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1. 100 T T T T T T T T T S y semimajor 3P 9 x semimajor 3P Average Elliptic True Elliptic 5 ui 13 L lt 50 L i 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 1 Axis Ratio Figure 3 7 Theoretical Percent Error for 3 Point Gaussian Averaged Elliptic and True Elliptic Sizing Methods The above results show that the averaged elliptic sizing method in theory reduces the error in the measurement by 5 to 10 times maxing at 12 5 percent at an eccentricity of 0 866 and an axis ratio of 0 5 It is also interesting to note that the averaged elliptic sizing method exhibits the same error whether the x axis is the semimajor axis or the semiminor axis Therefore the true elliptic and averaged elliptic sizing methods exhibit the ability to correct for non spherical particles within a flowfield while the conventional 3 point Gaussian exhibits an error that diverges greatly with eccentricity However the theoretical calculations presented above do not account for the error introduced by pixel discretization Future work in this area will include Monte Carlo Simulations of the elliptical sizing algorithm and its performance comparison to traditional Gaussian particle sizing methodologies 3 3 2 Experimental Analysis Monte Carlo Simulations were used in order to characterize the performance of the elliptical sizing method on simulated PIV data A total of 5000 images were generat
2. iii 8 FIGURE 1 7 SECOND ORDER DISCRETE WINDOW OFFSET PIV ri 9 FIGURE 2 1 ESM FLUID MECHANICS LABORATORY DPIV SYSTEM rie 20 FIGURE 2 2 EXPERIMENTAL SETUP FOR THE SPRAY PIV AND PDPA EXPERIMENT 23 FIGURE 2 3 EXAMPLE DIGITAL PARTICLE IMAGE VELOCIMETRY SPRAY DATA OMM PLANE 25 FIGURE 2 4 FULL RESULTS FOR ALL SIZING METHODS AND PDA OMM PLANE 27 FIGURE 2 5 RESULTS FOR ALL SIZING METHODS AND PDA 100 TO 150 MICRONS OMM PLANE datati cli dls des ii id o rio ki Peo doll Delo alien DLE le 28 FIGURE 2 6 HISTOGRAM RESULTS FOR 4MM SPRAY PLANE ALL SIZING METHODS 29 FIGURE 2 7 HISTOGRAM RESULTS FOR 4MM SPRAY PLANE ALL SIZING METHODS 30 FIGURE 2 8 HISTOGRAM RESULTS FOR 8MM SPRAY PLANE ALL SIZING METHODS 31 FIGURE 2 9 PLANE AVERAGED HISTOGRAM RESULTS FOR ALL PIV SIZING METHODG 32 FIGURE 2 10 PLANE AVERAGED RESULTS FOR 3 POINT GAUSSIAN METHOD AND PDA 33 TABLE 2 1 PARTICLE POPULATION FOR EACH METHOD OMM PLANE 34 TABLE 2 2 PARTICLE POPULATION FOR EACH METHOD OMM PLANE ii 34 FIGURE 2 11 CORRELATION COEFFICIENT VS PLANE FOR CONVENTIONAL SIZING METHODS 35 FIGURE 2 12 3 D ISOSURFACE PLOT OF AVERAGE DIAMETER 36 FIGURE 2 13 CORRESPONDING SLICE HEIGHT IN 3 D 37 FIGURE 2 14 PDA AND 3 POINT GAUSSIAN PIV
3. Sizing Method Particle Average Total Success Rate Population Successes Per Number of Number of Frame Particle Successes Detected 3 point Gaussian 554 497 34 7 556 111 99 71 4 point Gaussian 107 868 6 7 556 111 19 40 4 point Continuous 17 726 1 1 556 111 3 187 Continuous Least 21 187 1 3 556 111 3 810 Squares Table 2 1 Particle Population for Each Method 0mm Plane Table 2 2 below shows the correlation coefficient for each of the methods in tabulated form Figure 2 11 shows the results in Table 2 2 in graphical form Correlation Coefficient for Each Plane Each Sizing Method Plane mm 3 point 4 point 4 mod Isvl 8 0 9699 0 7605 0 1798 0 306 4 0 9761 0 5558 0 1957 0 5496 0 0 9571 0 7916 0 413 0 4144 4 0 9728 0 8904 0 6692 0 5745 8 0 9697 0 9642 0 6892 0 3265 Plane Averaged 0 9728 0 8915 0 5658 0 5883 Table 2 2 Particle Population for Each Method Omm Plane The results from Tables 2 1 and 2 2 along with Figure 2 11 show that only the 3 point method succeeds at a reliable rate above 99 percent and exhibits a high value of the correlation coefficient when compared to the PDA measurement over a diameter range from 100 to 150 microns The other conventional sizing methods did not perform adequately in this experiment exhibiting success rates ranging from 3 to 20 percent The other methods also exhibited low values for the correlation coefficient throughout the planes
4. lt ipm gt Name MAX Method Max Image1 2 Output Dir C Program Files Aeroprobi Ext lt fipm gt Figure 4 2 Added Preprocessing Tasks Editing Task Properties When a task is highlighted as Max is in Figure 4 2 above the properties of the task will be displayed in the lower left window as shown In order to edit these properties click on the desired task to highlight the task Then right click on the highlighted task and click Properties The corresponding dialog box will appear depending on the selected task Enter the desired properties and click OK You may also define the output directory for each task in the dialog box for the Image Math tasks Removing Image Math Tasks There are two ways to remove image mathematics tasks in FLOW IQ V2 2 as a group or individually To remove several image mathematics tasks from the active project click on Image Math in the upper left window Image Math should now be highlighted 121 Now right click on Image Math and click on Remove Image Math Tasks The Image Math Remove Tasks Dialog Box will appear as shown below in Figure 4 3 Remove Tasks xi Remove Cancel Figure 4 3 Removing Preprocessing Tasks To remove a task highlight the task by clicking on the task and click on REMOVE This will remove the task from the list When undesired tasks have been eliminated click on OK and the image math tree will be updated acco
5. A new tracking algorithm of PIV and removal of spurious vectors using Delaunay tessellation Exp Fluids 26 pp 371 80 Stark H and Woods JW 1994 Probability Random Processes and Estimation Theory for Engineers 2 ed Prentice Hall Upper Saddle River NJ Scarano F and Rieuthmuller M L 1999 Iterative multigrid approach in PIV image processing with discrete window offset Experiments in Fluids 26 513 523 Udrea D Bryanston Cross P Lee W Funes Gallanzi M 1996 Two sub pixel processing algorithms for high accuracy particle centre estimation in low seeding density particle image velocimetry Oprics amp Laser Technology Vol 28 no 5 Wereley ST Meinhart CD 2001 Second order accurate particle image velocimetry Experiments in Fluids 31 258 268 Westerweel J 1997 Fundamentals of particle image velocimetry Meas Sci amp Technol 8 pp 1379 1392 Westerweel J 1993a Digital Particle Image Velocimetry Theory and Application Delft University Press Westerweel J 1993b Optical Diagnostics in fluid and thermal flow SPIE 2005 624 35 Willert C E Gharib M 1991 Digital particle image velocimetry Exp in Fluids 10 pp 181 193 187 VITA Jason Bradley Carneal was born in Richmond Virginia on July 20 1979 He enjoyed a happy upbringing due to the generosity and kindness of his parents James H and Joan G Catneal and his grandparents who lived next door He lived i
6. Public members char Dir MAX_FN_ SIZE location of files 166 char BaseFileName MAX_FN_SIZE base name of files unsigned int StartIndex index of the first file unsigned int EndIndex index of the last file unsigned int Precision i e for spray0000 tif Precision 4 char Ext 8 file extension static const char id the beginning character of the info for a FileSequence object fs ToString 2 Image Preprocessing Module e Class Image It is responsible for reading writing image from a file and storing pixels This class is a wrapper about class CxImage Except raw image file read write and draw operations are delegated to the CxImage object Operations 1 Read image Image img test bmp 2 Write image Img Save testl bmp 3 Fork is used to clone the image then you can do image processing operation on the cloned image In this way original image is not affected Note don t forget to do this operation before do any image processing 4 Join false is used to update the original image using the cloned image then delete it Join true is used to merge the cloned image and original image and forget the change 5 Access the pixel matrix img Pixel 6 Get the image full path img GetID 7 Get image type img GetType 8 Get dimension img GetHeight img GetWidth 9 Test if a file is supported image file img IsSupportedImage 10 Draw the image img D
7. parameter s determines the skewness of this distribution The parameters and u can be manipulated to simulate particles of larger diameter This probability density function allows the simulation of particles that exhibit noncircular or skewed profiles 68 Rayleigh Distribution sigy 0 20 muy 0 00 s 6 00 o iy a Probability Density pe e n N e o a 20 Figure 3 16 Log Normal Surface Plot for 0 20 u 0 00 s 6 00 Rayleigh Distribution sigy 0 20 muy 0 00 s 6 00 Figure 3 17 Log Normal Contour Plot for 6 0 20 u 0 00 s 6 00 These probability density functions approximate the shape of a streaked particle and therefore may be of use in data recovery and high speed flow experiments Future work should also include 69 the application of the elliptical sizing technique to the other methods including the four point Gaussian continuous four point Gaussian and least squares sizing methods 3 5 Summary of Original Contribution In this Chapter the major original contribution is the development of a Gaussian particle sizing method that is not limited to spherical particles The method was confirmed with initial experimental Monte Carlo simulations The potential of this method is apparent from the theoretical and experimental analysis presented in this chapter The work on the development of the elliptical sizing method opens a door for the application of the sizing m
8. 0 03 0 02 0 01 F I 0 5 0 4 0 3 0 2 0 1 0 0 1 0 2 0 3 0 4 0 5 Displacement px Total Error T T T T T T T e Ultimate DPIV NDWO 4 DPIV FODWO DPIV SODWO Error px o o o T 0 04 0 02 I I I 0 5 0 4 0 3 0 2 0 1 0 0 1 0 2 0 3 0 4 0 5 Displacement px 0 1 1 1 Figure 5 1 Mean RMS and Total Errors for Ultimate and Flow IQ v2 2 NDWO and FODWO Figure 5 1 shows that the mean error for Flow IQ v2 2 is approximately 28 higher than the error for the ultimate code at a displacement of 0 5 pixels and the total error for the Flow IQ v2 2 program is approximately 20 higher than the ultimate code The RMS errors are approximately 179 equal for all of the cases in Figure 5 1 All of the Flow IQ v2 2 methods performed the same with no window offset which means that the first pass in each method is consistent 5 2 1 2 Vortex Results The results for a 3 0 maximum displacement vortex in the x and y direction for the First Order Discrete Window Offset Second Order Discrete Window Offset and No Discrete Window Offset are shown below in Figures 5 2 to 5 4 The algorithms used to obtain these results utilized a 16 pixel square first pass and an 8 pixel second pass when applicable The PIV algorithms analyzed in this section are the available algorithms in Flow IQ v2 2 Figures 5 2 to 5 4 are included here as a proof of concept for the n
9. 2 Read velocity vectors reader ReadAll pivrs where pivrs is a PIVResults object If the file is not in correct format this function returns false As a user check the return value to make sure reading is completed successfully e Class PIVResult This class models a velocity vector Public members enum INVALID 1 PARTIAL_VALID 0 VALID 1 INVALID the vector is invalid PARTIAL_VALID the vector is not validated yet VALID the vector is validated and valid double X X coordinate of position double Y Y corrdinate of position double U U component of velocity vector double V V component of velocity vector double W W component of velocity vector int Wsx window size in x int Wsy window size in y 172 double Ncc normalized cross correlation int Valid validity flag int Boundary boundary flag e Class PIV Results This class models a velocity vector matrix Public members std vector lt PIVResult gt velocities velocity matrix in vector format unsigned long nl number of row of velocity matrix unsigned long nJ number of row of velocity matrix int width image width int height image height e Class PIVTask Visitor The base class for PIV task visitors e Class PivValidation This class defines the interface for validation task Operations 1 Validate a velocity vector matrix pivv Run pivrs where pivv is a PivValidation object pivrs is a PIVResults object 2 Accept a visitor task A
10. 93 Median Task acts atico daa 124 Mean Tas e a le de dnd 124 STD Lask ini a 124 MADIISE ei ng GO A A A ae esau aie 124 Addi Phe Tei O 124 Subtract Task rd da ia bad 125 Andak A i i il e 125 A O serie edna a tee ela E eee 126 Chapter 5 Particle Sizing Task ss 127 Adding Particle Sizing Task is 127 Editing Task Proporta E e E E E 128 Removing Particle Sizing Tas ass 129 Running Particle Sizim Pass ii lei aio EE 130 Nomenclature for Fitting Schemes siii IERI 131 Centroid A E RS eh EE lei 131 Three Point A E EE A E E E sw daa pen NG 132 Four P t Gaussian Fits collana 132 TES ASUS OU ANC SN inoue Seite tn casts e one Deco el a 134 Modified Continuous Four Point Gaussian Fit i 135 A A RRE 135 Hierarchical Fit cadets lello 135 Chapter 6 Particle Image Velocimetry PIV Tasks 137 a TASKS A lea non 137 Editing Task Properties alia zi 138 Removin A ascii 138 Running PIV Task iii adi 139 No Discrete Window Offset DWO PIV i 140 RESCINDIR 142 Second Order DWO PIV acid lire adi 144 Hybrid PIV ici tes 145 CUATE VO o da 146 Adding Validation AAA A A 146 Editing Task Properties siii a ida isa arri 147 Removing Validation Task ii A Aid 147 Running Validation Task AR 148 3X3 PIV Validation A A a oats 149 Chapiers Sieteo PIV Lasks ds 151 Adding Stereo PIV TASKS uan tl diia nadie 151 Editing Task PLOT e 152 Removins 5 TEREGO PlV Task 152 Running Stereo PIV Tasks cuisine danna iii 1
11. In order to account for multiply counted particles in the histogram particle tracking was run on the complete set of images and tracked particles were removed to produce the compensated DPIV histograms These histograms were compared to PDA data over various diameter ranges in order to quantify the performance of DPIV sizing techniques with respect to 25 traditional particle sizing techniques All histograms were normalized with the total particle population in order to produce probability density functions pdf s for analysis 2 3 2 Average diameter Analysis In order to calculate the average diameter in the DPIV data a volume was constructed with user definable resolution The volume was constructed such that the z component moved across planes of data with the x and y direction in the plane of the DPIV data The output from each method was scanned and each particle was added to a region of the volume If the x and y position of a particle was in a particular region the average diameter was updated assuming the particle to be a perfect sphere 2 4 Particle Sizing Results This section presents the results for the traditional sizing algorithms used in this experiment and their histogram comparison to PDA measurements and the average diameter analysis performed in this work 2 4 1 Full Range Results The full theoretical range of the PIV sizing methods extends to less than one pixel diameter However at these low diameters t
12. about 40 microns higher than the PDA measurement in the center of the spray On the outer edge of the analyzed domain the values are approximately 10 to 20 percent higher than the PDA measurement This discrepancy can be explained by the design of the experiment which did not allow the PIV system to detect particles smaller than 2 pixels The previous histogram analysis shows that the 3 point Gaussian method detects no particles below the 44 micron range Therefore the average diameter detected by the 3 point Gaussian cannot be less than 44 pixels On the other hand the PDA can resolve down to 1 4 microns in diameter The PDA measurement accounts for all particles above 2 microns in diameter while the PIV system used in 37 this experiment could only resolve 24 micron particles or greater The mismatch between the resolvable diameters results in the discrepancy between the two systems The units in Figure 2 14 are average diameter in microns Figure 2 14 shows that the 3 point Gaussian fit overestimates the average diameter in comparison to the PDA measurement In the matching ranges the PDA reaches a maximum level of 40 microns The PIV values do not drop below 50 microns Therefore the PIV error ranges from 25 of the PDA to around 1000 in the center of the flow The reason for this discrepancy again is the inability of the PIV 3 point method to resolve diameters below 25 microns in diameter Even though a population of 25 micron particle
13. center estimators and the achievagble measurement density for particle tracking velocimetry Experiments in Fluids 29 2000 Nishino K Kato H Torii K Stereo imaging for simultaneous measurement of size and velocity of particles in dispersed two phase flow Meas Sci Tech 11 pp 633 645 2000 Powell M J D A Fortran Subroutine for Solving Systems of Nonlinear Algebraic Equations Numerical Methods for Nonlinear Algebraic Equations P Rabinowitz ed Ch 7 1970 Sakakibara J Wicker R B Eaton J K Measurements of the particle fluid Velocity Correlation and the Extra Dissipation in a Round Jet Int J Multiphase Flow 22 pp 863 881 1996 Udrea D Bryanston Cross P Lee W Funes Gallanzi M Two sub pixel processing algorithms for high accuracy particle centre estimation in low seeding density particle image velocimetry Optics amp Laser Technology Vol 28 no 5 1996 Wang X S Wu X P Liao G X Wei Y X Qin J Characterization of a water mist based on digital particle images Experiments in Fluids 33 2002 Willert C E Gharib M Experiments in Fluids 10 pp 181 1991 176 5 2 Test Bed for DPIV Software Methods Artificial and real PIV data were gathered and tested using the DPIV version 2 2 software Eleven sets of 50 256X256 pixel uniform displacement images were generated using the existing software for image generation The uniform displacement images ranged in displacement from 0 5 pi
14. generate an initial predictor of the velocity field On the subsequent passes the size of the interrogation window is dynamically allocated based on the results from the previous step Scarano amp Rieuthmuller 1999 as shown by figure 1 5 Figure 1 5 Traditional Multigrid Method Each initial window is broken down into several windows The size of the consecutive windows depends on the velocity obtained from the first pass 1 2 4 Discrete Window Offset The window offset feature introduced by Westerweel 1997 represented a real breakthrough in DPIV This feature significantly improves the accuracy of the DPIV method Using the first estimate obtained from the initial DPIV pass a second pass is applied by shifting the interrogation window in the second image by the rounded displacement found during the first pass The first 7 pass is subject to particles going in and out of the interrogation area while the second pass dramatically reduces this effect as illustrated by the Figure 1 6 This process is known as First Order Discrete Window Offset DPIV The second cross correlation pass after shifting the second image interrogation window by the previously estimated displacement provides a more accurate velocity evaluation Abiven and Vlachos 2002 First Order DWO PIV First Image Second Image Region 1 Region 2 Initial Pass Region 1 Region 2 Refining Passes Figure 1 6 First Order Discrete Wi
15. positions until you are satisfied with the order of operations 151 Editing Task Properties When a task is highlighted the properties of the task will be displayed in the lower left window In order to edit these properties click on the desired task to highlight the task Then right click on the highlighted task and click Properties The corresponding dialog box will appear depending on the selected task Enter the desired properties and click OK The individual properties are discussed below in detail for each STEREO PIV technique Removing STEREO PIV Tasks There are two ways to remove STEREO PIV tasks in FLOW IQ V2 2 as a group or individually To remove several sizing tasks from the active project click on STEREO PIV in the upper left window STEREO PIV should now be highlighted Now right click on STEREO PIV and click on Remove STEREO PIV Tasks The STEREO PIV Remove Tasks Dialog Box will appear as shown below in Figure 8 2 Remove Tasks A x Basic Stero PI Remove Cancel Figure 8 2 Removing Stereo PIV Tasks To remove a task highlight the task by clicking on the task and click on REMOVE This will remove the task from the list When undesired tasks have been eliminated click on OK and the preprocessing tree will be updated accordingly To remove individual Stereo PIV tasks click on the task to be removed The task should now be highlighted Now right click on the task to
16. return the result from the second method Operations 1 Get the last method id hrkpzm GetLastMethodID 2 Set the last method id hrkpzm SetLastMethodID e Class NonlinearEquation It gives the nonlinear equation specification Operation 1 Evaluate nonlinear equations f gt eval where is f is a pointer to a NonlinearEquation or its derived type object 170 e Class LMfunc It gives the least square function specification Operation 1 Evaluate least square functions f gt eval where is f is a pointer to a LMfunc or its derived type object e Class FourPointGaussFitEquation It specifies the nonlinear equations for four points gauss fit method It is derived from class NonlinearEquation e Class LMParticleSizing It specifies nonlinear least squares functions It is derived from class LMfunc e Class LabelConnectedComponent It is used to label connected components in a binary image Operations 8 Label the input image Icc doLabel img where lcc is a LabelConnectedComponent object 9 Get the number of labels Icc getNumberOfLabels 4 PIV Module e Class CPIV This class is the base for other PIV classes As an abstract class it cannot be instantiated It defines the PIV interface Operations 1 Get velocity vector piv Run imagel image2 results where imagel and image2 are consecutive images results are the returned velocity vector 2 Accept a visitor task Accept aVisitor 3 Reset the task s
17. 0 5882 respectively for this plane 2 4 2 Limited Range Results The sizing algorithms used in this portion of the experiment were the three point Gaussian four point Gaussian four point continuous and continuous least squares algorithms Histogram results for each plane were generated as well as an average histogram results for all of the combined planes Figure 2 5 below shows the single plane results for each method in the Omm plane which is located in the direct center of the spray The PDA results are also shown below in Figure 2 5 21 Probability Density Functions for All Methods Plane Omm T 0 25 T T T T T T T PDA 3 Point 4 4 Point Pe Cont 4 Cont LS 0 2 o a a T Normalized Probability Density e T 0 05 0 I li fi I 100 105 110 115 120 125 130 135 140 145 150 Diameter um Figure 2 5 Results for All Sizing Methods and BDA 100 to 150 microns Omm Plane The results in Figure 2 5 show that the histogram for the three point Gaussian method matches best with the PDA measurements in the range from 100 microns to 150 microns This range corresponds to approximately 4 2 to 6 25 pixels diameter in consideration of the overall magnification factor of 24 microns per pixel The three point Gaussian method follows the PDA trend closely exhibiting a correlation coefficient of 0 9571 The four point Gaussian and continuous four point Gaussian algorithms
18. 02 4 ua L sali a 1 nd di 0 15 0 2 0 25 0 3 0 35 0 4 0 45 0 5 Centerline Displacement px Figure 4 5 Wall Shear Error Compared to Uniform Displacement Etror Figure 4 5 shows that the error for the shear flows studied in this work are much higher than the error associated with uniform displacement The errors for uniform displacement agree with the error reported by Huang et al 1997 Therefore the introduction of velocity gradients into a flow significantly increases the error associated with DPIV velocity measurements 77 4 3 1 2 Tracking Results The artificial images used in the above analyses were also processed using the Hybrid Particle Tracking Velocimetry routine available in Flow IQ v2 2 Unlike the PIV results the tracking results produce a continuous velocity field The errors at each y location were computed from the output of the Hybrid PTV algorithm The shear rates analyzed were 0 025 0 050 0 075 0 100 and 0 125 pixels per pixel The total number of particles successfully tracked for each shear rate is listed below in Table 4 1 These results were obtained using a starting interrogation window of 16 which yielded approximately 5 to 6 particles per interrogation window Shear Rate px px Number of Particles Tracked per 100 frames 0 025 7068 0 050 4017 0 075 2748 0 100 1952 0 125 1667 Table 4 1 Tracked Particle Populations for Each Shear Rate The 16 starting interrog
19. 1 00 4 3 4 4 3 2 a o 1 2 3 4 Figure 3 2 Jointly Gaussian IIRV s with 0 O For a circular particle Brady et al showed that for circular particles O and O are given by the following equations Ina _ Ina Xina Ina 2Ina Eq 3 3 pp Aaa Es 24 Ina Ina 2Ina 2_ Ina na x si Xoni Xo E Eq 3 5 d y20 2 Eq 3 6 Soto _ aa a 10 Eq 3 7 49 Where a and a are the intensities at the center pixel and the pixel to the right of the center pixel x and x are the pixel positions of the center and right pixel x and x are the pixel positions of the center and right pixel respectively and d is the estimated diameter of the particle For an elliptical particle the above equations are reduced to the following equations for G O b and where b and c are the semimajor and semiminor axes dc lna ana ads Quo ir z Xoi ay as Ina Ina y xi vo Eq 3 9 3 Oyo T Ye Yor T Ye b 420 Eq 3 10 c 20 Eg 3 11 Figure 3 3 below shows some example plots of jointly Gaussian i i r v s with various values of and Using these equations elliptical particles can be accurately sized This distribution can be used to size particles that do not exhibit a circular shape such as elliptical droplets streaked particles particles detected in regions of high background noise or non symmetric cross correlation
20. 3 9 and 3 10 agree with previous results obtained by Brady et al 2002 in their study of the 3 point Gaussian sizing scheme Since the zero eccentricity case has been established the performance of the various sizing methods ate explored in the following paragraphs There are several ways to present the error analysis in this section The first approach used to determine the errors associated with the diameter measurement was to calculate the error in the x and y diameters For the 3 point Gaussian fit the x diameter is the only calculated diameter and therefore this diameter is used as a comparison to the actual y diameter in this simulation The averaged elliptic method assumes a spherical shape with the average of the diameter in the two directions Therefore for the averaged elliptic method the average diameter was compared to the actual diameter in the x and y directions For the true elliptic fit the corresponding diameters were compared The results from this analysis are shown below in Figure 3 11 and 3 12 The same procedure for Figures 3 9 and 3 10 were used to generate these graphs Figure 3 11 shows the comparative absolute and percentage error in the x and y diameter measurements versus x diameter and Figure 3 12 shows the comparative errors in the x and y diameter measurements versus eccentricity For the images used to obtain these results the x diameter was chosen at random in a range from 2 8 to 5 6 pixels in diameter The y diam
21. 4 Removing Particle Sizing Tasks To remove a task highlight the task by clicking on the task and click on REMOVE This will remove the task from the list When undesired tasks have been eliminated click on OK and the preprocessing tree will be updated accordingly To remove individual particle sizing tasks click on the task to be removed The task should now be highlighted Now right click on the task to be removed and click on Remove The task will be deleted from the Particle Sizing Tree Running Particle Sizing Tasks There are two ways to run particle sizing tasks in FLOW IQ V2 2 as a group or individually To run all of the listed particle sizing tasks in the tree click on Particle Sizing in the upper left window Particle Sizing should now be highlighted Now right click on Particle Sizing and click on Run Task s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data This will run the specified particle sizing tasks on the selected images in the project 130 In order to run individual particle sizing tasks click on the desired task The task should now be highlighted Now right click on the task to be removed and click on Run T
22. 67 um with probe volume dimensions of approximately 250 um in all directions The PDA receiver probe was configured for a maximum particle diameter of 147 um A refractive index of n 1 334 was assumed for the water spray droplets Sampling at a point was performed for 60 seconds or 100 000 particle counts The average data rate in the core of the spray was approximately 1 kHz this rate decreasing as the probe volume interrogated the edges of the spray Autocorrelations at various points in the spray near the core gave an integral time scale of approximately 2 5 ms Consequently the statistical uncertainty of the mean PDA data velocity and particle size was estimated at less than 1 The signal processor used FFT technology to determine the velocity and phase difference Three detectors were used to extend the diameter range without compromising resolution The resolution of the system was 16 bits on the selected bandwidth typically 3 75 MHz thus yielding negligible velocity and phase resolution uncertainty The location of the PDA probe volume was fixed in space while the spray was traversed relative to it so that measurement data can be obtained over several points along a cross plane located approximately 15 mm from the nozzle A total of 189 measurement points within a plane approximately 15mm above the spray with a total sampling time of 1min were acquired 21 Figure 2 below shows a the experimental setup employed in
23. 9 Remove tasks Basic Thresholdina Dynamic Thresholding Histogram Thresholding Median Thresholding Blur Smooth AGW Binarize Area Smooth 3x3 Remove Cancel Figure 2 9 Typical Remove Tasks Dialog Box To remove a task highlight the task by clicking on the task and click on REMOVE This will remove the task from the list When undesired tasks have been eliminated click on 106 OK and the tree in the task folder will be updated accordingly A detailed procedure for deleting tasks is presented in each chapter for the specific type of task To remove individual click on the task to be removed The task should now be highlighted Now right click on the task to be removed and click on Remove The task will be deleted from the project Running Tasks There are two ways to run tasks in FLOW IQ 2 2 as a group or individually To run all of the listed tasks in a tree click on the folder containing the tree in the upper left window The folder should now be highlighted Now right click on the folder and highlight Run Tasks on A submenu will appear that lists all of the available input packages Click on the input package you wish to run the task on This process is illustrated below in Figure 2 10 The Run message will vary with the type of task performed and specific properties of each type of task are presented in the following chapters In order to run individual tasks click on the desired task The
24. By X4 Ya Ya X2 Y3 Y4 X3 Y4 Y2 Ba X4 Y3 Y1 FX Y Ya X Y 4 Y 3 Bs X YY 2 X Yo Ya FX 2 Y 4 Y 1 By X3 Y2 Ya X Y Y 3 X Y3 Y2 se In a o In a a In a3 az In a a 5 i 2 In a P In a B In a3 B3 In a B4 _ In a y In as Ys In a3 Y3 In a Y4 6 2 In a B In a B In a3 B3 In a B4 o x4 x H Ya y3 x3 x Ya y 7 2 In a3 In a It is interesting to note that if any three points used in the four point fit are the same as the ones used in the three point fit for the x axis then the solution to x Equation 6 reduces to the three point estimator Equation 3 and similarly for the y axis It is also important to emphasize that the points selected for the four point Gaussian estimation are not arbitrary and do not always yield a unique solution The topology of the chosen points is paramount for the accuracy of the methodology and is determined by two additional 133 conditions The first condition depends upon the pixel coordinates x y only and is independent of the intensities Assuming that the previously stated requirement of unsaturated pixels is satisfied by observation of equations 5 and 6 it is obvious that if the denominators of x and y go to zero a solution cannot be determined It is possible to have the entire sum in the denominator go to zero but each term in the sum is independent and that solution is trivial Therefore each term must individually
25. Get the address of a row m GetRowAddr 2 This operation is provided for efficiency Use it only to get values of the row elements 24 Element by element matrix multiplication Matrix lt double gt x 2 2 y 2 2 x DotMultiply y result is saved to matrix x Matrix lt double gt z xy result is saved to matrix zZ 25 Treat a matrix as one dimension array Matrix lt double gt x 2 2 Then x 0 is the same as x 0 0 x 1 is the same as x 0 1 transpose ml m2 m3 e Class RealMatrix lt T gt The class is a wrapper of class Matrix lt T gt It only accepts Matrix lt T gt where T is real type So it will not work properly if user passes it a std complex matrix Operations 1 Creation RealMatrix lt double gt rm m where m is Matrix lt double gt 2 Matrix norm rm Norm 3 Matrix mean rm Mean 4 Matrix standard deviation rm StdDev 5 Find the max value rm Max 6 Find the min value rm min 7 Find the max value and return its indices rm Max rowIndex colIndex 8 Find the min value and return its indices rm Min rowIndex colIndex 9 Convert to a rounded matrix Matrix lt int gt rounded rm Round 162 10 Convert to a double type matrix Matrix lt double gt d rm ToDouble 11 Count the number of elements whose values greater than or equal to some value rm CountGEs 20 0 12 Count the number of elements whose values less than or equal to some value rm CountLEs 2 0 13 Set the e
