We address calibration and self-calibration of tomographic PIV experiments within a pinhole model of cameras. A complete and explicit pinhole model of a camera equipped with a 2-tilt angles Scheimpflug adapter is presented. It is then used in a calibration procedure based on a freely moving calibration plate. While the resulting calibrations are accurate enough for Tomo-PIV, we confirm, through a simple experiment, that they are not stable in time, and illustrate how the pinhole framework can be used to provide a quantitative evaluation of geometrical drifts in the setup. We propose an original self-calibration method based on global optimization of the extrinsic parameters of the pinhole model. These methods are successfully applied to the tomographic PIV of an air jet experiment. An unexpected by-product of our work is to show that volume self-calibration induces a change in the world frame coordinates. Provided the calibration drift is small, as generally observed in PIV, the bias on the estimated velocity field is negligible but the absolute location cannot be accurately recovered using standard calibration data.

A novel method performing 3D PTV from double frame multi-camera images is introduced. Particle velocities are estimated by following three steps. Firstly, separate particle reconstructions with a sparsity-based algorithm are performed on a fine grid. Secondly, they are expanded on a coarser grid on which 3D correlation is performed, yielding a predictor displacement field that allows to efficiently match particles at the two time instants. As these particles are still located on a voxel grid, the third, final step achieves particle position refinement to their actual subvoxel position by a global optimization process, also accounting for their intensities. As it strongly leverages on principles from tomographic reconstruction, the technique is termed Double-Frame Tomo-PTV (DF-TPTV). Synthetic tests on a complex turbulent flow show that the method achieves high particle and vector detection efficiency, up to seeding densities of around 0.08 particles per pixel (ppp), while its root-mean-square error of velocity estimation is lower to that of state-of-the-art similar methods. Results from an experimental campaign on a transitional round air jet at Reynolds number 4600 are also presented. During the tests, seeding density varies from 0.06 to 0.03 ppp on average. Associated to an outlier rejection scheme based on temporal statistics, DF-TPTV vector fields truthfully correspond to the instantaneous jet dynamics. Quantitative performance assessment is provided by introducing statistics performed by bin averaging, upon assuming statistical axisymmetry of the jet. Mean and fluctuating axial velocity components in the jet near-field are compared with reference results obtained from planar PIV at higher seeding density, with an interrogation window of size comparable to that of the bins. Results are found to be in excellent agreement with one another, confirming the high performance of DF-TPTV to yield reliable volumetric vector fields at seeding densities usually considered for tomographic PIV processing, or even higher.

We introduce a new method for estimating fluid trajectories in time-resolved PIV. It relies on a Lucas–Kanade paradigm and consists in a simple and direct extension of a two-frame estimation with FOLKI-PIV (Champagnat et al 2011 Exp. Fluids 50 1169–82). The so-called Lucas–Kanade Fluid Trajectories (LKFT) are assumed to be polynomial in time, and are found as the minimizer of a global functional, in which displacements are sought so as to match the intensities of a series of images pairs in the sequence, in the least-squares sense. All pairs involve the central image, similar to other recent time-resolved approaches (FTC (Lynch and Scarano 2013 Meas. Sci. Technol. 24 035305) and FTEE (Jeon et al 2014 Exp. Fluids 55 1–16)). As switching from a two-frame to a time-resolved objective simply amounts to adding terms in a functional, no significant additional algorithmic element is required. Similar to FOLKI-PIV the method is very well suited for GPU acceleration, which is an important feature as computational complexity increases with the image sequence size. Tests on synthetic data exhibiting peak-locking show that increasing the image sequence size strongly reduces both associated bias and random error, and that LKFT has a remaining total error comparable to that of FTEE on this case. Results on case B of the third PIV challenge (Stanislas et al 2008 Exp. Fluids 45 27–71) also show its ability to drastically reduce the error in situations with low signal-to-noise ratio. These results are finally confirmed on experimental images acquired in the near-field of a low Reynolds number jet. Strong reductions in peak-locking, spatial and temporal noise compared to two-frame estimation are also observed, on the displacement components themselves, as well as on spatial or temporal derivatives, such as vorticity and material acceleration.

Leading-edge vortex flows are often present on propeller blades at take-off, however, their characteristics and aerodynamic impact are still not fully understood. An experimental investigation using Time Resolved Particle Image Velocimetry (TR-PIV) has been performed on a model blade in order to classify this flow with respect to both delta wing leading-edge vortices and the low Reynolds number studies regarding leading-edge vortices on rotating blades. A numerical calculation of the experimental setup has been performed in order to assess usual numerical methods for propeller performance prediction against TR-PIV results. Similar characteristics were found with non slender delta wing vortices at low incidence, which hints that the leading-edge vortex flow may generate vortex lift. The influence of rotation on the characteristics of the leading-edge vortex is compared to that of the pressure gradient caused by the circulation distribution. A discussion on the quality of the PIV reconstruction for close-wall structures is provided.