Instantaneous planar pressure determination from PIV in turbulent flow

This paper deals with the determination of instantaneous planar pressure fields from velocity data obtained by particle image velocimetry (PIV) in turbulent flow. The operating principles of pressure determination using a Eulerian or a Lagrangian approach are described together with theoretical considerations on its expected performance. These considerations are verified by a performance assessment on a synthetic flow field. Based on these results, guidelines regarding the temporal and spatial resolution required are proposed. The interrogation window size needs to be 5 times smaller than the flow structures and the acquisition frequency needs to be 10 times higher than the corresponding flow frequency (e.g. Eulerian time scales for the Eulerian approach). To further assess the experimental viability of the pressure evaluation methods, stereoscopic PIV and tomographic PIV experiments on a square cylinder flow (Re _D  = 9,500) were performed, employing surface pressure data for validation. The experimental results were found to support the proposed guidelines.     

Investigation of liquid–liquid drop coalescence using tomographic PIV

High-speed tomographic PIV was used to investigate the coalescence of drops placed on a liquid/liquid interface; the coalescence of a single drop and of a drop in the presence of an adjacent drop (side-by-side drops) was investigated. The viscosity ratio between the drop and surrounding fluids was 0.14, the Ohnesorge number (Oh = μ_d/(ρ_dσD)^1/2) was 0.011, and Bond numbers (Bo = (ρ _d  − ρ _s )gD ²/σ) were 3.1–7.5. Evolving volumetric velocity fields of the full coalescence process allowed for quantification of the velocity scales occurring over different time scales. For both single and side-by-side drops, the coalescence initiates with an off-axis film rupture and film retraction speeds an order of magnitude larger than the collapse speed of the drop fluid. This is followed by the formation and propagation of an outward surface wave along the coalescing interface with wavelength of approximately 2D. For side-by-side drops, the collapse of the first drop is asymmetric due to the presence of the second drop and associated interface deformation. Overall, tomographic PIV provides insight into the flow physics and inherent three-dimensionalities in the coalescence process that would not be achievable with flow visualization or planar PIV only.     

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.     

Synchronized analysis of an unsteady laminar flow downstream of a circular cylinder centred between two parallel walls using PIV and mass transfer probes

Experiments are carried out in the wake of a cylinder of d _c  = 10 mm diameter placed symmetrically between two parallel walls with a blockage ratio r = 1/3 and a Reynolds number varying between 75 ≤ Re ≤ 277. Particle image velocimetry is exerted to obtain the instantaneous velocity components in the cylinder wake. A snapshot proper orthogonal decomposition (POD) is also applied to these PIV results in order to extract the dominant modes through the implementation of an inhomogeneous filtering of these different snapshots, apart from an interpolation to estimate the wall shear rate at the lower wall downstream the cylinder. Mass transfer circular probes are placed at the lower wall downstream this obstacle so as to further determine the time evolution of the wall shear rate, by bringing the inverse method to bear on the convective-diffusion equation. Comparisons between the two synchronized techniques demonstrate that electrochemical method can give more accurate information about the coherent structures present in the flow and about the interaction of the von Kármán vortices with the walls of the tunnel as well. The comparison between the two measurement techniques in the flow regions concerns the spatiotemporal evolutions of the wall shear rate obtained from PIV measurements and the wall shear rate using mass transfer probes. Discrepancy between the PIV measurements and the electrochemical ones near the wall, where the secondary vortices P ₁′ are generated at wall, are caused by a PIV bias and a limitations of the singular mass transfer probes.     

Stereoscopic PIV measurements of a turbulent boundary layer with a large spatial dynamic range

The flow in a streamwise/wall-normal plane of a turbulent boundary layer at moderate Reynolds number (Re _θ = 2,200) is characterized using two stereo PIV systems just overlapping in the streamwise direction. The aim is to generate SPIV data for near-wall turbulence with enough spatial dynamic range to resolve most of the coherent structures present in the flow and to facilitate future comparisons with direct numerical simulations. This is made possibly through the use of four cameras with large CCD arrays (4,008 px × 2,672 px) and through a rigorous experimental procedure designed to minimize the impact of measurement noise on the resolution of the small scales. For the first time, both a large field of view [S _x ; S _y ] = [2.6δ; 0.75δ] and a high spatial resolution (with an interrogation window size of 13.6⁺) have been achieved. The quality of the data is assessed through an analysis of some of the statistical results such as the mean velocity profile, the rms and the PDF of the fluctuations, and the power spectra.     

