Particle Image Velocimetry (eBook)

 Markus Raffel received his degree in Mechanical Engineering in 1990 from the Technical University of Karlsruhe, his doctorate in Engineering in 1993 from the University of Hannover and his lecturer qualification (Habilitation) from the Technical University Clausthal, in 2001. He started working on PIV at the German Aerospace Center (DLR) in 1991 with emphasis on the development of PIV recording techniques in high-speed ows. In this process he applied the method to a number of aerodynamic problems mainly in the context of rotorcraft investigations. Markus Raffel additionally works on the development of other ow metrology like the background-oriented schlieren technique and the differential infrared thermography. He is professor at the University of Hannover and head of the Department of Helicopters at DLR's Institute of Aerodynamics and Flow Technology in Goettingen. Christian Willert received his Bachelor of Science in Applied Science from the University of California at San Diego (UCSD) in 1987. Subsequent graduate work in experimental fluid mechanics at UCSD lead to the development of several non-intrusive measurement techniques for application in water (particle tracing, 3-D particle tracking, digital PIV). After receiving his Ph.D. in Engineering Sciences in 1992, he assumed post-doctoral positions first at the Institute for Nonlinear Science (INLS) at UCSD, then at the Graduate Aeronautical Laboratories at the California Institute of Technology (Caltech). In 1994 he joined DLR Goettingen's measurement sciences group as part of an exchange program between Caltech and DLR. Since 1997 he has been working in the development and application of planar velocimetry techniques (PIV and Doppler Global Velocimetry (DGV)) at the Institute of Propulsion Technology of DLR and now is heading the Department of Engine Measurement Techniques there. Fulvio Scarano graduated in Aerospace Engineering at University of Naples (1996). Obtained the Ph.D. in 2000 (von Karman Institute, Theodor von Karman prize) and joined TU Delft at the faculty of Aerospace Engineering in the Aerodynamics Section in the same year. Since 2008 he is full professor of Aerodynamics and acts as head of section since 2010. Starting director of Aerospace Engineering Graduate School (2012). Currently director of the AWEP department (Aerodynamics, Wind Energy, Flight Performance and propulsion). Recipient of Marie-Curie grant (1999), Dutch Science Foundation VIDI grant (2005) and of the European Research Council grant (ERC, 2009). European project coordinator (AFDAR, Advanced Flow Diagnostics for Aeronautical Research, 2010-2013). Promoted and supervised more than 20 PhDs. The research interests cover the development of particle image velocimetry (PIV) and its applications to high-speed aerodynamics in the supersonic and hypersonic regime. Notable developments are the image deformation technique, Tomographic PIV for 3D ow velocity measurements and its use to Preface XI quantitatively determine pressure uctuations and acoustic emissions in wind tunnel experiments. Recent works deal with the combination of PIV data with CFD techniques, extension of PIV to large-scale wind tunnel experiments and applications ranging from sport aerodynamics to ground vehicles, from aircraft to rocket aerodynamics. Author of more than 200 publications, delivered more than 20 keynote lectures worldwide. He acts as editorial board member of many international conferences and journals, Measurement Science and Technology and Experiments in Fluids, among others. Christian J. Kaehler received his Physics Diplom Degree from the Technical University Clausthal in 1997, his PhD in Physics