A microfluidic-based nanoscope

 A novel technique for noninvasively measuring the shapes of walls with resolution approaching tens of nanometers is presented. The nanoscope measures local wall position by measuring the velocity of a fluid with micron-scale spatial resolution as it flows over a surface. The location of the wall is estimated by assuming the no-slip velocity condition at the wall and extrapolating the velocity profile to zero. Nanoscope measurements were obtained in a 30 × 300-μm channel. The wall shape of the glass microchannel was determined to be flat to within a root mean square uncertainty of 62 nm. Numerical simulations show that noise in the velocity measurements contributes significantly to uncertainty in wall position. The technique can be used to measure surfaces that are immersed in liquids and in geometries that do not provide exposed surfaces, where traditional nanoscope techniques such as scanning probe microscopes (SPM) are not applicable. Received: 2 March 2001 / Accepted: 19 October 2001     

2D temperature measurements in the wake of a heated cylinder using LIF

A technique is described to measure the instantaneous 2D temperature distribution in the wake of a heated cylinder using `laser-induced fluorescence'. Rhodamine B, a fluorescent dye, is used as a temperature indicator. The relation between fluorescence intensity and temperature is determined by means of calibration experiments in the temperature range of 20–35 °C with an accuracy of ±0.1 °C. The temperature distribution behind the heated cylinder is well visible and can be measured with a high spatial resolution. Corrections for variation in laser energy and intensity distribution in the laser sheet have to be made to further improve the accuracy of the measuring method. Received: 3 January 2001/Accepted: 18 May 2001     

Comparisons of numerical methods with respect to convectively dominated problems

A series of numerical schemes: first‐order upstream, Lax–Friedrichs; second‐order upstream, central difference, Lax–Wendroff, Beam–Warming, Fromm; third‐order QUICK, QUICKEST and high resolution flux‐corrected transport and total variation diminishing (TVD) methods are compared for one‐dimensional convection–diffusion problems. Numerical results show that the modified TVD Lax–Friedrichs method is the most competent method for convectively dominated problems with a steep spatial gradient of the variables. Copyright © 2001 John Wiley & Sons, Ltd.     

Resistive probe for continuous measurement of electroconductive liquid levels facing electromagnetic fields

 We investigate experimentally the behaviour of the free surface of a mercury pool, whose shape is related to the shape of a continuous caster, subjected to an alternating magnetic field. Therefore, a probe allowing a continuous local measurement of the level was built and calibrated. The measurements of an electromagnetically shaped free surface, its local fluctuations and the spectrum of potential energy of these fluctuations are presented and discussed. Received: 11 May 2001 / Accepted: 30 June 2001     

Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics

 The interferometric particle imaging and the global phase Doppler techniques for multi-dimensional particle sizing are based on out-of-focus images of the particles illuminated in laser light sheets of finite width. For a given optical arrangement, an increase in particle number concentration will eventually lead to overlapping particle images on the recording medium, and this in turn will degrade or even prohibit the correct processing of individual particle images for size. The probability of overlapping images should therefore be minimized, which places constraints on the design of the optical system. These constraints are rigorously derived, using Poisson statistics to describe the particle spatial distribution in the flow. The main result consists of an overlap probability coefficient as a function of number density and the optical parameters of the system. However, the resolution of the third position coordinate normal to the laser sheet and the measurement size range also result from this analysis. These results are a prerequisite for designing such systems. Received: 25 May 2001 / Accepted: 12 October 2001     

An experimental contribution to near-wall measurements by means of a special laser Doppler anemometry technique

 A new experimental technique for the investigation of near-wall turbulence using laser Doppler anemometry is presented, which allows an accurate measurement of the flow field very close to the wall, with good resolution and a high data rate. Such a technique is tested in a fully developed turbulent flow (with Reynolds numbers between 4,300 and 67,000) by carrying out a careful statistical analysis of the streamwise and wall-normal velocity components within the near-wall region, at distances from the wall ranging from approximately y ⁺ = 1 to y ⁺ = 100. The velocity profiles, Reynolds stresses and higher-order moments of the two-dimensional boundary layer are presented. The results, which are in agreement with the most recent data in the literature, testify the validity of the proposed experimental solution. Moreover, the accuracy of the results allows the friction velocity to be calculated as the intercept at the wall of the best linear fit of the total stress profile; in this way, an unambiguous examination of the normalized statistics is possible. Received: 17 April 2001 / Accepted: 15 August 2001     