Dissipation rate estimation from PIV in zero-mean isotropic turbulence

Measuring the turbulent kinetic energy dissipation rate in an enclosed turbulence chamber that produces zero-mean flow is an experimental challenge. Traditional single-point dissipation rate measurement techniques are not applicable to flows with zero-mean velocity. Particle image velocimetry (PIV) affords calculation of the spatial derivative as well as the use of multi-point statistics to determine the dissipation rate. However, there is no consensus in the literature as to the best method to obtain dissipation rates from PIV measurements in such flows. We apply PIV in an enclosed zero-mean turbulent flow chamber and investigate five methods for dissipation rate estimation. We examine the influence of the PIV interrogation cell size on the performance of different dissipation rate estimation methods and evaluate correction factors that account for errors related to measurement uncertainty, finite spatial resolution, and low Reynolds number effects. We find the Re _λ corrected, second-order, longitudinal velocity structure function method to be the most robust method to estimate the dissipation rate in our zero-mean, gaseous flow system.     

Effect of apex strake incidence-angle on the vortex development and interaction of a double-delta wing

The vortex flow characteristics of a sharp-edged delta wing with an apex strake was investigated through the visualization and particle image velocimetry (PIV) measurement of the wing-leeward flow region, and the wing-surface pressure measurement. The wing model was a flat-plate, and 65°-sweep cropped-delta wing with sharp leading edges. The apex strake was also a flat-plate wing with a cropped-delta shape of 65°/90° sweep, and it can change its incidence angle. The flow Reynolds number was 2.2 × 10⁵ for the flow visualization and 8.2 × 10⁵ for the PIV and wing-surface pressure measurements. The physics of the vortex flow in the wing-leeward flow region and the suction-pressure distribution on the wing upper-surface were interrelated and analyzed. The effect of a positive (negative) strake incidence-angle was the upward movement of the strake and wing vortices away from (downward movement of the strake and wing vortices toward) the wing-upper surface and the delayed (enhanced) coiling interaction between them. This change of vortex flow characteristics projected directly on the suction pressure distribution on the wing upper-surface.     

Refractive-index and density matching in concentrated particle suspensions: a review

Optical measurement techniques such as particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) are now routinely used in experimental fluid mechanics to investigate pure fluids or dilute suspensions. For highly concentrated particle suspensions, material turbidity has long been a substantial impediment to these techniques, which explains why they have been scarcely used so far. A renewed interest has emerged with the development of specific methods combining the use of iso-index suspensions and imaging techniques. This review paper gives a broad overview of recent advances in visualization techniques suited to concentrated particle suspensions. In particular, we show how classic methods such as PIV, LDV, particle tracking velocimetry, and laser induced fluorescence can be adapted to deal with concentrated particle suspensions.     

Parametric analysis of a round jet impingement on a heated plate

In this study, the flow and heat transfer characteristics of a round air jet have been experimentally investigated in details using two techniques: Particle Image Velocimetry (PIV) and the Laser Doppler Velocimetry (LDV). The measurement of the mean velocity components are compared, and agree well with the experimental data obtained by Baydar (1999). The distributions of the velocity, turbulence quantities and temperature profiles are analyzed in the main characteristic regions of the jet where the heat transfer occurs. Parametric variations were conducted to produce information about the influences of the Reynolds number (Re = 1000, 2000, 3000), the distance between the pipe exit and the flat impingement plate (h/d = 1 and h/d = 2) and the temperature of the plane (T_p = 22 °C, 54 °C, 96 °C) on the impinging jet flow field.     

