Accuracy of tomographic particle image velocimetry data on a turbulent round jet

Tomographic particle image velocimetry (Tomo-PIV) was applied on a turbulent round air jet to quantitatively assess the accuracy of velocity gradients obtained in the self-similar turbulent region. The jet Reynolds number based on the nozzle diameter (d) was Re_d = 3000. Mean velocity, turbulent intensities, and Reynolds shear stress at the center plane of the jet were measured. In addition, statistical results of Tomo-PIV along the axial direction were assessed by performing a separate set of two-dimensional two-component PIV experiments on a “side view” plane along the jet axis. Moreover, the probability distribution functions of four components of the measured velocity gradients in the axial and radial directions were validated by these “side view” planar PIV data. The root mean square of the velocity divergence values relative to the norm of the velocity gradient tensor was 0.36. Furthermore, the on- and off-diagonal components of the velocity gradients satisfied the axisymmetric isotropy conditions. The divergence error in the data affected only areas with low gradient magnitude. Therefore, turbulent structures in the regions with intense vorticity and dissipation can be closely monitored. On this basis, the joint pdfs of the invariants of the velocity gradient and strain and rotation tensor rates were produced and compared well with those in isotropic turbulence studies.     

Time resolved visualization of structures of velocity gradients measured with near Kolmogorov-scale resolution in turbulent free-shear flows

A three-dimensional visualization of velocity gradients at the finest scales in a turbulent free-shear flow is obtained using a time-resolved scanning PIV system with near Kolmogorov-scale resolution. A minimal observation volume capable of capturing single velocity gradient structures is used. The structures are identified by iso-surfaces revealing four basic shapes in the makeup of the velocity gradients: sheets, tubes, square ribbons and spherical blobs. Their size is also obtained. The 3D local acceleration structure is visualized showing strong anti-alignment with the convective acceleration. The statistics of the velocity gradient, and higher order moments (skewness and kurtosis) are calculated and compared favorably with published experimental work and with homogeneous isotropic theory.     

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.     

Error quantification of 3D homogeneous and isotropic turbulence measurements using 2D PIV

Particle image velocimetry (PIV) has become a popular non-intrusive tool for measuring various types of flows. However, when measuring three dimensional flows with 2D PIV, there is inherent measurement error due to out-of-plane motion. Errors in the measured velocity field propagate to turbulence statistics. Since this can distort the overall flow characteristics, it is important to understand the effect of this out-of-plane error. In this study, the effect of out-of-plane motion on turbulence statistics is quantified. Using forced isotropic turbulence direct numerical simulation (DNS) flow field data provided by the Johns Hopkins turbulence database (JHTDB), synthetic image tests are performed. Turbulence statistics such as turbulence kinetic energy, dissipation rate, Taylor microscale, Kolmogorov scale, and velocity correlations are calculated. Various test cases were simulated while controlling three main parameters which affect the out-of-plane motion: PIV interrogation window size, camera inter-frame time, and laser sheet thickness. The amount of out-of-plane motion was first quantified, and then the error variation according to these parameters was examined. This information can be useful when examining fully three dimensional flows such as homogeneous and isotropic turbulence via 2D PIV.     

Experimental investigation of helicity in turbulent swirling jet using dual-plane dye laser PIV technique

This paper reports a new method of generating two light sheets using a dye laser system and the use of this dual-plane dye laser system to analyse average helicity and energy dissipation in a turbulent swirling flow. The dual-plane PIV system that was used in this study consisted of three cameras and a single frequency Nd:YAG laser, which was used to generate two parallel light sheet planes with differing wavelengths(colour). The method of generating two different light sheet wavelengths using a single laser source is an innovative and new technique. Stereoscopic PIV measurements were obtained in one plane with the use of two CCD cameras, and standard PIV measurements were obtained in the other plane with the use of one CCD camera. The light scattered by the particles on two different light sheets were separated using appropriate optical filters. The measurements obtained were used to estimate the components of the velocity gradient tensor. The tensor components were then used to determine the average vorticity components and helicity quantities of the fluid that was investigated. To determine the average turbulent kinetic energy dissipation, the continuity equation was used to infer the out-of-plane gradient of the out-of-plane velocity. From the analysis of the results, it was found that regions with high helicity were correlated with regions of high turbulent kinetic energy dissipation.     

