Christensen PIV

This content has been downloaded from IOPscience. Please scroll down to see the full text.

Download details:

IP Address: 128.174.133.185This content was downloaded on 07/05/2015 at 16:43

Please note that terms and conditions apply.

Robust suppression of background reflections in PIV images

View the table of contents for this issue, or go to the journal homepage for more

2013 Meas. Sci. Technol. 24 027003

(http://iopscience.iop.org/0957-0233/24/2/027003)

Home Search Collections Journals About Contact us My IOPscience

IOP PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY

Meas. Sci. Technol. 24 (2013) 027003 (6pp) doi:10.1088/0957-0233/24/2/027003

TECHNICAL DESIGN NOTE

Robust suppression of backgroundreflections in PIV imagesR Mejia-Alvarez1 and K T ChristensenMechanical Science and Engineering Department, University of Illinois, Urbana, IL 61801, USA

E-mail: [email protected]

Received 3 October 2012, in final form 13 December 2012Published 15 January 2013Online at stacks.iop.org/MST/24/027003

AbstractStrong background reflections in PIV images are known to bias velocity estimates and theirconcomitant statistical ensembles. Many methods have been developed to eliminatebackground reflections, with the common premise of generating a reference backgroundintensity map that is then subtracted from each individual PIV image prior to interrogation.This reference background intensity map can be generated in several ways, includingacquiring a background image without particles, calculating the average or minimum intensitymap based on an ensemble of PIV images, generating a reference intensity map for eachindividual PIV realization by means of various local sliding filters or considering the secondframe of any PIV realization as its reference intensity map. Motivated by the need to suppressbackground reflections in a PIV study of flow over highly irregular surface roughness thatgenerated significant diffuse background reflections from the complex topography, the efficacyof these methods was studied. It was found that all failed to adequately suppress suchreflections, rendering the resulting velocity fields biased. A local-median normalizationalgorithm was developed to further suppress background reflections and this note reports theperformance of this modified algorithm compared to those previously reported in the literature.

Keywords: velocimetry, PIV image processing, turbulence measurements

(Some figures may appear in colour only in the online journal)

1. Introduction

The accuracy in determining particle displacements fromparticle image velocimetry (PIV) images hinges on thequality of the correlation peak generated when correlating twotime-delayed interrogation windows containing tracer particleimages. Lack of sufficient particle seeding can reduce thequality of this correlation below that of noise peaks in thecorrelation plane and can result in a spurious measurement.Alternatively, high-intensity background noise in one or bothof the interrogation windows, or particle images with widelydisparate intensity values, can result in spurious correlationpeaks whose height well exceeds that of the true displacement

1 Present address: Physics Division, Los Alamos National Laboratory, LosAlamos, NM 87545, USA.

peak even when the particle seeding density is adequate.For instance, Shavit et al (2007) observed that when in agroup of particles some subset of them exhibit a much higherscattered light intensity than the others, the correlation mapstend to be biased toward the displacement of the brighterparticles. Similarly, laser lightsheet spatial heterogeneities canbias correlation maps (Keane and Adrian 1990, 1991), sincesharp boundaries between regions of different light intensitiesoverestimate the importance of the non-displacement peak.Renormalizing the image intensity has proven effective tocompensate for this effect (Westerweel 1993). In addition,poor contrast between the background and particle-imageintensities represents yet another common problem in PIVas it hampers accurate particle discrimination in correlationcalculation and consequently increases noise levels. Severalcontrast-enhancing techniques have been proposed to cope

0957-0233/13/027003+06$33.00 1 2013 IOP Publishing Ltd Printed in the UK & the USA

Meas. Sci. Technol. 24 (2013) 027003 Technical Design Note

with this issue (see Dellenback et al 2000, Roth and Katz2001, for example). In addition, symmetric phase only filtering(SPOF) (Wernet 2005) offers an alternative approach that cancope simultaneously with illumination heterogeneities and lowcontrast images. Finally, the presence of fixed reflective objectsin the background induces a detrimental effect resulting fromthe combination of multiple factors. First, fixed reflectionsincrease the background intensity, which reduces the dynamicrange available to adequately image the scattered light fromPIV tracer particles. In addition, if the background is brightenough, the contrast between it and the particles can be greatlyreduced. Since the intensity of the background would dominatethe overall intensity of the image, correlation maps computedfrom such images would be inevitably biased toward zerodisplacement.

