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An Investigation of Particle Image Velocimetry Techniques Applied

to the Analysis of Wheel-Soil Interaction on Mars Terrain Simulant

Mobolaji O. AkinpeluMIT Summer Research Program Intern, Summer 2011

Department of Mathematics and Computer Science

Coppin State University

Baltimore, MD 21216

Direct Supervisor: Carmine Senatore, Ph.D.Faculty Advisor: Karl Iagnemma, Ph.D.

Department of Mechanical Engineering, Robotic Mobility Group

Massachusetts Institute of Technology

Canbridge, MA 02139

August 6, 2011

Abstract

In 2009, the wheel of the Mars Rover got stuck because there was not enough traction. The aim of this

project is to create or modify software that will track Martian soil particle and show how the motion ofthe wheel affects the soil. The overall goal of the tasks described in this report is to investigate available

PIV software for the above purpose and understand how to modify the parameters of the software, based

on cross-correlation algorithm, to give the most accurate information on the motion of the soil.

1 Introduction

After landing in January 2004 to probe the past ge-ology and climate of Mars, in May 2009, the MarsRover Spirit got stuck in soft Martian sand [1]. At-tempts to get it out only drove it deeper [2]. In early2011, the Mars Rover went through a particularly

harsh Mars winter that sent it into hibernation whileexposing the scientific and engineering equipments onboard to damage. NASA scientists held out hope thatafter the passing of the winter, Spirit will get enoughenergy from the sun to recharge and resume commu-nication with scientists and engineers on earth. But

it did not. In May 2011, NASA abandoned efforts toresume communication with the Spirit Rover. Conse-quently, studying the interaction between the wheelof the Mars Rover and Martian soil has become an in-teresting and important problem, whose answer willhelp avoid future occurrences like the above. Thisproject simulates the motion of a wheel of the MarsRover on a Mars soil simulant. The simulation is used

to understand the forces the wheel exerts on the soiland the movement and shearing pattern of the soilparticles. The information from these experimentsis vital for understanding the mechanical propertiesof Mars soil and the interaction between the soil and

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the wheel. The result of the study of these propertiesand interactions can be important for the design of

future Mars rover wheels and motion mechanisms.

2 Problem Statement

To track the motion of the particles of the soil, weplan to use publicly available Particle Image Ve-locimetry (PIV) software. However, a sampling ofPIV software shows that they are made for partic-ular applications like the study of fluid flow in bi-ological and geological applications. Therefore, wehad to conduct an analysis of the instrumentation re-quirements (camera frame rate and pixel resolution),

software parameters (interrogation window size, de-gree of overlap of interrogation windows) and physicalconditions (lighting conditions and test rig container)and how to choose these variables so our PIV analy-sis gives accurate and useful data about the flow pat-terns in the soil. This analysis is important becauseit represents a preliminary study that will inform ourchoice of instruments, software parameters and phys-ical conditions for our experiments. There have beenattempts to conduct a more general analysis of theeffects of choice of parameters on the accuracy of PIVresults[4]. However, our approach differs from that ofresearchers like[4] because it is an investigation car-

ried out for a specific application instead of an analy-sis of the structure and results of the cross-correlationalgorithm that is the main feature in contemporaryliterature.

3 Methods

In this section, we explain how PIV analysis worksgenerally, how cross-correlation works, and how wecreated a statistical test based on our understandingof our PIV and cross-correlation work.

3.1 Particle Image Velocimetry

Particle Image Velocimetry (PIV) is a technique usedin experimental fluid mechanics to determine instan-taneous velocity vector fields by measuring the dis-placements of numerous fine particles that accurately

Figure 1: An artists rendering of the Mars Rover Spirit.

Figure 2: The test-bed for our experiments.

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follow the motion of the fluid [3]. This velocity ismeasured by recording images of the particles at more

than one precise time and deducing the displacementof the particles from the displacement of the image[3]. The steps in a PIV analysis are typically as fol-lows:

1. A fluid is seeded with marker particles that re-fract, absorb or scatter light, have a high con-trast with the rest of the fluid and do not inter-rupt the fluid flow.