Measurement of the conditioned turbulence and temperature field of a premixed Bunsen burner by planar laser Rayleigh scattering and stereo particle image velocimetry

The turbulence and temperature field of Bunsen-type turbulent lean methane/air flames has been investigated using planar laser Rayleigh scattering (PLRS) and stereo particle image velocimetry (stereo PIV). Temporally averaged reaction progress variable plots have been computed from PLRS measurements in order to provide a basis with regards to the verification of computational fluid dynamics (CFD) models. Turbulence was characterised by stereo PIV in one plane for all three velocity components. Averaged velocity fields have been calculated, as well as Reynolds-decomposed fluctuation vector fields. Conditioned root mean square (RMS) values of the turbulent fluctuations in terms of unburnt and burnt gas could be determined by making use of the information gained from a threshold setting procedure in the PIV raw images. Furthermore, several length scales were measured indirectly from PIV vector plots. In this context, all integral length scales being accessible with stereo PIV were computed separately for the burnt and unburnt regions and were compared to each other. It could be observed that all integral length scales increased in the burnt zone. Additionally, the conditioned Taylor and Kolmogorov lengths have been extracted from the PIV field data, derived either from the zero-radius curvature of the correlation function or from common turbulence theory relations.     

A scanning PIV method for fine-scale turbulence measurements

A hybrid technique is presented that combines scanning PIV with tomographic reconstruction to make spatially and temporally resolved measurements of the fine-scale motions in turbulent flows. The technique uses one or two high-speed cameras to record particle images as a laser sheet is rapidly traversed across a measurement volume. This is combined with a fast method for tomographic reconstruction of the particle field for use in conjunction with PIV cross-correlation. The method was tested numerically using DNS data and with experiments in a large mixing tank that produces axisymmetric homogeneous turbulence at \(R_\lambda \simeq 219\) . A parametric investigation identifies the important parameters for a scanning PIV set-up and provides guidance to the interested experimentalist in achieving the best accuracy. Optimal sheet spacings and thicknesses are reported, and it was found that accurate results could be obtained at quite low scanning speeds. The two-camera method is the most robust to noise, permitting accurate measurements of the velocity gradients and direct determination of the dissipation rate.     

Stereoscopic PIV: validation and application to an isotropic turbulent flow

 A new stereoscopic PIV system to measure the three velocity components is developed and applied to grid turbulence flows. This system uses two CCD cameras coupled with an accurate cross-correlation calculation method. An experimental test (based upon three-dimensional displacements) has been carried out to demonstrate the capability of this process to locate the maximum of correlation, and to detect accurately the 3D displacements. Experiments in a well-established turbulent flow have validated the method for quantitative measurements and a comparison with LDV results showed a good agreement in terms of mean and fluctuating velocities. Combined PIV and stereoscopic PIV measurements on a turbulent flow revealed the need to the stereoscopic systems to measure accurate 2D velocity fields. It has been shown that an error of up to 10% in the velocity fluctuation measured by conventional PIV could be attained due to 3D effects in highly turbulent cases. Finally, the digital cross-correlation technique adapted to the determination of small displacements seems to be the most suitable technique for stereoscopic PIV. Received: 22 July 1997/Accepted: 27 January 1998     

Comparison of PIV data using multiple configurations and processing techniques

Particle image velocimetry (PIV) data have been acquired using three different experimental configurations in the far-field of the interaction created by a transverse supersonic jet exhausting from a flat plate into a transonic crossflow. The configurations included two-component PIV in the centerline streamwise plane at two overlapping stations, as well as stereoscopic PIV in both the same streamwise plane and in the crossplane. All measurement planes intersected at a common line. Data from both two-component measurement stations and the stereoscopic streamwise configuration agreed to within the estimated uncertainty, but data from the crossplane exhibited reduced velocity and turbulent stress magnitudes by a small but significant degree. Subsequent reprocessing of the data in nominally the same manner using a newer software package brought all values into close agreement with each other, but produced substantially higher turbulent stresses. The error source associated with the choice of software was traced to the use of image deformation in the newer software to treat velocity gradients, which is shown by synthetic PIV tests to yield a more accurate result for turbulence measurements even for gradients within the recommended limits for classical PIV. These detailed comparisons of replicate data suggest that routine methods of uncertainty quantification used for a turbulent PIV experiment may not fully capture the actual error sources.     