Multiple approaches have been developed to mitigate theadverse effects of background reflections. In cases when thesereflections present very low spatial frequencies compared tothe PIV interrogation spatial frequency, it can be sufficient tosimply renormalize the image (Westerweel 1993) or use SPOF(Wernet 2005, particularly at low signal-to-noise ratios). Formore general cases, image levelization, whose fundamentaltenet is to subtract a reference intensity map from each PIVframe, is preferred. Ideally, the reference intensity map shouldmatch the intensity distribution of the background such that itssubtraction would eliminate these background reflections andleave only the particle images intact. Achieving such a scenariocan be accomplished in many ways, including acquiring animage of the background without particles (Honkanen andNobach 2005), calculating an average or minimum intensitymap based on an ensemble of PIV images (Gui et al 1997,Wereley and Gui 2002, respectively), generating a referenceintensity map for each individual PIV realization by means oflocal sliding median or low-pass smoothing filters (Jain 1989,Willert 1997, respectively) or considering the second frame ofany PIV realization as its reference intensity map (Honkanenand Nobach 2005).

While all of the aforementioned methods for generatinga background intensity map can adequately address issuesassociated with direct reflections owing to lightsheetimpingement on a surface, for example, they often cannotaccount for image noise generated by diffuse backgroundscattering of light originally scattered by the PIV tracerparticles. Background reflections due to this process willnecessarily change from image to image since it is a directfunction of the local particle population which will change intime for typical tracer-particle seeding. Thus, subtraction of areference intensity map acquired without particles is likely toleave a strong residual background that will vary from imageto image. In addition, pulsed lasers commonly employed forPIV measurements (Nd:YAG and Nd:YLF lasers, for example)can exhibit an energy variation of roughly 5% from pulse topulse. Consequently, a reference image based on the averageor minimum of the PIV ensemble will inevitably overestimateor underestimate the background intensity, again leading toresidual background effects. Overestimating the backgroundintensity is most detrimental when the average intensity isused to calculate the reference image because subtraction

might artificially eliminate particle images. This problemmay be somewhat attenuated if the average intensity is usedfor normalizing the PIV images rather than for backgroundsubtraction (Adrian and Westerweel 2011), but it cannoteliminate the issue of laser intensity variability. On the otherhand, local sliding filters are advantageous because they donot assume a single reference intensity map for an entireensemble of data. Rather, they capture a reference intensitymap from and for each individual image. Again, however,intensity variability between consecutive laser pulses cannotbe corrected with this technique. In addition, the accuracy indetermining the intensity map of the background is limitedby the spatial cutoff frequency of the filter. Consequently,the detection of intensity maps to mitigate spatially varyingbackground noise may not be very effective by means of low-pass smoothing or median filters. The alternative of usingthe second PIV frame as the reference intensity map, asfirst proposed by Honkanen and Nobach (2005) and recentlyemployed by Deen et al (2010), is based on the idea thatwhile the spatial distribution of particle images differs in thefirst and second PIV frames, the background in both imagesis the same so long as the background object remains fixedin space. Hence, subtracting the second PIV frame fromthe first should eliminate the background regardless of howirregular it is, leaving the distribution of particle images largelyunaffected. This technique is instantaneous in the sense thateach pair of PIV images is processed individually, allowingone to account for snapshot-to-snapshot variations in bothincident light intensity and background reflections owing tore-scattering of light from the PIV tracer particles.

The present contribution reports a modified version ofthe method proposed by Honkanen and Nobach (2005) whichhas been previously used for processing PIV data with highlyirregular background intensity (see Deen et al 2010, forexample). However, in recent studies of turbulent flow overhighly irregular roughness (Mejia-Alvarez 2010), for whichirregular and diffuse background noise is encountered in thePIV images, this algorithm was found to result in residualimage noise that impacted the interrogation of the PIV images.Modifications of this method are presented herein to furthersuppress this residual background noise.