PIV–LES analysis of channel flow rotating about the streamwise axis

The flow field of a channel rotating about the streamwise axis is analyzed experimentally and numerically. The current investigations were carried out at a bulk velocity based Reynolds number of Re_m = 2850 and a friction velocity based Reynolds number of Re_τ = 180, respectively. Particle-image velocimetry (PIV) measurements are compared with large-eddy simulation data to show earlier direct numerical simulation findings to generate too large a reverse flow region in the center region of the spanwise flow. The development of the mean spanwise velocity distribution and the influence of the rotation on the turbulent properties, i.e., the Reynolds stresses and the two-point correlations of the flow, are confirmed in both investigations. The rotation primarily influences those components of the Reynolds shear stresses, which contain the spanwise velocity component. The size of the correlation areas and thus the length scales of the flow generally grow in all three coordinate directions leading to longer structures. Furthermore, experimental results of the same channel flow at a significantly lower bulk Reynolds number of Re_{m, l} = 665, i.e., a laminar flow in a non-rotating channel, are introduced. The experiments show the low Reynolds number flow to become turbulent under rotation and to develop the same characteristics as the high Reynolds number flow.     

Instantaneous and simultaneous planar velocity field measurements of two phases for turbulent mixing of high pressure sprays

This paper describes the tests of accuracy and the first application of a combined planar visualization technique. Its goal is two-phase flow discrimination, i.e. simultaneous measurements of velocity of droplets and ambient gas in the case of two-phase flow mixing, at the same location and with possible conditioning by “apparent diameter” (AD) of the droplets. It combines the mature techniques of particle image velocimetry (PIV), planar Mie scattering diffusion (PMSD), planar laser-induced fluorescence (PLIF), and it necessitates two synchronized cross-correlation systems, digital image treatment and analysis. This technique was developed with the objective of better describing the mixing between liquid and gaseous phases as in the case of high-pressure spray atomization in quiescent ambient gas. The basic principle of separation is to seed the ambient gas with micrometer particles and to tag the liquid with fluorescent dye. We use digital image treatment and analysis to discriminate between the phases. We use two cross-correlation PIV systems in order to obtain the velocity field of the droplets and gas simultaneously and separately at the same location. The digital image processing for separating the phases involves geometric measurement of droplet shapes. This leads to measurement of droplet parameters close to their real diameter, which could be used for analysis of actual mixing. A synchronized system composed of two CCD cameras is used for image recording, and two Nd:YAG lasers are used for generating pulsed light sheets at times t and t + δt. Tests were performed to check for different sources of errors. The combined technique was applied to measurements in high-pressure spray flow atomizing in a quiescent ambient gas, and first results are presented.     

Volumetric reconstruction of the mean flow around circular cylinders fitted with strakes

The volumetric reconstruction technique presented in this paper employs a two-camera stereoscopic particle image velocimetry (SPIV) system in order to reconstruct the mean flow behind a fixed cylinder fitted with helical strakes, which are commonly used to suppress vortex-induced vibrations (VIV). The technique is based on the measurement of velocity fields at equivalent adjacent planes that results in pseudo volumetric fields. The main advantage over proper volumetric techniques is the avoidance of additional equipment and complexity. The averaged velocity fields behind the straked cylinders and the geometrical periodicity of the three-start configuration are used to further simplify the reconstruction process. Two straked cylindrical models with the same pitch (p = 10d) and two different heights (h = 0.1 and 0.2d) are tested. The reconstructed flow shows that the strakes introduce in the wake flow a well-defined wavelength of one-third of the pitch. Measurements of hydrodynamic forces, fluctuating velocity, vortex formation length, and vortex shedding frequency show the interdependence of the wake parameters. The vortex formation length is increased by the strakes, which is an important effect for the suppression of vortex-induced vibrations. The results presented complement previous investigations concerning the effectiveness of strakes as VIV suppressors and provide a basis of comparison to numerical simulations.     

