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This practical guide provides comprehensive information on PIV. The third edition extends many aspects of Particle image Velocimetry, in particular the tomographic PIV method, high-velocity PIV, Micro-PIV, and accuracy assessment.

In this book, relevant theoretical background information directly support the practical aspects associated with the planning, performance and understanding of experiments employing the PIV technique. It is primarily intended for engineers, scientists and students, who already have some basic knowledge of fluid mechanics and non-intrusive optical measurement techniques. It shall guide researchers and engineers to design and perform their experiment successfully without requiring them to first become specialists in the field. Nonetheless many of the basic properties of PIV are provided as they must be well understood before a correct interpretation of the results is possible.

### Chapter 1. Introduction

The introduction starts with a short summary of the historical background of PIV. Next, the fundamental principles of PIV are briefly explained in an easily understandable manner, so that the reader already becomes aware of the main advantages, problems and limitations of PIV, before starting to read the detailed explanations in the main part of the book. Several major technological milestones of PIV, achieved during the last decades, resulted in its wide-spread use within different areas today. This fact is illustrated taking examples from applications for fundamental research in turbulent flows and for industrial research in large test facilities.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 2. Physical and Technical Background

The choice of an appropriate tracer is of paramount importance for the success of a PIV experiment. This chapter guides the choice by giving a description of the physical mechanisms governing the motion of tracer particles in the flow. The discussion covers seeding particle generation techniques and their supply into the flow facility from water experiments to aerodynamics and compressible reactive flows. The properties of HFSB tracers are given a specific attention, given their recent introduction for PIV experiments at large scale. The light scattering properties of the tracer particles are of equal importance. The chapter presents the most used physical models to predict the amount of light scattered by the tracers. The fundamental properties of Lasers as the most used devices to illuminate the seeded flow are treated. The discussion includes the properties of emitted light pulses, low- and high-repetition rate systems, light transmission optics and methods of light sheet formation. The growing number of experiments with volume illumination justifies an expanded discussion on the working principles of LED illumination as an alternative approach to Lasers. Digital imaging systems needed to record the scattered light intensity from the particles are described from their working principle, electronic architecture and operating modes. The most relevant differences between CCD and CMOS imagers are explained guiding the choice to the most suited imager for a given experiment. The discussion includes the most recent developments in this domain with the sCMOS architecture.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 3. Recording Techniques for PIV

Based on the physical concepts of electronic imaging introduced in the previous chapter, this chapter focusses on the image sensor technology in the context of PIV image recording. Loosely based on the historical development of CCD image sensor technology, the chapter describes the advancements such as on-chip intermediate storage, asynchronous triggering and the lens-on-chip technique that were instrumental in making the “double-shutter” PIV camera possible, that has been the workhorse throughout the PIV community for the past two decades. Details such as the synchronization of these cameras with the light source are covered. Driven by the consumer market, CMOS imaging is nowadays increasingly replacing the CCD sensor in PIV-suitable cameras, in particular, through the introduction of low noise imagers such as the scientific CMOS. Beyond this, high-speed CMOS imager allow the extension of PIV technique to capture temporally highly resolved velocity data at rates in excess of 10,000 recordings per second.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 4. Mathematical Background of Statistical PIV Evaluation

In this chapter, a simplified mathematical model of the recording and subsequent statistical evaluation of PIV images will be presented. For this purpose the mathematical representation of the particle image locations, the image intensity field and the mean value, the auto-correlation, and the variance of a single exposure recording are described. Then, we analyze the cross-correlation of two frames of singly exposed recordings and expand the theory for the evaluation of doubly exposed recordings.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 5. Image Evaluation Methods for PIV

This chapter covers extensively the methods used to determine the flow velocity starting from the recordings of particle images. After an introduction to the concept of spatial correlation and Fourier methods, an overview of the different PIV evaluation methods is given. Ample discussions devoted to explain the details of the discrete spatial correlation operator in use for PIV interrogation. The main features associated to the FFT implementation (aliasing, displacement range limit and bias error) are discussed. Methods that enhance the correlation signal either in terms of robustness or of accuracy are surveyed. The discussion of ensemble correlation techniques and the use of single-pixel correlation in micro-PIV and macroscopic experiments is a novel addition to the present edition. A detailed description is given of the standard image interrogation based on multigrid image deformation, where the advantages in the treatment of complex flows are discussed as well as the issues in terms of resolution and numerical stability. Another new feature introduced in this chapter is the discussion of the recent developments of algorithms in use for PIV time series as obtained by high-speed PIV systems. Namely, the algorithms to perform Multi frame-PIV, Pyramid Correlation and Fluid Trajectory Correlation and Ensemble Evaluation are treated. Furthermore, a new section that discusses the methods used for individual particle tracking is introduced. The discussion describes the working principles of PTV for planar PIV. The potential of the latter techniques in terms of spatial resolution as well as their limits of applicability in terms of image density are presented.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 6. PIV Uncertainty and Measurement Accuracy

