11 results
An experimental investigation of turbulent free-surface flows over a steep permeable bed
- G. Rousseau, C. Ancey
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- Journal:
- Journal of Fluid Mechanics / Volume 941 / 25 June 2022
- Published online by Cambridge University Press:
- 06 May 2022, A51
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Steep streams involve shallow, supercritical turbulent flows over a permeable bed made up of coarse particles. They usually exhibit higher flow resistance and stronger mass and momentum exchanges between the stream and subsurface flow than low-gradient streams. Describing their flow dynamics using generalised Manning–Strickler equations has led to empirical relationships with weak predictive power (errors between predictions and data of over one order of magnitude). We studied shallow turbulent flows by employing a mesoscopic approach based on the double-averaged Navier–Stokes equations. More specifically, we were concerned with the possibility of modelling the turbulent and dispersive shear stress equations using simple algebraic equations. To that end, we studied shallow, supercritical turbulent flows over a sloping bed made up of randomly packed spherical particles. Using visualisation techniques based on particle velocimetry imaging and refractive index matched scanning, we were able to reconstruct the velocity field throughout the bed and stream, far from the sidewalls, and estimate the contributions of the dispersive and turbulent shear stresses to the total shear stress. The dispersive shear stress represented less than 20 % of the turbulent shear stress, but because it was concentrated within a thin layer (called the roughness layer) where it outweighed the turbulent shear stress, it had a significant influence on the mean velocity profile. We proposed an algebraic closure equation for dispersive shear stress, based on the mixing-length model used for turbulent shear stress, and we found that it captured closely the mean-velocity and turbulence-intensity profiles of shallow flows over horizontal or sloping permeable beds. Our data suggest that flow dynamics was affected largely by turbulence damping, drag forces and dispersion within the roughness layer, which may explain why steep streams differ from low-gradient streams.
An experimental scaling law for particle-size segregation in dense granular flows
- T. Trewhela, C. Ancey, J.M.N.T. Gray
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- Journal:
- Journal of Fluid Mechanics / Volume 916 / 10 June 2021
- Published online by Cambridge University Press:
- 20 April 2021, A55
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Particles of differing sizes are notoriously prone to segregation in shear driven flows under the action of gravity. This has important implications in many industrial processes, where particle-size segregation can lead to flow problems and reduced product quality, as well as longer product development and start-up times. Particle-size segregation also readily occurs in many hazardous geophysical mass flows (such as snow avalanches, debris flows and volcanic pyroclastic flows) and can lead to the formation of destructive bouldery flow fronts and significantly longer runouts. Although general theories exist to model particle-size segregation, the detailed functional dependence of the segregation flux on the shear rate, gravity, pressure, particle concentration, grain size and grain-size ratio is still not known. This paper describes refractive-index matched oscillatory shear-cell experiments that shed light on the segregation velocity in the two extreme cases of (i) a single large intruder rising up through a matrix of smaller grains, and (ii) a single small intruder percolating down through a matrix of large particles. Despite the sometimes markedly different time scales for segregation in these two situations, a unifying scaling law has been found that is able to collapse all the experimental data over a wide range of shear rates and grain-size ratios in the range $[1.17,4.17]$. The resulting functional form is easily generalizable to intermediate concentrations and can quantitatively capture laboratory experiments and numerical simulations with a $50\ {:}\ 50$ mix of large and small grains.
