Twenty years of particle image velocimetry
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- Adrian, R.J. Exp Fluids (2005) 39: 159. doi:10.1007/s00348-005-0991-7
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The development of the method of particle image velocimetry (PIV) is traced by describing some of the milestones that have enabled new and/or better measurements to be made. The current status of PIV is summarized, and some goals for future advances are addressed.
1 Historical development
The year 2004 marked the 20th anniversary since the term “particle image velocimetry” (PIV) first appeared in the literature. This article gives a personal view of the development of PIV over those 20 years, followed by a summary of the current state-of-the-art and a prospective view of some of the improvements that are needed and the future possibilities in the field. The presentation reflects the author’s experiences and views of certain developments that seemed particularly important or interesting. No attempt has been made to make the presentation exhaustive, or to credit in any way that is complete the many people who have advanced the field. The reader can achieve a much more complete understanding of the full scope of these developments by referring to the excellent compilation of papers by Grant (1994), to a very good book on PIV by Raffel et al. (1998), and to the bibliography of PIV by Adrian (1996), which is almost exhaustive through 1995 and documents much prior work, including all of the first decade. Three special issues on PIV (Kompenhans and Tropea 1997; Adrian 2000, 2002) contain very useful collections of the more recent work. Lastly, the reader can find many examples of state-of-the-art applications in this Special Issue.
The first investigators to achieve such measurements actually used the method of laser speckle, originally developed in solid mechanics, and showed that it could be applied to the measurement of fluid velocity fields. In 1977, three different research groups, Barker and Fourney (1977), Dudderar and Simpkins (1977), and Grousson and Mallick (1977), independently demonstrated the feasibility of applying the laser speckle phenomenon to fluid flow by measuring the parabolic profile in laminar tube flow. The principal elements of their experiments were the use of double-exposure photographs and planar laser light sheet illumination and interrogation by forming Young’s interference fringes from the many pairs of displaced laser speckles in small interrogation spots on the specklegrams. By 1983, a young doctoral student working at the v. Karman Institute, Belgium, Meynart (1979, 1980, 1982a, 1982b, 1983a, 1983b, 1983c), was the leading practitioner of this method, and he had shown that practical measurements could be made in laminar flow and turbulent flow of liquids and gases, thereby stimulating intense interest from the fluid mechanics community.
Many researchers became interested in PIV because it offered a new and highly promising means of studying the structure of turbulent flow. This goal strongly influenced the choices made in the development of the method. By its nature, turbulence is a phenomenon that occurs over a wide range of physical scales, extending from the largest scales of the flow down to the Kolmogorov scale. Hence, a successful measurement technique must be able to measure over a wide dynamic range of scales in length and velocity. Another salient feature of turbulence is its randomness, which may make it impossible to determine a priori the direction of flow. Hence, the measurement technique must be able to sense flows in all directions. Turbulence also occurs at high Reynolds number, which often means high velocity. Accelerations are large, and, therefore, the particles must be small enough to follow the flow in the presence of large local and randomly fluctuating accelerations. This implies the use of very small particles, a few microns in size, and the small light scattering cross-section of such particles implies the use of high intensity illumination. Coupled with the short time exposures needed to capture images of fine particles without blurring, these requirements lead naturally to the use of high intensity, pulsed lasers.
The energy necessary to illuminate fine particles and produce images of sufficient exposure and clarity was a major issue in PIV. From experience with laser Doppler velocimetry, there existed a good understanding of the particle sizes needed to follow turbulent flows, and of light scattering, so it was possible to compute, using Mie scattering theory, the exposure of images that would result for appropriate particles. In particular, it was possible to show that pulsed lasers would provide enough energy to obtain good photographic images from micron-sized particles in air and 10–30-μm-sized particles in water. Subsequently, a big step in PIV practice was to use double-pulsed solid-state lasers. They produced excellent double exposure photographs of particles without much limit on speed or fluid using high-resolution (300 line/mm) film. The earliest use of Nd:Yag lasers appears to be in 1986 (Kompenhans and Reichmuth 1986). Still later, Nd:Yag lasers became available in compact, dual oscillator packages with self-contained cooling supplies, and they have become the current workhorse of PIV.
