A fast multi-resolution approach to tomographic PIV

Tomographic particle image velocimetry (Tomo-PIV) is a recently developed three-component, three-dimensional anemometric non-intrusive measurement technique, based on an optical tomographic reconstruction applied to simultaneously recorded images of the distribution of light intensity scattered by seeding particles immersed into the flow. Nowadays, the reconstruction process is carried out mainly by iterative algebraic reconstruction techniques, well suited to handle the problem of limited number of views, but computationally intensive and memory demanding. The adoption of the multiplicative algebraic reconstruction technique (MART) has become more and more accepted. In the present work, a novel multi-resolution approach is proposed, relying on the adoption of a coarser grid in the first step of the reconstruction to obtain a fast estimation of a reliable and accurate first guess. A performance assessment, carried out on three-dimensional computer-generated distributions of particles, shows a substantial acceleration of the reconstruction process for all the tested seeding densities with respect to the standard method based on 5 MART iterations; a relevant reduction in the memory storage is also achieved. Furthermore, a slight accuracy improvement is noticed. A modified version, improved by a multiplicative line of sight estimation of the first guess on the compressed configuration, is also tested, exhibiting a further remarkable decrease in both memory storage and computational effort, mostly at the lowest tested seeding densities, while retaining the same performances in terms of accuracy.     

Lagrangian and Eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic PIV

This work investigates the rod-airfoil air flow by time-resolved Tomographic Particle Image Velocimetry (TR-TOMO PIV) in thin-light volume configuration. Experiments are performed at the region close to the leading edge of a NACA0012 airfoil embedded in the von Kármán wake of a cylindrical rod. The 3D velocity field measured at 5 kHz is used to evaluate the instantaneous planar pressure field by integration of the pressure gradient field. The experimental data are treated with a discretized model based on multiple velocity measurements. The time separation used to evaluate the Lagrangian derivative along a fluid parcel trajectory has to be taken into account to reduce precision error. By comparing Lagrangian and Eulerian approaches, the latter is restricted to shorter time separations and is found not applicable to evaluate pressure gradient field if a relative precision error lower than 10% is required. Finally, the pressure evaluated from tomographic velocity measurements is compared to that obtained from simulated planar ones to discuss the effect of 3D flow phenomena on the accuracy of the proposed technique.     

Eulerian and Lagrangian views of a turbulent boundary layer flow using time-resolved tomographic PIV

Coherent structures and their time evolution in the logarithmic region of a turbulent boundary layer investigated by means of 3D space–time correlations and time-dependent conditional averaging techniques are the focuses of the present paper. Experiments have been performed in the water tunnel at TU Delft measuring the particle motion within a volume of a turbulent boundary layer flow along a flat plate at a free-stream velocity of 0.53 m/s at Re _θ = 2,460 based on momentum thickness by using time-resolved tomographic particle image velocimetry (PIV) at 1 kHz sampling rate and particle tracking velocimetry (PTV). The obtained data enable an investigation into the flow structures in a 3D Eulerian reference frame within time durations corresponding to 28 δ/U. An analysis of the time evolution of conditional averages of vorticity components representing inclined hairpin-like legs and of Q2- and Q4-events has been performed, which gives evidence to rethink the early stages of the classical hairpin development model for high Reynolds number TBLs. Furthermore, a PTV algorithm has been applied on the time sequences of reconstructed 3D particle image distributions identifying thousands of particle trajectories that enable the calculation of probability distributions of the three components of Lagrangian accelerations.     

Multi-frame pyramid correlation for time-resolved PIV

A novel technique is introduced to increase the precision and robustness of time-resolved particle image velocimetry (TR-PIV) measurements. The innovative element of the technique is the linear combination of the correlation signal computed at different separation time intervals. The domain of the correlation signal resulting from different temporal separations is matched via homothetic transformation prior to the averaging of the correlation maps. The resulting ensemble-averaged correlation function features a significantly higher signal-to-noise ratio and a more precise velocity estimation due to the evaluation of a larger particle image displacement. The method relies on a local optimization of the observation time between snapshots taking into account the local out-of-plane motion, continuum deformation due to in-plane velocity gradient and acceleration errors. The performance of the pyramid correlation algorithm is assessed on a synthetically generated image sequence reproducing a three-dimensional Batchelor vortex; experiments conducted in air and water flows are used to assess the performance on time-resolved PIV image sequences. The numerical assessment demonstrates the effectiveness of the pyramid correlation technique in reducing both random and bias errors by a factor 3 and one order of magnitude, respectively. The experimental assessment yields a significant increase of signal strength indicating enhanced measurement robustness. Moreover, the amplitude of noisy fluctuations is considerably attenuated and higher precision is obtained for the evaluation of time-resolved velocity and acceleration.     