2. Then the particles in the fluid flow are illumi-nated by pulsed sheets of light at exact time in-tervals and images of the illuminated particles

are taken.

3. Next, the resulting images are processed withsoftware that is based on algorithms like thecross-correlation algorithm.

The analysis of the recorded images to measure theparticles displacement is an important part of anyfluid flow motion experiment. In particular, re-searchers have to make a choice on the technique,algorithm and software that gives them the most in-formed and accurate understanding of the dynam-ics of the fluid flow. For example, apart from PIV,

there are other techniques for analyzing motion ina fluid like Laser Speckle Velocimetry(Fomin 1998),Scalar Image Velocimtry(Dahm et al 1992), and Im-age Correlation Velocimetry (Tokumaru and Dimo-takis 1995) [3]. Compared with other velocity mea-surement techniques such as Laser Doppler Anemom-etry and Hot-Wire Anemometry, PIV offers manyadvantages for the study of fluid mechanics likerevealing the global structure of complicated and/orunsteady flow field quantitatively (Adrian, 1991) so it has been studied intensely and developed rapidlyin the past two decades [4]. In our case, we startedout applying Particle Tracking Velocimetry (PTV),

a technique quite similar to PIV, to our fluid flow.One difference between PIV and PTV is that the al-gorithm that drives PTV attempts to track individ-ual particles displacements to determine velocities,whereas in PIV, regions of flow are tracked. This fea-ture of PTV implies that there has to be a low particle

Figure 3: Why we chose PIV over PTV.

Figure 4: An outline of the PIV Steps.

density in the regions of the flow that are being com-pared to determine the displacement to ensure thatthe software can recognize and track the individualparticle elements from image frame to image frame[2]. This theoretical knowledge, our understandingof the physical properties of the Martian soil and apreliminary test of images of the soil with PTV soft-ware confirmed to us that PIV was a better choicethan PTV.

3.2 Cross-Correlation

Cross-correlation is an example of an algorithm forprocessing images in a PIV analysis. PIV images areprocessed by sub-dividing two consecutive images ofthe flow into a regular grid of sub-areas that overlapand finding the velocity vector for each sub-area by an

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Figure 5: The Martian soil we are experimenting on.

algorithm like cross-correlation. After obtaining theimages for a PIV analysis as explained above, a smallsub-area of the first image, usually called an inter-rogation area or interrogation window, is comparedwith a sub-area at the same location in the second im-age using cross-correlation. This processing producesa table of correlation values over a range of displace-ments, and the overall displacement of particles in thewindow is represented by a peak in this correlationtable. [5]. In other words, the process results inthe most probable displacement vector for that par-

ticular particle pattern. (Adrian 1991; Willert andGharib 1991; Stamhuis and Videler 1995) [6]. Theprocess is repeated for all interrogation areas of thepair of images to get a complete vector diagram ofthe flow. Errors in an analysis using cross-correlationoccur mainly from insufficient data like a lack of im-aged flow tracers or poor image quality, and/or fromcorrelation abnormalities from unmatched tracer im-ages in the correlated sample volume [5]. The cross-correlation algorithm is based on the cross-correlationfunction:

RII(x, y) =K

i=K

L

j=L

I(i, j)I(i+x, j+y)

The variables I and I are the intensity values ofthe images where I is larger than the template I.

Figure 6: Example of the formation of the correlationplane by direct cross-correlation: here a 4 4 pixel tem-plate is correlated with a larger8 8pixel sample to pro-duce a 5 5 correlation plane.

