This reduces the signal-to-noise ratio, and allows meaningful results to be obtained even when windows of a single pixel are used. However, if only the steady-state fields are required then more accurate results can be obtained by averaging all the cross-correlation functions before finding the single peak, representing the mean velocity in each window over time (Delnoij et al. These statistics are usually obtained by computing the instantaneous velocity at each time step and assimilating the ensemble properties of such measurements (e.g. Similarly, a sufficient quantity of transient measurements can be used to compute mean and fluctuating velocity components, which provide in-plane Reynolds stresses (in fluids) and granular temperature measurements (in particulate systems). 2012) to illuminate internal slices, but this involves the introduction of interstitial fluid that changes the flow dynamics.įor flows of both fluids and grains, PIV measurements of velocities at different spatial points can be used to derive additional quantities of interest such as strain-rate and vorticity fields. One method to overcome this difficulty is to use refractive index matched scanning (e.g. However, unlike regular fluids, PIV of granular materials is typically restricted to flow boundaries due to the opaque nature of grains, and therefore not necessarily representative of the bulk. 2000), which have the advantage that the grains already provide sufficient contrast without requiring additional flow seeding. Furthermore, the same principles of PIV can also be applied to optical imaging of dense granular flows (Lueptow et al. The accuracy of this classical PIV method has been thoroughly investigated, resulting in a series of guidelines about the interrogation window size, in-plane velocity gradients, out-of-plane motion and seeding particle density for reliable fluid flow measurements (Keane and Adrian 1992). By computing the peak of the cross-correlation function in these windows, it is possible to deduce the most likely in-plane particle displacement between the two images, hence providing two-dimensional velocity fields at each time and spatial location. A high-speed camera then captures two images in quick succession, each of which are split into a series of discrete interrogation windows. In the most common application of PIV, a transparent flow is seeded with opaque tracer particles and a laser sheet is used to illuminate an internal slice of a given experiment (Fig. This is due to its ability to unobtrusively measure instantaneous velocity fields at high spatial and temporal resolutions, which has been facilitated by rapid advances in sensor hardware and computer processing power. Since its initial development in the 1980s, particle image velocimetry (PIV) has proved to be an invaluable flow measurement tool, and is now arguably the dominant velocimetry technique in experimental fluid mechanics (Westerweel et al. The additional velocity information delivered by deep velocimetry could provide new insight into a range of fluid and granular flows where out-of-plane variation is significant. The method involves solving a deconvolution inverse problem to recover the distribution at each in-plane position, and is validated using artificial data as well as controlled laboratory x-ray experiments. Here, we introduce a new image analysis method, named deep velocimetry, that goes beyond established PIV methods and is capable of extracting full velocity distributions from projected images. However, projection-based imaging methods, such as x-ray radiography or shadowgraph imaging, encode additional out-of-plane information that regular PIV is unable to capture. It typically uses optical images, representing quasi-two-dimensional experimental slices, to measure a single velocity value at each in-plane position. Particle image velocimetry (PIV) is a powerful image correlation method for measuring bulk velocity fields of flowing media.
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