Variational optical flow estimation for particle image velocimetry

We introduce a novel class of algorithms for evaluating PIV image pairs. The mathematical basis is a continuous variational formulation for globally estimating the optical flow vector fields over the whole image. This class of approaches has been known in the field of image processing and computer vision for more than two decades but apparently has not been applied to PIV image pairs so far. We pay particular attention to a multi-scale representation of the image data so as to cope with the quite specific signal structure of particle image pairs. The experimental evaluation shows that a prototypical variational approach competes in noisy real-world scenarios with three alternative approaches especially designed for PIV-sequence evaluation. We outline the potential of the variational method for further developments.The publications of the CVGPR Group are listed under .

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Structure and dynamics of a bidimensional pattern of liquid columns

We report an experimental study of the structure and dynamics of a bidimensional array of liquid columns. This pattern is formed below a flat porous plate continuously supplied with liquid. It exhibits a marked hexagonal tendency. Its typical wavelength is close to that of the most dangerous mode of the Rayleigh–Taylor instability of a thin viscous layer hanging below a plate, defined by the competition between gravity and surface tension. Collective dynamical behaviors are also evidenced, involving oscillations of the column positions, columns migrations, coalescences and nucleations. Quantitative comparisons are presented with the equivalent one-dimensional pattern formed below the perimeter of an overflowing dish (circular fountain experiment).

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Limitations of accuracy in PIV due to individual variations of particle image intensities

The effect of independent variations of the intensity of individual tracer particles between consecutive images on the accuracy of common displacement estimation methods in particle image velocimetry (PIV) is investigated. Such variations can be observed, e.g., in flows with components perpendicular to the illumination sheet, leading to out-of-plane displacements of the tracer particles. The achievable accuracy of PIV measurements is shown to be limited by this effect alone to be of the order of 0.1 pixel, yielding a basic limitation of the PIV technique.

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Comment on the Clauser chart method for determining the friction velocity

A known difficulty with using the Clauser chart method to determine the friction velocity in wall bounded flows is that it assumes, a priori, a logarithmic law for the mean velocity profile. Using both experimental and DNS data in the literature, this note explicitly shows how friction velocities obtained using the Clauser chart method can potentially mask subtle Reynolds-number-dependent behavior.

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Microscale Synthetic Schlieren

We develop the axisymmetric Synthetic Schlieren technique to study the wake of a microscale sphere settling through a density stratification. A video-microscope was used to magnify and image apparent displacements of a micron-sized random-dot pattern. Due to the nature of the wake, density gradient perturbations in the horizontal greatly exceed those in the vertical, requiring modification of previously developed axisymmetric techniques. We present results for 780 and 383 μm spheres, and describe the limiting role of noise in the system for a 157 μm sphere. This technique can be instrumental in understanding a range of ecological and environmental oceanic processes on the microscale.

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Aging of an unstable w/o gel emulsion with a nonionic surfactant

We study an unstable highly concentrated emulsion of water droplets in oil with a nonionic surfactant. A technique of light diffusion coupled to a rheometer allows simultaneous measurement of average droplet radius and emulsion shear elastic modulus during time. Over the studied range of volume fraction (from 71 to 95%), we show that Princen and Kiss’ (J Colloid Interface Sci 112:427–437, 1986) model does not apply. A dimensional analysis based on the hypothesis of dominant van der Waals forces is proposed for nonionic surfactants, which is in good agreement with experimental data. We also show that the measured average droplet volume increases linearly with time and that the coalescence rate strongly depends on the volume fraction in relation with different topological conformations of droplets.

Analysis of velocity interpolation schemes for image deformation methods in PIV

The spatial resolution of PIV can be increased significantly by using an image deformation method (IDM) and very small grid distance (i.e. the final distance between vectors), therefore, also increasing the processing time. By using an interpolation scheme with a good spectral response, in the dense predictor step of the algorithm, it is possible to increase the grid distance without decreasing the spatial resolution therefore decreasing the total processing time.

