A survey is given of the major developments in three-dimensional velocity field measurements using the tomographic particle image velocimetry (PIV) technique. The appearance of tomo-PIV dates back seven years from the present review (Elsinga et al 2005a 6th Int. Symp. PIV (Pasadena, CA)) and this approach has rapidly spread as a versatile, robust and accurate technique to investigate three-dimensional flows (Arroyo and Hinsch 2008 Topics in Applied Physics vol 112 ed A Schroder and C E Willert (Berlin: Springer) pp 127–54) and turbulence physics in particular. A considerable number of applications have been achieved over a wide range of flow problems, which requires the current status and capabilities of tomographic PIV to be reviewed. The fundamental aspects of the technique are discussed beginning from hardware considerations for volume illumination, imaging systems, their configurations and system calibration. The data processing aspects are of uppermost importance: image pre-processing, 3D object reconstruction and particle motion analysis are presented with their fundamental aspects along with the most advanced approaches. Reconstruction and cross-correlation algorithms, attaining higher measurement precision, spatial resolution or higher computational efficiency, are also discussed. The exploitation of 3D and time-resolved (4D) tomographic PIV data includes the evaluation of flow field pressure on the basis of the flow governing equation. The discussion also covers a-posteriori error analysis techniques. The most relevant applications of tomo-PIV in fluid mechanics are surveyed, covering experiments in air and water flows. In measurements in flow regimes from low-speed to supersonic, most emphasis is given to the complex 3D organization of turbulent coherent structures.

Tomographic PIV: principles and practice

The free-surface impact of solid objects has been investigated for well over a century. This canonical problem is influenced by many physical parameters, including projectile geometry, material properties, fluid properties, and impact parameters. Through advances in high-speed imaging and visualization techniques, discoveries about the underlying physics have improved our understanding of these phenomena. Improvements to analytical and numerical models have led to critical insights into cavity formation, the depth and time of pinch-off, forces, and trajectories for myriad different impact parameters. This topic spans a wide range of regimes, from low-speed entry phenomena dominated by surface tension to high-speed ballistics, for which cavitation is important. This review surveys experimental, theoretical, and numerical studies over this broad range, utilizing canonical images where possible to enhance intuition and insight into the rich phenomena.

Water Entry of Projectiles

For tracking the motion of illuminated particles in space and time several volumetric flow measurement techniques are available like 3D-particle tracking velocimetry (3D-PTV) recording images from typically three to four viewing directions. For higher seeding densities and the same experimental setup, tomographic PIV (Tomo-PIV) reconstructs voxel intensities using an iterative tomographic reconstruction algorithm (e.g. multiplicative algebraic reconstruction technique, MART) followed by cross-correlation of sub-volumes computing instantaneous 3D flow fields on a regular grid. A novel hybrid algorithm is proposed here that similar to MART iteratively reconstructs 3D-particle locations by comparing the recorded images with the projections calculated from the particle distribution in the volume. But like 3D-PTV, particles are represented by 3D-positions instead of voxel-based intensity blobs as in MART. Detailed knowledge of the optical transfer function and the particle image shape is mandatory, which may differ for different positions in the volume and for each camera. Using synthetic data it is shown that this method is capable of reconstructing densely seeded flows up to about 0.05 ppp with similar accuracy as Tomo-PIV. Finally the method is validated with experimental data.

https://iopscience.iop.org/article/10.1088/0957-0233/24/2/024008/pdf

Iterative reconstruction of volumetric particle distribution

A novel three-dimensional (3D), three-component (3C) particle image velocimetry (PIV) technique based on volume illumination and light field imaging with a single plenoptic camera is described. A plenoptic camera uses a densely packed microlens array mounted near a high resolution image sensor to sample the spatial and angular distribution of light collected by the camera. The multiplicative algebraic reconstruction technique (MART) computed tomography algorithm is used to reconstruct a volumetric intensity field from individual snapshots and a cross-correlation algorithm is used to estimate the velocity field from a pair of reconstructed particle volumes. This work provides an introduction to the basic concepts of light field imaging with a plenoptic camera and describes the unique implementation of MART in the context of plenoptic image data for 3D/3C PIV measurements. Simulations of a plenoptic camera using geometric optics are used to generate synthetic plenoptic particle images, which are subsequently used to estimate the quality of particle volume reconstructions at various particle number densities. 3D reconstructions using this method produce reconstructed particles that are elongated by a factor of approximately 4 along the optical axis of the camera. A simulated 3D Gaussian vortex is used to test the capability of single camera plenoptic PIV to produce a 3D/3C vector field, where it was found that lateral displacements could be measured to approximately 0.2 voxel accuracy in the lateral direction and 1 voxel in the depth direction over a voxel volume. The feasibility of the technique is demonstrated experimentally using a home-built plenoptic camera based on a 16-megapixel interline CCD camera and a array of microlenses and a pulsed Nd:YAG laser. 3D/3C measurements were performed in the wake of a low Reynolds number circular cylinder and compared with measurements made using a conventional 2D/2C PIV system. Overall, single camera plenoptic PIV is shown to be a viable 3D/3C velocimetry technique.

https://iopscience.iop.org/article/10.1088/0957-0233/26/11/115201/pdf

Volumetric particle image velocimetry with a single plenoptic camera

In previous computational fluid dynamics studies of breaking waves, there has been a marked tendency to severely over-estimate turbulence levels, both pre- and post-breaking. This problem is most likely related to the previously described (though not sufficiently well recognized) conditional instability of widely used turbulence models when used to close Reynolds-averaged Navier–Stokes (RANS) equations in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity. While this problem has been known for nearly 20 years, a suitable and fundamentally sound solution has yet to be developed. In this work it is demonstrated that virtually all commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in such regions. A new formulation of the is the dissipation.)