Essentially the template I is linearly shifted aroundin the sample I without extending over edges of I

. For each choice of sample shift (x, y), the sum ofthe products of all overlapping pixel intensities pro-duces one cross-correlation valueRII(x, y). By apply-ing this operation for a range of shifts (M x +M,N y +N), a correlation plane the sizeof (2M+ 1) (2N + 1) is formed. For shift valuesat which the samples particle images align with eachother, the sum of the products of pixel intensities willbe larger than elsewhere, resulting in a high cross-correlation valueRIIat this position. Essentially the

cross-correlation function statistically measures thedegree of match between the two samples for a givenshift. The highest value in the correlation plane canthen be used as a direct estimate of the particle imagedisplacement[7]. One can imagine this procedure asmoving I over I until the best matching is found.The expression best matching is used because inpractice there is never a 100% matching due to par-ticles that have left or entered the imaged area in thesecond image compared with the first [6].

Few systematical researches have been performedto evaluate the effectiveness and accuracy of finalPIV results obtained using cross correlation. There-

fore, users of the cross correlation method have tospend a lot of time and cost to optimize various pa-rameters for PIV image acquiring and processing toget an accurate velocity field [4]. This absence ofliterature on the effectiveness and accuracy of PIVis inspiration for this research project: to analyze,

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Figure 7: The cross-correlation function as computedfrom real data by correlating a smaller template I (3232pixel) with a larger sample I (64 64 pixel). The meanshift of the particle images is approximately 12 pixels tothe right.

Figure 8: Diagrams of steps in PIV analysis of succes-sively recorded PIV patterns in a flow: two sub-imagesfrom the same location of two frames are compared in acrosscorrelation procedure resulting in a 2-D probabilitydensity distribution which shows a peak.

in an application-specific manner, the accuracy ofMATLAB-based PIV software we considered for ourPIV analysis of motion in Martian soil.

3.3 Rotated Images

To test the accuracy of the PIV software we con-sidered using, we simulated circular motion in ouracquired PIV images used the PIV software in de-tecting this motion. First, an image of the soilin the test bed was taken (see above) through theglass using a pointand-shoot camera. The image wastaken through the glass to ensure that the image on

which the analysis was conducted correctly simulatedthe conditions under which eventual experiment willbe conducted. Also, the acquired images was con-verted to grayscale because PIV software works bestwith grayscale images since grayscale images ensurethat there is a higher contrast between the particles

Figure 9: The image after being rotated 36 degrees.

the software searches for and the rest of the fluid.Then, MATLAB scripts were used to rotate this im-age about its center, for one revolution, in incrementsof 6 degrees. At the end of this process, there was a

stack of 60 images tilted 6 degrees from the previousimage.

The MATLAB code that produced the series of im-ages is in the Appendix. The MATLAB option cropwas chosen over the MATLAB option loose for thecode because this ensures that the images that areproduced by imrotate are all equal in size. Althoughthe crop option crops the images after they are ro-tated, a square region inscribed in a circular regioninscribed in the original image can be used for theanalysis because it is never cropped out of the image.The square region is outlined in white in the image

below.Mathematically, the motion simulated by the pro-cess of rotating the images is circular motion with aconstant angular velocity. All the vectors shown inthe diagram above have known theoretical velocityvalues based on the MATLAB code shown in the Ap-pendix. The analysis was conducted by inputting theseries of images, 1 to 60, in pairs of 1-2, 2-3, 3-4 andso on, into three publicly available MATLAB-basedPIV software (matpiv, pivlab, fluere) and setting upthe parameters so that the software were measuringthe velocity at the same points as the theoreticallyderived ones. After this, the resulting vectors from

each software were plotted on the same image as thetheoretical vector to get a visual perception of theaccuracy of the software results. It is important tonote now that each vector field like that below is theproduct of applying PIV to a pair of images. Thevectors in green are the theoretical vectors and those

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Figure 10: Sample image showing vectors used for analy-sis.

in red are the experimental ones from one of the soft-ware. The analysis carried out was percentage errorfor each pair of vectors that lie in the white square inthe field below, sum of percentage errors in the white

square of each field of vectors (each field is the resultof an analysis of a pair of images by a PIV software),and the sum of all the sums derived for each vectorfield created by each software.

