An application of Gappy POD

An iterative procedure, based on the proper orthogonal decomposition (POD), first proposed by Everson and Sirovich (J Opt Soc Am A 12(8):1657–1664, 1995) is applied to marred particle image velocimetry (PIV) data of shallow rectangular cavity flow at Mach 0.19, 0.28, 0.38, and 0.55. The procedure estimates the POD modes while simultaneously estimating the missing vectors in the PIV data. The results demonstrate that the absolute difference between the repaired vectors and the original PIV data approaches the experimental uncertainty as the number of included POD modes is increased. The estimation of the dominant POD modes is also shown to converge by examining the subspace spanned by the POD eigenfunctions.

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Density stratified environments: the double-tank method

We present an alternative method of producing density stratifications in the laboratory based on the ‘double-tank’ method proposed by Oster (Sci Am 213:70–76, 1965). We refer to Oster’s method as the ‘forced-drain’ approach, as the volume flow rates between connecting tanks are controlled by mechanical pumps. We first determine the range of density profiles that may be established with the forced-drain approach other than the linear stratification predicted by Oster. The dimensionless density stratification is expressed analytically as a function of three ratios: the volume flow rate ratio n, the ratio of the initial liquid volumes λ and the ratio of the initial densities ψ. We then propose a method which does not require pumps to control the volume flow rates but instead allows the connecting tanks to drain freely under gravity. This is referred to as the ‘free-drain’ approach. We derive an expression for the density stratification produced and compare our predictions with saline stratifications established in the laboratory using the ‘free-drain’ extension of Oster’s method. To assist in the practical application of our results we plot the region of parameter space that yield concave/convex or linear density profiles for both forced-drain and free-drain approaches. The free-drain approach allows the experimentalist to produce a broad range of density profiles by varying the initial liquid depths, cross-sectional and drain opening areas of the tanks. One advantage over the original Oster approach is that density profiles with an inflexion point can now be established.

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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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A classical problem revisited: rheology of nematic polymer monodomains in small amplitude oscillatory shear

We revisit the classical problem of the viscoelastic response of nematic (liquid crystal) polymers to small amplitude oscillatory shear. A multiple time scale perturbation analysis is applied to the Doi–Hess mesoscopic orientation tensor model to describe key features observed of longtime experiments, both physical (Moldenaers and Mewis, J Rheol, 30:567–584, 1986; Larson and Mead, J Rheol, 33:1251–1281, 1989b) and numerical (herein). First, there is a very slow time scale drift in the envelope of oscillations of the major director; we characterize the mean director angle and the envelope of oscillation. Second, there are bistable asymptotic orientational states, distinguished in that they are precisely the zero-stress orientational distributions noted in Larson and Mead (J Rheol, 33:185–206, 1989a). Third, the drift dynamics and asymptotic mean director angle are determined by the initial orientation of the director, not by material properties; we characterize the domain of attraction of each bistable state. Finally, the director drift leads to a predicted longtime decrease in the storage and loss moduli, consistent with experimental observations.

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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.

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.

Turbulence measurements in a swirling pipe flow

This paper reports laser-Doppler measurements of the mean flow and turbulence stresses in a swirling pipe flow. Experiments were carried out under well-controlled laboratory conditions in a refractive index-matched pipe flow facility. The results show pronounced asymmetry in mean and fluctuating quantities during the downstream decay of the swirl. Experimental data reveal that the swirl significantly modifies the anisotropy of turbulence and that it can induce explosive growth of the turbulent kinetic energy during its decay. Anisotropy invariant mapping of the turbulent stresses shows that the additional flow deformation imposed by initially strong swirling motion forces turbulence in the core region to tend towards the isotropic two-component state. When turbulence reaches this limiting state it induces rapid production of turbulent kinetic energy during the swirl decay.