Performance of digital image velocimetry processing techniques

Digital particle image velocimetry (DPIV)-processing techniques have become increasingly more sophisticated in recent years. However, much work is still done using standard traditional methods of analysis. This paper investigates several traditionally based techniques for cross-correlation image processing in terms of computational efficiency and measurement accuracy. Direct spatial domain correlation, standard fast Fourier transform (FFT) correlation, a dynamic FFT correlation technique, and a new hybrid correlation method are discussed and evaluated. In addition, a particle-tracking velocimetry scheme based on that of Cowen and Monismith (1997) is examined in the same context as the DPIV methods. A detailed examination of the behaviors of each correlation method reveals that direct spatial domain correlation is more accurate than FFT-based methods, with the standard FFT correlation showing the weakest performance. Using the more robust methods (dynamic FFT and hybrid correlation), accuracy can be improved significantly over the standard FFT method in many cases, while still remaining computationally efficient. The particle-tracking algorithm studied was found to yield comparable accuracy to the DPIV routines and can provide much higher spatial- resolution possibilities. Received: 3 September 1999 / Accepted: 21 June 2001 Published online: 29 November 2001     

The development of high-speed particle image velocimetry (20 kHz) for large eddy simulation code refinement in bluff body flows

Flow interaction with a bluff body generates a highly complex flow field and has been the subject of much experimental and theoretical analysis. It has been shown that large eddy simulation (LES) modelling provides a more realistic analysis of the flow for such situations where the large scales of turbulence must be resolved. The inherent small-scale spatial velocity averaging in particle image velocimetry (PIV) is commensurate with the sub-grid scale modelling of LES and, therefore, offers potential as a code refinement technique. To demonstrate this potential, however, PIV must be performed with a temporal resolution of typically kHz and a spatial resolution of sub-mm² to be relevant for the vast majority of flows of engineering interest. This paper reports the development of a high-speed PIV system capable of operating at 20 kHz with a spatial resolution of 0.9 mm². This is the combined highest speed, highest resolution PIV data reported to date. The experiment chosen to demonstrate the system is the study of the steady flow interaction with circular and square cross-section obstacles. A Reynolds number of 3,900 is chosen for the cylinder flow to extend the database used by Breuer M. (1998 Int J Heat Fluid 19:512–521) in his extensive LES modelling of this flow. Data presented include a sequence of two-dimensional velocity and vorticity fields, including flow streamlines. Importantly, the random error, inherent in a PIV measurement, is discussed and a formula presented which allows the error to be estimated and regions of the flow identified where LES comparisons would be uncertain.     

Application of the autoregressive method to the spectral analysis of a flow signal

Application of the autoregressive (AR) method to the spectral analysis of a turbulent-flow signal is discussed in this paper. When only a small number of samples are available because of the inherent nature of the flow or the limited memory size of the data acquisition device, the autoregressive method is more useful than the fast Fourier transform (FFT) method for spectral analysis, because its resolution is higher than the FFT method for this case. Especially, a low-frequency characteristic is much better analyzed by the autoregressive method. To illustrate the advantage of the AR method, some typical signals often encountered in practical flows are analyzed by the AR method. Received: 16 May 2000 / Accepted: 28 March 2001     

The analysis of thermal stresses in thermopiezoelastic semi-infinite body with an edge crack

Summary  Thermopiezoelastic materials have recently attracted considerable attention because of their potential use in intelligent or smart structural systems. The governing equations of a thermopiezoelastic medium are more complex due to the intrinsic coupling effects that take place among mechanical, electrical and thermal fields. In this analysis, we deal with the problem of a crack in a semi-infinite, transversely isotropic, thermopiezoelastic material by means of potential functions and Fourier transforms under steady heat-flux loading conditions. The problem is reduced to a singular integral equation that is solved. The thermal stress intensity factor for a crack situated in a cadmium selenide material is calculated. Received 20 March 2001; accepted for publication 18 October 2001     

On the application of the constant deflection-contour method in nonlinear vibrations of elastic plates

