimated

core radius that was previously found). The radius

of the vortex core is now defined by the point of inflection since that is where a maximum value for _Teis

reached. This procedure is considered to offer a more

rational approach for determining the size of the vortex, especially when the velocity peaks that are characteristic of vortices (and upon which core sizes are

traditionally based) are dependent on how the vortex

is sliced (vertical, horizontal, or otherwise).

The final processing stage involves the construction of contour plots for v, w, and wz together

with profiles of these variables along a horizontal cut

(y=constant) through the center of swirl. The convection of the vortex does not affect w and _, however

it does produce an offset (or distortion if the convection field is not uniform) in the u and v components of

velocity. In this study the vortex is assumed to be uniformly convected. Two methods for discovering the

convection velocity are considered. One method assumes that the convection velocity at any given wake

age is determined by the interior velocity measured

at the center of swirl (the y component is defined as

vi). In the other method the convection velocity of

the vortex is deduced from the record of swirl center

coordinates calculated at each wake age (the y component is defined as re). The velocity profile for v

relative to the convection velocity as determined by

each of these methods (either v - vi or v - vc) is included in the presentation of results.

RESULTS AND DISCUSSION

Including the basic rotor case, a total of 10 configurations were analyzed at 8 different wake ages (Tables 2 and 3).

Table 2: Configurations

Basic

Free Vortex Generator

0 ° Vortex Generator

+5 ° Vortex Generator

-5 ° Vortex Generator

+10 ° Vortex Generator

-10 ° Vortex Generator

+150 Vortex Generator

-15 ° Vortex Generator

90 ° Turbulence Generator

Table 3: Wake Ages

2 o

10o

300

60 o

100 °

1500

2100

280 °

The vortex generator is defined to be at a positive

angle when the trailing edge swings towards the tip
of the rotor blade. Forpositiveangles,the vortex

thattrailsfromthetip ofthegeneratorwill havethe

samesenseastheprimaryvortexthattrailsfromthe

tip of therotorblade.Theactualangleof attackof

thevortexgeneratormaybequitedifferentfromits

geometricanglebecauseof theinfluenceof theflow

aroundthetip of the rotorbladeonthelocalflow

approachingthegenerator.All datawereobtained

with therotor collectiveanglefixedat -80, andall

wakedatawereobtainedat aconstant rotor speed of

870 RPM.

Torque Summary- The rotor torque was

recorded at several intermediate speeds prior to reaching the ultimate test speed of 870 RPM. These measurements are summarized in fig. 14 and indicate that

all of the vortex generators that were oriented at fixed

angles (0 ° , +5 °, 4-10 °, +15 °) resulted in torques that

were lower than for the basic blade case. However,

the "free" (or unrestrained) vortex generator shows

an 8% increase in torque while the turbulence generator shows a 18% increase in torque. Given that

these devices are located near the tip of the rotor

blade, even small changes in the drag force on these

elements should produce a noticeable change in the

torque. The sizable increase in torque for the turbulence generator case is therefore in keeping with the

expected level of increase in drag for such a blunt

configuration, and demonstrates why such a device

should be retracted when not required. If properly

designed, the free vortex generator would be expected

to react to the local flow much like a weather vane,

and therefore generate a minimum level of drag. Since

this does not appear to be the case, the center of gravity may have been offset from the pitch axis, thereby

rendering the element at an angle sustained by a centripetal force that increases with RPM, or the element

may be in a state of flutter.

Wake Analysis- For tile 50 image pairs that

were recorded at each wake age, approximately 12%

were discarded due to excessive vortex wander from

the mean location. Even when the vortex wanders

by no more than one core diameter, a conditional

ensemble average is required to obtain an accurate

profile of the vortex. In contrast to a preferred conditional average of the data, a simple average results

in a lower peak velocity and an increased core radius

(fig. 15), although the circulation calculated along a

circular path in the outer 1/r region appears to be

independent of the method of averaging. The same

conclusions have been reported using an exponential

expression for the circumferential velocity and simulating different amplitudes of vortex displacement

(ref. 27). It was shown that a substantial degredation in the velocity profile occurs when the amplitude

is greater than one core radius.

Circulation, F, carried by the entire image will

be presented for each case. This value is obtained by

summing all of the individual circulation-box calculations within a given image, which amounts to 8,820

contributions for the grid used in this analysis. The

total image circulation is quite sensitive to the convection of vorticity through the scene. In very general

terms, the circulation calculated for a scene that contains slices of the vortex from two revolutions would

be expected to decrease by about 50% when the second slice is convected out of the scene. The total

image circulation is useful when comparing the wakes

from different rotors (or with different vortex diffusion devices) and for evaluating the overall accuracy

of numerical codes.

For an "ideal" vortex, all of the vorticity is contained within rc and the circulation remains constant

for r _> re. However, in the case of a "real" vortex

that is isolated and two-dimensional, the circulation

within this body of fluid will rapidly increase with r

until reaching some point beyond the core radius. For

larger values of r the circulation will approach a constant value as long as the integration path remains in

the outer "inviscid 1/r" region. For the present rotor

wake case the circulation appears to follow the classical trend and approach an asymptotic value only in

the immediate vicinity of the vortex, but then deviates from a constant value at distances greater than

about twice the core radius (fig. 16). This deviation is even less satisfactory after taking into account.

the vortex convection velocity. Since the axis of the

trailing vortex from a rotor actually follows a helical path, the flow field around any given segment of

the vortex will be affected by the induced flow caused

by neighboring segments from previous revolutions of

the blade. Another factor to be considered is the continual (although diminishing) accretion of chordwise

vorticity that was initially shed into the wake along

the span of the blade due to changing circulation. Regarding the variation of ve with r, there is less scatter in the relative-velocity data than there is in the

absolute-velocity data. This is because in the relative case the flow field is referenced to the convection

velocity of the vortex, which renders it more axisymmetric.

Given that any experimental technique is subject

to some degree of error, it is useful to compare the

present results with earlier measurements obtained

under similar conditions. After applying a coordinate

offset and accounting for the different tip speeds, previously obtained LV data (ref. 20) can be compared to

the present PIV data (fig. 17). The PIV data shows

a shortfall in the magnitude of the velocity peaks as

well as an overestimate of the core size. Since the

data in both cases was taken in the near wake, vor-
rexwander(whichwasnotaccountedforin theLV

data)is not believedto be a factor(whichif anything,wouldhaveloweredthepeakvelocitiesin the

LV data). Assumingthat theLV datais morecorrect,thedifferenceismostlikelytheresultof a PIV

inter-pulsedelaytimethat wastoo longto capture

theparticleshavingahigherthananticipatedout-ofplanecomponent.Whenthishappens,thereported

velocitiesat thegridpointswherethismayhaveoccurredwouldhavebeenthe resultof interpolations

usinglowervaluesat neighboringgridpoints.Asexpected,theouterportionof the profilesaregreatly

differentdueto thehigherwakevelocitythroughthe

rotordiskin the2 bladecase.

Considernowapopularalgebraicexpressionused

to approximatethevortexprofile(ref.28),

F. r

ve = 2_ (r_" + r2n)l/, (6)

where F. denotes the entire circulation for the vortex.

To compare the above vortex model with the present

data, it is assumed that F. has been reached at twice

the core radius (recall fig. 16). Focusing on data for

the basic blade at ¢ = 100 °, it appears that the model

(assuming r. = 2re) is in fairly good agreement when

n=2 (fig. 18), which is consistent with conclusions

about this model reported in earlier studies (refs. 28

and 29).

Basic Blade Wake- The distribution of vorticity in the wake of the basic blade provides an immediate view of the convection path of the vortex during the first revolution of the blade (fig. 19). The

strength of the vorticity carried by counter-clockwise

rotating fluid, Wz < 0, is indicated by the level of blue

saturation in the contour plot (with the trailing vortex being dominant), while vorticity of the opposite

sense is represented by various levels of red saturation. Also included are markers locating the 5 highest neighboring values of vorticity on both extremes.

These markers serve to expose the irregular complexion of the vorticity field as well as the migration of isolated concentrations of vorticity. The pattern shows

the spiraling accumulation of vorticity from the blade

wake toward the center of the vortex. The appearance of positive values of vorticity, wz > 0, initially

found along the inboard portion of the wake, are shed

from the blade where the lift is increasing with blade

radius.

The structure of the flow behind the basic blade

at different wake ages is shown in figs. 20 - 27, and the

more significant characteristics are summarized in fig.

28. The location of the center of vorticity appears to

be quite random from blade revolution to revolution,

with the extent of the wander increasing with wake

age. The center of vorticity (based on the centroid of

high values) is generally at a slightly different location

than the center of swirl. The midpoint between the

velocity peaks, based on either v vs. x or u vs. y

profiles across the vortex, is generally not located at

the center of swirl. As the vortex ages, the maximum

values of vorticity and swirl velocity decrease while

the core radius increases. Tracking the location of the

trailing vortex based on the centers of swirl at each

wake age, the rate of movement toward the rotor axis

of rotation, u, decreases toward an asymptotic value

while the rate of movement in the direction of the

flow through the rotor disk, v, increases toward an

asymptotic value.

More traditional displays of the vortex structure

are fashioned in figs. 29 - 36 for the quantities v, w,

and w_ in terms of contour plots and cross sections

through the center of the vortex. The dominant level

of vorticity is clearly contained in the trailing vortex, however the peak value of _;z is oftentimes not

reached monotonically. The out-of-plane component

of velocity, w, readily exposes the wake deficit, especially during the early wake ages (¢ _ 100°). Maximum excursions in w appear to coincide with the peak

circumferential velocity (as suggested by the profile

for v) and are directed back toward the rotor blade

(in keeping with the remainder of the wake deficit).

Based on the above algebraic model for re, it has been

shown (ref. 28) that for n = 2 (which best fits the

data) that w reaches peak values at about 0.76rc. A

distinctive zone near the center of the vortex exists

where w comes close to matching the velocity in the

outer 1/r region.

In certain cases (_p = 10° and 30 °) contour plots

show that w actually points in the opposite direction, coinciding with the direction of ,;_. It also

appears that during the early stages of wake development (¢ ,( 100 °) that the location of this region

of "excess" w is offset from the centers of swirl and

vorticity. Accompanying the display of the v profile

are portrayals of the velocity relative to the movement of the vortex in the wake. If the objective is

to obtain a more symmetric profile in the outer 1/r

region (thereby rendering a Lagrangian-like appearance), then the construction based on the convection

velocity (v- vc, solid line, calculated using actual

vortex locations) is much more satisfactory than the

construction based on the velocity measured at the

interior of the vortex (v - vi, dashed line).

0° Vortex Generator- In contrast to the: wake

for the basic blade, a map of the vorticity field with

the vortex generator attached and fixed at 0° reveals

the presence of an additional zone of vorticity with

the same sense as the primary vortex (fig. 37). In

relation to the primary vortex, this smaller vortex

persists as a distinct body of fluid for ¢ < 300 and

10
appearsto orbit the primaryvortexat anangular

rateof about6o foreverydegreeof wakeage.Prior

to themergingof thesetwovortices,featuresrelating

to theprimaryvortexarelesscertaindueto distortionsof theflowfieldcausedbytheproximityofthe

smallervortex(figs. 38- 45). Thisis supportedby

a theoreticalstudyof twosyntheticvorticeswhich

showsthat theresultingswirlingflowbecomesvery

differentasthevorticesbeginto overlap(ref. 30).

A portionof the chordwisevorticitythat normally

wouldhavegoneimmediatelyinto theprimaryvortexmayactuallyhavebeenshedwiththat fromthe

vortexgenerator.Laterwakeageshavetheappearanceofasinglevortex,howevertheyaremoreintense

(magnitudeof wz has increased and the core size has

decreased) than those measured for the basic blade

alone (fig. 46). Furthermore, this configuration yields

an ultimate trailing vortex that has traveled a shorter

distance (in both z and y) from the tip path traced by

the basic blade alone, thereby increasing its interaction with the rotor blade during the next revolution.

Contour plots and cross sections through the center

of swirl for the quantities v, w, and _z are shown in

figs. 47 - 54. When compared with the basic blade

case, the w_ profile shows that the primary vortex is

initially weaker during the early stages of its development (¢ < 30°), but quickly increases in strength

after the two vortices have merged (figs. 47 - 54).

The w component of velocity appears to be generally

weaker than for the basic blade, however, the shape

of the profile is similar.

45°,410°,415° Vortex Generator- The wake

effects that result from swinging the trailing edge of

the vortex generator toward the tip of the rotor blade

are shown in figs. 55 - 108. These angles tend to

produce tip vortices that have the same sign as that

trailing from the tip of the rotor blade. As the lift

on the vortex generator is increased, the tip vortex

that it produces appears to orbit the primary trailing

vortex more rapidly than in the 0° case and finally

merge with the primary vortex at an earlier wake age

(figs. 55, 73, 91). In each case, distortions in the

v component of velocity occur during the early wake

ages through ¢ = 30 ° (figs. 56 - 58, 74 - 76, 92 - 94).

A noticeable jump in the peak magnitude of the w_

profiles occurs at ¢ = 60 °, which coincides with the

merging of these two vortices (both rotating in the

same direction). Once the wake has reached _b = 60 °,

all three configurations yield a single vortex with a

higher peak wz and a smaller rc than occurred for

the basic blade alone (figs. 64, 82, 100). Placing the

vortex generator at 450 and 4100 causes the ultimate trailing vortex to travel farther away from the

tip path plane (increased y) and with less contraction (decreased z) than for the basic blade case. The

advantage at +5 o and +10 ° of an increased separation distance from the rotor plane is not achieved at

4150 possibly due to excessive flow separation from

the generator at this high angle.

-5 °,- 10°,- 15° Vortex Generator- The wake

effects that result from swinging the trailing edge of

the vortex generator away from the tip of the rotor

blade are shown in figs. 109 - 160. These angles tend

to produce tip vortices that have the opposite sign as

that trailing from the tip of the rotor blade. Vorticity

contours indicate that a secondary vortex does not

clearly appear until the vortex generator is rotated to

-15 o (figs. 109, 127, 145). This would suggest that

the local angle of incidence is different from the geometric angle of the generator, which is to be expected

in light of the skewed direction of the approaching

flow moving around the tip of the rotor blade. Although not obvious in the contour plots, there is a

gradually increasing influence on the primary vortex

as the generator angle is increased. This influence is

evident in the comparatively flat appearance (which

increases with the generator angle) on the left side of

the v profiles from ¢ = 2o to _p= 30 ° (figs. ll0 - 112,

128 - 130, 146 - 148). Although the sense of the secondary vortex is opposite that of the primary trailing

vortex, it orbits the primary vortex in the same direction as in the positive vortex generator cases, but

at half the angular rate. The wake eventually adjusts

to the presence of the secondary vortex by forming a

single vortex with a higher peak wz and a smaller rc

than occurred for the basic blade alone (figs. 118,136,

153). Placing the vortex generator at -50 causes the

ultimate trailing vortex to travel farther away from

the tip path plane (increased y) and with less contraction (decreased x) than for the basic blade case.

The vortex in the -150 case also travels farther away

from the tip path plane, but now the contraction is

increased as well. This combination of movements

places the vortex even farther away from the trace of

the rotor tip.

Free Vortex Generator- Assuming that the

center of gravity is located on the pitch axis, the angle of this element is free to respond only to local

flow conditions. Recalling the previous results with

and without a vortex generator, a review of the contour maps and cross sectional plots suggests that this

case is unique (figs. 161 - 178). There is no evidence

of a secondary vortex present in the contour maps

(fig. 161), nor are there any distortions in the v profiles during the early stages of wake development (figs.

162 - 164) comparable to those observed when the

generator was placed at fixed angles. However, the

initial vorticity field defining the trailing vortex does

have an annular appearance similar to the negative

generator cases, but remains less focused for a longer

11
periodoftime(fig. 161).Thismayexplainwhythe

magnitudeof the peakvorticityandthe maximum

swirlvelocityarenoticeablyreduceduringtheearly

wakeages(fig. 170).Thetrailingvortexin thiscase

hasmovedashorterdistancefromthetip pathofthe

rotorascomparedto thebasicbladecase.

TurbulenceGenerator-Althoughthiselement

wasorientednormaltothebladesurfaceandintended

to functionmuchlike a spoiler,the localflowmay

haverecognizedit asbeingmorelikea flat plateat

highincidence(andthereforeasourceof lift). Referenceto theprecedingvortexgeneratorcaseswill help

to understandtheunusualresultsforthisconfiguration(figs.179- 196).Thecontourmapsof vorticity

(fig. 179)showthat afterthetrailingvortexhasbeen

initiallydistortedbytheturbulencegenerator,it remainsdistributedovera muchlargerspatialregion

thanwasobservedfor allothercases.Theredoesappearto beaneighboringzoneofpositivevorticityat

= 20and_ = 10° (similar to that observed in the

-150 generator case), and is undoubtedly the result

of lift on this element. In keeping with the broadened

footprint of the resulting trailing vortex, the corresponding peak velocity and vorticity excursions are

substantially reduced (fig. 188). The wake contraction and its convection away from the rotor plane are

both less than observed for the blade alone case.

Overview- The merits of each configuration are

summarized in terms of vortex strength and location.

Tables 4 (near field) and 5 (far field) indicate how

these quantities have changed relative to the basic

blade. The value of the near-field results may become more important as the spacing between the rotor blades is reduced.

A quantity increases compared to basic blade

V quantity decreases compared to basic blade

o no significance difference

Table 4: Near Field (_b = 30 °)

Config Max-w_ Max vo rc x y

Free VG V V A o o

-15 0 VG A & o o o

-10 ° VG A A 27 o o

-5 ° VG o o o o o

0° VG A o V o o

+5 ° VG o V o o o

+10 ° VG o V o o V

+150 VG V V o o V

900 TG V V A o V

In terms of reducing the strength of the trailing

vortex in the near field (¢ = 30°), the free vortex

Table 5: Far Field (¢ = 280 °)

Config Max -wz Max vo rc x y

Free VG A V V o V

-150 VG A V V A A

-10 ° VG /X /_ V /x o

-50 VG A A V 27 A

0° VG A A V o V

+5 ° VG A A V V A

+10 ° VG A A V V A

+150 VG A A V V V

900 TG V V A V V

generator and the turbulence generator are clearly

superior to the other configurations. However, in

the far field (¢ = 280°), only the turbulence generator provides a sustained reduction in vortex strength.

In terms of increasing the displacement of the trailing vortex from the path of the rotor tip, none of

the configurations studied satisfies this requirement

in the near field. On the other hand, a few cases

suggest some benefit in the far field, either in terms

of a greater contraction or a greater convection away

from the rotor plane. The convection velocity, along

with the size and location of the trailing vortex, are

summarized for all cases at ¢ = 280 ° in figure 197.

Relative to the location of the trailing vortex from

the basic blade, vortices from all other configurations

remain somewhat clustered nearby and with a maximum separation of about one core diameter (or about

one blade thickness).

CONCLUSIONS

1. A robust procedure was developed for analyzing a vortex dominated flow field, extracting its principal features, and performing a conditional ensemble

average that accounts for vortex wander. Conditional

averaging is necessary in order to preserve the intensity and size of the vortex.

2. In vortex flows, the highest out-of-plane velocities often occur where the circumferential velocity

is highest. When the delay time between PIV pulses

is too long, interpolations will render in-plane peak

velocities that are too low. As a result, the vortex

will appear weaker due to a reduced circumferential

velocity and an enlarged core size.

3. The torque produced at 870 RPM in all of

the vortex generator cases where the angle was fixed

was lower (up to 6%) than for the basic blade alone.

However, there was an 8% increase in torque in the

free (unrestrained) vortex generator case and an 18%

increase in the turbulence generator case.

4. The peak value of vorticity generally occurs

close to the center of swirl. For the basic blade, the

12
componentof velocitythat is alignedwith theaxis

ofthevortex(theout-of-planecomponent, w, in this

study) has a somewhat annular shape, but is offset

from the center of swirl. Peak values of w are directed back toward the rotor blade and are roughly

associated with the core diameter defined by the peak

circumferential velocity, re. In some cases, the flow

in the center of this annular region may be pointed

in the opposite direction (away from the rotor). During the initial 280 ° of azimuth the diameter of the

vortex core increases from about 1.2 to 1.5 times the

thickness of the rotor blade.

5. A vortex trailing from a vortex generator with

a fixed angle will orbit the primary tip vortex at an

angular rate of about 6° for every degree of wake age

when the two vortices have the same sense. When the

subordinate vortex has the opposite sense, the direction of the orbit remains the same, but the angular

rate is greatly reduced. In both cases the subordinate

vortex cannot be distinguished from the primary vortex after ¢ = 600 , and eventually, a more intense

primary vortex is produced. As the angle of the vortex generator becomes more negative (producing a

stronger counter-rotating vortex), the annular shape

of the w component of velocity becomes more pronounced as the magnitude of the flow in the interior

increases in the direction of the rotor.

6. When the vortex generator is unrestrained,

the strength of the primary vortex during the initial

wake ages is significantly reduced. Unlike most of

the vortex generator cases at fixed angles, this case

shows no evidence of a subordinate trailing vortex.

Although the advantages in terms of maximum vorticity and core radius are diminished after reaching

¢ = 280 °, the maximum swirl velocity remains lower

for all wake ages.

7. The most dramatic changes occurred in the

turbulence generator case. The absence of an annular

shape and the significant reduction in vortex intensity suggest the effectiveness of the turbulent action

toward homogenizing the flow inside the trailing vortex and contributing to its rapid diffusion. Although

the torque increased by 18%, the maximum vorticity

was reduced by 65%, the maximum swirl velocity was

reduced by 57%, and the core size almost doubled

after reaching ¢ = 280 °.

8. All of the configurations had some effect on the

final position of the trailing vortex, with the greatest

departure from the basic blade case being about one

blade thickness farther away from the trace of the

rotor tip.

REFERENCES

[1] Beesten, B. M. J.: Influence of Non-Planar Blade

Tips on Rotor Performance. 18th European Rotorcraft Forum, Paper No. 73, Avignon, France,

1992.

[2] Miiller, R. H. G.: Special Vortices at a Helicopter

Rotor Blade. Journal of the American Helicopter Society, Vol. 35, (4), 1990.

[3] SplettstS13er, W. R.; Kube, R.; Seelhorst, U.; Wagner, W.; Boutier, A.; Michali, F.; Mercker, E.;

and Pengel, K.: Key Results from a Higher Harmonic Control Aeroacoustic Rotor Test (HART)

in the German-Dutch Wind 25mnel. Presented

at the 21st European Rotorcraft Forum, St. Petersburg, Russia, 1995.

[4] Dawson, S.; Straub, F.; Hassan, A.; Tadghighi, H.;

Marcolini, M.; Booth, E.; and Kelly, H.: Wind

Tunnel Test of an Active Flap Rotor: BVI Noise

and Vibration Reduction. Presented at American Helicopter Society 51st National Florum,

Fort Worth, TX, 1995.

[5] Jacklin, S. A.; and Nguyen, K.: Full Scale Wind

Tunnel Test of a Helicopter Individual Blade

Control System. Presented at American Helicopter Society 50th National Forum, Washington D.C., 1994.