Asymmetric breaking size-segregation waves in dense granular free-surface flows
- P. Gajjar, K. van der Vaart, A. R. Thornton, C. G. Johnson, C. Ancey, J. M. N. T. Gray
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- Journal:
- Journal of Fluid Mechanics / Volume 794 / 10 May 2016
- Published online by Cambridge University Press:
- 04 April 2016, pp. 460-505
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Debris and pyroclastic flows often have bouldery flow fronts, which act as a natural dam resisting further advance. Counter intuitively, these resistive fronts can lead to enhanced run-out, because they can be shouldered aside to form static levees that self-channelise the flow. At the heart of this behaviour is the inherent process of size segregation, with different sized particles readily separating into distinct vertical layers through a combination of kinetic sieving and squeeze expulsion. The result is an upward coarsening of the size distribution with the largest grains collecting at the top of the flow, where the flow velocity is greatest, allowing them to be preferentially transported to the front. Here, the large grains may be overrun, resegregated towards the surface and recirculated before being shouldered aside into lateral levees. A key element of this recirculation mechanism is the formation of a breaking size-segregation wave, which allows large particles that have been overrun to rise up into the faster moving parts of the flow as small particles are sheared over the top. Observations from experiments and discrete particle simulations in a moving-bed flume indicate that, whilst most large particles recirculate quickly at the front, a few recirculate very slowly through regions of many small particles at the rear. This behaviour is modelled in this paper using asymmetric segregation flux functions. Exact non-diffuse solutions are derived for the steady wave structure using the method of characteristics with a cubic segregation flux. Three different structures emerge, dependent on the degree of asymmetry and the non-convexity of the segregation flux function. In particular, a novel ‘lens-tail’ solution is found for segregation fluxes that have a large amount of non-convexity, with an additional expansion fan and compression wave forming a ‘tail’ upstream of the ‘lens’ region. Analysis of exact solutions for the particle motion shows that the large particle motion through the ‘lens-tail’ is fundamentally different to the classical ‘lens’ solutions. A few large particles starting near the bottom of the breaking wave pass through the ‘tail’, where they travel in a region of many small particles with a very small vertical velocity, and take significantly longer to recirculate.
Particle-size and -density segregation in granular free-surface flows
- J. M. N. T. Gray, C. Ancey
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- Journal:
- Journal of Fluid Mechanics / Volume 779 / 25 September 2015
- Published online by Cambridge University Press:
- 19 August 2015, pp. 622-668
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When a mixture of particles, which differ in both their size and their density, avalanches downslope, the grains can either segregate into layers or remain mixed, dependent on the balance between particle-size and particle-density segregation. In this paper, binary mixture theory is used to generalize models for particle-size segregation to include density differences between the grains. This adds considerable complexity to the theory, since the bulk velocity is compressible and does not uncouple from the evolving concentration fields. For prescribed lateral velocities, a parabolic equation for the segregation is derived which automatically accounts for bulk compressibility. It is similar to theories for particle-size segregation, but has modified segregation and diffusion rates. For zero diffusion, the theory reduces to a quasilinear first-order hyperbolic equation that admits solutions with discontinuous shocks, expansion fans and one-sided semi-shocks. The distance for complete segregation is investigated for different inflow concentrations, particle-size segregation rates and particle-density ratios. There is a significant region of parameter space where the grains do not separate completely, but remain partially mixed at the critical concentration at which size and density segregation are in exact balance. Within this region, a particle may rise or fall dependent on the overall composition. Outside this region of parameter space, either size segregation or density segregation dominates and particles rise or fall dependent on which physical mechanism has the upper hand. Two-dimensional steady-state solutions that include particle diffusion are computed numerically using a standard Galerkin solver. These simulations show that it is possible to define a Péclet number for segregation that accounts for both size and density differences between the grains. When this Péclet number exceeds 10 the simple hyperbolic solutions provide a very useful approximation for the segregation distance and the height of rapid concentration changes in the full diffusive solution. Exact one-dimensional solutions with diffusion are derived for the steady-state far-field concentration.