26. Monte Carlo Simulations Eccentricity 0 All Points 0 2 Trad 3 point Averaged Elliptic 0 18 True Elliptic 0 16 0 14 o a N Absolute Error 0 04 0 02 2 5 a a 4 45 5 5 5 6 Diameter Monte Carlo Simulations Eccentricity 0 All Data Points 8 Trad 3 point Averaged Elliptic 7 True Elliptic 6 e 4 5 4 fl g uw 3 2L il I 1t al 25 3 325 4 45 5 55 6 Diameter Figure 3 9 All Data Points for Eccentricity 0 Diameter range 2 8 to 5 6 pixels 58 Absolute Error Monte Carlo Simulations Eccentricity 0 0 2 T T T T I Trad 3 point Averaged Elliptic True Elliptic 0 18 0 16 N kS 0 14 ES 0 12 Ra N la PS ta 0 1 da 0 08 So LI Xx no a 0 04 1 1 2 5 3 3 5 4 4 5 5 Diameter Monte Carlo Simulations Eccentricity 0 7 T T T T I Trad 3 point Averaged Elliptic True Elliptic 6 lo E SL N po ab Error w T 4 0 I L I I I 2 5 3 3 5 4 45 5 Diameter Figure 3 10 Averaged Total Error over 250 points Eccentricity 0 59 Figures 3 9 and 3 10 above show that the 3 point Gaussian averaged elliptic and true elliptic sizing methods perform with a correlation coefficient of 1 00 The correlation coefficient is unity between all of the methods for the case of no eccentricity The absolute and percent error shown in Figures
27. agreement will appear After reading through the license agreement click on NEXT The following dialog box will appear User Information x Type your name below You must also type the name of the company you work for and the product serial number Name s tu Dent Company virginia Teh Serial x221 3323 6794 Enter your name company and serial number provided with your copy of FLOW IQ 2 2 in the fields provided Then click NEXT Now the destination folder dialog box will appear 97 Choose Destination Location x Setup will install DPI in the following folder To install to this folder click Next To install to a different folder click Browse and select another folder You can choose not to install DPI by clicking Cancel to exit Setup Destination Folder Program Files eroprobe DPI Browse ngi The default directory for installation is C Program Files Aeroprobe FLOW IQ If you wish to install the program to a different folder click on Browse and find the desired destination folder Once you have selected the destination folder click NEXT Now the FLOW IQ 2 2 program is ready to install If you wish to install the software at this time Click on NEXT in the following dialog box Start Copying Files x Setup has enough information to start copying the program files If you want to review or change any settings click Back If you are satisfied with the settings clic
28. and diameter of a particle when it contains saturated pixels For this scheme if 132 saturated pixels exist it is enforced that they do not contribute to the measurements They are discarded and the measurements are then performed from the adjacent un saturated pixels This is significant in the case of the maximum intensity pixel that is the one most likely to be saturated By removing the saturated high intensity pixels from the calculation we allow the accurate estimation of the particle maximum intensity value and the Gaussian spread thus reducing the overall error of the method Finally the method is truly two dimensional and accounts for the diagonal pixels Consider the two dimensional intensity distribution AAA y A I 20 4 We can solve for the four independent variables using the unsaturated intensities and coordinates at four points The solutions for the center and variance are shown in Equations 6 8 and depend upon twelve constants defined as a X 4 Yo Yo Xp Y Y y4 X Y4 Yo Og X4 Ya Y t Xs Yaa 4 FO VI Vas Ya Os X Ya Ya x a hy V1 E OO 4 X3 Ya Ya Xo Y Ya A Y VoMY1 Y Yo Y 3 Y Xy X4 x x Sat x4 Yo Y MY 2 Y3 X2 Xs i Ys sa 3 xa 4 si e Ys Ya X X3 X4 Xg3 X4 X4 Y3 Y1 X3 X4 Y Y4 X X3 X4 Y3 y Y3 X x3 X4 X X4 X Yo Yi X x y y X X x Y y Ya X X2 X3 X3 X3 Xa Ya Y X2 X3 Y Y JEX X gt X3 Y Y3
29. be removed and click on Remove The task will be deleted from the Stereo PIV Tree 152 Running Stereo PIV Tasks There are two ways to run Stereo PIV tasks in FLOW IQ V2 2 as a group or individually To run all of the listed PIV tasks in the tree click on Stereo PIV in the upper left window Stereo PIV should now be highlighted Now right click on Stereo PIV and click on Run Task s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data This will run the specified Stereo PIV tasks on the selected images in the project In order to run individual Stereo PIV tasks click on the desired task The task should now be highlighted Now right click on the task to be removed and click on Run Task s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data When the Stereo PIV tasks have finished processing and all the frames have been completed a Finished Processing message will appear in the lower right window under Console A description of each available Stereo PIV task follows Basic Stereo PIV In Basic Stereo PIV the user must input the angles used in the Stereo PIV experiment The user must define Alpha left Alpha Right Beta Left and Beta Right The user may also select the out
30. ecf GetSamplingTime 11 Set sampling time ecf SetSamplingTime x 12 Get exposure time ecf GetExposureTime 13 Set exposure time ecf SetExposureTime x 14 Get wave length ecf GetWaveLength 15 Set wave length ecf SetWaveLength x e Class Mathematics This class provides some mathematical utility used by this application Operations 1 test if a double is zero Mathematics IsZero x where x is double 2 round a double Mathematics Round x 3 get the max value from two doubles Mathematics Max a b 4 get the min value from two doubles Mathematics Min a b 5 integrate a one dimension function Mathematics Integral low high func where low is lower limit high is upper limit func is the function 6 Solve nonlinear equation Mathemtaics fsolve n x calfun dstep dmax acc maxfun Where n is the number of variables in the equations x is the initial value of the variables note it s an array starts from 1 not 0 calfun is the function used to evaluate the equations dstep is step length 165 dmax is the change in the vector x at each iteration does not exceed dmax dmax must be greater than dstep acc is the required accuracy maxfun is the maximum number of iterations 7 Levenburg Marquardt Least Squares Mathematics LMLeastSquare x na a ny y s f lambda termepsilon maxiter where x 1s the matrix contains input variables x1 x2 data Each column of the matrix represents an input variab
31. from the overall 3 point Gaussian results The tracking histogram was generated by histogramming the average diameter of each tracked particle The average diameter for a tracked particle was calculated by using all of the occurrences of the particle throughout the data files Most of the particles in this study were tracked through only two frames The results for the 3 point Gaussian fit the particle tracking and the PIV compensated histograms are shown below in Figure 2 15 x 10 Population Histograms for PTV Compensation 12 T T PIM 3 Point Total Compensated 3 Point Population o T l 100 150 Diameter um Figure 2 15 Total Population Histograms for 3 Point Guassian Tracking and PTV compensated methods Spray Omm plane 40 Figure 2 15 shows that approximately 80 percent of the particles detected at the 25 and 44 micron points were tracked using PIV Approximately half of the particles from the 50 to 90 micron range were tracked between frames Therefore the compensation using PTV decreases the overall population bias towards the lower diameters for the 3 point Gaussian method In order to compare the methods to the PDA measurement probability density functions were generated by dividing the populations shown in Figure 2 15 with the total population for each corresponding method These results are shown below in Figure 2 16
32. go to zero Solving for B 0 yields _ X3y1 X4Y1 X4Y3 X3Y4 Ya Ya 8 _ X3Y2 X4Yo X4 3 X3Y4 Ya Ya xy Xo Equation 8 represents the condition for all four points lying on the same line which does not result to a solution in the four point fit and therefore must be avoided The second combination of points that does not yield a unique solution occurs if the four selected points all lie in a circle of any arbitrary center or radius Assume any four points randomly located on a gaussian shaped particle as shown in Figure 2 left If the fourth point belongs on the circle determined by the first three then it can be shown that the solution to the particle center Equation 6 and 7 reduce to the solution of the center of the circle intersecting the four points and is independent of any intensity values In addition the variance in Equation 8 goes to zero The mathematical proof of the above condition is apparent by inspection However defining a circle using the first three points and then inspect if the fourth point satisfies the equation of the circle can be used as a criterion for the point selection Figure 2 shows examples of a acceptable left and unacceptable center right groups of points The four point Gaussian fit has the advantage over the three point fit in that it is more flexible in selecting virtually any four of the pixels that satisfy the above conditions Our practice showed that it is desirable to sel
33. higher velocity particles in the interrogation area The dominant factor in the error is the shear rate however This wotk also showed that the DADPIV method developed in the ESM Fluid Mechanics Laboratory performed better than other PIV algorithms currently in use The bias error associated with shear flows was shown to be the largest contribution to the error Methods for the reduction of velocity measurement error in shear flows were introduced including the power law correction which reduced the measurement error substantially Therefore this work succeeded in characterizing the performance of several PIV algorithms in the measurement of wall shear velocities with a wide range of velocity gradients In the wall shear area more intense methods for correcting the error due to velocity gradients in the flow should be developed A power law compensation should be explored and novel correlation peak detection algorithms should be tested in an attempt to improve these errors Another idea is the development of a correction scheme that will estimate the velocity at the centroid of the linear velocity profile For a linear profile the centroid is located at 2 3 of the window size from the top of the window if the velocity profile is in accordance with Figure 4 1 This and other correction methods will be explored in future efforts 4 5 Summary of Original Contribution The major contribution of this chapter was the characterization of the perform
34. in this work in the wall shear studies This software gives the user the ability to select several processing algorithms not yet available in DPIV v1 0 and allows processing at high speed in a DOS environment This software is known as Ultimate and was developed by Claude Abiven and Dr Pavlos Vlachos in the ESM Fluid Mechanics Laboratory at Virginia Tech 2 2 4 PDA System To confirm the feasibility of this method and quantify the accuracy of our system a validation experiment comparing our system and a PDA system was performed A one dimensional Phase Doppler Particle Analyzer PDPA was used to measure the spray droplet size and velocity in the axial direction It was a commercial system consisting of an integrated optical unit a signal 20 processor and software for system setup data acquisition and data analysis The integrated optical unit encompassed a 10 mW He Ne laser as the laser source A 632 8 nm Transmition was via a fiber optic probe 60 mm in diameter which encompassed necessary optics to transmit the red laser beams with an initial beam separation of 38mm The focal length of the lens used for the transmitting probe was 400 mm The PDA receiver was another fiber optical probe 60 mm in diameter with a focal length of 160 mm It was positioned in the forward scatter mode at a scattering angle of 35 degrees to allow measurements of droplet size in the reflection mode Given this arrangement the fringe spacing was 6
35. is shown in Figure 3 1 below 8 DPIY DPI 1 a File Edit View Project Image Window Help DS H I FOR Gm a DPIY Run Task s on Data gt Image Particle Particle PIV Validation Stero PIV Trajectory Add ImagePro Task s Remove ImagePro Tasks Task Add Dialog xj Selected Tasks Basic Thresholding Histogram Thresholding Binarize rea Boundary Removal Combo Pro Figure 3 1 Adding Image Preprocessing Tasks To add a task to the project click on the desired task to highlight it and then click 109 The available tasks are listed on the left and the tasks to be added are shown on the right When you have selected the desired tasks click OK The added tasks will be shown in a tree under Image Processing as shown below in Figure 3 2 These tasks will be performed from top to bottom in the tree If you wish to change the order of operations click and drag the tasks to new positions until you are satisfied with the order of Operations ae File Edit Image Project View Window He Dsum DPIV C General E Image Processing Tasks Basic Thresholding Dynamic Thresholding Histogram Thresholding Median Thresholding Blur Smooth AGW Binarize Area Smooth 3X3 CI Particle Sizing CI Particle Tracking Pr Validation 3 Post Processing lt ipp gt Name Basic Thresholding Method Basic Thresholding Low 120 High 255 lt fipp gt Fig
36. kindness inspires me evety day to be more understanding and accepting of the world around me You truly are my anchor Thank you to my brother for his inspiring zest for life and the affirmation that family and friends must always take a front burner on the stove of life Thank you my friends both at home and at school for making this appalling waste of time if anything more enjoyable and memorable To Yaz Ali Jose and Jagibbs for many hours of support venting time and comradery To Schwartz for keeping the dream alive And finally to anyone who is reading this thesis now for putting it down before continuing on and wasting any more of your precious time on this earth Dream out loud Everything you know 1s wrong interference from zoo tv TABLE OF CONTENTS CHAPTER L sige ee SRL 1 1 BACKGROUND AND INTRODUCTION 0 ccccsscsssscssscsscssscssscsssssssscssssssssssscosssees 1 1 1 MOTIVATION sorna Ada 1 1 2 PARTICLE IMAGE VELOCIMETRY iii 1 12 14 M O O 1 1 2 2 IMAGE PROCESSING AND MAXIMUM RESOLVABLE DISPLACEMENT 6 1 2 3 TRADITIONAL MULTIGRID TECHNIQUE iii 7 1 2 4 DISCRETE WINDOW OFFSET i 7 1 3 PARTICLE TRACKING VELOCIMETRY ii 10 1 4 ERROR ANALYSIS usuaria taa aaal 10 CHAPTERS urb d 12 2 PIV SIZING OF SPRAY DATA ANALYSIS AND COMPARISON TO PDA 12 2 1 INTRODUCTION trattante aio told aes 12 2 1 1 CONVENTIONAL PARTIC
37. measured displacement D is the real known displacement N is the number of measurements performed in the simulation Esu is the total error of the measurement E is the bias error of the measurement and E is the random error of the measurement 11 Chapter 2 2 PIV SIZING OF SPRAY DATA ANALYSIS AND COMPARISON TO PDA The purpose of this chapter was to explore the performance of the conventional sizing techniques developed by Brady et al 2002 in a real world spray atomization experiment DPIV analysis was performed on a 60 degree conical high pressure spray that generated a poly dispersed droplet distribution Measurements were preformed for five planes parallel to the spray axis and separated by 4mm A CMOS camera recorded the DPIV images at sampling rate of 10 KHz Advanced image processing techniques were employed to identify the droplets and calculate their diameter using the novel Flow IQ software Subsequently the size distribution of each droplet was quantified using geometric optics theory to convert the droplet image information to the true droplet size The droplet sizes from our direct imaging DPIV system were validated using a Phase Doppler Particle Analyzer PDPA The calculated sizes from the direct imaging methodology were found to agree with the measured PDPA results for droplets images larger than 3 to 4 pixels Resolution limitations introduced inaccuracy for smaller droplets This preliminary effort illustrates the po
38. methods and their industrial applications Prog Energy Combust Sci 22 pp 267 306 Brady M and Vlachos P 2003 Novel Particle Sizing and Centroid Estimation Techniques Proceedings of IMECE 2003 Brady M Abiven C Vlachos P and Papadopoulos G 2002 Time Resolved Spray Droplet Velocity and Size Measurements via Single Camera Laser Sheet Imaging and Planar DPIV Proceedings of IMECE 2002 Boedec T Simoens S 2001 Instantaneous and simultaneous planar velocity field measurements of tow phases for turbulent mixing of high pressure sprays Experiments in Fluids 31 pp 506 518 Cowen E Monismith S 1997 A hybrid digital particle tracking velocimetry technique Experiments in Fluids 22 pp 199 211 Damaschke N Nobach H Tropea C 2002 Optical limits of particle concentration for multi dimensional particle sizing techniques in fluid mechanics Experiments in fluids 32 143 152 Derou D and Herault L A new paradigm for Particle Tracking Velocimetry based on graph theory and pulsed neural networks 185 Dracos Th and A Gruen 1998 Videogrammetric methods in velocimetry Appl Mech Rev vol 51 no 6 1998 Etebari A Carneal J B Vlachos P 2004 On the Accuracy of Wall Shear Stress Using DPIV Proceedings of the ASME HTFE Summer Conference 2003 Gharib M and Willert C Particle Tracing Revisisted Review Paper Grant I 1997 Particle I
39. of Missouri Rolla 1983 Bachalo WD Experimental methods in multiphase flows Int J Multiphase Flow 20 pp 261 295 1994 Black D L Mcquay M Q Bonin M P Laser based techniques for particle sizing measurement a review of sizing methods and their industrial applications Prog Energy Combust Sci 22 pp 267 306 1996 Boedec T Simoens S Instantaneous and simultaneous planar velocity field measurements of tow phases for turbulent mixing of high pressure sprays Experiments in Fluids 31 pp 506 518 2001 Cowen E Monismith S A hybrid digital particle tracking velocimetry technique Experiments in Fluids 22 pp 199 211 1997 Fan L S Zhu C Principles of Gas Solid Flows Cambridge University Press 1997 Fincham AM Spedding G Low cost high resolution DPIV for measure3ment of turbulent flow Experiments in Fluids 23 1997 Guezennec Y G Kiritsis N Statistical Investigation of Errors in Particle Image Velocimetry Experiments in Fluids 10 pp 138 146 1990 Hardalupas Y Pantelides K Whitelaw J H Particle Tracking Velocimetry in Swirl stabilized Burners Experiments in Fluids 29 pp S220 S226 2000 Hassan A Blanchat T Experiments in Fluids 11 pp 293 1991 Hassan Y Blanchat T Seeley C Canaan R Simultaneous Velocity Measurements of Both Components of a Two phase Flow Using Particle Image Velocimetry Int J Multiphase Flow 18 pp 371 395 1992 Herpfer D C
40. on OK and the preprocessing tree will be updated accordingly To remove individual preprocessing tasks click on the task to be removed The task should now be highlighted Now right click on the task to be removed and click on Remove The task will be deleted from the Image Preprocessing Task Tree Running Preprocessing Tasks There are two ways to run preprocessing tasks in FLOW IQ V2 2 as a group or individually To run all of the listed preprocessing tasks in the tree click on Image Processing in the upper left window Image Processing should now be highlighted Now right click on Image Processing and click on Run Task s on Data A menu 111 will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data A list of the available input packages will appear Click on the desired input package to be processed with the preprocessing tasks The processed images will be saved in the ouput directory specified in the task The input images will not be overwritten In order to run individual preprocessing tasks click on the desired task The task should now be highlighted Now right click on the task to be removed and click on Run Task s on A list of the available input packages will appear Click on the desired input package to be processed with the preprocessing task The task will be run on all of the selected images i
41. part of this particle All pixels with intensity less than Picking Intensity surrounding the peak pixel will be ignored Image preprocessing tasks may be added and will be performed before the particle sizing algorithm is run Clicking the ADD button brings up the Add Preprocessing Task Dialog Box See Figure 3 1 Select the desired tasks and click OK To change the properties of the preprocessing tasks click on the desired task and then click on PROPERTIES The properties can then be modified as discussed in Chapter 2 To set the output directory click on BROWSE and select the desired destination directory The default output type is Tecplot plt format The rest of the particle sizing tasks are edited in a manner similar to that discussed above Removing Particle Sizing Tasks There are two ways to remove particle sizing tasks in FLOW IQ V2 2 as a group or individually To remove several sizing tasks from the active project click on Particle Sizing in the upper left window Particle Sizing should now be highlighted Now 129 right click on Particle Sizing and click on Remove Sizing Tasks The Particle Sizing Remove Tasks Dialog Box will appear as shown below in Figure 5 4 Remove Tasks A Centroid Fit Three Points Gaussian Fit Four Points Gaussian Fit Modified Four Points Gaussian Fit Least Squares Volume Fit Least Squares Mid Fit Hierachical method Remove Cancel Figure 5
42. run alone or in conjunction with other tasks The input files for Particle Sizing tasks are 8 bit tif images Adding Particle Sizing Tasks To add particle sizing tasks to the active project click on Particle Sizing in the upper left window Particle Sizing should now be highlighted Now right click on Particle Sizing and click on Add Sizing Tasks The Particle Sizing Dialog Box will appear as shown in Figure 5 1 below Task Add Dialog xj Tasks Selected Tasks Centroid Fit Three Points Gaussian Fit Four Points Gaussian Fit Modified Four Points Gaussian Least Squares Volume Fit Least Squares Mid Fit Hierachical method gt gt Figure 5 1 Add Particle Sizing Task Dialog Box To add a task to the project click on the desired task to highlight it and then click The available tasks are listed on the left and the tasks to be added are shown on the right When you have selected the desired tasks click OK The added tasks will be shown in a tree under Particle Sizing as shown below in Figure 5 2 These tasks will be performed from top to bottom in the tree If you wish to change the order of operations click and drag the tasks to new positions until you are satisfied with the order of operations 127 DPIY DPI 1 br File Edit Image Project View Window He Dsum a DPIY Y General Image Processing Tasks Particle Sizing Centroid Fit Three Points Gaussian Fit Fou
43. seen in Figure 4 8 The RMS error is at least an order of magnitude less than the mean error at corresponding shear rates and interrogation window sizes The shear rate is again the dominant factor in the velocity estimation error The interrogation window size has an increasing effect on the velocity error as 83 shear rate increases In the DADPIV case the error associated with the measurement increases dramatically for every shear rate when the 16 window nears the maximum resolvable displacement of 4 pixels displacement Ultra DPIV Mean Error Various Shear Stress Rates 0 0625 64 0 125 64 4 0 25 64 2 0 0625 32 S 0 125 32 0 25 32 0 0625 16 amp 0 125 16 ag L A 02516 Error px APR L Prati er 10 N i he es A A 10 0 0 5 1 15 2 eae 3 So 4 Centerline Displacement px Ultra DPIV RMS Error Various Shear Stress Rates 0 0625 64 0 125 64 0 25 64 0 0625 32 a 0 125 32 0 25 32 A 0 0625 16 gt 0 125 16 amp 0 25 16 Error px 10 0 5 1 1 5 2 2 5 3 3 5 4 Centerline Displacement px 84 l Ultra DPIV Total Error Various Shear Stress Rates 10 0 0625 64 H 0 125 64 f 0 25 64 t e 0 0625 32 0 125 32 F amp 0 25 32 4 0 0625 16 a amp 0 125 16 10 F a 0 25 16 E Ed Error px i ya ES 10 0 0 5 1 19 2 2 5 3 3 5 4 Centerline Disp
44. the tasks on the desired data The individual task will be run on all of the selected images in the project A message similar to the following will appear in the lower right window under Console lt ptk gt Name Velocity based Tracking Method Velocity Based Tracking Distance limit 0 000000 Step count 2 Output dir none Ext plt lt ptk gt Finished Processing When the Particle Tracking tasks have finished processing and all the frames have been completed a Finished Processing message will appear in the lower right window under Console A description of each available Particle Tracking task follows 156 Basic Trajectory The basic trajectory algorithm simply searches for particles in consecutive images within a user defined search radius Particles must be identified in each frame using the Particle Sizing tasks in Chapter 4 before running basic trajectory The basic trajectory algorithm reads the Particle Sizing plt files consecutively and searches for particles within a certain radius If a particle is found within the search radius the algorithm assigns this particle as tracked and continues the trajectory until no particle is found in the search radius Each tracked particle is assigned a number and is stored in the corresponding output plt file for particle trajectory in the destination directory The options screen for Basic Trajectory is shown below in Figure 9 3 Tracking Task Dialog
45. this section PIV tasks can be run alone or in conjunction with particle tracking The input files for PIV tasks are 8 bit tif images Adding PIV Tasks To add PIV tasks to the active project click on PIV in the upper left window PIV should now be highlighted Now right click on PIV and click on Add PIV Tasks The PIV Dialog Box will appear as shown in Figure 6 1 below Task Add Dialog x Tasks Selected Tasks No Discrete Window Offset First Order D WO PIV Second Order DW O PIV Hybrid PTW gt gt ES mul Cancel Figure 6 1 Add PIV Task Dialog Box To add a task to the project click on the desired task to highlight it and then click The available tasks are listed on the left and the tasks to be added are shown on the right When you have selected the desired tasks click OK The added tasks will be shown in a tree under PIV as shown below in Figure 6 2 These tasks will be performed from top to bottom in the tree If you wish to change the order of operations click and drag the tasks to new positions until you are satisfied with the order of operations 137 E File Edit Image Project View Window He Ow A O Q DPIV General Image Processing Tasks Particle Sizing Particle Tracking E PIV No Discrete Window Offset First Order DWO PIV Second Order DWO PIV validation EY Post Processing lt piv gt Name No Discrete Window Offset
46. user friendly and easy to use windows based environment FLOW IQ v2 2 also provides the user with many processing and task options that are novel in nature This manual presents the functions available in FLOW IQ v2 2 reviews the use of each function and provides basic theoretical foundations for the algorithms used in FLOW IQ v2 2 For more information on the algorithms used in FLOW IQ v2 2 please review the References section of this manual This manual also includes Documentation relating to the test bed supplied with FLOW IQ v2 2 96 Chapter 1 Program Installation In order to install FLOW IQ 2 2 on your system double click on the Setup exe in the root directory of the provided CD The following dialog box will appear Welcome E xj Welcome to the DPI Setup program This program will install DPI on pour computer Itis strongly recommended that you exit all Windows programs before running this Setup program Click Cancel to quit Setup and then close any programs you have running Click Next to continue with the Setup program WARNING This program is protected by copyright law and international treaties Unauthorized reproduction or distribution of this program or any portion of it may result in severe civil and criminal penalties and will be prosecuted to the maximum extent possible under law Cancel Use ALT TAB to switch to other running programs in Windows and shut them down Then click on NEXT The license
47. 0 0 5 1 19 2 25 3 s 4 Centerline Displacement px NDWO RMS Error Various Shear Stress Rates 10 f 0 0625 64 LI 0 125 64 0 25 64 0 0625 32 hc 1 S 0 125 32 Tm 0 0 25 32 A 0 0625 16 fa E gt 0 125 16 STT atin ee ee 10 L L2 0 25 16 jee eS pS j e 10 gt da sed TT S a ee de cia A 5 HA o ao oa oks a J EH MAR La A t T al a e ERA ea ames A x 10 0 5 1 15 2 25 3 3 5 4 Centerline Displacement px 80 NDWO Total Error Various Shear Stress Rates n 0 0625 64 i i H 0 125 64 0 25 64 t S 0 0625 32 o 0 125 32 ta A ge 0 25 32 __ PRE a H 0 0625 16 bm pe e A 0 125 16 a re E A 0 25 16 a p 10 RC ds 4 f 4 10 I yo Bb Error px i I l j 1 I I A i 10 bd 0 0 5 1 1 5 2 2 5 3 35 4 Centerline Displacement px Figure 4 7 Mean RMS and Total Error for No Discrete Window Offset The trends seen in Figure 4 7 are the same as the trends seen in Figure 4 6 The RMS error is at least an order of magnitude less than the mean error at corresponding shear rates and interrogation window sizes The shear rate is again the dominant factor in the velocity estimation error The interrogation window size has an increasing effect on the velocity error as shear rate increases In the ND
48. 02 Simultaneous time resolved velocity and size measurements are limited to single point methodologies using Phase Doppler Particle Analyzer PDPA Although these methods can measure with high accuracy the particle velocity and size they are limited by the requirement of spherical particles Kim et al 1999 In the case of spay atomization this requirement is not satisfied since the droplets deform forming ellipsoids In addition single point methodologies do not reveal the global temporal variation of the flow The above limitations generate the need for alternative global measurement methodologies based on visualization techniques Khalitov and Longmire 2002 presented an image based approach for resolving two phase flows between a flow tracer and a solid phase In their approach they were able to successfully discriminate the coexisting phases in the flow by employing image processing principles However they did not carry out any size quantification Recent efforts combine size measurements with DPIV using either fluorescence Mie scattering ratio Boedec and Simoens 2001 or interferometry principles Damaschke et el 2002 to carry out the sizing tasks Boedec and Simoens 2001 by employing a fluorescence Mie scattering ratio methodology were able to accurately measure the velocity and size distribution in a high pressure spray However such implementations require complicated experimental setups multiple cameras optical filters and cal
49. 25 3 3 9 4 Centerline Displacement px Figure 4 11 Error for Multigrid DADPIV and NDWO for Various Shear Rate 32 Window Figure 4 11 hows that for the shear rates of 0 0625 0 125 and 0 25 pixels per pixel the NDWO case has the highest error close to the wall but the peak locking phenomenon causes the multigrid and DADPIV algorithms to have a much higher oscillatory error at greater centerline velocities The traditional multigrid approach has comparable error to the DADPIV approach for shear rates of 0 0625 and 0 125 pixels per pixel but higher errors than the DADPIV algorithms for a shear rate of 0 25 pixels per pixel For the 0 25 shear rate the DADPIV algorithm performs better than the traditional multigrid algorithm and the NDWO method averaging approximately 0 12 pixels less total error than the multigrid method and approximately 1 pixel less total error than the NDWO case The peak locking phenomenon appears again at shear rates of 0 0625 and 0 125 There may be peak locking at the 0 25 shear rate but the measurement increments may be too coarse to detect the phenomenon 89 4 4 Conclusions and Future Work The wall shear results presented in this work show that velocity gradients produce significant error in PIV measurements The error associated with PIV measurements increases dramatically with shear rate Increased interrogation window size also increases the error associated with the measurement because of the inclusion of
50. 35 140 145 150 Diameter um Figure 2 9 Plane Averaged Histogram Results for All PIV Sizing Methods 32 The performance of the three point Gaussian estimator is shown in more detail below in Figure 2 10 Probability Density Curves for PDA and 3 Pnt PIV All Planes 0 2 T T T T T T T T PDA 3 Point 0 18 Q 4 o a T o Sa gt T e La N T 0 08 Ra SK Normalized Probability Density o T 47 Ye 0 06 Aa a T 3 I t t 0 04 0 02 ire O 0 i 100 105 110 115 120 125 130 135 140 145 150 Diameter um Figure 2 10 Plane Averaged Results for 3 Point Gaussian Method and PDA The particle population is also an important factor in this experiment Table 2 1 below lists the particle populations detected using the DPIV software for the Omm plane Table 2 1 shows that the 3 point Gaussian produces a result at a rate approximately 99 71 percent of the detected particle population while the four point Guassian scheme produces results at approximately 19 40 percent The 4 point continuous algorithm and the continuous least squares produce the lowest success rates at approximately 3 187 and 3 280 percent respectively Each method was performed 33 on the same images with identical image preprocessing procedures and therefore the number of particles fed to each algorithm for diameter estimation was identical
