The vortex-in-cell time-segment assimilation (VIC-TSA) method is introduced. A particle track is obtained from a finite number of successive time samples of the tracer’s position and velocity can be used for reconstruction on a Cartesian grid. Similar to the VIC + technique, the method makes use of the vortex-in-cell paradigm to produce estimates of the flow state at locations and times other than the measured ones. The working principle requires time-resolved measurements of the particles’ velocity during a finite time interval. The work investigates the effects of the assimilated length on the spatial resolution of the velocity field reconstruction. The working hypotheses of the VIC-TSA method are presented here along with the numerical algorithm for its application to particle tracks datasets. The novel parameter governing the reconstruction is the length of the time-segment chosen for the data assimilation. Three regimes of operation are identified, based on the track length and the geometrical distance between neighbouring tracks. The regime of adjacent tracks arguably provides the optimal trade-off between spatial resolution and computational effort. The VIC-TSA spatial resolution is evaluated first by a numerical exercise; a 3D sine wave lattice is reconstructed at different values of the particles concentration. The modulation appears to reduce (cut-off delay) when the time-segment length is increased. Large-scale PIV experiments in the wake of a circular cylinder at Re_d = 27,000 are used to evaluate the method’s suitability to real data, including noise and data outliers. Both primary vortex structures in the Kármán wake as well as interconnecting ribs are present in this complex flow field, with a typical diameter close to the average inter-particle distance. When the time-segment is increased to adjacent tracks and beyond, a more regular time dependence of local and Lagrangian properties is observed, confirming the suitability of the time-segment assimilation for accurate reconstruction of sparse velocity data. Graphical abstract: [Figure not available: see fulltext.]

An experimental methodology is proposed to study aeroelastic systems with optical diagnostics. The approach locally evaluates the three physical mechanisms that produce the forces involved in Collar’s triangle, namely aerodynamic, elastic, and inertial forces. Flow and object surface tracers are tracked by a volumetric particle image velocimetry (PIV) system based on four high-speed cameras and LED illumination. The images are analysed with Lagrangian particle tracking techniques, and the flow tracers and surface markers are separated based on the different properties of their images. The inertial and elastic forces are obtained solely analysing the motion and the deformation of the solid object, whereas the aerodynamic force distribution is obtained with pressure from PIV techniques. Experiments are conducted on a benchmark problem of fluid–structure interaction, featuring a flexible panel installed at the trailing edge of a cylinder. Data are collected in the resonant regime, where the panel exhibits a two-dimensional motion. The estimation of inertial and elastic forces is obtained enforcing a high-order polynomial fit to the surface motion and deformation. The aerodynamic loads on the panel are challenged by the need to devise adaptive boundary conditions complying with the panel motion. The closure of Collar’s triangle yields overall residuals of about one-half of the inertial force taken as reference. The simultaneous measurement of the three forces paves the way to assessing the equilibrium of forces closing the Collar’s triangle. The latter can be intended for uncertainty evaluation or, when only two forces are measured, for estimation of the remaining Collar element. Graphical Abstract: [Figure not available: see fulltext.].

Three-dimensional Lagrangian particle tracking measurements with helium filled soap bubbles provide quantitative flow visualizations in large measurement volumes up to the cubic metre scale. However, the instantaneously available fluid information density is severely restricted by the finite spatial resolution of the measurements. Therefore, the use of experimental data assimilation approaches are utilized to exploit the temporal information of the flow measurements, along with the governing equations of the fluid motion, to increase the measurement spatial resolution. Nevertheless, only in the last years, attempts to apply data assimilation methods to enhance the Lagrangian particle tracking (LPT) resolution in proximity of solid boundaries have been performed. Thus, in order to handle generic solid body intrusions within the densely interpolated LPT data, two different approaches based on the computational fluid-structure interaction frameworks are proposed. The introduced variants of the state of the art physics-driven data assimilation methods are assessed with a high fidelity numerical test case of flow over periodic hills. The accuracy superiority of the flow field reconstructions with the proposed approaches are denoted especially in close proximity of the interaction surface. An experimental application of the introduced methods is demonstrated to compute the pressure distribution over an unsteadily moving elastic membrane surface, revealing the time-resolved interaction between the flow structures and the membrane deformations.