Determination of complete velocity gradient tensor by using cinematographic stereoscopic PIV in a turbulent jet

Cinematographic stereoscopic PIV measurements were performed in the far field of an axisymmetric co-flowing turbulent round jet (Re _T ≈ 150, where Re _T is the Reynolds number based on Taylor micro scale) to resolve small and intermediate scales of turbulence. The time-resolved three-component PIV measurements were performed in a plane normal to the axis of the jet and the data were converted to quasi-instantaneous three-dimensional (volumetric) data by using Taylor’s hypothesis. The availability of the quasi-three-dimensional data enabled the computation of all nine components of the velocity gradient tensor over a volume. The use of Taylor’s hypothesis was validated by performing a separate set of time-resolved two component “side-view” PIV measurements in a plane along the jet axis. Probability density distributions of the velocity gradients computed using Taylor’s hypothesis show good agreement with those computed directly with the spatially resolved data. The overall spatial structure of the gradients computed directly exhibits excellent similarity with that computed using Taylor’s hypothesis. The accuracy of the velocity gradients computed from the pseudo-volume was assessed by computing the divergence error in the flow field. The root mean square (rms) of the divergence error relative to the magnitude of the velocity gradient tensor was found to be 0.25, which is consistent with results based on other gradient measurement techniques. The velocity gradients, vorticity components and mean dissipation in the self-similar far field of the jet were found to satisfy the axisymmetric isotropy conditions. The divergence error present in the data is attributed to the intrinsic uncertainty associated with performing stereoscopic PIV measurements and not to the use of Taylor’s hypothesis. The divergence error in the data is found to affect areas of low gradient values and manifests as nonphysical values for quantities like the normalized eigenvalues of the strain-rate tensor. However, the high gradients are less affected by the divergence error and so it can be inferred that structural features of regions of intense vorticity and dissipation will be faithfully rendered.     

Performances of motion tracking enhanced Tomo-PIV on turbulent shear flows

The motion tracking enhancement technique (MTE) is a recently introduced method to improve the accuracy of tomographic PIV measurements at seeding density higher than currently practiced. The working principle is based on the fact that the particle field and its projections are correlated between the two exposures. Therefore, information from subsequent exposures can be shared within the tomographic reconstruction process of a single object, which largely reduces the energy lost into ghost particles. The study follows a previous work based on synthetic particle images, showing that the MTE technique has an effect similar to that of increasing the number of cameras. In the present analysis, MTE is applied to Tomographic PIV data from two time-resolved experiments on turbulent shear flows: a round jet at Re = 5,000 (f _acq = 1,000 Hz) and a turbulent boundary layer at the trailing edge of an airfoil (Re _c = 370,000) measured at 12,000 Hz. The application of MTE is extended to the case of more than two recordings. The performance is assessed comparing the results from a lowered number of cameras with respect to the full tomographic imaging system. The analysis of the jet flow agrees with the findings of numerical simulations provided the results are scaled taking into account the concept of MTE efficiency based on the volume fraction where ghost-pairs (Elsinga et al. 2010a) are produced. When a large fraction of fluid has uniform motion (stagnant fluid surrounding the jet), only a moderate reduction in ghost intensity is expected by MTE. Nevertheless, a visible recovery of reconstruction quality is observed for the 3-cameras system when MTE is applied making use of 3 recordings. In the turbulent boundary layer, the objective is set to increase the seeding density beyond current practice, and the experiments are performed at approximately 200,000 particles/megapixel. The measurement robustness is monitored with the signal-to-noise ratio S/N for the cross-correlation analysis. An estimate of the precision error is obtained for the turbulent boundary layer case following the peak height of the spatio-temporal cross-correlation function (frozen-turbulence). The MTE approach appears to be essential for the increase in robustness and measurement precision at such seeding density.     

Experimental investigation into vortex structure and pressure drop across microcavities in 3D integrated electronics

Hydrodynamics in microcavities with cylindrical micropin fin arrays simulating a single layer of a water-cooled electronic chip stack is investigated experimentally. Both inline and staggered pin arrangements are investigated using pressure drop and microparticle image velocimetry (μPIV) measurements. The pressure drop across the cavity shows a flow transition at pin diameter–based Reynolds numbers (Re _d ) ~200. Instantaneous μPIV, performed using a pH-controlled high seeding density of tracer microspheres, helps visualize vortex structure unreported till date in microscale geometries. The post-transition flow field shows vortex shedding and flow impingement onto the pins explaining the pressure drop increase. The flow fluctuations start at the chip outlet and shift upstream with increasing Re _d . No fluctuations are observed for a cavity with pin height-to-diameter ratio h/d = 1 up to Re _d ~330; however, its pressure drop was higher than for a cavity with h/d = 2 due to pronounced influence of cavity walls.     

