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Discharge curves ͑ dimensionless flow depth h versus * dimensionless mass flow rate q ) for 0.36-mm glass beads flowing. * ͑ a ͒ W ϭ 25 mm and r ϭ 0.36 mm. ͑ b ͒ W ϭ 48 mm and r ϭ 0.36 mm. ͑ c ͒ W ϭ 48 mm and r ϭ 1 mm.
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This paper presents experimental results on dry granular flows down an inclined rough channel. Different flow regimes were identified depending on the Froude number. For Froude numbers exceeding a critical value (function of the channel slope), flow was characterized by a fairly linear velocity profile and a discharge equation in the form q varies...
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... set of experiments was performed with the broad channel equipped with the 1-mm roughness see Figs. 8c and 9c. For this configuration, the flow pattern differed from the two previous ones in that we did not observe the asymptotic regime U * cst. The mean velocities varied as q * m with m, ranging from 0.33 to 0.45. As the channel was rougher for this set of experiments, a lower mean velocity was expected. This was experimentally checked ...
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Citations
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... This behavior is consistent with previous measurements of downslope granular flows at the sidewall. 6,9,33 The thickness of the moving layer at the sidewall is also significantly less than in mid-chute. Note that as a result of the camera setup (Sec. ...
... Values of / have been obtained for dry, rapid granular flows Physics of Fluids ARTICLE pubs.aip.org/aip/pof using gamma radiation. 33 Attenuation of sound propagating through the moving layer offers a possible approach for quantifying the depthaveraged concentration for submerged flows. The amplitude of sound transmitted through a sediment layer of thickness h is given by A ¼ A 0 expðÀahÞ, where a is the attenuation coefficient and A 0 is the rms signal amplitude recorded with no sediment. ...
The vertical structure of downslope velocity within sub-aqueous gravity-driven flows of (smoother) glass beads and (rougher) natural sand is investigated for both fixed roughness and erodible beds using high-resolution, MHz-frequency acoustics. The observed velocity profiles within the O(1) cm thick, O(10) cm/s flows exhibit a negative shear layer extending downward from the sediment–water interface to a velocity maximum at ∼ 9 grain diameters depth within the layer, below which the velocities decrease to near-zero values at the pre-flow bed location for fixed roughness beds and to non-zero values for mobile beds. The attenuation of sound transmitted through the moving layer is used to constrain the depth-averaged solids concentration to a value of ∼ 0.52. The observed negative shear at the interface indicates that, unlike the sub-aerial case, interfacial friction is dynamically important in gravity-driven sub-aqueous granular flows. It is shown that the observed vertical structure of velocity within the layer can be well represented by continuum viscous flow models. Solids concentration and effective viscosity are estimated from the best-fit model parameters using the Zarraga–Hill–Leighton (2000) empirical relation for suspensions of negatively buoyant particles, yielding vertically averaged values ∼ 0.57. While the sub-millimeter vertical resolution of the measurements is too coarse to provide precise estimates of the friction velocity at the interface, the model-data comparisons nevertheless indicate that the vertical structure of the downslope flow consists of a weakly stratified dense layer and a thin, dilute transition layer between the dense flow and the overlying water.
... Within our approach, the measured μ a would thus correspond to some small but non-zero I, somewhere between 0 and I * , more representative of the characteristic collapse inertial numbers than the smallest ones typically used to extract μ stop from steady inclined flows, which are of order I I 0 = 0.279 (Pouliquen 1999;Jop et al. 2005). Note that setting a higher μ(I = 0) than μ a also appears consistent with the higher friction coefficient values deduced from uniaxial or triaxial compression tests on similar micrometric glass bead materials (Ancey 2001;Adjemian & Evesque 2004;Cui et al. 2017) where friction coefficient values range from tan 26.5 • ∼ 0.5 to tan 30 • ∼ 0.58, much larger than μ a = 0.44, illustrating the sensitivity of avalanche onsets to pressure conditions. Despite its simplicity, this ad hoc hysteretic model thus supports the prominence of low inertial number effects in granular collapses, which appear mostly driven by solid-liquid transitions in the transient case, where the slope is not sufficient to sustain steady flow. ...