In the first decade of PIV, the greatest challenge was the interrogation of the images, simply because computer capabilities were not adequate for the task. In 1985, the DEC PDP 11/23 was a common digital computer in many fluids laboratories. It typically had 128 KB of RAM and a 30 MB hard drive. Imagine holding the operating system, the executable program, and the data in a RAM space that is the same size as the minimum document file size used by current word processors. Practically, it was impossible to perform two-dimensional Fourier transforms or two-dimensional correlation analysis on such machines. Therefore, there was considerable interest in non-statistical methods, such as tracking particles individually. Alternatively, several groups seriously pursued the determination of two-dimensional correlations by analog optical means (Morck et al. 1993; Vogt et al. 1996). Particle tracking implied operating with low image density so that the probability of finding more than one pair of particles per interrogation spot was small. Then, using the principle that nearest-neighbor images corresponded to the same particle (which is only approximate for small, but finite image density), one could make successful measurements. The difficulty with this method was that, at the reduced image density that accompanied reduced particle concentration, the number of vectors per unit area was not large enough to resolve turbulent fields completely.
To improve the spatial resolution, various investigators sought to optimize the low image density method by using interrogation windows of variable size, shape, and displacement. This led to the implementation of adaptive windowing methods. Currently, adjustable window methods enjoy use as a means of optimizing single-exposed double-frame images obtained with digital cameras.
At the time that Meynart performed his work using Young’s fringes, the dynamic velocity range of the technique, defined as the maximum velocity measurable divided by the minimum velocity measurable, was somewhere between 5 and 10. PIV was a velocity-measuring instrument that had a 1-digit display! The dynamic range was clearly far too small for the method to be of value in serious fluid mechanics research. The problem was that the dynamic range corresponds to the maximum displacement of the images divided by the minimum displacement that can be measured. In the double-exposure images used at the time, the lower limit was determined by the images overlapping when the displacement was less than 1 image diameter. Thus, if the maximum displacement was 10 image diameters, the dynamic range was approximately 10:1.
The idea of applying an artificial spatial shift to the second image was developed to improve the dynamic velocity range and to provide a means of determining the direction of the particle displacement from double-exposed images (Adrian 1986b). In this method, the images were recorded in such a way that the second image was shifted precisely in a known direction so that the direction of flow could be determined unambiguously. Further, the probability of two images from the same particle overlapping was zero, and this solved the critical problem of limited dynamic range. By eliminating the overlap of particles images at small displacements, the dynamic range immediately increased to somewhere between 100 and 200, where it remains to this day. Although researchers continue to strive for a larger dynamic range, it is now large enough to permit good measurements, provided the PIV system is optimized.
One of the most important changes in the PIV technique was the move from photographic to videographic recording. This change profoundly influenced the usability and, hence, the popularity of PIV. Of course, many researchers had been using digital cameras in preference to film for years. For example, film recording was seld()om used in Japan. But, in the early 1990s, several investigators, most notably Willert and Gharib (1991) and Westerweel (1993), published results indicating that the low resolution of digital cameras was not as serious an issue as others had supposed, and that digital PIV could be accurate enough to provide useful results. Photographic film possessed very high resolution—100 line/mm for T-Max and 300 line/mm for Technical Pan on 25×35 mm, or even 100×125 mm films. In comparison, digital camera resolution was typically 500×500 pixels. However, digital cameras possessed high regularity in the location of the pixels relative to random locations of grains on a film, and clever methods were developed to enhance the accuracy of the interrogation of digital images. Moreover, the resolution of digital cameras increased rapidly to 1,000×1,000 pixels, and current 11-megapixel cameras are essentially equivalent to 100 line/mm 35 mm film.
