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.]

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This study describes the working principles of the coaxial volumetric velocimeter (CVV) for wind tunnel measurements. The measurement system is derived from the concept of tomographic PIV in combination with recent developments of Lagrangian particle tracking. The main characteristic of the CVV is its small tomographic aperture and the coaxial arrangement between the illumination and imaging directions. The system consists of a multi-camera arrangement subtending only few degrees solid angle and a long focal depth. Contrary to established PIV practice, laser illumination is provided along the same direction as that of the camera views, reducing the optical access requirements to a single viewing direction. The laser light is expanded to illuminate the full field of view of the cameras. Such illumination and imaging conditions along a deep measurement volume dictate the use of tracer particles with a large scattering area. In the present work, helium-filled soap bubbles are used. The fundamental principles of the CVV in terms of dynamic velocity and spatial range are discussed. Maximum particle image density is shown to limit tracer particle seeding concentration and instantaneous spatial resolution. Time-averaged flow fields can be obtained at high spatial resolution by ensemble averaging. The use of the CVV for time-averaged measurements is demonstrated in two wind tunnel experiments. After comparing the CVV measurements with the potential flow in front of a sphere, the near-surface flow around a complex wind tunnel model of a cyclist is measured. The measurements yield the volumetric time-averaged velocity and vorticity field. The measurements of the streamlines in proximity of the surface give an indication of the skin-friction lines pattern, which is of use in the interpretation of the surface flow topology.

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A novel approach to the measurement of large-scale complex aerodynamic flows is presented, based on the combination of coaxial volumetric velocimetry and robotics. Volumetric flow field measurements are obtained to determine the time-averaged properties of the velocity field developing around a three-dimensional full-scale reproduction of a professional cyclist. The working principles of robotic volumetric PIV are discussed on the basis of its main components: helium-filled soap bubbles as tracers; the compact coaxial volumetric velocimeter; a collaborative 6 degrees of freedom robot arm; particle image analysis based on Shake-the-Box algorithm and ensemble statistics to yield data on a Cartesian mesh in the physical domain. The spatial range covered by the robotic velocimeter and its aerodynamic invasiveness are characterised. The system has the potential to perform volumetric measurements in a domain of several cubic metres. The application to the very complex geometry of a full-scale cyclist in time-trial position is performed in a large aerodynamic wind tunnel at a flow speed of 14 m/s. The flow velocity in the near field of the cyclist body is gathered through 450 independent views encompassing a measurement volume of approximately 2 m³. The measurements include hidden regions between the arms and the legs, otherwise very difficult to access by conventional planar or tomographic PIV. The time-averaged velocity field depicts the main flow topology in terms of stagnation points and lines, separation and reattachment lines, trailing vortices and free shear layers. The wall boundary layers developing on the body surface hide below the level resolvable by the present measurements.

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The power spectral density and coherence of temporal pressure fluctuations are obtained from low-repetition-rate tomographic PIV measurements. This is achieved by extension of recent single-snapshot pressure evaluation techniques based upon the Taylor’s hypothesis (TH) of frozen turbulence and vortex-in-cell (VIC) simulation. Finite time marching of the measured instantaneous velocity fields is performed using TH and VIC. Pressure is calculated from the resulting velocity time series. Because of the theoretical limitations, the finite time marching can be performed until the measured flow structures are convected out of the measurement volume. This provides a lower limit of resolvable frequency range. An upper limit is given by the spatial resolution of the measurements. Finite time-marching approaches are applied to low-repetition-rate tomographic PIV data of the flow past a straight trailing edge at 10 m/s. Reference results of the power spectral density and coherence are obtained from surface pressure transducers. In addition, the results are compared to state-of-the-art experimental data obtained from time-resolved tomographic PIV performed at 10 kHz. The time-resolved approach suffers from low spatial resolution and limited maximum acquisition frequency because of hardware limitations. Additionally, these approaches strongly depend upon the time kernel length chosen for pressure evaluation. On the other hand, the finite time-marching approaches make use of low-repetition-rate tomographic PIV measurements that offer higher spatial resolution. Consequently, increased accuracy of the power spectral density and coherence of pressure fluctuations are obtained in the high-frequency range, in comparison to the time-resolved measurements. The approaches based on TH and VIC are found to perform similarly in the high-frequency range. At lower frequencies, TH is found to underestimate coherence and intensity of the pressure fluctuations in comparison to time-resolved PIV and the microphone reference data. The VIC-based approach, on the other hand, returns results on the order of the reference.@en