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Forced convection laminar film condensation on an inclined elliptical tube in the absence of gravity

In this paper, the problem of forced convection dominated laminar film condensation, in the absence of gravity, on an inclined elliptical tube is investigated theoretically. In this analysis, the interfacial vapour shear stress is modelled following Shekriladze approach. By employing the method of characteristics, expressions are analytically derived for calculating the local film thickness as well as the local and mean Nusselt numbers. The results show that the mean Nusselt number, enhances with the increase in the tube ellipticity. For the practical ellipticity range: 0.8 e 0.92, this enhancement is found from 7 to 14% compared to a circular tube with the same length and equivalent condensation surface area.

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A model of a subcritical Joule–Thomson cryocooler with condensation inside the recuperator

To develop a tool for predicting of heat and mass transfer in Joule–Thomson cryocoolers working at subcritical pressures, we study a counter flow heat exchanger with condensation by employing the integral method. The effects of inlet pressure and working fluid are predicted. We also show that there is an optimal value of the enthalpy difference along the heat exchanger for which its length is minimal.

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An analytical model of a matrix heat exchanger with longitudinal heat conduction in the matrix in application for the exchanger dynamics research

The paper presents an analytical method for the solution of the problem of a fixed matrix heat exchanger with axial heat conduction within the matrix. The small parameter method and Laplace transform have been applied. A general solution has been obtained for the unsteady state in the form of function series, using single and double convolutions of functions, as well as a particular solution for both the uniform and non-uniform initial temperature of the matrix and for an arbitrary function of the fluid temperature at the inlet. Particular solutions have been used in the study of the matrix dynamics in determining dynamic characteristics for the standard input signals in the form of: Dirac pulse, Heaviside function and the function of sinusoidal variable temperature of the fluid at the inlet. The results obtained both illustrate and enable the assessment of the effect of axial heat conduction in the matrix on the dynamic properties of the heat exchanger.

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Potential benefit from the application of autoregressive spectral estimators in the analysis of homogeneous and isotropic turbulence

Spectral estimators other than the conventional periodogram technique exist. The autoregressive (AR) method is one of the alternative spectral estimation procedures currently available. The technique is particularly adapted to the detection of narrow-band components in the lower frequency domain for short data records. However, the technique may also be used in the analysis of more standard turbulent flow configurations where no specific wave modes are necessarily expected. An example is given here in the case of homogeneous and isotropic turbulence developing freely downstream of a heated grid. The results reported in this paper are in good agreement with earlier findings and would thus tend to confirm the idea that the technique might be used successfully over a wider range of signals in fluid dynamics. They provide us with the opportunity to highlight one particular additional benefit of the AR method with respect to the identification of spectral regions with constant slopes.

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Transient analysis of sub-critical evaporation of fuel droplet in non-isothermal stagnant gaseous mixtures: effects of radiation and thermal expansion

Transient sub-critical droplet evaporation in non-isothermal stagnant gaseous mixtures taking into account the effects of radiation, liquid volumetric expansion and droplet heating is investigated numerically. We obtained equations for Stefan velocity and the rate of change of the droplet radius taking into account liquid volumetric expansion, and derived the boundary conditions taking into account the effect of liquid thermal expansion. It is shown that in the case of sub-critical evaporation neglecting the liquid volumetric expansion causes underestimation of the evaporation rate at the initial stage and overestimation of the evaporation rate at the final stage of droplet evaporation.

A pragmatic approach for deriving constitutive equations endowed with pom–pom attributes

The most important rheological and mathematical features of the pom–pom model are presently used to compare and improve other constitutive models such as the Giesekus and Phan-Thien–Tanner models. A pragmatic methodology is selected that allows derivation of simple constitutive equations, which are suited to possible software implementation. Alterations to the double convected pom–pom, Phan-Thien–Tanner and Giesekus models are proposed and assessed in rheometric flows by comparing model predictions to experimental data.

Local mass transfer measurements in an inclined enclosure at high Rayleigh number

An electrochemical technique is used to study local mass transfer coefficients on surfaces of inclined enclosures over the range 1.1×10⁴ < Ra_H < 1.4×10¹⁰ for a nominal Schmidt number of 2280. Scaling with gcos instead of g in the Rayleigh number correlates the data well at low angles of inclination; however, as either the aspect ratio or the angle of inclination increase, the longitudinal density stratification causes the data to deviate from a power law scaling.

