Jean Fabre

Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow

This work reports the first part of a series of numerical simulations carried out in order to improve knowledge of the forces acting on a sphere embedded in accelerated flows at finite Reynolds number, Re. Among these forces added mass and history effects are particularly important in order to determine accurately particle and bubble trajectories in real flows. To compute these hydrodynamic forces and more generally to study spatially or temporally accelerated flows around a sphere, the full Navier–Stokes equations expressed in velocity–pressure variables are solved by using a finite-volume approach. Computations are carried out over the range 0.1 ≤ Re ≤ 300 for flows around both a rigid sphere and an inviscid spherical bubble, and a systematic comparison of the flows around these two kinds of bodies is presented. Steady uniform flow is first considered in order to test the accuracy of the simulations and to serve as a reference case for comparing with accelerated situations. Axisymmetric straining flow which constitutes the simplest spatially accelerated flow in which a sphere can be embedded is then studied. It is shown that owing to the viscous boundary condition on the body as well as to vorticity transport properties, the presence of the strain modifies deeply the distribution of vorticity around the sphere. This modification has spectacular consequences in the case of a rigid sphere because it influences strongly the conditions under which separation occurs as well as the characteristics of the separated region. Another very original feature of the axisymmetric straining flow lies in the vortex-stretching mechanism existing in this situation. In a converging flow this mechanism acts to reduce vorticity in the wake of the sphere. In contrast when the flow is divergent, vorticity produced at the surface of the sphere tends to grow indefinitely as it is transported downstream. It is shown that in the case where such a diverging flow extends to infinity a Kelvin–Helmholtz instability may occur in the wake. Computations of the hydrodynamic force show that the effects of the strain increase rapidly with the Reynolds number. At high Reynolds numbers the total drag is dramatically modified and the evaluation of the pressure contribution shows that the sphere undergoes an added mass force whose coefficient remains the same as in inviscid flow or in creeping flow, i.e. C M = ½, whatever the Reynolds number. Changes found in vorticity distribution around the rigid sphere also affect the viscous drag, which is markedly increased (resp. decreased) in converging (resp. diverging) flows at high Reynolds numbers.

Oscillations and breakup of a bubble immersed in a turbulent field

A special facility was designed to obtain intense turbulence without significant mean flow. The experiments were performed under microgravity conditions to ensure that turbulence was the only cause of bubble deformation. A scalar parameter, characteristic of this deformation, was obtained by video processing of high-speed movies. The time evolution and spectral representation of this scalar parameter showed the dynamical characteristics of bubble deformation. The signatures of the eigenmodes of oscillation predicted by the linear theory were clearly observed and the predominance of the second mode was proved. In addition, numerical simulations were performed by computing the response of a damped oscillator to the measured turbulence forcing. Simulations and experiments were found to be in good agreement both qualitatively, from visual inspections of the signals, and quantitatively, from a statistical analysis. The role of bubble dynamics in the deformation process has been clarified. On the one hand, the time response of the bubble controls the maximum amount of energy which can be extracted from each turbulent eddy. On the other hand, the viscous damping limits the energy that the bubble can accumulate during its fluctuating deformation

Long waves at the interface between two viscous fluids

Using a perturbation method up to the second order, the equation for long waves at the interface between two viscous fluids is derived for plane Couette–Poiseuille flow, and for moderate surface tension. The leading order equation is the Burgers equation. Higher order terms take into account linear dispersive effects and stabilizing effect of surface tension, and involve two more nonlinear terms. The exactness of the coefficients of this equation has been checked by using symmetry properties. For zero gravity, Poiseuille flow is shown to be stable if and only if the velocity profile is convex. Stable Couette flow can become unstable when the Reynolds number of one fluid is decreased, while keeping the other dimensionless parameters unchanged. Introducing characteristic length scales, the interface equation is put into ‘‘canonical’’ form.

Experimental study of interfacial long waves in a two-layer shear flow

Interfacial stability of two-layer Couette flow was investigated experimentally in a channel bent into an annular ring. This paper is focused on the supercritical long-wave instability which arises for a broad range of flow parameters. Above the critical upper plate velocity, a slowly growing long wave appears with wavelength equal to the perimeter of the channel. Transients of this wave were studied within the theoretical frame of amplitude equations obtained from the long-wave interface equation. Near the onset of instability, the unstable fundamental harmonic is described by the Landau-Stuart equation, and the nonlinear dynamics of the harmonics closely follows the central and slaved modes analysis. For the higher upper plate velocity, harmonics gain some autonomy but they eventually are enslaved by the fundamental, through remarkable collapses of amplitudes and phase jumps leading to wave velocity and frequency locking. Dispersive effects play a crucial role in the nonlinear dynamics. Far from the threshold, the second harmonic becomes unstable and bistability appears: the saturated wave is dominated either by the fundamental harmonic, or by the even harmonics, after periodic energy exchange.