Summary  This paper concerns the application of the constant deflection-contour method to problems involving nonlinear vibrations. Two specific problems are considered: a clamped circular plate and an annular plate with free inner boundary. For the linear case, the results obtained offer excellent agreement with previous studies, indicating significant potential for the utilization of this method in different nonlinear cases. The analysis may be applied to other types of geometrical structures. Notwithstanding the fact that only a first-term approximation has been made for the deflection function, in conjunction with the Galerkin procedure, excellent agreement has been found. Additional analytical calculations could be made to improve accuracy, indicating that the method could prove particularly useful when employed with a symbolic manipulation package. Received 13 June 2001; accepted for publication 6 November 2001     

Determining Spatial Distributions of Permeability

Conventional laboratory experimentation provides an apparent value of hydraulic permeability which, at best, is representative of the entire sample. Nuclear magnetic resonance imaging (MRI) provides unique opportunities to probe spatial distributions of permeability at a much finer scale (Seto et al., Transp Porous Media 42:351–388, 2001). We advance the methodology for determining spatial distributions of permeability and provide, for the first time, laboratory determinations of permeability distributions with complete three-dimensional (3D) spatial resolution. We investigate new experimental designs that mitigate a possible lack of identifiability and provide for more accurate estimates of permeability. We demonstrate the application of MRI experiments and analyses that provide substantial improvements in the determination of the porosity distribution, an essential step for obtaining reliable measurements of spatially resolved velocity distributions. We investigate the use of global optimization to solve the associated inverse problem for determining permeability distributions from the measured velocity distributions. Our methodology is demonstrated with experimental data on sandstone and trabecular bone samples.     

Experimental investigation of three-dimensional flow instabilities in a rotating lid-driven cavity

The swirling flow between a rotating lid and a stationary cylinder is studied experimentally. The flow is governed by two parameters: the ratio of container height to disk radius, h, and the Reynolds number, Re, based on the disk angular velocity, cylinder radius and kinematic viscosity of the working liquid. For the first time, the onset of three-dimensional flow behavior is measured by combining the high spatial resolution of particle image velocimetry and the temporal accuracy of laser Doppler anemometry. A detailed mapping of the transition scenario from steady and axisymmetric flow to unsteady and three-dimensional flow is investigated for 1 ≥ h ≥ 3.5. The flow is characterized by the development of azimuthal modes of different wave numbers. A range of different modes is detected and critical Reynolds numbers and associated frequencies are identified. The results are compared to the numerical stability analysis of Gelfgat et al. (J Fluid Mech 438:363–377, 2001). In most cases, the measured onset of three-dimensionality is in good agreement with the numerical results and disagreements can be explained by bifurcations not accounted for by the numerical stability analysis.     

Accuracy and resolution issues in NO/acetone PLIF measurements of gas-phase molecular mixing

Under-resolved passive-scalar measurements in liquid and gaseous shear layers have been known to over-predict mixed-fluid quantities as a result of sub-resolution stirring. In recent studies, simultaneous cold-chemistry (nitric oxide) and passive-scalar (acetone) planar laser-induced fluorescence have been employed for the measurement of sub-resolution molecular mixing. In the current work, the theory and experimental approach of this technique are reviewed, and new analyses of quenching corrections, differential diffusion errors, and imaging resolution are presented. Results from both experimental work and direct numerical simulations indicate that this technique provides a successful means of quantifying macro- and micro-scale turbulent molecular mixing in gaseous shear flows. Received: 20 December 2000/Accepted: 24 September 2001     

High resolution digital flowfield imaging of jets

High resolution digital imaging, using planar laser-induced light scattering is being developed for analysis of gaseous flowfields. High resolution image data, implying both high spatial resolution and wide signal dynamic range, can be readily processed to yield two-dimensional distributions of species concentrations and, in turn, accurate two-dimensional images of concentration gradients and turbulence scales. Critical aspects of the technique are discussed; details of the design and the performance of the imaging system are presented; and results for laminar, transitional, turbulent and birfurcating nitrogen jets, using planar-laser-induced fluorescence of biacetyl, are reported. Initial results from imaging processing and the potential implications for flowfield analysis are described     