In the early 1990s, it was clear that digital imaging would become the standard at some point in the future. What was perhaps not appreciated was the extent to which digital imaging could simplify PIV and make it a process with which everybody was willing to work. The work by Nishino et al. (1989) was extremely influential in this regard. They presented the best turbulence statistics available from PIV at the time. They achieved highly stable averages by taking over 19,200 video images. This was far beyond anything one could do with photographic film. The appeal of digital PIV rested not only on the ease of acquiring images, but it also eliminated the problem of mounting and carefully registering each film frame on an interrogation table. The maximum number of PIV photographs taken by even the most determined investigators seldom, if ever, exceeded 1,000. If one wanted good, accurate turbulence statistics, it was necessary to use digital PIV. Hence, digital PIV enjoyed increasing use in the mid-1990s, and now it is used almost exclusively. The possibility of taking thousands of PIV images made it desirable to speed up the interrogation process and to automate the vector clean-up process. Dantec developed and sold an impressively fast hard-wired PIV correlator, but, ultimately, the incredible advance of PC capability and the flexibility of software drove the development away from specialized, hard-wired devices.
The other outstanding impact of digital PIV came with the advent of interline transfer cameras that could hold two images recorded in rapid succession by transferring the first image recorded by each pixel to an on-chip storage well, and then record a second image. It is the author’s understanding that the PIV community is indebted to Lourenco et al. (1994) for convincing Kodak to make such cameras for the PIV market. These cameras enabled three important improvements. First, it was known theoretically that cross-correlation of separately recorded images of the first and second exposures was superior to the auto-correlation of double exposures (Keane and Adrian 1992). But, cross-correlation could not be implemented conveniently until the new cameras became available. Second, the cross-correlation cameras eliminated the need for image shifting: the direction of flow was determined automatically by the order of the exposures. Third, and most importantly, small displacement image overlap was eliminated completely, so that a large dynamic range was possible. The introduction of these cameras was one of the most important developments in the field of PIV.
Many developments also occurred on the optical side of the PIV system. Stereographic imaging was used early to make photogrammetric measurements by particle tracking in volumes (Guezennec et al. 1994; Dracos et al. 1993; Maas et al. 1993; Kasagi and Nishino 1993). The consensus experience is that the projection of particles from 3D space onto 2D camera image planes creates particle image overlaps that limit the number of particles that can be imaged to about 3,000. Overlapping images could not be paired unambiguously. Recent work (Pereira and Gharib 2002) using clever, out-of-focus imaging has pushed this number to about 104. Stereographic imaging of particles in planar laser sheets does not encounter this limitation because the projected volume of particles is much smaller. In this approach, one can use ray tracing to determine the relationship between image plane locations and particle location (Arroyo and Greated 1991) or generalized calibration with a target in the flow (Soloff et al. 1997). Stereographic PIV solves the problem of perspective error, as well as giving the third velocity component, and it has proven to be a practical generalization of monoscopic PIV.
Why then, is holographic PIV not used more widely? First, it is expensive; second, it requires considerable skill; and third, one cannot realistically record enough holograms to give stable turbulence statistics. This situation would change dramatically if electronically readable and writable optical recording media were to become available with adequate resolution and sensitivity. The current multi-mega-pixel cameras are already adequate for this task if one is willing to confine attention to a very small volume. Microscopic inline holography has shown considerable promise (Jian et al. 2003).
2 Current status
Presently, the single-camera, planar light sheet, cross-correlation PIV with a double-pulsed Nd:Yag laser and a 2,000×2,000-pixel cross-correlation PIV camera is the standard system sold by commercial companies. Cooling the cameras to achieve a higher signal-to-noise ratio for the images improves the effectiveness of each pixel, thereby, improving the effective resolution. In turbulence research, just using simple 2D PIV has been enormously rewarding in revealing fundamental aspects of the structure of turbulence. Some of these aspects had been inferred or guessed from earlier flow visualization, but the reliability of PIV visualization has made it possible to eliminate the guessing, to quantify vorticity, and to reveal heretofore-unobservable phenomena that allow completion of the structural pictures of certain canonical flows, such as wall turbulence. More sophisticated forms of PIV will impact efforts to understand turbulence, but one should not rush into complexity before mining the wealth of information that can be had using 2D PIV.
Stereo PIV is now relatively common, and it is working well, except that the out-of-plane component is inherently less accurate than the in-plane components.