4 Results

4.1 MATPIV

Matpiv is a toolbox for PIV created by Kristian Sveenof the University of Cambridge [matpiv manual]. Asample of a matpivcommand for carrying out a PIV

analysis is this:The command above processes images

mpim1b.bmp and mpim1c.bmp using a 64 64kernel with 0% overlap between each processedsub-area. The number 0.0012 refers to the timeseparation between the images and single is an

Figure 11: Sample result from analysis.

option that specifies how many iterations (one inthis case) of cross-correlation should be carried outon the pair of images. The result consists of fourmatrices x, y, u and v which are measured in pixelsand pixels/second. We denote by x the matrix ofthe x-coordinates where the vectors are drawn (inthe center of each sub-area). We denote by y thematrix of the y-coordinates where the vectors aredrawn (in the center of each sub-area). The symbolsu and v are used to denote the x-components andy-components of the vectors calculated in eachsub-area. These results can be visualized with theMATLAB command quiver(x,y,u,v).

For this statistical analysis, the matpiv commandused was:

[ x , y , u , v ] = m a t p i v ( i m a ge 1 , i m a g e2

, 3 2 , 1 , 0 . 0 , s i n g l e ) ;

Based on this analysis, the following results wererecovered:where the sub-area coordinates refer to the sub-

areas that are in the white square discussed above.

After repeating the above process for the 59 vector

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Sample experimental values of x-component of velocitySub-Area Coordinates.

Sub-Area Coordinates 2 3 4 5 6 72 - 8. 21 16 3 - 8. 66 17 3 - 8. 73 04 3 -8 .4 82 26 36 81 - 8. 16 61 - 8. 34 83 33 - 5. 31 04 9 - 4. 84 56 - 4. 50 71 7 - 4. 67 53 09 2 - 5. 28 90 5 - 5. 06 49 44 - 1. 83 63 7 - 1. 62 80 4 - 1 .7 51 53 - 1 .8 01 00 78 77 - 1 .6 32 36 - 1. 81 91 55 1.616693 1.591556 1.464555 1.453186828 1.926127 1.8495096 4.924812 5.141235 5.017183 5.251215307 5.112303 5.3662897 8.199604 8.517288 8.517034 8.721054276 8.377348 8.159283

Sample experimental values ofy-component of velocity.

Sub-AreaCoordinates 2 3 4 5 6 72 8 .3 98 35 8 5.07 72 35 1 .7 32 08 3 -1 .6 53 06 -4.94 35 7 -8 .2 79 283 8 .2 74 31 5 4 .7 90 19 6 1 .3 18 84 7 -1.61 58 2 -5.21 65 -8.28 04 94 8 .5 44 50 4 4.79 65 86 1 .8 32 13 9 -1 .8 55 45 -5.15 18 3 -8 .4 31 215 8 .3 42 81 5 .1 44 72 5 1 .5 84 45 8 -1.84 38 7 -4.99 03 9 -8.25 07 66 8 .4 63 81 9 5 .0 87 71 4 1 .4 81 74 -1.68 68 3 -5.21 20 5 -8.29 54 87 8 .1 78 82 5 .1 31 27 8 1 .7 46 32 8 -1.74 05 5 -5.24 42 4 -8.43 49 6

Theoretical values ofx-component of velocity.

Sub-Area Coordinates 2 3 4 5 6 72 - 8. 37 75 8 - 8. 37 75 8 - 8. 37 75 8 - 8. 37 75 8 - 8.3 77 58 - 8 .3 77 583 - 5. 02 65 5 - 5. 02 65 5 - 5. 02 65 5 - 5. 02 65 5 - 5.0 26 55 - 5 .0 26 554 - 1. 67 55 2 - 1. 67 55 2 - 1. 67 55 2 - 1. 67 55 2 - 1.6 75 52 - 1 .6 75 525 1 .6 75 51 6 1 .6 75 51 6 1 .6 75 51 6 1 .6 75 51 6 1 .6 75 51 6 1 .6 75 51 66 5 .0 26 54 8 5 .0 26 54 8 5 .0 26 54 8 5 .0 26 54 8 5 .0 26 54 8 5 .0 26 54 87 8 .3 775 8 8 .377 58 8.3 7758 8.377 58 8.37 758 8 .3 775 8

Theoretical values ofy-component of velocity.