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.     

Turbulence properties in the cylinder wake at high Reynolds numbers

The present contribution analyses the turbulence properties in unsteady flows around bluff body wakes and provides a database for improvement and validation of turbulence models, concerning the present class of nonequilibrium flows. The flow around a circular cylinder with a low aspect ratio and a high blockage coefficient is investigated. This confined environment is used in order to allow direct comparisons with realisable 3-D Navier–Stokes computations avoiding ‘infinite’ conditions. The flow is investigated in the beginning of the critical regime at Reynolds number 140 000. The analysis is carried out by means of 2-D PIV, of 3-C PIV and of high-frequency 2-D PIV. The experimental analysis contributes to confirm the validity of advanced statistical turbulence modelling for unsteady flows around bodies.     

Three-dimensional flow of Newtonian and Boger fluids in square–square contractions

The flow of a Newtonian fluid and a Boger fluid through sudden square–square contractions was investigated experimentally aiming to characterize the flow and provide quantitative data for benchmarking in a complex three-dimensional flow. Visualizations of the flow patterns were undertaken using streak-line photography, detailed velocity field measurements were conducted using particle image velocimetry (PIV) and pressure drop measurements were performed in various geometries with different contraction ratios. For the Newtonian fluid, the experimental results are compared with numerical simulations performed using a finite volume method, and excellent agreement is found for the range of Reynolds number tested (Re₂ ≤ 23). For the viscoelastic case, recirculations are still present upstream of the contraction but we also observe other complex flow patterns that are dependent on contraction ratio (CR) and Deborah number (De₂) for the range of conditions studied: CR = 2.4, 4, 8, 12 and De₂ ≤ 150. For low contraction ratios strong divergent flow is observed upstream of the contraction, whereas for high contraction ratios there is no upstream divergent flow, except in the vicinity of the re-entrant corner where a localized atypical divergent flow is observed. For all contraction ratios studied, at sufficiently high Deborah numbers, strong elastic vortex enhancement upstream of the contraction is observed, which leads to the onset of a periodic complex flow at higher flow rates. The vortices observed under steady flow are not closed, and fluid elasticity was found to modify the flow direction within the recirculations as compared to that found for Newtonian fluids. The entry pressure drop, quantified using a Couette correction, was found to increase with the Deborah number for the higher contraction ratios.     

Assessment of dual plane PIV measurements in wall turbulence using DNS data

Experimental dual plane particle image velocimetry (PIV) data are assessed using direct numerical simulation (DNS) data of a similar flow with the aim of studying the effect of averaging within the interrogation window. The primary reason for the use of dual plane PIV is that the entire velocity gradient tensor and hence the full vorticity vector can be obtained. One limitation of PIV is the limit on dynamic range, while DNS is typically limited by the Reynolds number of the flow. In this study, the DNS data are resolved more finely than the PIV data, and an averaging scheme is implemented on the DNS data of similar Reynolds number to compare the effects of averaging inherent to the present PIV technique. The effects of averaging on the RMS values of the velocity and vorticity are analyzed in order to estimate the percentage of turbulence intensity and enstrophy captured for a given PIV resolution in turbulent boundary layers. The focus is also to identify vortex core angle distributions, for which the two-dimensional and three-dimensional swirl strengths are used. The studies are performed in the logarithmic region of a turbulent boundary layer at z ⁺ = 110 from the wall. The dual plane PIV data are measured in a zero pressure gradient flow over a flat plate at Re _τ = 1,160, while the DNS data are extracted from a channel flow at Re _τ = 934. Representative plots at various wall-normal locations for the RMS values of velocity and vorticity indicate the attenuation of the variance with increasing filter size. Further, the effect of averaging on the vortex core angle statistics is negligible when compared with the raw DNS data. These results indicate that the present PIV technique is an accurate and reliable method for the purposes of statistical analysis and identification of vortex structures.