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On the over-production of turbulence beneath surface waves in Reynolds-averaged Navier–Stokes models

We present a new method for resolving three-dimensional (3D) fluid velocity fields using a technique called synthetic aperture particle image velocimetry (SAPIV). By fusing methods from the imaging community pertaining to light field imaging with concepts that drive experimental fluid mechanics, SAPIV overcomes many of the inherent challenges of 3D particle image velocimetry (3D PIV). This method offers the ability to digitally refocus a 3D flow field at arbitrary focal planes throughout a volume. The viewable out-of-plane dimension (Z) can be on the same order as the viewable in-plane dimensions (X?Y), and these dimensions can be scaled from tens to hundreds of millimeters. Furthermore, the digital refocusing provides the ability to 'see-through' partial occlusions, enabling measurements in densely seeded volumes. The advantages are achieved using a camera array (typically at least five cameras) to image the seeded fluid volume. The theoretical limits on refocused plane spacing and viewable depth are derived and explored as a function of camera optics and spacing of the array. A geometric optics model and simulated PIV images are used to investigate system performance for various camera layouts, measurement volume sizes and seeding density; performance is quantified by the ability to reconstruct the 3D intensity field, and resolve 3D vector fields in densely seeded simulated flows. SAPIV shows the ability to reconstruct fields with high seeding density and large volume size. Finally, results from an experimental implementation of SAPIV using a low cost eight-camera array to study a vortex ring in a 65 ? 40 ? 32 mm3 volume are presented. The 3D PIV results are compared with 2D PIV data to demonstrate the capability of the 3D SAPIV technique.

https://iopscience.iop.org/article/10.1088/0957-0233/21/12/125403/pdf

Three-dimensional synthetic aperture particle image velocimetry

It is well known that the water entry of a sphere causes cavity formation above a critical impact velocity as a function of the solid–liquid contact angle; Duez et al. (Nat. Phys., vol. 3 (3), 2007, pp. 180–183). Using a rough sphere with a contact angle of , Aristoff & Bush (J. Fluid Mech., vol. 619, 2009, pp. 45–78) showed that there are four different cavity shapes dependent on the Bond and Weber numbers (i.e., quasistatic, shallow, deep and surface). We experimentally alter the Bond number, Weber number and contact angle of smooth spheres and find two key additions to the literature: (1) cavity shape also depends on the contact angle; (2) the absence of a splash crown at low Weber number results in cavity formation below the predicted critical velocity. In addition, we use alternate scales in defining the Bond, Weber and Froude numbers to predict the cavity shapes and scale pinch-off times for various impacting bodies (e.g., spheres, multidroplet streams and jets) on the same plots, merging the often separated studies of solid–liquid and liquid–liquid impact in the literature.

/pdf/water-entry-of-spheres-with-various-contact-angles-1r1svigmc5.pdf

Water entry of spheres with various contact angles

A methodology for resolving three-dimensional (3D) bubble fields using 3D synthetic aperture imaging (SA imaging) is developed and applied to the bubbly flows induced by a turbulent circular plunging jet. 3D SA imaging involves capturing entirely in-focus images in an array of cameras with multiple viewpoints, then reprojecting the images into the measurement volume and combining them post capture. The result is a stack of synthetically refocused images that span the measurement volume with each refocused image having a narrow focus on a particular plane. In this paper, bubble shadow images are captured by projecting diffuse backlight onto the measurement volume. 3D SA imaging is ideally suited to investigate optically dense multiphase flows due to the ability to reconstruct volumes that contain partial occlusions. Instantaneous bubble sizes and locations in the plunging jet bubble fields are extracted from the volumes using two feature extraction algorithms and presented for various jet heights. The data are compared with existing literature on bubble penetration depth and size distributions. A scaling law for the integrated air concentration as a function of depth below the free-surface is proposed. Coupled with scaling laws for a parameter describing the radius of the bubble cone and radial concentration profiles, this new scaling law can be used to determine the entire air concentration profile given a minimal number of single-point measurements.

Three-dimensional bubble field resolution using synthetic aperture imaging: application to a plunging jet

A method for performing bundle adjustment–based calibration of a multi-camera setup with refractive interfaces in the optical path is presented. The method contributes to volumetric multi-camera fluid experiments, where it is desirable to avoid tedious alignment of calibration grids in multiple locations and where a premium is placed on accurately locating world points. Cameras are calibrated from image point correspondences of unknown world points, and the location of the refractive interface need not be accurately known a priori. Physical models for two practically relevant imaging configurations are presented; the first is a planar wall separating cameras and a liquid, and the second is a liquid-containing cylindrical tank with finite wall thickness. Each model allows the cameras to be in general location and orientation relative to the interface. A thorough numerical study demonstrates the ability of the calibration method to accurately estimate camera parameters, interface orientation, and world point locations. The numerical study explores the convergence, accuracy, and sensitivity of the calibration method as a function of initialization, camera configuration, volume size, and interface type. The technique is applied to real calibration data where the algorithm is supplied with errant initial parameter estimates and shown to provide accurate results. The ease of implementation and accuracy of the refractive calibration method make the approach attractive for three-dimensional multi-camera fluid measurement methods.

Jesse Belden

Papers

Water Entry of Projectiles

Three-dimensional synthetic aperture particle image velocimetry

Water entry of spheres with various contact angles

Three-dimensional bubble field resolution using synthetic aperture imaging: application to a plunging jet

Calibration of multi-camera systems with refractive interfaces