Sub-Area Coordinates 2 3 4 5 6 72 8 .3 77 58 5.02 65 48 1.67 55 16 -1.67 55 2 -5.02 65 5 -8.37 75 83 8 .3 77 58 5.02 65 48 1.67 55 16 -1.67 55 2 -5.02 65 5 -8.37 75 84 8 .3 77 58 5.02 65 48 1.67 55 16 -1.67 55 2 -5.02 65 5 -8.37 75 85 8 .3 77 58 5.02 65 48 1.67 55 16 -1.67 55 2 -5.02 65 5 -8.37 75 8

6 8 .3 77 58 5.02 65 48 1.67 55 16 -1.67 55 2 -5.02 65 5 -8.37 75 87 8 .3 77 58 5.02 65 48 1.67 55 16 -1.67 55 2 -5.02 65 5 -8.37 75 8

Percentage errors of x-component of velocities in fieldidentified above.

Sub-Area Coordinates 2 3 4 5 6 72 - 0.0 00 2 0 .0 00 33 9 0 .0 00 42 1 0 .0 00 12 5 -0 .0 00 25 - 3 .5 E- 053 0 .0 00 56 5 -0 .0 00 36 - 0 .0 01 03 - 0.0 00 7 0 .0 00 52 2 7 .6 4E -0 54 0 .0 00 96 - 0. 00 02 8 0. 00 04 54 0. 00 07 49 - 0. 00 02 6 0.0 00 85 75 - 0. 00 03 5 - 0. 00 05 - 0.0 01 26 - 0. 00 13 3 0 .0 01 49 6 0 .0 01 03 86 - 0.0 00 2 0 .0 00 22 8 -1 .9 E- 05 0 .0 00 44 7 0 .0 00 17 1 0 .0 00 67 67 - 0. 00 02 1 0. 00 01 67 0. 00 01 66 0 .0 00 41 - 2. 8E -0 7 - 0. 00 02 6

Percentage errors of y-component of velocities in fieldidentified above.

Sub-Area Coordinates 2 3 4 5 6 72 2 .4 8E -0 5 0. 00 01 01 0 .0 00 33 8 - 0. 00 01 3 - 0.0 00 17 - 0. 00 01 23 - 0. 00 01 2 - 0. 00 04 7 - 0.0 02 13 - 0. 00 03 6 0. 00 03 78 - 0. 00 01 24 0 .0 00 19 9 -0 .0 00 46 0 .0 00 93 5 0. 00 10 74 0 .0 00 24 9 6 .4 E- 055 - 4.2 E- 05 0 .0 00 23 5 -0 .0 00 54 0 .0 01 00 5 -7 .2 E-0 5 - 0. 00 01 56 0 .0 00 10 3 0. 00 01 22 - 0 .0 01 16 6 . 75 E- 05 0 .0 00 36 9 - 9.8 E- 057 - 0. 00 02 4 0 .0 00 20 8 0. 00 04 23 0 .0 00 38 8 0. 00 04 33 6 .8 5E -0 5

Figure 12: MATLAB surf plot of percentage errors fora typical matpiv vector field.

Sample experimental values ofx-component of velocity.

