Fluid boundary of a viscoplastic Bingham flow for finite solid deformations

The modelling of viscoplastic Bingham fluids often relies on a rheological constitutive law based on a "plastic rule function" often identical to the yield criterion of the solid state. It is also often assumed that this plastic rule function vanishes at the boundary between the solid and fluid states, based on the fact that it is true in the limit of small deformations of the solid state or for simple yield criteria. We show that this is not the case for finite deformations by considering the example of a two state flow on a tilted plane where the solid state is described by a Neo-Hookean model with a Von Mises yield criterion. This opens new approaches for the modelling and the computation of the fluid state boundaries

On the existence and evolution of a spanwise vortex in laminar shallow water dipoles

The present work investigates the existence and evolution of a spanwise vortex at the front of shallow dipolar vortices. The vortex dipoles are experimentally generated using a double flap apparatus. Particle image velocimetry measurements are performed in a horizontal plane and in the vertical symmetry plane of the flow. The dynamics of such vortical structures is investigated through a parametric study in which both the Reynolds number Re=U0D0/ν∈[90,470] and the aspect ratio α = h/D0∈[0.075,0.7],associated with the shallowness of the flow, are varied, where U0 is the initial velocity of the vortex dipole, D0 is the initial diameter, h is the water depth, and v is the kinematic viscosity of the fluid. The present experiments confirm the numerical results obtained in a companion paper by Duran-Matute et al. [Phys. Fluids 22, 116606 (2010)], namely that the flow remains quasi parallel with negligible vertical motions below a critical value of the parameter α2Re. By contrast, for large values of α2Re and α≲0.6, a three-dimensional regime is observed in the shape of an intense spanwise vortex generated at the front of the dipole. The present study reveals that the early-time motion and dynamics of the spanwise vortex do not scale on the unique parameter α2Re but is strongly influenced by both the aspect ratio and the Reynolds number. A mechanism for the generation of the spanwise vortex is proposed. For α≳0.6, a third regime is observed, where the spanwise vortex is replaced by a vorticity tongu

Steady and unsteady shear flows of a viscoplastic fluid in a cylindrical Couette cell

Abstract Yield stress fluid flows in Couette cells have been widely studied in the last decades for their intriguingly exhibiting phenomena. In this paper, we use a {PIV} technique to investigate the axisymmetric flow and rheological properties of a Carbopol gel in a relatively wide cylindrical Couette device. Carbopol gel is known to exhibit viscoplastic behavior and is often described using a Herschel–Bulkley law, which is characterized by a plastic yield stress τ y and a shear-dependent nonlinear viscosity. In some cases, the elasticity of the material has to be accounted for to understand the whole dynamics of the system, in particular for unsteady flows as observed in the present study. Two set of experiments are conducted here in order to highlight these different rheological behaviors and the resulting dynamics: (i) a steady shear configuration and (ii) an unsteady shear configuration, in which the angular velocity of the inner cylinder is either constant or time dependent ( sin profile), respectively. In the steady configuration, a simple optimization model, based on the Herschel–Bulkley law, is developed to extract the rheological parameters of the viscoplastic contribution of the gel from the steady velocity fields. Results are shown to be in good agreements with rheological parameters obtained from a standard rheometer. On the other hand, the elastic contribution of the material is highlighted in the unsteady shear configuration, for which a spatio-temporal transition between solid-elastic and fluid behaviors is observed. Different models are proposed to describe the dynamics of the unsteady flow. First, quasi-steady state models allow to predict both the fluid shear zone close to the inner cylinder and the elastic deformation of the material as long as their contributions can be decoupled in space and in time. For more complex dynamics, i.e. when the flow becomes strongly unsteady, an elasto-viscoplastic model is developed to describe the flow dynamics. It is shown to quantitatively reproduce the experimental measurements. Finally, an elastic wave model is derived to describe an elastic front propagating from the inner cylinder to the outer one, and observed at every half forcing period. The front velocity is thus shown to scale on the phase velocity of an elastic wave in a deformable solid

Critical slope for laminar transcritical shallow-water flows

Backwater curves denote the depth profiles of steady flows in a shallow open channel. The classification of these curves for turbulent regimes is commonly used in hydraulics. When the bottom slope I is increased, they can describe the transition from fluvial to torrential regimes. In the case of an infinitely wide channel, we show that laminar flows have the same critical height hc as that in the turbulent case. This feature is due to the existence of surface slope singularities associated to plug-like velocity profiles with vanishing boundary-layer thickness. We also provide the expression of the critical surface slope as a function of the bottom curvature at the critical location. These results validate a similarity model to approximate the asymptotic Navier–Stokes equations for small slopes I with Reynolds number Re such that ReI is of order 1

Experimental characterization of the 3D dynamics of a laminar shallow vortex dipole

Experimental results on the dynamics of a vortex dipole evolving in a shallow fluid layer are presented. In particular, the generation of a spanwise vortex at the front of the dipole is observed in agreement with previous experiments at larger Reynolds numbers. The results show that this secondary vortex is of comparable strength to the dipole. The present physical analysis suggests that the origin of this structure involves the stretching induced by the dipole of the boundary-layer vorticity generated by the dipole's advection over the no-slip bottom