51. 4 4 were calculated without taking the absolute value Therefore as initial interrogation window size increases the first pass of all of the DPIV algorithms studied in this work overestimates At an interrogation window size of 64 this overestimation reaches the level of 2 pixels Since the multigrid and DADPIV methods exhibit a lower true error than the NDWO method the refining passes in both the multigrid and the DADPIV methods must correct for the overestimation in some manner The multiple pass methods can only correct by 0 5 pixels in each successive pass If the overestimation is greater than 0 5 pixels the multiple pass algorithms may not be able to correct for such an overestimation 76 4 3 1 1 Comparison to Uniform Displacement Measurements The wall shear results were compared to uniform displacement results in order to determine the difference between the measurement error in wall shear and the error associated with uniform displacement which has been well documented Figure 4 5 below shows the uniform displacement error in comparison to the wall shear velocity error for a starting interrogation window size of 32 pixels Total Error for Various Methods under Wall Shear and Uniform Displacement a a a a a El Ax A 0 18 DADPIV Ar N id MGRID et A NDWO Ei z 0 16 Uniform Disp g AX e f ETA 0 14 f al 0 12 i Y a y 5 0 1 r Y AA f os pre sh 0 08 f ee a 0 06 dA wae sy 0 04 sg J 0
52. 53 BASIC Stereo PIV ito oins iiis 153 Chapter 927 Tra estoy asks a a E E ae 154 Adding Particle Tracking Task ii niR 154 Editing Task Properties aura ia 155 Removing Particle Tracking Tasks ici sccccisascgssesaseackevaseseascaavecandssnsceeennnccaavaneduabdessineees 155 94 Running Particle Tracking Tasks titanio toos 156 e O A 157 Chapter 10 Output Types reia astre na e E EE E E EEEE EE pr 158 Patice S Aa OUI EON oc css seca acces nae Sash Saou RR SI SERIO 158 PIV OOU rtg e e a ita 158 Hybrid PTV Output iaia ilari 159 Partick Trajectory Quipulis talenti 159 Chapter 11 Advanced Topless ii 160 Copy Fora 160 Copy Feature Example adicionado coi 160 Chapter 12 FLOW IQ APIs Documentation 161 li Utlty Modules race 161 27 Image Preprocessino Module lano arida 167 3 Particle Sizing Modales rai 168 Ae PLY Modules Sie lab ipo rail hide por cre lita 171 Si Particle Tracking Module is Li ale 173 References for DPIV Documentation x scs 05schessasccatacoveach de teceoncdasceeeaisacedeioaac van eeaen 175 95 Introduction The purpose of this manual is to familiarize the user with the functions of FLOW IQ version 2 2 FLOW IQ v2 2 is Digital Particle Image Velocimetry program with built in image preprocessing particle sizing and post processing tasks FLOW IQ v2 2 provides the user with several options not found in other packaged software currently on the market The program provides excellent functionality in a
53. 89702 1 1 1 1 1 A list of the flags for the different sizing methods is shown below in Table 10 1 Sizing Method Output Flag Centroid 0 Three Point Gaussian 1 Four Point Gaussian 2 Modified Four Point Gaussian 3 Least Squares Volume 4 Least Squares Mid 5 Table 10 1 Output Flags for Sizing Methods If a hierarchical fit is used then the flag inserted in the output file will be the last sizing method that returned a result on the sizing PIV Output A portion of an output plt file using the Three Point Gaussian Fit is shown below The first three lines are the header required by the Tecplot plt format The data is arranged in columns with the first column listing the x coordinate of the velocity measurement The second column contains the y coordinate of the velocity measurement The third column is the estimated x component of the velocity U and the fourth column is the estimated y component of the velocity V The fifth column W is the z component of the velocity The sixth and seventh columns list the number of measurements in the x and y directions respectively The eighth column Correlation shows the value of the 158 normalized correlation peak The ninth column Valid lists a valid vector as 1 and invalid vector as 1 and an unvalidated vector as 0 TITLE FLOW IQ Data File VARIABLES X my ye yyy y nx Wy C
54. AVERAGE DIAMETER Z 15 4MM 39 FIGURE 2 15 TOTAL POPULATION HISTOGRAMS FOR 3 POINT GUASSIAN TRACKING AND PTV COMPENSATED METHODS SPRAY OMM PLANE iii 40 FIGURE 2 16 PDA 3 POINT GAUSSIAN PTV AND PTV COMPENSATED PDF S OMM PLANE 41 TABLE 2 3 PTV CORRELATION COEFFICIENTS FOR FULL RANGE RESULTS 0 MM PLANE 42 FIGURE 2 17 PTV COMPENSATED AND PDA HISTOGRAMS OMM PLANE e 42 FIGURE 2 18 POPULATION FOR PIV PTV METHODS AND PDF S FOR PIV PDA AND PTV 43 TABLE 2 4 PTV CORRELATION COEFFICIENTS FOR 100 TO 150 UM RANGE 0 MM PLANE 44 FIGURE 2 19 TRACKING COMPENSATION AND PDA FOR 100 TO 150 MICRON RANGE 44 FIGURE 3 1 DIAGRAM OF AN ELLIPSE iii 48 FIGURE 3 2 JOINTLY GAUSSIAN IIRV S WITH Ox Gy iii 49 FIGURE 3 3 JOINTLY GAUSSIAN IIIRV S WITH VARIOUS VALUES OF Ox AND Gy 51 FIGURE 3 4 THEORETICAL AREA CALCULATION ERROR VS ECCENTRICITY FOR CONVENTIONAIS SIZING METHOD ua ada ANR RS 53 FIGURE 3 5 THEORETICAL ERROR VS AXIS RATIO FOR 3 POINT GAUSSIAN SIZING METHOD 54 FIGURE 3 6 THEORETICAL PERCENT ERROR FOR 3 POINT GAUSSIAN AVERAGED ELLIPTIC AND TRUE ELLIPTIC SIZING METHODS ccccsccccsccccssssssssccsscccssssssscccsscccsssssssccceseccsssesssssessesess 55 vii FIGURE 3 7 THEORETICAL PERCENT ERROR FOR 3 POINT GAUSSIAN AVERAGED ELLIPTIC AND TRUE ELUIPTIC SIZING METHODS sti it a 56 FIGURE 3 8 SAMPLE
55. For example the first particle PID O in this data set was tracked from frame 0 to frame 1 from x y 135 493496 253 628721 in frame 0 to x y 140 790380 248 332298 in frame 1 but not beyond TITLE Particle Tracking Data File VARIABLES X Y Diameter FID PID Zone I 168 135 493496 253 628721 2 848859 0 O 140 790380 248 332298 2 866822 1 0 239 724143 253 009294 2 850054 0 1 245 026787 247 708276 2 859587 1 1 125 454566 252 157295 2 839976 0 2 130 746163 246 854155 2 844657 1 2 159 Chapter 11 Advanced Topics Flow IQ v2 2 has been updated to allow more efficient use of the provided algorithms by using the Copy Feature This feature allows the user to copy properties between classes of tasks For instance the user may select a image preprocessing task that is already set up and copy its properties to a particle sizing task This feature allows the user to quickly set up new tasks with saved properties from other projects Copy Feature In order to use the Copy Feature click on a task that has already been set up by the user The task may then be copied into the same tree or the copied task can be dragged to another tree that uses the features of the copied task A list of the compatible tasks is shown below in Table 11 1 Task Type Compatible With Can be copied and dragged to Image Processing Particle Sizing Image Math None Particle Sizing Hybrid PTV PIV Hybrid PT
56. INAL CONTRIBUTION cscssssscccccccsssssssssccececcesssssssssessecesessessaeess 90 CHAPTERS sandra nina na danni iii ciccia 92 5 DPIV DOCUMENTATION AND TEST BED 0 2 cccccssscssssssseccsssssecssssssscsscssssessscees 92 5 1 DPIV VERSION 1 0 DOCUMENTATION cccccccccccccssssssssscccccccessssssssccescccsssessssssssessseseeeees 92 5 2 TEST BED FOR DPIV SOFTWARE METHODS ccccscccccccccsssssssssccccsccsssssssssseessseeeeeees 177 5 2 1 TEST BED FOR FLOW IQ V2 2 RESULTS 177 5 2 1 1 UNIFORM DISPLACEMENT RESULTS cccccsssssccccccssssssssscesceccssssssssscssesceseessssaeess 178 5 2 1 2 VORTEX RESULTS cccccccccccccccccssssssssccccccccssssssssscssssccsssessssscssseceessesssssssssssceseeessaeess 180 5 3 SUMMARY OF ORIGINAL CONTRIBUTION cccssssssssccceccssssssssssesesccsssssssssesesseceeeeeees 184 REFERENCES siscestescicccciscnsccsctccssctesctacceoccscccceccscccvectsccctescdeseteoseecesuacSecesuacdecsdeacsecssedcdecdsotedesessve 185 MITA EE E EEEE OE EET 188 vi LIST OF FIGURES FIGURE 1 1 ILLUSTRATION OF INTERROGATION WINDOWS AND OVERLAP cccsssscsseesssseceeseees 3 FIGURE 1 2 CROSS CORRELATION PROCEDURE iii 4 FIGURE 1 3 GENERIC EXPERIMENTAL SETUP iii 5 FIGURE 1 4 BLOCK DIAGRAM FOR THE ESTIMATION OF VELOCITY VECTORS i 6 FIGURE 1 5 TRADITIONAL MULTIGRID METHOD 7 FIGURE 1 6 FIRST ORDER DISCRETE WINDOW OFFSET
57. IQ software All of the documented methods were developed by previous researchers The document is a portion of the work completed in the course of this work The other contribution in this chapter is a test bed that allows the comparison of plt PIV output files and a base program for the execution of error analysis This program will need to be modified by future researchers in order to handle multiple frames and multiple data sets 184 REFERENCES Abiven C Vlachos P P 2002 Super spatio temporal resolution digital PIV system for multi phase flows with phase differentiation and simultaneous shape and size quantification Int Mech Eng Congress Nov 17 22 2002 New Orleans LA Abiven C Vlachos P P and Papadopoulos G 2002 DPIV Strategies for resolving high shear and vortical flows Int Mech Eng Congress Nov 17 22 2002 New Orleans LA Adrian R Yao C 1985 Pulse laser technique application to liquid and gaseous flows and the scattering power of seed materials Applied Oprics 24 Adrian RJ 1991 Particle Imaging techniques for experimental fluid mechanics ARFM 23 261 304 Adrian RJ Meinhart CD Barnhart DH and Papen GC 1995 An HPIV System for turbulence research EP Rood ed ASME FED 148 17 21 Adrian R J 1996 Strategies for Imaging Flow Fields with PIV ATAA 96 1988 Black D L Mcquay M Q Bonin M P 1996 Laser based techniques for particle sizing measurement a review of sizing
58. Integration and Validation of Flow Image Quantification Flow IQ System Jason Bradley Carneal A thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Master of Science in Engineering Mechanics September 2004 Approved by Dr Pavlos Vlachos Chairperson of Supervisory Committee Dr Demetri Telionis Dr Marty Johnson Keywords DPIV Wall Shear Spray Particle Sizing Elliptical Gaussian Profile Copyright 2004 Jason B Carneal ABSTRACT Integration and Validation of Flow Image Quantification Flow IQ System Jason B Carneal The first aim of this work was to integrate validate and document a digital particle image quantification Flow IQ software package developed in conjunction with and supported by Aeroprobe Corporation The system is tailored towards experimental fluid mechanics applications The second aim of this work was to test the performance of DPIV algorithms in wall shear flows and to test the performance of several particle sizing algorithms for use in spray sizing and average diameter calculation Several particle sizing algorithms which assume a circular particle profile were tested with DPIV data on spray atomization including three point Guassian four point Gaussian and least squares algorithms A novel elliptical diameter estimation scheme was developed which does not limit the measurement to c
59. Jeng S M Planar Measurements of Droplet Velocities and Sizes within a Simplex Atomizer AJAA J 35 pp 127 132 1997 Huang H Dabiri D Gharib M On errors of digital particle image velocimetry Measurement Science and Technology 8 pp 1427 1440 1997 Jones A R Light scattering for particle characterization Prog Energy Sombust Sci 25 pp 1 53 1999 Kadambi J R Martin W T Amirthaganesh S Wernet M P Particle Sizing Using Particle Image Velocimetry for Two Phase Flows Powder Technology 100 pp 251 259 1998 Kato H Nishino A Shinshi A Torii K Flow Visualization and Image Processing of Multiphase systems FED Vol 209 ASME New York pp 115 122 1995 Keane R D Adrian R J Optimization of Particle Image Velocimeters Part 1 Double Pulsed Systems Measurement Science and Technology 1 pp 1202 1215 1990 175 Keane R D Adrian R J Optimization of Particle Image Velocimeters Part 2 Multiple Pulsed Systems Measurement Science and Technology 2 pp 963 974 1991 Khalitov D A Longmire E K Simultaneous two phase PIV measurements for high speed flows Third International Workshop on Particle Image Velocimetry Santa Barbara Sept 16 18 1999 Lindken R Gui L Merzkirch W Velocity Measurements in Multiphase Flow by Means of Particle Image Velocimetry Chem Eng Technol 22 pp 202 206 1999 Marxen M Sullivan P Loewen M Jahne B Comparison of Gaussian particle
60. LE SIZING TECHNIQUES 0 crei 14 2 1 1 1 AXIS SYMMETRIC GAUSSIAN SHAPE era ae a E A KE RETE E ETA 14 2 1 1 2 THREEPOINTGAUSSIANFIT ii 15 2 1 1 3 FOURPOINTGAUSSIANESTIMATOR i 16 214 CONTINUOUS EOUR POINT FIT i arri aia 17 2 1 1 5 CONTINUOUS LEAST SQUARES GAUSSIAN FIT 18 2 2 EXPERIMENTAL METHODS AND MATERIALS ccccssscsscesssssecessssceccesssssecesssssecessenseees 18 2 2 1 SPRAY GENERATION i 18 2228 PIN SYSTEM A as 18 2 23 DRPIV SOETWARE ata tai tele a li a lelalafala 20 224 PDA SYSTEM osta nds 20 2 2 5 COMPUTATIONAL AND COMPUTER RESOURCES iii 24 2 3 SPRAYDPIV PDA COMPARISON aida 24 2 3 1 HISTOGRAM ANALYSIS i 25 2 3 2 AVERAGE DIAMETER ANALYSIS iii 26 24 PARTIGLESIZING RESURS sns sostano nia dd e dee 26 2 41 PULESRANGE RESULTS 200 nana ERRE 26 2 4 2 LIMITED RANGE RESULTS nano 27 2 4 3 AVERAGE DIAMETER A AA 35 2 4 4 PTV CORRECTED HISTOGRAMS 40 2 5 CONCLUSIONS AND FUTURE WORK URI naaa 44 2 6 SUMMARY OF ORIGINAL CONTRIBUTION rei 45 CHAPTER 3 taa 47 3 ELLIPTICAL PARTICLE SIZING METHOD sccssssssssssnscssecssonsonecssecssonsonscssceses 47 y 3 1 INTRODUCTION A ione Pinar ake luisa latin Lats brio 47 3 2 ELLIPTICAL PARTICLE SIZING SCHEME METHODS AND MATERIALS 51 3 3 EELIP
61. MONTE CARLO SIMULATION IMAGES ci 57 FIGURE 3 9 ALL DATA POINTS FOR ECCENTRICITY 0 DIAMETER RANGE 2 8 TO 5 6 PIXELS 58 FIGURE 3 10 AVERAGED TOTAL ERROR OVER 250 POINTS ECCENTRICITY 0 59 FIGURE 3 11 ERROR IN THE X AND Y DIAMETER MEASUREMENTS VS X DIAMETER 61 FIGURE 3 12 X AND Y DIAMETER VS ECCENTRICITY FOR EACH SIZING METHOD 62 FIGURE 3 13 AREA ABSOLUTE AND PERCENT ERROR FOR ALL SIZING METHODS 64 FIGURE 3 14 LOG NORMAL SURFACE PLOT FOR 6x 0 80 oy 0 30 ux 1 00 uy 0 00 67 FIGURE 3 15 LOG NORMAL CONTOUR PLOT FOR ox 0 80 oy 0 30 Ux 1 00 uy 0 00 67 FIGURE 3 16 LOG NORMAL SURFACE PLOT FOR oy 0 20 uy 0 00 S 6 00 69 FIGURE 3 17 LOG NORMAL CONTOUR PLOT FOR oy 0 20 uy 0 00 S 6 00 69 FIGURE 4 1 ARTIFICIAL IMAGE DIAGRAM FOR WALL SHEAR EXPERIMENTS 00 72 FIGURE 4 2 TOTAL ERROR FOR ALL DPIV METHODS WINDOW 64 ie 74 FIGURE 4 3 TOTAL ERROR FOR ALL DPIV METHODS WINDOW 32 ccoonoccccccnoocccnnonncncnonanannnnnnn 75 FIGURE 4 4 TOTAL ERROR FOR ALL DPIV METHODS STARTING WINDOW 16 76 FIGURE 4 5 WALL SHEAR ERROR COMPARED TO UNIFORM DISPLACEMENT ERROR TI TABLE 4 1 TRACKED PARTICLE POPULATIONS FOR EACH SHEAR RATE 78 FIGURE 4 6 TOTAL ERROR FOR ALL PIV METHOD
62. Method No discrete window offset PIV Sizing method Three Points Fit Correlation FFT based Output dir Ext pit Window sizes 16 16 X grids 16 Y grids 16 lt imiw gt Figure 6 2 Added PIV Tasks Editing Task Properties When a task is highlighted as No Discrete Window Offset is in Figure 6 2 above the properties of the task will be displayed in the lower left window as shown In order to edit these properties click on the desired task to highlight the task Then right click on the highlighted task and click Properties The corresponding dialog box will appear depending on the selected task Enter the desired properties and click OK The individual properties are discussed below in detail for each PIV technique Removing PIV Tasks There are two ways to remove PIV tasks in FLOW IQ V2 2 as a group or individually To remove several sizing tasks from the active project click on PIV in the upper left window PIV should now be highlighted Now right click on PIV and click on Remove PIV Tasks The PIV Remove Tasks Dialog Box will appear as shown below in Figure 6 3 138 Remove Tasks S No Discrete Window Offset First Order D I WO PIV Second Order DWO PIV Remove Cancel Figure 6 3 Removing PIV Tasks To remove a task highlight the task by clicking on the task and click on REMOVE This will remove the task from the list When undesired tasks have been elimi
63. N_SIZE task name char m_OFDir MAX_FN_SIZE output file dir char m_OFExt 8 output file extension ExperimentConfig m_ExpCfg experiment configuration e Class BasicParticleTracking This class implements the basic particle tracking method It doesn t use any PIV information Its input is particle sizing results in a plt file It can be run in two modes one step one processing unit and All steps one processing unit In the first mode particle list is reset at each step Operations 1 Set step size task SetStepNo x where x 1s new step size Public member bool m_MultiSeg if true reset particle list at each step e Class VbParticleTracking This class implements the velocity based particle tracking method It uses both PIV and sizing information Pubic members public std vector lt PzMethod gt m_PzTasks particle sizing tasks std vector lt CPIV gt m_PIVTasks PIV tasks e Class TrackingPltFile This class is used to output tracking result to a plt file e Class TrackingTaskVisitor This class models a tracking task visitor 174 References for DPIV Documentation Adrian R Yao C Pulse laser technique application to liquid and gaseous flows and the scattering power of seed materials Applied Optics 24 1985 Adrian R J Yao C S Development of Pulsed Laser Velocimetry for Measurement of Fluid Flow Proceedings Eight Biennial Symposium on Turbulence G Patterson and J L Zakin Eds University
64. PIV methods and PTV Figure 4 11 above shows that the PTV method performs much better than the PIV methods in the estimation of velocity in shear flows The error for the PIV method is approximately half that of the PIV methods at corresponding displacements A larger number of images must be analyzed in order to improve this assessment however since the particle populations at higher shear rates are relatively low and unreliable 4 3 2 High Shear Rate Study The shear rates examined in the high shear portion of this work were 0 0625 0 125 0 25 0 50 and 1 00 pixels per pixel shear rate The images generated for this work had zero background noise in order to isolate the effects of shear rate on the velocity error The no discrete window offset case stands as the control case for these experiments 79 For the no discrete window offset NDWO case the interrogation windows were 64 32 and 16 In this case there were no consecutive passes performed in order to refine the velocity measurement The results for the NDWO case are shown below in Figure 4 7 NDWO Mean Error Various Shear Stress Rates 10 0 0625 64 0 125 64 0 25 64 0 0625 32 4 amp 0 125 32 n TE 0 25 32 TOTTI a amp 0 0625 16 Str AT 0 125 16 rta da g ee Aire mundi i 10 i A a Ss N tH de a ATE fot pia 2 silla ann CIS Pe D Fa vr es 47 A ie en ae 10 FE Gi A A _ Te E AA e ee 10
65. Probability Density Functions for PTY Compensation T T 0 35 PTV 3 Point Total Compensated 3 Point 0 3 PDA LI 0 25 4 c 0 21 4 2 5 Q o 2 0 151 4 150 Diameter um Figure 2 16 PDA 3 point Gaussian PIV and PTV compensated PDF s Omm plane Figure 2 16 above shows that the PTV and PTV compensated pdfs are much closer to the PDA measurement than the full 3 point Guassian results The correlation coefficients with the PDA measurement for each of the methods shown in Figure 2 16 are listed below in Table 2 3 41 Method Correlation Coefficient 3 Point Guassian Full Results 0 1465 Tracked 3 Point Gaussian 0 1099 PTV Compensated 3 Point Gaussian 0 1677 Table 2 3 PTV Correlation Coefficients for Full Range Results 0 mm Plane The correlation coefficient for the PTV compensated algorithm is 14 5 higher than the correlation coefficient of the 3 point Gaussian sizing method alone The PTV compensated comparison with the PDA sizing method is shown in greater detail in Figure 2 17 Probability Density Functions for PTV Compensated 3 point and PDA 0 14 T T A PTV 0 12 2 PDA Population 0 04 0 02 0 Diameter um Figure 2 17 PTV compensated and PDA histograms 0mm plane Figure 2 17 shows that the PTV compensated method significantly improves the estmation of diameter popula
66. S AND PTV 79 FIGURE 4 7 MEAN RMS AND TOTAL ERROR FOR NO DISCRETE WINDOW OFFSET 81 FIGURE 4 8 MEAN RMS AND TOTAL ERROR FOR MULTIGRID DPIV ALGORITHM 83 FIGURE 4 9 MEAN RMS AND TOTAL ERROR FOR DADPIV ALGORITHM 85 FIGURE 4 10 ERROR FOR MULTIGRID DADPIV AND NDWO FOR VARIOUS SHEAR RATE 64 VR EE 87 FIGURE 4 11 ERROR FOR MULTIGRID DADPIV AND NDWO FOR VARIOUS SHEAR RATE 32 WINDOW iii 89 FIGURE 5 1 MEAN RMS AND TOTAL ERRORS FOR ULTIMATE AND FLOW IQ v2 2 NDWO AND FOD WO toi lerara iaia Raina la nisi helaclklcnni 179 FIGURE 5 2 X AND Y LOCAL ERROR FOR NO DISCRETE WINDOW OFFSET 0 181 FIGURE 5 3 X AND Y LOCAL ERROR FOR FIRST ORDER DISCRETE WINDOW OFFSET 182 FIGURE 5 4 X AND Y LOCAL ERROR FOR FIRST ORDER DISCRETE WINDOW OFFSET 183 viii CHAPTER 1 1 BACKGROUND AND INTRODUCTION 1 1 Motivation The purpose of this work is to expand the usability and accuracy of Digital Particle Image Velocimetry DPIV in several significant applications These applications include whole field particle diameter and mass flux calculations in sprays the measurement of wall shear and the performance of novel sizing techniques on DPIV velocity measurement accuracy The first focus of this work is the analysis of errors associated with particle diameter and velocity measurements using DPIV in conjunction with nov
67. TICAL PARTICLE SIZING RESULTS ula eel AAS 51 3 3 1 THEORETICAL FOUNDATIONS cccccccccccccccssssssssscccccccessssssssssescccessesssessseseseseessssssseseess 52 3 3 2 EXPERIMENTAL ANALYSIS etici eee rece eee cicci 56 3 4 CONCLUSIONS AND FUTURE WORK cccccssssccccsccssssssssscccccccesesssssssssscecessesssssssesesceseeeees 65 3 4 1 LOG NORMAL NORMAL INDEPENDENT LNNI PDF 66 3 4 2 RAYLEIGH NORMAL INDEPENDENT RNI PDF 67 3 5 SUMMARY OF ORIGINAL CONTRIBUTION ccccssssscccccccssssssssscceccccessssssssssesseceseeesssasees 70 CHAPTER 4 evrivcccccccccctecstcscsescccccsscececscvnssecssessecsdenevscsdetesecsdetesesedesesesedesesesesestcevesedesesasesetesasesetesee 71 4 WALL SHEAR EXPERIMENTS cccccsccssssssssssssssccssssscscssssscssssssscsscssssecscsssscessssesse 71 4 1 INTRODUCTION cccccccccccccccssssssssscccccccessessssssssscccessssssssssssssccesssssssssssseesessesssssssesesceeeeeees 71 4 2 WALL SHEAR METHODS AND MATERIALS ccccccccccccsessssssscccccccssssssssssseseccssesssssssesseeees 72 4 3 WALL SHEAR RESULTS nera aaa ci 73 42350 LO WS HEAR RATES TUD ita 73 4 3 1 1 COMPARISON TO UNIFORM DISPLACEMENT MEASUREMENTS i TI 4 3 1 2 TRACKING RESULTS erre eee eee eee cere 78 4 32 HIGH SHEARRATESTUDYxSota tenete aora oa ona Doo ii 79 4 4 CONCLUSIONS AND FUTURE WORK cccccsssscccccccssssssssscccccccessssssssssesccccsssssssssseseeseseeeees 90 4 5 SUMMARY OF ORIG
68. The plane averaged correlation coefficient was 0 8915 for the 4 point Gaussian 0 5658 for the continuous 4 point Gaussian and 0 5883 for the continuous least squares fit 34 Correlation Coefficient vs Plane for Conventional Sizing Methods 4 3 point Gaussian 8 4 Point Gaussian Cont 4 Point lt Cont LS Correlation Coefficient Plane mm Figure 2 11 Correlation Coefficient vs Plane for Conventional Sizing Methods 2 4 3 Average Diameter In addition to histogram analyses average diameter calculations provide another comparison tool between the PIV and PDA diameter measurement techniques The 3 D isosurface plot for the average diameter for all of the spray planes is shown below in Figure 2 12 Figure 2 12 was generated using the Omm 4mm and 8mm results for the 3 point Gaussian sizing scheme and reconstructing a volume using Tecplot 10 The data from each plane was scanned and counted into 16 pixel bins with 50 percent overlap The grid spacing in Figure 2 12 is 8 pixels which allows a grid of 32X32X5 for the entire volume The average diameter was calculated assuming spherical patticles Figure 2 12 was generated in Tecplot using isosurfaces between values of 54 63 and 72 The results in Figure 2 12 were smoothed for 3 passes using the built in smoothing functionality of Tecplot 10 35 Frame 001 23 Sep 2004 Positive Planes Figure 2 12 3 D Isosurf
69. V Validation PIV tasks Stereo PIV None Trajectory None Table 11 1 Copy Feature Compatibility Copy Feature Example In this example the workspace has been set up by adding an Input Package named Input a Basic Thresholding Image Processing Task and a Centroid Fit Sizing Task The Basic Thresholding was updated using the procedures outline in Chapter 3 In order to copy the feature to the Centroid Sizing Tasks the user simply clicks on the Basic Thresholding tasks and drags it to the Centroid task as shown below in Figure 11 1 If the task is successfully copied the following message appears in the console window lmage Pro Task Basic Thresholding Added to Sizing Task Centroid Fit amp File Edit View Project Image Window Hr OeM FOm DPI tA Image J Image Math I Particle Sizing o C Particle Tracking yer Validation Y Stero PIV Y Trajectory Figure 11 1 Copy Example 1 160 Chapter 12 FLOW IQ APIs Documentation The purpose of the document is to describe in details how to use the FLOW IQ APIs At the time the document is written FLOW IQ is composed of image preprocessing particle sizing particle tracking and PIV modules Each module is a Win32 DLL that can be used by any Win32 application We don t include any MFC stuff in these DLLs in order to make it work with any Win32 application All of them share the same utility module that is also a DLL Particle sizin
70. Velocity based Tracking To remove a task highlight the task by clicking on the task and click on REMOVE This will remove the task from the list When undesired tasks have been eliminated click on OK and the preprocessing tree will be updated accordingly 155 To remove individual Particle Tracking tasks click on the task to be removed The task should now be highlighted Now right click on the task to be removed and click on Remove The task will be deleted from the Particle Tracking Task tree Running Particle Tracking Tasks There are two ways to run Particle Tracking tasks in FLOW IQ V2 2 as a group or individually To run all of the listed Particle Tracking tasks in the tree click on Particle Tracking in the upper left window Particle Tracking should now be highlighted Now right click on Particle Tracking and click on Run Task s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data This will run the specified Particle Tracking tasks on the selected images in the project In order to run individual Particle Tracking tasks click on the desired task The task should now be highlighted Now right click on the task to be removed and click on Run Task s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run
71. WO case as in the DADPIV case the error associated with the measurement increases dramatically for every shear rate when the 16 window nears the maximum resolvable displacement of 4 pixels displacement Figure 4 8 below shows the mean RMS and total error for the conventional multigrid algorithm The errors presented in Figure 4 6 are for the shear rates of 0 0625 0 125 and 0 25 with interrogation window sizes of 64 32 and 16 The error for shear rates of 0 50 and 1 00 were so high that they are not presented in this work For the 64 window consecutive window sizes of 64 32 16 and 8 were used in the multigrid algorithm For the 32 window consecutive window sizes of 32 16 and 8 were used Finally for the 16 window consecutive window sizes of 16 and 8 were 81 used This pattern of window sizes was also used with the dynamically adaptive DPIV algorithm presented later in this section Multigrid Mean Error Various Shear Stress Rates 0 0625 64 0 125 64 F 0 25 64 H e 0 0625 32 0 125 32 0 25 32 A 0 0625 16 amp 0 125 16 Di amp 0 25 16 Error px 10 f 0 0 5 1 1 5 2 2 5 3 39 4 Centerline Displacement px Multigrid RMS Error Various Shear Stress Rates a Error px t i 1 I 9 vi VI V A mM 10 f 0 0625 64 0 125 64 0 25 64 S 0 0625 32 0 125 32 0 25 32 4 0 0625 16 0 0 5 1 15 2 25 3 amp 0 125 16 Cen
72. ace Plot of Average Diameter In Figure 2 12 the spray is located at X Y Z 120 0 256 Figure 2 12 shows clearly shows the volume reconstruction of the spray The ligament can be clearly seen at in the bright green area Figure 2 12 shows that the larger particles are located near the ligament and the average particle diameter decreases as the distance from the spray increases Since this analysis allows the complete reconstruction of the entire volume y plane slices may be extracted from the volume in order to compare the average diameter at a certain height above the spray with the PDA measurements The slice of the reconstructed volume at an exact height of 15 4 mm is shown below in Figure 2 13 This elevation was located at 61 3097 pixels below the top of the spray images or at an elevation in the z plane of 194 69 pixels The magnification used to find the corresponding region was 79 1 microns per pixel 36 Figure 2 13 Corresponding Slice Height in 3 D The out of plane average diameter results for the 3 point Gaussian PIV sizing method are shown below in Figure 2 14 The PDA measurement is also shown in Figure 2 14 and was taken at an elevation above the spray of 15 4mm The PIV planes shown in Figure 2 14 are located at z 16 z 32 z 48 and z 64 pixels The grid spacing used in the out of plane results was 16 pixels The results in Figure 2 14 show that the PIV sizing results agree with the PDA measurement are
73. ackage the Input Package Dialog box shown in Figure 2 3 will appear In this box you can specify the desired name of the input package Input Package Dialog xj Name lE Figure 2 3 Input Package Dialog Box An icon will appear in the upper right box in the FLOW IQ v2 2 window with the name inputted as shown above in Figure 2 2 This icon is the created input package All output will be stored in the base directory where the project is saved in a folder with the same title as the input package 101 Deleting an Input Package From a Project To delete an input package from the workspace simply highlight the desired input package and press Delete on the keyboard You may also right click on the desired input package and click on Delete to delete the input package Modifying Input Package Properties In order to modify the name of an input package right click on the input package and click on Properties The Input Package Dialog Box will appear again and you will be able to input a new name for the input package Adding Images File Sequences and Directories to an Input Package To add files directories or file sequences to an input package simply double click on the icon for the input package you wish to modify Then follow the instructions below for adding images file sequences or directories The FLOW IQ program reads 8 bit tif images with intensities ranging from 0 to 255 In order to a
74. aditional qualitative particle flow visualizations The early work of Meynard 1983 established the foundations of its present form Over the past two decades several publications have appeared on the application and improvement of the PIV method Hasselinc 1988 Adrian 1991 1996 Grant 1994 1997 Willert and Gharib 1991 Westerweel 1993a b and Huang and Gharib 1997 established the digital implementation of PIV which replaced traditional photographic methods The DPIV technique is illustrated below in Figure 1 4 Abiven and Vlachos 2002 Figure 1 4 Block Diagram for the estimation of velocity vectors The standard implementation of the method uses a single exposure double frame digital cross correlation approach CCD cameras are commercially available that can sample at frame rates of 1000 fps or higher The velocity field calculated in DPIV can be treated as a linear transfer function that corresponds to the displacement between two consecutive images This transfer function can be interpreted in a statistical manner by incorporating second order statistical moments of the image patterns Westerweel 1993a 1997 In this manner a statistical cross correlation between the particle patterns of two successive images is performed in order to calculate the velocity field A typical cross correlation implementation of the velocity evaluation algorithm will produce a velocity grid with a vector every 8 to 16 pixels with an uncertainty
75. after use 168 b Particle label left top right bottom pixels If you have a matrix of pixels in hand use this method to create a Particle object label is the particle id left top right and bottom are the location of the particle in its container image 2 Least squares fit method to detect particle size and position p LeastSquaresFit where p is a Particle object By passing maptype VOLUME or MID one of the two least squares method is used 3 Four points gaussian fit method p FourPointsGaussFit 4 Modified four points gaussian fit method p ModifiedFourPointsGaussFit 5 Three points gaussian fit method p ThreePointsGaussFit 6 Centroid method p CentroidDiamFun Note to use 2 to 5 you must supply reasonable initial values for function arguments lo beta diam xc and yc If you don t want to bother giving good initial values then use 7 7 Sizing method that takes a method id as first argument For example if you want to use Three points gaussian fit method do this p Sizing ParticleBase THREE_POINTS_FIT minint Io beta xc yc 8 Add noise Particle AddNoise 9 Conversion between beta and diameter Particle btod Particle dtob 10 Filter particles FilterParticles particles selint where particles is a vector of particles selint means a particle has at least one pixel with value greater or equal to selint If a particle cannot mee
