Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session M12: Granular Flows: Shear and Drag |
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Chair: Eric DeGiuli, NYU Room: 200 |
Tuesday, November 24, 2015 8:00AM - 8:13AM |
M12.00001: Energy Dissipation in Inertial Granular Flow Eric DeGiuli, Jim McElwaine, Matthieu Wyart Experiments and simulations have shown the utility of considering dense inertial flow of frictional granular materials as a function of the inertial number $I$. However, the dependence of the rheology on the particle-particle friction coefficient $\mu_p$ has hardly been studied. In this work we use numerical simulations to systematically study the dense-flow rheology over a large range of $I$ and $\mu_p$, leading to a phase diagram with 3 phases: frictionless, frictional, and super-frictional. By studying carefully energy dissipation in steady flow, we delineate the boundary of the frictionless regime in the $(\mu_p, I)$ plane, and find, surprisingly, two regimes of frictional flow. We show that the flow dynamics of the frictionless regime quantitatively agrees with the theory proposed in DeGiuli et al PRE 91, 062206 (2015). Moreover, in the superfrictional regime at very large $\mu_p$, the rheology is also strikingly similar to frictionless flow. We are able to understand the crossovers between these regimes by a scaling analysis of energy dissipation. [Preview Abstract] |
Tuesday, November 24, 2015 8:13AM - 8:26AM |
M12.00002: A system-spanning vortex in granular shear flow explains a stress anomaly Prabhu Nott, Krishnaraj K P, Peter Varun Dsouza Rheometry of fluids is often conducted in a cylindrical Couette device, but when it is used for granular materials, unexpected behaviour emerges. Recent studies in our group have shown a striking anomaly in the stress: the vertical shear stress changes sign upon shearing, and the magnitudes of all components of the stress increase roughly exponentially with depth. This behavior is contrary to previous experiments, and the predictions of plasticity theories. In this presentation we show that the stress anomaly is caused by a novel secondary flow -- a single toroidal vortex that spans the entire granular column. The vortex differs fundamentally in its origin and manifestation from the Taylor-Couette vortices in fluids. It is driven by dilatancy, and is sustained by gravity. Our results raise the possibility of similar secondary flows arising in other flow geometries, and call for caution in the interpretation of rheological measurements for granular materials. [Preview Abstract] |
Tuesday, November 24, 2015 8:26AM - 8:39AM |
M12.00003: Anisotropy in rotating drums Timothy Povall, Andrew McBride, Indresan Govender An anisotropic relationship between the stress and the strain rate has been observed in two-dimensional simulations of rotating drums.\footnote{\label{C}P.-P. Cortet et al., EPL, {\bf 88}, 2009} The objective of this work is to investigate the structure of the constitutive relation using three-dimensional discrete-element-method simulations of a rotating drum containing identical rigid spheres for a range of rotational speeds. Anisotropy is quantified from the alignment of the stress and strain rate tensors, with the strain rate computed using a least-squares fit.\footnote{C.H. Rycroft et al., JMPS, {\bf 57}, 2009} It is shown that in certain regions there is a strong anisotropic relationship, regardless of the speed of rotation. The effective friction coefficient\footnote{Jop et al., Nature, \bf{441}, 2006} is examined in order to determine the phase space in which the $\mu(I)$ rheology is valid. Lastly, a depth-averaged approach through the flowing layer is employed to determine the relationship between the velocity tangential to the equilibrium surface and the height of the flowing layer. A power-law relationship that approaches linear at high speeds is observed. [Preview Abstract] |
Tuesday, November 24, 2015 8:39AM - 8:52AM |
