The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer

To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Re_θ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume “fat” light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.     

Strong vortex/boundary layer interactions

Detailed measurements with hot-wires and pressure probes are presented for the interaction between a turbulent longitudinal vortex pair with common flow down, and a turbulent boundary layer. The interaction has a larger value of the vortex circulation parameter, and therefore better represents many aircraft/vortex interactions, than those studied previously. The vortices move down towards the boundary layer, but only the outer parts of the vortices actually enter the it. Beneath the vortices the boundary layer is thinned by lateral divergence to the extent that it almost ceases to grow. Outboard of the vortices the boundary layer is thickened by lateral convergence. The changes in turbulence structure parameters in the boundary layer appear to be due to the effects of extra-rate-of-strain produced by lateral divergence (or convergence) and by free-stream turbulence. The effect of the interaction on the vortices (other than the inviscid effect of the image vortices below the surface) is small. The flow constitutes a searching test case for prediction methods for three-dimensional turbulent flows.     

Strong vortex/boundary layer interactions

This is the second of two papers on the interaction between a longitudinal vortex pair, produced by a delta-wing at angle of attack, and a turbulent boundary layer developing on a flat plate. In the first paper only the outer parts of the vortices entered the boundary layer whereas in this paper the vortices merge with it. In the resultant interaction, the boundary layer between the vortices is kept thin by lateral divergence and a three-dimensional separation line is formed outboard of each vortex. Turbulent, momentum-deficient fluid containing longitudinal vorticity is entrained from the boundary layer along these lines and wrapped around the vortices. As a consequence, the turbulent region of the vortices increases in size and the circulation slowly decreases. It is shown that the flow near the separation line and in the vortices is complicated, and this interaction is expected to be more difficult to calculate than the first. Detailed mean flow and turbulence measurements are reported.     

A depth-of-field limited particle image velocimetry technique applied to oscillatory boundary layer flow over a porous bed

Boundary layer flows are ubiquitous in the environment, but their study is often complicated by their thinness, geometric irregularity and boundary porosity. In this paper, we present an approach to making laboratory-based particle image velocimetry (PIV) measurements in these complex flow environments. Clear polycarbonate spheres were used to model a porous and rough bed. The strong curvature of the spheres results in a diffuse volume illuminated region instead of the more traditional finite and thin light sheet illuminated region, resulting in the imaging of both in-focus and significantly out-of-focus particles. Results of a traditional cross-correlation-based PIV-type analysis of these images demonstrate that the mean and turbulent features of an oscillatory boundary layer driven by a free-surface wave over an irregular-shaped porous bed can be robustly measured. Measurements of the mean flow, turbulent intensities, viscous and turbulent stresses are presented and discussed. Velocity spectra have been calculated showing an inertial subrange confirming that the PIV analysis is sufficiently robust to extract turbulence. The presented technique is particularly well suited for the study of highly dynamic free-surface flows that prevent the delivery of the light sheet from above the bed, such as swash flows.     

Stereo particle image velocimetry applied to a vortex pipe flow

Stereo particle image velocimetry (PIV) has been employed to study a vortex generated via tangential injection of water in a 2.25 inch (57 mm) diameter pipe for Reynolds numbers ranging from 1,118 to 63,367. Methods of decreasing pipe-induced optical distortion and the PIV calibration technique are addressed. The mean velocity field analyses have shown spatial similarity and revealed four distinct flow regions starting from the central axis of rotation to the pipe wall in the vortex flows. Turbulence statistical data and vortex core location data suggest that velocity fluctuations are due to the axis of the in-line vortex distorting in the shape of a spiral.     