76. al images then click the check box next to Overwrite Original Image File To specify an output directory click on Browse and select the desired output directory Binarize Area Dialog x Task Name Coefficient 0 65 I Overwrite Original Image File Output Directory C Program Files 4eroprobe DPI sbi Browse ce Figure 3 11 Binarize Area Options Smooth 3X3 The smooth 3X3 task uses 3X3 blocks of the selected image to apply a smoothing filter to the image Currently there are no user definable attributes for the smooth 3X3 filter The Dialog Box for Edge Detection is shown below in Figure 3 12 If you wish to overwrite the original images then click the check box next to Overwrite Original Image File To specify an output directory click on Browse and select the desired output directory Image Pro Task Property x Task Name Eee T Overwrite Original Image File Output Directory C Program Files Aeroprobe DPIV bi Browse Cancel Figure 3 12 Smooth 3X3 Options 116 Zero Boundary The zero boundary task zeros the boundary of the image as specified by the user The variables m and n stand for the boundary width in pixels for the boundary to be zeroed in the x and y directions respectively The Dialog Box for Zero Boundary is shown below in Figure 3 13 If you wish to overwrite the original images then click the check box next to Overwrite Original Image File To spe
77. ally adapt to size a given particle based on its intensity profile Monte Carlo simulations should be performed in order to confirm the theoretically improved performance of the elliptical sizing method The next step in the evolution of the Gaussian sizing methods is the development of a rotation for the elliptic Gaussian profile and conversion from the pixel domain to a rotated pixel domain This rotated elliptic Gaussian profile could accurately detect particles that are deformed and not restricted to the normal Cartesian coordinate system This sizing scheme could either perform a brute force axis rotation or utilize the assumption that the intensity is jointly Gaussian and dependent with correlation coefficient p New profiles could also be explored for future sizing value with streaked particles Two profiles of particular interest are the log normal normal independent LNNI and the Rayleight normal independent RNI probability density functions These functions are summarized below These profiles along with rotation techniques could provide a powerful tool for the estimation of diameter and particle shape using PIV 65 3 4 1 Log Normal Normal Independent LNNI PDF For the LNNI probability density function two random variables x and y were considered to be independent random variables The x r v was considered to be log normally distributed with standard deviation O and mean value p The y r v was considered to be normally distr
78. an Fit The traditional three point Gaussian estimator is a simple one dimensional approximation of the geometric particle image ie Xe a 2 na 2 a Eq 2 4 15 The three independent variables lo and x represent the maximum intensity the Gaussian distribution standard deviation and the center position respectively If the three points chosen to solve these equations are the maximum intensity pixel and the two neighboring pixels along the x axis then the standard three point Gaussian estimator can be derived Willert and Gharib 1991 ota Ina _ Ina Cc oO Eq 2 5 2 na _ Ina 2Ina The equation for finding the y center position is identical to equation 2 5 above The diameter measurement is directly related to the variance The variance is given below in equation 2 6 Ina hs ol o x x Fa x aN i Ina The three point estimator is computationally fast and very easy to implement Brady et al 2002 The major limitation of the diameter measurements made in Brady et al are the use of a single dimension as the diameter measurement and the assumption that the particles are in fact circular in profile 2 1 1 3 Four Point Gaussian Estimator The four point Gaussian estimator was developed in order to overcome the limitations of the three point Gaussian fit and allow determining the center and diameter of a particle when it contains saturated pixels In this scheme
79. ance of previously developed PIV methods multigrid DADPIV NDWO PIV in the measurement of velocity in the presence of a velocity gradient No new PIV methods or compensation methods were developed in the course of this work The development of correction schemes for the measurement of wall shear error is left to future researchers in this area To the knowledge of the author no other researcher has performed this type of analysis on the error of DPIV measurements in the presence of velocity gradients Therefore this chapter comprises the most original and significant contribution contained in this work This chapter also provides a basic 90 foundation for more work in the area of wall shear velocity measurement The programs and algorithms developed in the course of this work will serve to quicken further research in this area 91 Chapter 5 5 DPIV DOCUMENTATION AND TEST BED 5 1 DPIV Version 1 0 Documentation A comprehensive user s manual for DPIV version 2 2 was developed in this work The full user s manual is included below Flow IQ Version 2 2 Documentation and Help 9 7 2004 Jason B Carneal Aeroprobe Corporation 92 Table of Contents A 96 Chapter 1 Program Installation ricas iii 97 Chapter 2 Basic Operations iris aiar 100 Creating a New Proein daria 100 Savne a Polarnet 100 Loading a Projecti norni e i i E AE S TE E ia 100 Adding an Input Package to a PrOJEect tirreno 101 Deleting an I
80. and 0 25 pixels pixel the NDWO case has the highest error The traditional multigrid approach has comparable error to the DADPIV approach for a shear rate of 0 0625 pixels per pixel but higher errors than the DADPIV algorithms for shear rates of 0 125 and 0 25 pixels per pixel For the 0 25 sheat rate the DADPIV algorithm performs significantly better than the traditional multigrid algorithm and the NDWO method averaging approximately 2 pixels less total error than the other methods There appears to be a significant peak locking phenomenon occurring in the multigrid and DADPIV algorithms for a shear rate of 0 0625 and 0 125 Figure 4 11 below shows similar results as Figure 4 10 except for a starting interrogation window of 32 pixels 87 Error px Total Error for Each Method 32 Starting Window Shear Rate 0 0625 0 5 NDWO MGRID 0454 A ULTRA 0 4 0 35 0 3 0 25 0 2 0 15 0 1 y ay 0 5 1 1 5 2 2 5 3 3 5 4 Centerline Displacement px Total Error for Each Method 32 Starting Window Shear Rate 0 125 1 NDWO MGRID 0 9 A ULTRA 0 8 I 0 7 4 0 6 4 0 5 4 0 e 1 WE RA or 0 3 er Ba ki 0 2 a ig a A La 5 y 045 1 15 2 25 3 3 5 4 Centerline Displacement px 88 Total Error for Each Method 32 Starting Window Shear Rate 0 25 T E T NDWO K MGRID A ULTRA 1 5F 4 n ae Ed S 5 E ta a K P P a i pane 05 ES I ee 1 1 5 2
81. ask s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data The individual task will be run on all of the selected images in the project When the particle sizing tasks have finished processing a Finished Processing message will appear in the lower right window under Console A theoretical description of each available particle sizing task follows Nomenclature for Fitting Schemes The nomenclature for the description of each fitting scheme is listed below a discrete intensity value d particle diameter d pixel resolution of recording medium d geometric image diameter d diffraction limited spot diameter D i j true particle position D i j measured particle position Erue RMS error with respect to true value Emb mean bias error Ems RMS error with respect to mean f f number of the lens I maximum intensity M magnification of image Soye particle center X Y pixel location A illumination wavelength o standard deviation of gaussian curve Gn standard deviation of added noise level Centroid Fit The Centroid Fit uses pixel counting and center of mass estimation algorithms to determine the centroid and diameter of a particle A center of mass intensity weighted centroid estimator provides the simplest approach for estimating the center and area of a particle Al
82. ata 3 3 1 Theoretical Foundations The conventional 3 point sizing method takes only the x direction into account when sizing particle This procedure can certainly be improved by the addition of a y component to the diameter measurement The particle may either as a true ellipse or as a sphere by averaging the x and y diameter measurements This analysis assumes that the ellipse is axisymmetric around the x and y axes The error associated with the measurement in this work is considered as the percent difference in area of the measured particle as compared to the actual area of the particle The percent difference is defined below in Equation 3 12 ei A Eq 3 13 err Ari The area of the conventional method is simply md where d is the measured diameter of the particle in the x direction The theoretical error of the traditional method when x is the semimajor axis of the ellipse is given by Equation 3 13 which reduces to Equation 3 14 mb abe as Eq 3 14 b C xmaj a Eq 3 15 The theoretical error of the traditional method when x is the semiminor axis of the ellipse is given by Equation 3 15 which reduces to Equation 3 16 2 A E Eq 3 16 fo X MIN abe 52 xmin ea Eq 3 17 The theoretical error of the averaged elliptic sizing method where the diameter is considered to be the average of the semiminor and semimajor axes is given by Equation 3 17 This equation reduces to Equatio
83. ation window can only reliably resolve up to approximately 4 pixels displacement For the higher shear rates an increasing number of particles are in regions where accurate PIV measurement is impossible with a starting window of 16 pixels Therefore the number of tracked particles decreases with increasing shear rate Since the particle tracking process produces a continuous velocity field the error can be plotted as a function of the centerline velocity In order to compute this error the velocity calculated by the algorithm was compared to the known velocity at the particles distance from the top of the image The absolute value of the difference between the calculated and expected velocity values was used as the local error in this study In order to compare the Hybrid PTV results to the traditional PIV methods the errors were calculated for the 0 to 1 pixel displacement range The total error was defined by setting bins around pixel markers for the PIV method and averaging the error for the measurements within the bin The results are shown below in Figure 4 6 78 Total Wall Shear Error for PIV and PTV methods Window 16 0 2 T T T T T T T T T pi DADPIV otep MGRID a NDWO F 0 160 PTV 0 14 0 12 0 1 Error px 0 08 0 06 0 04 0 02 1 0 0 05 0 1 0 15 0 2 0 25 0 3 0 35 0 4 0 45 0 5 Centerline Displacement px Figure 4 6 Total Error for all
84. ay and stores the mad values in an 8 bit t1f format Currently there are no options available for the standard deviation task algorithm The output directory may be specified by clicking Browse and selecting the desired output directory Add The Add task adds an object image to the images in the input package The Dialog Box for the Add task is shown below in Figure 4 6 The user may select the object file by clicking Browse and selecting the desired image to be added to the images in the input package The output directory may be specified by clicking Browse and selecting the desired output directory 124 A S Task Name Add Object File C Program Files Aeroprobe cyl0006 tif Browse Dutput Directory C AWorkspace DPIVI out MT Browse Cancel Figure 4 6 Add Task Dialog Box Subtract Task The Subtract task subtracts an object image from the images in the input package The Dialog Box for the Subtract task is shown below in Figure 4 7 The user may select the object file by clicking Browse and selecting the desired image to be subtracted from the images in the input package The output directory may be specified by clicking Browse and selecting the desired output directory Diei NIN Task Name Subtract Object File je ADPIW Imagest cylinder cyl0015 tif Browse Output Directory CAD PIAbinAWorkspace DPI1 fout IMT Browse Cancel Figure 4 7 Subtract Task Dialog Box A
85. bin W orks Browse Cancel Figure 4 5 Min Task Properties 123 Median Task The Median task creates a 256X256 array and stores the median value across the input set of images at each location The algorithms searches from x y 0 0 to x y 255 255 and finds the median for each point in the input image set Currently there are no options available for the Median task algorithm The output directory may be specified by clicking Browse and selecting the desired output directory Mean Task The Mean task creates a 256X256 array and stores the mean intensity value across the input set of images at each location The algorithms searches from x y 0 0 to x y 255 255 and finds the Mean for each point in the input image set Currently there are no options available for the Mean task algorithm The output directory may be specified by clicking Browse and selecting the desired output directory STD Task The STD task creates a 256X256 array and stores the standard deviation of the intensity value across the input set of images at each location The algorithms searches from x y 0 0 to x y 255 255 and finds the standard deviation for each point in the input image set Currently there are no options available for the standard deviation task algorithm The output directory may be specified by clicking Browse and selecting the desired output directory MAD Task The MAD task creates a 256X256 arr
86. ccept aVisitor 3 Reset the task state task Reset 4 Get info about the task type task GetDesc 5 Get info aobut the task task GetHelpInfo 6 Get type id task GetID Public data members char m_Name MAX_FN_SIZE task name char m_OFDir MAX_FN_SIZE output file directory char m_OFExt 8 output file extension e Class C3x3PivValidation This class models 3X3 vector matrix validation Get a 3X3 matrix with the validating vector as center from the input velocity vector matrix Then calculate its mean and standard deviation without including the validating vector Public member double m_SdHigh standard deviation threshold 5 Particle Tracking Module e Class CParticleTracking This class defines the particle tracking interface This is an abstract class So it cannot be instantiated Operations 173 1 Run next step task GoNextStep fs where task is an CParticleTracking object fs is a FileSequence object Each derived particle tracking class has a step size Some class allows its modification but others does not 2 Query if the current file sequence is finished task IsFinished fs 3 Get start frame for current step task GetCurrentStartFrame fs 4 Get end frame for current step task GetCurrentEndFrame fs 5 Prepare for the next step task PrepareForNextStep Note once finish or give up a file sequence call task Reset Public members double m_Distance distance limit char m_Name MAX_F
87. cify an output directory click on Browse and select the desired output directory Zero Boundary Dialog x Task Name m 2 ni a TT Ovenwrite Original Image File Output Directory C Program Files Aeroprobe DPI bi Browse oros Figure 3 13 Zero Boundary Options Dewarp The Dewarp task zeros is for use with Stereo PIV images The Dialog Box for Zero Boundary is shown below in Figure 3 14 The template file is the file that contains the template Itis an unwarped orthogonal image that shows the calibration target which is usually rows and columns of circles or crosses To specify the template file click on Browse next to Template File and find the template image The calibration file is a picture of the calibration target at the angle at which data was collected which is warped To specify the calibration file click on Browse next to Calibration File and find the calibration image Spacing is the approximate spacing of the markers on the calibration image in pixels Once these parameters are set click on Generate to generate the necessary coefficients for dewarping The Calibration Matrix will be updated according to the calculated values You may either define a calibration matrix yourself generate a new matrix as above or import a calibration matrix To export a calibration matrix click on the Export button and save the file to the desired directory You may now
88. contributions in simultaneous global velocity and size quantification methods However all of the above methods do not resolve the time depended characteristics of the flow since they are limited to sampling rates in the order of 15 30Hz Especially in the case of spray atomization where the natural unsteadiness of the flow is the dominant parameter that governs the break up dynamics sampling rates in the order of KHz are necessaty 2 1 1 Conventional Particle Sizing Techniques The conventional particle sizing techniques used in this work were developed by Brady et al 2002 These techniques include the three point Gaussian four point Gaussian continuous four point and continuous least squares particle sizing algorithms Before the methods are introduced a discussion of the assumptions made in the traditional algorithms is given below 2 1 1 1 Axis symmetric Gaussian Shape The conventional particle sizing techniques follow the assumption that an axis symmetric Gaussian shape can be used to approximate the intensity distribution of the light scattered from small particles Adrian and Yao 1985 showed that the Airy distribution of the point spread function from a diffraction limited lens can be very closely characterized as a Gaussian function If the point spread function and the geometric image are Gaussian shaped then the intensity distribution can also be closely approximated by a Gaussian 14 In a PIV data set the recorded part
89. d Order DWO PIV In Second Order DWO PIV the initial pass is performed on identical areas in two corresponding image For successive passes the interrogation area in the second image is shifted by half of the rounded result from the initial pass and the interrogation window in the first image is shifted by negative one half of the rounded result from the initial pass If the rounded result is an odd number then the second window is shifted by the ceiling of the rounded result from the initial pass and the first window is shifted by the floor of the rounded result from the initial pass All successive passes are made on the resulting interrogation areas and the final pass is added to the rounded integer initial estimate If a pass fails the previous pass is used to update the estimated displacement For more information see Chapter 9 on Output Types The Second Order DWO Process 1s shown below in Figure 6 7 Second Order DWO PIV First Image Second Image olo Initial Pass Region 1 Region 2 Refining Passes Figure 6 7 Second Order Discrete Window Offset The options for Second Order DWO PIV are the same as the options for First Order DWO PIV See Figure 6 6 for a description of the available options in Second Order DWO PIV 144 Hybrid PTV In hybrid Particle Tracking Velocimetry PTV the results from PIV output are used to track particles using the local velocity field The options for Hybrid PTV are shown below
90. d item and click on Delete Setting Project Parameters To set the experimental parameters click on Project gt Set gt Experiment The Project Settings Dialog Box shown below in Figure 2 7 will appear In this dialog box you can specify the experimental parameters for the data you will process x Physical Size fll microns pixel Camera Size ft microns pixel Sampling Frequency fi Hz Exposure Time Apertures fo Wave Length Depth of Field fo Pixel Resolution Flow Tracer Specific Gravity fi Flow Tracer Diameter microns TAL Characteristic Length fi Characteristic Velocity Density 1000 Kinematic Vise ft T1e 006 m Derived Parameters Magnification e Dynamic Viscocit jooon Fopt p Reynolds B09090 st Refresh Mopt Bo Stokes 0 052970 Ds 0 TT Use Pixel Unit Figure 2 7 Project Settings Dialog Box The parameters specified in the Project Settings Dialog Box are used to convert the results from the tasks to the physical domain The options include system aperature magnification camera pixel size laser source wavelength sampling time and exposure time Sampling time is the inverse of the frame rate of the data collection camera and camera pixel size is the physical size of a single pixel in the data to be analyzed 104 Other experimental parameters that can be specified are the Pixel Resolution Depth of Field Flow Tracer Specific Gravity Flow Tracer Diameter C
91. d output from the FLOW IQ software Saving a Project In order to save a project click on File gt Save press Ctrl S or click on File gt Save As Browse for the directory in which you would like to save your project settings provide a filename for your project and click SAVE All project settings tasks images directories and file sequences in the project will be saved The directory in which the project is saved is the default directory for the output of files Loading a Project To load a saved project click on File gt 0Open Browse to the directory containing the saved project click on the saved project and click OPEN The project will be loaded into the FLOW IQ GUI 100 Adding an Input Package to a Project In FLOW IQ v2 2 you must add an input package in order to process files Images Directories and File Sequences can be added to the Input Package once it is created This setup allows the user to process separate sets of files without interfering with saved work To add an input package either click on T in the toolbar or click on Project gt Add Input Package as shown below in Figure 2 2 podas File Edit View Project Image Window Help DOS Input Package Set gt Files a DPIV Clear Input Directory Image Process File Sequence Image Math Y Particle Sizing 23 Particle Tracking Caer Y Validation Stero PIV Trajectory Figure 2 2 Adding an Input Package After clicking on Input P
92. dd images to the project either click on T in the toolbar or click on Project Add gt Files Browse for and select the desired images to be added to the project and click OK The images will be displayed in the upper right box in the FLOW IQ software as shown below in Figure 2 4 Pod File Edit view Project Image Window Help Os Input Package Set b Files E DPIV Clear Input Directory Y Image Process Fije Sequence C Image Math C Particle Sizing I Particle Tracking 3 Pre 9 Validation Y Stero PIV 9 Trajectory Figure 2 4 Adding Images Directories and File Sequences to an Input Package If you wish to perform tasks on a large number of images or data files it is best to add directories or file sequences to the project instead of images In order to add a directory to the project either click on D in the toolbar or click on Project Add Directory The Directory Dialog box will appear as shown in Figure 2 5 below Browse for the desired directory to be added to the project and click OK 102 Specify the extension of the files to be used in the directory either tif or plt The directory will be displayed in the upper right box in the FLOW IQ software Directory of Files Dialog 4 xj Dir je Program Files Aeroprobe DPlYbin Ext tif DK Cancel Figure 2 5 Directory Dialog Box For file sequences the procedure is the same as images and directories except that the file
93. des a 60 Watt copper vapor laser for illumination and a Phantom V4 CMOS 18 digital camera for data acquisition This system allows data acquisition up to a frame rate of 1kHz The camera has a resolution of 512X512 pixels The spray data used in this work was taken at a resolution of 256X256 pixels A 10KHz pulsing Copper Vapor Laser was used to deliver a sheet of light with illumination energy of 5 mJ The laser sheet was passed through a cylindrical lens and focused into a vertical plane parallel to the axis of the spray A Phantom V CMOS camera placed normal of the laser sheet captured the water droplets with pixel resolution of 256x256 and a frame rate of 10 KHz and total sampling time of 1 sec A second Phantom IV CMOS camera with resolution of 128x128 and sampling rate of 10KHz was employed in order to record off axis images in a stereo DPIV configuration A calibration target was used to assure that the interrogation areas of the two cameras overlap and subsequently used for the reconstruction of the images Due to space limitations in this paper and the preliminary nature of this study we will not elaborate on the three dimensional measurements The laser and the camera were synchronized in order to operate in a single pulse per frame mode The camera is equipped with an internal shutter which was set at 10microsecs in order to reduce the ambient background light thus increasing the signal to noise ratio of the images The laser pulse a
94. diameter measurement is directly related to the variance 2 Ina Ina Y ON a aa x X Kos X 3 The three point estimator is computationally fast and easy to implement Its limitations are that it is a one dimensional approximation thus when employed in 2 D it is practically a five point scheme that restricts the selection of points to the highest intensity pixel and its four neighbors along the rows and columns of the image In addition the diagonal pixels do not contribute to the measurement Because of its nature the three point Gaussian fit does not allow discarding any pixels on the basis of their intensity thus saturated pixels do contribute to the measurement Finally one more limitation stems from the fact that the center pixel which is the one with the highest intensity is an upper bound for the maximum intensity value of the particle thus always constraining its calculation Although this is not significant for the position estimation it is of great importance for the diameter measurement since it adjusts the height and spread of the Gaussian distribution and can be more detrimental when pixels are saturated The three point fit is also very susceptible to high errors for particles larger than three pixels in diameter Four Point Gaussian Fit A four point estimator is now presented The motivation behind this method was to overcome the limitations of the three point Gaussian fit and allow determining the center
95. distribution peaks 50 Jonty Gaussian ERVI sigy 0 50 ga 1 00 1 gt al 4 3 2 E o 1 2 3 4 Jonty Gaussian RVs sigy 1 00 siga 0 30 4 1 o E 2 3 al 4 3 2 E o g 2 3 4 Figure 3 3 Jointly Gaussian INRV s with various values of and o Errors were calculated in this work as the difference between the actual area of the particle and the measured area of the particle The area of an ellipse is simply nbc where b is the semimajor axis of the ellipse and c is the semiminor axis of the ellipse The eccentricity of an ellipse which describes the shape of the ellipse is defined below in equation 3 11 Eq 3 12 The eccentricity varies from 0 to 1 for an ellipse since the semiminor axis is by definition less than the semimajor axis 3 2 Elliptical Particle Sizing Scheme Methods and Materials A theoretical analysis of the elliptical sizing method was performed Monte Carlo simulations of the performance of the method will be left to future research 3 3 Elliptical Particle Sizing Results The theoretical advantages of using an elliptical particle sizing algorithm are explored in the following section These results provide the basis for future work in the development of elliptical 51 sizing techniques Section 3 3 2 presents the experimental portion of this work which consists of Monte Catlo simulations in order to determine the performance of the elliptical sizing method in simulated d
96. e Out of all the ambiguity the only certainty is that he hates engineering or at least the engineering to which he has been exposed to date With any luck his career decisions in the future will reflect his desires and not the desires of those around him 188
97. e three point Gaussian four point Gaussian continuous four point Gaussian and the continuous least squares are 0 9761 0 5558 0 1957 and 0 5496 respectively These results show that the 3 point Gaussian performs much better in comparison to the PDA measurements than all of the other PIV sizing methods Probability Density Functions for All Methods Plane 4mm T T 0 18 5 T T T T T T I Q PDA 3 Point 0416F 4 4Point 1 Cont 4 Cont LS 0 14 4 2 0 12 4 o A 2 3 Op 4 oO 8 a 5 0 08 4 o E 6 0 06 4 zZ 0 04 4 0 02 4 0 I I 1 I 100 105 110 115 120 125 130 135 140 145 150 Diameter um Figure 2 6 Histogram Results for 4mm Spray Plane All Sizing Methods 29 Probability Density Functions for All Methods Plane 4mm 0 18 T T T T T T T T I Q PDA 3 Point 016 4 4Point di A Cont 4 Cont LS 0 14 4 2 0 12 4 a 2 3 Ir 7 oO 2 E a o 0 08 Vv N T E 6 0 06 z 0 04 4 0 02 sj 0 I 100 105 110 115 120 125 130 135 140 145 150 Diameter um Figure 2 7 Histogram Results for 4mm Spray Plane All Sizing Methods The histograms for the positive and negative 8mm displacement measured from the center of the spray are shown below in Figure 2 8 Figure 2 8 shows the same general trends in the 8mm planes as seen in Figure 2 5 for the Omm plane exce
98. ear wall velocities from experimentally determined DPIV flow fields is most affected by the effect of spatial averaging due to window interrogation size This is particularly true as the shear rate increases which effectively skews the correlation matrix the consequence of which is the inability of the conventionally utilized Gaussian three point estimator to accurately determine the true displacement at the center of the window Marxen et al 2000 The signal is dominated by the flow away from the boundary due to higher velocities and better seeding density causing a biasing of the displacement estimation Only the effect of velocity gradient on the measurement accuracy will be considered here as the near wall seeding is a system dependent parameter 71 4 2 Wall Shear Methods and Materials Monte Carlo Simulations were performed in order to test the accuracy of several DPIV algorithms when measuring wall shear One hundred artificial Couette flow images were created using in house artificial image generation software for each shear rate studied in this work In order to compare the error associated with DPIV measurements of velocity under velocity gradients low shear rate images were generated in order to create centerline displacements of 0 1 to 0 5 pixels in 0 1 pixel increments The shear rates used to produce these centerline displacements were 0 025 0 050 0 075 0 100 and 0 125 pixels per pixel Shear rates of 0 0625 0 125 and 0 25
99. earch radius of 3 pixels was used in conjunction with No Discrete Window Offset PIV and 3 point Guassian sizing to track the particles in the artificial Couette images The velocities from PTV were then compared to the known velocity at the particle s y postion obtained from the sizing algorithm and errors were plotted as a function of displacement for the low shear rates discussed above 4 3 Wall Shear Results The first goal of the wall shear portion of this work was to characterize the expected error associated with wall velocity measurements using DPIV The wall shear characterization performed in this work was divided into two sections a high shear section and a low shear section The high shear section studied Couette flows with velocity gradients up to 1 pixel per pixel The low shear section targeted shear rates that would produce centerline displacements of 0 to 0 5 pixels in 0 1 pixel increments 4 3 1 Low Shear Rate Study The shear rates examined in the high shear portion of this work were 0 0 025 0 05 0 075 and 0 100 and 0 125 pixels per pixel shear rate These shear rates produced the desired centerline displacement of 0 to 0 5 pixels at the first measurement point The images generated for this work had zero background noise in order to isolate the effects of shear rate on the velocity error Procedures identical to the high shear rates were used for the analysis of the low shear images Errors were plotted to compare the per
100. ect pixels with high intensity and as close as possible to the maximum intensity pixel in order to reduce noise effects and minimize the error Least Squares Fit Local least squares LLS have been used in the past as alternatives to the three point Gaussian fit The position and the diameter can be estimated with sub resolution accuracy using a number of pixels greater than or equal to four The local least squares fit is employed in this study by minimizing y described by Equation 10 IAH YY dic 26 2 x Dia Le n 9 The minimization was performed using a Gauss Newton algorithm The least squares fit allow for selecting certain points while leaving others out with no topological constrains Two methods of point selection were investigated in the Monte Carlo simulations presented later First the conventional 3x3 pixel area around the one with highest intensity similarly to the standard three point Gaussian fit This scheme was also 134 investigated by Marxen and Sullivan 2000 Second all the available points with intensity over a certain threshold value are accounted for This is the equivalent of a high pass threshold filter and it is employed only for the larger particles in order to reduce excessive computational time Modified Continuous Four Point Gaussian Fit Based on the above an improved implementation of the four point fit is now proposed This is an integrated four point fit that eliminates the systematic err
101. ection also deals with the addition removal and performance of the image math tasks Image math tasks may be run alone or in conjunction with other tasks The input files for these tasks are 8 bit tif images Adding Image Math Tasks To add preprocessing tasks to the active project click on Image Math in the upper left window Image Math should now be highlighted Now right click on Image Math and click on Add Image Math Tasks The Image Preprocessing Add Task Dialog Box will appear This process is shown in Figure 4 1 below Task Add Dialog y xj Selected Tasks MAX Mean MAD Cancel Figure 4 1 Task Add Dialog Box To add a task to the project click on the desired task to highlight it and then click The available tasks are listed on the left and the tasks to be added are shown on the right When you have selected the desired tasks click OK The added tasks will be shown in a tree under Image Math as shown below in Figure 4 2 These tasks will be performed from top to bottom in the tree If you wish to change the order of operations click and drag the tasks to new positions until you are satisfied with the order of operations 120 8 DPIY DPI 1 br File Edit View Project Image Window DediIFDMW El DPIY 3 Image Processing E Image Math Min Median Mean Std MAD Add Subtract And Or Particle Sizing Particle Tracking PIY Validation Stero PIV 9 Trajectory