[6] Rorke, J. B.; and Moffitt, R. C.: Wind Tunnel

Simulation of Full Scale Vortices. 28th Annual

National Forum of the American Helicopter Society, Washington, D. C., 1972.

[7] Landgrebe, A. J.; and Bellinger, E. D.: Experimental Investigation of Model Variable-Geometry

and Ogee Tip Rotors. 29th Annual National Forum of the American Helicopter Society, Washington, D. C., 1973.

[8] Smith, D.: Helicopter Rotor Tip Shapes for Reduced Blade Vortex Interaction an Experimental

Investigation. 33rd Aerospace Sciences Meeting

and Exhibit, AIAA 95-0192, Reno, NV, 1995.

[9] Corsiglia, V. R.; Jacobsen, R. A.; and Chigier,

N.: An Experimental Investigation of Trailing

Vortices Behind a Wing with a Vortex Dissipator. Aircraft Wake Turbulence and Its Detection. Plenum Press, 1971.

[10] Rossow, V. J.: Lift-Generated Vortex Wakes

of Subsonic Transport Aircraft. Progress in

Aerospace Sciences, Vol. 35, (6), 1999.

Ill] Tangler, J. L.: The Design and Testing of a Tip

to Reduce Blade Slap. Presented at American

Helicopter Society 31st National Forum, Washington D.C., 1975.

[12] Tangler, J. L.: Experimental Investigation of the

Subwing Tip and Its Vortex Structure. NASA

CR-3058, 1978.

[13] Lau, B. H.; Wadcock, A. J.; and Heineck, J. T.:

Wake Visualization of a Full-Scale Tilt Rotor

in Hover. American Helicopter Society Techni13
calSpecialists' Meetingfor RotorcraftAcoustics

andAerodynamics, Williamsburg,VA,1997.

[14]Carlin,G.; Dadone, L.; and Spencer, R.: Results

of an Experimental Investigation of Blade Tip

Vortex Modification Devices. NASA CR-181853,

1989.

[15] Carlin, G.; Dadone, L.; Sternfeld, H.; Ziegenbein,

P.: Results of a Powered Model Wind Tunnel

Test of Helicopter Rotor Blade Vortex Alleviation Devices. NASA CR-181969, 1990.

[16] Meadowcroft, T.; Dadone, L.; and Sternfeld, H.:

Advanced Concepts for Rotorcraft Noise Reduction due to Blade-Vortex Interaction by Vortex

Alleviation Devices. NASA CR-189626, 1992.

[17] McAlister, K. W.; _ng, C.; Sharpe, D. L.;

Huang, S.; and Hendley, E. M.: Preliminary

Study of a Model Rotor in Descent. NASA TM2000-208785, 2000.

[18] McAlister, K. W.; Takahashi, R. K.: NACA

0015 Wing Pressure and Trailing Vortex Measurements. NASA TP-3151, 1991.

[19] Heineck, J. T.; Yamauchi, G. K.; Wadcock, A. J.;

Lourenco, L.; and Abrego, A. I.: Application

of Three-Component PIV to a Hovering Rotor

Wake. Presented at the American Helicopter Society 56th Annual Forum, Virginia Beach, VA,

2000.

[20] McAlister, K. W.: Measurements in the Near

Wake of a Hovering Rotor. Presented at 27th

AIAA Fluid Dynamics Conference, New Orleans, LA, 1996.

[21] Lourenco, L. M.: Particle Image Velocimetry. von

Karman Institute for Fluid Dynamics, Lecture

Series on Particle Image Velocimetry, 1996.

[22] Arroyo, M. P.; and Greated, C. A.: Stereoscopic

Particle Image Velocimetry. Measurement Science and Technology, 2, 1991.

[23] Prassad, A. K.; and Jensen, K.: Scheimpflug

Stereocamera for Particle Image Velocimetry in

Liquid Flows. Applied Optics, 34:7092-9, 1995.

[24] Lourenco, L.: Mesh-Free Second-Order Accurate

Algorithm for PIV Processing. Proceedings of

VSJ-SPIE98, Paper AB079, Yokohama, Japan,

1998.

[25] Raffel, M. ; Willert, C.; and Kompenhans, J.: Particle Image Velocimetry, Springer-Verlag, 1998.

[26] Westerweel, J.: Theoretical Analysis of the Measurement Precision and Reliability in PIV. Proceedings of the Third International Workshop on

PIV'99, 1999.

[27] Leishman, J. G.: Measurements of the Aperiodic

Wake of a Hovering Rotor. Experiments in Fluids, Vol. 25, (4), 1998.

[28] Vatistas, G. H.; Kozel, V.; and Mih, W. C.: A

Simpler Model for Concentrated Vortices. Technical Notes, Experiments in Fluids, Vol. 11, No.

1, 1991.

[29] Bhagwat, M. 3.; and Leishman, J. G.: On the

Relationship Between Blade Circulation and Tip

Vortex Characteristics. Presented at the 54th

Annual Forum of the AHS, Washington DC,

1998.

[30] Strawn, R. C.; Kenwright, D. N.; and Ahmad,

J.: Computer Visualization of Vortex Wake Systems. Presented at the 56th Annual Forum of

the AHS, Alexandria, VA, 1998.

14
)/I//_///////////I'///////I/I///_I//%_ <___'-- _ _ _ - -"_,_A

_1IIIIIIII

\

I

f

I

VIII/I//_

I

\

I

/

Figure 1: Hover Test Chamber with single-bladed rotor at Ames Research Center.

45.0

I

Vortex Generator Turbulence Generator

NACA 0020 Counter Weight

Figure 2: Single-bladed rotor configuration showing location of tip mounted devices.

15
pdiring oiffusion

vortex Turbulent

Figure 3: Concepts studied for altering tile trailing vortex.

amera 2

\

\

\

View 2

Light

Sheet

/

/

\ x -. _Exposure \ Particle Pairs --

:':':':'X':':':':':':':O:':':':':'- v-'.'.'-'-'_.::.:.:-:-:-:-;-:-:-:-:-:

-:-:-:-:/:-:-:.:.:-:-:-:-D:-:-:':':'. / 1 2":':':':':3 "'"'""9'"'"'"'""/

/ ... First Exposure

/"

,.i

.t

f

J

J

f

f

View 1

Figure 4: Perspective effect of particle displacement with Stereoscopic PIV.

16
_ Object

Plane Particles

iii!i!!i_ii!iii!_i!!iiii_iii._i:_:i_!!!!_!iiiiiiiii:._!i!i!!ii!ii

/ / /

// / / /

Lens / /" "I

Plane / / /

Ima_ge __ / / /

Light

Sheet

Figure 5: Scheimpflug condition for maintaining image focus.

IKxlK _

( _amera

t

f

J

J

Tip

vort _

1

I

I

1

I

1

137" [

I

I

I

I

I

Figure 6: Setup of light sheet and cameras relative to rotor.

17
Figure 7: In-situ calibration target as viewed by camera 2.

Figure 8: Example of image pair with calculation grid.

18
\\

/ / /

//

............ Z,W,_ z

Figure 9: Definition of coordinate system showing origin on rotor-tip path.

19
Locate vorticity ¢entroid

for each image p_r

1

Ensemble average velocity field

based on vorticity centroids

1

Locate center of swirl pattern

1

Calculate core radius

based on spline fit

1

Dete_ine vortex c_veeti_

velocity& path

1

",/i

Examine variable

profiles & contours

Figure 10: Analysis sequence for extracting trailing vortex characteristics.

2O
Configuration: turbulence generator

Wake age: 10 °

N

3

!

10000

8000

6000

4O00

2000

-2000

-360

Center of swirl

y-- -26]

y-- -24.0

i y= -21.3

y= -18.9

y-- -16.2

y== -13.5

• t

_,,_.__ y= - 10.8

y= -8.4

y---- -3.0

y= 2.1

y= 4.8

t I i I J J I I

-300 -250 -200 -150 -100 -50 0 50

x, mm

Figure 11: Example search for vorticity exceeding 50% of the maximum value.

t

100

21
O

O

E

E_

O

O

O

O

t'N

E

E_

0

0

Radial displacement of the vorticity center

for each image relative to the mean

I I I I

10 20 30 40

Image Pair

E

E

.O

IT

E

E

.O

IT

!

O

50 -30

Config: turbulence generator

Wake age: 10 °

Acceptance threshold = 100%

• • • •

!

..... L.

• "

D--blade thickn

Acceptance threshold = 50%

=

E_O _¢_0 _ • .--=_ •O

D=blade thickness_

} I L

-15 0 15

x-_, mm

I

3O

Figure 12: Effect of vorticity acceptance threshold on apparent vortex wander.

• 22
J b

a : possible swirl center

b : neighboring node

position velocity ",,,

vector vector

Figure 13: Angles used in the search for the center of swirl.

23
i

d

o

0

i-_ io

i

O"

• Basic

_, -5 ° Vortex Generator

,!, +5 ° Vortex Generator

/

/

• Basic

-15 ° Vortex Generator

s, +15 ° Vortex Generator

/

/

F• Basic

,: -10 ° Vortex Generator

,:, -t-10 ° Vortex Generator

/

• Basic

,:,' 0 ° Vortex Generator

....... _, Free Vortex Generator

o Turbulence Generator

I I I I t I I I I I

0 200 400 600 800 1000 0 200 400 600 800 1000

RPM RPM

Figure 14: Rotor torque resulting from vortex generator and turbulence generator.

24
0

E9

E

>:g

Method: Simple average

Configuration: Basic

Wake age: 100 o

................ _._ .......

Method: Conditional average

Configuration: Basic

Wake age' 100 °

0

E _

0

LO _

i

0

L,_ __ I I 1 I I I i __J

i

-350-300 -250 -200 -150 -100 -50 0 50

x, mm

E _ T .....

_I _m_ _" "_" " "____r''_'m_"

0 _- L .......... J

0 20 40 60 80 100

r, mm

i l I I I I

-350-300 -250 -200 -150 °100

x, mm

0 20 40 60 80 100

r, mm

Figure 15: Conditional ensemble average compared to simple average.

25
Basic, _= 100 ° , ,absolute velocity

I

I

L ......... _. I i I

-240 -160 -80 0

X, mm

8O

Basic, _= 100 ° , relative velocity

I

I

ve max= 19.2 m/s

Core radius= 17.7 mm

" x center=-69.1 mm

• -" y center= 20.7 mm

-g

i i

vre max= 20.2 m/s

Core radius= 16.8 mm

• x center=-69.1 mm

_,_.• y center= 20.7 mm

I I I I _l

,_ __ F = 2_'rve F T' = 2_rrvre

|

2rc j_ 2r c

o_ rc rc

o

0 20 40 60 80 100 0 20 40 60 80 100

r, mm r, mm

Figure 16: Effect of vortex convection on local circulation.

26
rr-

>

0

6

O3

6

¢d

0

0

0

0

i

0

|

O3

0

Basic blade

• 2 blade LV data, _b=29 ° (Ref 9)

• 1 blade PIV data, _b=30 °

,J

p',

,:=:o_,,_.;=:o:** • °:.:= o, ,. •

,

%

I I I

i

-150 -75 0 75

X, mm

Figure 17: Comparison with LV data obtained in an earlier experiment (ref. 9).

O

eq

o9

E_o

qb

>

O

Basic blade, wake age----lO0 °

t Fit to measured data

Vortex model, n=2

.... Vortex model, n-----1

•" r' t r

v 0 -

2rr (rc 2n + r2n) l/n

r C r_

i i i _ i

0 20 40 60 80 100

r, mm

Figure 18: Comparison with algebraic models of vortex.

27
Case: Basic

• max values< 0 • max values > 0

• max values < 0 • max values > 0

• max values< 0 • max values > 0

_k=30 o _-

n n "=

• max values < 0

f"JZ

• max values < 0

'i f'_Z

• max values < 0

• max values > 0

_k=100°

• max values > 0

o

• max values _ 0

........ j

i#=- 210 °

• max values < 0

_z

• max values > 0

V'= 6°°

• max values < 0 max values > 0

_/ 280 °

Figure 19: Locations ofw_ extrema at ¢ = 20 -+ 280 ° for the basic blade case.

28
Case: Basic _=2 °

std dev allowed = 1.5

account for wander: focus

max _z threshold= 50 %

E

E.o

0

0

Vorticity center wander from mean

0 10 20 30 40 50

Image Pair

v e max= 23.5 m/s o

J ,d Core radius= 14.1 mm =_

o=- . ¢_1 /

•A 0

Within Core o

._I- I- _. u eve=-4.6 m/a "

t//_., v ave---- 3.5 m/s o

E E

k_

# "_'_.'.._.............

l" °

0 20 40 6O 80 100

r, mm

rain max

/

-6753 _-- 6753 s "1

-9 mm

_z _ _ _.-_-_,_

Total image F=-5.9 m2/s

-5

mm

I J I I I

D

-320 -240 -160 -80 0 80

X, mm

o Swirl center

v---- 1.8 m/s

0

Eo

>"

0

i Peak

core

0

radius

' 13.1 mm

0

03 I ....

i

-350 -275

swirl

o Swirl center

03

u=-1.1 m/s

0

0

Eo

- mid

0

i

0

L_____J_ I L ...... J _ I

-200 -125 -50 25 100 ' -150 -75

x, mm

swirl

Peak

core

radius

13.3 mm

L J

225 300

Figure 20: Vortex statistics at ¢ = 2° for the basic blade case.

29
Case: Basic Ik=10 °

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

0

E

0

0

Vorticity center wander from mean

10 20 30 40 50

Image Pair

ve max = 22.5 m/s o

" Core radius = 14.1 mm

Within Core o

L _,," "_= u ave = 0.6 m/s

o I E "l v ave=-2.0 m/s o

E E

Eg

o _""'_

0 20 40 60 80 100

r, mm

o Swirl center . i

=- .

.................. m_-d"

Peak

core

o radius ¢d

' 11.2 mm

0

o3 J I I I

i

-350 -275 -200 -125 -50

O9

E o

=;

0

i

I I

25 100

x, mm

(/)

min max

-6

mm

Total image F=-5.2 m2/s

0

0

|

-320

0 _ _ 32 m/s

-15 mm

I I I

-240 -160 -80 0

X, mm

-6

mm

J

80

0

o3

0

t,q

0

0

¢fl

I

0

o3 ______ _ I

|

-150 -75 0 75

y, mm

E o

:3

o

I

Swirl center

u=-0.9 m/s

l .......

mid swirl

150

Peak

core

radius

17.2 mm

J_.... J

225 300

Figure 21: Vortex statistics at ¢ = 10° for the basic blade case.

3O
Case: Basic _=30 °

std dev allowed = 1.5

account for wander: yes

max wz threshold = 50 %

E

E=

Vorticity center wander from mean

0 I

0 10 20 30 40

Image Pair

0

o3 - '"_ vo max = 21.5 m/s

• Core radius = 16.4 mm

• Within Core

L" _'__ u ave = 0.5 m/s

9 \.

/ ° I 1 1 I I

0

0

ave

50

20 40 60 80 100

r, mm

o Swirl center

O3

v = 11.7 m/s

0

Eo

0

! Peak

core

° radius

' 17.1 mm

0

o3 _ I

i

-350 -275

swirl

I I __._J_ ..... _ ......

-200 -125 -50 25 100

x, mm

0

E

Eg

>:

0

min max

-5407 _ 5407 s -1

-31 mm

Total image F=-4.2 m2/s

0

mm

i i i i i

-240 -160 -80 0 80

x, mm

o Swirl center

o3

u---1.8 m/s

0

0

aO

Eo

"1

0

!

0

o4

!

- - " h#id: - -

swirl

0

03 I ___

!

-150 -75 0

I L

Peak

core

radius

14.6 mm

J J

75 150

y, mm

225 300

Figure 22: Vortex statistics at ¢ = 300 for the basic blade case.

31
Case: Basic _=60 °

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

E

E_

0

o

o3

o

E

>

o

Vorticity center wander from mean

10 20 30 40 50

Image Pair

ve max = 21.3 m/s

Core radius = 15.3 mm

A u aW:te_ n1.C°r:/s

_ ,, V ave= 3.4 m/s

o

0

o

0

E

Eo°

o

o

o

o I I I I I _ I

i

0 20 40 60 80 100 -320 -240

r, mm

Swirl center

_ ,

........_t

_ / mid- _,.._,'-"

o, j_ Peak mid" V

/ core _"

_ radius

' / 17.0 mm

/

L_ _ j L .... J_ t

i

-350 -275 -200 -125 -50 25

0

O3

0

O4

0

min max

Eo

0

|

-5046 m 5046 s "1

-47 mm

Total image F=-2.9 m2/s

I I

0

i

-160 -80

X, mm

16

mm

Swirl center

U-----0.1 m/s

mid

o

I o3

!

100 -150

Peak

core

radius

14.6 mm

I I L J I J

-75 0 75 150 225 300

x, mm y, mm

Figure 23: Vortex statistics at ¢ = 600 for the basic blade case.

32
Case: Basic _=100 °

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

O

t-4

E

Eo

O

O

E

&

>

O

Vorticity center wander from mean

_/t__=_ % tf ave

I I I I

10 20 30 40 50

Image Pair

v e max= 19.1 m/s

Core radius= 17.8 mm

Within Core

f

r..

0 1 i 1 I I

0 20 40 60 80 100

r, m m

O

03

O

¢N

O

CO

Eo

>"

0

i

Swirl center

mid"

Peak

core

o radius ¢N

' 16.7 mm

O

!

-350 -275 -200 -125

X, mm

swirl

O

O

03

....... E o

!

J L I

-50 25 100

min max

_= 4365 s "1

-68 mm

,, - . -._. ..:. - :1_ " ""_ ,

Total image F=-3.3 m2/s

2O

mm

I I I I

-240 -160 -80 0 80

X, mm

O

o_

O

O

O

i

O

|

-150 -75

Swirl center

u------3.1 m/s

........ rSi_- - ' ......

Peak

core

radius

14.6 mm

I I I J. ]

0 75 150 225 300

y, ITIm

Figure 24: Vortex statistics at ¢ = 100 ° for the basic blade case.

33
0

¢N

E

Es

0

0

0

0

E

&

>

0

0

0

0

Eo

=:

0

i

Case: Basic _= 150 °

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

Vorticity center wander from mean

I I I I

10 20 30 40

Image Pair

50

ve max= 20.6 m/s

Core radius = 14.9 mm

.,_, UaW_teh=inoC; rem/s

/ vave=1.7m/s

i . ...:__.._._,

ave

I I

20 40

r, mm

I I I

60 80 100

Swirl center

:j

........ _n idz _-

Peak

core

o radius

' 13.1 mm

0

03 _ I .....

i

-350 -275

.L_

-200

L _ L

-125 -50 25

X, mm

0

Lo

E

Eoo

0

min

-4639

max

ml 4639 s "1

-107 mm

('_Z

Total image ['=-3.6 m2/s

0

|

-320 -240 -160 -80 0 80

X, mm

0

_3

0

0

¢/}

Eo

0

i

0

|

0

!

100 -150

Swirl center

u=-1.7 m/s

W

m ! I J-m

-75 0 75

y, mm

k

swirl

Peak

core

radius

17.3 mm

I I J

150 225 300

Figure 25: Vortex statistics at ¢ = 1500 for the basic blade case.

34
Case: Basic _=210 °

std dev allowed = 1.5

account for wander: yes

max ¢Jz threshold= 50 %

E

Eo

0

o

V0rticity center wander from mean

I I 1 J J

0 10 20 30 40 50

Image Pair

r

/ v e max= 20.3 m/s

Core radius= 16.6 mm

! % Within Core

o I- ._t_" u ave= 0.7 m/s

.._ / A vave-- 1.9 m/s

rl

o, f , , _ " _._,

0 20 40 60 80 100

r, mm

ave

o Swirl center

o

¢N

E o .............

>- mid _

o

' Peak

core

o

c_ radius

' 17.0 mm

o

ct) .... L_+_

i

-350 -275

o)

o

0

o

o

E

Eoo

>:

o

u_

0

i

-320

min max

-4543 === 4543 s"1

-124 mm

• + ++ " S '++ i

:+_ +# ++, _ ++-+: +++ (

• - • L _+# • • " J+ "- " • • + - '-

'++ ++ ++ 76

Total image ['=-3.1 m2/s

77

mm

i L I I

-240 -160 -80 0 80

x, mm

o Swirl center

03

u-----1.6 m/s

o

cN

o

,+ swirl

............ E o

0

04

i

o

i

-200 -125 -50 25 100 -150 -75 0 75

x, mm y, mm

swirl

Peak

core

radius

14.7 mm

_ __J_ . __J

150 225 300

Figure 26: Vortex statistics at ¢ = 2100 for the basic blade case.

35
0

to

E

E_

0

0

0

0

E

>

0

Case: Basic lb=280 °

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

Vorticity center wander from mean

0ve

I ] i I I

10 20 30 40 50

Image Pair

ve max = 18.7 m/s

Core radius = 17.3 mm

Within Core

J, u ave= 0.3 m/s

",_, v ave = 1.7 m/s

• • m•_

0

0

0

0

E

E_

0

min max

-4328 i 4328 s -1

-150 mm

IL 115

mm

Total image ['=-3.0 m2/s

115

mm

0 _ i 24 m/s

-151 mm

ii!]ii!i]ili!iii!i_ii

i i i I

0

0

m

0 20 40 60 80 100 °320 -240 -160 -80 0 80

r, mm x, mm

o Swirl center o Swirl center

O3 o3

v= 0.1 u=-O.7 m/s

. swirl

E o E o ............ mid_ ....

>- mid _" :_

0 0

=

' corePeak __' _'_ cPc::

o radius _ o _' rad=us

' 17.0 mm ' 15.9 turn

_'_ __ I I d ______.i_ ........ I I _ ______ L _ L I J

'-350 -275 -200 -125 -50 25 100 '-150 -75 0 75 150 225 300

x, mm y, mm

Figure 27: Vortex statistics at ¢ = 2800 for the basic blade case.

36
Configuration: Basic

O

X

N

3

O

|

Max (-) Vorticity

uljj j,.o.J m'° _ °_m'°m •

o

o

(D

Eo

x_

0

0

Max Swirl Velocity

0

0

_o

Vortex Wander

a_ • _ o °_ 8"_gSgj_qlSgt_lp_e

o

o

E

-:2

0

0

Vortex Core Radius

• I IO_ o

_OJo- •

o Swirl Center Location ©

E _o_" _° E

_Oxo 1_:=_L ........................... o_ _,=;°=,

, _e 'q"

O0 • X '

i i

0 60 120 180 240 300 360

Wake Age, deg

Swirl Convection

V

U

I I I I___

0 60 120 180 240 300

Wake Age, deg

I

360

Figure 28: Summary of vortex development from _ = 20 --4 2800 for the basic blade case.

37
o

ua

E

Eoo

o

to

o

ill

E

Eg

o

o

Case: Basic ,_== 2 °

rain max 0

o3

-26

rain

-34

max

min max

26 m/s

34 m/s

0

o4

0

o3

Eo

0

!

0

cN

0

0

o3

o

E

i

Swirl

center

..... V f

--- V-V i

==_= V-V C

Swirl

center

......................... ;_,_._ -

A i

.......

l I i I --J

'-375 -300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0 75

x, mm x, mm

Figure 29: Velocity and vorticity components at _b = 20 for the basic blade case.