Dual-plane stereo particle image velocimetry (DSPIV) for measuring velocity gradient fields at intermediate and small scales of turbulent flows

A two-frequency dual-plane stereo particle image velocimetry (DSPIV) technique is described for highly resolved measurements of the complete nine-component velocity gradient tensor field u_i/x_j on the quasi-universal intermediate and small scales of turbulent flows. The method is based on two simultaneous, independent stereo particle image velocimetry (PIV) measurements in two differentially spaced light sheet planes, with light sheet characterization measurements demonstrating the required sheet thicknesses, separation, and two-axis parallelism that determine the measurement resolution and accuracy. The present approach uses an asymmetric forward–forward scatter configuration with two different laser frequencies in conjunction with filters to separate the scattered light onto the individual stereo camera pairs, allowing solid metal oxide particles to be used as seed particles to permit measurements in nonreacting as well as exothermic reacting turbulent flows.     

Scaling investigation of plasma-induced flows over curved and flat surfaces: Comparison to the wall jet

The present investigation deals with Dielectric Barrier Discharge (DBD) induced jets flowing over curved surfaces and studied in the framework of a circulation control application, carried out by acting near the rounded trailing-edge of an airfoil. These jets are characterized experimentally via Particle Image Velocimetry (PIV) in quiescent air conditions. The study assesses the evolution of these flows in terms of self-similarity of the mean flow and of its turbulent components. DBD wall jets evolution in the streaming direction is also analyzed through the rate of spread and the maximum velocity decay evolution as commonly done for fluidic wall jets, and also through several normalized quantities deriving from different length and velocity scales. A comparison with a canonical flow, such as the classical wall jet flowing over plane or curved surfaces, is made in order to find out the similarities and the discrepancies between these two flows. Results reveal that DBD wall jets and canonical fluidic wall jets show comparable properties in the diffusion zone. Compared to the plane DBD wall jet, centrifugal forces are responsible of the greater spread of curved DBD wall jets and are likely the source of instabilities leading to their transitional state. The momentum flux of the induced jet and the radius of curvature of the surface are two relevant scales for DBD induced flows developing over curved surfaces.     

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.     

湍流能量耗散率标度律实验研究

应用粒子图像测速(PIV)系统对平板湍流边界层内流向和法向的瞬时速度进行了测量。湍流的能量耗散率由轴对称假设得到,同时在研究湍流动能耗散率标度律的过程中采用传统的统计学方法。实验结果显示,对于不同尺度上和不同法向位置湍流耗散率标度律来说,湍流耗散主要发生在小尺度上,也就是说湍动能耗散率标度律在小尺度上具有普适性。另外,根据层次结构理论假设,通过PIV实验数据对最高激发态的标度指数进行了研究,结果发现,最高激发态存在绝对标度指数,并且绝对标度律是由信号中最强耗散涨落的局部结构产生的。     

PIV measurements in a weakly separating and reattaching turbulent boundary layer

A high Reynolds number flat plate turbulent boundary layer was studied in a wind-tunnel experiment using particle image velocimetry (PIV). The flow is subjected to an adverse pressure gradient (APG) which is designed such that the boundary layer separates and reattaches, forming a weak separation bubble. With PIV we are able to get a more complete picture of this complex flow phenomenon. The view of a separation bubble being composed of large scale coherent regions of instantaneous backflow occurring randomly in a three-dimensional manner in space and time is verified by the present PIV measurements. The PIV database was used to test the applicability of various velocity scalings around the separation bubble. We found that the mean velocity profiles in the outer part of the boundary layer, and to some extent also the Reynolds shear-stress, are self-similar when using a velocity scale based on the local pressure gradient. The same can be said for the so called Perry–Schofield scaling, which suggests that the two velocity scales are connected. This can also be interpreted as an experimental evidence of the claimed relation between the latter velocity scale and the maximum Reynolds shear-stress.     