The analysis of the unsteady flow field of an axisymmetric subsonic jet at Reynolds numbers between 5,000 and 20,000 and computation of its unsteady pressure field is carried out from single snapshots of tomographic PIV measurements (acquisition rate 0.8 Hz). This is achieved by a recently developed pressure-evaluation technique based upon the vortex-in-cell (VIC) methodology. The technique allows for a finite time-marching of the instantaneous 3D velocity fields obtained from low-repetition PIV systems. A time series of velocity fields in 3D is obtained, which is integrated into unsteady pressure by use of the Navier-Stokes momentum equation. Despite the limitations in the finite-time marching of the measured structures due to the size of the acquired tomographic volume, spectra of pressure fluctuations can be extracted in a frequency range between 800Hz and 20kHz. Fair agreement was found between the experimentally computed pressure spectra and the respective values found in literature. Further work is dedicated to exploit the full potential of the technique by attempting a sound pressure level integration of the noise sources from the unsteady fields.@en

The flow field around a turboprop aircraft scaled model is investigated with attention to the propeller slipstream and the wing near wake. The experiments are conducted in the Low-Speed Tunnel (LST) of the German-Dutch Wind Tunnels (DNW) as part of a collaboration among DNW, Delft University of Technology and Airbus. Quantitative flow visualization in a three-dimensional measurement domain of 150 liters is made possible by the use of the recently developed Robotic Volumetric Velocimetry technique. Time averaged velocity and vorticity fields are obtained for experiments carried out at 8 m/s and 50 m/s, respectively. The measurements are conducted with high-speed acquisition in multi-frame mode at 8 m/s, and require double-frame mode at 50 m/s. The presence of three coherent streamwise vortices is revealed, emanating from the wing tip, the flap side edge and the engine nacelle, respectively. A comparison between the two measurement conditions shows limited Reynolds number effects on the wing tip vortex, and that the multi-frame measurements are superior in terms of spatial resolution and measurement accuracy.@en

A procedure is proposed to reconstruct the instantaneous velocity field from full particle trajectories in a data assimilation framework that includes the vorticity transport equation. The technique is christened as time-segment assimilation (TSA). The work addresses the common problem of low seeding concentration in 3D experiments, usually leading to limited spatial resolution. In the present study the measurement fidelity and spatial resolution are increased by considering finite time-segments as a whole for instantaneous velocity reconstruction. The use of a time-segment for velocity field reconstruction from measurement data extends previously proposed data assimilation techniques that consider only instantaneous measurement data (e.g. VIC+ and FlowFit), to use finite measurement time-segments. The assessment with sinusoids indicates lower errors due to modulation. However, the appearance of a range of amplified peaks is not fully understood. In the case of a simulated turbulent boundary layer measurement more vortical structures are recovered when a longer time-segment is used for the velocity field reconstruction. @en

The track benchmarking method (TBM) is proposed for uncertainty quantification of particle tracking velocimetry (PTV) data mapped onto a regular grid. The method provides statistical uncertainty for a velocity time-series and can in addition be used to obtain instantaneous uncertainty at increased computational cost. Interpolation techniques are typically used to map velocity data from scattered PTV (e.g. tomographic PTV and Shake-the-Box) measurements onto a Cartesian grid. Recent examples of these techniques are the FlowFit and VIC+ methods. The TBM approach estimates the random uncertainty in dense velocity fields by performing the velocity interpolation using a subset of typically 95% of the particle tracks and by considering the remaining tracks as an independent benchmarking reference. In addition, also a bias introduced by the interpolation technique is identified. The numerical assessment shows that the approach is accurate when particle trajectories are measured over an extended number of snapshots, typically on the order of 10. When only short particle tracks are available, the TBM estimate overestimates the measurement error. A correction to TBM is proposed and assessed to compensate for this overestimation. The experimental assessment considers the case of a jet flow, processed both by tomographic PIV and by VIC+. The uncertainty obtained by TBM provides a quantitative evaluation of the measurement accuracy and precision and highlights the regions of high error by means of bias and random uncertainty maps. In this way, it is possible to quantify the uncertainty reduction achieved by advanced interpolation algorithms with respect to standard correlation-based tomographic PIV. The use of TBM for uncertainty quantification and comparison of different processing techniques is demonstrated.