Sub-Area Coordinates 2 3 4 5 6 7

2 0.00 000 0.00 00 0 0.00 00 0 0.0 000 0 15.2 493 7 -7.97 2613 4.82 961 0.00 00 0 1 5.37 748 - 4.77 448 0 .0 00 00 -1.61 9234 8.26 11 81 0 .00 00 0 0.00 00 0 15 .144 9 - 6.87 25 3 0.0 00 005 0 .0 00 00 7 .4 77 85 4 - 4. 97 15 3 0 .0 00 00 1 .7 79 35 8 0.0 00 006 0.00 000 13 .0 44 7 0.00 00 0 12.68 63 4 0.0 00 00 - 14.6 7837 0.00 000 0.00 00 0 11.07 954 -2.25 074 0 .0 00 00 0 .0 00 00

fields produced by matpiv, the total percentage error

for the x-components of velocities produced by mat-pivwas found to be 0.2277 and the total percentageerror for the y-components of velocities produced bymatpivwas found to be 0.2328. This statistical anal-ysis was also carried out for the magnitudes of thevelocities and the angle (direction) of the velocities.

4.2 PIVLAB

Pivlab is another MATLAB-based PIV software thatwe proposed using. It comes with a GUI and wascreated by William Thielicke and Eize J. Stamhuis. It

has options in its interface to carry out a similar kindof analysis as matpiv and output results in a .matfile. The contents of the produced .mat file (x,y,u,v)was used to carry out the analysis in MATLAB in asimilar way as above.

The theoretical values are the same as identified

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Sub-Area Coordinates 2 3 4 5 6 72 0 .00 00 0 0. 00 00 0 0. 000 00 0. 000 00 - 11. 577 2 -9. 754 433 - 8. 01 02 0 .00 00 0 - 3. 57 61 - 1. 76 88 8 0. 00 000 9 .29 503 34 - 3. 99 83 0 .00 00 0 0. 000 00 1 5. 30 452 14 .97 41 4 0 .00 00 05 0 .00 00 0 1 3.9 337 4 1 2. 958 76 0. 000 00 - 4.2 010 8 0 .00 00 06 0 .00 00 0 -14 .55 19 0. 000 00 - 3. 66 65 6 0 .00 000 - 5. 138 467 0 .00 00 0 0 .00 00 0 7 .23 05 83 7. 163 633 0 .00 000 0 .00 00 0


Sub-Area Coordinates 2 3 4 5 6 72 -0.01 -0.01 -0.01 -0.01 -0.0282 -0.00048

3 -0.01961 -0.01 -0.04059 -0.0005 -0.01 -0.006784 -0.05931 -0.01 -0.01 -0.10039 0.031017 -0.015 -0.01 0.03463 -0.03967 -0.01 0.00062 -0.01

6 -0.01 0.015952 -0.01 0.015239 -0.01 -0.03927 -0.01 -0.01 0.003225 -0.01269 -0.01 -0.01

under MATPIV. Also, the zero values above arethe result of converting the NaN returned by pivlabto zero for the sake of the error calculations.

After repeating the above process for the 59 vectorfields produced by pivlab, the total percentage errorfor thex-components of velocities produced bypivlabwas found to be 19.6012 and the total percentage er-ror for the y-components of velocities produced bypivlabwas found to be 19.3999. This statistical anal-ysis was also carried out for the magnitudes of thevelocities and the angle (direction) of the velocities.

4.3 FluereFluere is the third MATLAB-based PIV software thatwe proposed using. It comes with a GUI and wascreated by Kyle Lynch. It has options in its interfaceto carry out a similar kind of analysis as matpiv andpivlab and output results in series of .dat files. Thecontents of the produced .dat files (x,y,u,v) was usedto carry out the analysis in MATLAB in a similar wayas above.

After repeating the above process for the 59 vector

Percentage errors of y-component of velocities in field

identified above Sub-Area Coordinates.


2 -0.01 -0.01 -0.01 -0.01 0.013032 0.0016433 -0.01956 -0.01 -0.03134 0.000557 -0.01 -0.02114 -0.01477 -0.01 -0.01 -0.10134 -0.03979 -0.01

5 -0.01 0.01772 0.067342 -0.01 -0.00164 -0.016 -0.01 -0.03895 -0.01 0.011883 -0.01 -0.003877 -0.01 -0.01 0.033154 -0.05275 -0.01 -0.01

Figure 13: MATLAB surf plot of percentage errors fora typical pivlab vector field.