The chapter starts with an overview of common PIV measurement error contributions. Then important parameters for the optimization of PIV measurements are discussed and the significance of the dynamic velocity range and dynamic spatial range is outlined. Thereafter, the concept of measurement error is introduced and the error propagation essentials are discussed. The sensitivity of the measurement uncertainty on the particle image size, particle image density, background noise, particle image shift, out-of-plane motion, light-sheet mismatch, displacement gradients and streamline curvature is discussed in detail. The chapter finishes with strategies to optimize PIV uncertainties and outlines the main implications of the uncertainty analysis for multi-camera recording systems. The aim of this chapter is to familiarize the reader with various sources and sensitivities of PIV measurement uncertainty which will be instructive for optimizing PIV measurements in practice.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 7. Post-processing of PIV Data

While the previous chapter have dealt with recording and evaluation of PIV images, the extracted data require further post-processing in the context of data validation and further data reduction to retrieve fluid mechanical relevant information. This chapter introduces a variety of validation schemes that operate either globally or locally on the data along with methods of data interpolation to fill in data gaps in both space and time. The validated data can then be subjected to differentiation to, for instance, extract gradient information such as vorticity fields. Issues and errors arising through applying differentials to the finitely-spaced data grid are discussed and illustrated. Alternatively, the velocity data can be integrated to retrieve streamlines, body forces or even pressure fields.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 8. Stereoscopic PIV

By extending the “classical” single camera PIV implementation with a second camera the planar light sheet can be imaged stereoscopically from two directions allowing the recovery of the velocity vector normal to the light sheet. This chapter on stereo-PIV introduces two primary implementations of stereoscopic imaging along with the concept of Scheimpflug imaging of obliquely viewed light sheet planes. The stereoscopic reconstruction can follow a variety of approaches but collectively rely on some sort of calibration to recover 3-C velocity data from two separate 2-C vector maps. The error introduced through camera misalignment is discussed along with possible mitigation strategies. The application of the stereo-PIV technique in environments with index-of-refraction changes such as in water facilities requires specific imaging arrangements. The chapter closes with a list of recommendations for successful implementation of the stereo-PIV technique.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 9. Techniques for 3D-PIV

This chapter initially provides the reader with an extensive survey of the many methods available to measure the flow velocity in three-dimensional problems. Afterwards, the chapter devotes three main sections to the most common or emerging methods: Tomographic PIV, 3D-PTV techniques and Shake-the-Box. Tomographic PIV is considered the technique of choice at present, and is extensively discussed. Aspects cover hardware components, requirements for illumination of a volume and techniques to increase particles visibility. A discussion is given of the effects of number of cameras and their configuration to deal with densely seeded experiments, where the phenomenon of ghost particles dominates the experimental errors. The theoretical background is given about the techniques used for tomographic reconstruction of 3D particle intensity distribution, followed by a critical evaluation of the accuracy of reconstruction. The discussion of Tomographic PIV closes with the description of the most recent algorithms based on multi-exposure reconstruction and time-resolved data analysis. The second part of the chapter is a new addition to the book and it deals with the fundamental principles of 3D-PTV. Particle detection, triangulation and pairing are the most important operations to perform a successful 3D-PTV evaluation. Hybrid methods based on tomographic reconstruction and individual particle tracking are discussed. The section concludes suggesting the working range of PTV techniques in 3D experiments. The Shake-the-Box technique is an emerging method that performs Lagrangian particle tracking with high potential in terms of computation speed and for the high accuracy of particle motion estimation. Its rapid diffusion among research laboratories justifies a detailed description of its working principles, main features and characteristic performance. The section elaborates on the concepts of Iterative Particle Reconstruction, Optical Transfer Function calibration and Data Assimilation to restore the results on a Cartesian mesh. Algorithms for image sequences as well as for four-frame recordings are detailed.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 10. Micro-PIV

The chapter begins with a motivation of microfluidic flow analysis and summarizes the main diagnostic tools commonly used for flow measurements in microscopic systems. Thereafter, the typical implementation of 2D planar micro-PIV is presented, followed by a short historical background of significant development steps since 1993. Next, the imaging of volume-illuminated small particles is discussed and the essentials of three-dimensional diffraction pattern are outlined. The concept of depth-of-field and depth-of-correlation are introduced and the problem of particle visibility is discussed in detail. The second half of the chapter focuses on 3D micro-PIV and micro-PTV techniques. First, scanning, stereoscopic and tomographic micro-PIV recording techniques are presented. Thereafter, the confocal scanning microscopy and defocusing techniques are discussed. Finally, the 3D astigmatism PTV technique is outlined in detail and the strength of the technique for 3D time resolved flow analysis in micro-scale systems is demonstrated.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 11. Applications: Boundary Layers