In this paper, transient granular flows are examined both numerically and experimentally. Simulations are performed using the continuous three-dimensional (3-D) granular model introduced in Daviet & Bertails-Descoubes ( ACM Trans. Graph. , vol. 35, no. 4, 2016 b , p. 102), which represents the granular medium as an inelastic and dilatable continuum subject to the Drucker–Prager yield criterion in the dense regime. One notable feature of this numerical model is to resolve such a non-smooth rheology without any regularisation. We show that this non-smooth model, which relies on a constant friction coefficient, is able to reproduce with high fidelity various experimental granular collapses over inclined erodible beds, provided the friction coefficient is set to the avalanche angle – and not to the stop angle, as generally done. In order to better characterise the range of validity of the fully plastic rheology in the context of transient frictional flows, we further revisit scaling laws relating the shape of the final collapse deposit to the initial column aspect ratio, and accurately recover established power-law dependences up to aspect ratios of the order of 10. The influence of sidewall friction is then examined through experimental and simulated collapses with varying channel widths. The analysis offers a comprehensive framework for estimating the effective flow thickness in relation to the channel width, thereby challenging previously held assumptions regarding its estimation in the literature. Finally, we discuss the possibility to extend the constant coefficient model with a hysteretic model in order to refine the predictions of the early-stage dynamics of the collapse. This illustrates the potential effects of such phenomenology on transient flows, paving the way to more elaborate analysis.
... In these flows, the mean downslope velocity 〈V x 〉(y) is maximized at the free surface, decreasing down to zero near the bottom ( Figure 6). Such convex velocity profiles are observed in flows confined in narrow channels (see e.g., Ancey, 2001;Courrech du Pont et al., 2003;Jop et al., 2005Jop et al., , 2007Mandal & Khakhar, 2017;GDR MiDi, 2004;Taberlet et al., 2003) and differ from the Bagnold-like velocity profiles obtained for steady and uniform flows in wide channels (see GDR MiDi (2004) or Figure 4 of Fernández-Nieto et al. (2018)). These profiles have a shape that can be approximately fitted by the velocity profiles assumed in Josserand et al. (2004) to describe heap flows: ...
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Granular flows are highly dissipative due to frictional resistance and inelasticity in collisions among grains. They are known to exhibit shock waves at velocities that are easily achieved in industrial and nature-driven flows such as avalanches and landslides. This experimental work investigates the formation of strong shock waves on triangular obstacles placed in a dry rapid granular stream in a confined two-dimensional set-up. Oblique attached shock waves are formed for mild turning angles and higher flow velocities, whereas strong bow shock waves are formed for higher turning angles and slower granular streams. A shadowgraph imaging technique elucidates interesting characteristics of the shock waves, especially in the vicinity of shock detachment. Velocity distributions in the form of scatter plots and probability distribution functions are calculated from the flow field data obtained by particle imaging velocimetry. The flow field around the granular shock wave region represents a bimodal distribution of velocities with two distinct peaks, one representing the supersonic flow within the free stream, and the other corresponding to the subsonic faction downstream of a shock wave. Connecting the two is a population that does not directly belong to either of the modes, constituting the non-equilibrium shock wave region. The effect of grain size and scaling, for fixed free-stream conditions and fixed channel width, on the shock detachment is presented. The mechanisms of the static heap formation and the shock detachment process in a confined environment are discussed.
... To highlight some sections of the velocity field, we plotted profiles along the inclined flume's longitudinal and transverse sections (see continuous white plots in Fig. 3a and b). The velocity field measurements revealed a quasi-uniform behaviour for u(z), with particles at the top moving faster than those at the bottom and a significant basal-slip condition, which was to be expected in such granular experiments (Louge and Keast 2001;Ancey 2001;Hsu et al. 2008). Vertical velocity w(x) profiles were notably less consistent along the flow, where we observed much more vertical particle movement in the flow's leading edge than in its tail, where particle layers just moved on top of each other. ...