38
Case: Basic _= 10 °

rain max

o

E

Eoo

o

-30 30 m/s

min max

o

ID

E

Eoo

o

itJ

10 m/s

min max

o

o

o

o

iz3

E

Eoo

o

o

i

-375

0

0

Eo

>"

0

i

0

!

o

u3

E

o

5406 s -1 o

I I I I I i a}

-300 -225 -150 -75 0 75

x, mm

t

- - - -_,-_2.2.2.;.;_._.2.-.._L/

........................

--- V-Vi

i_= V.Vc

Swirl

center

I

i

, Swirl

center

I

I

I

Swirl

I

center

..... '_.-.,- ............ ,..,_.-.,",,.,._-,0.._,m,,.._--= I ._ 0,_°.,_.._

.I

VI

I

I

I

I

I

I I I I , I I 3

375 -300 -225 -150 -75 0 75

X, mm

Figure 30: Velocity and vorticity components at _b= 100 for the basic blade case.

39
Case: Basic _= 30 °

min

msx

max

32 m/s

7 m/s

5407 S "1

0

o3

0

o4

0

Eo

>"

0

!

0

o4

i

0

co

I

o

u_

E

_o

i

a0

q

o

i

o

o4

|

o

X '

cSei;ler

............... s- S- - -ii i ......

.......... _

°°*°° V

--- v-vi

V-Vc tI s S

I i I

t#

Swirl

center

I

I

I

,f

I I I

i __j co

i

-225 -150 -75 0 75 -375 -300 -225 -150 -75

x, mm x, mm

Swirl

center

I

i

I

I

I

I

I

I

I

75

Figure 31: Velocity and vorticity components at ¢ = 300 for the basic bla_te case.

4O
Case: Basic _----60 °

rain max

O

_D

E

Eoo

o

u_

-26

min msx

26 m/s

-7 7 m/s

o

E

to

>:

o

to

o

u3

i

-375

-504

O3

0

O0

0

04

0

E 0

>-

0

!

0

04

!

O

i

0

Lo

o') =

E

_o

i

Lo

i

o

i

5046 s -1 o

I

Swirl center _ =,

....... .-:: _-: ....

I l I I

-300 "225 -150 -75 0 75

x, mm

Swirl

.% } center

..'I

V-V c

I

. Swirl

center

I

i

=

-375

Swirl

center

T

I •

I:l

I

I

I

I

t

}

I

f • _ L I I I

-300 -225 -150 -75 O 75

x, mm

Figure 32: Velocity and vorticity components at _b = 60 _ for the basic blade case.

41
Case: Basic _=100 °

min

o -13

IL)

max

msx

24 m/s

13 m/s

4365 s "1

(/)

i

-375 -300 -225

0

03

0

c_4

0

E 0

=;

0

i

0

(N

i

Swirl

center

°°**" V

- - - V-Vj

=,=i=V-Vc

= Swirl

center

o .................. i---L;-_;;-

.......... "_, iv'

_=, ",,, i;v!

'i.]

E

' V

o

i

0

X '

Swirl

, center

•_,i,I _•

.,_

_'.,!

f'l

I I I I O_ I I I If I .....

i

-150 -75 0 75 -375 -300 -225 -150 -75 0

x, mm x, mm

J

75

Figure 33: Velocity and vorticity components at _b = 100 ° for the basic blade case.

42
Case: Basic _= 150 °

mJn

-46:

max

25 m/s

max

12 m/s

4639 s "1

I I I

-150 -75 0

x, mm

0

o4

0

¢0

Eo

0

a

0

i

0

o

E

T

i

c,3

i

0

X '

i

r

Ilolo V

___ v-vi

V-Vc

I El i

75 -375 -150

x, mm

Swirl

center

Swirl

center

•

i

, Swirl

center

r

\

!

t

I I _ t J

-300 -225 -75 0 75

Figure 34: Velocity and vorticity components at ¢ = 1500 for the basic blade case.

43
Case: Basic

0

= -11

c>

tO

E

E_

"375

o

o

o

tO

E

E_

>. :t

rain

-4541

=300

#== 210 °

min

-75

11 m/s

4543 s-1

75

m/s

(3

SWirl

center

tOr _SWirl

;center

El il,

_o 1!;

i

I/) ¢N

?

(3

X '

tO

,= ----___..L____.___ L

-37_

Swirl

.... •_........,.........,_ I c e n te r

:/

/I

"300 -225 -150 __

-75 0

X, mm 75

Figure 35: Velocity and vorticit,y COmponents at ¢ _ 2]0 o for the basic blade ease.

44
o

E

o

o

o4

o

o

o

E

o

o

o

o

o

Lo

E

Eoo

0

o

o

[o

-375

Case: Basic

-21

_= 280 °

rain mex

21 m/s

max

10 m/s

min

-4:

max

0

o3

0

0

Eo

>-

0

i

0

cN

!

0

o3

|

ID

E

_o

4328 s "1 o

I I I I I

-300 -225 -150 -75 0

x, mm

• =e,= V

--_ V-Vi

mmm V_Vc

Swirl

center

I

..i f

Swirl

center

.............. L .............

I, _

\;

Swirl

t

center

/

tj

} _ I I I I I I

75 -375 -300 -225 -150 -75 0 75

x, mm

Figure 36: Velocity and vorticity components at ¢ = 280 ° for the basic blade case.

45
Case: 0 ° Vortex generator

• max values< 0 • max values > 0

_== 2°

• max values< 0 • max values > 0

• max values < 0 • max values > 0

• max values < 0 • max values > 0

• max values < 0

_2

!

|

• max values _ 0

100o

• max values < 0 • max values > 0

• max values < 0 • max values > 0

;' _z ! _,= ?_ !:_',i_;i_!_:;;_ "_= 280 ° i

Figure 37: Locations of wz extrema at _ = 2° --_ 280 ° for the 0° vortex generator case.

46
E

Case: 0 ° Vortex generator

std dev allowed = 1.5

account for wander: focus

max _z threshold= 50 %

_= 2 °

Vorticity center wander from mean

o I_" " ., "V TM , "_ ,_ _" ',V' ,

0 lO

°

E

o

O

O

03

O

O

(/3

Eo

>"

0

i

min

-6188

-7 mm

20 30 40 50

Image Pair

Total image I'=-6.6 m2/s

v e max= 19.2 m/s

Core radius = 16.3 mm

Within Core

• "_. u ave=-2.8 m/s

• "%" v ave=-2.5 m/s

0 20 40 60 80 100

r, mm

O

O

O

¢N

O

to

E

E_

>_

O

O -8

mm

o

to i

|

-320 -240 -160 -80 0 80

x, mm

O

¢N

!

Swirl center

v=J0.3 __ m/s

................... m;d-"

Peak

core

radius

15.6 mm

0

I

-350 -275 -200 -125

X, mm

O

03

O

O

03

,,. swirl _-

....... E O

3

O

t

O

(N

i

O

l ±___J ¢o

i

-50 25 100 -

Swirl center

u=-O.7 m/s

mid _

I

50 -75

swirl

Peak

core

radius

14.3 mm

______ ..... _=_ .... • ...... J

0 75 160 225 300

¥,mm

Figure 38: Vortex statistics at _b = 2 o for the 0 ° vortex generator case.

47
E

E=

,5

0

o

0

o_

0

E

>

0

Case: 0 ° Vortex generator

std dev allowed= 1.5

account for wander: focus

max _az threshold = 50 %

_= 10 °

Vorticity center wander from mean

_,.,A- _ _'- /%,_ -- ave

10 20 30 40 50

Image Pair

v e max= 19.7 m/s

Core radius= 16.3 mm

Within Core

u ave=-O.2 m/s

v ave-----l.6 m/s

0 -- I _ I I t

0 20 40 60 80 100

r, mm

o Swirl center

03

v = 0.0 m/s

0

0

o)

Eo

>"

0

| Peak

core

0

radius

' 17.6 mm

0

03 _ . _

i

-350 -275

i L l 1

-200 -125 -50

X, mm

J

25 100

0

0

0

E)

E

eoo

0

rain

-5447

max

m 5447 s "1

-14 mm

Total image F=-5.7 m2/s

-16

mm

[ l

-240 -160 -80 0

x, mm

-12

mm

8O

0

03

o

o

0

0

|

o

!

o

i

-150

Swirl center

u=-O.7 m/s

- - -m-hi -. ..............

Peak

core

_ radius

_I_ 14.5 mm

___ T____u_ __u .... __ _-J

-75 0 75 150 225 300

y, mm

Figure 39: Vortex statistics at %b= 10 ° for the 0° vortex generator case.

48
Case: 0 ° Vortex generator

std dev allowed = 1.5

account for wander: focus

max _z threshold= 50 %

lb= 30 °

0

E

E=

0

¢/J

E

>

0

V0rticity center wander from mean

10 20 30 40 50

Image Pair

vg max= 20.8 m/s

Core radius= 12.9 mm

"'_. Within Core

_. u ave = 3.1 m/s

/ ._ " vave= 1.5 m/s

r" "-%

* *1_i_'=%'** * tl

Q I _ I I I

0 20 40 60 80 100

r, mm

o Swirl center i

v=-5.8 m/s . J

Q

¢N

0

E o ............... hn-id ........

0

, P°ak I /

core l_Z

o radius

' 9.9 mm _'

0

L J 1 L _ __ ___j

i

-350 -275 -200 -125 -50 25 100

x, mm

0

tO

¢N

0

0

0

uO

E

E_

>_

0

uo

tO

rain max

-7338 i 7338 s "1

-38 mm

-6

Total image ['=-5.2 m2/s

0

0

|

-320

E 0

0

i

0

!

0

0 _ _ 30 m/s

-38 mm

-240 -160 -80 0

X, mm

Swirl center

u= 5.2 m/s

I

80

mid

Peak

core

radius

13.1 mm

L I I L J J

-6

mm

!

-150 -75 0 75 150

y, mrr,

225 3OO

Figure 40: Vortex statistics at ¢ = 300 for the 0° vortex generator case.

49
Case: 0 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

,_= 60 °

E

E=

0

0

Vorticity center wander from mean

0 10 20 30 40

Image Pair

50

ave

F

/ vo max = 20.6 m/s oLO

Core radius = 12.7 mm 0

| ,_ Within Core o

L _ u ave = 2.2 m/s

0 It "" E°°0

0 I I I L I J

0 20 40 60 80 100

r, mm

O

Eo

=;

0

|

0

|

Swirl center

mid _

Peak

core

radius

11.6 mm

O

|

-350 -275 -200 -125

swirl

FA____

-50 25

X, mm

O

o4

O

E o

o

|

o

¢N

!

min

-5885

max

_5885 s .1

-50 mm

Total image F=-2.9 m2/s

5

mm

0 _ ......._ 26 m/s

-50 mm

-240 -160 -80 0 80

X, mm

8

mm

Swirl center

u = 4.0 m/s

mid- _,

O

i

100 -150 -75

Peak

_, core

radius

14.3 mm

I I I L -- .--J

0 75 150 225 300

y, mm

Figure 41: Vortex statistics at _ = 600 for the 0 ° vortex generator case.

5O
Case: 0 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 100 °

0

E

E_

0

0

Vorticity center wander from mean

0 10 20 30 40

Image Pair

I va max = 21.7 m/s

Core radius= 11.9 mm

/ .._ Within Core

[ ._r_ u ave = 1.1 m/s

"_° _ ".t_. f '_'. v ave---- 3.5 m/s

5O

ave

0

LO

C_

0

0

0

LO

E

eg

0

LO

0

0 20 40 60 80 100

r, mm

Swirl center _ o

_ o

Eo F ............. mid_|- - - _._.2- Eo

o, Peak _ f .......... _ _

| core W

}-. radius _" oO4

' I 11.8 mm

|

¢_0 L_._________ I I J

|

-350 -275 -200 -125 -50 25 100

X, mm

min max

-5784 m 5784 s "1

-69 mm

• _ _,._o" i_-:

Total image F=-2.7 m2/s

25

mm

0 __. _ 27 m/s

-70 mm

}! ,?lllllllllIlll1

ill ,,,! iiii, ,?i!i !:!ll;!iitil;l 

I I 1

-240 0

0

0

|

-320 -160 -80 80

x, mm

Swirl center

u= 1.2 m/s

..... mid_

L

Peak

core

radius

11.9 mm

0

¢_3 ..... J J I ...... _ ...... J

=

-150 -75 0 75 150 225 300

y, mm

Figure 42: Vortex statistics at ¢ = 100 ° for the 0 ° vortex generator case.

51
0

¢M

E

ES

0

0

0

E

>

0

0

it)

Eo

0

i

0

0

Case: 0 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 150 °

Vorticity center wander from mean

0

i

0

o3

I I i I

0 10 20 30 40

Image Pair

ve max = 19.1 m/s

Core radius = 13.6 mm

Within Core

.,I, u ave = 0.6 m/s

j= e o = ,

I I t J

20 40 60

r, mm

Swirl center 1

V _- ,

mid"

Peak

core

radius

11.7 mm

L I I

ave

50

0

E

0

0

J

i

80 100 -

0

o3

0

0

_. s_wi.[I ..... E o

f -

-'1

i

0

|

min

-5572

max

II 5572 s "1

-96 mm

(.dz

Total image ['=-3.1 m2/s

58

mm

0 I 27 m/s

-96 mm

,

 iiii!iii 00mm

I I I I

20 -240 -160 -80 0 80

X, mm

Swirl center

u = 0.2 m/s

mid-.

swim

Peak

core

radius

17.0 mm

0

L I I 03 ..... _ i I I Ji i

-350 -275 -200 -125 -50 26 100 -150 . -75 0 75 160 226

x, mm y, mm

300

Figure 43: Vortex statistics at ¢ = 150 ° for the 0° vortex generator case.

52
Case: 0 ° Vortex generator

std dev allowed= 1.5

account for wander: yes

max _)z threshold= 50 %

_= 210 °

0

o_

E

Eo

0

0

0

0

o4

(0

%%

E

:>

0

Vorticity center wander from mean

I I I I I

10 20 30 40 50

Image Pair

v e max= 19.6 m/s

Core radius= 15.4 mm

Within Core

i. u ave= 0.6 m/s

..f_, v ave= 2.7 m/s

!"

0 I I I I I

0 20 40 60 80 100

r, m m

(/)

Eo

>"

0

i

0

0

0

Peak

core

o

radius

' 13.6 mm

0

03 ____± .....

I

-350 -275

Swirl center

z , ,

mid'

0

0

_o

0

0

|

-320

min max

Total image F=-3.3 m2/s

54

mm

o

¢0

0 _ i_.i 27 m/s

-128 mm

IL

;iii;_iirii !iii iiiii

I i I I t

-240 -160 -80 0 80

x, mm

0

swirl

........... E o

0

i

0

i

Swirl center

u= 0.2 m/s

...... mid _i "" swirl "_....

Peak

core

radius

15.7 mm

0

I I J I ¢0 __ I J l ± ..... J_ ..... !

i

-200 -125 -50 25 100 -150 -75 0 75 150 225 300

X, mm y, mm

Figure 44: Vortex statistics at ¢ = 2100 for the 0 ° vortex generator case.

53
Case: 0 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

@= 280 °

0

ix)

E

E_

o

o

o

CN

E

&

>

o

o

Vorticity center wander from mean

,

I I I I I

10 20 30' 40 50

Image Pair

v e max = 21.0 m/s

Core radius = 13.2 mm

.___ Within Core oo

_1_ • u ave=-0.3 m/s

• I I I I J

0 20 40 60 80 100

r, m m

o _ Swirl center ± o

£ £

_Eo I "_.......... I,_- swirl Eo

o £

| / Peak I! '

/ core I1_

o F radius _ _o

' | 13.6 mm

|

0_ [_.._ ______ I JL_ .... J 1 I

|

-350 -275 -200 -125 -50 25 100

rain max

o

o

UO

!

-320

-5445 mm 5445 s "1

-148 mm

- _. - :: #_ _ ...........

Total image £=-3.0 m2/s

0 IIl_! _ ._ 27 m/s

-147 mm

I i

' _ _ii!iiiiiiii!iiiiiiiil;iiii;

i_i!i!!iiiiii_!iiiiiii iii

1 I I I I

-240 -160 -80 0 80

x, mm

Swirl center

u= 0.4 m/s

mid_ L

Peak c0re

radius

13.2 mm

0

C") ..... I I _ I L J

I

-150 -75 0 75 150 225 300

x, mm y, mm

99

mm

Figure 45: Vortex statistics at _b= 2800 for the 0 ° vortex generator case.

54
e-_.--_, • Basic

0 ° Vortex generator

o Max (-) V0rticity

0_

X

0

20 %

0

O_

Eo

×o

0

0

Max Swirl Velocity

_|olloiBa_nmme_o__ 10 %

0

_D

0

q

E

Vortex Wander

.,

0

0

,¢

E_

E

,_.o

0

0

Vortex Core Radius

_.e_°_:-19 %

o Swirl Center Location Swirl Convection

o• -- • y °t,e

j•_O

_iii"-16 % . _.;;_,;_;_-r__ ,,,_. v

o_? "_ .................... :; o ............................

:_° _-o]I.:

x o _ = ' _.dogW"-

o x1% _' "•--

O

t'_ _ I I I I L J _ I J ; I ____L___----

i i

0 60 120 180 240 300 360 0 60 120 180 240 300

Wake Age, deg Wake Age, deg

J

360

Figure 46: Summary of vortex development from ¢ = 20 -+ 2800 for the 0° vortex generator case.

55
o

to

o

o

o

to

E

c)

to

o

to

E

o

to

o

to

E

Eoo

o

to

Case: 0 ° Vortex generator

rain

-23

_= 2 °

max

m/s

O

o3

O

{N

min max

-18 18 m/s

Eo

0

|

o

|

0

03

l

min

-6188

max

to

E

i

6188 S"1 o

o

o

to

i

-375

" 3N

I I I ] I I ¢0i

-300 -225 -150 -75 0 75 - 375

x, mm

Swirl

center

• I

A"I

I

• '''" V !_

--- V-Vl

I

i V.Vc I

I

I

I

I

Swirl

center

i

% I

........ -,,,,-*,".....,,:.- - :,,;,],_ ?......,,;,,;

"-,'.,..,.,,..,,"-" -'.% .-_ _ I I

F

Swirl i

i center

,o,_..,,..%.,. %,

_ _'._.____" ....... "%,,._,._,,,.,,-*,",,_% - i-_-_,.•,

i"

iI

V

___ 1 I I

-300 -225 o150 -75 0

x, mm

Figure 47: Velocity and vorticity components at ¢ = 20 for the 0° vortex generator case.

56
Case: 0 ° Vortex generator _--10 °

min max

0

u0

E

Eoo

>.

o

ID

-25

min

25 m/s

max

o

o

10 m/s

o

uo

E

Eoo

o

u3

o

L_

min max

o

E

Eg

o

L_

E

=:

_Z

o

"T

Lt_

Q

Ct}

O

5447 s "1 o

0

. o_

=

" O

• ! : X '

Swirl

center

"°''" V .'_'

__. v-v i

V-Vc

or)

i

= Swirl

center

..................-...........;/_. •/" .......

-,.. t. £,"

V;

o Swir center * ,_

I_O I I I d I I o0

m

-375 -300 -225 -150 -75 0 75 -375 -300 -225 -150

x, mm x, mm

Swirl

center

!

I/

V

I

I

I

I

I

I

I

I II

-75 0 75

Figure 48: Velocity and vorticity components at ¢ = 10 ° for the 0 ° vortex generator case.

57
Case: 0 ° Vortex generator IP---30 °

min max

o

-28 28 m/s

o

o -

o

E

E ° _

o

o -

min msx

o

C'4

0

0

-8 8 m/s

o

u3 -

E

Eoo

>.

o

u_

min max

o

.=

o

o

o

E

Eo

o

u_

o

-73 7338 s "1

0

o

u0

|

-375

0

P4

o

Eo

>-

0

!

0

¢0

t

E

._'o

_,, 0

N

I

t

I l

|i

_i Swirl

center

#

##

,, _-I

.......................... l

--_ V-Vi

V-Vc

t

Swirl

center

I

i

!

Swirl

center

%% I 0_.

°

,!I

I I I I I O0 -- I I I L_ L_J__ __ _1

-300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0 5:'5

x mm x. mm

Figure 49: Velocity and vorticity components at _b = 30 ° for the 0 ° vortex generator case.

58
Case: 0 ° Vortex generator _---60 °

mill max

o

-24 24 m/s

o

o -

0

to -

E

_o_

>.

o

to

o

o

to

min msx

o

o

0

o

ao

E

Eoo

>.

-6 6 m/s

min max

5885 s "1

0

0

¢,l

9

Eo

=:

O

!

i

O

e

E

i

o

to_l

i

o

X '

N

3

old

I I J L J CO .... ±

-225 -150 -75 0 75 - 375 -150

x, mm x, mm

Swirl

• i center

• I

---i::: !(

Swirl

center

...................... _,,._.,,"_.T,..,_,_,

V,_.•

Swirl

, center

I

I •

I

i

I

I

L I I I L J

-300 -225 °75 0 75

Figure 50: Velocity and vorticity components at _ = 600 for the 0 ° vortex generator case.

59
o

Lfl

¢N

O

UO

E

Eoo

o

u3

o

u_

o

o

o

u_

E

E_

>:

o

u_

Case" 0 ° Vortex generator _=100 °

min max

-25 m/s

O

03

rain max

-10 10 m/s

O

¢N

O

Eo

0

i

0

!

0

l

min max

o

ID

¢M

O

o

=o

o

o

o

to

i

-375

-5784 5784 s "1

I I I l I I

-300 -225 -150 -75 0 75

x, mrn

E

_o

|

o

D

o

o

i

o

_r

X i

N

3

i •

____m_mzz_Z_Z_ .....

lee,= V

_._ v-v i

,m= V-Vc

Swirl

center

FI

I

, I

II

, Swirl

, center

'

F

................ _ - -.,_.;,.:,._

i B

ii,

V:

=

Swirl

I

center

",,i'i

i

I ] ] I] i J

375 -300 -225 -150 -75 0 75

x, mm

Figure 51: Velocity and vorticity components at _b = 100 ° for the 0 ° vortex generator case.

6O
Case: 0 ° Vortex generator tb = 150 °

rain max

o

E

E_

>.

o

u3

o

O

u0

-25 25 m/s

min msx

o

ID

g

o

u0

E

Eo

:>.

o

o

up

E

-6 6 m/s

min max

-55721 '_ 5572 s "1

i_ z _.,

E°o

Swirl center :, _"-

o

o

to I I

i

-375 -300 -75 0

O

Eo

=;

0

i

0

c_

0

0

09

u

E

_o

i

i

0

X i

=

Swirl

center

iiiii

V-Vc

............. Y

Swirl

center

I

4

......... ,fi,;,."._.,,i"_,- - ,-_._,_,_-,-'.._,%,.,-,,..,,'--

I. ;,! W

Swirl

center

i"

i

I

i

I

I t I t i I

"225 -150 75 375 -300 -225 -150 -75

X, mm x, mm

75

Figure 52: Velocity and vorticity components at ¢ = 1500 for the 0 ° vortex generator case.