Time-resolved reconstruction of the full velocity field around a dynamically-scaled flapping wing

The understanding of the physics of flapping flight has long been limited due to the obvious experimental difficulties in studying the flow field around real insects. In this study the time-dependent three-dimensional velocity field around a flapping wing was measured quantitatively for the first time. This was done using a dynamically-scaled wing moving in mineral oil in a pattern based on the kinematics obtained from real insects. The periodic flow is very reproducible, due to the relatively low Reynolds number and precise control of the wing. This repeatability was used to reconstruct the full evolving flow field around the wing from separate stereoscopic particle image velocimetry measurements for a number of spanwise planes and time steps. Typical results for two cases (an impulsive start and a simplified flapping pattern) are reported. Visualizations of the obtained data confirm the general picture of the leading-edge vortex that has been reported in recent publications, but allow a refinement of the detailed structure: rather than a single strand of vorticity, we find a stable pair of counter-rotating structures. We show that the data can also be used for quantitative studies, such as lift and drag prediction.

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Selective seeding for micro-PIV

A novel seeding method for microscale particle image velocimetry (micro-PIV) is presented. The method relies on selective seeding of a thin fluid layer within an otherwise particle-free flow. In analogy to the laser sheet in macroscale PIV, the generated particle sheet defines both the depth and the position of the measurement plane, independent of the details of the optical setup. Selectively seeded micro-PIV is applied to measure the instantaneous velocity field in a microchannel with a depth-wise resolution 20% below the estimated optical measurement depth of the micro-PIV system. In principle, a measurement depth corresponding to the diameter of the tracer particles may be achieved.

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The effect of cross flow on one-dimensional spectra measured using hot wires

Expressions were developed to estimate the cross-flow error that occurs in the one-dimensional velocity spectra determined by applying Taylors frozen field hypothesis to measurements with single- and cross-wire probes. The cross-flow error and the error caused by the unsteady convection of the small-scale motions were evaluated for typical measurements. It was found that the cross-flow error could be significant in inertial range of the measured one-dimensional spectra, and was much larger than the error caused by the unsteady convection of the small-scale motions in the one-dimensional spectra of the cross-stream velocity components, and . The results indicate that the one-dimensional spectra of the streamwise velocity component measured with a single-wire probe should be significantly more accurate than the spectra measured with a cross-wire probe. The cross-flow error in the one-dimensional spectra also becomes much less important in the dissipation range of the measured spectra.

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XPIV–Multi-plane stereoscopic particle image velocimetry

We introduce the three-dimensional measurement technique (XPIV) based on a Particle Image Velocimetry (PIV) system. The technique provides three-dimensional and statistically significant velocity data. The main principle of the technique lies in the combination of defocus, stereoscopic and multi-plane illumination concepts. Preliminary results of the turbulent boundary layer in a flume are presented. The quality of the velocity data is evaluated by using the velocity profiles and relative turbulent intensity of the boundary layer. The analysis indicates that the XPIV is a reliable experimental tool for three-dimensional fluid velocity measurements.More information at:

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Coupled Strain and Fresnel Response of Photoelastic Coatings at Oblique Incidence

This paper presents a theoretical model and corresponding experimental results of the oblique-incidence response of a luminescent photoelastic coating (LPC). LPCs use a luminescent dye that both partially preserves the stress-modified polarization state and provides high emission signal strength at oblique surface orientations. These characteristics enable the technique to acquire full-field strain separated measurements and principal strain directions, potentially on complex three-dimensional geometries, without the use of supplemental experimental or analytical techniques. Results of a single-layer LPC on a disk in diametral compression are presented to assess a theoretical model and evaluate the measurement sensitivity.

A new interpretation for the dynamic behaviour of complex fluids at the sol–gel transition using the fractional calculus

We propose to analyse power law shear stress relaxation modulus observed at the sol–gel transition (SGT) in many gelling systems in terms of fractional calculus. We show that the critical gel (gel at SGT) can be associated to a single fractional element and the gel in the post-SGT state to a fractional Kelvin–Voigt model. In this case, it is possible to give a physical interpretation to the fractional derivative order. It is associated to the power law exponent of the shear modulus related to the fractal dimension of the critical gel. A preliminary experimental application to silica alkoxide-based systems is given.