2. Benchmark experiment: turbulent flow overcomplex surface roughness

The motivation for developing a more robust background-subtraction methodology stemmed from stereo PIVmeasurements in turbulent flow overlying an irregular roughwall. The surface topography under consideration (figure 1(a))was reproduced from the previous profilometry measurementsof a turbine blade damaged by deposition of foreign materials(see Bons et al 2001, Mejia-Alvarez and Christensen 2010).These measurements were conducted to study the flow inthe immediate vicinity of the roughness, so the PIV laserlightsheet was positioned parallel to the wall (figure 1(b)) andapproximately 4 mm above the midplane of the roughness witha field of view of approximately 80 mm 100 mm (spanwise,z, by streamwise, x). As such, while the lightsheet did not

2


4.0 mm

2.01.81.61.41.21.0

0 50 100 150 200

0

50

100

150

X (mm)

Z (m

m)(a) (b)

(c) (d)

Flow

Figure 1. (a) Top view of the roughness pattern. The yellow rectangle demarcates the field of view acquired in the present experiments. (b)Cartoon representing the side view of the experimental configuration. (c) Raw PIV image showing that the light scattered from PIV tracersinduces strong reflections from roughness protrusions. (d) Contour map of the ensemble averaged wall-normal Reynolds normal stressv2+, showing how roughness protrusions bias single-point statistics of turbulence flows. Note how artificially intense v2+ spots coincidewith the roughness protrusions shown in part (c).

directly impinge upon the roughness features, reflectionsfrom the surface irregularities were clearly apparent in thePIV images owing to secondary scattering of light originallyscattered by the PIV tracer particles (1 m olive oil dropletsyielding particle-image diameters of 2 pixels). The rough-wall turbulent boundary layer had a friction Reynolds numberof Re = 5215 and a boundary-layer thickness of =101.9 mm (see Mejia-Alvarez (2010) for further details).

A stereo PIV arrangement was utilized to capture largeensembles of instantaneous, three-component velocity fieldson the measurement plane using two 4k 2.75k pixel,12-bit, frame-straddle CCD cameras (TSI 11MP) at angles of13 from the wall-normal (y) direction through a transparentsection in the wind-tunnel ceiling. A sample PIV image ispresented in figure 1(c), in which the strong backgroundreflections due to the largest topographical features areobvious. In particular, the intensity of this background noiseis comparable to that of the scattered light from the tracerparticles. Unfortunately, these background reflections corruptthe PIV interrogation and induce strong bias in turbulencestatistics derived from ensembles of instantaneous velocityfields. This effect can be observed, for example, in the spatialdistribution of wall-normal Reynolds normal stress normalizedby the friction velocity, v2+ v2/u2 , as shown infigure 1(d). The background reflections yield artificially-elevated turbulence levels in v2+ in spatial patterns entirely

consistent with that of the background reflections noted infigure 1(d). If not for the clear consistency between the spatialpatterns of the background noise in the raw PIV image and theelevated turbulence levels in v2+, a cursory interpretationof this result might lead to the incorrect conclusion that theseelevated turbulence levels are physical, owing to interactionsof the flow with the complex surface topography.

Three-thousand statistically independent instantaneousvelocity fields were acquired and each individual realizationwas interrogated using interrogation windows of size 32 32pixel2 for the first frame and 36 36 pixel2 for the secondframe to compensate for loss of pairs due to out-of-planeturbulent motions. The second interrogation windows wereoffset by 10 pixels in the streamwise direction to account formean advection of the flow. A recursive interrogation approachwas used to refine this offset, during which the size of theinterrogation window was fixed. Stereo reconstruction wasaccomplished via calibration of the imaging system with adual-plane target containing dots spaced at 10 mm intervalsthat was placed coincident with the lightsheet. The least-squares approach of Soloff et al (1997) was used to generatemapping functions for transforming the two-dimensionaldisplacement fields from each camera into the physicalspace of the laser lightsheet for the final reconstruction ofinstantaneous, three-component velocity fields (see Mejia-Alvarez 2010).

3


(a)

(e)

(d)

(c)

(b) (f )

(i)

(h)

(g)

( j )

(m)

(l)

(k)

-4 -3 -2 -1 0 1 2 3 4 ui

+1.0 1.2 1.4 1.6 1.8 2.0

+

Figure 2. (a) Raw PIV image; the white box in (a) is zoomed within (b) without any processing, (c) after subtracting the ensemble averageintensity, (d) after using the Honkanen and Nobach (2005) maximum-intensity-based algorithm and (e) after using the median-basedalgorithm proposed herein. The instantaneous velocity fields (not all vectors are shown for clarity) and ensemble-averaged wall-normalReynolds normal stress, v2+, in the zoomed-in region for each of these cases are presented in ( f )(i) and ( j)(m), respectively.