A simple immersed-boundary method for solid-fluid interaction in constant- and stratified-density flows

The present work reports on the simulation of two- and three-dimensional constant- and stratifieddensity flows involving fixed or moving objects using an immersed-boundary method. The numerical approach is based on a simple immersed-boundary method in which no explicit Lagrangian marking of the immersed boundary is used. The solid object is defined by a continuous solid volume fraction which is updated thanks to the resolution of the Newton’s equations of motion for the immersed object. As shown on several test cases, this algorithm allows the flow field near the solid boundary to be correctly captured even though the numerical thickness of the transition region separating the fluid from the object is within three computational cells approximately. The full set of governing equations is then used to investigate some fundamental aspects of solid–fluid interaction, including fixed and moving objects in constant and stratified-density flows. In particular, the method is shown to accurately reproduce the steady-streaming patterns observed in the near-region of an oscillating sphere, as well as the so-called Saint Adrew’s cross in the far-field when the sphere oscillates in a rotating stratified fluid. The sedimentation of a particle in a stratified ambient is investigated for particle Reynolds numbers up to Oð103Þ and the effect of stratification and density ratio is addressed. While the present paper only consider fluid–solid interaction for a single object, the present approach can be straightforwardly extended to the case of multiple objects of arbitrary shape moving in a stratified-density flow

Investigation of the swash zone evolution at wave time scale

The present work is dedicated to the study of the swash zone bed evolution at a high temporal and spatial resolution to investigate single-wave to wave-group time scales. The measurements are obtained in a large scale wave flume with a 1/15 sloping beach of well-sorted sand (d₅₀= 250 μm). The wave regime considered is a random Jonswap spectrum (peak enhancement factor γ = 3.3, significant wave height Hₛ= 0.53 m and peak period Tₚ = 4.14 s). A stereoscopic technique (Astruc et al., 2012) has been used to measure the sand bed evolution in the swash zone over a 3×2 m² area. This experiment allows us to capture the swash dynamics and the bottom evolution at the different temporal scales. The results prove the strong correlation between wave forcing and swash zone response over the entire experiment, even if the bottom evolves. At shorter time scales, we can observe the signature of gravity and infragravity waves. We showed that at both time scales, the erosion process exhibits a strong variability in time as accretion and erosion events are observed. The spatial variability of the bottom evolution is stronger at gravity than at infragravity time scales. These results reinforce the now-admitted idea that the mean evolution of the sand bed in the swash zone is the result of several events of a very different nature, which themselves depend on the details of the swash hydrodynamics

Dynamique d'un fluide élasto-viscoplastique cisaillé

L'écoulement de fluides viscoplastiques dans une cellule de Couette a été souvent considéré comme écoulement canonique pour décrire les différents phénomènes associés à ces fluides. Dans ce papier, nous utilisons une technique PIV pour caractériser l'écoulement axisymétrique d'un gel Carbopol dans une cellule de Couette relativement large. Le Carbopol présente un comportement viscoplastique et est souvent décrit par le modèle de Herschel-Bulkley, caractérisé par un seuil plastique Τy et une viscosité dépendant du cisaillement. Dans certains cas, l'élasticité du gel doit être prise en compte pour comprendre la dynamique du système, en particulier pour des écoulements instationnaires comme considérés dans cette étude. Un cisaillement instationnaire, imposé par un mouvement oscillant du cylindre intérieur (fonction sin), est considéré ici. Dans ce cas, la contribution élastique est mise en évidence, avec en particulier la description d'une transition spatio-temporelle entre des comportements élastiques et visqueux. Un modèle élasto-viscoplastique est développé pour décrire ces écoulements. Un bon accord quantitatif est obtenu avec les expériences. Enfin, un modèle d'onde élastique est présenté pour décrire l'évolution d'un front d'onde se propageant du cylindre intérieur vers le cylindre extérieur, observé à chaque demi-période du forçage. La vitesse du front peut alors être comparée à la célérité d'une onde élastique d'un milieu solide déformable

A three-dimensional experimental investigation of the structure of the spanwise vortex formed by a shallow vortex dipole

The three-dimensional dynamics of shallow vortex dipoles is investigated by means of an innovative 3D-3C (three dimensions, three components) scanning PIV technique. In particular, the three-dimensional structure of a frontal spanwise vortex is characterized. The technique also allows the computation of the pressure field, which is not available using standard 2D PIV measurement. The influence of such complex vortex structures on the mass transport is discussed in light of the available pressure field

A three-dimensional experimental investigation of the structure of the spanwise vortex generated by a shallow vortex dipole

The three-dimensional dynamics of shallow vortex dipoles is investigated by means of an innovative three-dimensional, three-component (3D-3C) scanning PIV technique. In particular, the three-dimensional structure of a frontal spanwise vortex is characterized. The technique allows the computation of the three-dimensional pressure field and the planar (x, y) distribution of the wall shear stress, which are not available using standard 2D PIV measurements. The influence of such a complex vortex structure on mass transport is discussed in the context of the available pressure and wall shear stress fields