Volumetric particle image velocimetry (PIV) is a laser technique measuring three-component velocity field in a volume. Common volumetric PIV techniques are defocusing PIV, multi-view PIV and holographic PIV. Tomographic PIV is an advanced approach of multi-view PIV, which significantly improves the spatial resolution of the measurement by using the multiplicative algebraic reconstruction technique (MART) to reconstruct the particle field. Due to the rapid progress being made in volumetric PIV measurements, this article focuses on introducing the principles of different volumetric PIV methods from aspects of particle reconstruction and velocity reconstruction. Advantages and limitations on applications are elaborated. Issues specific to volumetric PIV regarding illumination, digital imaging, depth of focus, ghost particle and spatial resolution are discussed.

Vortex structures are very popular research objects in turbulent boundary layers (TBLs) because of their prime importance in turbulence modelling. This work performs a tomographic particle image velocimetry measurement on the near-wall region ( $y<0.1\unicode[STIX]{x1D6FF}$ ) of TBLs at three Reynolds numbers $Re_{\unicode[STIX]{x1D70F}}=1238$ , 2286 and 3081. The main attention is paid to the wall-normal evolution of the vortex geometries and topologies. The vortex is identified with swirl strength ( $\unicode[STIX]{x1D706}_{ci}$ ), and its orientation is recognized by using the real eigenvector of the velocity gradient tensor. The vortex inclination angles in the streamwise–wall-normal plane and in the streamwise–spanwise plane as functions of wall-normal positions are investigated, which provide useful information to speculate on the three-dimensional shape of the vortex tubes in a TBL. The difference between the orientations of vorticity and swirl is discussed and their inherent relationship is revealed based on the governing equation of vorticity. Linear stochastic estimation (LSE) is further deployed to directly extract three-dimensional vortex models. The LSE velocity fields for ejection events happening at different wall-normal positions shed light on the evolution of the topologies for the vortices dominating ejection events. LSE based on a centred prograde spanwise vortex provides a typical packet model, which indicates that the population density of the packets in a TBL is large enough to leave footprints in conditionally averaged flow fields. This work should help to settle the severe debate on the existence of packet structures and also lays some foundation for the TBL model theory.

Particle image velocimetry (PIV) is essential in experimental fluid dynamics. In the current work, we propose a new velocity field estimation paradigm, which is a synergetic combination of cross correlation and fully convolutional network (CC-FCN). Specifically, the fully convolutional network is used to optimize and correct a coarse velocity guess to achieve a super-resolution calculation. And the traditional cross correlation method provides the initial velocity field based on a coarse correlation with a large interrogation window. As a reference, the coarse velocity guess helps with improving the robustness of the proposed algorithm. CC-FCN has two types of input layers, one is for the particle images, and the other is for the initial velocity field calculated using cross correlation with a coarse resolution. First, two pyramidal modules extract features of particle images and initial velocity field, respectively. Then the fusion module appropriately fuses these features. Finally, CC-FCN achieves the super-resolution calculation through a series of deconvolution layers to obtain the single-pixel velocity field. As the supervised learning strategy is considered, synthetic data sets including ground-truth fluid motions are generated to train the network parameters. Synthetic and real experimental PIV data sets are used to test the trained neural network in terms of accuracy, precision, spatial resolution and robustness. The test results show that these attributes of CC-FCN are further improved compared with those of other tested PIV algorithms. The proposed model could therefore provide competitive and robust estimations for PIV experiments.