Sample experimental values ofx-component of velocity.

Sub-Area Coordinates 2 3 4 5 6 72 - 2. 994 62 - 3. 925 4 - 4. 66 27 9 - 5. 17 047 - 5 .17 41 - 5. 20 043 -0.45 40 5 -2.12 05 8 -3 .9 48 11 -4.39 77 6 -4.74 46 5 -4 .8 42 814 0 .6 36 01 -0.22 35 9 -1 .5 20 12 -1.81 06 3 -1.72 64 3 -2.93 35 45 1 .74 26 6 1 .49 695 0 .9 96 216 1 .0 78 95 1. 439 09 0 .00 575 26 1.72815 1 .68268 1.7567 2.22117 3.17362 2.49337 2.03651 1 .78522 2.2365 2.82498 3.41779 3.7096



2 2 .4 90 51 1. 94 80 2 0 .9 90 23 0 .2 64 21 8 - 2. 60 79 5 - 4. 70 67 13 2.3307 2.23345 1.31027 -1.34655 - 4.48242 -4.5719

4 2 .4 43 11 2. 26 91 5 1 .5 10 04 - 1. 79 39 1 -4 .7 88 46 -4 .1 20 715 2 .2 87 15 2. 12 28 2 1 .3 95 24 - 1. 74 56 6 - 4. 57 70 4 - 4. 34 42

6 1 .9 63 53 1 .5 61 94 0 .7 68 39 2 - 1. 44 97 5 - 4. 29 57 2 -4 .6 39 037 1 .4 79 92 0 .9 72 09 0 .1 06 77 4 - 1. 24 52 5 - 3. 84 47 4 -4 .6 67 45



2 - 0. 00 64 3 -0 .0 05 31 -0 .0 04 43 - 0. 00 38 3 - 0. 00 38 2 - 0. 00 37 93 - 0. 00 91 - 0. 00 57 8 - 0.0 02 15 -0 .0 01 25 - 0. 00 05 6 -0 .0 00 374 - 0. 01 38 - 0. 00 86 7 - 0.0 00 93 0. 00 08 06 0. 00 03 04 0. 00 75 08

5 0 .0 00 40 1 -0 .0 01 07 - 0.0 04 05 - 0. 00 35 6 - 0. 00 14 1 - 0. 00 99 76 - 0. 00 65 6 -0 .0 06 65 -0 .0 06 51 - 0. 00 55 8 - 0. 00 36 9 - 0. 00 50 47 - 0. 00 75 7 -0 .0 07 87 -0 .0 07 33 - 0. 00 66 3 - 0. 00 59 2 - 0. 00 55 7

Percentage errors of y-component of velocities in field

identified above.Sub-Area Coordinate 2 3 4 5 6 7

2 -0.00 70 3 -0 .0 06 12 -0.00 40 9 -0 .0 11 58 -0 .0 04 81 -0.00 43 83 -0.00 72 2 -0 .0 05 56 -0.00 21 8 -0 .0 01 96 -0 .0 01 08 -0.00 45 44 -0.00 70 8 -0 .0 05 49 -0.00 09 9 0.00 07 07 -0.00 04 7 -0 .0 05 08

5 -0.00 72 7 -0 .0 05 78 -0.00 16 7 0.00 04 19 -0.00 08 9 -0 .0 04 816 -0.00 76 6 -0 .0 06 89 -0.00 54 1 -0 .0 01 35 -0 .0 01 45 -0.00 44 6

7 -0.00 82 3 -0 .0 08 07 -0.00 93 6 -0 .0 02 57 -0 .0 02 35 -0.00 44 3

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Figure 14: MATLAB surf plot of percentage errors fora typical fluere vector field.

fields produced by fluere, the total percentage errorfor thex-components of velocities produced by fluerewas found to be 10.8576 and the total percentageerror for the y-components of velocities produced byfluere was found to be 10.7915. This analysis wasalso carried out for the magnitudes of the velocitiesand the angle (direction) of the velocities.

