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Optics and Lasers in Engineering 44 (2006) 190207

0143-8166/$ -

doi:10.1016/j

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Schlieren PIV for turbulent flows

Dennis R. Jonassen, Gary S. Settles, Michael D. Tronosky

Gas Dynamics Lab, Mechanical and Nuclear Engineering Department, Penn State University,

University Park, PA 16802, USA

Available online 31 May 2005

Abstract

The possibility of using commercial PIV equipment combined with schlieren optics to

measure the velocity fields of turbulent flows is explored. Given a sufficiently high Reynolds

number and adequate refractive flow differences, turbulent eddies can serve as the PIV

particles in a schlieren image or shadowgram. The PIV software analyzes motion between

consecutive schlieren or shadowgraph frames to obtain velocity fields. Velocimetry examples

of an axisymmetric sonic helium jet in air and a 2D turbulent boundary layer at Mach 3 are

shown. Due to optical path integration, axisymmetric flows require the inverse Abel transform

to extract center-plane velocity data. Conditions for optimum schlieren sensitivity are

examined. In its present embodiment, schlieren PIV is not useful for laminar flows nor for

fully 3D flows. Otherwise it functions much like standard PIV under conditions where

individual particles are not resolved and velocimetry is instead based on correlation of the

motion of turbulent structures. Schlieren PIV shows significant promise for general

refractive turbulent flow velocimetry if its integrative nature can be overcome through sharp-

focusing optics.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Schlieren imaging; PIV; Velocimetry; Turbulent flows; Jets; Boundary layers

1. Introduction and literature review

Particle image velocimetry (PIV) has recently become the most important new toolof experimental fluid dynamics. Two consecutive images of a particle-laden flow are

see front matter r 2005 Elsevier Ltd. All rights reserved.

.optlaseng.2005.04.004

nding author. Tel.: +1814 863 1504; fax: +1 814 865 0118.

dress: [email protected] (G.S. Settles).

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D.R. Jonassen et al. / Optics and Lasers in Engineering 44 (2006) 190207 191

interrogated for small particle displacements, from which a slice through a velocityfield is measured. This depends upon modern digital camera equipment and desktopcomputing capability previously beyond the reach of the individual investigator, butnow commercial PIV systems with convenient user interfaces are available to anyonewho can afford them.

One of the main issues in PIV is seeding the flowfield with particles. These particlesshould match the density of the fluid in order to avoid gravitational forces, and at thesame time must not change the flow dynamics [1]. However, if the flowfield issufficiently turbulent and this turbulence involves refractive-index changes, thenturbulent eddies themselves might act as PIV particles when the flow is viewedusing either schlieren or shadowgraph methods. In such a case the flowfield is self-seeding. An underlying assumption here is that the evolutionary time scale of theeddies is much longer than the time separation of the images in a PIV pair, otherwiseno PIV correlation can occur. Likewise some flow symmetry, e.g. planar oraxisymmetric, is required in order that integrative optical methods may present aninterpretable view of a flow.

The aim of the present approach is to explore such velocimetry, not themeasurement of the refractive-index field per se. The use of the schlieren method andPIV software for the related purpose of refractive-index or temperature measure-ment is described by others, e.g. [2,3].

Schlieren velocimetry was first tried in 1936 by Townend [4], but was not pursued inthat pre-computer era. In 1989, Papamoschou [5] used a pattern-matching algorithmto compute the convective velocity of a supersonic shear layer from two consecutiveschlieren images. Since then, Tokumaru and Dimotakis [6] proposed an ambitiousmethod of image correlation velocimetry for fluid flows, while Fu and Wu appliedimage analysis to extract velocity fields from sequences of schlieren images [79].Kegerise and Settles also performed schlieren velocimetry on a convective plume [10].

All the cited velocimetry examples require specific home-grown algorithms toextract the desired velocity data from schlieren image sequences. In contrast, thepresent goal is to explore the validity of using a commercially available PIV systemand software to measure velocity fields from schlieren images and shadowgrams.

2. Experimental equipment

The PIV system used here is a single-camera system made by IDT Inc. [11]. Itssoftware offers two different algorithms for extracting displacements from an imagepair: standard and adaptive interrogation modes. The former is the cross-correlationapproach most often used in PIV, but is prone to errors such as loss of pairing, imagetruncation, and spatial averaging of velocity gradients. The adaptive interrogationmode [12] is designed to reduce or avoid such errors. Although both algorithmsproduce similar results in the present test cases, only the adaptive interrogationmode has been used in obtaining the results presented here. Insofar as schlierenPIV measurements are concerned, comparable equipment and software by othermanufacturers is expected to function similarly.