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Two- and three-dimensional flows in nearly rectangular cavities driven by collinear motion of two facing walls

Two- and three-dimensional flows in nearly cuboidal cavities are investigated experimentally. A tight cavity is formed in the gap between two long and parallel cylinders of large radii by adding rigid top, bottom, and end walls. The cross-section perpendicular to the axes of the cylinders is nearly rectangular with aspect ratio Γ. The axial aspect ratio Λ > 10 is large to suppress end-wall effects. The fluid motion is driven by independent and steady rotation of the cylinders about their axes which defines two Reynolds numbers Re _1,2. Stability boundaries of the nearly two-dimensional steady flow have been determined as functions of Re _1,2 for Γ = 0.76 and Γ = 1. Up to six different three-dimensional supercritical modes have been identified. The critical thresholds for the onset of most of the three-dimensional modes, three of which have been observed for the first time, agree well with corresponding linear-stability calculations. Particular attention is paid to the flow for Γ = 1 under symmetric and parallel wall motion. In that case the basic flow consists of two mirror symmetric counter-rotating parallel vortices. They become modulated in span-wise direction as the driving increases. Detailed LDV measurements of the supercritical three-dimensional velocity field and the bifurcation show an excellent agreement with numerical simulations.

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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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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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Objective flow classification parameters and their use in general steady flows

Three quantitative flow classification parameters have been studied in the context of Tanner and Huilgol’s suggestion of strong and weak flows. Seen in this context, the different types of streamlines possible for general 3-D flows furnish no indication with respect to the flow strength. This is in total contrast to 2-D flows, where the type of the streamline and the strength of the flow go hand in hand. Astarita’s [J Non-Newton Fluid Mech, 6:69–76, 1979] flow classification parameter takes care of this fact and, if properly generalized, can be applied to more general flows: Two other flow classification parameters also have their basis in homogeneous 2-D flows, but their generalization leads, for general flows, to nonuniqueness and other unacceptable results. For 3-D flows, none of the parameters can quantitatively be used in general, and additional parameters, with their basis outside the 2-D flow regime, seem to be called for.

A random synthetic jet array driven turbulence tank

We measure the flow above an array of randomly driven, upward-facing synthetic jets used to generate turbulence beneath a free surface. Compared to grid stirred tanks (GSTs), this system offers smaller mean flows at equivalent turbulent Reynolds numbers with fewer moving parts.

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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.

Thermoacoustically driven flame motion and heat release variation in a swirl-stabilized gas turbine burner investigated by LIF and chemiluminescence

Laser-induced fluorescence and chemiluminescence, both phase-locked to the dominant acoustic oscillation, are used to investigate phenomena related to thermoacoustic instability in a swirl-stabilized industrial scale gas turbine burner. The observed sinusoidal phase-averaged flame motion in axial (main flow) direction is analyzed using different schemes for defining the flame position. Qualitative agreement between experimental data and theoretical analysis of the observed flame motion is obtained, interpreted as originating primarily from variation of the burning velocity. The heat release variation during an acoustic cycle is determined from the sinusoidally varying total OH* chemiluminescence intensity.

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Analysis of weighting windows for image deformation methods in PIV

The use of a weighting window (WW) in the evaluation of the cross-correlation coefficient and in the iterative procedure of image deformation method for particle image velocimetry (PIV) applications can be used to both stabilise the process and to increase the spatial resolution. The choice of the WW is a parameter that influences the complete PIV algorithm. Aim of this paper is to examine the influence of this aspect on both the accuracy and spatial resolution of the PIV algorithm. Results show an overall accordance between the theoretical approach and the simulation both with synthetic and real images. The choice of the combination of WW influences significantly the spatial resolution and accuracy of the PIV algorithm.

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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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Quantitative planar Raman imaging through a spectrograph: visualisation of a supersonic wedge flow

Planar Raman imaging through a spectrograph is demonstrated as a diagnostic tool for quantitative flow visualisation of internal supersonic wedge flow. A dedicated Bayesian deconvolution filter is used to remove the spectral structure that is introduced by the spectrograph. The 2D density field is determined with ca. 10% precision using average images over 6,000 laser pulses, down to 0.5 mm from the surface of the wedge. Direct interpretations of Raman intensities provide more precise density data than indirect interpretations based on shock geometry in 2D inviscid flow.

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