61
Case: 0 ° Vortex generator _=210 °

min max

0

= -24

04

max

m/s

E

E8

o

o

i

-1C

min

10 m/s

max

o

=3

t_

o

o

o

I=

o

o

u_

- 375

-4784

0

0

o

Eo

0

i

,i

0

i

E

4784 s "1 o

,._ _'_;_ -__:_:_, _ _.'_--_ '0 ..,_

Swirl c

I I I I I I

-300 -225 °150 -75 0 75

x. mm

]

=D000 Y

--- V-Vi

V-V C

Swirl

center

Swirl

center

....................... _,_ *,,_

.: ]

,i

V

-375

-%

,i

I •

"i

!

I

I

I

I

-300 -225 -150

x, mm

;wirl

center

!

-75 O 75

Figure 53: Velocity and vorticity components at ¢ = 2100 for the 0° vortex generator case.

62
Case: 0 ° Vortex generator _=2800

rain max

o

Lo

E

E_

o

Lo

o

-25

V-V c

25 m/s

min max

o

u0

E

E_

>.

o

uo

-10

min max

10 m/s

o

ID

¢N

g

O

LD

E

Eoo

o

ut}

o

Lo

- 375

5445 s "1

0

03

0

cM

0

Eo

>-

0

|

0

(N

!

0

D

o

c/) *

E

_o

i

I

0 '

e_ L

D

?"

0

N

3

_D

i

Swirl

center

.4 ,

_,,,e,@'

**''* V , __

--- v-vi

,m_., V.Vc

Swirl

center

•.. /;,:....-"

'.\]*

Swirl

center

.................... _"-_ " _ t ..........................

"'i

t, i

I,

I I I I OO [ I I I I

=

-300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0 75

x, mm x, mm

Figure 54: Velocity and vorticity components at ¢ = 280 ° for the 0 ° vortex generator case.

63
Case: +5 ° Vortex generator

• max values< 0 • max values > 0

• max values< 0 • max values > 0

_= 10 °

• max values < 0 • max values > 0

 =3oo

i m _ Hi "

• max values< 0

• max values < 0 • max values > 0

• max values < 0 • max values :> 0

,_, .. =_...... ,_............. _ 280 °

m

Figure 55: Locations ofw_ extrema at ¢ = 2 0 ---> 280 ° for the +50 vortex generator case.

64
0

E

E_

,o"

0

o3

0

0

o

E

o

Case: +5 ° Vortex generator

std dev allowed = 1.5

account for wander: focus

max caz threshold= 50 %

4= 2 °

Vorticity center wander from mean

I _.= _ _- _,.% .=.A N ave

10 20 30 40 50

Image Pair

v e max = 18.8 m/s

Core radius = 16.5 mm

Within Core

I I I I__J

20 40 60 80 100

r, mm

0

¢o

0

0

(D

Eo

=;

Swirl center

v-- 1.9 m/s

............... mid "_-

0

' Peak

core

o radius

' 15.6 mm

0

eo j

i

-350 -275

0

rain max

Total image F=-6.6 m2/s

0

0

0

E

E_

>_

0

LO

0

0

tO

|

-320 -240 -160 -80 0

X, mm

o Swirl center

u=-1.6 m/s

0

-8

mm

i

80

0

swirl _o

.... E o

f °o|

mid

0

_q

swirl

0

]- ± _ I J O_ _____ ...... I J

i

-200 -125 -50 25 1.00 -150 -75 0 75 150

x0 mm y, mm

Peak

core

radius

14.3 mm

225 300

Figure 56: Vortex statistics at ¢ = 20 for the +5 o vortex generator case.

65
Case: +5 ° Vortex generator

std dev allowed----- 1.5

account for wander: focus

max _z threshold= 50 %

t_ = 10 °

0

E

E_

0

0

0

o3

Vorticity center wander from mean

°" +i + V'_ "- '%.+.]_ +, "J ._

10 20 30 40 60

Image Pair

va max= 17.2 m/s

C6re radius= 17.3 mm

Within Core

" u ave=-O.9 m/s

"" v eve = 1.5 m/s

E

O t" L I h I I

0 20 40 60 80 100

r, mm

o Swirl center

03

v= 3.6 m/s

0

cN

0

o3

Eo

=:

0

|

0

Peak

core

radius

15.5 mm

I I I

i

-360 -275

m

-50 25 lOO

1:3

o

i£J

E

E o°

0

Total image F=-5.8 m2/s

0

0

L_

|

-320

-21

mm

-240 -160 -8o

x, mm

o Swirl center

O3

u=-0.6 m/s

0

0

|

o

i

o

i

-14

mm

i ___J

o 80

m,c_ .

Peak

I cor_

radius

j_ 14.2 mm

-200 -125 50 -75 0 75 150 225 300

X, mm y, mm

Figure 57: Vortex statistics at ¢ = 10° for the +50 vortex generator case,

66
0

E

E_

0

0

0

o

Case: +5 ° Vortex generator

std dev allowed= 1.5

account for wander: focus

max _z threshold= 50 %

Vorticity center wander from mean

E

&

2

0

_= 30 °

10 20 30 40 50

Image Pair

va max = 18.1 m/s

Core radius= 16.8 mm

Within Core

, il u ave=-0.4 m/s

v ave = 1.3 m/s

0

o4

0

0

¢N

0

u0

E

o

>:

0

u0

0

• 0

I I J t I

=

0 20 40 60 80 100 -320

r, m m

o Swirl center

(f)

v=-6.3 m/s

0

cM

Peak

core

o radius ¢N

' 13.5 mm

0

t

-350 -275

0

03

0

Eo

0

i

min max

-5177 m 5177 s "1

-38 mm

Total image F=-4.6 m2/s

0

(/)

Eo

>-

0

i

0

• 1 L__ _ • ..... J ¢'}

=

-200 -125 -50 25 100 -150

X, mm

0 _ i_l 26 m/s

-37 mm

I L I I

-240 -160 -80 0 80

X, mm

Swirl center

u=-0.3 m/s

mid _ swirl

Peak

core

radius

15.7 mm

-75 0 75 150 225 300

y, mm

-7

mm

Figure 58: Vortex statistics at tb : 300 for the +5 ° vortex generator case.

67
0

¢M

E

Eo

,d

0

0

0

(fJ

E

d,

>

0

Case:+6 °vortex generator "_=60 °

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

Vorticity center wander from mean

==l.._ A P_

I I I

10 20 30 40

Image Pair

ve max = 20.1 m/s

Core radius = 12.5 mm

ave

J

5O

0

0

(N

0

0_

Eo

>"

0

P

|

". " .i _._._....

I I i I I

20 40 60 80 100

r, mm

Swirl center

v-- 1.2 m/s

_, swirl

............ m id_ .......f

E

E

E

Peak

core

o radius P,I

' 9.8 mm

0

__£ ...... ___ __

!

-350 -275 -200

min max

-6125

0

mm 6125 S "1

-46 mm

6

...... mm

o

Total image F=-2.9 m2/s

0 _ .... _ 26 m/s

°47 mm

0

I I I i --J

I

-320 -240 -160 -80 0 80

X, mm

mid

o Swirl center

03

u = 2.0 m/s

0

¢N

0

0

0

=

0

i

0

('0 .... _ .... 1

i

-150 -75 0

7

mm

• i L J

-126 -50 25 100 75

x, mm y, mm

Peak

core

radius

14.3 mm

i ..... _ .....

150 225 300

Figure 59: Vortex statistics at ¢ = 60° for the +5 ° vortex generator case.

68
Case: +5 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 100 °

E

Eo

O

O

09

E

>

O

O

Vorticity center wander from mean

10 20 30 4o

Image Pair

I

50

v e max= 21.3 m/s

Core radius= 13.8 mm

• "._I. Within Core

,.,_ u ave = 1.2 m/s

r "'_"_li_.. v ave= 0.2 m/s

•

• ._=...._

ave

O

O

O

O

u;3

E

Eoo

O

O

O

I I I I 1

i

O 20 40 60 80 100 -320

r, mm

o Swirl center

E o ............. -r_ i.d-_,. ...........

0

, Peak I,#'

core Ill

radius

' 9.8 rnm V

0

L _ ..... _ ..... J L

i

-350 -275 -200 -125 -50 25

O

03

rain max

-7109 B 7109 S "1

-77 mm

x, mm

Total image F---2.9 m2/s

O _. _ 27 m/s

-77 mm

-240 -160 -80 0 80

x, mm

O

O

Eo

O

!

O

¢N

i

O

I e9

i

100 -150

Swirl center

u= 4.6 m/s

mid ._,

Peak

core

radius

12.0 mm

...... _ ___ k ..... ____ ....... J___ _

-75 O 75 150 225 300

y, mm

Figure 60: Vortex statistics at ¢ = 100 ° for the +50 vortex generator case.

69
0

E

Eo

0

0

0

0

E

&

0

0

0

0

Eo

0

i

Case: +5 ° Vortex generator

std dev allowed= 1.5

account for wander: yes

max _z threshold= 50 %

_--- 150 o

Vorticity center wander from mean

I ____. t J

10 20 30 40 50

Image Pair

ve max= 19.9 m/s

Core radius= 13.9 mm

± Within Core

0

0

0

0

E

Eg

0

0

0

l I I l I r _

i

0 20 40 60 80 100 -320

r, m m

Swirl center

mid _

Peak

core

o radius

' 13.9 mm

0

..... L......

=

-350 -275

swirt

0

0

min max

=5075 5075 s "1

-85 mm

__ o-_:_, __-_: 53

- __-_ C-_ _ __ .... - ..... m m

Total image ['-----3.1 m2/s

0

Eo

0

0 26 m/s

-85 mm

, ill I!1 i iiiil

_lllll!!ll!;l z!iis, !::?_.

i i i i __J

-240 -160 -80 0 80

x, mm

0

m

Swirl center

u=-O.3 m/s

mid  ̧

-%

0

L ...... t ...... A_ I __J _'}

-200 -125 -50 25 100 • -150

x, mm

swirl

Peak

core

radius

14.5 mm

I L ] L I --_J

-75 0 75 150 225 300

y, mm

54

mm

Figure 61: Vortex statistics at ¢ = 1500 for the +50 vortex generator case.

7O
Case: +5 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

@= 210 °

0

t_

E

E9

,o"

0

O3

0

E

>

0

I

0 10

Vorticity center wander from mean

I I I

20 30 40

Image Pair

ve max= 18.7 m/s

Core radius= 15.6 mm

Within Core

• !, u ave----- 1.9 m/s

v ave = 1.0 m/s

".. ;:.......;..._,-_......._.._._._;.

I

50

ave

0 I I i i I

0 20 40 60 80 100

r, mm

o Swirl center

V

>'Eo II Peak ......... mlor_d - s w-i_-._....,.._....-,..-=..'-""-

!

o l core V _. I- radius T

l_ 9.8 mm

....... J- 1 L I A____

i

-350 -276 -200 -126 -50 26

x, mm

o

>:o

0

min

-5581

0

t_

Eo

-1

0

!

max

mm 5581 s "1

-115 mm

78

mm

Total image F=-3.1 m2/s

0

0 _ _ 25 m/s

o -116 mm

I ....I I I, '1, J I J...... H., _..... .......... .......... :

0

-320 -240 -160 -80 0 80

x, mm

o Swirl center

o3

u----- 3.1 m/s

°

!

0

o3

i

100 -150

....... m i_d__

-75 0 76

y, mm

t

Peak

core

radius

15.8 mm

160 226 300

Figure 62: Vortex statistics at ¢ = 210 ° for the +50 vortex generator case.

71
Case: +5 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max w z threshold= 50 %

"_= 280 °

Vorticity center wander from mean

E o

E

0

0

o3

E

0

I I l I

10 20 30 40

Image Pair

50

ve max = 19.4 m/s

Core radius = 16.3 mm

ave

0

Io

0

Within Core o

.I

•._. u ave=-0.3 m/s o_

v ave = 3.4 m/s o

• _

E

• • '%_.,,_. E g

• =o

. -'" ¢_'r._.__

0

I I I I I LID

i

0 20 40 60 80 100 -

r, mm

o Swirl center o

v= 6.9 m/s _ o_

o _ t swirl £

.............................. _ 0

,=o mi, 

0 0

' Peak V

core "[

o radius - o

' 15.5 mm

........ J._ I L ...... .L I l 0

l i

-350 -275 -200 -125 -50 25 100 -

x, mm

rain max

-4950 _4950 sH

-140 mm

Total image F=-2.9 m2/s

124

mm

0 _ _ 25 m/s

-139 mm ....... i ....

! , 'I _i__ "_ "::_ ;

rl, ' _1 -i_iii[][_}!i}hi::i i: ! ; !i':::[i

'_ _ ' I ' _ i ?]if_'iii=,i;::_ii':':iii!ii!i 126

........... i))

I 1 I I J

20 -240 -160 -80 0 80

X, mm

Swirl center

u= 0.3 m/s

II - swirl

"-"" '_ _ Peak

_.._j core

_ radius

_ 13.0 mm

__ _____ I i I 1 I

50 -75 0 75 150 225 300

y, mm

Figure 63: Vortex statistics at ¢ = 280 o for the +5 o vortex generator case.

72
e_. Basic

•,i,. +5 ° Vortex generator

o Max (-) V0rticity _o

0

m

0 o

Max Swirl Velocity

ele_e_o---.----o,m..._... 4 %

0

0

Vortex Wander

• _ i _• ••

Jl

o

o

E_

E

c_

0

o

Vortex Core Radius

, %

o

0

o

o

E _

E

>:o

XO

0

i

o

Q

i

Swirl Center Location

Y

Swirl Convection

h

360

Figure 64: Summary of vortex development from _, = 20 --4 280 o for the +50 vortex generator case.

73
Case: +5 ° Vortex generator _=2 °

min max

O

L_

O

O

O

E

Eoo

o

u_

o

u3

=

-22 m/s

rain max

o -18

U3

18 m/s

o

o

o

E

E_

>.

o

up

min max

o

u_

E

Eoo

>.

o

u_

o

o

u0

m

-375

-584; 5847 s "1

l I I I I J

-300 -225 -150 -75 0 75

x, mm

O

03

O

(N

O :

Eo

Swirl

center

I

i i ........................ ..... v _V _

--- v-vi

iii V.Vc

i

(i Swirl

= _ i t center

o r-........ ..-,'- - -'-.;..... ,_...., ._,o.......,.

"..e %,

E

_o

i

i

O

X '

N

3

c0

|

-375

, Swirl

f center

_ _ • • -

...-

.i

I

I

I

I

I

i

I i I I I --J

-300 -225 -150 -75 0 75

x, mm

Figure 65: Velocity and vorticity components at ¢ = 20 for the +50 vortex generator case.

74
Case: +5 ° Vortex generator _---10 °

min max

o

-25 25 m/s

o

0

o

E

Eo°_

o

min max

o

Lo -

-9 9 m/s

o

o -

¢N

o

u0 -

E

Eoo

o

=3

min max

o

u0

E

Eoo

o

-4969

E

=:

0

0

oa

i

u_

4'

E

_o

4969 s "I o

i

-375

c0

: " :_:? ":' : X '

_ N

:3

Swirl center

I I I J

Swirl

r center

• I

.-- ,,_-Vi

V-Vc

Swirl

center

Swirl

center

.................................... f ......

V

I I t_l I I I I J

-300 -225 -150 -75 0 75 -375 -300 -225 -150 -75

x, mm x, mm

I

75

Figure 66: Velocity and vorticity components at ¢ = 10 ° for the +5 ° vortex generator case.

75
Case: +5 ° Vortex generator

min

° I - -23 I

o

o -

o

E

Eo°

>.

o

itl

0

min max

o -6

U3

04

o

E

E o _

>

o

uo

o

min max

o -6125

o

E

E ° _

0

___ I 1 I

i

-375 -300 -225 -150

X, mm

_= 60 °

max

3 m/s

6 m/s

0

0

2

Eo

>-

0

!

i

0

i

E

6125 s "1 o

=

-75 O 75 -375

, Swirl

center

..................... / .... ..-_"=_

• _,,._ ._

Swirl

center

I

I

..................... I- - - i_"_,,,T_,_

% I •

\_..V!J

I I I

-300 -225 -150

X, mm

i

I

I

I

-75

Figure 67: Velocity and vorticity colnponents at ¢ = 600 for the +50 vortex generator case.

76
Case: +5 ° Vortex generator _=30 °

min max

o

ID

E

Eoo

>,

o

a0

-24

rain max

m/s

o

E

E_

o

u0

o

o

i

-8 8 m/s

min max

o

u0

¢N

o

o

o

E

Eg

o

u;)

-5177

E

16JZ . ._

_D

4'

E

Swirl center

o :, . Swirl

t,, center

0 S_ d

I I* II

i_|No._,lt,_p_DpB_jbo,_itD_ n I

5.177 s -1 o

• - O

"- N

3

++.e+ Y

.._ v-v i

=_== V-Vc

• +._v= ,f • ++

I • -+'

I e+

Swirl

center

o .........................

+._++p+.,.+w+_=+

IAY

t...+,..+

Swirl

center

I

I!/.

o

i +

-375 -300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0 75

x, mm x, mm

Figure 68: Velocity and vorticity components at ¢ = 300 for the +5 ° vortex generator case.

77
Case: +5 ° Vortex generator 1_=100 °

min max

o

26 m/s

o

o

¢N

o

u0

E

Eo° _

>.

o

u_

o

o

14) _

i

0

o

o -

o

E

Eo° _

>.

o

u_

min

-8

max

8 m/s

E

0

0

0

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0

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m

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, Swirl

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l J I I I J co I i I II I --J

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-300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0 75

x, mm x, mm

Figure 69: Velocity and vorticity components at ¢ = 100 ° for the +5 o vortex generator case.

78
Case: +5 ° Vortex generator _--150 °

min max

rain msx

o -9

¢3 -

0

0

04

E

Soo

0 ....

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o

o

uo

i

min msx

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to

9 m/s

m/s

5075 s "1

o

li3 __ I I I 1 I --

=

-375 -300 -225 -150 -75 0

x, mm

75

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=:

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3

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center

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--- v-v i i i_

==_= V-Vc

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center

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x, m m

Swirl

center

4

'i'i

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I

I

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Figure 70: Velocity and vorticity components at, _ = 150 ° for the +50 vortex generator case.

79
o

Lq

E

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o

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o

up

E

Soo

o

u_

o

uo

E

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o

u_

Case: -t-5 ° Vortex generator

rain

-25

1_= 210 °

max

25 m/s

min

-7

msx

7 m/s

min max

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Eo

>-

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0

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22-72..2 j

..................... _,,___-_---

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center

I

i•!

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x, mm

75

Figure 71: Velocity and vorticity components at ¢ = 210 ° for the +50 vortex generator case.

8O
Case: +5 ° Vortex generator _=280 °

min max

o

E

Eoo

>,

o

u0

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min max

22 m/s

-11 11 m/s

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I

l I J _ * I l I I I

"300 -225 -150 -75 0 75 "375 "300 -225 -150 -75 0 75

x, mm x, mm

Figure 72: Velocity and vorticity components at ¢ = 2800 for the +50 vortex generator case.

81
Case: -I-10 ° Vortex generator

• max values < 0 • max values > 0

• max values < 0

I _z

• max values > 0

_-_ '; ;_ === o

• max values < 0 • max values > 0

• max values < 0 • max values > 0

,," NG?-'""

• max values < 0 • max values > 0

"_._ _ ,_._

• max values < 0 • max values > 0

" (_z _= 150 ° ;.:

Figure 73: Locations of Wz extrema at ¢ = 2° --4 2800 for the +10 ° vortex generator case.

82
Case: +10 ° Vortex generator

std dev allowed= 1.5

account for wander: focus

max _z threshold= 50 %

1_= 2°

Vorticity center wander from mean

E

E_

0 10 20. 30 40

Image Pair

0

ve max = 17.0 m/s

Core radius = 15.4 mm

ave

__)

50

Total image F=-6.1 m2/s

Within Core

o u ave=-1.3 m/s

_ ._"_r" v ave-----2.6 m/s _°

E "" " E

Eg

0 I °''J " "i

0 20 80 100

t_

0

40 60 -320 -240 -160 -80 0

r, mm x, mm

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v= 2.1 m/s

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0

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mm

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i

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_' swirl

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-200 -125 25 100 0 75 150

x, mm y, mm

Peak

core

radius

13.1 mm

l .......

225 300

Figure 74: Vortex statistics at ¢ = 20 for the +10 ° vortex generator case.

83
Case: +10 ° Vortex generator

std dev allowed = 1,5

account for wander: focus

max _z threshold= 50 %

_= 10 °

E

E_

0

0

Vorticity center wander from mean

10 20 30 40 50

Image Pair

ve max = 14.8 m/s

Core radius = 17.1 mm

Within Core

o u ave=-1.8 m/s

v ave=-1.3 m/s

o_

O

0 20 40 60 80 100

r, mm

o

Eo

0

i

0

i

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E°o

>:

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-19

mm

Swirl center o

03

v= 3.0 m/s

swirl

Eo

Peak V '

core l _

radius T _o

i

13.5 mm

0 _ _ 24 m/s

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0

I I I I

i

-320 -240 -160 -80 0

x, mm

0

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mm

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0

03 I I I J I -.J J _- J

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-360 -275 -200 -125 -50 25 100 -150 -75 0 75 150

x, mm y, mm

Peak

core

radius

13,0 mm

L-- J

225 300

Figure 75: Vortex statistics at ¢ = 10° for the +10 ° vortex generator case.

84
Case: +10 ° Vortex generator

std dev allowed= 1.5

account for wander: focus

max _z threshold= 50 %

lb= 30 °

0

E

E=

0

0

0

t_4

o9

E

g

0

0

0

Vorticity center wander from mean

0 10 20 30 40 50

Image Pair

v8 max= 18.6 m/s

Core radius= 16.0 mm

Within Core

::::°:'

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min

-5669

max

Total image r-----5.0 m2/s

0

O

O

I I I I p LO I J

|

20 40 60 80 100 -320 -240 -160 -80

r, mm x, mm

Swirl center

v=-1.3 m/s j

Peak

core

0

¢_ radius

' 21.2 mm

0

03 k

=

-350 -275

m= 5669 s

-39 mm

I

I

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-6

mm

o Swirl center

03

u= 1.3 m/s

0

04

0

mid f

mid .

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|

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-200 -125 -50 25 100 -150 -75 0 75

x, mm y, mm

25 m/s

-6

mm

8O

Peak

core

radius

10.4 mm

L__ ______ J

150 225 300

Figure 76: Vortex statistics at ¢ = 300 for the +10 ° vortex generator case.

85
E

E=

0

E

>

0

Case: +10 ° Vortex generator

std dev allowed = 15

account for wander: yes

max _z threshold= 50 %

0

o_

Eo

0

i

_= 60 °

Vorticity center wander from mean

i I I I

10 20 30 40

Image Pair

5O

ave

v a max = 19.6 m/s

Core radius = 14.2 mm

Within Core

• . . _.,.