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D.R. Jonassen et al. / Optics and Lasers in Engineering 44 (2006) 190207192

Three different schlieren optical instruments were used in this study, one lens-based and two mirror-based systems [13]. The lens-based system had two 152mmdiameter f =5:67 telescope objective lenses as field elements. The mirror-basedsystems had z-type layouts with twin f/8 parabolic mirrors of either 108 or 152mmdiameter as field elements.

Special schlieren light sources are required in order to provide pulsed illuminationfor PIV. For low- to moderate-speed flows, inexpensive microsecond white-lightxenon strobe lamps suffice, e.g. [14]. Two such lamps are mounted perpendicularly toone another as shown in Fig. 1. A 50/50 beamsplitter combines the beams from theselamps and directs them, via a condenser lens and slit, along the optical axis of thepresent 108mm-aperture z-type schlieren system. Neutral density filters are requiredafter each bulb to balance the illumination from the two flashes. One flashbulb istriggered by PIV trigger signal A from the controlling computer and timing box, thesecond by trigger signal B. In our case, since the PIV system is designed for pulsedlasers, proper strobe timing required an external delay circuit between the PIV timingbox and the first strobe lamp [15].

For high-speed flows requiring time separations less than 5 ms between images Aand B of a PIV pair, strobe illumination fails and pulsed laser illumination isrequired. This is provided by a New Wave Gemini 200 dual-head Nd:YAG laser.This powerful laser (200mJ/pulse) needs strong attenuation for use as a schlierenilluminator, here accomplished by two beam reflections from the planar sides offused silica plano-concave lenses. Finally, a beam expander overfills the first mirrorof the 152mm-diameter z-type schlieren system to yield approximately uniform laserillumination.

Dual pulsed-laser illumination has the distinct advantage of a virtually unlimitedrange of pulse-separation timing. However, coherent laser light produces schlierenimages that are inferior to those produced by non-coherent white light for reasonsgiven in [13] and [16]. Briefly, the geometric-optical approach to schlieren systemperformance breaks down and a very small focal spot occurs in the cutoff plane. Thefirst issue produces coherent artifact noise and a reduced signal-to-noise ratiocompared to the usual evenly illuminated white-light schlieren image. The second

Fig. 1. Diagram of the twin strobe arrangement for schlieren PIV.

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issue rules out the traditional knife-edge cutoff for laser illumination, requiringinstead one of several milder cutoff options (graded filter, partially transmittingcutoff, etc.). Here, a simple half-plane sooted microscope slide cutoff [13] is used.The schlieren sensitivity using this cutoff is determined by the optical transmission ofthe sooted section, which is measured by transmission densitometry. Within limits,greater optical transmission of the cutoff yields less sensitivity in a laser-illuminatedschlieren system and vice versa. By comparison, schlieren sensitivity with atraditional extended white-light source and a knife-edge cutoff is determined bythe amount of cutoff and the width of the light source image.

All of the present schlieren instruments are easily converted to focusedshadowgraphy [13] by the removal of the cutoff, image focus adjustment, andreduction of the source slit size to an effective point in the case of white-lightillumination. Of course, these optical methods present somewhat different views of aflowfield, but both reveal refractive turbulence, thus both are included in principleunder the general name schlieren PIV.

Two different turbulent flows, both 2D in the mean, are used here to test thevalidity of the schlieren PIV concept: a planar turbulent boundary layer and anaxisymmetric turbulent jet. The boundary layer is formed on the test section floor ofthe Penn State Supersonic Wind Tunnel, a cold-flow blowdown facility with a15 16.3 60 cm test section, up to 2min test duration, and a Mach number rangeof 1.54.0. Present tests are conducted at Mach 3, boundary-layer thicknessd 25mm, and momentum-thickness Reynolds number Rey 98000. The lens-typeschlieren system described above was used in these experiments.

A converging nozzle of exit diameter 0.787mm, discharging helium into ambientair, produces the axisymmetric jet tested here. The nozzle stagnation pressure of208 kPa yields a choked helium jet with a theoretical exit velocity of 890m/s and aReynolds number of about 7300. The small nozzle scale allows a large non-dimensional jet length to be studied (up to about 200 nozzle diameters downstream)within the fields-of-view of the z-type schlieren instruments employed here.