5 Discussion

Based on these results, we chose matpivfor our anal-ysis of the motion. Recently, we have also begun totake a look at how the quality of our input images(image pre-processing) and the filtering tools avail-able for each software (vector post-processing) mayaffect these accuracy estimates. Also, there are de-fault or basic settings that are not common to allof the three software. We took this into considera-

tion in making decisions based on these results. Onelimitation of this project is that we cannot tell howimportant other choices like kernel size will affect theaccuracy results. Also we do not know if the fact thatit is a simple circular motion affects the accuracy ofthe error values.

6 Appendix

6.1 MATLABcodeusedtorotateim-ages

E = 1;

f or k = 1 :6 :3 60

f i g u r e ( 1 ) ;

A = i m r o t a t e ( i m r e a d ( i m g 1 ) , k ,

c r o p ) ;

i m w ri t e ( A , [ ro t - n u m 2s t r ( E

) . ti f ]) ;

E = E + 1 ;

en d

endMATLAB code for theoretical value of circular ve-

locity

dx = 32;

t x = [ 32 : d x: x ma x ];

t x = tx - x m ax / 2 ;

N x = l e ng th ( t x );

% y - d i m e n si o n

y ma x = 2 56 ;

dy = 32;

t y = [ 32 : d y: y ma x ];

t y = ty - y m ax / 2 ;

N y = l e ng th ( t y );% a n g ul a r v e l oc i t y

w = 6; % d e g / s e c

w = w * pi / 18 0; % r a d / s e c

% C re at e v el o ci ty f ie ld m a tr ic e s

v x = z er os ( Ny , N x ) ;

v y = z er os ( Ny , N x ) ;

% V = 1 ;

f or i = 1: Nx

f o r k = 1 : N y

r = s q rt ( t x ( i ) . ^ 2+ t y ( k ) . ^ 2) ; %

radius

V = w * r ;

v x (k , i ) = - V *t y (k ) / r;v y (k , i ) = V * tx ( i )/ r ;

en d

end

[ x x , y y ] = m e s hg r i d ( t x + x ma x / 2 , t y + y ma x

/ 2 ) ;

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q u i v e r ( x x ( 1 : 1 : e n d ) , y y ( 1 : 1 : e n d ) , v x

( 1 : 1 : e n d ) , v y ( 1 : 1 : e n d ) ) ;

References

[1] Keane, Richard D., and Ronald J. Adrian. The-ory of Cross-Correlation Analysis of PIV Images.Applied Scientific Research (1992): 1-25. Print.

[2] Muthanna, Chittiapaa. Particle Image Ve-locimetry. (2006): 1-63. Web. July 2011.

[3] Adrian, R. J., and J. Westerweel. Particle ImageVelocimetry. New York: Cambridge UP, 2011. 1-36. Print.

[4] Hu H., T. Kobayashi, K. Okamoto, and N.Taniguchi. Evaluation of the Cross CorrelationMethod by Using PIV Standard Images. The Vi-sualization Society of Japan and Ohmsha: Jour-nal of Visualization 1st ser. 1 (1998): 1-8. Print.

[5] Hart, Douglas P. The Elimination of Correla-tion Errors in PIV Processing. 9th InternationalSymposium on Applications of Laser Techniquesto Fluid Mechanics (1998): 1-8. Print.

[6] Stamhuis, Eize J. Basics and Principles of Par-ticle Image Velocimetry (PIV) for Mapping Bio-

genic and Biologically Relevant Flows. AquaticEcology (2006): 1-17. Print.

[7] Raffel, Markus, Christian Willert, Jurgen Kom-penhans, and Steve Wereley. Image EvaluationMethods for PIV. Particle Image Velocimetry: aPractical Guide. Heidelberg: Springer, 2007. 123-76. Print.

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