0 I I I I t

0 20 40 60 80 100

r, mm

0

i

Swirl center

v = 0.0 m/s

............ mid-: __

Peak

core

radius

13.7 mm

0

zl3

(N

50

I

-275

0

0

04

0

E

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0

tf}

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0

L,3

min

-5754

max

Total image E=-31 m2/s

3

mm

o

swirl

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f.. 3

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i

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I I I I

|

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o Swirl center

03

u = 2.9 m/s

0

04

mid -..

0

04

i

0

_ ..... 3. ....... I

i

-150 -75 0

5

mm

-160 -80 0 80

x, mm

I L ........ _ ..... _ .... J J 1

-200 -125 -50 25 100 75 150

x, mm y, mm

Peak

core

radius

14.6 mm

J_ __ __

225 300

Figure 77: Vortex statistics at ¢ = 600 for the +10 ° vortex generator case.

86
E

E£

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0

0

0

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(/)

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&

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0

0

0

o_

0

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i

Case: +10 ° Vortex generator

std dev allowed= 1.5

account for wander: yes

max _z threshold= 50 %

_= 100 °

Vorticity center wander from mean

10 20 30 40

Image Pair

v a max-- 19.8 m/s

Core radius= 14.5 mm

, u

e** •

I I I I I

ave

I

50

0

E3

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0

0

i

0 20 40 60 80 100 -320

r, m m

swirl center

v=-1.6 m/s

Peak

core

o radius

' 11.7 mm

O

03 _____

|

-350 -276

min max

-6889 _ 5889 s"1

-78 mm

mid _'

14

mm

Total image £-----3.2 m2/s

0 _ m 24 m/s

-78 mm

I I

O

¢N

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|

-240 -160 -80 0 80

x, mm

Swirl center

u= 2.6 m/s

mid

0

J_-- --__L .... J {'0 .... I i I

!

-200 -125 -50 25 100 -150 -75 0 75

x, mm y, mm

Peak

core

radius

14.5 mm

150 225 300

Figure 78: Vortex statistics at _p = 100 ° for the +lO ° vortex generator case.

87
min max

Case: 4-10 ° Vortex generator _--150 °

std dev allowed = 1.5 -6516 m 6516 s "1

account for wander: yes

max _z threshold= 50 % -93 mm

Vorticity center wander from mean ,_ __c,_-_;. , _:_._,_:_,_;;_._:_-.,_:_:_:_:_?_,_:._;;_;_:__.

EEo _ (_ ave _:_ -_' _ -_'_=

0 I I l I _d z .... ?_ _.

0 10 20 30 40 50

Image Pair

o Total image F=-3.1 m2/s

I va max = 20.2 m/s o

| Core radius = 12.3 mm _ _- 0 ,_ 24 m/s

/

/

o / , -93 mm

| [ Within Core o FI I . ;

L ,if=,.. uave=0.0m/s I [ ,, :,_i

o / _F..._I__. v ave = 1.5 m/s o i :

e_, >:_o IIIllIll_iii_i ii_4:_®_ii'!!',i_!iiiii!i ii_! ii

o " 51mm

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0 _ / I I 1 I _____1

0 20 40 60 80 100 -320 -240 -160 -80 0 80

r, mm x, mm

o _ Swirl center o Swirl center

iu.o m s B °

Eo _ ................ _- . swirl ,. "_Eo .... rgid- ....

. ' swr

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| core _" "_ core

o __ radius I o _ radius

' | 11.7 mm ' _ 11.8 mm

o!• , , _ ___ _______• o _ _ ....._ , , ,

i |

-350 -275 -200 -125 -50 26 100 - 60 -76 0 76 150 225 300

X, mm y, mm

Figure 79: Vortex statistics at ¢ = 1500 for the +10 ° vortex generator case.

88
Case: +10 ° Vortex generator

std dev allowed= 1.5

account for wander: yes

max _z threshold= 50 %

1//= 210 °

E.o

E

0

0

Vorticity center wander from mean

U I /vWI I

0 10 20 30

Image Pair

I I

40 50

¢o F

r v a max= 19.1 m/s

Core radius= 14.7 mm

/ Within Core

L .._ uave-----1.5 m/s

o / _ v ave---- 1.1 m/s

0 I J I I I

ave

0 20 40 60 80 100

r, mm

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0

i

0

0_

0

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core

o radius

' 13.5 mm

0

00 ____l

i

-350 -275

Swirl center

v= 2.1 m/s

mid _

0

LO

min max

-5854 _5854 s"1

0

1.13

E

Eg

0

u3

51

mm

o

o

u_

l

-320

0

¢n

£

swirl

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0

i

0

i

0

I L_ _..___ ___L .___ _ I

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-200 -125 -50 25 100 -150 -75

X, mm

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I

-240

Swirl center

u = 2.7 m/s

I I

-160 -80

X, mm

0 80

mid

I I .... J

0 75 150

y, mm

Peak

core

radius

15.7 mm

I I

225 300

Figure 80: Vortex statistics at _p = 2100 for the +10 ° vortex generator case.

89
Case: +10 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max w z threshold = 50 %

#= 280 °

0

E

E_

0

0

03

0

¢,4

(/J

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>

0

0

Vorticity center wander from mean

1 I I I

10 20 30 40

Image Pair

5o

va max = 18.7 m/s

Core radius = 15.1 mm

Within Core

_. u ave= 1.2 m/s

,_,_ v ave = 0.3 m/s

-. .. ._._.._,

ave

I L ] I 1

0 20 40 60 80 100

r, mm

0

t_

0

o

o

>:

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0

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o o

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core

o, 1;dlluSmm _ _,o

!

-350 -275 -200 -125 -50 25 100

X, mm

rain max

-5090 i 5090 s"1

-139 mm

q

--_ -_: _._ _._<,_- -

Total image F=-2.8 m2/s

0

L_

|

-320

0 "___i 24 m/s

-139 mm

I I I i 1

-240 -160 -80 0 80

X, mm

0

i

-150

Swirl center

u= 2.0 m/s

...... mid- =_,

__I ........ i 1

-75 0 75

y, mm

Peak

core

radius

15.7 mm

L ....... _ -- -- -- J

150 225 300

Figure 81: Vortex statistics at ¢ = 2800 for the +10 ° vortex generator case,

9O
eae Basic

..._...i +10 ° Vortex generator

o Max (-) Vorticity

O9

° ='o

I

_nm- __nn_,,,nn 24 %

m"

0

0

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0

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0

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0 0

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o Swirl Center Location

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.

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m

0 60 120 180 240 300

Wake Age, deg

=3

J

o

360

Swirl Convection

__ L _ ] i • ....

0 60 120 180 240 300

Wake Age, deg

J

360

Figure 82: Summary of vortex development from _b= 20 --+ 2800 for the +10 ° vortex generator case.

91
Case: +10 ° Vortex generator

rain

min

-15

o

o

e4

o

E

e_

o

ID

o

o

u3

0

E

Eo

o

_ 2 °

msX

1_23 m/s

max

15 m/s

min max

-5296 5296 s -1 o

X '

N

3 ©

375 -300 -225 -150 -75 0 75

X, mm

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; %,,._ ,....... ,t_,0_tZ - _ i_%,,, .

J

375 -300 -225 -150 -75 0 75

X, rf_m

Figure 83: Velocity and vorticity components at ¢ = 20 for the +100 vortex generator case.

92
o

ID

E

E o

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Case: +10 ° Vortex generator

min

-21 _

rain max

_= 10 °

max

21 m/s

o

o

o

E

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>.

o

to

,

-9 9 m/s

min max

o

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center

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X, rnm

Figure 84: Velocity and vorticity components at ¢ = 10 ° for the +10 ° vortex generator case.

93
o

E

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uP

0

u_

E

E_

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Case: +10 ° Vortex generator

min

-23

min max

-11

_= 30 °

max

23 m/s

i

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5669 s "1

0

0

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x, mm x, mm

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f

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Figure 85: Velocity and vorticity components at ¢ = 300 for the +10 ° vortex generator case.

94
Case: +10 ° Vortex generator _--600

min max

O

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o

E

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uo

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min max

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t'i \/

I I I I I l CO I I I ___J______J

-300 -225 -150 -75 0 75 -375 -300 -225 -150 0 75

x, mm x, mm

i

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Figure 86: Velocity and vorticity components at ¢ = 600 for the +10 ° vortex generator case.

95
Case: +10 ° Vortex generator _=100 °

min max

o

-21 21 m/s

o

o -

(N

O

u_ -

E

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=o_

o -

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to

0

rain max

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center

I

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i

-300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0 "75

x, mm x, mm

Figure 87: Velocity and vorticity components at _ = 100 ° for the +10 ° vortex generator case.

96
o

to

E

Eo

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o

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to

i

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to

E

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to

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,

Case: +10 ° Vortex generator

rain

-21 I I

min max

-12 I

min max

_= 150 °

max

21 m/s

12 m/s

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x, mm x, mm

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I

I

.,.o,

I

t i

:.,f

I

I

I

I

I

I

I

I

Swirl

' center

I

i'l

I

J I I } ___

-300 -75 0 75

Figure 88: Velocity and vorticity components at _, = 1500 for the +10 ° vortex generator case.

97
Case: +10 ° Vortex generator

min

0

- -20

o

o -

o

to -

E

Eo° _

0 -

uO

0

LO

o

u0

o

oo

u0 -

E

Eo° _

iV-V

min max

-13

o ....

u3

o -

min max

o

o

[D -

E

0 -

ID

0 -

0

- 375

,_---- 210 °

max

20 m/s

__ I

-150

x, mm

13 m/s

5854 s "1

I I

-300 -225 -75 0 75

0

o3

0

E

=:

u0

4'

E

_o

to

4

o

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=

o

co o4

o_

|

o

X '

N

3

co

co

i

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g

J

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V-V C

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center

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center

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center

m.% I .-

I,!

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!:l

IJ

V

i

I

I

I

I

-300 -225 -150 -75 0 75

x, mm

Figure 89: Velocity and vorticity components at _; = 2100 for the +100 vortex generator case.

98
Case: +10 ° Vortex generator

min

0

it}

E

Eoo

o

=o

E

E_

>.

o

u3

-23

V-V c

min max

0

zD

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o

o

O4

O

uo

E

E_

o

m

o

o

m

i

-375

-509

_= 280 °

max

23 m/s

O

o3

O

O

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O

|

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!

7 m/s

0

o3

i

I I I I I J

i

-300 -225 -150 -75 0 75 -375

x, m m

#!

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....

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- - _ V-V i

V-V C

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center

..... _.. _.- " " - "

#' .i

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i center

I

I

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, center

I

I

I

I

I

I

I

I I i i I I I

-150 -75 0 75

x, mm

-300 -225

Figure 90: Velocity and vorticity components at ¢ = 2800 for the +10 ° vortex generator case.

99
Case: +15 ° Vortex generator

• max values < 0 • max values > 0

;! _z ": " ..... _'_'" .e=_: _ 2 ° ;

• max values < 0 mm max values > 0

_ ..-_ _= 10° ,

lllll • -m

=;

• max values < 0 • max values > 0

_z i " _k= 60 °

• max values < 0 max values > 0

,= 100°

• max values < 0 • max values > 0

i=

i

• ax values • max values > 0

_z ! _,;., ._ _k= 280 °

Figure 91: Locations ofw_ extrema at ¢ = 20 -4 2800 for the +150 vortex generator case.

100
Case: +15 ° Vortex generator

std dev allowed = 1.5

account for wander: focus

max Uz threshold= 50 %

,l_= 2 °

Vorticity center wander from mean

0

E_

?t I_ _ A ,_,_ ,_ ave

0 I I I

0 10 20 30 40 50

Image Pair

0

eo

0

U)

v a max = 15.8 m/s

Core radius = 16.4 mm

Within Core

u ave=-2.0 m/s

v ave=-O.3 m/s

0

0 J

0 20 40 60 80 100

r, mm

o Swirl center

er)

v---- 8.4 m/s

0

¢,0

Eo

>"

0

i Peak

core

o radius

' 25.3 mm

0

o') [

|

-350 -275

• L J I

swirl

0

0

0

¢N

0

I.o

E

Eg

0

l.o

¢,0

0

0

i

-320

Total image ['------6.4 m2/s

-9

mm

o

03

E o

=-

0

i

0

i

-240 -160 -80 0

X, mm

Swirl center

u=-0.3 m/s

mid-

__J

8O

-8

mm

swirl

0

I 03 ___J .....

-200 -125 -50 25 100 -150 -75 0 75

X, mm y, mm

Peak

core

radius

14.3 mm

__ __L .... J ...... J

150 225 300

Figure 92: Vortex statistics at _/, = 20 for the +15 ° vortex generator case.

101
Case: +15 ° Vortex generator

std dev allowed = 1.5

account for wander: focus

max _z threshold= 50 %

_= 10 °

0

E

E_

O

O

o3

O

¢N

o3

Vorticity center wander from mean

,ve

10 20 30 40 50

Image Pair

v e max= 14.0 m/s

Core radius = 15.8 mm

Within Core

u ave=-2.4 m/s

v ave==-2.1 m/s

0

0 I I J

0 20 40 60 80

r, mm

lOO

o Swirl center

v=-0.6 m/s

0

o3

Eo

0

|

mid _

Peak

core

o radius

' 15.5 mm

0

e

-350 -275

__ s wi r_l

(

o3

0

rain max

1

-3427 _ I 3427 s "t

-10 mm

Total image F=-5.6 m2/s

O

O

¢N

O

E o

o

i

-240 -160 -80 0

x, mm

0

L _L I J _____J {_

-200 -125 -50 25 100 -150

X, mm

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u-----2.4 m/s

mid_

" swirlswirl

Peak

core

radius

19.5 mm

l __ l I __ ___ ..... 1

-75 0 75 150 225 300

y, mm

Figure 93: Vortex statistics at _b = 10 ° for the +150 vortex generator case.

102
O

Case: +15 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_b= 30 °

Vorticity center wander from mean

E

E,o

O I t

0 10 20 30 40

Image Pair

O

ve max = 18.8 m/s

Core radius = 15.4 mm

O

E

O

ave

I

50

Within Core

.._ u ave =

0.7 m]s

• . v ave= 2.1 m/s

P.,,,.

° _

o I I I I I

0 20 40 60 80 100

r, m m

O

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O

t_4

O

e,D

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>-

0

a

Swirl center

v=-1.3 m/s

Peak

core

o radius

' 11.7 mm

O

L

i

• -350 -275

O

E

Eoo

>:

O

tD

_9

_s_wirl E o

f -

0

a

min max

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-35 mm

:': :

Total image ['=-4.5 m2/s

0

0

i

-320

-5

mm

0 _ . _ 23 m/s

-34 mm

-240 -160 -80 0

X, mm

o

-6

mm

i

80

Swirl center

u = 2.2 m/s

O

!

-200 -125 -50 25 100 -150 -75 0 75 150

x, mm y, mm

Peak

core

radius

15.7 mm

..... J

225 300

Figure 94: Vortex statistics at ¢ = 30 ° for the +15 ° vortex generator case.

103
0

E

o

c/)

E

&

>

o

o

o

o

o

¢#)

Eo

o

i

Case: +15 ° Vortex generator

std dev allowed= 1.5

account for wander: yes

max _Jz threshold= 50 %

_= 60 °

Vorticity center wander from mean

0

ave I t I I q

10 20 30 40 50

Image Pair

ve max---- 18.3 m/s

Core radius = 14.3 mm

Within Core

u ave---- 0.5 m/s

. %_ v ave---- 0,4 m/s

•..._.._.._

I I L 1 •

20 40 60 80 100

r, mm

Swirl center

v=-1.5 m/s

mid _

Peak

core

o¢N radius

' 11.6 mm

o

_'J k

|

-350 -275

._S_WLrl....

r

o

0

o

0

E

o

min max

-5812 BIB 5812 S"1

-50 mm

- _

6

Total image F-----3.0 m2/s

o Swirl center

03

u= 2.8 m/s

o

(N

o

Eo

o

|

o

¢,4

|

mid- ._

%

I I I I

-160 -80 0 80

X, mm

o

J [...... J- I J _ __ I ____ ___L___ • ....

!

-200 -125 -50 25 100 -150 -75 0 75 150

x, mm y, mm

Peak

core

radius

14.3 mm

.... J

225 300

Figure 95: Vortex statistics at ¢ = 600 for the +150 vortex generator case.

104
Case: +15 ° Vortex generator

std dev allowed= 1.5

account for wander: yes

max _z threshold= 50 %

#= 100 °

E

E_

,&

0

0

co

o

O3

E

>

£

Vorticity center wander from mean

i r

10 20 30 40 50

Image Pair

v e max= 18.5 m/s

Core radius= 14.7 mm

Within Core

I _. u ave= 0.2 m/s

_. v ave= 0.0 m/s

o_,= • •

• • •o

0 I I I I I

0 20 40 60 80 100

r, mm

0

_3

0

o4

0

oO

Eo

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0

u

Swirl center

v=-1.7 m/s

............... mid._,

Peak

core

o radius

' 13.5 mm

O

03 ..... •

i

-350 -275

0

LD

0

E

Eg

0

0

0

a

-320

rain max

_Z

0

i

Total image F=-2.9 m2/s

0

_)

_. _s.wid .... E o

f -

-I

O

i

0 _ _,.U 22 m/s

-69 mm

lllllll]llliil 'lilllllIII I1!i

 ltlll

L I t i )

-240 -160 -80 0 80

X, mm

0

i

Swirl center

u = 1.6 m/s

0

i

-200 -125 -50 25 100 -150 -75 0

x, am

Peak

core

radius

13.1 mm

I .... _L _ . •

75 150 225 300

y, mm

26

mm

Figure 96: Vortex statistics at ¢ = 100 ° for the +150 vortex generator case.

105
E

Eo

0

0

0

_3

0

¢N

ca)

E

>

0

Case: +15 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

0

_0

Eo

0

i

#= 150 °

Vorticity center wander from mean

10 20 30 40 50

Image Pair

ave

v e max = 17.8 m/s

Core radius = 16.3 mm

Within Core

u ave= 0.4 m/s -

.:..__ v ave =

1.0 m/s

0 I I I I I

0 20 40 BO 80 100

r, mm

Swirl center

v=-3.1 m/s

Peak

core

o radius C,,l

' 11.8 mm

O

03 _____

i

-350 -275

mid"

0

cN

0

0

E

-I

min max

-5553 II 5553 s "1

-101 mm

C_ z

Total image F----3.6 m2/s

0

i

-320

41

mm

0 ..... 21 m/s

-100 mm

' ,_:_i_i?i!ii_iii: : i: i:iiiii:,iiiiiiii

' __1 IiI_=' 'ih':iii_!: i!

' .

I I I I J

-240 -160 -80 0 80

X, mm

0

o

0

0

i

0

i

Swirl center

u = 2.5 m/s

0

l I I I I (_ J- _.

i

-200 -125 -50 25 100 -150 75 160

x, mm y, mm

Peak

core

radius

15.8 mm

L ]

225 300

Figure 97: Vortex statistics at ¢ = 150° for the +15 o vortex generator case.

106
Case: +15 ° Vortex generator

std dev allowed= 1.5

account for wander: yes

max _z threshold= 50 %

_= 210 °

0

E

Eo

,o"

0

0

0

03

Vorticity center wander from mean

I I I I 11

10 20 30 40 50

Image Pair

v e max-- 18.2 m/s o

Core radius= 13.4 mm

0

Within Core

i u ave= 0.5 m/s

E _

"'" "_"_._a_'._._. o

0 I I J I J 0

0 20 40 60 80 100

r, mm

0

Eo

>"

0

i

0

o

CN

Peak

core

0

radius

' 9.9 mm

0

i

-350 -275

Swirl center

v=-2.0 m/s

....... mid_ E

min

-5862

max

m 5862 s "1

-128 mm

_Z

,]-

!

" I

78

mm

Total image F=-3.2 m2/s

0 _ _m 22 m/s

-127 mm

' ,' i Lii!i!i_iiii!7!iii!!!ii!!7!_! i !iiii;!!!i_!i!_

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I I I I I

i

-320

0

o

0

-240 -160 -80 0 80

X, mm

o

I

Swirl center

u= 2.1 m/s

mid

O

i __L .... • ...... j_____j _ .......

-200 -125 -50 25 100 -150 -75

x, mm

L 1

0 75

y, mm

L ....

Peak

core

radius

14.5 mm

.... L ..... J

150 225 300

Figure 98: Vortex statistics at ¢ = 2100 for the +150 vortex generator case.

107
0

,¢

E

Eo

o

0

o

o

c*d

o9

E

&

>

Q

Case: +15 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

o

o9

Eo

o

i

#= 280 °

Vorticity center wander from mean

: /%

10 20 30 40

Image Pair

50

v8 max = 19.3 m/s

Core radius = 14.1 mm

Within Core

.V u ave = 0.5 m/s

•." .. v ave=-0.6 m/s

=_% -_._..

Q I I I I J

0 20 40 60 80 100

r, m m

ave

o

o4

|

o

(9

Swirl center

v=-1.4 m/s .j

mid _

Peek

core

radius

11.7 mm

,,._swirl .........

_ t I k 1 I

i

-350 -275 -200 -125 -50

x, mm

E

E

>:

o9

o

Lo

i

-320

o

o

(N

o

min max

-5598 mm 5598 S "1

-132 mm i

•- i

:: ._ii _,_.,

i

[_z i

i

111

mm

Total image F=-2,9 m2/s

E o

o

|

0 ====ram _m= 22 m/s

-132 mm

f] _ J ,lliiiiii!iiiiii_il;i_il

_f'}'_ii_:'_ _ ) m! ! iiiiiiiiii_iiii)iii::. mm112

lll li ii!iiiii!ii!i:, i

!

I I L ' ] J

-240 -160 -80 0 80

x, mm

o

¢N

i

Swirl center

u= 1.5 m/s

........... m_Ld:_,

o

!

25 100 -150 -75 0

<

Peak

core

radius

14.5 mm

L___ J-...... • -- J

75 150 225 300

y, mm

Figure 99: Vortex statistics at _b = 2800 for the +15 o vortex generator case.

108
o_.-,o Basic

.._.=_i +15 o Vortex generator

o Max (-) Vorticity o

O

|

,o_,__ __.-..----.------ Eo

i___=_= 31%

× _a

_ :_o

0

, 0

Max Swirl Velocity

_"o-=o_o==.__.

id.il,,.u"_n_n _m_O 4 %

E

E

o Vortex Wander

0

0

0

0

E

,_.-o

0

0

Vortex Core Radius

o0 Swirl Center Location Swirl Convection

o Y "_

E£ _" -1%

_ o _b _ ........... _ o ..................... in-u --- l l ..g =_, •

o 10 % _,

_'' ' ' ' _ ' J T L , t J j

0 60 120 180 240 300 380 0 60 120 180 240 300 360

Wake Age, deg Wake Age, deg

Figure 100: Summary of vortex development from ¢ = 2o --+ 280 ° for the +150 vortex generator case.

109
o

LO

E

e_

9

0

=3

Case: +15 ° Vortex generator

rain

-22

_== 2 °

max

22 m/s

0

03

0

o4

E

{

min

-15 15 m/s

min

-400_

I •

max

- 4000 s "1.

e3

Swirl

, center

I

I

I

s

... V-V i

V.Vc I c

Ii

I

75

Figure 101: Velocity and vorticity components at _b = 2_ for the +150 vortex generator case.