Stereo particle image velocimetry of nonequilibrium turbulence relaxation in a supersonic boundary layer

Measurements using stereo particle image velocimetry are presented for a developing turbulent boundary layer in a wind tunnel with a Mach 2.75 free stream. As the boundary layer exits from the tunnel nozzle and moves through the wave-free test section, small initial departures from equilibrium turbulence relax, and the boundary layer develops toward the equilibrium zero-pressure-gradient form. This relaxation process is quantified by comparison of first and second order mean, fluctuation, and gradient statistics to classical inner and outer layer scalings. Simultaneous measurement of all three instantaneous velocity components enables direct assessment of the complete turbulence anisotropy tensor. Profiles of the turbulence Mach number show that, despite the M = 2.75 free stream, the incompressibility relation among spatial gradients in the velocity fluctuations applies. This result is used in constructing various estimates of the measured-dissipation rate, comparisons among which show only remarkably small differences over most of the boundary layer. The resulting measured-dissipation profiles, together with measured profiles of the turbulence kinetic energy and mean-flow gradients, enable an assessment of how the turbulence anisotropy relaxes toward its equilibrium zero-pressure-gradient state. The results suggest that the relaxation of the initially disturbed turbulence anisotropy profile toward its equilibrium zero-pressure-gradient form begins near the upper edge of the boundary layer and propagates downward through the defect layer.     

Particle image velocimetry measurements of a shock wave/turbulent boundary layer interaction

Particle image velocimetry is used to investigate the interaction between an incident shock wave and a turbulent boundary layer at Mach 2.1. A particle response assessment establishes the fidelity of the tracer particles. The undisturbed boundary layer is characterized in detail. The mean velocity field of the interaction shows the incident and reflected shock wave pattern, as well as the boundary layer distortion. Significant reversed flow is measured instantaneously, although, on average no reversed flow is observed. The interaction instantaneously exhibits a multi-layered structure, namely, a high-velocity outer region and a low-velocity inner region. Flow turbulence shows the highest intensity in the region beneath the impingement of the incident shock wave. The turbulent fluctuations are found to be highly anisotropic, with the streamwise component dominating. A distinct streamwise-oriented region of relatively large kinematic Reynolds shear stress magnitude appears within the lower half of the redeveloping boundary layer. Boundary layer recovery towards initial equilibrium conditions appears to be a gradual process.     

Longitudinal vortex pair imbedded in a turbulent boundary layer: Comparative performances of several turbulence models

Four turbulence models, namely, the basic and nonlinear stress-transport models and the basic and anisotropick-ε models, have been tested in the case of interaction between a longitudinal vortex pair and a flat-plate boundary layer. The results of their predictions were compared with Mehta and Bradshaw's measurements. In this paper, part of the results involving those of the nonlinear stress-transport model and anisotropick-ε model are presented and discussed. The project supported by the National Natural Science Foundation of China under Contract No. 19132012     

Measurement of atmospheric boundary layer based on super-large-scale particle image velocimetry using natural snowfall

This work intended to study the behavior of the instantaneous vapor fraction in the turbopump inducer of a liquid propellant rocket engine. Experimentations held on an experimental pump test facility and cavitation was attained by reducing the inlet pressure in the machine while maintaining constant the inducer rotational speed. Measurements of vapor fraction through the rotating inducer were achieved by means of an X-ray-based system. The system exerted an industrial X-ray generator and 10 collimated scintillation detectors. Detectors were functioning in current mode thus permitting an acquisition at 5 kHz for each detector. A reference X-ray detector situated between the X-ray generator and the machine permitted the treatment of X-ray beam energy fluctuations related to industrial generators. Acquisitions were performed in three axial positions on the inducer. For each measurement position, three cavitation sequences with different flow rate conditions (Q/Q _n = 0.9, 1, 1.1, where Q _n is the nominal flow rate) were accomplished. Each cycle is performed by decreasing gradually the pressure while maintaining an imposed rotational speed of 4,000 rpm. Each test is constituted of 10 pressure points varying from 2.40 to 0.48 bars representing a complete cavitation sequence. X-ray acquisition was performed for each pressure point, and it was carried out for 10 s thus corresponding to 667 tours of the inducer. Vapor fraction was determined instantaneously thus showing the applicability and the precision of the method in such measurements despite of the geometry and rotation speed constraints. Consequently a quantitative and qualitative evaluation of the vapor fraction is presented. Results show that the vapor distribution is well related to cavitation development on the blades of the inducer for steady cavitation condition.     