3. Schlieren sensitivity to turbulence

As in traditional PIV, image quality is a key issue in schlieren PIV. The image scaleand resolution are determined by the nature of the CCD sensor in the PIV cameraand by the lens employed, and vary with the scale of the flow under study.

Aside from these traditional concerns, however, schlieren PIV has additionalimage quality issues arising from the sensitivity of the optics to the refractivedisturbances in the turbulent flows under investigation. Schlieren sensitivity is hereanalogous to particle size selection and seeding density in traditional PIV. For bothschlieren and shadowgraphy an optimum sensitivity range can be defined over whichthe best PIV results are had.

In simple geometricoptical terms, schlieren sensitivity S is given by Eq. (1)(adapted from [13]), where a is the width of the unobstructed light-source image inthe schlieren cutoff plane, b is the width of the entire light-source image, and f 2 is the

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focal length of the second schlieren field lens or mirror. Since f 2 and b are typicallyfixed for a given schlieren instrument, we may conveniently discuss sensitivity interms of the percent of knife-edge cutoff of the light-source image. For example,100% cutoff refers to the complete blockage of the source image by the knife-edge (asituation in which Eq. (1) predicts infinite sensitivity, the geometricopticaldescription fails, and diffraction effects take over [13]).

S f 2a f 2

b 1 %cutoff=100 . (1)

For the white-light strobe-illuminated schlieren system described earlier, a razorblade knife-edge oriented perpendicular to the streamwise direction of the flow isused as the cutoff. Fig. 2 shows the results of the range of cutoffs used with thepresent helium jet. For 10% and 20% cutoff only an underlying very-slightshadowgraph effect is seen. These images contain insufficient information for PIVprocessing. On the other hand, high-cutoff images result in over-ranging, shown forexample by the entirely white regions in the 90%-cutoff image in Fig. 2. When over-ranging occurs the local flow details are washed out, which is likewise detrimental toschlieren PIV.

To avoid over-ranging, especially when high cutoff is required by a need for highschlieren sensitivity, one can increase the overall measuring range by increasing thelight-source slit width b. Better solutions, such as replacing the knife-edge by agraded filter [13] are also available.

The optimum case for schlieren PIV requires sufficient sensitivity to reveal thesmallest turbulent structures without significant over-ranging. This occurs, forexample, in the 3060% cutoff range in Fig. 2. Here, unlike the case in some otherschlieren applications, it is the fine-scale turbulencePIV particlesthat must berevealed.

As noted earlier, laser schlieren illumination requires a less-severe cutoff than theknife-edge just described, whose optical transmission f is 0%. In Fig. 3, different half-plane-sooted microscope slides are used as cutoffs to vary the schlieren sensitivity.Cutoffs with fp26%, being almost as opaque as a knife-edge, yield binarized imagesin which some or all of the fine turbulence scales are washed out. Likewise the f 93% cutoff is almost transparent, yielding practically no cutoff and a vanishingschlieren effect. Therefore, the present optimum sensitivity range for laser-illuminatedschlieren with partially transmitting cutoffs is roughly 50%ofo90%.

Coherent artifact noise is quite apparent in Fig. 3. It has the undesirable effect inschlieren PIV of obscuring some of the fine-scale turbulent motion. Moreover, withtwin pulsed-laser illumination a pseudo-velocity can result from the coherent artifactnoise if the two laser beams are not aligned with perfect coincidence.

As already noted, focused shadowgram pairs can also be used for PIV analysis.Here, since shadowgrams involve no cutoff, the product of the focus offset distanceL and the Laplacian of the refractive-index field dictates the sensitivity [13]. Fig. 4shows an example of laser-illuminated shadowgrams of the helium jet with L rangingfrom 0 to 130 cm. As expected, the sharply focused case yields no usable informationfor PIV analysis. Shadowgraph PIV becomes possible in this example when L

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Fig. 2. Helium-jet white-light schlieren images with different amounts of knife-edge cutoff (b 0:86mmsource-slit width).

Fig. 3. Helium-jet laser-schlieren results with different optical transmission values f of the half-planesooted microscope slide cutoff: (a) f 13%, (b) 26%, (c) 61%, (d) 72%, (e) 88%, and (f) 93%.