II0
Case: +15 ° Vortex generator "_=10 °

min max

o

-18 18 m/s

0

o -

e_

o

up

E

Eo° _

o

to

o -

o

i

min max

o

E

Eoo

o

-8 8 m/s

0

0

o

Eo

0

i

I

0

i

E

i

o o

: i

o - 3427 3427 s -1 0

LO -

min max

("_ Z "- "= - : . - . T

o - Swiilcehter _:_

o

I_ I I I I I I

-375 -300 -225 -150 -75 O 75

x, mm

o

E

E ° -

>:

o

i]3

Swirl

center

°

""_ ..... "% ............ _ I

1

Swirl

center

.......................... _,_,,_

--,-" T..,

-375 . -300 -225 -150

x, m m

, Swirl

center

vI

I

I

t

I

I

I

I

I

I

-75 0 75

Figure 102: Velocity and vorticity components at ¢ = 10 ° for the +150 vortex generator case.

111
Case: +15 ° Vortex generator _--30 °

min max

o

o

o4

-21 21 m/s

o i

F

E

>.

o

uo

o -

rain msx

o

ID

E

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min max

7 m/s

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x, mm

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i V-Vc

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center

Swirl

center

I

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I

i'l1

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1

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-300 -225 -150 -75 0 75

X, mm

Figure 103: Velocity and vorticity components at ¢ = 300 for the +15 ° vortex generator case.

112
o

ttJ

E

E_

>.

o

to

o

u3

i

o

_D

E

E?,

o

up

o

o

UP

Case: +15 ° Vortex generator

min

-2oi I

min max

-9

min max

_= 60 °

max

20 m/s

9 m/s

O

('0

O

cN

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=:

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i

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i

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up

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to

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/# .j

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center

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center

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........... i - - _,"*- ""_.7,,,p

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-300 -225 -150 -75 0 75 -375 -300 -225 -150

x, mm x, mm

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center

#

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t_ I I

-75 0 75

Figure 104: Velocity and vorticity components at _b = 600 for the +150 vortex generator case.

113
Case: +15 ° Vortex generator I#-- 100 °

min max

o

-20 20 m/s

o

o -

0

u_ -

E

Eo° _

o

u_

o

o

u0

min max

o

LO -

-9 9 m/s

¢N

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E

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u3

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min max

o

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o

|

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o

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x, mm

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................... ..*% _

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center

I

•, i ,

'i

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I

I I I _I I I

-300 -225 . -150 -75 0 75

x, mm

Figure 105: Velocity and vorticity components at ¢ = 100 ° for the +15 ° vortex generator case.

114
Case: +15 ° Vortex generator _=150 °

min max

o

tO

E

Eoo

o

io

-2C 20 m/s

min max

o

o

o

o

LcJ

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u_

o

o

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-11

rain max

11 m/s

5553 s "1

0

0

ed

£

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0

|

0

|

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m=,mm, V.Vc

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t_

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-375 -300 -225 -15C) -75 0 75

x, mm

Fig.ure 106: Velocity and vorticity components at _, = 1500 for the +150 vortex generator case.

115
o

u_

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to

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Eg

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uo

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u3

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o

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Io

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#

Case: +15 ° Vortex generator _==210 °

rain max

-2_

min max

-10

min max

-586:

-300

20 m/s

10 m/s

5862 s "7

E

>-

_=,

E

o_

X J

0

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center

I

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s_ J

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X, mm

x, mm

Figure 107: Velocity and vorticity components at ¢ = 2100 for the +150 vortex generator case.

116
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Case: +15 ° Vortex generator

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Figure 108: Velocity and vorticity components at _b = 2800 for the +15 _ vortex generator case.

117
Case:-5 ° Vortex generator

• max values< 0 • max values > 0

• max values< 0 • max values > 0

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Figure 109: Locations ofwz extrema at ¢ = 20 --+ 280 ° for the -5 ° vortex generator case.

118
O

Case:-5 ° Vortex generator

std dev allowed = 1.5

account for wander: focus

max _z threshold= 50 %

_= 2 °

Vorticity center wander from mean

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x, mm y, mm

Figure ll0: Vortex statistics at ¢ = 2 0 for tile -5 ° vortex generator case.

119
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Case:-5 ° Vortex generator

std dev allowed = 1.5

account for wander: focus

max _z threshold= 50 %

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0 10 20 3O 40

Image Pair

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r, mm

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Figure 111: Vortex statistics at _ : lO ° for the -50 vortex generator case.

120
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Case:-5 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

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Vorticity center wander from mean

ve 0 10 20 30 40 50

Image Pair

ve max = 24.1 m/s

,,,_, Core radius = 13.3 mm

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Figure 112: Vortex statistics at ¢ = 300 for the -50 vortex generator case.

121
Case:-5 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

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Figure 113: Vortex statistics at ¢ = 600 for the -50 vortex generator case.

122
Case:-5 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 100 °

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Figure 114: Vortex statistics at _/,= 100 ° for the -50 vortex generator case.

123
Case:-5 ° Vortex generator

std dev allowed= 1.5

account for wander: yes

max _z threshold= 50 %

_= 150 °

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Figure 115: Vortex statistics at ¢ : 150 ° for the -5 ° vortex generator case.

124
Case:-5 ° Vortex generator

std dev allowed = 1,5

account for wander: yes

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Figure 116: Vortex statistics at, ¢ = 210 ° for the -50 vortex generator case.

125
Case:-5° Vortex generator

std dev allowed = 1.5

account for wander: yes

max w z threshold = 50 %

#= 280 °

0

E

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x, mm Y, mm

Figure 117: Vortex statistics at _b = 280 ° for the -5 ° vortex generator case.

126
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Figure 118: Summary of vortex development from _ = 20 --+ 280 ° for the -5 ° vortex generator case.

127
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x, mm

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20 m/s

Figure 119: Velocity and vorticity components at _ = 2 0 for the -5 ° vortex generator case.

128
Case:-5 ° Vortex generator _=10 °

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x, mm x, mm

Figure 120: Velocity and vorticity components at ,¢ = 10 ° for the -50 vortex generator case,

129
Case: -5 ° Vortex generator _=30 °

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130
Case:-5 ° Vortex generator 1#--60°

min max

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x, mm x, mm

Figure 122: Velocity and vorticity components at ¢ = 600 for the -50 vortex generator case.

131
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Figure 123: Velocity and vorticity components at ¢ = 100 ° for the -5 ° vortex generator case.

132
Case:-5 ° Vortex generator _--150 °

rain max

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Figure 124: Velocity and vorticity components at ¢ = 1500 for the -5 ° vortex generator case.

133
Case:-5 ° Vortex generator 1D-- 210 °

min max

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- iv-vc!

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Figure 125: Velocity and vorticity components at _ = 2100 for the -50 vortex generator case.

134
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Case:-5 ° Vortex generator

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min max

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rain max

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x, mm x, mm

Figure 126: Velocity and vorticity components at _b = 2800 for the -50 vortex generator case.

135
Case:-10 ° Vortex generator

• max values < 0 • max values > 0

,_" ;_k=2 o

• max values < 0 • max values > 0

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• max values > 0

• max values > 0

_;_;_ "_= 150 °

• max values < 0

_Z _

max values > 0

!_:-': "_= 210° I

• max values < 0 • max values > 0

_, , _= 2_oo_

B

Figure 127: Locations of_ extrema at _ = 2° -+ 280 ° for the -10 ° vortex generator case.

136
E

E_

Case:-10 ° Vortex generator

std dev allowed= 15

account for wander: focus

max _z threshold= 50 %

_ 2 °

Vorticity center wander from mean

0 10 20 30 40 50

Image Pair

0

c_

E

0

v o max = 19.5 m/s

Core radius = 18.7 mm

." • Within Core

I.

0

0

0

0

E

E o

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0

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r, mm

o Swirl center

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0

0

¢9

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=:

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t Peak

core

o radius

' 15.6 mm

0

i

-350 -275 -200 -125 -50 25 100

'i

x, mm

(/)

min max

Total image F-----64 m2/s

0 _ _ 37 m/s

-4 mm

E o

o

|

o

e_

t

o

i

-150

Swirl center

u= 05 m/s

.... m Ld:.................

Peak

core

radius

157 mm

L ...... £ ...... L _ _ J

-75 0 75 150 225 300

y, mm

Figure 128: Vortex statistics at ¢ = 2° for the -10 ° vortex generator case.

137
0

E

E=

o

0

0

o

E

£

o

0

o

0

o

Eo

0

e

Case:-10 ° Vortex generator

std dev allowed = 1.5

account for Wander: focus

max w z threshold = 50 %

-_= 10 °

Vorticity center wander from mean

, . ...-_. ._ _ . ._L ave

10 20 30 40 50

Image Pair

va max----- 18.4 m/s

Core radius = 20.3 mm

Within Core

.-.--.. u ave = 0.7 m/s

v ave = 0.1 m/s

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20 40 60

r, mm

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Y _ .

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min max

I 5182 S"1

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Total image £=-6.2 m2/s

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mm

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X, mm

o Swirl center

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_,- swirl ,_

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-200 -125 -50 25 100 -150 -75 0 75 150

x, mm y, mm

Peak

core

radius

15.7 mm

• .... J

225 300

Figure 129: Vortex statistics at _ = 10° for the -10 ° vortex generator case.

138
Case:-10 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 30 o

Vorticity center wander from mean

O

0 10 20 30 40

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r, mm

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Total image F=-5.4 m2/s

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mid

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-160 -80 0 80

x, mm

-1

mm

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-150 -75 0

Peak

core

radius

17.1 mm

75 150 225 300

y, mm

Figure 130: Vortex statistics at 9 = 300 for the -10 ° vortex generator case.

139
Case:-10 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _)z threshold= 50 %

_= 60 °

V0rticity center wander from mean

0

_ _V________ ave

0

o

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0

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-150 -75 0 75

y, mm

Peak

core

radius

19.8 mm

L_ __J

225 300

Figure 131: Vortex statistics at ¢ = 600 for the -10 ° vortex generator case.

140
Case:-10 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 100 °

O

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19

mm

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-77 mm

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radius

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=

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x, mm

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core

radius

t5.9 mm

i

=___L __ A ____ ...... _._ _ J_ j

-75 0 75 150 225 300

y, mm

Figure 132: Vortex statistics at _p -- 100 ° for the -10 ° vortex _enerator case.

141
Case:-10 ° Vortex generator

std dev allowed= 1.5

account for wander: yes

max _z threshold= 50 %

-_= 150 °

E£

E

f,,O_

0

0

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03

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Vorticity center wander from mean

__ I J I

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Image Pair

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J

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0

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45

mm

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...... mid. __swir; - -

-75 0 75

y, mm

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core

radius

14.4 mm

150 225 3O0

Figure 133: Vortex statistics at _ = 1500 for the -10 ° vortex generator case.

142
Case:-10 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 210 °

0

LO

E

E_

0

0

0

Vorticity center wander from mean

_,_/_ _ /,% I/_ ave

I _ I _ I r

10 20 30 40 50

Image Pair

ve max= 21.5 m/s

• , Core radius = 14.7 mm

/ ._... Within Core o°

o I- _ u ave= 0.9 m/s

E _

_

0

,° om

0 20 40 60 80 100

r, mm

o Swirl center

v=-1.9 m/s

0

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core

0

radius

' 11.9 mm

0

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mid

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min max

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14.5 mm

L_____ A__._ J

150 225 300

Figure 134: Vortex statistics at ,/_ = 2100 for the -10 ° vortex generator case.

143
Case:-10 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 280 °

O

E

Eo

{3

(t)

E

&

0

Vorticity center wander from mean

U_'_____ i ave

10 20 30 40 50

Image Pair

ve max = 19.7 m/s

Core radius = 15.6 mm

Within Core

/

• / u ave=-0.3 m/s

v ave = 2.5 m/s

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0 20 40 60 80 100

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radius

15.5 mm

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.. swirl

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i

-275 -200 -125 -50 25 100 -150 -75 0 75

x, mm y, mm

15.8 mm

L ........ L ....

150 225 300

Figure 135: Vortex statistics at _, = 2800 for the -10 ° vortex generator case.

144
e_e Basic

i_u -10° Vortex generator

O

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minim

0 60 120 180 240 300 360 0 60 120 180 240 300

Wake Age, deg Wake Age, deg

J

360

Figure 136: Summary of vortex development from 4' = 2° -+ 280° for the -10 ° vortex generator case.

145
o

to

E

E_

0

to

Case:-10° Vortex generator

rain

-31

1/)= 20

msx

31 m/s

0 --

0

to

rain max

19 m/s

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center

t,.= o.

Swirl

center

_____a_________j_____ _ .... J

-375 -300 -225 -150 -75 0 75

X, mm

Figure 137: Velocity rand vorticity components at @ = 20 for the -10 ° vortex generator case.

146
Case:-lO ° Vortex generator _=10 °

min max

o

o

o

E

E8

>.

o

-30 30 m/s

min max

o

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-11

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x, mm x, mm

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Figure 138: Velocity and vorticity components at ¢ = 10 ° for the -10 ° vortex generator case.

147
o

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up

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Case:-lO ° Vortex generator _= 30 °

min max

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min

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mex

7 m/s

min

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x, mm

Figure 139: Velocity and vorticity components at _b= 300 for the -10 ° vortex generator case.

148
Case: -10 ° Vortex generator 1_=60 °

min max

o

up

E

E8

0

u0

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min

30 m/s

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r

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x, mm

Figure 140: Velocity and vorticity components at ¢ = 60 ° for the -10 ° vortex generator case.

149
Case:-10 ° Vortex generator _-- 100 °

min max

o

-27 27 m/s

o

o -

o

=3 -

E

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u_

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' -375 -300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0 75

x, mm x, mm

Figure 141: Velocity and vorticity components at ¢ = 100 ° for the -10 ° vortex generator case.

150
Case: -10 ° Vortex generator _----150 °

min max

-27 m/s

o

to

E

Eoo

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o

Lo

o

L_

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min max

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x, mm x, mm

Figure 142: Velocity and vorticity components at _, = 1500 for the -10 ° vortex generator case.

151
o

tt_

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u_

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u0

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Case:-lO ° Vortex generator _--210 °

min max

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m/s

min

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max

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Figure 143: Velocity and vorticity components at ¢ = 2100 for the -10 ° vortex generator case.

152
o

u0

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u3

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o

to

o

ao

Case:-10 ° Vortex generator

rain

-23 _

V-V c

min max

@= 280 °

mex

23 m/s

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r

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-300 -225 -150 -75 0 75

x, mm

Figure 144: Velocity and vorticity components at _b = 2800 for the -10 ° vortex generator case.

153
Case:-15 ° Vortex generator

• max values< 0 • max values > 0

• max values < 0 • max values > 0

= 10°

• max values < 0 • max values > 0

•7" "

• max values< 0

G] z

• max values < 0 • max values > 0

• max values < 0 • max values > 0

_z I _= 210 °

• max value

_z

<0 • max values > 0

_,---- 280 °

Figure 145: Locations of _)_ extrema at ¢ = 2° _ 2800 for the -15 ° vortex generator case.

154
O

Case:-15 ° Vortex generator

std dev allowed = 1.5

account for wander: focus

max _z threshold= 50 %

,_/--_-'_ 2 °'

Vorticity center wander from mean

E

E_

0

0

0

0

E

>

0

10 20 30 40 50

Image Pair

ve max = 20.0 m/s

Core radius = 19.6 mm

•. Within Core

u eve=-2.1 m/s

'__IL V ave = 2.8 m/s

_.° °

Q I

O 20

o Swirl center

co

v= 3.6 m/s

ave

0

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40 ao 80

r, m m

min

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swirl

L _ __ ._ J.____J..__ J

-2OO -125 -50 25 100

X, mm

max

i 5202 S -1

-8 mm

Total image F=-6.5 m2/s

-14

mm

o

(xl

o

o

o

E

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>_

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0

0

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1OO -320 -240 -160 -80 0 80

x, mm

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U=-0.4 m/s

t._

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9

mid -,_

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|

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o

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Peak

core

radius

15.7 mm

_£ .......... J.............. 1- ..... 1 ......... J

0 75 150 225 300

y, mm

Figure 146: Vortex statistics at ¢ = 20 for the -15 _ vortex generator case.

155
Case:-15 ° Vortex generator

std dev allowed= 1.5

account for wander: focus

max _z threshold= 50 %

_= 10 °

Vorticity center wander from mean

E

E_

oIt' ,

0 10 2O 30 40 50

Image Pair

0

03

o

E

9

0

v e max = 21.8 m/s

Core radius = 18.7 mm

A Within Core

u ave=-1.4 m/s

v ave---- 3.6 m/s

,/'"•

min

-4795

max

m 4795 s "1

-19 mm

-14

mm

Total image F=-5.7 m2/s

0

LID

E

Eo°

>:

0

Lo

0

-6

mm

o

I I I I [ _ 1 I I I __J

|

20 40 60 80 100 -320 -240 -160 -80 0 80

r, mm x, mm

o Swirl center

v-- 7.0 m/s

swirl

o Swirl center

03

u=-O.6 m/s

0

..... mid.

0

|

0

0

Peak

core

o radius

' 19.5 mm

0

i

-350 -275

0

(/)

Eo

>-

0

|

0

Eo

0

i

swirl

i

-200 -125 -50 25 100 -150 -75 0 75 150

x, mm y, mm

Peak

core

radius

14.4 mm

I _ __J

225 300

Figure 147: Vortex statistics at 0 = 10° for the -150 vortex generator case.

156
O

E

E_

O

o_

E

4,

>

O

O

0

O

co

O

¢N

£

Eo

>"

0

|

o

m

o

|

Case:-15 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

tb= 30 °

Vorticity center wander from mean

;v _

0 10 20 30 40

Image Pair

_,_1_ v e max = 27.7 m/s

F_ Core radius = 11.2 mm

I k. " Uv:W_i_i3_i remind:

• v_.__:

ave

I

5O

I i 1 I I

20 40 60 80 100

r, mm

1

Swirl center _,

Peak _ I

core I

- radius l_

9.8 mm U

350 -275 -200 -125 -50y 25 100

=

x, mm

O

cN

O

O

O

E

eoo

>:

O

_3

o9

Total image ['=-4.0 m2/s

3

mm

0

0

0

-320 -240

o Swirl center

co

u= 2.1 m/s

0

o mid

|

0

|

0

__ L____ I

|

-150 -75 0

-160 -80 0 80

X, mm

75

y, mm

2

mm

Peak

core

radius

15.8 mm

150 225 300

Figure 148: Vortex statistics at ¢ = 30° for the -15 ° vortex generator case.

157
Case:-15 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 100 °

E

Eo

O

O

¢o

O

¢N

E

>

O

O

Vorticity center wander from mean

_, -_/_ )"_/_ _-/_ ave

0 10 20 30 40 50

Image Pair

v e max = 19.5 m/s

Core radius = 17.7 mm

O

uo

O

Within Core o

• "_. u ave= 0.5 m/s

ave= 1.2 m/s

E

•

1 L__ I I J

20 40 60 80 100

r, mm

o Swirl center o

a °

oN°,_l

_Eo _ ............ _..__; swirl Eo

°t' Peak V

| core

_- radius | o

' I 15.6 mm

/

0 _ I I J J J- J

0

| I

-350 -275 -200 -125 -50 25 100 -

x, mm

min

-4467

max

HI 4467 S "1

-73 mm

r.'.

Total image F=-2.9 m2/s

21

mm

o

o

up

i

-320 -240 -160 -80

X, mm

l J

0 80

Swirl center

u=-2.4 m/s

mid swirl

Peak

core

radius

18.4 mm

______ ........... _

50 -75 0 75 150 225 300

y, mm

Figure 149: Vortex statistics at ¢ = 100 ° for the -15 ° vortex generator case.

158
Case:-15 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max w z threshold= 50 %

_= 150 °

0

o3

E

0

0

¢,4

(t)

E

&

>

0

Vorticity center wander from mean

I I I t !

10 20 30 40 50

Image Pair

va max= 21.7 m/s

Core radius = 13.9 mm

o.'_ Within Core

/-k

.... ,_.'.. _

.m I I I I I

0 20 40 60 80 100

r, rnm

o Swirl center

O3

v=-1.8 m/s

0

0

0g

Eo

>"

0

i Peak

core

0

radius

' 11.8 mm

0

o3 .... _.

i

-350 -275 -200

.... _L __ _A-__ _J

-125 -50 25 100

x, mm

0

0

0

0

to

E

E_

>_

0

to

0

0

L_

|

-320

min max

-5539 m 5539 s"1

-100 mm

....... 51

.# m m

Total image T'=-3.3 m2/s

0 _- _ 26 m/s

-100 mm

J I I I J

-240 -160 -80 0 80

x, mm

o Swirl center

03 u=-0.1 m/s

0

¢N

0

Eo

...... mid_ swirl

' "_"_,_ Pea k

core

radius

0

i

-150 -75 0 75 150 225 300

y, mm

52

mm

Figure 150: Vortex statistics at ¢ = 1500 for the -15 ° vortex generator case.

' 159
Case:-15 ° Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 210 °

0

E

Eo

0

0

0

0_

E

>

0

Vorticity center wander from mean

10 20 30 40 50

Image Pair

v e max-- 18.6 m/s

Core radius = 17.2 mm

Within Core

•, u,v;=__ o:_2_:

I i I 1 I

0 20 40 60 80 100

r, mm

0

o3

0

0

Eo

=:

0

i

0

!

0

03

i

-350

S_ _ swirl

Peak _I_

core

radius

15.5 mm

______ Z_ ....... t __._L J J

-275 -200 -125 -50 25 100

X, mm

0

E

Eg

>t

0

0

0

up

!

-320

0

o3

rain max

-4417 4417 s-1

-139 mm

:. _,7._ :r_._, i_. 1'13 m

:= -_'_-_-=,'_'_"_:i_'._-_" _!_ -

Total image F=-3.2 m2/s

0

¢N

0 _- _ 28 m/s

-139 mm

Li '!I ''....... ,,, o,

L I l £------J

-240 -160 -80 0 80

x, mm

0

Eo

0

|

0

|

0

o3

e

-150

Swirl center

u-----0.9 m/s

........ mid_ _ _ ____.

swirl

Peak

core

radius

15.7 mm

-75 0 75 150 225 300

y, mm

Figure 151: Vortex statistics at, _p= 2100 for the -15 ° vortex generator case.

160
Case:-15 ° Vortex generator

std dev allowed= 1.5

account for wander: yes

max _z threshold= 50 %

#= 280 °

O

E

Eo

O

0

O

o3

O

¢M

(D

E

>

O

Vorticity center wander from mean

I J I t

10 20 30 40

Image Pair

ve max= 17.2 m/s

Core radius= 16.2 mm

ave

I

50

O

¢M

O Within Core o

".;- u ave= 0.4 m/s o_

v ave = 3.1 m/s o

E

Eo

=l . •

0 I I I t I

0 20 40 60 80 100

r, mm

O

Eo

>"

0

|

swirl £

- Eo

i

Q

i

J L ........ • __ J

-125 -50 25 100

x, mm

O

mid _'

Peak

core

O

radius

' 15.6 mm

O

=

-350 -275 -200

rain max

-4941 I 4941 s "1

-162 mm

-c .

