Simultaneous PIV and pulsed shadow technique in slug flow: a solution for optical problems

A recent technique of simultaneous particle image velocimetry (PIV) and pulsed shadow technique (PST) measurements, using only one black and white CCD camera, is successfully applied to the study of slug flow. The experimental facility and the operating principle are described. The technique is applied to study the liquid flow pattern around individual Taylor bubbles rising in an aqueous solution of glycerol with a dynamic viscosity of 113×10^–3 Pa s. With this technique the optical perturbations found in PIV measurements at the bubble interface are completely solved in the nose and in annular liquid film regions as well as in the rear of the bubble for cases in which the bottom is flat. However, for Taylor bubbles with concave oblate bottoms, some optical distortions appear and are discussed. The measurements achieved a spatial resolution of 0.0022 tube diameters. The results reported show high precision and are in agreement with theoretical and experimental published data.Symbols D internal column diameter (m) - g acceleration due to gravity (m s^–2) - l _w wake length (m) - Q _v liquid volumetric flow rate (m³ s^–1) - r radial position (m) - r * radial position of the wake boundary (m) - R internal column radius (m) - U _s Taylor bubble velocity (m s^–1) - u _z axial component of the velocity (m s^–1) - u _r radial component of the velocity (m s^–1) - z distance from the Taylor bubble nose (m) - Z * distance from the Taylor bubble nose for which the annular liquid film stabilizes (m) Dimensionless groups Re Reynolds number ( ) - N _f inverse viscosity number ( ) Greek letters liquid film thickness (m) - liquid kinematic viscosity (m² s^–1) - liquid dynamic viscosity (Pa s) - liquid density (kg m^–3)     

Theoretical analyses on boiling critical heat flux with porous media

Porous media has been widely applied to enhance boiling heat transfer in industry, especially for increasing the value of critical heat flux (CHF). Two cases were considered in the paper: boiling within porous bed and boiling above on porous coatings. For boiling within porous bed, simplified Rayleigh–Taylor stability was analyzed and parametric effects of porous media on boiling critical heat flux were revealed. For boiling above on porous coatings, a simple new critical heat flux model was proposed basing on the analysis of liquid film stability and parametric effect of porous coatings on CHF was elaborated.     

Use of Faraday instabilities to enhance fuel pulverisation in air-blast atomisers

The atomization of liquids into a spray is an important process in many industrial applications and particularly in the aero-engine sector. Conventional air-blast injectors in aircraft engines today use aerodynamic shearing effects to atomize the liquid fuel. However, at operating conditions where the air velocity is below 30 m/s (such as ground start and high altitude restart) the atomization quality is poor. Consequently combustion is less efficient with high pollutant emissions. The objective of this study is to validate a new concept of injector which couples the shearing effects with the principle of ultrasonic atomization. The latter consists of using piezoelectric actuators to generate the oscillations of a wall in contact with the liquid film. This excitation perpendicular to the liquid film surface creates Faraday instabilities at the liquid/air interface. Amplitudes higher than a defined threshold value induce the break-up of ligaments and the formation of droplets. To cite this article: M. Boukra et al., C. R. Mecanique 337 (2009).     

Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).     

A new formulation of immiscible compressible two-phase flow in porous media

A new formulation is proposed to describe immiscible compressible two-phase flow in porous media. The main feature of this formulation is the introduction of a global pressure. The resulting equations are written in a fractional flow formulation and lead to a coupled system which consists of a nonlinear parabolic (the global pressure equation) and a nonlinear diffusion–convection one (the saturation equation) which can be efficiently solved numerically. To cite this article: B. Amaziane, M. Jurak, C. R. Mecanique 336 (2008).     

Asymptotic modeling of assemblies of thin linearly elastic plates

We derive various models of assemblies of thin linearly elastic plates by abutting or superposition through an asymptotic analysis taking into account small parameters associated with the size and the stiffness of the adhesive. They correspond to the linkage of two Kirchhoff–Love plates by a mechanical constraint which strongly depends on the magnitudes of the previous parameters. To cite this article: C. Licht, C. R. Mecanique 335 (2007).     