Denoising methods for time-resolved PIV measurements

The increasing capabilities of currently available high-speed cameras present several new opportunities for particle image velocimetry (PIV). In particular, temporal postprocessing methods can be used to remove spurious vectors but can also be applied to remove inherent noise. This paper explores this second possibility by estimating the error introduced by several denoising methods on manufactured velocity fields. It is found that PIV noise, while autocorrelated in space, is uncorrelated in time, which leads to a significant improvement in the efficiency of temporal denoising methods compared to their spatial counterparts. Among them, the optimal Wiener filter presents better results than convolution- or wavelet-based filters and has the valuable advantage that no adjustments are required, unlike other methods which generally involve the tuning of some parameters that depend on flow and measurement conditions and are not known a priori. Further refinements show that denoised data can be successfully deconvolved to increase the accuracy of remaining small-scale velocity fluctuations, leading in particular to the recovery of the true shape of turbulent spectra. In practice, the computation of the filter function is not always accurate and different procedures can be used to improve the method depending on the flow considered. Some of them are derived from the properties of the time-frequency spectrum provided by the wavelet transform.     

An efficient anti-aliasing spectral continuous window shifting technique for PIV

A new sub-pixel correlation peak locating algorithm for PIV analysis is introduced. The method is theoretically consistent with the method of continuously shifting interrogation sub-windows by fractional displacements, which has proven to be an effective way to reduce the bias error associated with integer pixel aliasing, or peak-locking. However the proposed algorithm performs continuous window shifting in the spatial frequency domain using the shift property of the Fourier transform, thus it is equivalent to interpolating the original digital image with the Fourier transform reconstruction. Synthetic and real PIV images are used to test the new algorithms performance relative to that of traditional (non-iterative) peak-finding methods and other peak-locking reduction algorithms, such as the continuous window shifting technique. The resultant bias error of the proposed algorithm is smaller (by an order of magnitude in some cases), and importantly, the periodic nature of the bias error, the characteristic signature of peak-locking, is eliminated as long as the discrete particle images have been sampled at a rate greater than the Nyquist sampling frequency. Moreover, this new algorithm is shown to be computationally efficient and it converges faster than the competing algorithms.     

An efficient simultaneous reconstruction technique for tomographic particle image velocimetry

To date, Tomo-PIV has involved the use of the multiplicative algebraic reconstruction technique (MART), where the intensity of each 3D voxel is iteratively corrected to satisfy one recorded projection, or pixel intensity, at a time. This results in reconstruction times of multiple hours for each velocity field and requires considerable computer memory in order to store the associated weighting coefficients and intensity values for each point in the volume. In this paper, a rapid and less memory intensive reconstruction algorithm is presented based on a multiplicative line-of-sight (MLOS) estimation that determines possible particle locations in the volume, followed by simultaneous iterative correction. Reconstructions of simulated images are presented for two simultaneous algorithms (SART and SMART) as well as the now standard MART algorithm, which indicate that the same accuracy as MART can be achieved 5.5 times faster or 77 times faster with 15 times less memory if the processing and storage of the weighting matrix is considered. Application of MLOS-SMART and MART to a turbulent boundary layer at Re _θ = 2200 using a 4 camera Tomo-PIV system with a volume of 1,000 × 1,000 × 160 voxels is discussed. Results indicate improvements in reconstruction speed of 15 times that of MART with precalculated weighting matrix, or 65 times if calculation of the weighting matrix is considered. Furthermore the memory needed to store a large weighting matrix and volume intensity is reduced by almost 40 times in this case.     

A new facility for time-resolved PIV measurements in rotating channels

A new facility to measure the time evolution of 2D velocity fields in a rotating channel is presented, and the accuracy is discussed in detail. Measurements are made by means of a time-resolved PIV system composed of a continuous laser diode, coupled by a fiber optics cable to a laser plane optical module, and a CMOS high-speed camera. Both the PIV system and divergent channel are fixed on a 2.5 m rotating disk. This allows a direct measurement of the relative velocity of flows with Reynolds numbers between 3 × 10³ and 3 × 10⁴ and Rotation numbers between 0.0 and 0.52. These values correspond to the flow conditions in small radial impellers and can be independently adjusted by a change of the relative flow velocity and RPM. It is shown that this new facility allows high signal-to-noise ratios, and that the direct acquisition of the data in a rotating frame drastically reduces the measurement error. The accuracy and high spatial and temporal resolution of the measurements allow a detailed analysis of boundary layer characteristics in stationary and rotating conditions.     