.... _,_,#__ ,._,r::-.___,.. _ ,?".: _.._... _' "_ " 122 l 9 "3_,F ..........

.... " " " "-.t.,::':: 1.:"

w z " - , .-: ._?'R.. "/9

Total image F=-2.8 m2/s

0

0

i

-320

0 _, _ 28 m/s

-162 mm

---- I I I I J

-240 -160 -80 0 80

X, mm

123

mm

O

I

-150

Swirl center

u=-0.6 m/s

..... mid ......

c°9

-75 0 75 150 225 300

y, mm

Figure 152: Vortex statistics at _p = 2800 for the -15 ° vortex generator case.

161
eIe Basic

.._i -15 ° Vortex generator

(I}

X

Max (-) Vorticity

e_ e_ 11%

O

¢_

E•

>

x_

O

Max Swirl Velocity

-7 %

O

E

O

Vortex Wander O

L•

O

E

c_

O

O

Vortex Core Radius

e_ e--

o Swirl Center Location © O

cM

Y ,,

I i3 %

, O_o x _,

o°/ -"-'8% • I I I L I J qD

| i

0 60 120 180 240 300 360

Wake Age, deg

Swirl Convection

v

.......................

, , I I u

i I I I I

60 120 180 240 300

Wake Age, deg

J

360

Figure 153: Summary of vortex development from ¢ = 20 --+ 280 o for the -15 o vortex generator case.

162
o

u_

o

o

o

it)

E

Eoo

>.

o

o

E

E_

o

u0

o

u}

E

E_

>.

=o

0_O f-- -

-375

Case:-15 ° Vortex generator

min

-30

min max

-2C

_= 2 °

max

30 m/s

20 m/s

E

>-

0

03

0

o

min max

5202 s "1 o

- ._. - _ - _ :,.T,_: _,-

I I I I .L_____J CO

-300 -225 -150 -75 O 75 -375

x, mm

.1

.......................

--- v-vi

V-V c

Swirl

center

I- -

Swirl

center

_... t .....

..... =, ........... ___._ _.,: \_/- ".,.._..,_

I I i I __

-300 -225 -150 -75

x, mm

Swirl

center

1

!:

!

Figure 154: Velocity and vorticity components at _, = 20 for the -150 vortex generator case,

163
o

u_

E

E_

>.

o

u0

o

u_

E

Eo_

>.

o

u_

o

o

E

E_

o

Case:-15 ° Vortex generator

min

-26

min

-8

_= 10 °

msx

26 m/s

msx

8 m/s

E

=:

min

-4795

max

4795 s "1

0

o

|

-375

E

_o

03

E)

x _

3

=,

._ I l I I I J ¢0

*

-300 -225 -150 -75 0 75 -375

x, mm

Swirl

center

p*t I !

I

...........................

J

***** V J

--- V-Vi I

V-V c #

Swirl

center

................. ,,'-'_.;_ A _ ,,,,,.__,'_%._

........ \j..

•* Swirl

......... ,!\;in=

iN

II

I I I

-300 -225 -150

x. mm

i i ___J

-75 0 75

Figure 155: Velocity and vorticity components at _b = 10 ° for the -150 vortex generator case.

164
o

up

E

Eo_

>:

o

E

Eoo

o

uo

E

>.

Case: -15 ° Vortex generator _=30 °

min max

-34

_V-V

34 m/s

min

-7

msx

7 m/s

min

-896E

max

8968 s "1

_Z ..

E

=;

O

o)

E

?"

O

N

3

1 I

p_L

J #I,

et_IODDI_DOnD_DtD'*=_O npl

l.tOe V

------ V--Vi

V-V C

Swirl

center

z_

/ ¢._,t*'_

;/

_wirl

Lq I

center

i

o ............... i- -,,"°"-"'_',,

= "%.!

Swirl

center

!'l

Swirl center t

' -375 -300 -225 -150 -75 0 75 -375 -300 -225 -150 -75

x, mm x, mm

I __1

0 75

Figure 156: Velocity and vorticity components at g, = 300 for the -150 vortex generator case.

165
o

E

to

>.

ID

Case:-15 ° Vortex generator !//= 100 °

rnin max

-23 _ 23 m/s

min max

0

to

o

E

to

):

o

o

-6 6 m/s

rain max

-446 4467 S-1

I

O

CI

E

¢v)

n

o

E

o

o

0

X '

Swirl

center

.................... 5 .......

==ell V f

___ v-vi

===== V-Vc

Swirl

I

center

I

J

I

.................. F - - -.*_',_,_-.._. - .;o

',.i,",:

V

Swirl

center

I

0 75 -375 =300 -225 -150 -75 0 75

x, mm

Figure 157: Velocity and vorticity components at ¢ = 100 ° for the -15 0 vortex generator case.

166
Case:-15 ° Vortex generator

min

-251 I

_= 150 °

msx

25 m/s

o

E

Eoo

=:

o

min max

o

u0

E

Eo

>

o

_D

-9 9 m/s

min max

0

Eo

Q

I

i

0

!

E

_-o

=

J

75

_° J

sL

. :ft."

Swirl

center

.................. . ..... _.._--

***=* V

___ v-vi

=_== V-Vc

..._ _.**,_._w *,_'_*'v=

• .v _=

Swirl

center

..................... ,_.._..._.-,_..,_.:..:,,;

%.., _

-. I|!

t.l

v

0

X '

N

3

%

t.

Swirl

center

!

"1!,

i

-375 -300 -225 -150 -75 0

x, mm

I

75

Figure 158: Velocity and vorticity components at ¢ = 1500 for the -15 ° vortex generator case.

167
Case:-15 ° Vortex generator _--210 °

min max

o

u_

E

Eoo

-25

min max

25 m/s

o

u_

=o

E

Eoo

o

u0

,

-11

W

min max

11 m/s

o

L_

0

0

0

E

Eoo

o

o

u0

=

-375

-4417 4417 s "1

Swirl

E

=;

0

0

IN

LO

r

E

i

o

,

o

X '

N

3

i

;wirl

center

,,_*° I

S" _-" .......

___ v-vi _

I I

V-V c

, Swirl

center

L

................ _.......... ,,_,__L'°"E'

°*\i' '

Swirl

center

___ 1 .... I I I I _ CO I I L _ I __ L__ __ _J

-300 -225 -150 -75 0 75 -375 *300 -225 -150 -75 0 75

x, mm x, mm

Figure 159: Velocity and vorticity components ut ¢ = 210 ° for the -150 vortex generator case.

168
o

to

E

E8

o

LID

0

to

E

E8

o

to

o

to

o

_0

e_

o

o

to

E

58

o

Lo

Case: -15 ° Vortex generator _---280 °

min max

-24 m/s

min

-9

max

9 m/s

_f_

min max

4941 s "1

o

o

u0

}_Z

_:LF.t

--_ I 1 l I

E

i

-375

0

c_

0

0

0

!

o

_,

E

i

to

o

Swirl

center

0j ̧ if

.,¢_,.._._,o ,_''_'_ /,#if

..o"

___ v-vi

i_ V.Vc if

Swirl

' center

t

_ _ _ _,,_..,;-,,.,,._,_,,_,-_ _ _ -_........... Iv

('9

O

X '

N

3

, Swirl

center

¥

-300 -225 -150 -75 0 76 -375 -300 -225 -150 -76 0

x, mm x, am

J

75

Figure 160: Velocity and vorticity components at _t, = 2800 for the -15 _ vortex generator case.

169
Case: Free Vortex generator

• max values < 0 • max values > 0

.,: • ?

• max values < 0 • max values > 0

 1i, :,oo

• max values < 0

(

I Wz

• max values > 0

• max values< 0 • max values > 0

_= 60 °

• max values < 0

• _ . ,_

• max values < 0

. ,;<

• max values > 0

_ : "' " _ o

_ _',';_,_ I_= I0 0

• max values > 0

150°:

II •

• max values < 0

o z

• max values > 0

,._-----210 °

• max values < 0 • max values > 0

r_z ' _:: .... ,,:- 10= 280 °

. "+ _,4"_,s_:,:

m . m

Figure 161: Locations ofwz extrema at ¢ -----2 ° --+ 2800 for the free vortex generator case.

170
Case: Free Vortex generator

std dev allowed= 1.5

account for wander: focus

max _z threshold= 50 %

,_= 2 o

E

E=

0

0

Vorticity center wander from mean

.ve

10 20 30 40 50

Image Pair

o_ |r_ ve max-- 16.3 m/s

Core radius= 22.7 mm

Within Core

u ave=-3.5 m/s

o ".'._. v ave = 0.1 m/s

E

O I [ I I

0 20 40 60 80 100

r, mm

0

O9

Eo

>-

0

|

0

to

0

0

0

E

Eoo

>:

0

to

Swirl center o

v= 3.8 m/s

_ swirl

.............. rqid2' ........

Peak f

core

radius o

¢-q

23.4 mm °

0

up

i

-320

min max

-4308'

Total image F=-6.2 m2/s

0

o4

0

o9

Eo

0

°

I l I I J

-240 -160 -80 0 80

X, mm

Swirl center

u = 0.3 m/s

.... rn_i_l:_

-75

0

I ± i I I ...... J (n __ _ .... _ _____

i

50 -275 -200 -125 -50 25 100 -150 0 75 150

x, mm y, mm

Peak

core

radius

19.5 mm

.... J

225 300

-14

" mm

-11

mm

Figure 162: Vortex statistics at ¢ : 2 ° for the free vortex generator case.

171
Case: Free Vortex generator

std dev allowed = 1.5

account for wander: focus

max _z threshold= 50 %

_= 10°

Vorticity center wander from mean

E

E=o

0

0

O3

,v 7, v,1;

0 10 20 30 40

Image Pair

ve max = 16.1 m/s

Core radius = 22.8 mm

ave

I

50

Within Core

o u ave = 0.8 m/s

¢N I v ave = 1.4 m/s

E

O

0 20 40 60 80 100

r, mm

o

o9

Eo

=:

0

i

Swirl center

v = 0.2 m/s

__.__.2

mid"

Peak

core

o radius

' 21.6 mm

O

e0 ......... i

i

-350 -275

0

LO

C_

0

0

(N

0

L_

E

E o

>_

0

uo

0

0

LO

rain max

Total image ['=-5.1 m2/s

0

o3

I I I I

!

-320

-14

mm

-240 -160 -80 0 80

X, mm

o

_.

..... swirl "_ 0

f i

Swirl center

u= 0.5 m/s

mid

0

1 • J I I 03 ____ I I • I

I

-200 -125 -50 25 100 -150 -75 0 75 150

x, mm y, mm

Peak

core

radius

18.3 mm

225 300

Figure 163: Vortex statistics at ¢ = 10 ° for the free vortex generator case.

172
E

Eo

0

0

0

E

0

Case: Free Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

¢= 30 °

Vorticity center wander from mean

_,""i , ? _' '_' ' 'a'_ ave

I J I I J

10 20 30 4o 5o

Imaga Pair

v e max= 19.6 m/s

Core radius = 17.1 mm

j_.= v ave= 0.9 m/s

f '--,.

O I I [ I I

0 20 40 60 80 100

r, m m

0

03

0

0

Eo

0

i

Swirl center

mid-"

Peak

core

0

radius

' 15.6 mm

0

O3 ___ ......

t

-350 -275

0

0

0

0

E

Eg

0

to

0

Eo

0

min max

0

0

ID

|

-320

Total image r=-5.1 m2/s

0 _-, _ 23 m/s

-31 mm

!i_l!,.,,_" .:!!:<:/:!),E [

1 I I I J

-240 -160 -80 0 80

X, mm

o Swirl center

O3

u = 1.1 m/s

0

mid

!

o

o

|

-150 -75 0

L ...... _L I £ I

-200 -125 -50 25 100 75

x, mm y, mm

Peak

core

radius

18.3 mm

J---__L ..... J

150 225 300

-8

mm

-8

mm

Figure 164: Vortex statistics at ¢ = 300 for the free vortex generator case.

173
Case: Free Vortex generator

std dev allowed = 1.5

account for wander: yes

max w z threshold = 50 %

1_= 60 °

E_

E

0

0

E

0

Vorticity center wander from mean

,.

10 20 30 40

Image Pair

I

50

v8 max = 16.9 m/s

Core radius = 19.4 mm

Within Core

u ave= 0.5 m/s

v ave = 0.8 m/s

I t _je •

I I 1 I I

ave

0

o_

0

0 20 40 50 80 100

r, mm

o

Eo

0

i

Swirl center

v=-0.9 m/s

mid- _'

Peak

core

o radius

' 15.6 mm

0

L'_ J

|

-350 -275

0

0

0

o4

0

LO

E

Eg

0

=D

0

0

iz3

min

-3573

.=.

max

0

_,,:_swirl _ E o

f -

O

!

i 3573 s"1

-47 m m

Total image F---3.2 m2/s

0 _ I 21 m/s

-45 mm

I 1 I I

!

-320 -240

o Swirl center

u = 1.4 m/s

0

¢N

.... mid=_

o I

i

0

i

-150 -75 0

7

mm

-160 -80 0 80

X, mm

i J_ .... ____J- ........ J

-200 -125 -50 25 100 75 150

x, mm y, mm

Peak

core

radius

18.3 mm

j [ _ I

225 300

Figure 165: Vortex statistics at. _b = 600 for the free vortex generator case.

174
Case: Free Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_p= 100 °

E

Eo

0

E

£

Vorticity center wander from mean

_/___/_ 1_%__/_ ave

I I I J I

0 10 20 30 40 50

Image Pair

ve max = 16.2 m/s

Core radius = 20.2 mm

Within Core

u ave = 0.3 m/s

._, v ave = 1.4 m/s

I l I I I

0 20 40 60 80 100

r, mm

o Swirl center

v=-O.9 m/s

0

mid t

E o ............

o

' Peak

core

o radius

' 15.6 mm

0

i

-350 -275 -200 -125

X, mm

, swirl .......

qo.ol,0o i

f

0

O

E

Eg

0

0

0

0

Eo

0

i

min max

-3312 3312 s "1

19

...... mm

Total image I'=-3.0 m2/s

0 _ i 19 m/s

-66 mm

i 'i'i1

I ] I I

i

-320

2O

mm

0

!

-240 -160 -80 O 80

X, mm

Swirl center

u = 1.7 m/s

....... mid ._

0

] ...... _ ...... _ _2_ L J- ....... _- ....

|

-50 25 100 -160 -75 0 75

y, mm

Peak

core

radius

22.4 mm

1 ....... 2__ --J

150 225 300

Figure 166: Vortex statistics at _b = 100 ° for the free vortex generator case.

175
Case: Free Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 150 °

E

Es

0

0

E

o

0

Vorticity center wander from mean

10 20 30 40 50

Image Pair

v8 max = 15.6 m/s

Core radius= 20.8 mm

Within Core

u ave= 0.0 m/s

v ave= 0.7 m/s

O

oJ

Eo

>"

0

!

0

0

('4

0

E

E o

>:

0

to

0

0

I I I __ l I

|

20 40 60 80 100 -320

r, m m

O

O

¢N

O

Peak

core

o radius ¢N

' 19.5 mm

O

o3 [

D

-350 -275

O

o3

Swirl center

v=-0.4 m/s

............ _ id

0

0

=. swirl Eo j.. 0

i

0

|

max

m 3568 s "1

-101 mm

Total image F=-3.5 m2/s

35

mm

0 _ ..... _ 19 m/s

-101 mm

I I I I

-240 -160 -80 0

x, mm

Swirl center

u = 0.7 m/s

8o

..... mi.d_ _

0

I ._._____ j j 03 ...... _L I I

=

-200 -125 -50 25 100 -150 -75 0 75

x, mm y, mm

swirl

Peak

core

radius

21.1 mm

J- I J

150 225 300

Figure 167: Vortex statistics at ¢ = 1500 for the free vortex generator case.

176
E o

E

_'o

Case: Free Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

-_= 210 °

Vorticity center wander from mean

I I I I

ave

0

03

0

0

0

_3

E

0

0

03

0

03

Eo

=;

0

i

10 20 30 40 50

Image Pair

ve max = 17.0 m/s

Core radius = 16.2 mm

Within Core

u ave = 0.7 m/s

t v ave= 0.9 m/s

.

........_.._.

I t _ I I

20 40 60 80 100

r, mm

o

¢,q

i

Swirl center

v=-O.4 m/s

...... rSrd _

Peak

core

radius

13.5 mm

0

03

i

-350 -275

0

LO

0

o

o

o

0

0

.. s_w!r_l.... Eo

_0 *,,_ ,itD,o -'l

O

!

min max

-4286

k

i4286 s

-120 mm

I

I

I

-1

: 58

mm

Total image F=-3.3 m2/s

0

!

-320

0 _,- _ 19 m/s

-120 mm

ill ]! lilt

_ I I I I i

-240 -160 -80 0 80

x, mm

o Swirl center

u= 0.9 m/s

0

0

03 .....

i

-150 -75

....... ___ __ ....... l -- ) J k J

-200 ' -125 -50 25 100 0 75 150

x, mm y, mm

Peak

core

radius

18.3 mm

225 300

Figure 168: Vortex statistics at ¢ = 2100 for the free vortex generator case.

177
Case: Free Vortex generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 280 °

0

E

E_

0

Vorticity center wander from mean

0 10 20 30 40 50

Image Pair

ave

m _- ve max = 16.3 m/s o

l

Core radius = 14.3 mm

Within Core o

u ave = 0.7 m/s

_,. v ave = 0.6 m/s =o

E ._'" _

o >_

0

o =o

0 20 40 60 80 100

r, mm

o

o

o

Eo

=:

0

i

0

tN

i

0

03

i

-350

Swirl center

v-----l.0 m/s

.... m _d_-__

Peak

core

radius

13.5 mm

-275 -200 -125

X, mm

o

_: swirl ........... E o

"1

°

i

L L ...... J

-50 25 100

min max

Total image F=-3.1 m2/s

0 _:-:-i 20 m/s

-150 mm

i= '="iiiiiii!iiliii]i!i i .,,,,!I '!iiii!i!ii! if', 

I I i I I

i

-320 -240 -160 -80 0 80

X, mm

o Swirl center

ca}

u= 1.0 m/s

0

0

¢N

I

0

i

-150 -75 0 75 150

--swi rl......

Peak

core

radius

14.2 mm

225 300

y, mm

Figure 169: Vortex statistics at ¢ = 2800 for the flee vortex generator case.

178
=-_._ = Basic

,,._.,, Free Vortex generator

O3

b_ |

1.,-

X

N

3

Max (-) Vorticity o

to

0

,,¢

¢n

_i==.. _,.____ E o

a %

0

0

Max Swirl Velocity

nm_m_== n • nl-14 %

0

E

E

b"

o

0

Vortex Wander 0

0

_P

E o

E

 .Oo

0

Vortex Core Radius

o0 Swirl Center Location

c_

eY '¢

FE- -Z_" "11% 4_

; o _i|oit_l_-: ..................... _ o

o_ I I J J q_

! |

0 60 120 180 240 300 360 0

Wake Age, deg

Swirl Convection

__d,_.p• V

..............................

_._no _ u

llolill;_ IT.

60 120 180 240 300 360

Wake Age. deg

Figure 170: Summary of vortex development from ¢ = 20 -+ 2800 for the free vortex generator case.

179
Case: Free Vortex generator _,=2 °

rain max

o

u0

E

o

ao

-2O 20 m/s

min max

o

04

o

o

¢N

-11 11 m/s

o

uo

E

E_

o

up

rain msx

=o

o4

?,

o

E

E_

o

u0

o

J

-375

-430 4308 s "1

I I I i I

0

0

0

Eo

0

i

0

ol

i

0

03

i

Swirl

center

" ..... i

',

°'''' V i_

_-- v-vi _

i V-Vc

u0

E

i

O

¢/) o4

i

o

Swirl

I

center

I

......... ...'-_._,, ............. 7 - _ _ ,_-

"..iV".. i;

Y

Swirl

center

p._..,.

V#

I CO I I i I I I . ----J

-300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0 75

x, mm x, mm

Figure 171: Velocity and vorticity components at ¢ = 20 for the free vortex generator case.

180
Case: Free Vortex generator "_---10 °

min max

o

o

o

o4

o

u0

E

E8

>.

o

ul

-20 20 m/s

min max

o

o

o

E

Eoo

>.

o

-9

min

9 m/s

max

o

8

o

E

E_

>-

o

E)

o

o

-375

-29T 2977 s "1

E

=:

0

0

o3

i

UD

E

o

J

Swirl

center

I

I

o,_ _

___ v-v i

_, V-V c

Swirl

center

........................ ._,,,,T,.,:,_...,T.

j

_.

[ I I I I _ _J I J I

-300 -225 -150 -75 0 75 -375 -300 -225 -150

x, mm x, mm

Swirl

center

•.... i" .......

i,V

,t

-75 75

Figure 172: Velocity and vorticity components at #, = 10 ° for the free vortex generator case.

181
o

LO

¢N

o

o

_N

o

i.o

E

Eo

>:

o

to

Case: Free Vortex generator

rain

-= I I

o

rain max

o -9

c,,i

_

c,,I

o

to -

E

E o

>.

o

o -

o

t

rain max

_= 30 °

msx

_22. m/s

9 m/s

0

Eo

=:

0

i

0

i

0

o3

I

to

E

_o

o

¢1

o

0

g

E

Eg

>.

g

-38 3818 s "1 o

Swirl

' center

I

_.¢,"_A' "

• ,,

.... .: - -..:.: -- -;-,_'_" I,

:;............... -. ...... _ ])

2 .................

' !:V'c If

Swirl

center

........................ L - ,..._,._.,_._

t ' t

_ ,,,

i,,.t

, Swirl

, center

I

% , ,,-

I

0

ID I I [ I I I _ I _ I I I --

' -375 -300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0

x, mm x, mm

]

75

Figure 173: Velocity and vorticity components at ¢ = 300 for the free vortex generator case.

182
o

up

• o

o

¢N

O

u0

E

Eoo

o

o

o

u0

E

Eoo

o

uo

o

u0

E

zo°

Case: Free Vortex generator

min

-19

min max

-11

min

-3

max

_Z

Swirl center

tD= 60 °

max

19 m/s

11 m/s

3573 s "1

., , "]

I k I I I J

=

-375

0

03

0

¢N

0

Eo

>"

0

i

0

B

E

=

i

f

Swirl

center

olloo Y

i d'

,,,==== V-V C

Swirl

center

o ...........................

o

¢N

=

o

t m

! i

a

o

X '

I

s

J

°l

-375

Swirl

center

I

_, i

!/

I I I I I

-300 -225 -150 -75 0 7.5 -300 -225 -150 -75 0 75

X, mm X, mm

Figure 174: Velocity and vorticity components at _b = 600 for the free vortex generator case.