Much of the focus over the last 5 years has been on developing accurate, robust means of measuring the image displacement from the image field. It appears that we are closing in on algorithms that are near optimum, and that relatively little can be expected in terms of future improvements in performance. The standard for 2D measurements is now about 300×300 vectors with a velocity dynamic range of no more than 200:1. Because of this small dynamic range, many PIV experiments are still exercises in optimization. Framing rates have increased dramatically with the introduction of new cameras and high-repetition-rate lasers, and this development offers a straightforward path for the expansion of PIV capability. Coupling PIV with simultaneous planar laser-induced fluorescence (PLIF) has also enjoyed success and seems relatively straightforward. Making combined measurements of fluid velocity and the velocity of a second phase such as particulate, droplet or vapor phase is a viable and valuable extension of PIV into multi-phase flow. The simultaneous measurements of liquid velocity and bubble phase by Lindken and Merzkirch (2002) in Fig. 9 is an excellent example.
3 Desirable developments
- 1.A master theory should be developed that integrates all of the following aspects of PIV:
Particle dynamics and the relationship between measured particle displacement, particle velocity, and fluid velocity
Imaging, including the accuracy and precision of mapping and distortion compensation
Image recording and the effect of pixelization with good noise models for the cameras
Optimum algorithms for locating particles with maximum accuracy
Optimum algorithms for pairing particle images with maximum reliability
Interpolating and smoothing regularly sampled data from correlation interrogation or randomly sampled data from particle tracking velocimetry or super-resolution PIV
- 2.New, more versatile particle seeding methods are needed to:
Enable easy optimization of concentration and higher concentrations in large volumes
Produce new particles for flows with severe acceleration—e.g., high-drag particles with large scattering cross-sections, such as spiny spheres
The goal should be set to achieve a velocity dynamic range of 1000:1—this would enormously increase the utility of PIV and render tedious optimization of experimental parameters less important
- 4.The results of PIV experiments should be held to increasingly rigorous standards. In particular, experimentalists should routinely:
Demonstrate the adequacy of the spatial resolution by performing grid resolution tests and/or spatial frequency response tests
Demonstrate the accuracy and reproducibility of the velocity measurements
Routinely examine the probability density histograms of the velocity data for evidence of experimental artifacts
- 5.Means should be sought to reduce total system costs by:
Reducing the costs of light sources and cameras
Developing low-cost, restricted-purpose systems, such as probe-PIV
There may be many earlier papers from different fields that suggested using correlation in somewhat different contexts. For example, Soo et al. (1959) presented a particularly prescient proposal for the “determination of turbulence characteristics of solid particles in a two-phase stream by optical cross-correlation.” Leese et al. (1971) describe “an automated technique for obtaining cloud motion from geosynchronous satellite data using cross-correlation.”
This paper was prepared with the support of the U.S. Department of Energy, Los Alamos National Laboratory. The author would like to take this opportunity to acknowledge with gratitude the many contributions of the students, post-doctoral associates, senior visiting scholars, and academic collaborators who, over the past 20 years, have studied particle image velocimetry in the Department of Theoretical and Applied Mechanic’s Laboratory for Turbulence and Complex Flow. They are, in rough chronological order: C.-S. Yao, C. Landreth, J. Kompenhans, M. Lee, R. Keane, Z. C. Liu, D. L. Reuss, T. J. Hanratty, P. Offutt, A. Prasad, M. Cui, C. Wark, H. Xu, T. Urushihara, J. Westerweel, C. Westergaard, C. Meinhart, K. Paschal, J. Brouillette, Y. Zhang, D. Barnhart, G. Papen, V. Troy, T. Oakley, E. Loth, C. Tomkins, S. Soloff, U. Ullum, K. Christensen, R. Fernandes, K. Sharp, N. Fujisawa, C. Kaehler, K. Nishino, J. Sakakibara, K.C. Kim, D. Hill, K. Takehara, J. Santiago, M. Olsen, Z. Deng, B. Balasubramanian, E.Yamaguchi, M. Murphy, W. Lai, G. Elliott, and P. Vedula.