Amplitude modulation and its relation to streamwise convection velocity

The paper is devoted to show the relation between the amplitude modulation and the convection velocity in a turbulent boundary layer. The analysis has been performed based upon velocity profiles measured with the hot-wire technique in a turbulent boundary layer with pressure gradient corresponding to turbomachinery conditions. The VITA detection method of small-scale structures was used in order to show the impact of the pressure gradient on phase averaged time-traces changes in the aspect of amplitude modulation. The physical significance of the large scales influence on the small scales, formerly known as the amplitude modulation, has been elucidated. It was demonstrated that the measure of amplitude modulation can be used as an indicator of the convection velocity of coherent structures. The convection velocity profile can be described in the inner region using the amplitude modulation term when the proper scale is applied. The convection velocity prediction in favourable and adverse pressure gradients shows that t the strongest impact of the pressure gradient occurs in the buffer layer. The stronger increase occurs in the buffer layer. It was also found that the skewness factor of phase-averaged VITA waveforms, is very similar in shape with the cross-product term of the streamwise skewness factor, which quantifies amplitude modulation. It indicates that the well-known modification of quadrant events in pressure gradient flows is a result of the amplitude modulation phenomenon.     

Reynolds number effects on the behavior of a non-buoyant round jet

The behavior of a non-buoyant circular water jet discharged from a contraction nozzle was experimentally investigated. In this experiment, the Reynolds number of the jet, based on the mean velocity results obtained by particle image velocimetry (PIV), ranged from 177 to 5,142. From the experimental results, we found that the cross-sectional profile of the axial velocity for a laminar flow near the nozzle did not show a top-hat distribution, whereas the profiles with Reynolds number higher than 437 were almost top-hat. The length of the zone of flow establishment (ZFE) was found to decrease with increasing Reynolds number. The measured centerline velocity decayed more rapidly and, consequently, approached the theoretical equation earlier near the nozzle as the Reynolds number increased. The decay constant for the centerline velocity of the turbulent cases was relatively lower than that discovered in theory. It is assumed that this probably resulted from the use of the contraction nozzle. Verifying the similarity of the lateral velocity profiles demonstrated that the Gaussian curve was properly approximated only for the turbulent jets and not for the laminar or transitional flows. The jet half width seldom grew for the laminar or transitional flows, whereas it grew with increasing axial distance for the turbulent flows. The spreading rates for the turbulent flows gradually decreased with increasing Reynolds number. The normalized turbulence intensity along the jet centerline increased more rapidly with the axial distance as the Reynolds number increased, and tended to the constant values proposed by previous investigators. The Reynolds shear stress levels were also found to increase as the Reynolds number increased for the turbulent jets.     

Particle image velocimetry investigation of the flow-field of a 3D turbulent annular swirling decaying flow induced by means of a tangential inlet

Particle image velocimetry (PIV) has been used in order to measure the three mean components and turbulence intensities of the velocity vector in a swirling decaying flow induced by a tangential inlet in an annulus. This kind of flow motion is found to be very complex, exhibiting three-dimensional and non-axisymmetric characteristics coupled with a free decay of the swirling intensity along the flow path, thereby making it difficult to study. A method allowing the measurement of the three components of the velocity flow-field with a standard PIV system with two-dimensional acquisitions, is presented. The evolution of each velocity component between the inlet and the outlet of the annulus is obtained. Furthermore, the PIV technique is extended to the measurement of turbulent characteristics such as turbulent intensities and dimensionless turbulent energy. The main characteristics of the swirling flow are discussed and the swirl number is estimated as a function of the axial distance from the tangential inlet. Received: 6 July 1998/Accepted: 20 March 1999     

Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows

The lattice Boltzmann method (LBM) is coupled with the multiple-relaxation-time (MRT) collision model and the three-dimensional 19-discrete-velocity (D3Q19) model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high-order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investigated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity (ESS) method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This validation provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.     

Measurement of spectrum with particle image velocimetry

The purpose of this paper is to show that the measurement of turbulent spectrum using wholefield velocity techniques such as particle image velocimetry (PIV) is possible. Toward this end, data from the axial plane of a self-similar turbulent axisymmetric jet, at a Reynolds number, based on Taylor microscale of 30 has been analyzed. The two-dimensional velocity data are first high-pass filtered, which educes the vortices. An automated method is then used to identify the vortices and measure their properties. By directly measuring the energy of the vortices, it is possible to plot the turbulence spectrum. The spectrum presented here shows the presence of energy containing and inertial regimes. However, the smallest scales have not been resolved in the measurements. The slope of the spectrum in the inertial subrange is about −1.6. The number of vortices in the two regimes have also been measured. The number of vortices in the energy containing regime is substantially smaller than those in the inertial subrange. The technique has been verified by analyzing another dataset. These results show that the direct measurement of vortex properties with reasonable confidence is possible using PIV and an appropriate vortex eduction technique.