A microstructural approach to bed load transport: mean behaviour and fluctuations of particle transport rates
- C. Ancey, J. Heyman
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- Journal:
- Journal of Fluid Mechanics / Volume 744 / 10 April 2014
- Published online by Cambridge University Press:
- 10 March 2014, pp. 129-168
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This paper concerns a model of bed load transport, which describes the advection and dispersion of coarse particles carried by a turbulent water stream. The challenge is to develop a microstructural approach that, on the one hand, yields a parsimonious description of particle transport at the microscopic scale and, on the other hand, leads to averaged equations at the macroscopic scale that can be consistently interpreted in light of the continuum equations used in hydraulics. The cornerstone of the theory is the proper determination of the particle flux fluctuations. Apart from turbulence-induced noise, fluctuations in the particle transport rate are generated by particle exchanges with the bed consisting of particle entrainment and deposition. At the particle scale, the evolution of the number of moving particles can be described probabilistically using a coupled set of reaction–diffusion master equations. Theoretically, this is interesting but impractical, as solving the governing equations is fraught with difficulty. Using the Poisson representation, we show that these multivariate master equations can be converted into Fokker–Planck equations without any simplifying approximations. Thus, in the continuum limit, we end up with a Langevin-like stochastic partial differential equation that governs the time and space variations of the probability density function for the number of moving particles. For steady-state flow conditions and a fixed control volume, the probability distributions of the number of moving particles and the particle flux can be calculated analytically. Taking the average of the microscopic governing equations leads to an average mass conservation equation, which takes the form of the classic Exner equation under certain conditions carefully addressed in the paper. Analysis also highlights the specific part played by a process we refer to as collective entrainment, i.e. a nonlinear feedback process in particle entrainment. In the absence of collective entrainment the fluctuations in the number of moving particles are Poissonian, which implies that at the macroscopic scale they act as white noise that mediates bed evolution. In contrast, when collective entrainment occurs, large non-Poissonian fluctuations arise, with the important consequence that the evolution at the macroscopic scale may depart significantly that predicted by the averaged Exner equation. Comparison with experimental data gives satisfactory results for steady-state flows.
The dam-break problem for concentrated suspensions of neutrally buoyant particles
- C. Ancey, N. Andreini, G. Epely-Chauvin
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- Journal:
- Journal of Fluid Mechanics / Volume 724 / 10 June 2013
- Published online by Cambridge University Press:
- 29 April 2013, pp. 95-122
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This paper addresses the dam-break problem for particle suspensions, that is, the flow of a finite volume of suspension released suddenly down an inclined flume. We were concerned with concentrated suspensions made up of neutrally buoyant non-colloidal particles within a Newtonian fluid. Experiments were conducted over wide ranges of slope, concentration and mass. The major contributions of our experimental study are the simultaneous measurement of local flow properties far from the sidewalls (velocity profile and, with lower accuracy, particle concentration) and macroscopic features (front position, flow depth profile). To that end, the refractive index of the fluid was adapted to closely match that of the particles, enabling data acquisition up to particle volume fractions of 60 %. Particle migration resulted in the blunting of the velocity profile, in contrast to the parabolic profile observed in homogeneous Newtonian fluids. The experimental results were compared with predictions from lubrication theory and particle migration theory. For solids fractions as large as 45 %, the flow behaviour did not differ much from that of a homogeneous Newtonian fluid. More specifically, we observed that the velocity profiles were closely approximated by a parabolic form and there was little evidence of particle migration throughout the depth. For particle concentrations in the 52–56 % range, the flow depth and front position were fairly well predicted by lubrication theory, but taking a closer look at the velocity profiles revealed that particle migration had noticeable effects on the shape of the velocity profile (blunting), but had little impact on its strength, which explained why lubrication theory performed well. Particle migration theories (such as the shear-induced diffusion model) successfully captured the slow evolution of the velocity profiles. For particle concentrations in excess of 56 %, the macroscopic flow features were grossly predicted by lubrication theory (to within 20 % for the flow depth, 50 % for the front position). The flows seemed to reach a steady state, i.e. the shape of the velocity profile showed little time dependence.