3. Algorithm for background elimination

As noted in section 1, several methods have been previouslyproposed to mitigate background-reflection problems similarto that illustrated in figure 1. Of those, we consider thatframe subtraction (Honkanen and Nobach 2005) has thebest potential to become a robust method for backgroundsubtraction with the modification proposed herein. Forexample, Deen et al (2010) applied this technique to single-phase flow in spacer-filled channels wherein they compensatedfor variation in laser energy between frames A and B with localminimummaximum filters. To sample for extreme values oflight intensity and normalize locally, they used an intensitysampling spot of size larger than the average particle-imagediameter but smaller than the PIV window size utilized inthe interrogation (see Westerweel (1993) for details on thisstrategy). The local normalization was then carried out as

N(x) = I(x) Imin(x)Imax(x) Imin(x) , (1)

where I(x) is the sliding local intensity and Imax(x) andImin(x) are its maximum and minimum values, respectively.Upon normalization, any intensity variations between laserpulses should be accounted for, leaving frames A and B withnormalized intensity values ranging from 0 to 1. Thus, thetwo PIV frames can be subtracted from one-another to yielda dual-frame image that should now be free of backgroundreflections. Frame A is then recovered from this dual-frameimage by extracting the positive values of intensity whileframe B is recovered by extracting the negative values ofintensity and taking their absolute value.

To illustrate the notion of background subtraction, thePIV image from figure 1(a) is reproduced in figure 2(a).Figure 2(b) presents a zoomed-in view of the white-boxedregion in 2(a) that highlights a region of this PIV imageseverely impacted by background reflections from the complexroughness topography below. Figure 2(c) presents the sameregion as figure 2(b) but after the ensemble-averaged referenceintensity image was subtracted from the full PIV image infigure 2(a). While the background reflections are somewhatmitigated, there still exist clear residuals of the backgroundnoise that are comparable or even exceed the size of theinterrogation windows. This residual background noise is dueto the fact that the ensemble-averaged reference image doesnot perfectly match the intensity profile of the backgroundreflections in this specific PIV image.

Alternatively, figure 2(d) presents an example of the resultobtained after applying the algorithm posed in equation (1) tothe original image in figure 2(a). This method should provemore robust than simply subtracting an ensemble-averagedreference intensity image as it can account for laser-intensityvariations between frames A and B as well as backgroundintensity variations from one PIV image pair to the next.While this approach was reported to work well for the flowapplication presented by Deen et al (2010), its use in thepresent case yields clear residual imprints of the intensitysampling spots in the formerly bright regions of the PIV images(see zoomed-in view of a portion of figure 2(d) enclosed inthe yellow rectangle). Since the local maximum intensity willcertainly vary from frame A to frame B owing to particledisplacement, the relative intensity of the background will

4


also be different after local normalization with this maximumintensity. This effect is a byproduct of at least a portionof the background light being associated with re-scatteringof light already scattered by nearby tracer particles. Thus,any corrective method based upon local maximum intensity(equation (1)) is found to be quite sensitive to extreme values.In addition, since the normalization in each individual intensitysampling spot is based on a local constant (i.e. the differencebetween the local maximum and minimum intensities), anintensity jump is often noted at the boundaries betweenadjacent intensity sampling spots. Since the PIV interrogationwindows are larger than the intensity sampling spots, thisintensity jump yields a fixed grid in the background that couldpotentially bias correlation peaks toward zero displacement(as shown in the zoomed-in view of figure 2(d)). Westerweel(1993) proposed a homogeneous spatial filter to mitigatethese abrupt intensity transitions between adjacent intensitysampling spots.

To overcome this drawback of the maximum-intensity-based background subtraction method, it is proposed hereinto mitigate extreme value sensitivity by normalizing with thelocal median (instead of maximum) and minimum intensityvalues as

N(x) = I(x) Imin(x)Imedian(x) Imin(x) . (2)

The rationale for this modification is two-fold. First, themedian is a measure of the central tendency insensitive toextreme values. Second, the median is more representativeof the dominant intensity (Kiger and Pan 2000), which in thepresent case corresponds to the background. Thus, normalizingby the median could potentially bring the background of PIVframes A and B to a more common normalized value. Doing socould potentially yield a dual-frame image that is less pollutedwith residual imprints of the local intensity sampling spots.