102. ed Output dir C Documents and Settings My Documents Ext plt Window sizes 16 16 X grids 16 Y grids 16 lt piv gt Processing Frames 0 1 16 320000000 seconds Processing Frames 0 1 16 320000000 seconds Finished Processing When the PIV tasks have finished processing and all the frames have been completed a Finished Processing message will appear in the lower right window under Console A description of each available PIV task follows No Discrete Window Offset DWO PIV In No Discrete Window Offset DWO PIV only a single interrogation pass is made Regions within the two consecutive images undergoing PIV analysis will have the same coordinates in No Discrete Window Offset PIV The user selects the interrogation window size as shown in Figure 6 4 below The available window sizes are 8 16 32 and 64 pixels x Task Name No Discrete Window Offset Peak Detection Method Three Points Gaussian Fit y Window Size 1 16 y 2016 iz x Grid Spacing la I Boundary Y Grid Spacing la TT Zero Padding Correlation Method FFT based Normalize Fast y Validation Task 33 PIV Validation Add Delete Properties Dutput Directory C Program Files Aeroprobe DPIV bin Workspac Browse Output File Ext plt Input Filter Type Sequence Frames Skip fo Cancel Figure 6 4 No Discrete Window Offset Task Dialog Box 140 Peak Detection Method controls the method used
103. ed with particles with 56 eccentricities varying from 0 circular to 0 8660 50 percent difference between the semimajor and semiminor axes Two example images are shown below in Figure 3 8 The generated images were 32 X 32 pixels square and the center of the particle was forced to be located at x y 7 25 7 25 in order to fix the particles within the image Figure 3 8 Sample Monte Carlo Simulation Images The images used in this experiment were generated using MatLAB 6 0 The profiles were assumed to be elliptical Gaussian profiles as developed in the introduction of this chapter The pixel values were obtained by integration of the elliptical Gaussian profile over the pixel area in order to simulate the optics of a CCD device The traditional and novel elliptical sizing methods were performed on each image and the error was calculated according to Equation 3 13 The results obtained from this analysis follow In order to test the methods on a basic level circular particles were generated in order to provide a baseline method to ensure that the different methods developed in this work agreed with the traditional 3 point Gaussian method The total error in the diameter measurement is shown below in Figures 3 9 and 3 10 To generate Figure 3 10 the error values shown in Figure 3 9 were averaged over 250 measurements which generated 20 data points over the data range from 2 8 pixels to 5 6 pixels in steps of 0 14 pixels DI
104. el particle sizing techniques PIV allows a full two dimensional analysis of particle diameter as compared to the traditional Phase Doppler Anemometry PDA measurements This paper explores the application and performance of novel particle sizing techniques to the measurement of particle diameter and mass flux in sprays The second focus of this paper is the performance of traditional and novel PIV algorithms in the measurement of wall shear Wall shear especially in boundary layer analyses contributes significant error to velocity measurements using DPIV This work explores the errors involved in the measurement of shear rate with DPIV and provides some novel methods for correcting these errors The third portion of this work explores the application of novel sizing techniques to displacement estimation algorithms used in DPIV and the errors associated with each method 1 2 Particle Image Velocimetry 1 2 1 Method Particle Image Velocimetry PIV is the process of analyzing consecutive digital images of data using cross correlation in regions of interest to estimate a displacement in the image This displacement is then converted to a velocity using the frame rate of the camera which is a known experimental parameter A great deal of study has been performed on PIV and methods to improve the accuracy of the method Digital Particle Image Velocimetry DPIV has emerged as a 1 standard in global flow measurements In this technique a fluid is
105. elation Coefficient 3 Point Guassian Full Results 0 9571 Tracked 3 Point Gaussian 0 9739 PTV Compensated 3 Point Gaussian 0 9558 Table 2 4 PTV Correlation Coefficients for 100 to 150 um Range 0 mm Plane Table 2 4 shows that the tracking method improves the correlation coefficient of the method since the tracked histogram matched the PDA better at diameters less than 110 microns The compensated histogram is shown below in Figure 2 19 Probability Density Functions for PTV Compensated 3 point and PDA T 0 25 T T T T T T I PTV A PDA A y 0 2 4 k A 0 15 4 s 2 5 a o a 0 1 4 0 05 4 T PN l j ser vela 0 I L l 100 105 110 115 120 125 130 135 140 145 150 Diameter um Figure 2 19 Tracking Compensation and PDA for 100 to 150 micron range The correlation coefficient between the PDA and the compensated PTV method may improve over different diameter ranges The exploration of different diameters will be left to future researcher in the particle sizing arena 2 5 Conclusions and Future Work The particle sizing portion of this work showed that the design of DPIV experiments is vital for the accurate measurement of particle size using PIV sizing methodologies An experiment must contain particles that are at least 3 pixels in diameter in the PIV data plane in order to produce 44 accurate results Therefore the minimum suggested particle diameter for siz
106. eter was held constant at 5 6 pixels in order to fix the eccentricity range from 0 to 0 8660 60 Diameter Absolute Error Y Diameter Error 2 T T T T T T 1 5 NN Boa i 1H ee sa N mm 0 5 Tago oF na ANI E ATTI pi pig 0 5 Ai Trad 3 point X 1 5F Averaged Elliptic X True Elliptic X Trad 3 point Y aa Averaged Elliptic Y True Elliptic Y 2 5 3 I I 2 5 3 3 5 4 45 5 5 5 X Diameter IS Cane IIS LU Y V LU LU 60 T T T T I I Trad 3 point X a Averaged Elliptic X fu True Elliptic X DEN Trad 3 point Y 40 F Sau Averaged Elliptic Y H es True Elliptic Y 20 0 be 20 40 60 I li L li I 1 2 5 3 3 5 4 4 5 5 55 X Diameter Figure 3 11 Error in the x and y diameter measurements vs x diameter Monte Carlo Simulations Eccentricity O to 0 8660 61 Diameter Error Diameter Absolute Error Monte Carlo Simulations Eccentricity O to 0 8660 60 T T T T T T T T Trad 3 point X Averaged Elliptic X 40 True Elliptic X Y a Trad 3 point Y A Averaged Elliptic Y eo True Elliptic Y pe ge 20 ee 4 paro per agg si cas pria ee pers EST e AN 0 rro AT Luna E E t i 20 H a 404 al 60 1 1 1 i 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Eccentricity Monte Carlo Simulati
107. ethods to elliptical and deformed seed particles in DPIV data sets which represents a first next step in the development of advanced particle sizing methods The work presented in this chapter is intended as an initial step for the continuation of the development of elliptical sizing algorithms 70 Chapter 4 4 WALL SHEAR EXPERIMENTS 4 1 Introduction A major aim of this work is to quantify the accuracy of wall velocity estimation using DPIV Velocity measurement error for DPIV has been quantified in the past Huang et al 1997 Even in the presence of strong velocity gradients the accuracy of the velocity measurements is better than 0 1 pixels px for state of the art systems However in the case of wall bounded flows cross correlation induced spatial averaging effects can significantly affect the measurement due to very strong localized shear rates The particle pattern displacements are determined with sub pixel resolution from the cross correlation peak for each interrogation window using a Gaussian fit that is applied to the correlation coefficient matrix Detailed analyses of these methods can be found in several of the referenced papers in this work Marxen et al 2000 Meunier and Leweke 2003 Raffel et al 1998 Wereley and Meinhart 2001 Nogueira et al 1999 For near wall measurements the cross correlation signal to noise ratio is often compromised by reduced seeding density compared to the outer flow Evaluation of n
108. etry etc will be discussed in the following chapters An example dialog box for this process is shown below in Figure 2 8 n Task Add Dialog x Selected Tasks Three Points Gaussian Fit Four Points Gaussian Fit Least Squares Mid Fit Modified Four Points Gaussian Least Squares Volume Fit Cancel Figure 2 8 Example Add Task Dialog Box 105 Editing Task Properties When a task is highlighted the properties of the task will be displayed in the lower left window as shown In order to edit these properties click on the desired task to highlight the task Then right click on the highlighted task and click Properties The corresponding dialog box will appear depending on the selected task Enter the desired properties and click OK The individual properties are discussed below in detail for each PIV technique Properties specific to each type of task Image Processing Particle Tracking etc will be discussed in the following chapters Removing Tasks from a Project There are two ways to remove tasks in FLOW IQ 2 2 as a group or individually To remove several tasks from the active project click on the folder containing the tree you wish to modify in the upper left window The folder should now be highlighted Now right click on the folder and click on Remove Tasks The Remove message will vary with the type of task For example the Image Preprocessing Remove Tasks Dialog Box 1s shown below in Figure 2
109. ew test bed No complete error analysis was performed on this data The complete error analysis is left to future researchers The purpose of the test bed is to develop an interface for error analysis Testbed2 m a Matlab program contains functionality for uniform and vortex error analysis for the Flow IQ software Future researchers should update the code to include ultimate processing capability and to handle a wider variety of test cases 180 y px y px X Local Vortex Error for NDWO ySeen3 0 200 150 100 x px Y Local Vortex Error for NDWO Seen3 0 200 150 100 x px Figure 5 2 X and Y Local Error for No Discrete Window Offset 181 50 100 150 200 50 100 150 200 2 0 X Local Vortex Error for FODWO Seen3 0 200 150 y px 100 50 50 100 150 200 x px Y Local Vortex Error for FODWO seen3 0 200 150 y px 100 50 50 100 150 200 x px Figure 5 3 X and Y Local Error for First Order Discrete Window Offset 182 X Local Vortex Error for SODWO Seen3 0 200 150 y px 100 50 50 100 150 200 x px Y Local Vortex Error for SODWO seen3 0 200 150 y px 100 50 50 100 150 200 x px Figure 5 4 X and Y Local Error for First Order Discrete Window Offset 183 5 3 Summary of Original Contribution The original contribution in this work is a complete and comprehensive user s manual for Flow
110. exhibit a bias toward higher diameters as compared to PDA measurement The correlation coefficients for the four point Gaussian continuous four point Gaussian and the continuous least squares are 0 7916 0 4130 and 0 4144 respectively for the Omm plane The continuous least squares pdf exhibits a high degree of noise over this range of diameter measurement which stems from the low number of relative particles successfully detected The histograms for the positive and negative 4mm displacement measured from the center of the spray ate shown below in Figures 2 6 and 2 7 The results in Figures 2 6 and 2 7 also show that the histogram for the three point Gaussian method matches best with the PDA measurements in 28 the range from 100 microns to 150 microns The three point Gaussian method again follows the PDA trend with a correlation coefficient of 0 9728 In the 4mm plane the four point Gaussian and continuous four point Gaussian algorithms exhibit the same trend as in the Omm plane a bias towards the higher diameters The correlation coefficients for the four point Gaussian continuous four point Gaussian and the continuous least squares are 0 8904 0 6692 and 0 5745 respectively for the 4mm plane The same general trends appear in the 4mm plane but the histograms are more erratic than in the 4mm plane results for the four point Gaussian and four point continuous sizing algorithms In the 4mm plane the correlation coefficients for th
111. formance of the various methods at different window sizes Figure 4 2 below shows the total error for all methods studied in this work with a starting interrogation window of 64 pixels Figure 4 2 shows that the NDWO method has the highest error at a starting interrogation window of 64 The conventional multigrid method exhibits a spike in bias and rms error at centerline 73 displacements of 0 4 and 0 5 pixels The DADPIV method however performs consistently over the range of displacements shown in Figure 4 2 The DADPIV and multigrid methods exhibit similar behavior at displacements ranging from 0 to 0 3 pixels Total Wall Shear Error for DADPIV Multigrid and NDWO Window 64 3 T T T T T T T T T S DADPIV P 25 MGRID n NDWO 2 4 s 151 be ui 4 A y A 05 a J e E o zu ai A E A tb 0 0 05 0 1 0 15 0 2 0 25 0 3 0 35 0 4 0 45 0 5 Centerline Displacement px Figure 4 2 Total Error for all DPIV methods Window 64 Figure 4 3 below shows the total errors for a starting interrogation window of 32 pixels 74 Total Wall Shear Error for DADPIV Multigrid and NDWO Window 32 S DADPIV A 0 9 MGRID E NDWO 0 8 Error px o o o o A n n N T T A 1 1 o wo T 1 0 1 0 15 0 2 0 25 0 3 0 35 0 4 0 45 0 5 Centerline Displacement px Figure 4 3 Total Error for all DPIV methods Window 32 According to Figure 4 3 the multigrid and DADPIV algorit
112. g particle tracking and PIV modules work depending on the existence of image preprocessing module PIV module also depends on particle sizing module Particle tracking module depends on both particle sizing and PIV modules The document is organized as follows section 1 describes utility module image preprocessing module is given in section 2 section 3 illustrate particle sizing module PIV is demonstrated in section 4 next section is particle tracking module 1 Utility Module The purpose of the module provides functionality common to other modules It is reusable across projects e Class Matrix lt T gt As a first class template class it provides basic matrix operations such as etc Although it is a user defined type it can be used in the similar way to the basic types 1 e int It can be used with any first class class as its template type that has constructor T int value Operations 1 Matrix construction Create a m n double matrix Matrix lt double gt mat m n Create a m n double matrix based on a one dimension array X Matrix lt double gt mat m n X Create a m n double matrix based on a two dimension array Y Matrix lt double gt mat m n Y Note X and Y must have longer life than mat 2 Subscript operator m 0 0 represents the first row first column element If m 1s a double matrix and z is a double then you can do mQ 0 0 10 3 z m 0 0 3 unary opera
113. g velocimetry Experiments in Fluids 29 Meynard R 1983 Measure de champs de vitesse d ecoulements fluids par analyse de suites images obteneues par diffusion d un fueillet lumineux Ph D Dissertation Faculte des Science Appliquees Universite Libre de Bruxelles McKenna S P and McGillis W R 2002 Performance of digital image velocimetry processing techniques Exp Fluids 32 pp 106 115 186 Mayer S 2002 A generalized processing technique in digital particle image velocimetry with direct estimation of velocity gradients Exp Fluids 33 pp 443 457 Meunier P Leweke T 2003 Analysis and treatment of errors due to high velocity gradients in particle image velocimetry Exp in Fluids 35 pp 408 421 Nogueira J Lecuona A Rodriguez P A 1999 Local field correction PIV on the increase of accuracy of digital PIV systems Exp in Fluids 27 pp 107 116 Pereira F Gharib M Dabiri D and Modarress D 2000 Defocusing digital particle image velocimetty a 3 component 3 dimensional DPIV measurement technique Application to bubbly flows Experiments in Fluids 29 7 SO78 S084 Prasad A K and Adrian R J 1993 Stereoscopic particle image velocimetry applied to liquid flows Experiments in Fluids 15 49 60 Raffel M Willert C E Kompnhans J 1998 Particle image velocimetry a practical guide Springer Berlin Heidelberg New York Song X Yamamoto F 1999
114. gned to provide the necessary particle size for comparable results to PDA measurements This work was performed as a validation of the particle sizing methodologies as an application of the new sizing software in a real experiment The only original algorithm in this work is the PTV corrected method for particle sizing which will be further developed by future researchers 46 Chapter 3 3 ELLIPTICAL PARTICLE SIZING METHOD The purpose of this chapter is to explore the development of a novel elliptical sizing algorithm developed by the author Previous sizing methodologies have made the assumption that particles are spherical in shape and present a circular profile in DPIV data In some applications this assumption can be justified However in several applications such as spray atomization droplets or seed particles deform and may present elliptical profiles in DPIV data Therefore this work explores the development of an elliptical sizing method that is not limited to circular profiles Monte Carlo simulations were also performed in order to validate the performance of the method on simulated DPIV data 3 1 Introduction In this work an elliptical particle sizing technique was developed in order to overcome the assumption that all particles in a flow field are spherical The assumption of spherical particles introduces error into the measurement of diameter using the conventional PIV sizing schemes presented above in Chapter 2 In orde
115. haracteristic Velocity and Length Density of the fluid and the kinematic viscosity of the fluid FLOW IQ v2 2 is able to derive the magnification dynamic viscosity optimal focal length Fop Reynolds Number Stokes Number and diffraction limited diameter Ds If you wish to keep all measurements in the pixel domain click on Use Pixel Unit in order to halt conversion to the physical domain Adding Tasks to the Project To add tasks to the active project click on the folder that represents the general task you wish to perform in the upper left window Image Processing Particle Sizing etc The desired folder should now be highlighted Now right click on the folder and click on Add Tasks The Add message varies with each method and the various methods will be discussed in the corresponding chapter for each type of operation A dialog box will appear To add a task to the project click on the desired task to highlight it and then click The available tasks are listed on the left and the tasks to be added are shown on the right When you have selected the desired tasks click OK The added tasks will be shown in a tree under the selected folder These tasks will be performed from top to bottom in the tree If you wish to change the order of operations click and drag the tasks to new positions until you are satisfied with the order of operations The procedures for adding each type of task Image Processing Particle Image Velocim
116. he error in the PIV measurement increases dramatically It is however important to characterize the behavior of the PIV sizing methodologies on real data at these diameters The magnification in this experiment was approximately 24 microns per pixel diffraction terms were included in the calculation of the magnification factor Therefore the approximate lower limit of detectable diameter in this experiment is approximately 15 to 20 microns The PDA system used in this experiment could resolve diameters as low as 0 5 microns Therefore in this particular experimental setup the PIV method could not resolve diameters at the lower range of the PDA data The full results from the Omm plane are shown below in Figure 2 4 26 D10 Probability Density Curves for PDA and 3 4 and 4 Modified and LSVL Methods 0 9 6 PDA D10 2 3P 60 100 0 8 L A A 4P 60 100 4M 60 100 LSVL 60 100 0 7 2 o T I e on T e ES T Normalized Probability Density o w T S N T Diameter um Figure 2 4 Full Results for All Sizing Methods and PDA 0mm Plane The results in Figure 2 4 show that there is a significant locking on particles in the 20 to 30 micron range for all of the PIV sizing algorithms The correlation coefficients for the three point Gaussian four point Gaussian continuous four point Gaussian and the continuous least squares are 0 1465 0 2762 0 2465 and
117. hms have nearly identical performance over the range 0 to 0 5 pixels for an initial interrogation window size of 32 pixels As in Figure 4 2 the RMS errors are an order of magnitude less than the associated mean errors The NDWO method also exhibits a much higher error than the multigrid or DADPIV algorithms Figure 4 4 below shows the total errors for an initial interrogation window of 16 pixels 75 Total Wall Shear Error for DADPIV Multigrid and NDWO Window 16 0 2 T 178 T T T T T T PA E 0 18 DADPIV A cp MGRID ox amp NDWO A SU 0 16 g e N ug 0 14 f ES 4 K 0 12 i 4 2 g 5 0 1 di f 0 08 f A 0 06 Fi ye 4 7 A f 0 04 ES al Y Ly E 0 02 H A dd 1 A A A 0 0 05 0 1 0 15 0 2 0 25 0 3 0 35 0 4 0 45 0 5 Centerline Displacement px Figure 4 4 Total Error for all DPIV methods Starting Window 16 For an initial interrogation window size of 16 the multigrid and DADPIV methods have a higher error than the NDWO method except at the displacements of 0 4 and 0 5 where all three methods have similar performance The above results suggest that for measurement of wall velocity in shear flows that exhibit relatively low velocity gradients the initial interrogation window size plays a major role in the error associated with the measurement The NDWO offset case represents the first pass in the multigrid and DADPIV methods The errors shown in Figures 4 2 through
118. ibration for the fluorescence intensity quantification Damaschke et el 2002 use Global Phase Doppler GPD which is an interferometry based methodology where the particle droplet diameter is proportional to the number of fringes formed by out of focus particle images Despite the high accuracy and the global character of the method the optical resolution of the system can be a limiting parameter soon generating overlapping particle images because of the out of focus effects while it is limited to small interrogation areas 13 Pereira et al 2000 introduced an out of focus method for size measurements based on a defocusing DPIV principle applied on liquid bubble flows Using the out of focus images of the recorded bubbles enhances the capabilities of conventional DPIV systems by allowing bubble droplet size information in two phase flows An off axis aperture collecting light from a point source bubble generates an out of focus image By collecting the information of the light intensity the particle pattern and the blurriness for each image pair the method resolves both the velocity and the size of the bubble In addition by analyzing the intensity of the defocused particle Airy disks can provide information for the out of plane velocity component This method requires a minimum of three cameras in order to overcome measurements ambiguities This discussion although not comprehensive represents some of the most recent and significant
119. ibuted with standard deviation and mean value u For a log normally distributed variable x the pdf is defined as follows In x X 20 x 3 20 fe x Eq 1 O N2T 5 For a normally distributed variable y the pdf is defined as follows y E j Eq f Oy 3 21 Y 3 D e For independent r v s the joint pdf can be expressed as Stark and Woods 1986 fyy x y fx x 8r Eq 3 22 Therefore the joint pdf for an LNNI system can be written as 1 aco al Lig x y ea e 20 20 Eq 3 23 T0 0 where 0 is the standard deviation of r v x G is the standard deviation for r v y direction u is the mean of r v x and u is the mean of tv y Figures 3 14 and 3 15 below show the a 2 D probability density function with x as a log normal random variable with 0 80 and u 1 00 and y as a Gaussian random variable with O 0 30 and u 0 00 The variables in these plots are assumed to be independent random variables x and y This pdf may prove to be extremely useful in simulating streaked particles The parameters and u determine the skewness and length of the pdf s tail The parameters and u can be manipulated to simulate particles of larger diameter This probability density function allows the simulation of particles that exhibit skewness and streaking characteristics 66 Log Normal sigy 0 30 sigx 0 80 muy 0 00 mux 1 00 o Probability De
120. icle image d can be expressed in terms of the particle diameter d the diffraction limited spot diameter d and the resolution of the recording medium d This relationship is shown below in Equations 2 1 to 2 3 d de d Eq 2 1 d 244M 1 f Eq 2 2 d M d 42 Eq 2 3 In these equations M is the magnification f is the numerical aperture of the lens and A is the wavelength of a coherent monochromatic light source Equation 1 4 3 includes the combined effects of the optical system s magnification and diffraction on the particle image when optical aberrations are not present Gaussian fitting schemes such as the three point estimator and local least squares estimator reduce the error associated with particle center estimation of a geometric image when compared to more traditional methods such as center of mass Udrea et al 1996 Marxen et al 2000 Willert and Gharib 1991 In addition these techniques also decrease the peak locking effect in the bias error when compared to centroid analysis Willert and Gharib 1991 The use of the conventional Gaussian sizing schemes for finding particle positions has been documented further in Brady et al 2002 Other studies such as Marxen et al 2000 have also investigated the use of the three point fit as a sizing algorithm The conventional Gaussian sizing techniques developed by Brady et al 2002 are given in the following sections 2 1 1 2 Three Point Gaussi
121. import this file for other projects if necessary If you wish to overwrite the original 117 images then click the check box next to Overwrite Original Image File To specify an output directory click on Browse and select the desired output directory ITT x Task Name Dewarp Tl Overwrite Original Image File m Calibration Matrix Generator Template File je Program Files 4eroprobe DPIV Images tes Browse Calibration File C Program Files 4eroprobe DPI mages cyli Browse Spacing 20 I Big Ref Point Generate r Calibration Matrix fo 1 0 2 0 05 0 16 0 5 0 6 ni 0 115 0 21 21 0 132 0 163 0 134 0 366 Export Dutput Directory C Program FilestAeroprobe DPIAbinAW orksp Browse coa Figure 3 14 Dewarp Function Options Boundary Removal The boundary removal task removes the boundaries in the image as specified by the user The strength of the algorithm can be increased by increasing the value of Coefficient The Dialog Box for Boundary Removal is shown below in Figure 3 15 If you wish to overwrite the original images then click the check box next to Overwrite Original Image File To specify an output directory click on Browse and select the desired output directory Boundary Removal Dialog x Task Name Aa Coefficient fo 65 T Overwrite Original Image File Output Directory C Program FilestAeroprobe DPIbi Browse Figure 3 15 Bounda
122. in Figure 6 8 The algorithm uses the output from particle sizing and PIV to produce the hybrid PTV results The user must select a Particle Sizing method under Particle Sizing by clicking on Add and adding the desired sizing tasks The properties of the sizing tasks can be modified by highlighting the desired task and clicking on Properties under Particle Sizing The user must also select a PIV method under PIV by clicking on Add and adding the desired sizing tasks The properties of the sizing tasks can be modified by highlighting the desired task and clicking on Properties under PIV Distance specifies the search radius the algorithm uses to determine tracked particles and is in pixel units In the example shown in Figure 6 8 three point Gaussian sizing and First Order Discrete Window Offset PIV will be used with a search radius of 3 pixels to produce hybrid PTV results The user may also specify an output directory for the PTV results by clicking on Browse and selecting the desired output directory The default output type is Tecplot plt format Velocity Based Tracking Dialog x Task Name Hybrid PTV Distance la Particle Sizing Three Points Gaussian Fit Add Delete Properties PIV First Order D WO PIV Add Delete Properties Output Directory C Program Files Aeroprobe DPI sbi Browse Output File Ext IP Cancel Figure 6 8 H
123. ing with PIV methods is approximately 3 pixels This conclusion is in agreement with the errors reported in Brady et al 2002 which showed that at diameters less than 3 pixels the conventional PIV sizing methods exhibit increasing error as particle diameter decreases The spray results analyzed in this work did not take this criterion into consideration at the time of data acquisition and only portions of the analyzed data were accurate Therefore it is the conclusion of this work that PIV experiments that include sizing as a project goal should be designed with sufficient magnification to provide a minimum of 3 pixels diameter for all particles the experimenters wish to size This means that the burden of producing accurate sizing results depends heavily on the appropriate setup and design of the PIV experiment New spray experiments ate underway to test this criterion and preliminary results show that experiments with sufficient magnification produce results that match closely with PDA measurements across the entire range of particle diameters The PTV method has shown initial promise in improving the correlation coefficient of PIV sizing methodologies with the traditional PDA methods Future work should focus on the improvement of the PTV corrected method for PIV particle sizing The spray sizing analysis completed in this work should be extended to further experiments with adequate optical design to perform PIV average diameter analysis This wo
124. interrogation window sizes to be performed There is no limit on the number of passes that can be performed The windows must be a power 142 of 2 in order to use the FFT based correlation If a non power of 2 window is entered the user will be prompted and direct correlation will be used for correlating regions of interest The task option dialog box for First Order DWO PIV is shown below in Figure 6 6 Another feature added to the First Order DWO PIV is the Aggressive Multiple Pass which is the dynamically adaptive algorithm developed by Claude Abiven and Dr Pavlos Vlachos in the ESM Fluid Mechanics Laboratory PIY Dialog x Task Name First Order DWO PIV Peak Detection Method Three Points Gaussian Fit y Window Sizes 1 32 168 2 32164 X Grid Spacing la TT Aggressive Multiple Pass Y Grid Spacing la I Zero Padding T Boundary Correlation Method FFT based Normalize Fast y Validation Task 3X3 PIV Validation Add Delete Properties Dutput Directory C Program Files Aeroprobe DPIV bin Workspa Browse Output File Ext Pl Input Filter Type Sequence Frames Skip fo cono Figure 6 6 First Order DWO PIV Options To enter a series of interrogation window sizes enter the desired sequence as shown in Figure 6 6 with commas separating the window sizes In this example FLOW IQ V2 2 will perform PIV with 3 interrogation passes of 32 16 and 8 pixels in that order 143 Secon
125. ircular patterns The elliptic estimator developed in this work is able to estimate the diameter of a particle with an elliptic shape and assumes that the particle is axisymmetric about the x or y axis Two elliptical schemes the true and averaged elliptical estimators were developed and compared to the traditional three point Gaussian diameter estimator using theoretical models If elliptical particles are theoretically used the elliptical sizing schemes perform drastically better than the traditional scheme which is limited to diameter measurements in the x direction The error of the traditional method in determining the volume of an elliptical particle increases dramatically with the eccentricity Monte Carlo Simulations were also used to characterize the error associated with wall shear measurements using DPIV Couette flow artificial images were generated with various shear rates at the wall DPIV analysis was performed on these images using PIV algorithms developed by other researchers including the traditional multigrid method a dynamically adaptive DPIV scheme and a control set with no discrete window offset The error at the wall was calculated for each data set The dynamically adaptive scheme was found to estimate the velocity near the wall with less error than the no discrete window offset and traditional multigrid algorithms The shear rate was found to be the main factor in the error in the velocity measurement In wall shear velocity meas