M12.00004: Dynamics of an intruder pulled slowly from a granular material Yue Zhang, Abe Clark, Robert Behringer What is the response of a granular material and an object buried in the material as the object is pulled out? To address this question, we use an experiment where the grains are 2D photoelastic disks to visualize the pull out dynamics for different circular intruders. We apply forces that are close to the minimum to initiate intruder motion. We observe the intruder motion, z(t), and the disk photoelastic response. We numerically differentiate z(t), to yield the intruder velocity, v(t), and acceleration, a(t). After transients, we find v(t)$=$c*exp(b*t), where coefficients c and b depend on the intruder, particularly, b decreases when increasing intruder size. Why does velocity depend exponentially on time, or equivalently why does acceleration linearly change with displacement? To answer this question, we compute the drag force caused by the granular disks from the acceleration of the intruder. The result shows that the drag force depends linearly on the thickness of disks above the intruder, which also changes linearly with the displacement of the intruder. However, the drag force is much bigger than the weight of particles above the intruder. Ongoing work focuses on illuminating the cause for the observed drag force. [Preview Abstract] |
Tuesday, November 24, 2015 8:52AM - 9:05AM |
M12.00005: Continuum equations for dense shallow granular flows Viswanathan Kumaran Simplified equations are derived for a granular flow in the `dense' limit where the volume fraction is close to that for dynamical arrest, and the `shallow' limit where the stream-wise length for flow development ($L$) is large compared to the cross-stream height ($h$). In the dense limit, the equations are simplified by taking advantage of the power-law divergence of the pair distribution function $\chi$ proportional to $(\phi_{ad} - \phi)^{- \alpha}$, where $\phi$ is the volume fraction, and $\phi_{ad}$ is the volume fraction for arrested dynamics. When the height $h$ is much larger than the conduction length, the energy equation reduces to an algebraic balance between the rates of production and dissipation of energy, and the stress is proportional to the square of the strain rate (Bagnold law). The analysis reveals important differences between granular flows and the flows of Newtonian fluids. One important difference is that the Reynolds number (ratio of inertial and viscous terms) turns out to depend only on the layer height and Bagnold coefficients, and is independent of the flow velocity, because both the inertial terms in the conservation equations and the divergence of the stress depend on the square of the velocity/velocity gradients. [Preview Abstract] |
Tuesday, November 24, 2015 9:05AM - 9:18AM |
M12.00006: Drag on intruder in dense granular flows Hu Zheng, Jonathan Bares, Dong Wang, Robert Behringer We perform an experimental study on an intruder dragged at a constant force in a quasi-statically cyclic-sheared granular medium. A Teflon disk is embedded in a layer of bidisperse photoelastic disks. The granular medium is contained in a horizontal square cell, which can be deformed into a parallelogram with the same area to produce simple shear. We find that the forward motion of the intruder happens at the fragile state during shear reversals, while only reversible affine motion could be found at the Jammed state. There is a burst of non-affine motion for the granular particles at each shear reversal. For a range of packing fractions, the cumulative intruder displacement shows a linear increase proportional to the number of cycles of shear. To explain the behavior of intruder motion, we analyze the coordination number, density, affine and non-affine motion of disk-granular system variations as the shear strain. [Preview Abstract] |
Tuesday, November 24, 2015 9:18AM - 9:31AM |
M12.00007: Steady State Erosion of Granular Particles by Shear Flow Benjamin Allen, Arshad Kudrolli Despite decades of scientific observation of rivers, streams and laboratory experiments the process of erosion still is not understood. Empirical fits are used to determine when erosion starts with more than an order of magnitude scatter or a shifting power law determining how much material erodes away. In order to study the many body problem of multiple particles we first need to understand the basics of a single particle eroding from a potential well in laminar flow. Using different particle densities and different barrier heights we looked at the onset of erosion and the balance of forces and torques to create a predictive model of when a single particle will erode over a barrier of a given height as a function of shear rate and viscosity. We then create a steady state system in which to image erosion as it happens and simultaneously measure flow velocity and particle movement. Measuring particle movement allows us to determine when steady state erosion occurs and calculate the fluxes and slip velocities at the beginning of the erosion process as we transition from rolling particles to particles suspended in the fluid flow. [Preview Abstract] |