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A test case for pressure field reconstruction from particle image velocimetry (PIV) and Lagrangian particle tracking (LPT) has been developed by constructing a simulated experiment from a zonal detached eddy simulation for an axisymmetric base flow at Mach 0.7. The test case comprises sequences of four subsequent particle images (representing multi-pulse data) as well as continuous time-resolved data which can realistically only be obtained for low-speed flows. Particle images were processed using tomographic PIV processing as well as the LPT algorithm ‘Shake-The-Box’ (STB). Multiple pressure field reconstruction techniques have subsequently been applied to the PIV results (Eulerian approach, iterative least-square pseudo-tracking, Taylor’s hypothesis approach, and instantaneous Vortex-in-Cell) and LPT results (FlowFit, Vortex-in-Cell-plus, Voronoi-based pressure evaluation, and iterative least-square pseudo-tracking). All methods were able to reconstruct the main features of the instantaneous pressure fields, including methods that reconstruct pressure from a single PIV velocity snapshot. Highly accurate reconstructed pressure fields could be obtained using LPT approaches in combination with more advanced techniques. In general, the use of longer series of time-resolved input data, when available, allows more accurate pressure field reconstruction. Noise in the input data typically reduces the accuracy of the reconstructed pressure fields, but none of the techniques proved to be critically sensitive to the amount of noise added in the present test case.

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The existing time-resolved tomographic particle image velocimetry (PIV) measurements by Jodai and Elsinga (J Fluid Mech 795:611–633; Jodai, Elsinga, J Fluid Mech 795:611–633, 2016) in a turbulent boundary layer (Re_θ = 2038) are reprocessed using tomographic particle tracking velocimetry (PTV) and vortex-in-cell-plus (VIC+). The resulting small-scale flow properties, i.e. vorticity and turbulence dissipation, are compared. The VIC+ technique was recently proposed and uses the concept of pouring time into space to increase reconstruction quality of instantaneous velocity. The tomographic PTV particle track measurements are interpolated using VIC+ to a dense grid, making use of both particle velocity and Lagrangian acceleration. Comparison of the vortical structures by visualization of isosurfaces of vorticity magnitude shows that the two methods return similar coherent vortical structures, but their strength in terms of vorticity magnitude is increased when using VIC+, which suggests an improvement in spatial resolution. Further statistical evaluation shows that the root mean square (rms) of vorticity fluctuations from tomographic PIV is approximately 40% lower in comparison to a reference profile available from a DNS simulation, while the VIC+ technique returns rms vorticity fluctuations to within 10% of the reference. The dissipation rate is heavily underestimated by tomographic PIV with approximately 50% damping, whereas the VIC+ analysis yields a dissipation rate to within approximately 5% for y⁺ > 25. The fact that dissipation can be directly measured by a volumetric experiment is novel. It differs from existing approaches that involve 2d measurements combined with isotropic turbulence assumptions or apply corrections based on sub-grid scale turbulence modelling. Finally, the study quantifies the spatial response of VIC+ with a sine-wave lattice analysis. The results indicate a twofold increase of spatial resolution with respect to cross-correlation interrogation.