High resolution flux‐difference‐splitting scheme on adaptive grid for open‐channel flows

The effectiveness and usefulness of further enhancing the shock resolution of a second‐order accurate scheme for open‐channel flows by using an adaptive grid is investigated. The flux‐difference‐splitting (FDS) scheme based on the Lax–Wendroff numerical flux is implemented on a fixed as well as on a self‐adjusting grid for this purpose. The grid‐adjusting procedure, developed by Harten and Hyman, adjusts the grid by averaging the local characteristic velocities with respect to the signal amplitude in such a way that a shock always lies on a mesh point. This enables a scheme capable of perfectly resolving a stationary shock to capture a shock that moves from mesh point to mesh point. The Roe's approximate Jacobian is used for conservation and consistency, while theoretically sound treatment for satisfying entropy inequality conditions ensures physically realistic solutions. Details about inclusion of source terms, often left out of analyses for the homogeneous part of governing equations, are also explained. The numerical results for some exacting problems are compared with analytical as well as experimental results for examining improvements in resolution of discontinuities by the adaptive grid. Copyright © 2001 John Wiley & Sons, Ltd.     

Spatial behavior of an epidemic model with migration

It was reported that there are traveling patterns in the spatiotemporal data of epidemics (Cummings et al., Nature 427:344, 2004; Grenfell et al., Nature 414:716, 2001). To well understand the mechanism, we present a spatial epidemic model with migration, which means that the individuals exhibit a correlated motion toward certain direction, and obtain traveling pattern. Our results may be helpful to understand the mechanism of the spatiotemporal epidemics and have potential application of control of the epidemics.     

Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves

The accuracy and efficiency of two methods of resolving the exact potential flow problem for nonlinear waves are compared using three different one horizontal dimension (1DH) test cases. The two model approaches use high‐order finite difference schemes in the horizontal dimension and differ in the resolution of the vertical dimension. The first model uses high‐order finite difference schemes also in the vertical, while the second model applies a spectral approach. The convergence, accuracy, and efficiency of the two models are demonstrated as a function of the temporal, horizontal, and vertical resolutions for the following: (1) the propagation of regular nonlinear waves in a periodic domain; (2) the motion of nonlinear standing waves in a domain with fully reflective boundaries; and (3) the propagation and shoaling of a train of waves on a slope. The spectral model approach converges more rapidly as a function of the vertical resolution. In addition, with equivalent vertical resolution, the spectral model approach shows enhanced accuracy and efficiency in the parameter range used for practical model applications. Copyright © 2015 John Wiley & Sons, Ltd.     

Two-dimensional numerical simulations of multi-headed detonations in oxygen-aluminum mixtures using an adaptive mesh refinement

Abstract. Two-dimensional numerical simulations of detonations in two-phase lean mixtures of aluminum particles and pure oxygen have been performed. The computational procedure adopts an adaptive mesh refinement methodology in order to increase spatial resolution in the most interesting parts of the flow field. A one-step heterogeneous reaction describes the evaporation and combustion of aluminum. Depending on the gas-phase temperature, the combustion product is aluminum oxide or aluminum monoxide. The results show that the heterogeneous detonations resemble gaseous single-phase ones although the scale of the phenomena is very different. The detonation of aluminum dust evolves into the 2-headed mode of propagation with the characteristic detonation cell width equal to cm. For aluminum dust the cellular structure is much finer. The detonation initially propagates in the 11-headed mode with the characteristic cell width equal to cm and evolves into the 8.5-headed mode with the characteristic cell size $\lambda_{\rm cell}$ equal to cm. Received 7 May 2001 / Accepted 25 March 2002 Published online 23 January 2003 Correspondence to: K. Benkiewicz (e-mail: kbenk@cow.me.aoyama.ac.jp)     

Harmonic analysis in rheological property measurement

 Sudden change in the linear stress-strain relationship has long been known to produce interesting discontinuities in the flow properties of polymer melts, concentrated particle suspensions, and gels as the shear rate amplitude is increased. The non-linear effect produces stress harmonics, which contain information about the material properties that is otherwise difficult to obtain. This note describes a generalized procedure for extracting yield stress material functions from the discrete Fourier transform of the stress signal. Received: 23 April 2001 Accepted: 27 July 2001