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Fig. 4. Helium-jet shadowgrams with increasing sensitivity: (a) L 0 cm, (b) 12.5 cm, (c) 38 cm, (d) 53 cm,and (e) 130 cm.


exceeds 12 cm, but fails for L4130 cm because the increasing blur eventuallyobscures the fine-scale turbulence that serves as PIV particles. These L limits willbe different, of course, for schlieren objects of different strength than the presenthelium jet.

Note especially that a shadowgram is not a focused image, and that coherentartifact noise in the case of laser illumination can pose the same troublesome issue ofpseudo-velocity as described above for schlieren PIV.

To better understand exactly how PIV algorithms perceive schlieren images,120 120pixel turbulence samples were taken from each image in Fig. 2 andconverted into binarized 2D intensity maps, which were then analyzed for the numberand size of the particles within a 24 24 pixel interrogation window. For simplicity,no window overlap was used in the determination of the number of particles perwindow, and the particles found at the edges of the window were included in theparticle count. As shown in Fig. 5, the number of apparent particles decreases withincreasing knife-edge cutoff, while the average particle size increases.

Keane and Adrian [17] proposed a method to quantify the minimum number ofparticles required in a PIV interrogation window. It is based on the number ofparticles N, the out-of-plane displacement F 0, and the in-plane displacement F i. Inorder to achieve 95% accuracy in the probability of displacement detection, theyclaim that the product of these three parameters should be larger than five. However,Raffel et al. [1] claim that a value of three or four for this product is sufficient forpractical situations. When applied to schlieren PIV, F 0 equals unity since allparticles are always in the plane. F i can likewise be set essentially to unity whenthe adaptive interrogation mode is used. Thus the number of schlieren particles inthe PIV interrogation window should be at least four.

Fig. 5 reveals that a knife-edge cutoff of 50% or less thus ensures an adequatenumber of particles in a 24 24 pixel window for the schlieren equipment usedhere (f 2 864mm, b 0:86mm). Cutoffs exceeding 50% may yield interrogationwindows without particles, thereby requiring software interpolation to computedisplacements.

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Percent Cutoff

0 10 20 30 40 50 60 70 80 90 100

Num

ber

of A

ppar

ent "

Par

ticle

s" in

a24

x 2

4 pi

xel i

nter

roga

iton

win

dow

0

2

4

6

8

10

12

14

16M

ean

App

aren

t "P

artic

le"

Dia

met

er [p

ixel

]

0

2

4

6

8

10

12

14

16

Fig. 5. Particle size and concentration vs. percent schlieren cutoff (based on Fig. 2 and using a 108mm

diameter f =8 z-type schlieren system with b 0:86mm source-slit width).


Particle size is likewise a key parameter in PIV analysis. According to Raffel et al.[1], the optimum particle diameter for conventional PIV is two pixels, based on asimulation of particles traveling one pixel per frame in a light sheet. In this controlledcase, particle size is directly related to the RMS uncertainty of particle displacement.Above a particle diameter of two pixels, however, the RMS uncertainty increasesexponentially, although it decreases as the interrogation window grows [1]. Based onthis, particle diameters should be minimized for successful schlieren PIV, especiallywhen small interrogation windows are needed for high spatial resolution. Fig. 5 showsthat the present particle size increases almost linearly over the range of 1060%cutoff, above which over-ranging of the helium-jet schlieren image begins.

We therefore conclude that effective schlieren PIV calls for the minimum knife-edge cutoff compatible with particle visibility. One may anticipate extreme caseswhere a combination of low cutoff and a weak turbulent refractive field prevents thesuccess of schlieren PIV. Even for the present strongly refractive helium jet, a cutoffin the ideal range of 10% produces insufficient contrast between the turbulenceand the background, i.e. a signal-to-noise ratio that is too small to be effective. Thusthe optimum schlieren sensitivity for PIV measurements in the present experimentoccurs within the 3060% range of knife-edge cutoff using white-light illumination.

4. PIV image processing

Processing schlieren image pairs with commercially available PIV software is nodifferent than in standard PIV. The first consideration is spatial resolution: high

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resolution of the velocity field requires small interrogation windows. But errors canresult due to the particle size and concentration constraints noted above. Smallerwindows also increase the probability of other errors such as loss of pairing andparticle truncation. Both errors result in velocity underestimation [12]. The adaptiveinterrogation window described earlier alleviates most of these problems.

To further increase the probability of detection, a PIV image offset may sometimesbe required. This literally shifts the second image of the PIV pair with respect to thefirst by a predetermined integer pixel value. Such an offset helps the correlationalgorithm to determine sub-pixel displacements, permitting the use of smallerinterrogation windows.