Stereoscopic and tomographic PIV of a pitching plate

This paper applies particle image velocimetry (PIV) to a simplified, canonical, pitch-hold-return problem of a pitching plate in order to gain some understanding of how three dimensionality develops in such flows. Data from a progression of PIV studies, from stereoscopic PIV yielding three-component, two-dimensional (3C-2D) data to tomographic PIV yielding three-component, three-dimensional (3C-3D) data are presented thus providing progressively more detailed information. A comparison of results is made between the two techniques. The PIV study is performed in a water tunnel facility with cross-sectional area 500 × 500 mm, and involves a full-span (nominally two-dimensional) plate, suspended between a wall end boundary condition and a free surface, pitching at a dimensionless pitch rate of K _c  = 0.93 in flow at Re = 7,500. Results demonstrate the existence of spanwise flows in both the leading edge and trailing edge vortices, but with strong directionality in the leading edge vortex towards the wall end boundary condition. Observations of instantaneous flow patterns suggest also the existence of three-dimensional coherent vortex filament structures in the outer regions of the leading edge vortex.     

An efficient numerical approach to the micromorphic hyperelasticity

Continuum Mechanics and Thermodynamics - A computationally efficient numerical strategy called as variational differential quadrature-finite element method (VDQFEM) is developed herein for the...     

Spatial resolution and dissipation rate estimation in Taylor--Couette flow for tomographic PIV

This paper assesses the spatial resolution and accuracy of tomographic particle image velocimetry (PIV). In tomographic PIV the number of velocity vectors are of the order of the number of reconstructed particle images, and sometimes even exceeds this number when a high overlap fraction between adjacent interrogations is used. This raises the question of the actual spatial resolution of tomographic PIV in relation to the various flow scales. We use a Taylor--Couette flow of a fluid between two independently rotating cylinders and consider three flow regimes: laminar flow, Taylor vortex flow and fully turbulent flow. The laminar flow has no flow structures, and the measurement results are used to assess the measurement uncertainty and to validate the accuracy of the technique for measurements through the curved wall. In the Taylor vortex flow regime, the flow contains large-scale flow structures that are much larger than the size of the interrogation volumes and are fully resolved. The turbulent flow regime contains a range of flow scales. Measurements in the turbulent flow regime are carried out for a Reynolds number Re between 3,800 and 47,000. We use the measured torque on the cylinders to obtain an independent estimate of the energy dissipation rate and estimate of the Kolmogorov length scale. The data obtained by tomographic PIV are assessed by estimating the dissipation rate and comparing the result against the dissipation rate obtained from the measured torque. The turbulent flow data are evaluated for different sizes of the interrogation volumes and for different overlap ratios between adjacent interrogation locations. The results indicate that the turbulent flow measurements for the lowest Re could be (nearly) fully resolved. At the highest Re only a small fraction of the dissipation rate is resolved, still a reasonable estimate of the total dissipation rate could be obtained by means of using a sub-grid turbulence model. The resolution of tomographic PIV in these measurements is determined by the size of the interrogation volume. We propose a range of vector spacing for fully resolving the turbulent flow scales. It is noted that the use of a high overlap ratio, that is, 75?%, yields a substantial improvement for the estimation of the dissipation rate in comparison with data for 0 and 50?% overlap. This indicates that additional information on small-scale velocity gradients can be obtained by reducing the data spacing.     

An accurate and efficient computational method for seeking two equi-tangential stress hole shapes

Archive of Applied Mechanics - As an infinite elastic plane containing two holes subjected to uniform remote loading, the tangential stress concentration degree around the holes is related to the...     

Phase discrimination method for simultaneous two-phase separation in time-resolved stereo PIV measurements

A phase discrimination method for two-phase PIV is presented that is capable of simultaneously separating the two phases from time-resolved stereoscopic PIV images taken in a particle-laden jet. The technique developed expands on previous work done by Khalitov and Longmire (Exp Fluids 32:252–268, 2002), where by means of image processing techniques, a raw two-phase PIV image can be separated into two single-phase images according to particle size and intensity distributions. The technique is expanded through the use of three new image processing algorithms to separate particles of similar size (up to an order of magnitude better than published work) for fields of view much larger than previously considered. It also addresses the known problem of noisy background images produced by high-speed CMOS cameras, which makes the particle detection and separation from the noisy background difficult, through the use of a novel fast Fourier transform background filter.     

Visual hull method for tomographic PIV measurement of flow around moving objects

Tomographic particle image velocimetry (PIV) is a recently developed method to measure three components of velocity within a volumetric space. We present a visual hull technique that automates identification and masking of discrete objects within the measurement volume, and we apply existing tomographic PIV reconstruction software to measure the velocity surrounding the objects. The technique is demonstrated by considering flow around falling bodies of different shape with Reynolds number?~1,000. Acquired image sets are processed using separate routines to reconstruct both the volumetric mask around the object and the surrounding tracer particles. After particle reconstruction, the reconstructed object mask is used to remove any ghost particles that otherwise appear within the object volume. Velocity vectors corresponding with fluid motion can then be determined up to the boundary of the visual hull without being contaminated or affected by the neighboring object velocity. Although the visual hull method is not meant for precise tracking of objects, the reconstructed object volumes nevertheless can be used to estimate the object location and orientation at each time step.