Development of a high-speed UV particle image velocimetry technique and application for measurements in internal combustion engines

A flexible, high-frame rate particle image velocimetry technique that can be applied to operating internal combustion engines in highly luminous combustion situations was developed. Two high-repetition rate diode-pumped Nd:YAG lasers operated at 355 nm and a CMOS camera were used to devise a system that allowed measurements of velocity fields near the spark plug in a firing engine at a rate of 6 kHz for 500 consecutive cycles. The 6 kHz acquisition rate enables recording one velocity field every other crank angle at 2,000 RPM engine speed. Sample results such as individual and average flow fields and kinetic energy evolutions are presented.     

Receptivity of the inclined-cylinder attachment-line boundary layer to vortex perturbations

The receptivity of the boundary layer in the neighborhood of the attachment line of a cylinder inclined to the flow with respect to periodic vortex perturbations frozen into the stream is investigated. The problem considered simulates the interaction between external turbulence and the leading-edge swept wing boundary layer. It is shown that if the direction of the external perturbation vector is almost parallel to the leading edge, then the external perturbations are considerably strengthened at the outer boundary layer edge. This effect can cause laminar-turbulent transition on the attachment line at subcritical Reynolds numbers.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 72–85. Original Russian Text Copyright © 2004 by Ustinov.     

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.     

Two-color particle image velocimetry technique for an internal combustion engine

A two-color particle image velocimetry (PIV) technique has been applied to a single-cylinder motored research engine. Two-color PIV is a quantitative planar velocity measurement technique that can unambiguously determine the velocity magnitude and direction.

The work includes the development of an interrogation system, a series of computer simulations to determine the performance of the technique under various conditions, the comparison of these results to similar ones obtained for an autocorrelation PIV system, and a test of the technique by reconstructing the velocity field of a uniform jet flow.

The technique was then applied to the in-cylinder flow field of a motored single-cylinder, cup-in-head, research engine. A total of 27 instantaneous velocity fields were obtained at a single measurement plane for a single operating condition of the engine. The data were analyzed to yield ensemble-averaged velocity and velocity fluctuation.     

Application of digital particle image velocimetry to insect aerodynamics: measurement of the leading-edge vortex and near wake of a Hawkmoth

Some insects use leading-edge vortices to generate high lift forces, as has been inferred from qualitative smoke visualisations of the flow around their wings. Here we present the first Digital Particle Image Velocimetry (DPIV) data and quantitative analysis of an insect’s leading-edge vortex and near wake at two flight speeds. This allows us to describe objectively 2D slices through the flow field of a tethered Tobacco Hawkmoth (Manduca sexta). The near-field vortex wake appears to braodly resemble elliptical vortex loops. The presence of a leading-edge vortex towards the end of the downstroke is found to coincide with peak upward force production measured by a six-component force–moment balance. The topology of Manduca’s leading-edge vortex differs from that previously described because late in the downstroke, the structure extends continuously from wingtip across the thorax to the other wingtip.     

Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries

The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise–wall-normal plane of a 536 μm capillary over the Reynolds-number range 1,800 ≤ Re ≤ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re ≅ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 ≤ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non-laminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these “trains” of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the non-laminar subsets at each transitional Re, including root-mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.     

A new artificial neural network tracking technique for particle image velocimetry

 The analysis of Particle Image Velocimetry (PIV) data requires effective algorithms to track efficiently the particles suspended in the fluid flow. The artificial neural network algorithm method described here presents a new approach to solve this problem. Contrary to the classic cross correlation method, this new method does not require a large number of particles per frame, it can handle flows with large velocity gradients, and is suited for tracking images with multiple exposures as well as tracking through consecutive images. The algorithm was tested on synthetic and available experimental data to provide a thorough performance analysis. Received: 28 May 1996/Accepted: 25 December 1996