Tuesday, November 24, 2015 9:31AM - 9:44AM |
M12.00008: DEM simulation of flow of dumbbells on a rough inclined plane Sandip Mandal, Devang Khakhar The rheology of non-spherical granular materials such as food grains, sugar cubes, sand, pharmaceutical pills, among others, is not understood well. We study the flow of non-spherical dumbbells of different aspect ratios on a rough inclined plane by using soft sphere DEM simulations. The dumbbells are generated by fusing two spheres together and a linear spring dashpot model along with Coulombic friction is employed to calculate inter-particle forces. At steady state, a uni-directional shear flow is obtained which allows for a detailed study of the rheology. The effect of aspect ratio and inclination angle on mean velocity, volume fraction, shear rate, shear stress, pressure and viscosity profiles is examined. The effect of aspect ratio on probability distribution of angles, made by the major axes of the dumbbells with the flow direction, average angle and order parameter is analyzed. The dense flow rheology is well explained by Bagnold's law and the constitutive laws of JFP model [Jop et. al., Nature 441, 727 (2006)]. The dependencies of first and second normal stress differences on aspect ratio are studied. The probability distributions of translational and rotational velocity are analyzed. [Preview Abstract] |
Tuesday, November 24, 2015 9:44AM - 9:57AM |
M12.00009: The propagation and deposition process of a finite dry granular mass down a rough incline Geng Lin Lee, Fu-Ling Yang This work presents a theoretical analysis on the propagation and arresting process of a $2D$ finite granular mass in shallow configuration down a rough incline. The coherence-length constitutive model proposed by Ertas and Halsey (2002) is used to solve the bulk motion and local coherence length scale, $l(x,t)$, that characterizes internal granular clusters. Flow depth profile, $h(x,t)$, governed by an advection-diffusion equation is solved by the matched asymptotic method under shallowness and used to determine a flow front trajectory, $x_f(t)$. The solutions reveal $l(x,t) < h(x,t)$ in the front indicating the clusters can move freely and transport momentum flux in a flowing bulk. The trend of $l(x,t)$ shows monotonic growing and becomes comparable to $h(x,t)$ upstream, indicating clusters transmit basal decelerating impulse to decelerate the flow, giving rise to rear deposit. The critical location where $l(x,t)=h(x,t)$ is solved to the leading order to determine a deposition front trajectory, $x_d(t)$. Under the constraint of conserved total mass, finite run-out distance, $L_d$, and arrested time, $T_d$, are estimated and used to construct a modified front propagation model, $x_{fm}(t)$, which compares well to the experimental data reported in Pouliquen and Forterre (2002) [Preview Abstract] |
Tuesday, November 24, 2015 9:57AM - 10:10AM |
M12.00010: How do fish hide in the sand: erosion by an oscillating foil Alban Sauret, Cyprien Morize, Guillaume Quibeuf, Philippe Gondret In a large number of natural and technological situations, a granular bed can be resuspended by a fluid flow. In some situations, this resuspension may be to avoid, for instance when a helicopter lands in sandy environments and the generated sand cloud limits the visibility, which can lead to catastrophic events. Here, we focus on a unique situation, in which the resuspension of particles is both sought after and well controlled. Indeed, some bottom-dwelling fish, such as the flounders and stingrays, generate a flow capable of resuspending sand, to bury themselves and avoid predators. By flapping their fins with oscillating motions, they create vortices and a recirculating flow that lifts the sand particles up and deposits them on top of their backs. A simple model experiment has been developed to study this situation: a rigid or flexible foil is placed above a sand bed to mimic the fin motion. We experimentally characterized the influence of the amplitude and frequency of the motion, the distance to the granular bed and the nature of the granular material on the onset of erosion. These experimental findings are rationalized to predict the required motion to erode and resuspend the granular bed. [Preview Abstract] |
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