Multi-component particle-size segregation in shallow granular avalanches
- J. M. N. T. GRAY, C. ANCEY
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- Journal:
- Journal of Fluid Mechanics / Volume 678 / 10 July 2011
- Published online by Cambridge University Press:
- 01 June 2011, pp. 535-588
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A general continuum theory for particle-size segregation and diffusive remixing in polydisperse granular avalanches is formulated using mixture theory. Comparisons are drawn to existing segregation theories for bi-disperse mixtures and the case of a ternary mixture of large, medium and small particles is investigated. In this case, the general theory reduces to a system of two coupled parabolic segregation–remixing equations, which have a single diffusion coefficient and three parameters which control the segregation rates between each pair of constituents. Considerable insight into many problems where the effect of diffusive remixing is small is provided by the non-diffusive case. Here the equations reduce to a system of two first-order conservation laws, whose wave speeds are real for a very wide class of segregation parameters. In this regime, the system is guaranteed to be non-strictly hyperbolic for all admissible concentrations. If the segregation rates do not increase monotonically with the grain-size ratio, it is possible to enter another region of parameter space, where the equations may either be hyperbolic or elliptic, depending on the segregation rates and the local particle concentrations. Even if the solution is initially hyperbolic everywhere, regions of ellipticity may develop during the evolution of the problem. Such regions in a time-dependent problem necessarily lead to short wavelength Hadamard instability and ill-posedness. A linear stability analysis is used to show that the diffusive remixing terms are sufficient to regularize the theory and prevent unbounded growth rates at high wave numbers. Numerical solutions for the time-dependent segregation of an initially almost homogeneously mixed state are performed using a standard Galerkin finite element method. The diffuse solutions may be linearly stable or unstable, depending on the initial concentrations. In the linearly unstable region, ‘sawtooth’ concentration stripes form that trap and focus the medium-sized grains. The large and small particles still percolate through the avalanche and separate out at the surface and base of the flow due to the no-flux boundary conditions. As these regions grow, the unstable striped region is annihilated. The theory is used to investigate inverse distribution grading and reverse coarse-tail grading in multi-component mixtures. These terms are commonly used by geologists to describe particle-size distributions in which either the whole grain-size population coarsens upwards, or just the coarsest clasts are inversely graded and a fine-grained matrix is found everywhere. An exact solution is constructed for the steady segregation of a ternary mixture as it flows down an inclined slope from an initially homogeneously mixed inflow. It shows that for distribution grading, the particles segregate out into three inversely graded sharply segregated layers sufficiently far downstream, with the largest particles on top, the fines at the bottom and the medium-sized grains sandwiched in between. The heights of the layers are strongly influenced by the downstream velocity profile, with layers becoming thinner in the faster moving near-surface regions of the avalanche, and thicker in the slowly moving basal layers, for the same mass flux. Conditions for the existence of the solution are discussed and a simple and useful upper bound is derived for the distance at which all the particles completely segregate. When the effects of diffusive remixing are included, the sharp concentration discontinuities are smoothed out, but the simple shock solutions capture many features of the evolving size distribution for typical diffusive remixing rates. The theory is also used to construct a simple model for reverse coarse-tail grading, in which the fine-grained material does not segregate. The numerical method is used to calculate diffuse solutions for a ternary mixture and a sharply segregated shock solution is derived that looks similar to the segregation of a bi-disperse mixture of large and medium grains. The presence of the fine-grained material, however, prevents high concentrations of large or medium particles being achieved and there is a significant lengthening of the segregation distance.
Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts
- J. M. N. T. GRAY, C. ANCEY
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- Journal:
- Journal of Fluid Mechanics / Volume 629 / 25 June 2009
- Published online by Cambridge University Press:
- 15 June 2009, pp. 387-423
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Stratification patterns are formed when a bidisperse mixture of large rough grains and smaller more mobile particles is poured between parallel plates to form a heap. At low flow rates discrete avalanches flow down the free surface and are brought to rest by the propagation of shock waves. Experiments performed in this paper show that the larger particles are segregated to the top of the avalanche, where the velocity is greatest, and are transported to the flow front. Here the particles are overrun but may rise to the free surface again by size segregation to create a recirculating coarse-grained front. Once the front is established composite images show that there is a steady regime in which any additional large grains that reach the front are deposited. This flow is therefore analogous to finger formation in geophysical mass flows, where the larger less mobile particles are shouldered aside to spontaneously form static lateral levees rather than being removed by basal deposition in two dimensions. At the heart of all these phenomena is a dynamic feedback between the bulk flow and the evolving particle-size distribution within the avalanche. A fully coupled theory for such segregation–mobility feedback effects is beyond the scope of this paper. However, it is shown how to derive a simplified uncoupled travelling-wave solution for the avalanche motion and reconstruct the bulk two-dimensional flow field using assumed velocity profiles through the avalanche depth. This allows a simple hyperbolic segregation theory to be used to construct exact solutions for the particle concentration and for the recirculation within the bulk flow. Depending on the material composition and the strength of the segregation and deposition, there are three types of solution. The coarse-particle front grows in length if more large particles arrive than can be deposited. If there are fewer large grains and if the segregation is strong enough, a breaking size-segregation wave forms at a unique position behind the front. It consists of two expansion fans, two shocks and a central ‘eye’ of constant concentration that are arranged in a ‘lens-like’ structure. Coarse grains just behind the front are recirculated, while those reaching the head are overrun and deposited. Upstream of the wave, the size distribution resembles a small-particle ‘sandwich’ with a raft of rapidly flowing large particles on top and a coarse deposited layer at the bottom, consistent with the experimental observations made here. If the segregation is weak, the central eye degenerates, and all the large particles are deposited without recirculation.