from the Georg August University of Goettingen in 2004 and his Habilitation from the Technical University in Brunswick in 2008. From 1996 to 2001 Dr. Kaehler worked at the German Aerospace Center (DLR) in Goettingen (Dr. Kompenhans), during which he had research stays at the University of Illinois at Urbana Champaign in 1996 (Prof. Adrian) and at Caltech in 1998 (Prof. Gharib). From 2001 to 2008 he was the head of the research group on Flow Control and Measuring Techniques at the Technical University Brunswick (Prof. Radespiel). He then became Professor for Fluid Dynamics and was appointed director of the Institute of Fluid Mechanics and Aerodynamics of the University at der Bundeswehr Muenchen in 2008. In 2012, he was offered an Einstein professorship for Aerodynamics at the Technical University Berlin (declined) and in 2017 the Technical University Darmstadt offered him to become head of the chair of Fluid Mechanics (declined). His research covers a broad range of topics involving the development of optical measurement techniques on the micro and macro scale in order to further investigate complex phenomenon in microfluidics and turbulent flows at subsonic, transonic, and supersonic conditions. He is an associate editor of Experiments in Fluids (Springer Nature), an editorial advisory board member of Flow, Turbulence and Combustion (Springer Nature) and editorial board member of Theoretical & Applied Mechanics Letters (Elsevier) and a Steering committee member and organizer of the International PIV Challenge (2001 Goettingen, 2003 Busan, 2005 Pasadena, 2014 Lisbon). Steven T. Wereley received both his Bachelor of Arts in Physics from Lawrence University at Appleton, Wisconsin, and his Bachelor of Science in Mechanical Engineering from Washington University at St. Louis in 1990. He received his Master of Science and Ph.D. degrees from Northwestern University in Evanston, Illinois, in 1992 and 1997, respectively. Subsequently, he spent two years at the Mechanical and Environmental Engineering Department at the University of California in Santa Barbara developing particle image velocimetry algorithms for micro-domain investigations. Since 1999 he has been a professor at Purdue University in the School of Mechanical Engineering - as an Assistant Professor from 1999 to 2005 and an Associate Professor since then. Professor Wereley's research is largely concerned with microparticle image velocimetry techniques and micro-electromechanical systems with applications in bio-physics and bio-engineering. Juergen Kompenhans received his doctoral degree in physics in 1976 from the Georg-August University of Goettingen. From 1977 until 2011 he worked for the German Aerospace Center (DLR) in Goettingen, Germany, mainly developing and applying non-intrusive measurement techniques for aerodynamic research, starting with the PIV technique back in 1985. Since 2001 he has been head of the Department of Experimental Methods of DLR's Institute of Aerodynamics and Flow Technology in Goettingen. Within this department, image based methods such as Pressure Sensitive Paint, Temperature Sensitive Paint, Particle Image Velocimetry, model deformation measurement techniques, density measurement techniques, acoustic field measurement techniques etc. are developed for application as mobile systems in large industrial wind tunnels. As coordinator of several European networks he has contributed to promote and to disseminate the use of image based measurement techniques for industrial research. At present his interest is focused on contributing to the development of ow meters as well as of components required for the use of the PIV technique.

Preface to the Third Edition 5