The following two experiments have been performed in the second half of the 1990s’ in the DLR low turbulence wind tunnel (TUG), which is of an Eiffel type. Screens in the settling chamber and a high contraction ratio of 15:1 lead to a low turbulence level in the test section (cross section $$0.3 \times 1.5\,\text {m}^2$$). The basic turbulence level in the test section of the TUG of $$Tu= 0.06\%$$ (measured by means of a hot wire) allows the investigation of acoustically exited transition from laminar to turbulent flow as well as turbulent boundary layers that develop in the relatively long test section. The flow was seeded in the settling chamber upstream of the screens used to reduce the turbulence of the wind tunnel flow.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 12. Applications: Transonic Flows

Solid surfaces in like actuators, fluid mechanical models and surrounding walls can influence the fluid flow and/or can be deformed or displaced by it. The knowledge of the actual surface shape and location is therefore important for many fluid mechanical investigations. In compressible fluids density variations is another important fluid parameter besides velocity. Both, the measurement of density gradients in a flow and the detection of the deformation and position of solid surfaces in contact with the fluid can be easily obtained based on PIV imaging hard- and software. The correlation based procedures for deformation, displacement, and strain analysis have been developed and applied more and more frequently during the past decade. The most common method, the deformation measurement by Digital Image Correlation (DIC) is described first together with examples of applications. The later section describes the theory of the Background-Oriented Schlieren Technique (BOS), which determines density gradients without using any sophisticated optical equipment. Practical aspect of the technique are addressed by the description of its application to a helicopter in hovering flight and to the transonic flow behind a cylinder.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 13. Applications: Helicopter Aerodynamics

In this chapter a number of applications of the PIV technique will be described, contributed by leading PIV experts from different research establishments and universities worldwide. Primarily, the objective of presenting these applications is to show how the PIV technique has spread out to the most different research areas. However, it is of even higher importance to gain the reader access to a wide variety of ideas for PIV measurements by presenting many different applications in fundamental or industrial research. For each experiment the most important parameters of the object under investigation, of the illumination and recording setup, etc. will be given. These data together with the hints and tricks briefly described and the references to further, more detailed, literature may be useful for the reader when trying to solve problems of his own application.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 14. Applications: Aeroacoustic and Pressure Measurements

In the research field of aeroacoustics, fluctuations in turbulent flows which are part of a sound generating process can be identified by means of the so-called causality correlation technique [5,6,29]. In this approach, the coefficient matrix resulting from the calculated correlation coefficients between the acoustic pressure fluctuations in the far field and velocity fluctuations in a turbulent flow field is analysed. The temporal resolution of the coefficient matrix is set by the sampling rate of the pressure signal in the far field. The spatial resolution is determined by the spatial sampling rate of the measured flow quantity (Table  11.22).
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 15. Applications: Flows at Different Temperatures

These experimental investigations of flows by means of PIV have been carried out in 1996 by DLR in cooperation with the Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, in order to complete their numerical simulations and LDV measurements.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 16. Applications: Micro PIV

This section discusses various applications and techniques used in $$\mu \text {PIV}$$. The applications include very high spatial resolution measurements of pressure-driven flow in a rectangular capillary and measurements in a challenging toroidal vortex.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 17. Applications: Stereo PIV and Multiplane Stereo PIV

The various methods of image reconstruction and calibration as described in Sect. 8.1 were applied in the measurement of the unsteady vortex ring flow field in 1995. Figure 11.125 outlines a vortex ring generator having a simple construction with very reproducible flow characteristics. The vortex ring is generated by discharging a bank of electrolytic capacitors ($$60\,000\,\upmu \text {F}$$) through a pair of loudspeakers which are mounted facing inward on to two sides of a wooden box. By forcing the loudspeaker membranes inward, air is impulsively forced out of a cylindrical, sharpened nozzle (inner diameter $$=34.7\,\text {mm}$$) on the top of the box. The shear layer formed at the tip of the nozzle then rolls up into a vortex ring and separates from the nozzle as the membranes move back to their equilibrium positions due to the decay in supply voltage. As long as the charging voltage is kept constant, the formation of the vortex ring will be very reproducible. The generator also has a seeding pipe with a check valve allowing the interior of the box and ultimately the core of the vortex ring to be seeded.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 18. Applications: Volumetric Flow Measurements

The transition to turbulence in circular jets is a complex three-dimensional process that requires the use of 3D-PIV and temporal resolution for the full understanding the dynamical behavior of coherent vortices. Jets are used in a multitude of engineering systems and their study often regards the process heat and mass transfer.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans

### Chapter 19. Related Techniques

As noted in Sect.1.3, PIV developed from Laser Speckle Interferometry. Therefore, one of the early names for this technique was ‘Laser Speckle Velocimetry’ before ‘Particle Image Velocimetry’ was established. The Laser Speckle Interferometry (or Laser Speckle Photography) was mainly developed for the determination of displacement and strain in engineering structures. The laser speckles are created due to random interference of scattered light from an optically rough surface illuminated by coherent light.
Markus Raffel, Christian E. Willert, Fulvio Scarano, Christian J. Kähler, Steven T. Wereley, Jürgen Kompenhans