The dam-break problem for viscous fluids in the high-capillary-number limit
- C. ANCEY, S. COCHARD, N. ANDREINI
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- Journal:
- Journal of Fluid Mechanics / Volume 624 / 10 April 2009
- Published online by Cambridge University Press:
- 10 April 2009, pp. 1-22
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Experiments were undertaken to investigate dam-break flows where a finite volume of highly viscous fluid (glucose with viscosity μ ≈ 350 Pa s) maintained behind a lock gate was released into a horizontal or inclined flume. The resulting sequence of flow-depth profiles was tracked using a three-dimensional visualization system. In the low-Reynolds-number and high-capillary-number limits, analytical solutions can be obtained from the Navier–Stokes equations using lubrication theory and matched asymptotic expansions. At shallow slopes, similarity solutions can also be worked out. While the variation in the front position scaled with time as predicted by theory for both horizontal and sloping flumes, there was a systematic delay in the front position observed. Moreover, taking a closer look at the experimental flow-depth profiles shows that they were similar, but they noticeably deviated from the theoretical similarity form for horizontal planes. For sloping beds, the flow-depth profile is correctly predicted provided that different scalings are used at shallow and large slopes.
Entrainment and motion of coarse particles in a shallow water stream down a steep slope
- C. ANCEY, A. C. DAVISON, T. BÖHM, M. JODEAU, P. FREY
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- Journal:
- Journal of Fluid Mechanics / Volume 595 / 25 January 2008
- Published online by Cambridge University Press:
- 08 January 2008, pp. 83-114
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We investigate the entrainment, deposition and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope. This is an idealization of bed-load transport in mountain streams. Earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics. The intermittent character of particle transport at low-water discharges led us to consider it as a random process. Sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles. We develop a birth–death immigration–emigration Markov process to describe the particle exchanges between the bed and the water stream. A key feature of the model is its long autocorrelation times and wide, frequent fluctuations in the solid discharge, a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments. We present experimental data obtained using a nearly two-dimensional channel and glass beads as a substitute for sediment. Entrainment, trajectories, and deposition were monitored using a high-speed digital camera. The empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model. Experiments confirmed the existence of wide and frequent fluctuations of the solid discharge, and revealed the existence of long autocorrelation time, but theory overestimates the autocorrelation times by a factor of around three. Particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model, which performs well when a single particle is moving. For our experiments, the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity. We also noted significant changes in the behaviour of particle transport when the bed slope or the water discharge was increased. The more vigorous the stream was, the more continuous the solid discharge became. Moreover, although 90% of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10%, particles dissipate more and more energy when the bed slope is increased, but surprisingly, the dissipation rate is nearly independent of fluid velocity. A movie is available with the online version of the paper.
Transmission Electron Microscopy Study of FeHfN Thin Films for Magnetic Properties Optimization and Integration Above Silicon Circuits.
- R Pantel, S Couderc, P Ancey, C Wyon, B Viala
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- Journal:
- Microscopy and Microanalysis / Volume 11 / Issue S02 / August 2005
- Published online by Cambridge University Press:
- 01 August 2005, pp. 1804-1805
- Print publication:
- August 2005
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Extended abstract of a paper presented at Microscopy and Microanalysis 2005 in Honolulu, Hawaii, USA, July 31--August 4, 2005