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A series of techniques is proposed for volumetric air flow measurements that are based upon the principles of particle image velocimetry (PIV). The proposed techniques fall in two categories; part 1 of this dissertation considers measurement data processing using constitutive laws and part 2 focuses on development of a coaxial volumetric flow measurement system that uses helium filled soap bubbles (HFSB) as tracer particles. In part 1, first a technique is proposed to measure instantaneous volumetric pressure using a low repetition rate tomographic PIV system. Instead of time-resolved measurement of the flow temporal evolution, which typically required for pressure-from-PIV procedures, the required temporal information is obtained by solution of the incompressible Navier-Stokes equations in vorticity-velocity formulation using the spatial information available from the instantaneous measurements. The reverse is proposed for cases where temporal resolution is more abundant, but spatial resolution is limited. The vorticity transport equation is leveraged to couple temporal information with instantaneous velocity data in the proposed VIC+ framework, in an attempt to obtain a dense velocity field at high spatial resolution. The governing principle is that by using the flow governing equations, the data ensemble used for interpolation is increased beyond instantaneous velocity measurements only. The technique is demonstrated to allow for measurement of vorticity and dissipation in a real-world experiment, which would otherwise be underestimated by more than 40% using the established tomographic PIV approach. The proposed VIC+ technique uses a data ensemble for dense velocity interpolation consisting of the instantaneous velocity and material derivative measurements obtained from Lagrangian particle tracking velocimetry. An extension of the VIC+ framework that uses a measurement time-segment instead of instantaneous data only is shown to potentially improve the measurement fidelity further, when a cost-effective three-dimensional implementation can be realized. An uncertainty quantification technique is proposed for future developments of such dense interpolation techniques. It is shown that the results from Lagrangian particle tracking measurements can be directly used for uncertainty quantification of dense interpolations and no independent measurement data is required. In part 2 of this dissertation, a technique is first proposed for large-scale volumetric pressure measurement. The method follows recent developments of large-scale measurements using HFSB tracer particles, in combination with Lagrangian particle tracking and ensemble bin-averaging. This allows for evaluation of accurate velocity statistics and in turn the time-averaged pressure field. The dissertation concludes with the proposal of the coaxial volumetric velocimeter (CVV). The CVV brings imaging and illumination together in a compact box, viewing and illuminating a measurement volume from a single viewing direction. The theoretical background that is derived shows that measurements in air using the CVV are only possible using tracer particles that scatter significantly more light than traditional micron sized tracer particles. Here, HFSB tracer particles are used. Due to the small solid angle of the imaging system, tracer particles need to be imaged over an extended number of snapshots to increase particle positional accuracy, making use of particle trajectory regularization. A prototype CVV has been realized, which is first used to confirm that the flow around a sphere is measured with acceptable correspondence to a potential flow solution. Second, in the case of the flow around a cyclist, the CVV is shown to allow for measurements near both concave and convex surfaces within one measurement volume. This allows for flow analysis using skin-friction lines. In addition, the compact nature of the CVV allows mounting on a robotic arm for time-averaged of a large and complex wind tunnel model. The full-scale measurement of the flow around Giro d’Italia cyclist Tom Dumoulin shown using the CVV is an example of the latter.@en

A novel approach for trailing-edge noise diagnostics with low-repetition rate Particle Im- age Velocimetry systems is presented. The approach is based on the application of di_rac- tion theory and implements a recently developed single-snapshot pressure reconstruction in boundary layers using the Vortex-in-cell method in combination with a frozen turbulence assumption to estimate the relevant statistical descriptors of the surface pressure _eld. The present communication describes the required planar and tomographic Particle Im- age Velocimetry experiments with a high spatial-dynamic-range system and demonstrates the applicability of the approach by comparison of hydrodynamic and acoustic pressure statistics with available data. The frequency spectra of the hydrodynamic pressure near the surface are found to be sensitive to the model employed for the convective velocity in the application of the frozen turbulence assumption for reduced frequencies f_?=u1 > 0:5 (2:3kHz). For lower reduced frequencies, excellent agreement with the reference data is observed. @en

The manuscripts presents the working principle of a novel technique to interpolate sparse and scattered particle tracking velocimetry (PTV) measurements onto a dense grid, by using the velocity measurements along a full particle trajectory. The method performs iteratively a vortex-in-cell simulation (Schneiders et al. 2014 in Exp Fluids 55:1692) to minimize the difference between the simulation and the scattered velocity measurements. The optimization is solved using the L-BFGS algorithm where gradients are evaluated efficiently using the adjoint of the vortex-in-cell code. In the numerical assessment, the case of a vortex is considered. At a given seeding concentration, the reconstruction quality of velocity was shown to improve by 50% when a full track is used in comparison to a divergence free reconstruction using only instantaneous velocity. The numerical assessment demonstrates the potential of the method to increase measurement quality and spatial resolution, in comparison to techniques that interpolate velocity using only instantaneous flow information and for example the divergence free constraint.@en