A model for film-forming with Newtonian and shear-thinning fluids

The formation of a thin film by (i) the slow penetration of a gas bubble into a liquid filled tube, (ii) the withdrawal of a planar substrate from a liquid filled gap, is investigated theoretically for the cases of both Newtonian and shear-thinning liquids; the latter conforming to either a power–law or Ellis model. Formulated as a boundary value problem underpinned by lubrication theory, the analysis gives rise to a system of ordinary differential equations which are solved numerically subject to appropriate boundary conditions. For Newtonian liquids comparison of the predicted residual film thickness for a wide range of capillary number, Ca  (10⁻⁴, 10), is made with others obtained using existing expressions, including the classical one of Bretherton, in the region of parameter space over which they apply. In the case of (i), prediction of the behaviour of the residual fluid fraction and gap-to-film thickness ratio, for a Newtonian liquid and one that is shear-thinning and modelled via a power–law, is found to be in particularly good agreement with experimental data for Ca < 0.2. For (ii), both shear-thinning models are utilized and contour plots of residual film thickness generated as a function of Ca and the defining parameters characteristic of each model.     

Missing boundary data recovering for the Helmholtz problem

This Note is dedicated to the numerical treatment of the ill-posed Cauchy–Helmholtz problem. Resorting to the domain decomposition tools, these missing boundary data are rephrased through an ‘interfacial’ equation. This equation is solved via a preconditioned Richardson algorithm with dynamic relaxation. The efficiency of the proposed method is illustrated by some numerical experiments. To cite this article: R. Ben Fatma et al., C. R. Mecanique 335 (2007).     

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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Forced convective flow and heat transfer of upward cocurrent air–water slug flow in vertical plain and swirl tubes

This experimental study comparatively examined the two-phase flow structures, pressured drops and heat transfer performances for the cocurrent air–water slug flows in the vertical tubes with and without the spiky twisted tape insert. The two-phase flow structures in the plain and swirl tubes were imaged using the computerized high frame-rate videography with the Taylor bubble velocity measured. Superficial liquid Reynolds number (Re_L) and air-to-water mass flow ratio (AW), which were respectively in the ranges of 4000–10000 and 0.003–0.02 were selected as the controlling parameters to specify the flow condition and derive the heat transfer correlations. Tube-wise averaged void fraction and Taylor bubble velocity were well correlated by the modified drift flux models for both plain and swirl tubes at the slug flow condition. A set of selected data obtained from the plain and swirl tubes was comparatively examined to highlight the impacts of the spiky twisted tape on the air–water interfacial structure and the pressure drop and heat transfer performances. Empirical heat transfer correlations that permitted the evaluation of individual and interdependent Re_L and AW impacts on heat transfer in the developed flow regions of the plain and swirl tubes at the slug flow condition were derived.     

A two grid algorithm based on perturbation and homotopy methods

In this paper, we propose a new class of bi-grid algorithm to solve large scale linear algebraic equations. This method is based on homotopy, perturbation technique and Padé approximants. To cite this article: R. El Mokhtari et al., C. R. Mecanique 330 (2002) 825–830.     

Identification de la relation de dispersion dans les barresIdentification of the dispersion relation in rods

Dispersion and attenuation of longitudinal waves in elastic or weakly viscoelastic rods are measured by analysing the resonant frequencies present in the strain spectrum due to an unknown loading. The method takes the finite measuring time of the test into account. It is applied to an aluminium bar, in which the dispersion relation is identified very accurately at frequencies up to 60 kHz. To cite this article: R. Othman et al., C. R. Mecanique 330 (2002) 849–855.     

Homogénéisation de problèmes d''évolution dans une structure renforcée de fibresHomogenization of evolution problems in a fiber reinforced structure

We study the homogenization of evolution equations such as:

where the coefficient a is -periodic and takes very high values on a subset TΩ (fibered structure) of very small measure. We find a non-local effective equation deduced from a homogenized system of several equations. To cite this article: M. Bellieud, C. R. Mecanique 330 (2002) 843–848.     

Investigation of the effect of the Coriolis force on a thin fluid film on a rotating disk

The effect of the Coriolis force on the evolution of a thin film of Newtonian fluid on a rotating disk is investigated. The thin-film approximation is made in which inertia terms in the Navier–Stokes equation are neglected. This requires that the thickness of the thin film be less than the thickness of the Ekman boundary layer in a rotating fluid of the same kinematic viscosity. A new first-order quasi-linear partial differential equation for the thickness of the thin film, which describes viscous, centrifugal and Coriolis-force effects, is derived. It extends an equation due to Emslie et al. [J. Appl. Phys. 29, 858 (1958)] which was obtained neglecting the Coriolis force. The problem is formulated as a Cauchy initial-value problem. As time increases the surface profile flattens and, if the initial profile is sufficiently negative, it develops a breaking wave. Numerical solutions of the new equation, obtained by integrating along its characteristic curves, are compared with analytical solutions of the equation of Emslie et al. to determine the effect of the Coriolis force on the surface flattening, the wave breaking and the streamlines when inertia terms are neglected.     