Gas-liquid pipe flow under microgravity conditions: Influence of tube diameter on flow patterns and pressure drops

Abstract Gas-liquid flow experiments have been performed in small tubes of 19 mm, 10 mm and 6 mm diameter, during parabolic flights, for a range of superficial liquid velocities from 0.1 to 2 m/s and superficial gas velocities from 0.05 m/s to 10 m/s. Results are compared to those previously obtained by Colin et al., /1/, in a 40 mm i.d. tube. The flow patterns identified are: bubbly flow, slug flow and a pattern halfway between slug and annular flows. The main difference between the experiments in small tubes and the previous ones, concerns the transition between bubbly flow and slug flow, the role of coalescence and the wall friction factor. Coalescence is shown to play a major role in the transition from bubbly to slug flow. In particular at small Reynolds number coalescence seems to be partly inhibited. Single-phase flow correlations for wall shear stress underestimate the wall friction factor in the intermediate range of Reynolds number between laminar and turbulent flow.

Diffusive turbulence in a confined jet experiment

An experimental analysis of the turbulence in an axisymmetrical jet within a closed tube is presented. At some distance from the nozzle, a turbulent region develops, where the kinetic energy of the mean flow almost vanishes. In this region, the turbulence is transported by turbulent diffusion and its energy decreases with the distance from the inlet. A complete description of the flow field has been achieved using laser Doppler anemometry. Some unusual features are highlighted: the statistical moments of the velocity decay exponentially, the integral length scales remain constant, the radial profiles are self-similar and the Reynolds stress tensor is isotropic and homogeneous in the radial direction. These results highlight the roles of pressure fluctuations and any mean residual motion in the return to isotropy.

Influence of gravity on void distribution in two-phase gas-liquid flow in pipe

Abstract The first results concerning the velocity and void fraction distributions for an air-water bubbly flow in a pipe under microgravity conditions are presented. They are compared to those obtained in upward flow in order to highlight the influence of gravity on the void distribution. In upward flow, a bubble concentration appears near the wall, due to the action of both lift force and of turbulence. In microgravity, the maximum in void fraction is obtained at the pipe axis. Although the lift force becomes very weak, this coring effect cannot easily be explained without considering the local structure of turbulence.

Forward scattered light intensities by a sphere located anywhere in a Gaussian beam

Forward scattering by a sphere located anywhere in a Gaussian beam is calculated by using a simple numerical model based on the Fraunhofer approximation. Comparison to experimental results obtained for glass particles placed in a He–Ne laser beam shows excellent agreement. Computed diffraction patterns are displayed for centered and off-centered particles.

Comparison of diffraction theory and generalized Lorenz-Mie theory for a sphere located on the axis of a laser beam

Scattered light patterns from a spherical particle located on the axis of a Gaussian beam are computed with localized interpretation of the generalized Lorenz-Mie theory and compared with diffraction theory results as well as experimental results.

Le cycle molassique dans le Rameau trans-saharien de la chaîne panafricaine

The fundamental structures of the Pan-African chain are also reflected by the different types of molasse. From west to east, across the Tuareg Shield, one can make the following observations. The West African foreland, 200 km west of the collision zone does not seem to have received detritic material coming from the chain. On the site of the suture zone, there are localities where no major sedimentological discontinuity occurs between the deposition of flysch and molasse. The fluviatile environment is late to appear, mostly to the NW, in the Pan-African segment between the corner of the Tuareg Shield and the Ougarta Mountains. On the active margin characterized by the late calc-alkaline batholiths the molassic series are always incomplete and discontinuous. Many phases of rhyolitic and ignimbritic volcanism occurred, followed by volcanosedimentary formations. In the Eastern Pharusian branch the molassic relics, resting unconformably on the Pan-African basement, have mixed characteristics: volcanics similar to those of the active margin and/or coarse or fine detritics with some carbonates and more or less rhythmic deposits like those in the suture zone. To the east, in the Hoggar Polycyclic domain, here considered as the eastern unit of the chain, outcrops on the western margin testify that the molasses were also deposited here. All these volcanics and sediments were more or less folded by a unique phase of N to NW trend. The first zones to emerge seem to have been the active margin (between 0 to 3°E) and the polycyclic domain. Then, with the exception of the Anti-Atlas, the continental environment prevails everywhere, nearly up to the end of the peneplanation. The formation of a polygenetic surface occurs during the Lower (and perhaps Middle) Cambrian and reveals glacial and aeolian features probably preceded by intense tropical weathering. The final “molassic” detritics (Unite I, arkoses de la Sebkha El Melah), after the last episode of folding, resting unconformably upon the Pan-African series and the true molasses, were deposited during the first step of a marine transgression, coming from the north or the northwest. It is during this latest phase, at the limit of the marine and continental realms, that metals derived from the calc-alkaline rocks were sporadically concentrated.