Organization of the Book 7
Getting Started 9
About the Authors 9
Acknowledgements 12
Contents 18
1 Introduction 26
1.1 Historical Background 26
1.2 Principles of Measuring Velocities 31
1.3 Principle of Particle Image Velocimetry (PIV) 33
1.4 Development of PIV During the Last Decades 40
1.4.1 Early Development of PIV 40
1.4.2 PIV Today 41
1.4.3 Major Technological Milestones of PIV 42
1.4.4 PIV for Fundamental Research in Turbulent Flows 45
1.4.5 PIV for Industrial Research in Large Test Facilities 51
References 54
2 Physical and Technical Background 58
2.1 Tracer Particles 58
2.1.1 Fluid Mechanical Properties 58
2.1.2 Neutrally Buoyant Particles 62
2.1.3 Effect of Centrifugal Forces 63
2.1.4 Brownian Motion 65
2.1.5 Light Scattering Behavior 67
2.1.6 Effective Size of Polydisperse Particles 71
2.2 Particle Generation and Supply 74
2.2.1 Seeding of Liquids 74
2.2.2 Seeding of Gases 76
2.2.3 Seeding Distribution in Wind Tunnels 84
2.3 Light Sources 85
2.3.1 Lasers 85
2.3.2 Features and Components of PIV Lasers 91
2.3.3 Light Emitting Diodes 98
2.3.4 White Light Sources 102
2.4 Light Delivery 102
2.4.1 Light Sheet Optics 102
2.4.2 Fiber Based Illumination 105
2.4.3 Illumination of Small Volumes 106
2.4.4 Illumination of Large Volumes 108
2.5 Imaging of Small Particles 109
2.5.1 Diffraction Limited Imaging 109
2.5.2 Lens Aberrations 113
2.5.3 Perspective Projection 116
2.5.4 Basics of Microscopic Imaging 118
2.5.5 In-Plane Spatial Resolution of Microscopic Imaging 120
2.5.6 Microscopes Typically Used in Micro-PIV 121
2.5.7 Confocal Microscopic Imaging 124
2.6 Sensor Technology for Digital Image Recording 124
2.6.1 Characteristics of CCD Sensors 125
2.6.2 Characteristics of CMOS Sensors 126
2.6.3 Sources of Noise 129
2.6.4 Spectral Characteristics 130
2.6.5 Linearity and Dynamic Range 131
References 132
3 Recording Techniques for PIV 137
3.1 Digital Cameras for PIV 139
3.1.1 Full-Frame CCD 140
3.1.2 Frame Transfer CCD 142
3.1.3 Interline Transfer CCD 143
3.1.4 CMOS Imaging Sensors 145
3.1.5 High-Speed Cameras 147
3.2 Single Frame/Multi-exposure Recording 149
3.2.1 Image Shifting 149
References 150
4 Mathematical Background of Statistical PIV Evaluation 152
4.1 Particle Image Locations 152
4.2 Image Intensity Field 154
4.3 Mean Value, Auto-correlation and Variance of a Single Exposure Recording 156
4.4 Cross-Correlation of a Pair of Two Singly Exposed Recordings 159
4.5 Correlation of a Doubly Exposed Recording 161
4.6 Expected Value of Displacement Correlation 164
References 166
5 Image Evaluation Methods for PIV 167
5.1 Correlation and Fourier Transform 168
5.1.1 Correlation 168
5.1.2 Optical Fourier Transform 169
5.1.3 Digital Fourier Transform 171
5.2 Overview of PIV Evaluation Methods 171
5.3 PIV Evaluation 172
5.3.1 Discrete Spatial Correlation in PIV Evaluation 173
5.3.2 Correlation Signal Enhancement 180
5.3.3 Evaluation of Doubly Exposed PIV Images 189
5.3.4 Advanced Digital Interrogation Techniques 191
5.3.5 Cross-Correlation Peak Detection 204
5.3.6 Interrogation Techniques for PIV Time-Series 209
5.4 Particle Tracking Velocimetry 211
5.4.1 Particle Image Detection and Position Estimation 212
5.4.2 Particle Pairing and Displacement Estimation 214
5.4.3 Spatial Resolution 214
5.4.4 Performance of Particle Tracking 215
5.4.5 Multi-frame Particle Tracking 218
References 218
6 PIV Uncertainty and Measurement Accuracy 225
6.1 Common PIV Measurement Error Contributions 225
6.1.1 Measurement Error Due to Invalid Measurements 228
6.1.2 Relative Uncertainty, Dynamic Velocity Range and Dynamic Spatial Range 230
6.1.3 Measurement Error 231
6.1.4 Error Propagation 233
6.2 PIV Measurement Error Estimation 236
6.2.1 Synthetic Particle Image Generation 238