Certain situations further require that the PIV field be analyzed in zones, ratherthan as a whole. For example, high velocity gradients can produce neighboringregions of a flowfield requiring different image offsets (often by just a single pixel).This zonal evaluation technique was required in analyzing the present compressibleboundary layer test case.

5. Schlieren PIV results

5.1. Helium jet

The helium jet studied here has distinct near- and far-field zones. The near-fieldextends to about 15 nozzle diameters downstream of the nozzle exit. Its definingfeature is its laminar core, containing no turbulent structures (particles) for schlierenPIV. The effect is clearly seen in Fig. 6: a double peak appears in the integratedvelocity profile at about y 8mm from the nozzle exit. The reason for this is thepath-integration of the schlieren beam through this axisymmetric flow. A light raythrough the edge of the laminar jet core incurs more refraction due to turbulencethan one traversing the jet centerline. The former ray thus yields a greater apparentparticle displacement and a higher velocity is found.

No schlieren PIV is possible within y 1mm of the nozzle exit, where theaccompanying shadowgram reveals an initially laminar jet. Also, due to opticalpath integration and turbulent mixing, the measured velocities in the 40m/s range inFig. 6 are low compared to the theoretical jet nozzle-exit speed of 890m/s.

The far-field jet region begins around 15 diameters (12mm) from the nozzle exitand is fully turbulent. Fig. 7 shows laser- and white-light-illuminated schlierenimages and a laser shadowgram of this region. The white-light schlieren image,Fig. 7b, has a more severe knife-edge cutoff than the laser schlieren image, and bothlaser frames have coherent artifact noise that can lead to velocity errors.Nonetheless, each of these three varied depictions of the helium jet does in factyield, with good accuracy, the same convective velocity field upon schlieren PIVanalysis (150 image pairs at a time delay of 5 ms between paired images). Theresulting mean velocity profile normal to the jet axis is given in Fig. 8.

For comparison, traditional laser-sheet-illuminated PIV measurements were madeusing micron-sized oil droplets that were entrained into the helium jet by way of a

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Fig. 7. (a) Laser schlieren, (b) white-light schlieren, and (c) laser shadowgram of helium jet showing

far-field.

Fig. 6. Laser shadowgram of the helium jet near field (left, L20 cm, nozzle exit diameter 0.787mm)and the corresponding schlieren PIV velocity contour plot (right). Velocities are given in m/s.


slow coaxial seeded jet. Only far-field measurements were possible in this manner.Example flowfield images and PIV velocity results are compared in Fig. 9. It is clearfrom this comparison that traditional PIV yields higher velocities than schlieren PIVin this helium jet case, as expected. The difference is attributed to the path-integration of the schlieren optics. Since the jet is axisymmetric, a proper comparison

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X (mm)-15 -10 -5 0 5 10 15

Axi

al V

eloc

ity, p

ath-

aver

aged

(m

/s)

0

5

10

15

20

25

30

Schlieren, white-light illuminationSchlieren, laser illuminationShadowgraph, laser illumination

Fig. 8. Mean helium-jet velocity profiles from schlieren PIV analysis of the cases of Fig. 7 (y 42mmdownstream of nozzle exit). Only half-profiles are shown for the laser schlieren and shadowgraph cases.


can be made by applying the Abel transform to the traditional PIV results, Eq. (2)(see, e.g. [18]).

Vpai; j

Piedgeiio

Vpli; j

Nio!iedge, (2)

where Vpai; j is the path-averaged velocity, Vpli; j is the planar velocity, Nio!iedge isthe number of discrete points between io and iedge, and the subscripts o and edgerepresent the location of V pai; j within the jet and the jet edge, respectively. Theresult is shown in Fig. 10, where the Abel transform applied to the traditional-PIV jetcenter-plane data recovers approximately the same velocity profile as that measureddirectly by schlieren PIV.

Alternatively, the inverse Abel transform can be applied to the schlieren PIVresults to yield equivalent jet center-plane data. In most cases this is the preferableprocedure, since the equivalent center-plane data are the most useful form of theexperimental results. The opposite procedure has been adopted here merely as amatter of convenience, since deconvolution of the data makes the inverse Abeltransform approach somewhat more involved. Nonetheless modern digital comput-ing power is more than sufficient for either of these procedures.