126. it The three and four point fits will contain an error even without the presence of noise sources due to the digital medium pixel discretization In order to address this error Brady et al 2002 developed a continuous four point scheme The continuous four point fit eliminates the systematic error introduced by pixel descretization The continuous four point scheme corrects for pixel discretization through equating an integrated Gaussian profile over each pixel with the discrete gray value Brady et al 2002 ICAA as ff Le 2 dydx Eq 2 9 Equation 2 9 cannot be solved in closed form and the expanded equations are shown below in Equation 2 10 where Erf is the error function In this equation x and y represent the position of the lower corner of each pixel Brady et al 2002 rl o x x x 1 x y y_ y 1 y 2 10 o Erf c Erf c Erf c Erf c Eq A a 5 Erf Bo Teo Erfl Bo Erf To D Brady et al 2002 used a form of the Powell dogleg optimization routine to solve these nonlinear equations The same point selection criteria in the four point Gaussian fit apply to the continuous four point fit 17 2 1 1 5 Continuous Least Squares Gaussian Fit The continuous least squares scheme developed by Brady et al 2002 is an integrated local least square fit Similarly to the continuous four point fit introduced above this scheme improves the error by taking into account the di
127. ite Original Image File To specify an output directory click on Browse and select the desired output directory Blur Dialog ES Task Name ATA Strength fi TT Overwrite Original Image File Output Directory C Program Files Aeroprobe DPIAbi Browse cr Figure 3 9 Smooth AGW Strength Edge Detection The edge detection task uses an edge detection algorithm to detect and remove boundaries in the selected images Currently there are no user definable attributes for the edge detection task The Dialog Box for Edge Detection is shown below in Figure 3 10 If you wish to overwrite the original images then click the check box next to Overwrite Original Image File To specify an output directory click on Browse and select the desired output directory Aa Task Name MPAA TT Overwrite Original Image File Output Directory C Program Files 4eroprobe DPI sbi Browse cn Figure 3 10 Edge Detection Options 115 Binarize Area The binarize area task identifies regions of interest in the image Any intensity greater than the median threshold is set to 255 and any intensity less than the threshold is set to 0 This process binarizes the image into on and off regions The strength of the Binarize Area algorithm may be defined by entering a number in the Coefficient box The Dialog Box for Edge Detection is shown below in Figure 3 11 If you wish to overwrite the origin
128. k Next to begin copying files Current Settings En lt Back Cancel The files for FLOW IQ will be copied to your computer When installation is complete the following dialog box appears 98 You may select to view the Read Me file and or launch FLOW IQ 2 2 when you are finished installing Choose the options and click FINISH to complete the installation of FLOW IQ 2 2 on your computer The installation program automatically creates a shortcut in your Start menu under Start gt Programs gt FLOW IQ Click on FLOW IQ to start FLOW IQ 2 2 on your computer 99 Chapter 2 Basic Operations Creating a New Project In order to create a new project either click on File gt New Press Ctrl N or click the New icon in the top left corner of the FLOW IQ GUI A new project will initialize as illustrated in Figure 2 1 below 8 DPIY DPI 1 amp File Edit View Project Image Window Help Ds W I FDM 0 3 Image Processing E Image Math 3 Particle Sizing Y Particle Tracking er Y Validation Y Stero PIV A Trajectory Image Viewer Figure 2 1 New Project Screen This screen is the main GUI for the operation of FLOW IQ 2 2 The upper left box shows the project tasks The lower left shows the properties of selected tasks The upper right window displays images directories and file sequences included in the project The lower right window displays console commands images an
129. lacement px Figure 4 9 Mean RMS and Total Error for DADPIV Algorithm In addition to comparing the effects of shear rate and interrogation window size on the wall shear velocity measurement using DPIV the effects of the various algorithms must also be compared Since the RMS error was found to be an order of magnitude less than the bias error for all of the methods studied only total error is presented in the remainder of this work Figure 4 10 below compares the error of the various methods for various shear rates and an initial interrogation window size of 64 pixels 85 Error px Error px Total Error for Each Method 64 Starting Window Shear Rate 0 0625 15 NDWO MGRID A ULTRA 1 05 AE 4 e _ 2 LA ar 0 0 0 5 1 15 2 25 3 35 Centerline Displacement px Total Error for Each Method 64 Starting Window Shear Rate 0 125 3 NDWO MGRID amp ULTRA 0 5 Rae 0 0 5 1 1 5 2 Za 3 3 5 Centerline Displacement px 86 Total Error for Each Method 64 Starting Window Shear Rate 0 25 YE T T T NDWO MGRID ULTRA 35 al A g 3 4 BS o Ed 5 dia 2 a 4 I AA 15 1 A A ee oh Ll 0 5 _ __1 i at 1 1 5 2 25 3 3 5 4 Centerline Displacement px Figure 4 10 Error for Multigrid DADPIV and NDWO for Various Shear Rate 64 Window Figure 4 10 shows that for the shear rates of 0 0625 0 125
130. lding If you wish to overwrite the original images then click the check box next to Overwrite Original Image File To specify an output directory click on Browse and select the desired output directory CI x Task Name Dynamic Thresholding Coefficient fi I Overwrite Original Image File Output Directory C Program Files Aeroprobe DPIbi Browse cn Figure 3 5 Dynamic Thresholding Properties Histogram Thresholding Histogram thresholding creates a histogram of the intensities contained in an image and sets a threshold based on this histogram Any pixel intensity values less than this value are set to zero This process is applied to all selected images in the project Currently there are no user definable options for the task of histogram thresholding The Dialog Box for Histogram Thresholding is shown below in Figure 3 6 If you wish to overwrite the original images then click the check box next to Overwrite Original Image File To specify an output directory click on Browse and select the desired output directory Image Pro Task Property x Task Name IEEE dll TT Overwrite Original Image File Output Directory C Program FilestAeroprobe DPI bi Browse ce Figure 3 6 Histogram Thresholding Options 113 Median Thresholding In median thresholding the median intensity for each image is found and any pixel with intensity less than the median intensity is set to zero This p
131. le na is the dimension of a a is the estimated paramters ex lo belta xc yc ny is the dimension of y and s y is the output variable data y f x1 x2 al a2 s 1s normally set to 1 0 f is the function y f x1 x2 al a2 lambda is blend between steepest descent lambda high and jump to bottom of quadratic lambda zero termepsilon is termination accuracy maxiter is max iterations public member static const double pi 3 1415926 e Class PltFile This class is the base class for any other format of plt file Don t use this class directly Design and use a class that derives from it Operations 1 Get the number of lines in the plt file pItfile GetNumOfLines where pltfile is a PItFile object 2 Get file name pltfile GetFileName e Class FileSequence This class models a sequence of files For example spray0000 tif spray0001 tif spray0002 tif If a FileSequence object has accessory directory and extension plt then that means it not only represent a sequence of tif files but also plt files In fact there are two sequences with same base name sequence no but different extension or location Operations 1 Get full file name of the ith file fs GetFullFileNameOflIndex i filename where fs is a FileSequence object filename is the returned file name 2 Convert to a string fs ToString aString where aString is the returned string 3 GetAccessoryDir 4 GetAccessoryExt 5 SetAccessories
132. lected Tasks Basic Tracking Basic Tracking Velocity based Tracking Velocity based Tracking OK Cancel Figure 9 1 Add Particle Tracking Task Dialog Box To add a task to the project click on the desired task to highlight it and then click The available tasks are listed on the left and the tasks to be added are shown on the right When you have selected the desired tasks click OK The added tasks will be shown in a tree under Particle Tracking 154 Editing Task Properties When a task is highlighted the properties of the task will be displayed in the lower left window as shown In order to edit these properties click on the desired task to highlight the task Then right click on the highlighted task and click Properties The corresponding dialog box will appear depending on the selected task Enter the desired properties and click OK The individual properties are discussed below in detail for each Particle Tracking technique Removing Particle Tracking Tasks There are two ways to remove Particle Tracking tasks in FLOW IQ V2 2 as a group or individually To remove several sizing tasks from the active project click on Particle Tracking in the upper left window Particle Tracking should now be highlighted Now right click on Particle Tracking and click on Remove Tracking Tasks The Particle Tracking Remove Tasks Dialog Box will appear as shown below in Figure 9 2 I xi
133. lements whose values greater than or equal to some value x to x rm ThreshHigh 20 0 14 Set the elements whose values less than or equal to some value x to x rm ThreshLow 5 15 Set the elements whose values less than or equal to some value x to 0 rm ThreshLow 5 true 16 Sort elements from left to right top to bottom m Sort e Class RealSquareMatrix lt T gt The class is derived from class RealMatrix lt T gt It only accepts Matrix lt T gt where T is real type and the matrix is square All of its operations are supposed to work with a real square matrix Operations 1 Creation RealSquareMatrix lt double gt rm m where m is Matrix lt double gt 2 Determinant m Det 3 Inversion m Inv 4 Cofactor m Cofact 5 Adjoin m Adj 6 Condition number m Cond 7 Set to identity matrix m Unit 8 Find eigen values vectors m eig 9 Solve linear equation by LU factorization for AX B call A solve B to get X 10 Check if the matrix is singular m IsSingular 11 Check if the matrix is diagonal m IsDiagonal 12 Check if the matrix is scalar m IsScalar 13 Check if the matrix is unit m IsUnit 14 Check if the matrix is symmetric m IsSymmetric 15 Check if the matrix is skew symmetric m IsSkewSymmetric 16 Check if the matrix is upper triangular m IsUpperTriangular 17 Check if the matrix is lower triangular m isLowerTriangular e Class DSP The responsibility of this clas
134. ll appear with the current location listed in the window Viewing Image Histograms in Flow IQ v2 2 In order to view an image histogram images must first be added as files to an input package See Adding Images to an Input Package for more information To view an image histogram right click on the image and select Histogram The image histogram will appear as shown in Figure 2 11 below You may zoom in on an area by creating a box around the desired area with the mouse The selected area will be enlarged to fit the full view Histogram ha E D E tm 0 000 Intensity 0 000 Figure 2 11 Image Histogram 108 Chapter 3 Preprocessing Tasks Several preprocessing tasks are included in Flow IQ v2 2 to aid the user in producing quality results The available preprocessing tasks and corresponding user definable options are briefly summarized in this section This section also deals with the addition removal and performance of preprocessing tasks Preprocessing tasks may be run alone or in conjunction with other tasks The input files for Preprocessing are 8 bit tif images Adding Preprocessing Tasks To add preprocessing tasks to the active project click on Image Processing in the upper left window Image Processing should now be highlighted Now right click on Image Processing and click on Add ImagePro Tasks The Image Preprocessing Add Task Dialog Box will appear This process
135. lts for the combined five planes 0mm 4mm 8mm 4mm and 8mm are shown below in Figure 2 9 In order to generate these results all of the particle populations were added together separated into bins and normalized with the total particle population These results represent the average across all of the data planes considered in this work In this case the correlation coefficients for the three point Gaussian four point Gaussian continuous four point Gaussian and the continuous least squares are 0 9728 0 8915 0 5658 and 0 5883 respectively Figure 2 9 shows that the histogram for the three point Gaussian method matches best with the PDA measurements in the range from 100 microns to 150 microns The four point Gaussian continuous four point Gaussian and continuous least squares all exhibit a bias toward higher diameters as compared to the PDA measurement Therefore all of the above results show that in this experiment the 3 point Gaussian diameter estimation technique performs most accurately when compared with the corresponding PDA measurements over a range of 100 to 150 microns Probability Density Functions for All Methods All Planes 0 2 T T T T T T T PDA 3 Point 0 18 Q 2 4 Point t Cont 4 k Cont LS 0 16 o Ex P T o ey N T 0 08 Normalized Probability Density o T 0 06 0 04 0 02 0 I J i 100 105 110 115 120 125 130 1
136. mage Velocimetry A Review Proceedings Institute of Mechanical Engineers Grant I 1994 Selected papers on Particle Image Velocimetry SPIE Milestone Series MS99 SPIE Optical Engineering Press Bellingham Washington Guezennec Y G and Kiritsis N 1990 Statistical investigation of errors in particle image velocimetry Exp Fluids 10 pp 138 146 Harris J W and Stocker H Ellipse 3 8 7 in Handbook of Mathematics and Computational Science New York Springer Verlag p 93 1998 Hasselinc L 1988 Digital Image Processing in Flow Visualization ARFM 20 421 85 Huang H Dabiri D Gharib M 1997 On errors of digital particle image velocimetry Meas Sci Technol 8 pp 1427 1440 Huang H T and Gharib M 1997 Processing Error in Digital Particle Image Velocimetry FEDSM97 3068 Keane R D Adrian R J and Zhang Y 1995 Super resolution particle imaging velocimetry Meas Sci Tech 6 pp 754 68 Keane R D and Adrian R J 1990 Optimization of particle image velocimeters Part I Double pulsed systems Meas Sci Tech 1 1202 1205 Khalitov D A Longmire E K 1999 Simultaneous two phase PIV measurements for high speed flows Third International Workshop on Particle Image Velocimetry Santa Barbara Sept 16 18 Marxen M Sullivan P Loewen M Jahne B 2000 Comparison of Gaussian particle center estimators and the achievagble measurement density for particle trackin
137. n 3 18 b c m a abc Eq 3 18 Ed xavg abe aya b ce 1 Eq 3 19 4c 4b 2 The theoretical error of the true elliptic sizing method where the area is defined as bc is identically zero Figure 3 4 below shows the theoretical error introduced by using only the x direction as a measurement of an ellipse with varying eccentricity Eccentricity is defined as the square root of one minus the square of the ratio of the semiminor axis to the semimajor axis Error Percent vs Eccentricity 100 D y semimajor x semimajor d 50 i A 5 E 5 o E o we 2 E eli ope SO T 50 i L I 1 l L L L E gt J 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Eccentri Figure 3 4 Theoretical Area Calculation Error vs Eccentricity for Conventional Sizing Method 53 Figure 3 4 above shows that theoretically the error introduced by measuring the diameter with only the x information diverges as the eccentricity increases At an eccentricity of 0 866 the error is 100 percent for the case of an x semimajor axis and 50 percent for the case of a y semimajor axis This analysis was performed in order to demonstrate the need for improvement in the three point Gaussian sizing method Another presentation of the theoretical error introduced by the 3 point Gaussian sizing method is shown below in Figure 3 5 These errors are plotted as a function of axis ratio for the case of x and y semimajor axes Error Percent vs Ra
138. n Ashland VA until his valedictory graduation from Patrick Henry High School and his matriculation at Virginia Tech in August of 1997 His eatly college years were marked by confusion exhibited by his three major changes in a single year from Physics to Biology to Aerospace Engineering and finally to Engineering Science and Mechanics This final decision of major reflected his natural inability to make rational decisions During his senior year he met and started dating the love of his life Catherine Orifici whom he matried on July 31 2004 He graduated Summa Cum Laude with a Bachelor of Science in Engineering Science and Mechanics and a Minor in Mathematics in May of 2001 In a fit of utter madness he matriculated at the University of Michigan Ann Arbor in the Biomedical Engineering for a masters degree in August 2002 One year 50 pounds and one Grave s Disease later he returned to Virginia Tech for a masters degree in Engineering Mechanics the culmination of which is this document During his masters education Jason developed an interest in shooting and now owns five firearms Perhaps his crowning achievement during graduate school was taking and passing a motorcycle class and the subsequent purchase of a 1998 Kawasaki Vulcan All of this aside he still doesn t know what he wants to do with his life and he isn t quite sure that he should know at all His life could easily meander into medicine defense research law or real estat
139. n the project The processed images will be saved in the ouput directory specified in the task The input images will not be overwritten When the preprocessing tasks have finished processing a Finished Processing message will appear in the lower right window under Console A description of each available preprocessing task follows Basic Thresholding Basic thresholding eliminates integer intensity values in the selected images that are less than the user specified threshold level as shown in Figure 3 4 below Fore example in the case shown in Figure 3 4 the selected images images in selected directories or images in selected file sequences included in the project will be screened and any value less than 120 will be set to O If you wish to overwrite the original images then click the check box next to Overwrite Original Image File To specify an output directory click on Browse and select the desired output directory Thresholding Dialog x Task Name Basic Thresholding Threshold 120 F Overwrite Original Image File Dutput Directory C Program Files 4eroprobe DPI bi Browse Cancel Figure 3 4 Basic Thresholding Options Dynamic Thresholding 112 The dynamic thresholding task performs a dynamic threshold on the images included in the project The user definable attributes of this task are shown below in Figure 3 5 The Coefficient determines the strength of the dynamic thresho
140. n the selected task Enter the desired properties and click OK The individual properties are discussed below in detail for each Validation technique Removing Validation Tasks There are two ways to remove Validation tasks in FLOW IQ V2 2 as a group or individually To remove several sizing tasks from the active project click on Validation in the upper left window Validation should now be highlighted Now right click on Validation and click on Remove Tracking Tasks The Validation Remove Tasks Dialog Box will appear as shown below in Figure 7 2 Remove tasks x 33 PIV Validation Figure 7 2 Removing Validation Tasks To remove a task highlight the task by clicking on the task and click on REMOVE This will remove the task from the list When undesired tasks have been eliminated click on OK and the preprocessing tree will be updated accordingly To remove individual Validation tasks click on the task to be removed The task should now be highlighted Now right click on the task to be removed and click on Remove The task will be deleted from the Validation Task tree 147 Running Validation Tasks There are two ways to run Validation tasks in FLOW IQ V2 2 as a group or individually To run all of the listed Validation tasks in the tree click on Validation in the upper left window Validation should now be highlighted Now right click on Validation and click on Run Task
141. nated click on OK and the preprocessing tree will be updated accordingly To remove individual PIV tasks click on the task to be removed The task should now be highlighted Now right click on the task to be removed and click on Remove The task will be deleted from the PIV Tree Running PIV Tasks There are two ways to run PIV tasks in FLOW IQ V2 2 as a group or individually To run all of the listed PIV tasks in the tree click on PIV in the upper left window PIV should now be highlighted Now right click on PIV and click on Run Task s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data This will run the specified PIV tasks on the selected images in the project In order to run individual PIV tasks click on the desired task The task should now be highlighted Now right click on the task to be removed and click on Run Task s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data The individual task will be run on all of the selected images in the project A message similar to the following will appear in the lower right window under Console Name No Discrete Window Offset 139 Method No discrete window offset PIV Sizing method Three Points Fit Correlation FFT bas
142. nd Task The And task performs an AND operation between an object image and the images in the input package The Dialog Box for the And task is shown below in Figure 4 8 The user may select the object file by clicking Browse and selecting the desired image to be subtracted from the images in the input package The output directory may be specified by clicking Browse and selecting the desired output directory 125 CADPIWAImagestcylinder cyl001 5 tif CADPIV bin Workspace DPIV1 out IMT ok con Figure 4 8 And Task Dialog Box Or Task The Or task performs an OR operation between an object image and the images in the input package The Dialog Box for the Or task is shown below in Figure 4 9 The user may select the object file by clicking Browse and selecting the desired image to be subtracted from the images in the input package The output directory may be specified by clicking Browse and selecting the desired output directory C Program Files Aeroprobe DPIV Images cy C Program FilestAeroprobe DPIVAbinAW orks Figure 4 9 Or Task Dialog Box 126 Chapter 5 Particle Sizing Tasks Several particle sizing techniques are included in Flow IQ v2 2 to aid the user in producing quality results This section deals with the addition removal and performance of preprocessing tasks The available particle sizing tasks are briefly summarized in this section Preprocessing tasks can be
143. nd the shutter trigger to the camera were synchronized and controlled with a PC workstation A multifunction National Instruments 6025E board was used to control the data acquisition Two 20MHz digital counters with timing resolution of 50nsecs were used to generate the sequence of pulses necessary to accurately trigger the laser and the camera Once the laser and the camera received the trigger pulses a feedback signal was recorded in order to assure the accurate timing of the process The overall timing uncertainly of the control system accounting also for the laser pulse jitter was estimated in the order of 1nsec which is negligible for the velocity ranges of approximately 10m s measured during this experiment 19 60W Copper Vapor Lascr Field of View Laser Shect Phantom TV CMOS Camera Figure 2 1 ESM Fluid Mechanics Laboratory DPIV system 2 2 3 DPIV Software The DPIV software used throughout this work consisted of in house software For the spray particle sizing results with tradtitional sizing algorithms DPIV version 1 0 was used DPIV version 1 0 is a DPIV software package developed by Aeroprobe Inc This software includes DPIV algorithms sizing algorithms particle tracking velocimetry image pre processing and post processing options for DPIV in a single Windows based platform The user s manual for DPIV version 1 0 written by the author of this work can be found in Appendix A DOS based DPIV software was also used
144. ndow Offset The second cross correlation is preformed between two windows that contain the same particles The signal to noise is drastically increased during this operation The iterative nature of this process significantly reduces the effects of spatial averaging which improves the resolution and accuracy of system Abiven and Vlachos 2002 Wereley and Meinhart 2001 developed a second order accurate DPIV scheme that further reduced the errors associated with velocity measurement particularly in vertical flowfields This method known as Second Order Discrete Window Offset PIV is illustrated below in Figure 1 7 Second Order DWO PIV First Image Second Image o o Initial Pass Region 1 Region 2 Refining Passes Figure 1 7 Second Order Discrete Window Offset PIV In Second Order Discrete Window Offset PIV the interrogation windows are shifted in both images by a value half of the initial estimate If the initial estimate is an odd number then one window is shifted by the floor of half of the estimate and the other is shifted by the ceiling of the initial estimate This process reduces the error of the method in relation to vortical flows 13 Particle Tracking Velocimetry Digital Particle Tracking Velocimetry is defined as the tracking of particles as they progress in DPIV data The DPTV method used in this work utilizes the output from particle sizing and PIV algorithms to track particles The particles in tw
145. nput Package From a Project 102 Modifying Input Package Properties viii 102 Adding Images File Sequences and Directories to an Input Package 102 Removing Images File Sequences and Directories from an Input Package 104 Serino Project Parametri leer r 104 Adding Tasks fo tHe Projet relatori 105 Editing Task Properties nao 106 Removing Tasks from a Project crolla A di 106 Running Tasks errero eA a rt 107 Navigating Windows and Checking Location in FLOW IQ V2 2 ii 108 Viewing Image Histograms in Flow IQ V2 2 i 108 Chapter 3 Preprocessing Tasks iiciscstcacivansedecasvsidesvesjocetaseadansa deydadeasussen ati ici 109 Adding Preprocessing Tasks ii ila 109 Editing Fask Properties ern o 110 Removing Preprocessing Tas ia 111 Running Preprocessing Task in rat 111 Basie LAO ilaele 112 is agata lorella ta 112 Histogram Thresholding sila ala rin ide 113 Median Thresholdind pcrera aaa tata 114 MS 114 A A II A ce 115 Edge Detection aiii sde 115 Bara a a del ln ea eo el ei cu 116 SODA A lalla alien tend coni lano Miseria 116 Zero Boundary telaio lande 117 Dewi elio 117 Boundary Removal ina iii 118 Combo Processi O e 119 Chapter 4 mage Mathcl asks 0 ie 120 Adding Image Math TaskKs iii iaia 120 Editing Task Proposal od bs 121 Removing Image Math Task oe ah nea i eke ae ees 121 BRU LWA AC ASKS tdt a 122 A ER REC a I deel IO SII TRIO 123 Min Fask iii ia eni eroe lio iride 123
146. ns which are listed below FFT Based Fast Fourier Transform FFT correlation FFT Based Normalize Normalized Fast Fourier Transform FFT correlation FFT Based Fast Efficient Fourier Transform FFT correlation FFT Based Normalize Fast Normalized and Efficient FFT correlation Direct Direct correlation Direct Normalize Normalized Direct correlation Direct Fast Efficient Direct correlation Direct Normalize Fast Normalized and Efficient Direct correlation These options are available in all of the PIV algorithms used in Flow IQ v2 2 141 First Order DWO PIV In First Order DWO PIV the initial pass is performed on identical areas in two corresponding image For successive passes the interrogation area in the second image is shifted by the rounded result from the initial pass All successive passes are made on the resulting areas and the final pass is added to the rounded integer initial estimate Ifa pass fails the previous pass is used to update the estimated displacement For more information see Chapter 9 on Output Types The First Order DWO Process is shown below in Figure 6 5 First Order DWO PIV First Image Second Image Region 1 Region 2 Initial Pass Region 1 Region 2 Refining Passes Figure 6 5 First Order Discrete Window Offset The options for First Order DWO PIV are much the same as in No DWO PIV except that the user can specify a sequence of
147. nsity o 2 gt h e no 40 Figure 3 14 Log Normal Surface Plot for 0 80 6 0 30 u 1 00 u 0 00 Log Normal sigy 0 30 sigx 0 80 muy 0 00 mux 1 00 Figure 3 15 Log Normal Contour Plot for 0 0 80 6 0 30 u 1 00 u 0 00 3 4 2 Rayleigh Normal Independent RNI PDF For the RNI probability density function two random variables x and y were considered to be independent random variables The x r v was considered to be Rayleigh distributed with skewness 67 factor s The y r v was considered to be normally distributed with standard deviation o and mean value u For a Rayleigh distributed variable x the pdf is defined as follows fx x gt ole For a normally distributed variable y the pdf is defined as follows y 8 20 1 0 i o Nn For independent r v s the joint pdf can be expressed as Stark and Woods 1986 fyy x y fy x 8r O Therefore the joint pdf for an RNI system can be written as toco a leet Eq 3 24 Eq 3 25 Eq 3 26 Eq 3 27 Figures 3 16 and 3 17 below show the a 2 D probability density function with x as a log normal random variable with s 6 00 and y as a Gaussian random variable with o 0 20 and u 0 00 The variables in these plots are assumed to be independent random variables x and y This distribution may be useful in quantifying particles that are slightly streaked or skewed The
148. o consecutive frames are detected and the local velocity from PIV is used to search for a particle within a given radius of the expected velocity If a particle is found this particle is used to estimate the displacement between this particle and the particle from the original frame Other developed methods use size shape brightness or closeness criteria for particle differentiation and identification The difference in particle position serves as the displacement estimation in DPTV The major difficulty in DPTV is the ability to distinguish unique particles However DPTV eliminates the averaging effect seen in DPIV results The Hybrid DPTV method Abiven and Vlachos 2002 is used in this work DPIV is classified in the same general category as DPIV since they are similar methods based on similar fundamentals Dracos and Gruen 1998 Adrian et al 1995 Prasad and Adrian 1993 Adrian 1996 In DPTV the velocity is determined from the displacement of particles within a fixed time interval The major experimental difference between the methods is that the DPTV algorithms need low seeding density whereas PIV algorithms require relatively high seeding density Seeding density is the number of tracer particles in a given frame or window DPTV is limited to slower flows than PIV Abiven and Vlachos 2002 Guezennec and Kiritsis 1990 developed the first DPTV algorithms based on DPIV which uses the DPIV output as a priori knowledge for the sea
149. of the velocity on the order of 0 1 pixels 1 2 2 Image Processing and Maximum Resolvable Displacement DPIV algorithms can benefit greatly through the use of image pre processing tasks to remove boundaries and reduce the effects of noise in the data Since the images used in DPIV are purely digital image pre processing tools were developed to allow direct phase separation within the flow Khalitov and Longmire 1999 presented an image based approach for resolving two phase flows between a flow tracer and a solid phase In this work previously implemented methods by Abiven and Vlachos 2002 were used including dynamic thresholding Gaussian smoothing Laplacian edge detection filtering erosion and many more These techniques are included in Chapter 5 Flow IQ documentation In order to satisfy the Nyquist frequency criterion the measured displacement must be smaller than one half the length of the interrogation window in order to prevent aliasing effects However previous work Keane and Adrian 1990 illustrated that the statistical cross correlation 6 velocity evaluation has the maximum confidence levels when the displacement is less than one quarter of the interrogation window size In this work one quarter of the interrogation window size is referred to as the maximum resolvable displacement 1 2 3 Traditional Multigrid Technique The tradidtional iterative multigrid DPIV employs a first cross correlation pass in order to
150. ons Eccentricity O to 0 8660 2 T T T T T T T T 1 55 4 cal 1 LE a 4 edili 0 5 ciali 4 pl muli e Ni pa rare 0 5 4 Trad 3 point X 1F Averaged Elliptic X 3 True Elliptic X 15 Trad 3 point Y ad Averaged Elliptic Y True Elliptic Y Ze 4 2 5 4 3 fi fi fi fi fi fi 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Eccentricity Figure 3 12 X and Y diameter vs Eccentricity for each sizing method 62 Figures 3 11 and 3 12 above shows that the true elliptical sizing method exhibits a correlation coefficient of 1 00 with the 3 point Gaussian in relation to x diameter The averaged elliptic method exhibits diverging error in the x and y diameter measurement as eccentricity increases This phenomenon should be expected since the averaged elliptic method uses the average of the two diameters and assumes a spherical particle profile Therefore when the x diameter is less than the y diameter the averaged elliptic method will overestimate the x diameter and underestimate the y diameter This behavior is clearly visible in Figures 3 11 and 3 12 The true elliptic sizing method exhibits the lowest error in the y direction since the true elliptic method is the only method that performs a true sizing scheme in the y direction Figures 3 11 and 3 12 show the behavior of each sizing method with respect to diameter and eccentricity Figure 3 12 shows that the true elliptical sizing method performs identically with