6.2.2 Optimization of Particle Image Diameter 240
6.2.3 Peak Locking 241
6.2.4 Optimization of Particle Image Density 246
6.2.5 Effect of Background Noise 247
6.2.6 Effect of Particle Image Shift 249
6.2.7 Effect of Out-of-Plane Motion 250
6.2.8 Effect of Displacement Gradients 251
6.2.9 Effect of Streamline Curvature 253
6.3 Optimization of PIV Uncertainty 254
6.4 Multi-camera Systems 257
References 260
7 Post-processing of PIV Data 264
7.1 Data Validation 265
7.1.1 Vector Difference Test 270
7.1.2 Median Test 270
7.1.3 Normalized Median Test 270
7.1.4 Z-Score Test 272
7.1.5 Global Histogram Operator 272
7.1.6 Other Validation Filters 274
7.1.7 Implementation of Data Validation Algorithms 276
7.2 Replacement Schemes 277
7.3 Data Assimilation Techniques 277
7.3.1 Error Minimization 278
7.3.2 Enhancing Temporal Resolution 278
7.3.3 Enhancing Spatial Resolution 280
7.4 Vector Field Operators 280
7.5 Estimation of Differential Quantities 281
7.5.1 Standard Differentiation Schemes 283
7.5.2 Alternative Differentiation Schemes 286
7.5.3 Uncertainties and Errors in Differential Estimation 290
7.6 Estimation of Integral Quantities 292
7.6.1 Path Integrals – Circulation 292
7.6.2 Path Integrals – Mass Flow 293
7.6.3 Area Integrals 294
7.6.4 Pressure and Forces from PIV Data 296
7.7 Vortex Detection 300
References 301
8 Stereoscopic PIV 305
8.1 Implementation of Stereoscopic PIV 306
8.1.1 Reconstruction Geometry 307
8.1.2 Stereo Viewing Calibration 310
8.1.3 Camera Calibration 312
8.1.4 Disparity Correction 316
8.1.5 Stereo-PIV in Liquids 321
8.1.6 General Recommendations for Stereo PIV 325
References 325
9 Techniques for 3D-PIV 328
9.1 Three-Component PIV Measurements in a Volume 328
9.2 Tomographic PIV 331
9.2.1 General Features 331
9.2.2 3D Object Reconstruction 342
9.2.3 3D Motion Analysis 352
9.2.4 4D-PIV Analysis 354
9.2.5 Media Gallery 354
9.3 Volumetric Particle Tracking Velocimetry 354
9.3.1 Overview of PTV Measurement Techniques 355
9.4 Shake-The-Box for Lagrangian Particle Tracking ƒ 360
9.4.1 Iterative Particle Reconstruction 361
9.4.2 Calibration of Optical Transfer Function 363
9.4.3 Shake-The-Box Algorithm 366
9.4.4 Shake-The-Box for multi-pulse systems: 3D Lagrangian particle tracking in high speed flows 370
9.4.5 Fitting Particle Positions Along the Trajectory 372
9.4.6 Data Assimilation for Interpolation to Cartesian Mesh 373
References 377
10 Micro-PIV 385
10.1 Introduction 385
10.1.1 Microfluidics Background 385
10.1.2 Microfluidic Diagnostics 387
10.2 Typical Implementation of 2D Planar ?PIV 388
10.3 2D Planar Micro-PIV Development 390
10.4 Imaging of Volume-Illuminated Small Particles in ?PIV 392
10.4.1 Three-Dimensional Diffraction Pattern 392
10.4.2 Depth of Field 394
10.4.3 Depth of Correlation 395
10.4.4 Particle Visibility 399
10.5 3D Micro-PIV 402
10.5.1 Overview 402
10.5.2 Epi-Fluorescence Scanning Microscopy 404
10.6 Multi Camera Approaches 405
10.6.1 (Scanning) Stereoscopic Imaging 405
10.6.2 Tomographic Imaging 406
10.7 Single Camera Approaches 408
10.7.1 Confocal Scanning Microscopy 408
10.7.2 Techniques Based on Out-of-Focus Imaging Without Aperture 410
10.7.3 Defocused Imaging with Aperture (Three-Pinhole Technique) 411
10.7.4 Imaging Based on Aberrations (Astigmatism) 415
10.7.5 General Defocusing Particle Tracking (GDPT) 420
References 421
11 Applications: Boundary Layers 430
11.1 Boundary Layer Instabilities 430
11.2 Near Wall Turbulent Boundary Layer 433
11.3 Boundary Layer Characterization 436
11.4 Turbulent Boundary Layer Analysis by Means of Large-Scale PIV and Long-Range µPTV 441
11.5 Shock Wave/Turbulent Boundary Layer Interaction 447
References 451
12 Applications: Transonic Flows 455
12.1 Cascade Blade with Cooling Air Ejection 455