The instantaneous volumetric pressure in the near-wake of a truncated cylinder is measured by use of tomographic particle tracking velocimetry (PTV) using helium-filled soap bubbles (HFSB) as tracers. The measurement volume is several orders of magnitude larger than that reported in tomographic experiments dealing with pressure from particle image velocimetry (PIV). The near-wake of a truncated cylinder installed on a flat plate (ReD = 3.5 × 104) features both wall-bounded turbulence and large-scale unsteady flow separation. The instantaneous pressure is calculated from the time-resolved 3D velocity distribution by invoking the momentum equation. The experiments are conducted simultaneously with surface pressure measurements intended for validation of the technique. The study shows that time-averaged pressure and root-mean-squared pressure fluctuations can be accurately measured both in the fluid domain and at the solid surface by large-scale tomographic PTV with HFSB as tracers, with significant reduction in manufacturing complexity for the wind-tunnel model and circumventing the need to install pressure taps or transducers. The measurement over a large volume eases the extension toward the free-stream regime, providing a reliable boundary condition for the solution of the Poisson equation for pressure. The work demonstrates, in the case of the flow past a truncated cylinder, the use of HFSB tracer particles for pressure measurement in air flows in a measurement volume that is two orders of magnitude larger than that of conventional tomographic PIV.@en

A method is proposed to reconstruct the instantaneous velocity field from time-resolved volumetric particle tracking velocimetry (PTV, e.g., 3D-PTV, tomographic PTV and Shake-the-Box), employing both the instantaneous velocity and the velocity material derivative of the sparse tracer particles. The constraint to the measured temporal derivative of the PTV particle tracks improves the consistency of the reconstructed velocity field. The method is christened as pouring time into space, as it leverages temporal information to increase the spatial resolution of volumetric PTV measurements. This approach becomes relevant in cases where the spatial resolution is limited by the seeding concentration. The method solves an optimization problem to find the vorticity and velocity fields that minimize a cost function, which includes next to instantaneous velocity, also the velocity material derivative. The velocity and its material derivative are related through the vorticity transport equation, and the cost function is minimized using the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm. The procedure is assessed numerically with a simulated PTV experiment in a turbulent boundary layer from a direct numerical simulation (DNS). The experimental validation considers a tomographic particle image velocimetry (PIV) experiment in a similar turbulent boundary layer and the additional case of a jet flow. The proposed technique (‘vortex-in-cell plus’, VIC+) is compared to tomographic PIV analysis (3D iterative cross-correlation), PTV interpolation methods (linear and adaptive Gaussian windowing) and to vortex-in-cell (VIC) interpolation without the material derivative. A visible increase in resolved details in the turbulent structures is obtained with the VIC+ approach, both in numerical simulations and experiments. This results in a more accurate determination of the turbulent stresses distribution in turbulent boundary layer investigations. Data from a jet experiment, where the vortex topology is retrieved with a small number of tracers indicate the potential utilization of VIC+ in low-concentration experiments as for instance occurring in large-scale volumetric PTV measurements.@en

A test case for PIV-based pressure evaluation techniques has been developed by constructing a simulated experiment from a ZDES simulation for an axisymmetric base flow at Mach 0.7. The test case comprises sequences of four subsequent particle images (representing multi-pulse data) as well as continuous time-resolved data. Particle images were processed using tomographic PIV processing as well as the PTV algorithm ‘Shake-The-Box’. Multiple pressure reconstruction techniques have subsequently been applied to the PIV results (Eulerian approach, iterative least-square pseudo-tracking, Taylor’s hypothesis approach, instantaneous Vortex-in-Cell) and PTV results (FlowFit, Vortex-in-Cell-plus, Voronoi-based pressure evaluation and iterative least-square pseudo-tracking). All methods were able to reconstruct the main features of the instantaneous pressure fields, including methods that reconstruct pressure from a single PIV velocity snapshot. Highly accurate pressure field reconstructions could be obtained by using PTV approaches in combination with more advanced techniques. In general, the use of longer series of time-resolved input data, when available, allows more accurate pressure field reconstruction. Noise in the input data typically reduces the accuracy of the reconstructed pressure fields, but none of the techniques was found to be critically sensitive to the amount of noise added in the present test case@en