151. or introduced by the pixel descretization The integrated four point fit simply corrects for the pixel discretization by equating the integrated Gaussian profile over each pixel to the discrete gray value x ZX y HY y y a fioe 20 dydx 10 Equation 9 cannot be solved in a closed form the expanded equations are shown in Equation 10 where Erf is the error function Here x and y represent the position of the lower corner of each pixel not the midpoint as in the Gaussian fits described above tI o x x_ x 1 x y y_ y 1 y_ o E 1 c E 1 c E 1 C E 1 c 11 are gg pg pe o i A The nonlinear equations were solved using a form of the Powell dogleg optimization routine as described by Powell 1970 The same rules for point selection used in the Four Point fit were employed to the Integrated Four Point fit Least Squares Volume Fit The third novel sub resolution scheme developed during this study is the integrated local least square fit Similarly to the integrated four point fit introduced above this scheme improves the error by taking into account the discretization error of the individual pixels ATI 1 D a Le Zee dydx az As with the standard least squares y was minimized using a Gauss Newton algorithm The same analysis as the standard least square for the point selection was performed on the integrated least square Hierarchical Fit The hierarchical fit allows the user to select a
152. orrelation Valid Boundary zone I 16 J 16 15 000000 241 000000 0 544723 3 497631 0 000000 16 16 0 481796 0 0 31 000000 241 000000 2 900743 1 608065 0 000000 16 16 0 496196 0 0 47 000000 241 000000 0 868580 0 099177 0 000000 16 16 0 386605 0 0 63 000000 241 000000 2 261536 0 880877 0 000000 16 16 0 325937 0 0 79 000000 241 000000 1 252156 6 046097 0 000000 16 16 0 359740 0 0 95 000000 241 000000 2 127558 0 524451 0 000000 16 16 0 391176 0 0 111 000000 241 000000 1 755754 0 549097 0 000000 16 16 0 389217 0 0 127 000000 241 000000 2 095121 1 906425 0 000000 16 16 0 418114 0 0 143 000000 241 000000 0 000000 0 000000 0 000000 0 0 0 000000 1 0 Hybrid PTV Output Particle Trajectory Output A portion of an output plt file using Velocity Based Tracking is shown below The first three lines are the header required by the Tecplot plt format The data is arranged in columns with the first column listing the x coordinate of the tracked particle The second column contains the y coordinate of the tracked particle The third column is the diameter of the tracked particle The fourth column is the FID or Frame ID of the tracked particle The fifth column is the Particle ID or PID of the tracked particle Each time a new particle is found for tracking it is assigned a sequentially increasing PID starting with 0 Then the particle is tracked through the successive frames and FID is updated if the particle is tracked
153. ot use it directly e Class BaseException This is the base class for all exception classes in this project e Class MatrixException This is the generic exception class for matrix e Class SingularMatrixException 164 It is derived from class MatrixException It is thrown when there is a singular matrix exception e Class IOException It is thrown when there is error in reading wriging file e Class UnsupportedDataFormat It is thrown when file contains bad data e Class UnsupportedImageFormat It is thrown when a file has unsupported image format e Class ExperimentConfig This class models experiment configuration It provides info about number of apertures magnification camera pixel size etc It is used to convert pixel unit to physical unit Operations 1 Get particle diameter in physical unit ecf GetTrueParticleDiameter x where x is particle diameter in pixel unit ecf is an ExperimentConfig object 2 Get veleocity in physical unit ecf GetTrueVelocity x where x is velocity in pixel unit per sampling time 3 Convert to physical unit ecf Pixel2PhysicalUnit x 4 Get the number of apertures ecf GetNumberOfApertures 5 Set the number of apertures ecf SetNumberOfApertures x 6 Get magnification factor ecf GetMagnificationFactor 7 Set magnification factor efc SetMagnificationFactor x 8 Get camera pixel size ecf GetCameraPixelSize 9 Set camera pixel size ecf SetCameraPixelSize x 10 Get sampling time
154. pares the center vector to the mean of the surrounding vectors and if the difference between the center vector and the mean of the surrounding vectors is greater than the user defined standard deviation threshold the center vector is replaced by the mean of the surrounding vectors and is flagged as invalid in the output file This process is illustrated below in Figure 7 3 In Figure 7 3 the red vector is the vector to be validated The black vectors are the surrounding vectors for which the mean and standard deviation are calculated In this case the center vector would most likely be flagged as invalid Figure 7 3 3X3 PIV Validation Scheme The options for 3X3 PIV Validation are shown below in Figure 7 4 Standard Deviation Threshold High is the upper threshold the algorithm uses to flag vectors as valid or invalid Low is the lower threshold value used to flag vectors as valid or invalid Nx and Ny are the number of measurements in the x and y direction to use in the calculation of the standard deviation in a validation area Filter can be set to Mean or Median depending on which parameter the user wishes to use in the validation analysis The user can also check the Adaptive box to use an adaptive algorithm which sequentially decreases the threshold values for the validation by half for each validation pass The number of passes is determined by the value in Number of Loops The user can specify the output di
155. pecified in the task The input images will not be overwritten When the image mathematics tasks have finished processing a Finished Processing message will appear in the lower right window under Console A description of each available image mathematics task follows Max Task The Max task creates an array and stores the maximum value across the input set of images at each location The algorithms searches from x y 0 0 to x y 255 255 and finds the maximum for each point in the input image set Currently there are no options available for the Max task algorithm The Dialog box for the Max task is shown below in Figure 4 4 The output directory may be specified by clicking Browse and selecting the desired output directory pi Task Name Dutput Directory C Program Files Aeroprobe DPIV bin W orks Browse cn Figure 4 4 Max Task Options Min Task The Min task creates a 256X256 array and stores the minimum value across the input set of images at each location The algorithms searches from x y 0 0 to x y 255 255 and finds the minimum for each point in the input image set Currently there are no options available for the Min task algorithm The Dialog box for the Min task is shown below in Figure 4 5 The output directory may be specified by clicking Browse and selecting the desired output directory E5555 lt Task Name Mir Dutput Directory C Program Files Aeroprobe DPI
156. pixel intensity discretization introduces significant error into the measurement of particle area The errors are higher than the theoretical errors by approximately 10 to 20 percent However the trends in Figure 3 9 agree with the theoretical findings in Section 3 3 1 for the averaged elliptic method The true elliptic method exhibits higher error than the traditional 3 point method for eccentricities less than 0 60 The error for the averaged elliptic method is lower than the traditional 3 point Gaussian method by approximately 5 at an eccentricity of 0 03 The error is decreased by using the averaged elliptic method by approximately 80 percent when compared to the traditional 3 point Gaussian method These results show that the averaged elliptic method performs the best out of the three methods tested in this section 3 4 Conclusions and Future Work In this chapter an elliptical sizing methodology was introduced and tested using Monte Carlo simulations These studies found that for particles of elliptical profile the averaged elliptic method performs the best in the measurement of particle area The trends seen in the Monte Carlo Simulations agree with the trends predicted by theory Therefore the elliptical sizing method has been theoretically introduced and validated experimentally using Monte Carlo Simulations Future work in the particle sizing area should concentrate on the development of more adaptive sizing algorithms that can dynamic
157. pixels per pixel were examined in order to determine the effects of increased shear rate on DPIV performance The artificial images were then analyzed using several different DPIV methods The methods tested in this work were no discrete window offset DPIV single pass DPIV multi grid DPIV traditional DPIV algorithm and a novel ultra DPIV method developed in our laboratory After the artificial data was analyzed using each DPIV method the mean RMS and total errors were calculated for each case The flow field used in these experiments is shown below in Figure 4 1 Artificial Image Interrogation Point Interrogation Window c Centerline Displacement Slope Shear Rate Maximum Velocity Figure 4 1 Artificial Image Diagram for Wall Shear Experiments In order to obtain the desired shear rates maximum velocities of 16 32 64 128 and 256 were used in the artificial image generation software 72 For the low shear portion of this work maximum velocities of 6 4 12 8 19 2 25 6 and 32 were used to yield shear rates of 0 025 0 050 0 075 0 100 and 0 125 These shear rates were targeted in order to produce centerline displacements ranging from 0 1 to 0 5 pixels for error analysis and comparison to traditional PIV error uniform displacement results The tracking portion of this work utilized the Hybrid PTV algorithm available in Flow IQ v2 2 to calculate the error associated with particle tracking in a shear flow A s
158. pt that the four point method performs better than in the previously analyzed frames in the 8mm case In the 8mm plane the correlation coefficients for the three point Gaussian four point Gaussian continuous four point Gaussian and the continuous least squares are 0 9697 0 9642 0 6892 and 0 3265 respectively In the 8mm plane the correlation coefficients for the three point Gaussian four point Gaussian continuous four point Gaussian and the continuous least squares are 0 9699 0 7605 0 1798 and 0 3060 respectively The discrepancies between the 4 point 4 point continuous and least squares methods are most likely due to the absence of sufficient points in the data to arrive at a solution for diameter 30 Probability Density Functions for All Methods Plane 8mm T T T T T T T T 0 18 G PDA gt 3 Point 2 4 Point 4 Cont 4 Cont LS 0 16 0 14 e gt N e ae 0 08 0 06 Normalized Probability Density 0 04 0 02 0 100 105 110 115 120 125 130 135 140 145 150 Diameter um Probability Density Functions for All Methods Plane 8mm 0 2 T T T T T T T T G PDA 3 3 Point 0 18 amp 4 Point Cont 4 Cont LS 0 12 Normalized Probability Density S o a 2 o D e o EH 0 02 0 105 110 115 120 125 130 135 140 145 150 Diameter um Figure 2 8 Histogram Results for 8mm Spray Plane All Sizing Methods 31 The averaged resu
159. put directory for the results by clicking on Browse and selecting the desired output directory Figure 8 3 below shows the available options for the Basic Stereo PIV task in Flow IQ v2 2 Basic Stero PIY Dialog 3 x Task Name PRE Alpha Left 45 deg Alpha Right 45 deg Belta Left 45 deg Belta Right 45 deg Output Directory C Program Files 4eroprobe DPI bin Workspace Browse Cancel Figure 8 3 No Discrete Window Offset Task Dialog Box 153 Chapter 9 Trajectory Tasks In addition to Particle Image Velocimetry FLOW IQ V2 2 also includes particle tracking algorithms This section deals with the addition removal and performance of particle tracking tasks FLOW IQ V2 2 includes basic tracking and Particle Tracking Velocimetry PTV tasks As with the other available tasks particle tracking can be run alone or in conjunction with particle tracking The input files for particle tracking tasks are the output files from the Particle Sizing and PIV processes which are Tecplot format pit files See Chapter 11 on Output Types Adding Particle Tracking Tasks To add particle tracking tasks to the active project click on Particle Tracking in the upper left window Particle Tracking should now be highlighted Now right click on Particle Tracking and click on Add Tracking Tasks The Particle Tracking Dialog Box will appear as shown in Figure 9 1 below Task Add Dialog 1 x Tasks Se
160. r Points Gaussian Fit Modified Four Points Gaussian Fit Least Squares Yolume Fit Least Squares Mid Fit Hierachical method CI Particle Tracking Pry Validation Post Processing lt psz gt Name Centroid Fit Method Centroid Fit Minimum intensity 0 Selection intensity 0 Output dir Ext pit lt Ipsz gt Figure 5 2 Added Particle Sizing Tasks Editing Task Properties When a task is highlighted as Centroid Fit is in Figure 5 2 above the properties of the task will be displayed in the lower left window as shown In order to edit these properties click on the desired task to highlight the task Then right click on the highlighted task and click Properties The Edit Sizing Task Properties Dialog Box will appear as shown below in Figure 5 3 128 Particle Sizing Task Dialog x Task Name Centroid Fit Picking Intensity o Maximum Pixel Selection Intensity 120 Image Preprocessing Task Basic Thresholding Dynamic Thresholding Histogram Thresholding Add Delete Property Dutput Directory My Documents Browse Output File Est JP Cancel Figure 5 3 Editing Particle Sizing Task Maximum Pixel Selection Intensity is the minimum intensity a local maximum pixel intensity in the image must have to be considered a particle by the algorithm Around this local maximum every pixel greater than Picking Intensity will be considered
161. r to create an elliptical particle the intensity in the x and y directions were assumed to be jointly Gaussian identically independent random variables Two random variables x and y are considered Jointly Gaussian is their joint pdf is defined as Stark and Woods 1986 L da fy x y e da 270 0 1 p where is the standard deviation in the x direction O is the standard deviation in the y direction Eq 3 1 H is the mean of the x variable u is the mean of the y variable and pis the correlation coefficient between the x and y random variables 47 When the x and y are considered to by identically independent random variables p 0 equation 1 A e y Eg 3 2 f Xs cies 5 q xy 270 0 e This equation describes an elliptical Gaussian curvature whose semimajor axis is related to the 3 1 reduces to greater of 6 or 0 and whose simeminor axis is related to the lesser of 0 or 0 The semimajor and semiminor axes are the particle width in the x and y direction An ellipse is shown below in Figure 3 1 Harris and Stocker 1998 iz SIND JOUR 0 Figure 3 1 Diagram of eee resis an ellipse Brady et al 2004 examined particles using the assumption that particle distributions were normally distributed 1 1 v s with equal to 0 which produces a circular distribution as shown below in Figure 3 2 48 Jointly Gaussian IIRVs sigy 1 00 sigx
162. raw e Class ImageProTask The class is the virtual base class for other image processing task classes It defines the image processing task interface that must be conformed by other image processing classes Operations 1 Process image bool Run Image imag 2 DoTasks Does a set of processing tasks on an image 3 Accept a visitor task Accept aVisitor 4 Reset the task state task Reset 5 Get info about the task type task GetDesc 6 Get info aobut the task task GetHelpInfo 167 7 Get type id task GetID Public member char m_Name MAX_FN_SIZE task name e Class ThresholdImageTask Basic thresholding Public members UBYTE m_Low m_High low and high threshold values e Class DynamicThresholdImageTask Dynamic thresholding e Class HistogramThresholdImageTask Histogram thresholding e Class BlurImageTask Blur mage Pubic member unsigned int strength e Class SmoothAGWTask Smooth image Pubic member unsigned int strength e Class EdgeDetectionTask Edge detection e Class BinarizeAreaTask Binarize area 3 Particle Sizing Module e Class Particle The responsibility of this class is to implement particle detection and various particle sizing methods Operations 1 Creation There are two methods to create a Particle object a Particle MapParticles It extracts Particle objects from an image Keep in mind that this function returns a vector of pointers So delete them
163. rch of particles The estimation of the displacement is uncomplicated A simple search radius is input by the user in order to define the search area around the predicted velocity from DPIV results Most particles will be detected by a correctly designed DPTV algorithm given optimal experimental conditions Abiven and Vlachos 2002 1 4 Error Analysis The major error analysis technique used in this work is the Monte Carlo Simulation In a Monte Carlo Simulation for PIV artificial data with a known displacement field are generated Then the PIV method in question is performed on the artificial data Errors are calculated by comparing the 10 PIV output with the known input The major error sources are bias error and random error Bias error ot mean error represents a true bias in the measurement and indicates a consistent error in the measurement Random error or RMS error quantifies the expected error in the measurement that does not fit a specific pattern Total error is the complete error of the measurement and consists of the random and bias errors summed in quadrature The equations for total bias and random error are given below in equations 1 4 1 to 1 4 3 The reliability of this error analysis increases with the number of measurements performed in the simulation E sm 5 gt IDG j D G DI Eq 1 4 1 En D 20 3 Eq 1 42 27 p N o x Eee A Eq 1 4 3 n 1 In equations 1 4 1 through 1 4 3 D is the
164. rdingly To remove individual image math tasks click on the task to be removed The task should now be highlighted Now right click on the task to be removed and click on Remove The task will be deleted from the Image Math Task Tree Running Math Tasks There are two ways to run image mathematics tasks in FLOW IQ V2 2 as a group or individually To run all of the listed image mathematics tasks in the tree click on Image Math in the upper left window Image Math should now be highlighted Now right click on Image Math and click on Run Task s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data A list of the available input packages will appear Click on the desired input package to be processed with the image mathematics tasks The processed images will be saved in the ouput directory specified in the task The input images will not be overwritten 122 In order to run individual image mathematics tasks click on the desired task The task should now be highlighted Now right click on the task to be removed and click on Run Task s on A list of the available input packages will appear Click on the desired input package to be processed with the image mathematics task The task will be run on all of the selected images in the project The processed images will be saved in the ouput directory s
165. rectory by Clicking on BROWSE and selecting the desired output directory When the desired options have been selected press OK to update the task to the specified options The default output file extension is Tecplot plt format 149 PIY Yalidation Dialog C Program Files Aeroprobe D PIV bin W orks LK ance Figure 7 4 3X3 PIV Validation Options 150 Chapter 8 Stereo PIV Tasks FLOW IQ V2 2 includes algorithms for the performance of Stereo PIV This section deals with the addition removal and performance of Stereo PIV tasks Adding Stereo PIV Tasks To add STEREO PIV tasks to the active project click on STEREO PIV in the upper left window STEREO PIV should now be highlighted Now right click on STEREO PIV and click on Add STEREO PIV Tasks The STEREO PIV Dialog Box will appear as shown in Figure 8 1 below Task Add Dialog x Tasks Selected Tasks Basic Stero PIY Basic Stero PIV Cancel Figure 8 1 Add Stereo PIV Task Dialog Box To add a task to the project click on the desired task to highlight it and then click The available tasks are listed on the left and the tasks to be added are shown on the right When you have selected the desired tasks click OK The added tasks will be shown in a tree under STEREO PIV These tasks will be performed from top to bottom in the tree If you wish to change the order of operations click and drag the tasks to new
166. rk The computational aspects of this work were performed on three personal computers These resources included a desktop computer with a 2 8GHz Pentium IV processor and 512MB of RAM a desktop with a 1 8GHz Pentium IV processor and 256MB of RAM and a laptop with a 2 4GHz Pentium IV processor and 512MB of RAM Another resource used heavily in this work were both in house and purchased programs available in the ESM Fluid Mechanics Laboratory The in house programs included DPIV version 1 0 a particle image velocimetry and sizing program developed by Aeroprobe Corporation which was used to perform all of the spray sizing results presented in this paper The artificial images used in this work were created using in house artificial image generation software developed by Claude Abiven in the ESM Fluid Mechanics laboratory The DPIV analyses used in the wall shear Monte Carlo simulations were performed using Ultimate a DOS based particle image velocimetry program developed by Dr Pavlos Vlachos of the Mechanical Engineering Department at Virginia Tech Several other programs were used in order to produce the results presented in this work The researcher relied heavily upon MATLAB 6 5 for data analysis and presentation 2 3 Spray DPIV PDA Comparison In order to provide a comparison between DPIV and PDA data the particle size histogram and average diameter for each method was calculated and compared Spray data from a previous experiment was analyzed
167. rk showed that the optimal design should magnify all desired particles to a minimum of three pixels diameter in order to provide accurate spray sizing results The new elliptical sizing methods should also be tested on real data in order to determine their performance in real world experiments 2 6 Summary of Original Contribution The original contribution of this work is the application of the sizing methods developed by previous researchers to an entire set of spray atomization data No new sizing methods were developed or used in the spray sizing portion of this work The histogram analysis found that the 3 point Gaussian sizing method exhibited a correlation coefficient of up to 0 9728 when compared to the PDA method over a range of 100 to 150 microns in diameter 4 to 7 pixels in diameter Although the PIV average diameter results in this section do not agree with the PDA measurement several important observations were made from this analysis The PIV experiment must be designed to have sufficient magnification such that the particles the experimentor s wish 45 to size are greater than 3 pixels in diameter in the PIV data Over the detectable range of PIV sizing greater than 3 pixels in diameter the PIV sizing method performed with a correlation coefficient of up to 0 9728 when compared statistically to the PDA sizing method Therefore the major finding of this work is the conclusion that PIV sizing experiments must be carefully desi
168. rn to give user the flexibility to modify pzm attributes through dialog serialize them into file or implement any other extensible functionality For example PzUIVisitor and PzSrlzvisitor are implemented in DPIV exe so that we don t have any GUI and MFC stuff in the dll 4 Get description about the type of current task pzm GetDesc 5 Get detailed description about the task pzm GetHelpInfo Info Size where Info is an array at least 1024 bytes Size is the array size 6 Get the task type id pzm GetID 7 Reset the state of the task pzm Reset It is recommended to call this function before calling Run Public members char m_Name MAX_FN_SIZE task name UBYTE minint minimum intensity UBYTE selint selection intensity std vector lt ImageProTask gt m_ImgProTasks char m_OFDir MAX_FN_SIZE output file directory char m_OFExt 8 output file extension ExperimentConfig m_ExpCfg experiment configuration e Class HrkPzMethod This class models hierarchical sizing method There are three levels of methods The first two are fixed They are centroid fit and three point User can choose the third method By default it is least square volume method If the first method succeeds use the result as initial Io beta diameter xc yc and apply the second method If it fails return the result from the first method Otherwise apply the third method using the result If the third method succeeds return the result Otherwise
169. rocess is applied to all selected images in the project Currently there are no user definable options for the task of median thresholding The Dialog Box for Median Thresholding is shown below in Figure 3 7 If you wish to overwrite the original images then click the check box next to Overwrite Original Image File To specify an output directory click on Browse and select the desired output directory A x Task Name Median Thresholding Coefficient ft I Overwrite Original Image File Output Directory C Program FilesAeroprobe DPIbi Browse Figure 3 7 Median Thresholding Options Blur The blur preprocessing task applies a blur filter to each selected image in the project The user may select the strength of the blur filter as shown below in Figure 3 8 If you wish to overwrite the original images then click the check box next to Overwrite Original Image File To specify an output directory click on Browse and select the desired output directory x Task Name IHM Strenath fi TT Overwrite Original Image File Output Directory C Program FilestAeroprobe DPIbi Browse cn Figure 3 8 Blur Dialog Box 114 Smooth AGW This task applies a smoothing Adaptive Gaussian Window filter to the selected project images The user may select the strength of the Smooth AGW filter as shown below in Figure 3 9 If you wish to overwrite the original images then click the check box next to Overwr
170. ry Removal Dialog 118 Combo Processing The Combo Pro task allows the user to do a variety of image preprocessing tasks in a single task The Dialog Box for Combo Processing is shown below in Figure 3 16 To add a list of processing tasks click on Add and add the tasks in the same manner described in Figure 3 1 To remove tasks from the list simply click on Delete and remove the tasks as shown in Figure 3 3 To edit the properties of a specific task highlight the task under Image Preprocessing Task and click on Properties The properties of each task will appear as shown above for each individual task You may also select a blanket output directory for the combo processing by clicking on Browse and selecting the desired output directory Combo Image Pro Task Dialog i x Task Name Combo Pro m Image Preprocessing Task d Basic Thresholding Dynamic Thresholding Histogram Thresholding Median Thresholding Blur 33 Delete Properties Output Directory C Program Files AeroprobeDPIW bin y Browse OK Cancel Figure 3 16 Combo Processing Options 119 Chapter 4 Image Math Tasks In addition to the Image Preprocessing tasks available in Flow IQ v2 2 several image mathematics tasks are included to aid the user in producing superior results The available image mathematical tasks and corresponding user definable options are briefly summarized in this section This s
171. s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data This will run the specified Validation tasks on the selected images in the project In order to run individual Validation tasks click on the desired task The task should now be highlighted Now right click on the task to be removed and click on Run Task s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data The individual task will be run on all of the selected images in the project A message similar to the following will appear in the lower right window under Console lt vid gt Name 3X3 PIV Validation Method 3X3 PIV Validation Output dir C Documents and Settings jcarneal Desktop Ext plt Standard deviation threshold 0 100 lt vid gt Finished Processing When the Validation tasks have finished processing and all the frames have been completed a Finished Processing message will appear in the lower right window under Console A description of each available Validation task follows 148 3X3 PIV Validation The 3X3 PIV Validation task takes a 3 X 3 window centered around each velocity vector and calculates the standard deviation and mean of the vectors surrounding the center vector to be validated The algorithm then com
172. s exists in the data the data shown in Figure 2 14 is the average particle diameter passing through bins of 16 pixels square or 1 6 square millimeters A bin size of 1 6 square millimeters is more than enough to capture particles of several sizes in this experiment This means that for every 25 micron particle that passes through the center at 15 4mm above the spray a larger particle traverses the same area within the entire data set Therefore the PIV method cannot produce results in this analysis for diameters less than 25 pixels at the minimum under ideal bin selection criteria while the PDA measurement can resolve down to 1 4 microns Therefore due to the limitations of the PIV method this analysis cannot produce a viable comparison between the PDA and PIV methods for this data set 38 PDA Average Diameter microns y position mm 8 6 4 2 0 2 4 6 8 X position mm ENANA AvgDiam 1015202530 354045505560 Y mm X mm Figure 2 14 PDA and 3 Point Gaussian PIV Average Diameter z 15 4mm 39 2 4 4 PTV Corrected Histograms PIV was performed on the spray data for the Umm plane case using the 3 point Gaussian sizing method The PTV method used in this portion of the work was the Basic Trajectory option in Flow IQ v2 2 Histograms were generated for the tracking the 3 point fit and the compensated tracking algorithm The PTV compensated histogram was obtained by subtracting the tracking algorithm
173. s is to provide digital signal processing routines Operations 1 1D FFT Matrix lt std complex lt double gt gt min mout mout DSP fft min 2 1D inverse FFT 163 Matrix lt std complex lt double gt gt min mout mout DSP ifft min 3 2D FFT Matrix lt std complex lt double gt gt min mout mout DSP fft2d min 4 2D inverse FFT Matrix lt std complex lt double gt gt min mout mout DSP ifft2d min 5 direct 2D convolution Matrix lt double gt A B C C DSP conv2d A B DSP CONV_SHAPE_ FULL 6 fft based 2D convolution C conv2 A B 7 direct 2D cross correlation Matrix lt double gt A B C C DSP xcorr2d A B 8 direct 2D auto correlation Matrix lt double gt A C C DSP xcorr2d A 9 normalized direct 2D cross correlation C DSP xcorr2_norm A B 10 fft based 2D cross correlation C DSP xcorr2 A B 11 fft based 2D auto cross correlation C DSP xcorr2 A 12 normalized fft based cross correlation C DSP xcorr2_norm A B e Class EigenValueVector This class is used to realize the algorithm for finding eigen values vectors Example RealSquareMatrix lt double gt t m EigenValueVector evv t eig std vector lt double gt r evv GetRealEigenValues std vector lt double gt imag evv GetImagEigenValues e Class SVD This class is used to do singular value decomposition We just use part of its implementation to calculate the norm of a matrix User should n
174. saturated particles do not contribute to the measurement of diameter The removal of saturated pixels from the calculation allows for a more accurate estimation of the Gaussian shape of the particle and reduces the error of the method Brady et al 2002 In order to derive the four point Gaussian estimator Brady et al 2002 considered the two dimensional intensity distribution given below in equation 2 7 max HO a L 20 Eq 2 7 Four independent intensities were solved in order to arrive at the following set of equations These intensities were used to derive equation 1 4 8 below which is the equation used for variance in the four point Gaussian scheme 16 A X a V3 Ky HO IO Y O Ya O Ys a X 0 YAA 0 94 OI Or Y OS Y a X Vy I 01 Y A 07 Y O Ya a X 0 YA O Y ODO 3 2 Ys y MASAYA 228 2 In a In a ae If the points selected are the same as the three point estimator then equation 2 8 reduces to equation 2 6 The points selected for the four point Gaussian estimation are by no means arbitrary and will not always yield a unique solution Two conditions must be met for the method to produce a solution Firstly a cannot be equal to a or the denominator in equation 2 8 will go to zeto The second criterion is that the four selected points cannot all lie in a circle of any arbitrary center or radius Brady et al 2002 2 1 1 4 Continuous Four Point F