183
o

uo

('4

o

u:

E

eo

>:

0

to

Case: Free Vortex generator _=100°

min max

?,

t_4

0

u:

E

eo

>-

o

up

o

to

o

o

to

E

E_

>:

0

u_

-18

18 m/s

rain max

12 m/s

-12

rain max

-3312 i,n •

• 3312 s "1

• Swirl

O

_ center

t

t

t

0 4 •,I,, ¢

..... v IV

_-- V-V i

V-V c

o_

I

Swirl

u_ center

i

o ............ i

%. !

i !

ix/

I

I

I

I

I

I

J

75

Figure 175: Velocity and vorticity components at ¢ = i00 ° for the free vortex gener_.tor case.

184 .
Case: Free Vortex generator lk----150 °

min max

u0

E

Eoo

>.

o

o

== -17 I

o

o

=

17 m/s

min max

ew

E

Eoo

o

o -15

o

o

_w

o

o

=

15 m/s

0

0

o4

0

min max

o

E

Eoo

o

u0

o

o

I

-375

3568 s "1 o

Swirl

center

..."_

E 0 ............................

i

°°''° V °-°

--- V'Vi O

eq _ V-V c

i I

I

0

03 I

|

= ,Swirl

,center

I

I

l I I I I I

i

o

X '

N

3

_0

k

t

t

t

t

t

!

!

!

; /

I

t!

Swirl

- center

_.,!V

_ I I I I I I

-300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0 75

x, mm x0 mm

Figure 176: Velocity and vorticity components at ¢ = 1500 for the free vortex generator case.

185
Case: Free Vortex generator _=210 °

min max

o

- -19

04

19 m/s

min max

o

LO -

-13 13 m/s

o4

0

L¢)

E

E o _

o

o -

i

min max

o

c_

o

o

o

t_

E

Eo

>_

o

Lo

o

ID

i

-375

4286 s "I

0

¢q

0

o4

Swirl

center

E 0 ..........................

o o,"

i

ellel V

--- v-vi

_ V-V c

i

0

03

!

© Swirl

center

o ............... _ .... .,_._..;.:.,.:..,,;.,.T_

e_'_ _'l_'_ 0._,_n_ i_0, ' m.jj!

V,..'

o

o4

i

o

i

o

X '

Swirl

center

t L I I' I l _ I I I I I I J

-300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 0 75

x, mm x, mm

Figure 177: Velocity and vorticity components at ¢ = 2100 for the free vortex generator case.

186
0 76

Figure 178: Velocity and vorticitY components at _ = 280° for the free vortex generator case,

187
Case: Turbulence generator

• max values < 0

_z

• max values < 0 • max values > 0

•_ .'_,J,_._,._,_._ .... _.+

• max values < 0 max values > 0

• max values < 0

• ";+_+(_ _,_ ._._;

)._._ . "11"ii 3'..

m

• max values > 0

_ _= 6o°

• max values < 0 • max values > 0

!_= 100 ° •

.77<_', '11,

• max values< 0 • max values > 0

::_;., _= 280 °

Figure 179: Locations of _ extrema at _b = 20 --4 2800 for the turbulence generator case.

188
Case: Turbulence generator

std dev allowed= 1.5

account for wander: focus

max _z threshold= 50 %

_ 2 °

0

E

E_

0

or)

V0rticity center wander from mean

ve

10 20 30 40 50

Image Pair

ve max-- 14.0 m/s

Core radius = 24.3 mm

Within Core

o u ave=-1.6 m/s

v ave= 5.2 m/s

_= "" " I..

£

...... D 0

0 I i I I I

0 20 40 60 80 100

r, mm

0

03

0

¢N

0

Eo

>-

0

i

Swirl center

v= 5.4 m/s

Peak

core

0

radius

' 25.3 mm

0

03 I _

e

-350 -275

I I I

swirl

0

min max

-5130 _ m 5130 s "1

-20 mm

i

+!

_Z

Total image F=-5.5 m2/s

-13

mm

o

03

E o

o

i

o

o_

i

0 31 m/s

-15 mm

I I I I q

-240 -160 -80 0 80

X, mm

Swirl center

u=-O.4 m/s

swirl

0

L __j ,_ ____±

|

-200 -125 -50 25 100 -150 -75 0 75

X, mm y, mm

t

Peak

core

radius

20.9 mm

150 225 30o

Figure 180: Vortex statistics at ¢ = 20 for the turbulence generator case.

189
O

¢N

E

Eo

O

0

O

03

O

O

O

0

O

O

O

o_

Eo

0

!

0

|

Case: Turbulence generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 10°

Vorticity center wander from mean

I I _-- I

10 20 30 40 50

Image Pair

ve max = 16.4 m/s

Core radius = 23.6 mm

Within Core

u ave=-1.0 m/s

= v ave---- 1.0 m/s

• .,.t ,, _'_ F

I I I I I

20 40 60 80 100

r, mm

Swirl center

v---- 3.7 m/s

mid -_'

Peak

core

radius

23.4 mm

0

u_

P4

0

0

0

E

E_o

0

Lo

J L

:50 -275 -200

min max

!

-2132 _ mm 2132 s -I

-20 mm

Total image F=-4.1 m2/s

O

•.._== 22 m/s

-18 mm

O

u_ I I I I _____

i

-320 -240 -160 -80 0

x, mm

O

O

o4

O

swirl

...... E o

o

|

o

cN

i

Swirl center

u=-0.8 m/s

_ svwrl Peak core

radius

22.4 m m

± J 1 _ _ J II I J

i

-125 -50 25 100 -150 -75 0 75 150 225 300

x, mm y, mm

-8

mm

-8

mm

J

8O

Figure 181: Vortex statistics at ¢ = 10° for the turbulence generator case.

190
0

o4

E

E£

+o"

0

0

0

E

£

0

0

0

0

0

(/)

Eo

=;

0

i

Case: Turbulence generator

std dev allowed= 1.5

account for wander: yes

max _z threshold= 50 %

_= 30 °

V0rticity center wander from mean

I I I I

10 20 30 40

Image Pair

ve max= 15.9 m/s

Core radius= 21.2 mm

ave

I

50

0

0

Within Core o

u ave--- 0.0 m/s

v ave---- 0.8 m/s o

E

** • O

0

L I I I I

20 40 60 80 100

r, mm

Swirl center

v-----1.2 m/s

............ _n] i.dz __

Peak

core

0

radius

' 19.5 mm

0

e3 I

i

-350 -275

0

to

|

-320

0

0

cq

£

Eo

0

|

0

|

max

I

i 2807 s "1

_z

•"_ _i - _;

Total image F=-4.5 m2/s

0 _ n 20 m/s

-30 mm

I I I I I

-240 ' -160 -80 0 80

X, mm

Swirl center

u = 2.9 m/s

mid

0

I i L l I eO I 2 I

i

-200 -125 -50 25 100 -150 -75 0 75

x, mm y, mm

Peak

core

radius

19.7 mm

k J j

150 225 300

-4

mm

-4

mm

Figure 182: Vortex statistics at ¢ = 30o for the turbulence generator case.

191
E

Eo

0

0

0

03

0

03

E

£

Case: Turbulence generator 1D=60 °

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

Vorticity center wander from mean

____ 1 L I I

10 20 30 40

Image Pair

5O

ve max = 12.8 m/s

Core radius = 25.5 mm

Within Core

u ave=oO.4 m/s

v ave = 0.8 m/s

0 I i i I I

0 20 40 60 50 100

r, m m

o Swirl center

e0 v=-0.6 m/s

0

ol

0

03

Eo

>"

0

I

.......... mid..J

Peak

core

o radius

¢N

' 21.3 mm

0

¢'1 I

i

-350 -275

ave

0

cM

0

0

0

E

E°o

>_

0

E}

0

min

-1858

max

mm 1858 s

-53 mm

-1

0

..... mm

Total image I'=-4.2 m2/s

0 _ _ 16 m/s

-53 mm

0

I_ I I I I

i

-320 -240 -160 -BO 0

x, mm

0

1

mm

8O

0

03

flwi[l_ _ _ E o

0

i

0

!

Swirl center

u = 2.2 m/s

_ mJd - Peakcoreradius

26.2 mm

0

t __, .... _ j j (_ L L I J-- ...... _ .... J

-200 -125 -50 25 100 ' -150 -75 0 75 150 225 300

x, mm y, mm

Figure 183: Vortex statistics at 4' = 60° for the turbulence generator case.

192
Case: Turbulence generator

std dev allowed= 1.5

account for wander: yes

max _z threshold= 50 %

_= 100 °

0

E

0

0

0

o9

E

>

0

0

Vorticity center wander from mean

I I J I

0 10 20 30 40 50

Image Pair

ve max = 10.8 m/s

Core radius= 29.6 mm

Within Core

u ave=°0.6 m/s

v ave= 1.2 m/s

I I I I J

0 20 40 60 80 100

r, mm

0

03

0

o4

0

(/)

Eo

>"

0

!

0

i

0

L

-350 -275

Swirl center

v= 0.3 m/s

swirl

core

radius

27.3 mm

1 I J 1

-200 -125 -50 25

X, mm

ave

0

8

0

LO

E

e_

0

t_

E

=-

(.,d z

Total image r---3.1 m2/s

16

mm

: ii:_iI Sea'rt_,hi

ii' iiii' Lirat

0

-320 -240 -160 -80 0 80

x, mm

14 m/s

-73 mm

0

o3

17

mm

o

o

o

o

i

o

!

o

j 03

i

lOO -150

Swirl center

u= 0.6 m/s

.... ffnid_-

Peak core

radius

31.4 mm

_ ____ _ ....... 1 .... ± ..... 1__ __t

-75 0 75 150 225 300

y, mm

Figure 184: Vortex statistics at ¢ = 100 ° for the turbulence generator case.

193
Case: Turbulence generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 150 °

0

E

Eo

0

0

03

0

¢'4

0_

E

&

0

Vorticity center wander from mean

10 20 30 40 5o

Image Pair

ve max-----9.7 m/s

Core radius = 30.8 mm

Within Core

u ave=-1.5 m/s

v ave----- 0.5 m/s

0

° " I I I I • "*

0 20 40 60 80 _100

r, mm

0

03

0

0

oO

Eo

>-

0

=

E

E

Swirl center o

03

v=-0.7 m/s

min max

Total image F=-3.3 m2/s

0

_ 0

.... swirl ..... _- E o

k _ _o

Pea

core

0

radius

30.9 mm

0

l i • ..... L___ L J

-27.5 -200 -125 -50 25 100 -150

1575 S"1

22

........ mm

X, mm

0

o_

-350

I I I

-160 -80 0

X, mm

J

8O

Swirl center

u= 0.3 m/s

mid

# ......swirl "

t_

radius

26.2 mm

____ I L J I L__

-75 0 75 150 225 300

y0mm

Figure 185: Vortex statistics at ¢ = 1500 for the turbulence generator case.

194
Case: Turbulence generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

_= 210 °

O

[D

E

E_

0

0

0

_9

E

>

V0rticity center wander from mean

10 20 30 40 50

Image Pair

ve max = 8.0 m/s

Core radius = 37,5 mm

Within Core

u ave=-1.1 m/s

v ave = 1.4 rn/s

Q _ 1 I I I

0 20 40 60 80 100

rnin

o Swirlcenter

v= 0.2 m/s

O

¢N

O

Eo

>-

0

i

0

cN

|

-1112

max

1112 s"1

-125 mm

68

rnm

Total image F=-3.1 m2/s

_- 0 _ -_ 12 m/s

/

| , ,!!9 mm

o V :!i!lil!!llt!l!l/lilll L 

....., ,, :,,, o

I Lit_ _ _. _i_;_i? i '11ii i!i

i

-320 -240 -160 -80 0 80

r, mm x, mm

o Swirl center

u= 0.2 m/s

0

0

0

0

i

O

cq

|

0

03 .... _ .....

_. swirl

....... mid:" _- -

Peak

core

radius

40.9 rnrn

O

('3 .... _ i I I [ J

-350 -275 -200 -125 -50 25 100

E

"1

..... -mid- - ".....

Peak

core

radius

31.6 turn

L L

|

-150 -75 0 75

x, mrn y, mm

150 225 300

Figure 186: Vortex statistics at ¢ = 2100 for the turbulence generator case.

195
Case: Turbulence generator

std dev allowed = 1.5

account for wander: yes

max _z threshold= 50 %

#= 280 °

E

E_

0

0'}

0

E

g

>

Vorticity center wander from mean

__)_? (____j ave

10 20 30 40 50

Image Pair

ve max = 8.0 m/s

Core radius= 30.7 mm

Within Core

u ave-----O.9 m/s

v ave= 1.2 m/s

0

f "" _["'_"_-_.I__,._-._..

0;

I J

0 L I__ I i

0 20 40 60 80 100

r, mm

o Swirl center

03 v=-0.4 m/s

0

c_

0

¢/3

Eo

>-

0

i

0

i

0

c_

O

0

c_

O

P

E

E_

0

0

min

-1556

o

Eo

9

Peak

core

radius

29.3 mm

0

L_

i

-320

102

mm

Total image F=-2.9 m2/s

0 _ .... I 11 m/s

-140 mm

S.r0. .... ii

Li m it iiiiiiiiii_iiii!_!!ii!: !ii

'_' 104

...... _-__:" _,_//_;;_'_!_%;%%_]_T m m

-240 -160 -80 0 80

x, mm

o Swirl center

o_

u= 0.1 m/s

0

0

i

0

01 ___

¢

-150 -75

o

(_ L I I L J J

i

-350 -275 -200 -125 -50 25 100 0 75

X, mm y, mm

._" swirl Peak

core

radius

27.6 mm

150 225 300

Figure 187: Vortex statistics at ¢ = 2800 for the turbulence generator case.

196
e----,_- • Basic

---_.-.- Turbulence generator

O

¢/)

i

,¢.-

X

N

3

O

i

Max (-) V0rticity

-65 %

O Max Swirl Velocity

O

.¢

Eo

qb

L,,.

o m_m_mm m -57 %

O

o Vortex Wander o

E_o

110

0

Vortex Core Radius

='Sr_•_J'_• = _ 99 %

oO Swirl Center Location ¢o

y +

o

0

E E

_. o _pu_IP-' ..................... >-o

% =",

× o _ "_w----- x .

e_

[

__I i t

----_e;

I

-5f % J

i !

0 60 120 180 240 300 360

Wake Age, deg

Swirl Convection

:l!l,+p,#o+O,.--,o v

...............................

I _ J I l

0 60 120 180 240 300

Wake Age, deg

J

360

Figure 188: Summary of vortex development from ¢ = 2° -+ 2800 for the turbulence generator case.

197
Case: Turbulence generator _=2 °

rain max

-25 m/s

o

o

c4

o

tD

E

Eoo

>.

o

=3

o

o

i

min max

o

LO

-15 15 mrs

o

o

O

UP

E

Eg

>:

O

Lo

o

O

(N

O

Eo

0

I !

0

cM

i

E

o o

, *

o -5130 5130 s "1 o

Swirl

center

, I, q'

- v y.._#,d !

...... .--._1 q}o

f$. o_.

___ v-v i ,,,,

V-V C

min max

Swirl

center

o ............................

., "-.' x.....\t,, ,/"

_!\ /

,..,'

Swirl

center

', I 1i,, i

_1I I --_ I L I I __--J

-375 -300 -225 -150 -75 0 75

X, m.rn

Figure 189: Velocity and vorticity components at ¢ = 2 0 for the turbulence generator case.

198
Case: Turbulence generator _=10 °

min max

O

-21 21 m/s

o

o

N

o

u3

E

Eo° _

u0

o

o

0

min max

o

_m

E

Eo°

o

u_

-9

rain max

9 m/s

o

u_

o

E

E o

>.

o

o

-21:

E

=:

O

03

|

o

ID

4'

E

_o

o

i

2132 s "1 o

o

-375

Qolot Y

_._ v-vi

V-Vc

Swirl

center

(

I • I

t=/

, Swirl

center

[

d

I

.................................."_ ._ t

•....%,o.: •

0

Swirl

center

i

J

75

Figure 190: Velocity and vorticity components at _ = 10 ° for the turbulence generator case.

199
o

=3

o

ID

E

Eoo

>.

o

o_

o

o

o

io

E

o

ID

o

(N

O

O

O

=3

E

E_o

o

Case: Turbulence generator _=30 °

min max

-18 m/s

min max

-15 15 m/s

o

Eo

0

=

o

=

0

i

min

-28(

max

=3

E

o

J

2807 s "1 o

o

=3

i

-375

Swirl.cen,ter=,- _ _ .

-300 -225 -150 -75 0 76 -375

x, mm

--- v-vi

V-V C

Swirl

center

Swirl

center

..................... - - _.._.._.

!

i

•%..,.-0"%0 I °

\:i

#

'.,..

, Swirl

i center

\:i

L I i I I --

-300 -225 -150 -75 0

x, mm

J

75

Figure 191: Velocity and vorticity components at ¢ = 300 for the turbulence generator case.

200
Case: Turbulence generator _= 60 °

min max

o

o

¢w

o

u0

E I

=o

o F --

o

L

,

-14 14 m/s

E

min max

o

o

L_ -

E

E ° -

o

L_

0 .....

-12

min mBx

12 m/s

0

o3

0

o4

E

_o

0

o

i

1858 S .1 o

Swirl

I

r center

I

I

I

I

..... V

--- v-vl i

i

i V-Vc

I

I

I

I

,Swirl

t center

I

I

.,,"

,

!

,..j

,Swirl

a center

I

%% I

l,!

_...,..-"

, ¢_, I I I i L J

-375 -300 -225 -150 -75 0 75 -375 -300 -225 -150 -75 O 75

x, mm x, mm

Figure 192: Velocity and vorticity components at ¢ = 600 for the turbulence generator case.

201
Case: Turbulence generator _----100 °

min max

o

iz)

o

o

¢N

O

L_

E

Eoo

>.

o

u0

O

o

L0

i

-11 11 m/s

min max

o

u0

¢N

¢N

o

E

E_

-12

2

o

o

i

12 m/s

min max

o

u3

E

E_

>.

o

LiD

O

O

I

-375

E

=;

E

o Swirl

o_ center

O

¢N

03

i

1484 s "1 o

I I

-75 0

I

-150

x, mm

.-. V-V i

_, V-Vc

= Swirl

center

" I

"+.

'.',i +......

,Swirl

center

•. , ...-

%_.."

I I ) O_ L L _ i J

i

-300 -225 75 -375 -300 -225 -150 -75 0 75

x, mm

Figure 193: Velocity and vorticity components at ¢ = 1000 for the turbulence generator case.

202
Case:Turbutence generator "_=150° Swirl

o _center

mln msx _ I i

12 m/s o ,

o -12

u_ t

• Swift

rain max = I Iicenter

12 m/s

-12 o_ ................ _ _ ......_" "

A ",, ',i

_ X 'I

Swarl

rain max _,center

0

0

o

E

E_

0

-375

-1575

1575 s "1 o

4 " -

't_ Z

_ _ _ Swi_ nter .........

-300 -225 -150 -75 0 75

X, mm

o

X '

-375 -300 -225 -150 -75

X, mitt

Figure 194: Velocity and vorticity components at _ = 1500 for the turbulence generator case.

203
Case: Turbulence generator _=210 °

rain max

0

uo

0

o

-9 m/s

0

ID

E

Eoo

>.

O

u_

0

u3

i

rain max

0

ID

E

Eo_

>.

0

up

-10 10 m/s

min max

-1112 1112 s "1

E

0

o_

E

i

?

o

X '

Swirl

center

II_.i V

- - - V'Vj

=,=_= V-V C

Swirl

center

,/

_._,/

Swirl

center

.... _'_"_'_"_"_,_,",_,- - T - _.,_,,=_""_"_"_""_'_"'_

i

-300 -225 -150 -75 O 76 -375 -300 -225 -150 -75 0 75

x, mm x, mm

Figure 195: Velocity and vorticity components at ¢ = 2100 for the turbulence generator case.

204
0

0

o

to

E

E°o

0

to

Case: Turbulence generator

rain

0

O

¢.4

0

E

EO

o

to

-9

rain max

o

0

to

o

o

o

E

0

to

rain

-1556

max

4= 280 °

max

9 m/s

0

o

to -J- --

-375 -300

_L __.1---

-225 -150

x, mm

E

0

O

0

03

!

....,.-..'=%

• .-++ Y

. .- V-V i

,,==_=, V-V C

Swirl

center

.... - _ _ :,,_,.,- ,;,--.

Swirl

center

I

10 m/s

,.... ,/

"-........,._

Swirl

center

I

,,,..;+,-

1556 s "1 o

•:-..

+_

. -, :+. _++-

........ +_+

.],+

o

:3

,,p,

O_ I- LIj--+_J+-j_J-'_+L--_-- --

-75 0 75 375 -300 -225 -150 -75 0

x, mm

75

Figure 196: Velocity and vorticity components at _P = 2800 for the turbulence generator case.

205
0

uD

E

Eo

t

0

|

_> -->

u c-t-v c at %D=280 ° for all cases

Free_._ kTurb 15°

0 o "

4 m/s

0

E

Eo

t

Vortex size & relative location at 39=280 ° for all cases

0 j_ I

'-50 -25 0

25 50

x,mm

-_ Blade

Thickness

Figure 197: Summary of convection velocity, size, and location of vortex when _p = 280 °.

206

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1. AGE_tI_IhJd_WaI_N, LY ,¢. r_=rv_= u_== I_,. ru=rur_= ==r'=euluu_==_a_.,uv=r_=u

February 2001 Technical Memorandum

!4.T_TLEANDSUBTtTLE S. FUNDINGNUMBERS

Devices that Alter the Tip Vortex of a Rotor

6. AUTHOR(S) 712-10-12

K.W. McAlister, C. Tung, J.T. Heineck

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) S. PERFORMING ORGANIZATION

REPORT NUMBER

ArmyNASA Rotorcraft Division, Aeroflightdynamics Directorate

(AMR EC), U.S. Army Aviation and Missile Command, A-00V0036

Ames Research Center, Moffett Field, CA 94035

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORINGIMONITORING

AGENCY REPORT NUMBER

National Aeronautics and Space Administration NASA/TM-2001-209625

Washington, DC 20546-0001 and U.S Army Aviation and Missile

Command, Redstone Arsenal, AL 35898-5000 AFDD/TR-01-A-003

I I

11. SUPPLEMENTARY NOTES

Point of Contact: K.W. McAlister, Ames Research Center, MS 215-1, Moffett Field, CA 94035-1000

i

I za. ul_ I KJ=U i IUN/AVAILAUltd _ r _ IA I '-M"N I t2b. DISTRIBUTION CODE

Unclassified - Unlimited

Subject Category 02

Distribution: Standard

Availability: NASA CASI (301) 621-0390

13. ABSTRACT (Maximum 200 words)

Small devices were attached near the tip of a hovering rotor blade in order to alter the structure and

trajectory of the trailing vortex. Stereo particle image velocimetry (PIV) images were used to quantify the

wake behind the rotor blade during the first revolution. A procedure for analyzing the 3D-velocity field is

presented that includes a method for accounting for vortex wander. The results show that a vortex

generator can alter the trajectory of the trailing vortex and that a major change in the size and intensity of

the trailing vortex can be achieved by introducing a high level of turbulence into the core of the vortex.

14. SUBJECT TERMS

Rotor wake, Trailing vortex, Vortex diffusion, Model rotor

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It_. NUMIdI:I'( Of" I"A_I:,_

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Prescribed by ANSI _td. 239.-18

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