To carry out a median-based normalization, the locallysampled values of the median were used to construct a matrixof sampling spots, the same size as the original images.Thereafter, the resultant matrix was used to apply equation (2)using matrix operations. For this study, the sampling spotswere 8 8 pixels in size (following Deen et al 2010) whichwas larger than the average particle-image diameter (2pixels) but smaller than the interrogation window size (32 32 pixels). Frame subtraction was then applied to eliminatethe background. Frame A was recovered by extracting thepositive values of normalized intensity, while frame B wasrecovered by extracting the negative values of normalizedintensity and taking their absolute value. After these steps,the background is expected to have been eliminated. However,if the background objects are highly irregular, their reflectedintensity is likely to vary across the PIV images. Consequently,the particle-image intensity after background subtraction is notexpected to be homogeneously distributed across the images.Moreover, the background intensity could occupy most ofthe dynamic range of the imaging device in regions of highbackground object reflectivity. As such, the ability of capturingthe scattered-light intensity from the tracer particles in theseregions will be limited by the residual of the dynamic rangeof the imaging device. Therefore, particles recovered after

background subtraction would exhibit a reduced maximumintensity in regions where background intensity was high.

To compensate for this intensity inhomogeneity, a localnormalization according to equation (1) was applied to theimages after background subtraction. Finally, the intensityvalues were stretched according to the original dynamic rangeof the images at the time of acquisition. A sample result ofthis algorithm is shown in figure 2(e). Note the clear reductionin residual imprints of the background subtraction procedureas well as the homogeneity of the particle-image intensityacross the image. This is in contrast to the clear residualbackground reflections noted in the results achieved withremoval of an ensemble-averaged reference intensity image(figure 2(c)) and the Honkanen and Nobach (2005) maximum-intensity-based algorithm (figure 2(d)). Furthermore, sincethe median intensity is insensitive to extreme values, abruptintensity variations between intensity sampling spots are muchless apparent compared to the maximum-based normalizationof equation (1). While one could also implement thehomogeneous filtering proposed by Westerweel (1993) tofurther reduce any intensity steps between adjacent intensitysampling spots after implementing the median-normalizedprocedure proposed herein, this strategy was tested but didnot yield significant additional improvements in the results.

4. Results

The fluctuating velocity fields corresponding to the zoomed-in region of figures 2(b)(e) are presented in figures 2( f )(i).The vectors represent the in-plane velocity fluctuations, whilethe background contours display the out-of-plane velocityfluctuations. While some differences are observed in thein-plane motions between the three different backgroundsubtraction methods, these differences are notably amplifiedin the estimation of the out-of-plane velocity component.This effect is particularly apparent in the results obtainedfor the raw and ensemble-averaged reference intensity imagesubtraction results (figures 2( f ) and (g), respectively); whereinlocalized spots of either dissimilar or unusually intense out-of-plane motion are observed. The impact of these residualeffects on the turbulence statistics is evident in figures 2( j)(m) which present contour maps of the wall-normal (out-of-plane) Reynolds normal stress, v2+. The influence ofintense background reflections is particularly apparent inthe results corresponding to the raw, ensemble-averagedreference intensity image subtracted, and maximum-basednormalized images. A more continuous field of v2+ isevident in the result garnered from the median-based algorithmproposed herein (figure 2(m)) that is devoid of localizedpeaks in v2+ that are evident in the other three image-processing cases. Of interest, the intensity of these localizedpeaks in v2+ are more intense in the maximum-intensity-based algorithm result (figure 2(l)) compared to that basedon subtraction of an ensemble-averaged reference intensityimage (figure 2(k)). This difference highlights the particularlyadverse impact that image intensity discontinuities can haveon the interrogation results owing to residuals of the intensitysampling spots associated with the use of a maximum-intensity-based approach (figure 2(d)).

5


Local normalizationLocal normalizationbased on local medianbased on local median

Raw imageRaw image Frame subtractionFrame subtraction Local normalizationLocal normalizationbased on local Max.based on local Max.

Figure 3. Flow chart illustrating the image pre-processing protocol proposed herein.