Numerical studies of the fingering phenomena for the thin film equation

We present a new interpretation of the fingering phenomena of the thin liquid film layer through numerical investigations. The governing partial differential equation is h_t + (h²?h³)_x = ??·(h³?Δh), which arises in the context of thin liquid films driven by a thermal gradient with a counteracting gravitational force, where h = h(x, y, t) is the liquid film height. A robust and accurate finite difference method is developed for the thin liquid film equation. For the advection part (h²?h³)_x, we use an implicit essentially non‐oscillatory (ENO)‐type scheme and get a good stability property. For the diffusion part ??·(h³?Δh), we use an implicit Euler's method. The resulting nonlinear discrete system is solved by an efficient nonlinear multigrid method. Numerical experiments indicate that higher the film thickness, the faster the film front evolves. The concave front has higher film thickness than the convex front. Therefore, the concave front has higher speed than the convex front and this leads to the fingering phenomena. Copyright © 2010 John Wiley & Sons, Ltd.     

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations. To cite this article: A. Lefebvre, B. Maury, C. R. Mecanique 333 (2005).     

Calculation of the averaged three-dimensional boundary layer at the axisymmetrical boundaries of the interblade channels of turbine machines

The article discusses the flow of a gas at the blade rim of an axial turbine, consisting of an external steady-state continuous flow of an ideal compressible liquid and a three-dimensional turbulent boundary layer of a compressible liquid at the end surfaces of the rim, averaged in a peripheral direction. It presents an example of a calculation of flow in fixed blades, with a different form of the meridional cross section. In a flow through the rim of a turbine machine between the convex and concave surfaces of adjacent blades there arises a transverse gradient of the static pressure. At the end surface in the boundary layer the lines of the flow are shifted toward the convex side of the profile, and a secondary transverse flow of the liquid arises [1–3]. The article discusses the following: an external two-dimensional steady-state adiabatic flow of an ideal compressible liquid at the surface S₂, which can be taken as the mean surface of the interblade channel, with boundary lines at the peripheral and root end surfaces of the rim; a two-dimensional steady-state adiabatic flow of an ideal compressible liquid at the end surfaces of the rim between the convex and concave sides of the profiles [3, 4]; and a three-dimensional turbulent boundary layer, averaged in a peripheral direction at the end surfaces of the blade rim. The averaged boundary layer is calculated along one coordinate line s, and a simplified model of the quasi-three-dimensional flow is used. The coefficients of friction and heat transfer, and the inclination of the bottom flow lines are averaged.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–31, May–June, 1975.The author thanks G. Yu. Stepanov for posing the problem and evaluating the results.     

Gas entrainment by a liquid film falling around a stationary Taylor bubble in a vertical tube

Gas entrainment by a liquid film falling around a stationary Taylor bubble in a 0.1 m diameter vertical tube is studied experimentally with the purpose of validating a model formulated in an earlier phase of our research. According to this model for a fixed liquid velocity the gas entrainment should be proportional to the waviness of the film (its intermittency) and the wave height and inversely proportional to the film thickness. For Taylor bubble lengths ranging from 1D to 15D these film parameters have been measured with a Laser Induced Fluorescence technique. The gas entrainment has been determined from the net gas flux into the liquid column underneath the Taylor bubble by using data on gas re-coalescence into the rear of the Taylor bubble. These data are available for lengths ranging from 4.5D to 9D. The model results with the measured film characteristics compare well with the observed gas entrainment. The fact that the net gas flux becomes constant for long Taylor bubbles, whereas the wave height still increases, warrants further study.     

Transfert à une interface liquide/liquide au fond d'une cuve cylindrique à couvercle tournantTransfer at a liquid/liquid interface at the bottom of a cylindrical vessel

The mass transfer at liquid/solid and liquid/liquid interface in the same geometrical and hydrodynamical conditions is the aim of this study. We used an electrodiffusion method with a working electrode in Gallium the melting point of which is near to the room temperature (29.8 °C).We observed similar transfer laws in the liquid/solid and liquid/liquid cases for laminar flow; on the contrary a great difference appears in turbulent flow. This feature can be interpreted by the occurrence of waves at the liquid/liquid interface which strongly increases the transfer. To cite this article: M. Al Radi, G. Cognet, C. R. Mecanique 330 (2002) 327–332.