To further test the schlieren PIV results, one may compare the jet centerlinevelocity distribution vs. y with traditional PIV results and with the extensive jet data

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Fig. 9. (Above left) white-light helium-jet schlieren image, (above right) particle-seeded image of the same

flow with laser sheet illumination through the jet center-plane. Below the images are shown average PIV

velocity contour maps for comparison (schlieren PIV left, traditional PIV right).


correlation by Kleinstein and Witze [19]:

uc 1 exp1

kx re 0:5 X c

!, (3)

where k 0:074, x x=rj, re re=rj (e and j refer to the ambient and jet exitconditions, respectively), and X c 0:7. The centerline velocity is normalized by thejet nozzle-exit velocity, 890m/s.

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X (mm)0 10

Axi

al V

eloc

ity (

m/s

)

0

10

20

30

40

50

Particle PIV

Particle PIV, Abel transformed

Schlieren PIV

8642

Fig. 10. Velocity half-profiles of the far-field helium jet at y 65mm, comparing schlieren PIV withtraditional particle PIV results with and without the application of the Abel transform to the latter.


The results show that the present helium-jet centerline velocity data, obtained bytraditional PIV in two separate experiments, agree well with the KleinsteinWitzecorrelation as shown in Fig. 11. Also, applying the Abel transform to the traditionalPIV data yields results comparable to the schlieren PIV data, demonstrating onceagain that schlieren PIV gives a path-integrated representation of the axisym-metric velocity field. The noise level of the traditional PIV data in Fig. 11 makes itdifficult to determine the exact jet edge location, which may account for some errorincurred during the Abel transformation.

5.2. Compressible turbulent boundary layer

The above helium-jet schlieren PIV results reveal the dominant effect of opticalpath integration in measuring an axisymmetric flowfield. No such effect is expectedin a true 2D flow, however, where schlieren PIV and traditional PIV results shouldbe directly comparable even though the former still integrates across the flow.

To test this, the compressible turbulent boundary layer on the test-section floor ofthe Penn State Supersonic Wind Tunnel was measured by schlieren PIV. Given aspan of 6d and end effects of less than one d, approximately 2D flow is expected.Note, however, that it is not possible with the current schlieren optics to eliminateend effects by focusing on the center-plane of this flow.

Double-pulsed laser illumination through the lens-type schlieren system describedearlier is the only approach that allows a sufficiently small time delay between PIVframes (0.55 ms) for this Mach 3 flow. To provide adequate schlieren sensitivity a

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Fig. 11. Helium jet centerline velocity decay as measured by traditional PIV, predicted by the Kleinstein-

Witze correlation, and measured by schlieren PIV with path integration.


half-plane sooted microscope slide with 72% light transmission was required. Giventhe 15 cm extent of the boundary layer along the optical axis, converting toshadowgraphy required only the removal of the knife-edge, without any focusadjustment. (In other words, the shadowgraph image is always present and iscombined with the schlieren image when a schlieren cutoff is used.)

An example of schlieren image and shadowgram are given in Fig. 12. In both casesfine-scale turbulence is observed, though it does not end as expected at theboundary-layer edge, but rather appears to continue into the freestream. This is, infact, an end effect due to the wind-tunnel sidewall boundary layers on the glasswindows. Slight over-ranging is also seen in the schlieren image, but this is notserious enough to affect the overall PIV results.

One hundred and fifty schlieren PIV image pairs were processed, as before, usingthe IDT softwares adaptive mode with a 20 20 pixel interrogation window.However, since the boundary-layer velocity profile extends from 0 at the wall to613m/s in the freestream, the required image offset varies across the height of theboundary layer as discussed earlier, starting at 6 pixels near the wall and ending at8 pixels near the freestream. Since three separate image-offset zones are needed toanalyze this flow, three different meshes are also required. The zones with their meshlocations and corresponding image offsets are as follows:

1.
0.0py/dp0.17 6-pixel offset,2. 0.14py/dp0.30 7-pixel offset,3. 0.27py/dp1.01 8-pixel offset.

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Fig. 12. Example schlieren image (left) and shadowgram (right) of the Mach 3 turbulent boundary layer

on the test section floor of the Penn State Supersonic Wind Tunnel.


