Jerry Westerweel

Fundamentals of digital particle image velocimetry

The measurement principle of digital particle image velocimetry (PIV) is described in terms of linear system theory. The conditions for PIV correlation analysis as a valid interrogation method are determined. Limitations of the method arise as consequences of the implementation. The theory is applied to investigate the statistical properties of the analysis and to optimize and improve the measurement performance. The theoretical results comply with results from Monte Carlo simulations and test measurements described in the literature. Examples of both correct and incorrect implementations are given.

Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment

Direct numerical simulations (DNS) and experiments are carried out to study fully developed turbulent pipe flow at Reynolds number Re c ≈ 7000 based on centreline velocity and pipe diameter. The agreement between numerical and experimental results is excellent for the lower-order statistics (mean flow and turbulence intensities) and reasonably good for the higher-order statistics (skewness and flatness factors). To investigate the differences between fully developed turbulent flow in an axisymmetric pipe and a plane channel geometry, the present DNS results are compared to those obtained from a channel flow simulation. Beside the mean flow properties and turbulence statistics up to fourth order, the energy budgets of the Reynolds-stress components are computed and compared. The present results show that the mean velocity profile in the pipe fails to conform to the accepted law of the wall, in contrast to the channel flow. This confirms earlier observations reported in the literature. The statistics on fluctuating velocities, including the energy budgets of the Reynolds stresses, appear to be less affected by the axisymmetric pipe geometry. Only the skewness factor of the normal-to-the-wall velocity fluctuations differs in the pipe flow compared to the channel flow. The energy budgets illustrate that the normal-to-the-wall velocity fluctuations in the pipe are altered owing to a different ‘impingement’ or ‘splatting’ mechanism close to the curved wall.

Efficient detection of spurious vectors in particle image velocimetry data

A statistical model is introduced that describes the occurence of spurious vectors in PIV data. This model is used to investigate the performance of three different post-interrogation procedures: the global-mean, the local-mean and the local-median test. The model is also used to optimize the performance of these procedures. Predicted performances agree very well with those obtained from an artificially generated PIV record. It is demonstrated that the “detectability” as the conventional measure for the reliability of a measured displacement vector is very inefficient, compared to the three tests described here. The local-median test has the highest efficiency.

Momentum and scalar transport at the turbulent/non-turbulent interface of a jet

Conditionally sampled measurements with particle image velocimetry (PIV) of a turbulent round submerged liquid jet in a laboratory have been taken at Re = 2 × 10 3 between 60 and 100 nozzle diameters from the nozzle in order to investigate the dynamics and transport processes at the continuous and well-defined bounding interface between the turbulent and non-turbulent regions of flow. The jet carries a fluorescent dye measured with planar laser-induced fluorescence (LIF), and the surface discontinuity in the scalar concentration is identified as the fluctuating turbulent jet interface. Thence the mean outward ‘boundary entrainment’ velocity is derived and shown to be a constant fraction (about 0.07) of the the mean jet velocity on the centreline. Profiles of the conditional mean velocity, mean scalar and momentum flux show that at the interface there are clear discontinuities in the mean axial velocity and mean scalar and a tendency towards a singularity in mean vorticity. These actual or asymptotic discontinuities are consistent with the conditional mean momentum and scalar transport equations integrated across the interface. Measurements of the fluxes of turbulent kinetic energy and enstrophy are consistent with computations by Mathew & Basu ( Phys. Fluids , vol. 14, 2002, pp. 2065–2072) in showing that for a jet flow (without forcing) the entrainment process is dominated by small-scale eddying at the highly sheared interface (‘nibbling’), with large-scale engulfing making a small (less than 10%) contribution consistent with concentration measurements showing that the interior of the jet is well mixed. (Turbulent jets differ greatly from the free shear layer in this respect.) To explain the difference between velocity and scalar profiles, their conditional mean gradients are defined in terms of a local eddy viscosity and eddy diffusivity and the momentum and scalar fluxes inside the interface. Since the eddy diffusivity is larger than the eddy viscosity, the scalar profile is flatter inside the interface so that the scalar discontinuity is relatively greater than the mean velocity discontinuity. Theoretical arguments, following Hunt, Eames & Westerweel (in Proc. of the IUTAM Symp. on Computational Physics and New Perspectives in Turbulence , ed. Y. Kaneda, vol. 4, 2008, pp. 331–338, Springer), are proposed for how the vortex sheet develops, how the internal structure of the interface layer relates to the inhomogeneous rotational and irrotational motions on each side and why the dominant entrainment process of jets and wakes differs from that of free shear layers.

Ensemble correlation PIV applied to bubble plumes rising in a bubble column.

This paper discusses an ensemble correlation, double-exposure single-frame, particle image velocimetry (PIV) technique that can be applied to study dispersed gas?liquid two-phase flows. The essentials of this technique will be reviewed and several important issues concerning the implementation of the PIV technique will be discussed. The capabilities of the newly developed PIV technique will be demonstrated by examining the gas and liquid flow fields induced by a bubble plume rising in a rectangular bubble column.