5. Summary

A modified algorithm for the robust removal of fixedbackground reflections from PIV images is proposed. PIVimages from stereo PIV measurements just above a complexsurface topography highlight how intense backgroundreflections in PIV images can introduce strong biases inboth instantaneous velocity fields and turbulence statisticscalculated from ensembles of PIV realizations. Methodslike average intensity subtraction and maximum-intensity-based local normalization have been previously proposed toovercome these challenges. However, the present contributionhighlights how these methods fail to completely removebackground biases, particularly in the case of ensemblestatistics. Random variations in laser-light intensity areresponsible for residual background noise in the case ofremoval of an ensemble-averaged background intensity image,while sensitivity to extreme values leaves similar residualbackground noise in PIV images when a maximum-intensity-based local normalization is performed.

A variation of the local normalization method wasintroduced herein, whereby the intensity normalization isbased on the local median rather than the local maximum.The residual imprint of the intensity sampling spots notedstrongly in the maximum-intensity-based approach is lessenedconsiderably in the median-based algorithm, reducing biasof instantaneous fields and resulting turbulence statistics.Figure 3 presents a flow chart summarizing the image pre-processing protocol proposed herein.

Acknowledgments

This work was supported by the Air Force Office ofScientific Research under grant no. FA9550-07-1-0129 (DrJohn Schmisseur, Program Manager).

References

Adrian R J and Westerweel J 2011 Particle Image Velocimetry (NewYork: Cambridge University Press)

Bons J P, Taylor R P, McClain S T and Rivir R B 2001 The manyfaces of turbine surface roughness J. Turbomach. 123 73948

Deen N G, Willems P, van Sint Annaland M, Kuipers J A M,Lammertink R G H, Kemperman A J B, Wessling M and vander Meer W G J 2010 On image pre-processing for PIV ofsingle- and two-phase flows over reflecting objectsExp. Fluids 49 52530

Dellenback P A, Macharivilakathu J and Pierce S R 2000Contrast-enhancement techniques for particle-imagevelocimetry Appl. Opt. 39 597890

Gui L, Merzkirch W and Shu J Z 1997 Evaluation of low imagedensity recordings with the MQD method and application tothe flow in a liquid bridge J. Flow Vis. Image Process. 4 33343

Honkanen M and Nobach H 2005 Background extraction fromdouble-frame PIV images Exp. Fluids 38 34862

Jain A K 1989 Fundamentals of Digital Image Processing(Englewood Cliffs, NJ: Prentice-Hall)

Keane R D and Adrian R J 1990 Optimization of particle imagevelocimeters: part I. Double pulsed systems Meas Sci. Technol.1 120215

Keane R D and Adrian R J 1991 Optimization of particle imagevelocimeters: part II. Multiple pulsed systems Meas Sci.Technol. 2 96374

Kiger K T and Pan C 2000 PIV technique for the simultaneousmeasurement of dilute two-phase flows J. Fluids Eng.122 8118

Mejia-Alvarez R 2010 Experimental study of low-order models ofhighly-irregular roughness and their impact on turbulentboundary layers PhD Thesis University of Illinois atUrbana-Champaign

Mejia-Alvarez R and Christensen K T 2010 Low-orderrepresentations of irregular surface roughness and their impacton a turbulent boundary layer Phys. Fluids 22 015106

Roth G I and Katz J 2001 Five techniques for increasing thespeed and accuracy of PIV interrogation Meas. Sci. Technol.12 238

Shavit U, Lowe T J and Steinbuck J V 2007 Intensity capping: asimple method to improve cross-correlation PIV results Exp.Fluids 42 22540

Soloff S M, Adrian R J and Liu Z-C 1997 Distortion compensationfor generalized stereoscopic particle image velocimetry Meas.Sci. Technol. 8 144154

Wereley S T and Gui L 2002 Advanced algorithms for microscaleparticle image velocimetry AIAA J. 40 104755

Wernet M P 2005 Symmetric phase only filtering: a newparadigm for DPIV data processing Meas. Sci. Technol.16 60118

Westerweel J 1993 Digital particle image velocimetry: theory andapplication PhD Thesis Delft University

Willert C 1997 Stereoscopic digital particle image velocimetryfor application in wind tunnel flows Meas. Sci. Technol.8 146579

6

1. Introduction2. Benchmark experiment: turbulent flow over complex surface roughness3. Algorithm for background elimination4. Results5. SummaryAcknowledgmentsReferences

Documents

Christensen PIV