Unfortunately, traditional particle PIV is not currently possible in this boundarylayer due to particle seeding difficulties. Instead, the schlieren PIV results areevaluated by comparison with mean velocity profiles derived from pitot-pressuresurveys by Garg and Settles [20], and with the established wake-wall similarity lawfor turbulent boundary layer profiles. The Van Driest transformation was used toconvert measured compressible-flow velocity values, u, obtained from both theoptical PIV and the pitot surveys, to equivalent incompressible values, u* (see, e.g.[21]). The results are plotted in Fig. 13 in traditional u+ vs. y+ coordinates alongwith the incompressible wall-wake law of Coles [22].

Fig. 13 reveals that the schlieren PIV data are in substantial agreement with thepitot-survey results for this boundary layer, even though the differences in the twomeasurement methods are striking. Schlieren PIV measures, in principle, thebroadband convective velocity of turbulent structures directly. Pitot pressure surveysare converted, with the assumption of constant stagnation temperature, to meanMach number profiles from which the mean velocity is extracted by way of anassumed static temperature profile. Agreement between the two indicates thatschlieren PIV actually measures, by way of refractive eddy motion, the mean velocityprofile of the boundary layer.

Fig. 13 also reveals that this boundary layer has an unusually high wake-strengthcomponent, P 1:9 vs. the usual P0:55 for a flat-plate boundary layer [22]. Thisdoubtless results from the pressure-gradient history along the wall of the windtunnels long asymmetric variable-Mach-number sliding-block nozzle.

There are two boundary-layer regions in which schlieren PIV is unable tomeasure the velocity satisfactorily: very near the wall and near the boundary-layeredge. Failure near the wall is due to poor spatial resolution caused by wind-tunnelvibrations and by laser diffraction that obscures the true location of the wall. Evenso, schlieren PIVbeing non-intrusivemeasures closer to the wall than does the

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Y+ = y(u/w)102 103 104 105

U+

= u

*/u

15

20

25

30

35

40

Pitot Pressure SurveyWall LawShadowgraph PIVSchlieren PIVWall-Wake Law

M = 3 Tw = 260 K = 25 mm cf = 8.98 x 10

-4

u = 18.5 m/s

Re = 98,000 = 1.9

w = 2.52 x 10-5 m2/s

Fig. 13. Mean velocity profiles of the Mach 3 turbulent boundary layer in wall-wake coordinates.


pitot survey method. Near the boundary-layer edge, however, schlieren PIV failsby yielding velocities that are too low. The outer 20% of the turbulent boundarylayer is quite intermittent, so the eddies serving as PIV particles are fewer there.Eddies in the sidewall boundary layers contaminate the integrated schlierenmeasurement with incorrect end-effect velocities in this region, as shown in Fig.12. By way of focusing schlieren optics [20,23], it should be possible to eliminatethese end effects and make an accurate measurement up to the boundary-layer edge,but that is beyond the present scope.

6. Conclusion

Schlieren PIV is shown to yield valid velocimetry data, within certain limits, fora 2D compressible turbulent boundary layer and an axisymmetric turbulent heliumjet in air. Effective schlieren PIV calls for the minimum knife-edge cutoffcompatible with the visibility of fine-scale turbulence. Due to optical pathintegration, axisymmetric flows require the inverse Abel transform to extractcenter-plane velocity data. Path integration also causes velocimetry errors due to endeffects in the boundary-layer experiment. In both flows studied here the evolutionarytime scale of turbulent eddies was much longer than the proper time separationbetween the images in a PIV pair, so eddy evolution did not limit the schlieren PIVmeasurements.

Despite its limitations, the method shows promise as a new optical velocimetrytool. Schlieren PIV combines commercially available PIV equipment and software

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with a standard schlieren optical instrument. It requires no actual particle seeding ofthe flow, since it uses fine-scale turbulence as PIV particles. Otherwise it functionsmuch the way standard PIV does under conditions where individual particles are notresolved and velocimetry is instead based on correlation of the motion of turbulentstructures. In its present embodiment, schlieren PIV is not useful for laminar flowsor for fully 3D flows, but it shows significant promise for general refractive turbulentflow velocimetry if its integrative nature can be overcome through sharp-focusingschlieren optics [20,23]. A study of that possibility is recommended for future work,as is the potential use of simple means to generate non-coherent schlierenillumination directly from coherent PIV laser pulses [24]. Additional informationon the present study is given in [25].

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Schlieren Introduction and literature reviewExperimental equipmentSchlieren sensitivity to turbulencePIV image processingbm_st3Outline placeholderHelium jetCompressible turbulent boundary layerConclusionReferences