12.2 Transonic Flow Above an Airfoil 458
12.3 Transonic Flow Around a Fan Blade 460
12.4 Stereo PIV Applied to a Transonic Turbine 465
12.5 PIV Applied to a Transonic Centrifugal Compressor 470
12.6 Transonic Buffeting Measurements on a 1:60 Scale Ariane 5 Launcher Using High Speed PIV 477
12.7 Supersonic PIV Measurements on a Space Shuttle Model 482
12.8 PIV in a High-Speed Wind Tunnel 485
References 490
13 Applications: Helicopter Aerodynamics 493
13.1 Rotor Flow Investigation 493
13.2 Wind Tunnel Measurements of Rotor Blade Vortices 494
13.3 Measurement of Rotor Blade Vortices in Hover 497
13.3.1 The Experimental Setup 498
13.3.2 Evaluation and Analysis 499
13.3.3 Conclusions 503
13.4 Flow Diagnostics of Dynamic Stall on a Pitching Airfoil 504
13.5 Investigation of Laminar Separation Bubble on Helicopter Blades 509
References 513
14 Applications: Aeroacoustic and Pressure Measurements 516
14.1 PIV Applied to Aeroacoustics 516
14.2 PIV in Trailing-Edge Noise Estimation 520
14.3 A High-Speed PIV Study on Trailing-Edge Noise Sources 523
14.4 Three-Dimensional Vortex and Pressure Dynamics of Revolving Wings 527
14.5 PIV-Based Pressure and Load Determination in Transonic Aircraft Propellers 531
References 535
15 Applications: Flows at Different Temperatures 537
15.1 Study of Thermal Convection and Couette Flows 537
15.2 Combined PIT/PIV of Air Flows Using Thermochromic Liquid Crystals 542
15.3 PIV for Characterisation of Plasma Actuators 546
15.4 PIV in Reacting Flows 550
15.5 Flow Field Measurements Above Wing of High-Lift Aircraft Configuration at High Reynolds Number 555
References 558
16 Applications: Micro PIV 561
16.1 Flow in a Microchannel 561
16.1.1 Analytical Solution to Channel Flow 561
16.1.2 Experimental Measurements 563
16.2 Flow in an Electrothermal Micro-Vortex 565
16.3 Proper Orthogonal Reconstruction of 3D Micro PIV Data 569
16.4 Hybrid Experimental-Numerical Technique for 3D Reconstruction 570
16.5 Particle Velocimetry Using Evanescent-Wave Illumination for Near-Wall Flows 572
16.6 Measurements of the Flow around a Growing Hydrogen Bubble Using Long-Range µPIV and Shadowgraphy 579
16.7 In Vivo Blood Flow Measurements Using Micro-PIV 585
16.8 Reconstruction of Fluid Interfaces using 3D Astigmatic Particle Tracking Velocimetry 588
References 594
17 Applications: Stereo PIV and Multiplane Stereo PIV 599
17.1 Stereo PIV Applied to a Vortex Ring Flow 599
17.2 Multiplane Stereo PIV 604
References 610
18 Applications: Volumetric Flow Measurements 611
18.1 Vorticity Dynamics of Jets with Tomographic PIV 611
18.2 Near-Wall Turbulence Characterization in a Turbulent Boundary Layer Using Shake-The-Box 614
18.3 Large-Scale Volumetric Flow Measurement of a Thermal Plume Using Lagrangian Particle Tracking (Shake-The-Box) 620
18.4 Lagrangian Particle Tracking in a Large-Scale Impinging Jet Using Shake-The-Box 624
18.5 3D Lagrangian Particle Tracking of a High-Subsonic Jet Using Four-Pulse Shake-The-Box 630
18.6 Flow over a Full-Scale Cyclist Model by Tomographic PTV 637
References 643
19 Related Techniques 647
19.1 Deformation Measurement by Digital Image Correlation (DIC) 648
19.1.1 Deformation Measurement in a High-Pressure Facility 649
19.2 Background-Oriented Schlieren Technique (BOS) 652
19.2.1 Introduction 652
19.2.2 Principle of the BOS Technique 652
19.2.3 Application of the BOS to Compressible Vortices 655
19.2.4 Conclusions 661
References 662
Appendix A Suggested Text Books 664
Appendix B Mathematical Appendix 667
B.1 Convolution with the Dirac Delta Distribution 667
B.2 Particle Images 667
B.3 Convolution of Gaussian Image Intensity Distributions 667
B.4 Expected Value 668
Appendix C List of Symbols and Acronyms 669
Index 677