Magnetically-actuated artificial cilia for microfluidic propulsion

In this paper we quantitatively analyse the performance of magnetically-driven artificial cilia for lab-on-a-chip applications. The artificial cilia are fabricated using thin polymer films with embedded magnetic nano-particles and their deformation is studied under different external magnetic fields and flows. A coupled magneto-mechanical solid-fluid model that accurately captures the interaction between the magnetic field, cilia and fluid is used to simulate the cilia motion. The elastic and magnetic properties of the cilia are obtained by fitting the results of the computational model to the experimental data. The performance of the artificial cilia with a non-uniform cross-section is characterised using the numerical model for two channel configurations that are of practical importance: an open-loop and a closed-loop channel. We predict that the flow and pressure head generated by the artificial cilia can be as high as 18 microlitres per minute and 3 mm of water, respectively. We also study the effect of metachronal waves on the flow generated and show that the fluid propelled increases drastically compared to synchronously beating cilia, and is unidirectional. This increase is significant even when the phase difference between adjacent cilia is small. The obtained results provide guidelines for the optimal design of magnetically-driven artificial cilia for microfluidic propulsion.

Measurements of the wall shear stress distribution in the outflow tract of an embryonic chicken heart

In order to study the role of blood–tissue interaction in the developing chicken embryo heart, detailed information about the haemodynamic forces is needed. In this study, we present the first in vivo measurements of the three-dimensional distribution of wall shear stress (WSS) in the outflow tract (OFT) of an embryonic chicken heart. The data are obtained in a two-step process: first, the three-dimensional flow fields are measured during the cardiac cycle using scanning microscopic particle image velocimetry; second, the location of the wall and the WSS are determined by post-processing flow velocity data (finding velocity gradients at locations where the flow approaches zero). The results are a three-dimensional reconstruction of the geometry, with a spatial resolution of 15–20 µm, and provides detailed information about the WSS in the OFT. The most significant error is the location of the wall, which results in an estimate of the uncertainty in the WSS values of 20 per cent.

Measurement of fully-developed turbulent pipe flow with digital particle image velocimetry

A new and unique high-resolution image acquisition system for digital particle image velocimetry (DPIV) in turbulent flows is used for the measurement of fully-developed turbulent pipe flow at a Reynolds number of 5300. The flow conditions of the pipe flow match those of a direct numerical simulation (DNS) and of measurements with conventional (viz., photographic) PIV and with laser-Doppler velocimetry (LDV). This experiment allows a direct and detailed comparison of the conventional and digital implementations of the PIV method for a non-trivial unsteady flow. The results for the turbulence statistics and power spectra show that the level of accuracy for DPIV is comparable to that of conventional PIV, despite a considerable difference in the interrogation pixel resolution, i.e. 32 × 32 (DPIV) versus 256 × 256 (PIV). This result is in agreement with an earlier analytical prediction for the measurement accuracy. One of the advantages of DPIV over conventional PIV is that the interrogation of the DPIV images takes only a fraction of the time needed for the interrogation of the PIV photographs.

Effect of Sensor Geometry on the Performance of PIV Interrogation

This paper describes the mathematical investigation of the effect of the sensor geometry, i.e. the pixel size and pixel fill ratio, on the performance of PIV interrogation. Two sub-pixel estimators are investigated: the particle-image centroid, and the Gaussian peak fit. It is found that no bias errors occur when the particle-image diameter is at least two pixels, and the measurement error is determined by random errors only. When particle images are much smaller than one pixel, an irrecoverable signal loss deteriorates the measurement performance. For intermediate resolutions the bias errors are of the same magnitude as the random errors. It is demonstrated that image blurring by de-focussing reduces the bias error, but increases the random error. The analysis shows that sensors with a high fill ratio have a better performance.

Mechanics of inhomogeneous turbulence and interfacial layers

The mechanics of inhomogeneous turbulence in and adjacent to interfacial layers bounding turbulent and non-turbulent regions are analysed. Different mechanisms are identified according to the straining by the turbulent eddies in relation to the strength of the mean shear adjacent to, or across, the interfacial layer. How the turbulence is initiated and the topology of the region of turbulence are also significant factors. Specifically the cases of a layer of turbulence bounded on one, or two, sides by a uniform and/or shearing flow, and a circular region of a rotating turbulent vortex are considered and discussed. The entrainment processes at fluctuating interfaces occur both at the outer edges of turbulent shear layers, with and without free-stream turbulence (e.g. jets, wakes and boundary layers), at internal boundaries such as those at the outside of the non-turbulent core of swirling flows (e.g. the ‘eye-wall’ of a hurricane) or at the top of the viscous sublayer and roughness elements in turbulent boundary layers. Conditionally sampled data enables these concepts to be tested. These concepts lead to physically based estimates for critical modelling parameters such as eddy viscosity near interfaces, entrainment rates, maximum velocity and displacement heights.