175. scretization error of the individual pixels The equation for the continuous least squares fit is gtven below in equation 2 11 Ga HOY X gt a Le cli dydx Eq 2 11 In equation 2 11 y was minimized using a Gauss Newton algorithm Point selection was determined by the 3X3 area surrounding the peak intensity pixel Brady et al 2002 2 2 Experimental Methods and Materials This work relied heavily on the experimental and computational resources available in the ESM Fluid Mechanics Laboratory at Virginia Tech A summary of the major resources used in this work is found below The objective of this pilot experiment was to demonstrate the ability of the system to characterize the time depended characteristics of a poly dispersed distribution of droplets by resolving the individual velocities and their apparent size 2 2 1 Spray Generation The spray employed in this study was generated using a 60deg cone angle nozzle and a pressure of approximately 10Psi was applied A low speed annular co flow was introduced but was not seeded The water pressure going through the spray nozzle was delivered using a high precision computer controlled gear pump and was varied as a sinusoid with a desired offset at 10Hz frequency 2 2 2 DPIV System The spray data used in this work was acquired using the DPIV system in the ESM Fluid Mechanics Laboratory at Virginia Tech A diagram of the system is shown below in Figure 2 1 The system inclu
176. seeded with neutrally buoyant reflective microparticles and interrogated with a sheet of light expanded from a high power laser Willert and Gharib 1991 Reflected light from the particles is recorded using a digital CMOS camera with high frame rate generally 30 Hz Time resolved systems TRDPIV such as the one developed and employed by our group use CMOS cameras with kHz sampling rates Abiven and Vlachos 2002 Images of the seeded flow are captured successively within a very short time interval so that the particles in a single frame appear in the previous and subsequent frames as well Velocity is obtained by measuring the displacement between particles in successive frames through cross correlation Westerweel 1997 The two accepted ways of resolving displacement ate DPIV and DPTV DPIV applications typically use digital imaging technology since it is possible to acquire and store a large amount of data on a computer Digital images are characterized by their intensity pixel values corresponding to the ones given by the camera sensors One pixel thus defines the smallest element of a digital image In DPIV images are usually coded in an 8 bit grayscale with each pixel taking a value between 0 and 255 An intensity value of 0 represents a black pixel and an intensity value of 255 represents a white pixel Abiven and Vlachos 2002 In DPIV the target image pair is divided into subdivisions called interrogation windows Each subdivi
177. sequence requires input from the user to run the desired file sequence To add a file sequence either click on F in the toolbar or click on Project gt Add Add gt File Sequence Browse for the desired directory containing the images you wish to analyze and click OK The File Sequence Dialog Box shown below in Figure 2 6 will appear File Sequence Dialog x Directory je Documents and Settings jcarneal Desktop what Browse Base lima efilenam File Name 2 e Extension fti Start Index fo Avanced End Index fio Accessory Precision E OK Cancel __ Cancel Figure 2 6 File Sequence Dialog Box The program will automatically select the base filename file extension and precision The user must select the start and end indices The files must be numbered with the same basename For example the files for the options shown in Figure 2 6 would be named imagefilename0000 tif imagefilename0001 tif etc Precision is the number of digits the integer in the filename is forced to have If the integer is not forced to have a certain 103 number of digits use 1 for precision This will cause the program to look for filenames listed with only the integer value no padding zeros Removing Images File Sequences and Directories from an Input Package To remove files directories or file sequences from an input package highlight the items to be deleted and press Delete on the keyboard or right click on the desire
178. series of sizing methods to perform The options for the hierarchical fit are shown below in Figure 5 5 The setup for this method is the same as all of the other methods except that the user may select a third method to perform after the Centroid and Three Point Gaussian Fit 135 Hierachical Particle Sizing Dialog Task Name JH ierachical method Picking Intensity feo Maximum Pixel hao Selection Intensity Particle Sizing Method Heirachy 1 Centroid Fit 2 Three Point Gaussian Fit Least Squares Volume Fit Image Preprocessing Task Basic Thresholding Dynamic Thresholding Histogram Thresholding Median Thresholding Add Delete Property Dutput Directory C My Documents DPI Browse Output File Ext IP Cancel Figure 5 5 Hierarchical Sizing Properties The user may select the third method with the pull down menu under Particle Sizing Method Hierarchy The methods will be performed in order 1 to 3 and the output will contain the last method that succeeds For instance if the Least Squares Volume Fit produces no result in this hierarchy the results from the Three Point Gaussian Fit will be outputted to the destination file 136 Chapter 6 Particle Image Velocimetry PIV Tasks Several Particle Image Velocimetry techniques are included in Flow IQ v2 2 This section deals with the addition removal and performance of PIV tasks The available PIV techniques are briefly summarized in
179. sion is processed independently to calculate a local velocity vector The subdivisions are determined by the grid spacing and interrogation window size Grid spacing is the space between measurements in the image For example a grid spacing of 4 pixels means that the final output will have a velocity every 4 pixels in the image or a 64 X 64 grid of velocity measurements for an image size of 256 pixels Typically interrogation window sizes range from 8 to 128 pixels depending on the size of the digital image and the seed particle size and seeding density Figure 1 1 below illustrates an image broken down into four interrogation windows with no overlap on the left This case represents no overlap between the velocity measurements On the right the 50 overlap case is shown along with the resulting measurement grid Abiven and Vlachos 2002 No overlap Figure 1 1 Illustration of interrogation windows and overlap In order to get a displacement out of each interrogation window a process called cross correlation is performed Typically fast Fourier transforms FFT s are used to calculate the cross correlation between two corresponding interrogation windows from successive images However direct correlation and normalized methods have also been used in the past Figure 1 2 illustrates the DPIV process In essence the cross correlation shifts the second window across the first and sums the matching values At the point where the images ma
180. t this requirement it is filtered out 11 Destroy the particle list generated from MapParticles Particle Destroy particles Public members Matrix lt UBYTE gt pixels the pixel matrix e Class ParticleT lt T gt A template class cannot be exported And we don t need it is exported We only need ParticleT lt double gt is exported which is used in PIV to find particle displacement e Class PzMethod This class models a particle sizing task Given an image it can return you a ParticleSizingResults object see class ParticleSizingResults It implements a standard particle sizing workflow including image preprocessing particle extraction filtering and sizing If you do have special workflow you can design a new class derive the class Operations 1 Run in one step pzm Run image results where pzm is a PzMethod object image is an Image object results is the returned ParticleSizingResults object 2 Run in multiple steps 169 Particles Pzm Start image Pzm RunAParticle Particlel image psr where Particlel is the ith element of Particles psr is the returned ParticleSizingResult object Repeat this class until all particles are processsed Pzm End Particles this call must be made to free resources Note if you want to do sth for example display info on console to let user know what s going on then Run in multiple steps 3 Accept a visitor pzm Accept aVisitor here we user Visitor design patte
181. task should now be highlighted Now right click on the task to be removed and click on Run Task s on Data A menu will appear with a list of the available input packages for analysis Click on the input package to be processed to run the tasks on the desired data The task will be run on all of the selected images or files in the project Any task specific procedures are covered in the following chapters DPIY DPI 1 br File Edit View Project Image Window Help D S Hi FDE Gm DPIY C Image Processing Image Math Particle Sizing Centroid Fit 7 Run Task s on Data gt Inputi i a EL Copy E Properties Parti PIV Validation Stero PIV Trajectory Figure 2 10 Running a Task 107 When all running tasks have finished a Finished Processing message will appear in the lower right window under Console Navigating Windows and Checking Location in FLOW IQ v2 2 In order to navigate between input packages in Flow IQ v2 2 use the _ a amp buttons to navigate up one directory and return to the home directory and to navigate into a directory double click as is standard in windows The following chapters discuss the setup and performance of each class of task provided in FLOW IQ 2 2 In order to check the current location of the files in the active file window upper right window right click in the upper right window and select Where Am I A dialog box wi
182. tate task Reset 4 Get info about the task type task GetDesc 5 Get info aobut the task task GetHelpInfo 6 Get type id task GetID Public members enum NODMO_MULTIPASS FIRST_ORDER_MULTIPASS SECOND_ORDER_MULTIPASS N_METHODS enum CorrType FFT_BASED DIRECT N_CORRS m_Wss window size m_Mx x grid m_My ygrid char m_Name MAX_FN_SIZE task name char m_OFDir MAX_FN_SIZE output file directory 171 char m_OFExt 8 output file extension int m_PzMethod particle sizing method ExperimentConfig m_ExpCfg experiment configuration int m_CorrType cross correlation type e Class NoDWOPIV This class models no discrete window offset PIV method e Class FirstOrderPIV This class models the first order PIV method e Class SecondOrderPIV This class models the second order PIV method e Class WinSize This class models a window dimension Public members int x y e Class PIVPItFile This class models a PIV plt file for writing purpose only Operations 1 Creation PIVPItFile pltfile filename nI nJ where nl is the number of rows nJ is the number of columns of a velocity vector matrix 2 Output a velocity to file pltfile Write Velocity pivresults where pivresults is a velcocity vector e Class PIVFileReader This class is used to read velocity vectors from a plt file Operations 1 Creation PIVFileReader reader filename if the file filename doesn t exist IOException is thrown
183. tch best the correlation is at its peak value This peak is located and provides the best estimate for the displacement of the particles in the window Abiven and Vlachos 2002 There are several sources of error in DPIV that prevent the deterministic evaluation of the flow field Particles are moving in and out of a frame and the particles within the same window do not necessatily have diverse velocities Also particles might appear differently from one frame to the other in terms of light intensity or shape as they move within the light sheet The combination of 3 all these phenomena coupled with noise from the recording media constitute a random process that introduces significant error levels to the measurement Abiven and Vlachos 2002 Image captured at time t Image captured at time t dt Cross correlation displac ement obtained from the NR di Figure 1 2 Cross correlation procedure Both DPIV and DPTV use digital images as an input A typical experimental setup for DPIV is shown below in Figure 1 3 Cylinder Laser Camera Control and Image DAQ System Host Computer Figure 1 3 Generic experimental setup In Figure 1 3 above the experimental setup for flow around a cylinder is shown The test section can be anything from an airfoil to a biological system The atea of interrogation is fixed to observe the desired region of fluid behavior in a given experiment The origin of DPIV hails back to tr
184. tential of performing global time resolved size measurements using a simple DPIV configuration based on CMOS imaging technology 2 1 Introduction Simultaneous time resolved velocity and size measurements are limited to single point methodologies using Phase Doppler Particle Analyzer PDPA Although these methods can measure with high accuracy the particle velocity and size they are limited by the requirement of spherical particles Kim et al 1999 In the case of spay atomization this requirement is not satisfied since the droplets deform forming ellipsoids In addition single point methodologies do not reveal the global temporal variation of the flow The above limitations generate the need for alternative global measurement methodologies based on visualization techniques The dynamics of spray droplet break up and the accurate measurement of droplet sizes and velocities in high pressure sprays is an increasingly important problem in fluid mechanics During 12 the past decade there has been a wide spread use of DPIV techniques employed on the analysis of single phase or multi phase flow systems DPIV measurements provide global instantaneous velocity distributions revealing the internal structure of the flow However despite the numerous advances of the method in polydispersed multi phase flows very few attempts have been made to deliver simultaneous velocity size and shape quantification of the dispersed phase Abiven et al 20
185. terline Displacement px 0 25 16 82 Multigrid Total Error Various Shear Stress Rates T T 0 0625 64 i 0 125 64 0 25 64 e 0 0625 32 0 125 32 lima e t 0 25 32 ei A 0 0625 16 amp 0 125 16 ei 10 H amp 0 25 16 o Le A Error px 107 0 0 5 1 1 5 2 2 5 3 35 4 Centerline Displacement px Figure 4 8 Mean RMS and Total Error for Multigrid DPIV Algorithm There are several important observations to make from Figure 4 6 Firstly the RMS error is approximately one to two orders of magnitude less than the mean error at corresponding shear rates and interrogation window sizes Therefore the total error is almost identical to the bias error The shear rate represented as different line types is clearly the dominant factor in the velocity estimation error The interrogation window size has a marked effect on the velocity error at the higher shear rates However at low shear rates the interrogation window size does not significantly affect the error associated with the measurement It should also be noted that as the 16 window nears the maximum resolvable displacement 1 4 window tule of 4 pixels displacement the error associated with the measurement increases at shear rates of 0 125 and 0 25 Figure 4 9 below shows the mean RMS and total error for the dynamically adaptive DPIV or DADPIV algorithm Figure 4 7 exhibits many of the same phenomena
186. the traditional 3 point Gaussian sizing scheme in the x direction However the 3 point Gaussian method exhibits error that reaches a level of 50 at an eccentricity of 0 8660 which corresponds to an axis ratio x y of 0 50 Another method for calculating the error associated with the various sizing methods is the area estimation In this section the actual area was compared to the estimated area by the various sizing schemes Therefore this section deals with the area in the projected area of a particle image in DPIV data The area error results from the Monte Carlo Simulations are shown below in Figure 3 13 The error was plotted as a function of eccentricity For the data shown in Figure 3 13 the x axis was considered to be the semimajor axis 63 Area Error px Area Error Monte Carlo Simulations Elliptic Sizing Method x axis semiminor 10 1 n T a o T 15 T T T T T J di prof anny aw A al Trad 3 point Averaged Elliptic True Elliptic 20 0 1 0 2 0 3 i 0 4 0 5 Eccentricity 0 6 0 7 Monte Carlo Simulations Elliptic Sizing Method x axis semiminor 0 8 0 9 10 T T T Trad 3 point Averaged Elliptic True Elliptic 0 1 0 2 0 3 1 0 4 0 5 Eccentricity 0 6 0 7 0 8 0 9 Figure 3 13 Area absolute and percent error for all sizing methods 64 Figure 3 13 shows that the
187. this study including the two cameras and the Dantec PDA system b a view of the high pressure conical spray illuminated by the laser sheet and c a schematic overview of the timing synchronization and control arrangement The experiment involved the acquisition of several planes parallel to the center plane of the spray A total of five planes placed at 8 4 0 4 and 8 mm with respect to the center plane were acquired reconstructing a volume of the flow The volumetric data were subsequently used to generate the statistical distributions of the droplet sizes for horizontal planes normal to the spray axis These statistics were compared with the corresponding PDA measurements 22 Transferring Images Green Lines Transferring Images to PC Transferring Images Blue Line Trigger AAA s h Signal to yne Camera 1 and e Data Processing Workstation arire rese Signal to Camera 2 Sequence Camera 2 Light Sheet Delivery Closed Loop Positioning Control for Laser Sheet and System Cameras Field of View Black Lines Synch Signal to Laser and Camera Red Lines Feedback Signal into DA Board E Figure 2 2 Experimental Setup for the Spray PIV and PDPA experiment 23 2 2 5 Computational and Computer Resources Since the majority of this work was performed using simulations and massive amounts of data the computational and computer resources available were key components of this wo
188. though not limited by the size of a particle the accuracy of this method is significantly compromised by saturation and noise Moreover it is subject to severe peak locking effects for particles with small diameters Pixel Counting gives an estimate of the apparent diameter of a particle with a easy to implement algorithm The image is first preprocessed with a basic threshold filter Each pixel is then sorted by its distance from an estimated center using centroid method The intensity of each pixel from the sorted list is summed until it is equal to four standard deviations defined as the particle diameter as explained below Pixel counting is computationally fast however the method is very sensitive to the preprocessing task as will be shown 131 Three Point Gaussian Fit The three point Gaussian estimator is a simple one dimensional approximation of the geometric particle image Gy 2 a I The three independent variables Io o and x represent the maximum intensity the Gaussian distribution standard deviation and the center position respectively If the three points chosen to solve these equations are the maximum intensity pixel and the two neighboring pixels along the x axis then the standard three point Gaussian estimator can be derived Willert and Gharib 1991 da Ina _ Ina 2 2dna _ Ina 2Ina The equation for finding y is equivalent therefore five points are actually needed The
189. tio of Semiminor to Semimajor Axes 100 T T T T T T T S y semimajor x e x semimajor 50 4 5 ui oO 2 XL 0 L 50 L I I fi fi 0 5 0 55 0 6 0 65 0 7 0 75 0 8 0 85 0 9 0 95 1 Axis Ratio Figure 3 5 Theoretical Error vs Axis Ratio for 3 point Gaussian Sizing Method Figure 3 5 above is more intuitively obvious as the error diverges when the discrepancy between the semimajor and semiminor axes increases The novel sizing methods presented in this work are the averaged elliptic and true elliptic sizing methods The averaged elliptic method uses the average of the two axes to arrive at a measurement diameter The true elliptic method sizes a particle using the two independent measurements thus forming a true ellipse The theoretical error for the averaged elliptic and true 54 elliptic methods are compared to the theoretical error for the 3 point Gaussian sizing method in Figures 3 6 and 3 7 below Theoretical Error Percent vs Eccentricity All Methdos 100 S y semimajor 3P e x semimajor 3P Average Elliptic True Elliptic Area Error ne sce cca A HA 50 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 Eccentricity Figure 3 6 Theoretical Percent Error for 3 Point Gaussian Averaged Elliptic and True Elliptic Sizing Methods Theoretical Error Percent vs Ratio of Semiminor to Semimajor Axes All Methods
190. tion at the lower diameters However the correlation coefficient is still very low due to the inability of the 3 point method to resolve diameters smaller than 25 microns Therefore the methods were also analyzed over the 100 to 150 micron range as in the previous sections The histogram results for the 100 to 150 micron diameter range are shown below in Figure 2 18 Figure 2 18 shows the total population for the PIV PTV methods and the probability density functions for the PIV PDA and PTV methods Figure 2 18 suggests that the PTV 3 point 42 Gaussian method improves the correlation of the PIV method with the PDA measurement A list of the correlation coefficients over the 100 to 150 micron range is given in Table 2 4 Population Histograms for PTV Compensation 450 T T T T T T I PTV 3 Point Total 400 Compensated 3 Point 350 4 300 3 N n o T L Population N o o T a 150 a 4 100 _ SA SE 4 50 a 1 4 0 L 1 1 1 ATA i 100 105 110 115 120 125 130 135 140 145 150 Diameter um Probability Density Functions for PTV Compensation 0 25 T T T T T T j I PTV 3 Point Total Compensated 3 Point PDA 0 2 e 0 15F 5 5 3 S a 0 1 4 0 05 4 0 i 4 4 4 1 Lr TC 100 105 110 115 120 125 130 135 140 145 150 Diameter um Figure 2 18 Population for PIV PTV methods and PDFs for PIV PDA and PTV 43 Method Corr
191. to estimate displacement on the correlation Window Size 1 determines the window size to use initially Window Size 2 specifies a second try which allows the user to specify a smaller window for attempting the NDWO PIV algorithm X Grid Spacing and Y Grid Spacing specify the x and y grid spacing in the final output and can take any value specified by the user Boundary specifies whether boundary detection should be used to detect and remove the boundaries in the image Zero padding if clicked forces the algorithm to pad the interrogation window sizes with zeros near the boundary in order to allow measurements very close to the wall The user may add a validation task to the PIV algorithm in order to perform validation during PIV analysis by clicking on Add under Validation Task The properties of the validation task can be modified by highlighting the task and clicking Properties The user may specify the output directory by clicking BROWSE selecting the desired output directory and clicking OK The user may also specify the output file extension which defaults to Tecplot plt format Input Filter Type Specifies the sequence for the input files in the input package to be read whether single frame double frame or sequence frames Skip determines the desired skip between the input files which defaults to O no skip Correlation allows the user to select between FFT based and direct correlation and a variety of other optio
192. to provide a test bed for the basic accuracy testing of Flow IQ v2 2 Programs were developed for the analysis of the output plt files from both Flow IQ v2 2 and Ultimate A comparison program was also developed to compare the output from the two programs A set of basic images was constructed in order to provide a wide range of situational testing 177 5 2 1 1 Uniform Displacement Results A set of uniform displacement images with displacements ranging from 0 5 to 0 5 pixels were created and analyzed using various options in Flow IQ v2 2 Figure 5 1 below shows the mean RMS and total error for the u fizzate code as compared to the Flow IQ v2 2 No Discrete Window Offset First Order Discrete Window Offset and Second Order Discrete Window Offset algorithms with interrogation window sizes of 16 pixels square Only a single pass was used in order to check the accuracy of the first pass in all of the algorithms presented in the uniform case Mean Error 0 1 T T T T T T T I I e Ultimate DPIVNDWO 0 09 4 amp DPIV FODWO H y DPIV SODWO 0 08 a 4 0 07 FN A 0 06 4 8 5 0 05 4 ui 0 04 4 0 03 4 0 02 4 0 01 4 0 I I I 0 5 0 4 0 3 0 2 0 1 0 0 1 0 2 0 3 0 4 0 5 Displacement px 178 RMS Error 0 08 T T T T T T T I I e Ultimate DPIV NDWO d 4 DPIV FODWO 0 07 DPIV SODWO 0 06 0 05 Error px o E T
193. tor positive matrix i e m 4 unary operator negative matrix i e m 5 assignment operator ml m2 161 6 Arithmetic operators 2 A ml m2 ml m2 m1 3 m1 3 m1 5 power 7 Logic operators ml m2 ml m2 8 Friend arithmetic operators 9 A ml m2 m3 ml m2 3 ml m25 ml m2 9 I O stream operators lt lt gt gt cout lt lt m cin gt gt m fout lt lt m fin gt gt m 10 Set all elements to a certain value m Value 0 11 Change the size of the matrix m SetSize 3 3 12 Change the values of a row m SetRow 13 Change the values of a column m SetColumn 14 Geta copy of a row m GetRow 15 Geta copy of a column m GetColumn 16 Get sub matrix m GetSubMatrix 0 0 2 2 17 Get sub matrix m GetSubMatrixEx 1 1 3 3 Note GetSubMatrixEx allows index out of left to right or top to bottom range of matrix m And set those unavailable elements from m as T 0 You cannot do this using GetsubMatrix 18 Flip the matrix from left to right m FlipLRO 19 Flip the matrix from top to down m FlipUD 20 Check if the matrix is square m IsSquare 21 Get the dimension of the matrix m GetRowNo m GetColNo 22 A matrix can be accessed in the way like an way by using operator suppose m is a 2x3 matrix then m 2 means m 0 3 m 4 means m 1 0 m 6 means m 1 2 23
194. ure 3 2 Added Preprocessing Tasks Editing Task Properties When a task is highlighted as Basic Thresholding is in Figure 3 2 above the properties of the task will be displayed in the lower left window as shown In order to edit these properties click on the desired task to highlight the task Then right click on the highlighted task and click Properties The corresponding dialog box will appear depending on the selected task Enter the desired properties and click OK You may also define the output directory for each task in the dialog box for the image processing tasks 110 Removing Preprocessing Tasks There are two ways to remove preprocessing tasks in FLOW IQ V2 2 as a group or individually To remove several preprocessing tasks from the active project click on Image Processing in the upper left window Image Processing should now be highlighted Now right click on Image Processing and click on Remove ImagePro Tasks The Image Preprocessing Remove Tasks Dialog Box will appear as shown below in Figure 3 3 Remove Tasks xi Basic Thresholding Dynamic Thresholding Histogram Thresholding Median Thresholding Blur Smooth AGW Binarize Area Smooth 3x3 Remove Cancel Figure 3 3 Removing Preprocessing Tasks To remove a task highlight the task by clicking on the task and click on REMOVE This will remove the task from the list When undesired tasks have been eliminated click
195. urement the mean bias error was an order of magnitude greater than the RMS random error A least squares scheme was used to correct for this bias error with favorable results The major contribution of this effort stems from providing a novel elliptical particle sizing scheme for use in DPIV and quantifies the error associated with wall shear measurements using several DPIV algorithms A test bed and comprehensive user s manual for Flow IQ v2 2 was also developed in this work ACKNOWLEDGMENTS The author is truly at a loss when it comes to thanks in relation to this work The reason for this loss is the difficulty of imagining anyone who would want to be associated with a pile of paper that will never make any real or imaginary difference in the world as we know it However the one saving grace of the acknowledgements section is that of all the theses I have picked up the acknowledgements are the only section I have bothered to read So therefore for people like me reading this now I must submit My deepest thanks to my parents for raising me with a healthy disrespect for all those in authority I also owe them the need for people to earn their respect from me rather than simply respecting them for their shiny titles medals and pieces of paper Thank you again mom and dad for teaching me to be my own person and to hell with anyone who would have me any other way Thank you to my precious wife Catherine whose example of unending
196. using our DPIV version 1 0b software Image preprocessing was used in this experiment A basic thresholding of 20 intensity 0 255 and subsequent dynamic thresholding were used on the images in order to generate the data presented in this work The data contained a DPIV dataset at 8 4 0 4 and 8 mm from the center of the spray An example picture from the Omm dataset at the center of the spray is shown below in Figure 2 3 24 Figure 2 3 Example Digital Particle Image Velocimetry Spray Data Omm Plane Each of these datasets included 16 304 images similar to the one shown in Figure 2 2 Each of these frames was analyzed using each method studied in this work The methods used in this work were the three point Gaussian four point Gaussian continuous four point Gaussian and continuous least squares sizing methods A total of 81 520 images were processed using each method combining to a total of 326 080 images processed The experimental magnification in this experiment was approximately 24 microns per pixel Diffraction terms were included in all of the diameter conversions and analysis Bin ranges were matched for each method in order to provide completely comparable histograms between measurement techniques 2 3 1 Histogram Analysis The output from each method was analyzed in MATLAB to produce histograms for each method Histograms were created for each plane of data The total volume and total method histograms were also calculated
197. xels to 0 5 pixels in 0 1 pixel increments These images were analyzed using the DPIV version 2 2 software and the original w mate software Errors were calculated and plotted in order to compare the performance of the two systems The output files from both tests were saved and a comparison program was developed in C to characterize output by comparison with the original systems Several test cases were included in the test bed PIV data from the IMP experiment cylindrical vortex shedding mining experiment and spray data are included in the test bed along with artificial Couette flow images and Osceen vortex images The artificial image software generated by Claude Abiven 2002 was used for all artificial images in this work All of the images in the test bed were analyzed with Flow IQ v2 2 and utimate In the case of artificial input images the errors were calculated and plotted In the case of real PIV data the results are compared directly to each other using the ultimate output as the base for comparison The test bed was developed in C for data analysis and MATLAB for data visualization in order to provide ease of use for future participants in the analysis of DPIV software performance 5 2 1 Test Bed for Flow IQ v2 2 Results A test bed was developed in addition to the user s manual provided in this work The basic ertor analysis portion of the test bed is included here Uniform displacement images were generated in order
198. xj Task Name Distance fo Step 2 TT Multiple Segments Count e 3 PREA C Program Files Aeroprobe DPI bin Workspa Browse Output File Ext IP Figure 9 3 Basic Tracking Options Distance is the search radius in pixels that the algorithm will use to search for particles in successive frames Step count is the incremental step between frames in case the user wishes to skip a certain number of frames for processing Output directory can be specified by clicking BROWSE and selecting the desired output directory The output type for particle trajectory is Tecplot format plt 157 Chapter 10 Output Types This chapter discusses the output types for each class of tasks in detail Particle Sizing Output A portion of an output plt file using the Three Point Gaussian Fit is shown below The first three lines are the header required by the Tecplot plt format The data is arranged in columns with the first column listing the x coordinate of the particle The second column contains the y coordinate of the particle The third column is the estimated diameter of the particle and the fourth column is a flag identifying the sizing method TITLE Particle Sizing Data File VARIABLES X Y Diameter MID zone I 6 135 493496 253 628721 2 848859 239 724143 253 009294 2 850054 125 454566 252 157295 2 839976 223 564297 252 016439 2 846193 48 457762 249 068571 2 844447 1 89 926630 249 042028 2 8
199. ybrid PTV Properties Dialog 145 Chapter 7 Validation FLOW IQ V2 2 includes validation algorithms for support with PIV applications This section deals with the addition removal and performance of validation tasks FLOW IQ V2 2 includes several validation options to the user Validation must be run on the plt output from PIV tasks Adding Validation Tasks To add particle tracking tasks to the active project click on Validation in the upper left window Validation should now be highlighted Now right click on Validation and click on Add Tracking Tasks The Validation Dialog Box will appear as shown in Figure 7 1 below Task Add Dialog E x Tasks Selected Tasks 3X3 PIV Validation 3x3 PIV Validation OK Cancel Figure 7 1 Add Validation Task Dialog Box To add a task to the project click on the desired task to highlight it and then click The available tasks are listed on the left and the tasks to be added are shown on the right When you have selected the desired tasks click OK The added tasks will be shown in a tree under Validation 146 Editing Task Properties When a task is highlighted the properties of the task will be displayed in the lower left window as shown In order to edit these properties click on the desired task to highlight the task Then right click on the highlighted task and click Properties The corresponding dialog box will appear depending o

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