This paper shows how a conveyor belt setup can be used to study the dynamics of stationary granular flows. To visualise the flow within the granular bulk and, in particular, determine its composition and the velocity field, we used the refractive index matching (RIM) technique combined with particle tracking velocimetry and coarse-graining algorithms. Implementing RIM posed varied technical, design and construction difficulties. To test the experimental setup and go beyond a mere proof of concept, we carried out granular flow experiments involving monodisperse and bidisperse borosilicate glass beads. These flows resulted in stationary avalanches with distinct regions whose structures were classified as: (i) a convective-bulged front, (ii) a compact-layered tail and, between them, (iii) a breaking size-segregation wave structure. We found that the bulk strain rate, represented by its tensor invariants, varied significantly between the identified flow structures, and their values supported the observed avalanche characteristics. The flow velocity fields’ interpolated profiles adjusted well to a Bagnold-like profile, although a considerable basal velocity slip was measured. We calculated a segregation flux using recent developments in particle-size segregation theory. Along with vertical velocity changes and high expansion rates, segregation fluxes were markedly higher at the avalanche’s leading edge, suggesting a connection between flow rheology and grain segregation. The experimental conveyor belt’s results showed the potential for further theoretical developments in rheology and segregation-coupled models.
Graphic Abstract
... Mass flows are thus typically studied as simplified models of granular flows created in laboratory flumes or chutes [3]. Physical models of this type are based on Froude similarity scaling [1,2,9,28]. However, they create stress fields that only roughly approximate field conditions [15]. ...
... In this paper, we analyze simulated flows obtained with different values of , tuned to obtain different scaling factors N = [1,2,5,10,20,50] . Each acceleration state is in turn tested within centrifuges with normalized radius R/h increasing from 10 to 10 5 . ...
Granular flows are typically studied in laboratory flumes based on common similarity scaling, which create stress fields that only roughly approximate field conditions. The geotechnical centrifuge produces stress conditions that are closer to those observed in the field, but steady conditions can be hardly achieved. Moreover, secondary effects induced by the apparent Coriolis acceleration, which can either dilate or compress the flow, often obscure scaling. This work aims at studying a set of numerical experiments where the effects of the Coriolis acceleration are measured and analyzed. Three flow states are observed: dense, dilute, and unstable. It is found that flows generated under the influence of dilative Coriolis accelerations are likely to become unstable. Nevertheless, a steady dense flow can still be obtained if a large centrifuge is used. A parametric group is proposed to predict the insurgence of instabilities; this parameter can guide experimental designs and could help to avoid damage to the experimental apparatus and model instrumentation.
Graphic abstract
... figure 1 in Forterre & Pouliquen 2008). For a more quantitative comparison, figure 7 shows experimental results by Ancey (2001) for channel flow of glass beads of 1 mm diameter down a rough incline (width 48 mm, slope 27 • , layer thickness 26 mm), see figure 17 in Ancey (2001). We find good agreement between the experimental and numerical density profiles. ...
... figure 1 in Forterre & Pouliquen 2008). For a more quantitative comparison, figure 7 shows experimental results by Ancey (2001) for channel flow of glass beads of 1 mm diameter down a rough incline (width 48 mm, slope 27 • , layer thickness 26 mm), see figure 17 in Ancey (2001). We find good agreement between the experimental and numerical density profiles. ...
... We find good agreement between the experimental and numerical density profiles. The different asymptotic density (Φ for small y) may be attributed to the fact that the experiment uses slightly polydisperse grains ('poorly sorted', no interval given, see table 1 in Ancey 2001). Note that the width of the numerically obtained profile in figure 7 extends to y ≈ 26 mm, which is larger than the initial layer width, h, given above. ...
Granular systems are of a discrete nature. Nevertheless, it can be advantageous to describe their dynamics by means of continuum mechanical methods. The numerical solution of the corresponding hydrodynamic equations is, however, difficult. Therefore, previous numerical simulations are typically geared towards highly specific systems and frequently restricted to two dimensions or mild driving conditions. Here, we present the first robust general simulation scheme for granular hydrodynamics in three dimensions which is not bound to the above limitations. The performance of the simulation scheme is demonstrated by means of three applications which have been proven as notoriously difficult for numerical hydrodynamic description. Although, by construction, our numerical method covers grain-inertia flows, the presented examples demonstrate that it produces reliable results even in the jammed or high density limit.
