Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session D20: Granular Flows IGranular
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Chair: Daniel Lathrop, University of Maryland, College Park Room: 704 |
Sunday, November 19, 2017 2:15PM - 2:28PM |
D20.00001: The Granular Blasius Problem: High inertial number granular flows Jonathan Tsang, Stuart Dalziel, Nathalie Vriend The classical Blasius problem considers the formation of a boundary layer through the change at $x=0$ from a free-slip to a no-slip boundary beneath an otherwise steady uniform flow. Discrete particle model (DPM) simulations of granular gravity currents show that a similar phenomenon exists for a steady flow over a uniformly sloped surface that is smooth upstream (allowing slip) but rough downstream (imposing a no-slip condition). The boundary layer is a region of high shear rate and therefore high inertial number $I$; its dynamics are governed by the asymptotic behaviour of the granular rheology as $I\rightarrow\infty$. The $\mu(I)$ rheology (Jop \textit{et al.} 2006) asserts that $\mathrm{d}\mu/\mathrm{d}I = O(1/I^2)$ as $I\rightarrow\infty$, but current experimental evidence is insufficient to confirm this (Saingier \textit{et al.} 2015). We show that `generalised $\mu(I)$ rheologies', with different behaviours as $I\rightarrow\infty$, all permit the formation of a boundary layer. We give approximate solutions for the velocity profile under each rheology. The change in boundary condition considered here mimics more complex topography in which shear stress increases in the streamwise direction (e.g. a curved slope). Such a system would be of interest in avalanche modelling. [Preview Abstract] |
Sunday, November 19, 2017 2:28PM - 2:41PM |
D20.00002: Towards a universal description of cohesive-particle flows Casey LaMarche, Peiyuan Liu, Kevin Kellogg, Aaron Lattanzi, Christine Hrenya A universal framework for describing cohesive granular flows seems unattainable based on prior works, making a fundamental continuum theory to predict such flows appear unachievable. For the first time, universal behavior of cohesive-grain flows is demonstrated by linking the macroscopic (many-grain) behavior to grain-grain interactions via two dimensionless groups: a generalized Bond number Bo$_{G}$ – ratio of maximum cohesive force to the force driving flow – and a new Agglomerate number Ag – ratio of critical cohesive energy to the granular energy. Cohesive-grain flow is investigated in several systems, and universal behavior is determined via collapse of a cohesion-dependent output variable from each system with the appropriate dimensionless group. Universal behavior is observed using Bo$_{G}$ for dense (enduring-contact-dominated) flows and Ag for dilute (collision-dominated) flows, as Bo$_{G}$ accounts for the cohesive contact force and Ag for increased collisional dissipation due to cohesion. Hence, a new physical picture is presented, namely, Bo$_{G}$ dominates in dense flows, where force chains drive momentum transfer, and Ag dominates in dilute systems, where the dissipative collisions dominate momentum transfer. Apparent discrepancies with past treatments are resolved. [Preview Abstract] |
Sunday, November 19, 2017 2:41PM - 2:54PM |
D20.00003: Blurring the boundary between rapid granular flow and dense granular flow regimes: Evidence from DEM simulations Anurag Tripathi, Mahesh Prasad, Puneet Kumar The saturation of the effective friction coefficient for granular flows at high inertial numbers has been assumed widely by researchers, despite little simulation/experimental evidence. In contrast, a recent simulation study of plane shear flows by Mandal and Khakhar, Phys. Fluids. 28, 103301(2016) suggests that the effective friction coefficient becomes maximum and then starts to decrease with increase in the inertial number for $I>0.5$. In order to investigate whether such a dip at higher inertial numbers is indeed a feature of granular rheology, we perform DEM simulations of chute flow of highly inelastic disks. We show that steady, fully developed flows are possible at inclinations much higher than those normally reported in literature. At such high inclinations, the flow is characterised by a significant slip at the base; the height of the layer increases by more than $300\%$ and kinetic energy of the layer increases by nearly 5 orders of magnitude. We observe, for the first time, steady chute flows at inertial number $I \approx 2$ and show that the dip at higher inertial numbers can be observed in case of chute flow as well. The predictions of modified $\mu-I$ rheology, however, seem to remain valid in the bulk of the layer for packing fractions as low as 0.2. [Preview Abstract] |
Sunday, November 19, 2017 2:54PM - 3:07PM |
D20.00004: ABSTRACT WITHDRAWN |
Sunday, November 19, 2017 3:07PM - 3:20PM |
D20.00005: Ill-posedness of Dynamic Equations of Compressible Granular Flow Michael Shearer, Nico Gray We introduce models for 2-dimensional time-dependent compressible flow of granular materials and suspensions, based on the \begin{figure}[htbp] \centerline{\includegraphics[width=0.22in,height=0.17in]{280720171.eps}} \label{fig1} \end{figure} rheology of Pouliquen and Forterre. The models include density dependence through a constitutive equation in which the density \begin{figure}[htbp] \centerline{\includegraphics[width=0.13in,height=0.17in]{280720172.eps}} \label{fig2} \end{figure} or volume fraction of solid particles with material density $\rho $* is taken as a function of an inertial number I: $\rho =\rho $*$\Phi $(I), in which $\Phi $(I) is a decreasing function of I. This modelling has different implications from models relying on critical state soil mechanics, in which $\rho $ is treated as a variable in the equations, contributing to a flow rule. The analysis of the system of equations builds on recent work of Barker et al in the incompressible case. The main result is the identification of a criterion for well-posedness of the equations. We additionally analyze a modification that applies to suspensions, for which the \begin{figure}[htbp] \centerline{\includegraphics[width=0.22in,height=0.17in]{280720173.eps}} \label{fig3} \end{figure} rheology takes a different form and the inertial number reflects the role of the fluid viscosity. [Preview Abstract] |
Sunday, November 19, 2017 3:20PM - 3:33PM |
D20.00006: Electromagnetic phenomena in granular flows in the laboratory and dusty plasmas in geophysics and astrophysics Daniel Lathrop, Skylar Eiskowitz, Ruben Rojas In clouds of suspended particles, collisions electrify particles and the clouds produce electric potential differences over large scales. This is seen in the atmosphere as lightning in thunderstorms, thundersnow, dust storms, and volcanic ash plumes, but it is a general phenomena in granular systems. The electrification process is not well understood. To investigate the relative importance of particle material properties and collective phenomena in granular and atmospheric electrification, we used several tabletop experiments that excite particle-laden flows. Various electromagnetic phenomena ensue. Measured electric fields result from capacitive and direct charge transfer to electrodes. These results suggest that while particle properties do matter (as previous investigations have shown), macroscopic electrification of granular flows is somewhat material independent and large-scale collective phenomena play a major role. As well, our results on charge separation and Hall effects suggest a very different view of the dynamics of clouds, planetary rings, and cold accretion disks in proto-planetary systems. [Preview Abstract] |
Sunday, November 19, 2017 3:33PM - 3:46PM |
D20.00007: First Observation of a Hall Effect in a Dusty Plasma: A Charged Granular Flow with Relevance to Planetary Rings Skylar Eiskowitz, Nolan Ballew, Rubén Rojas, Daniel Lathrop The particles in Saturn's rings exhibit complex dynamic behavior. They experience solar radiation pressure, electromagnetic forces, and granular collisions. To investigate the possibility of the Hall Effect in the dusty plasma that comprise Saturn's rings, we have built an experiment that demonstrates the Hall Effect in granular matter. We focus on the Hall Effect because the rings' grains become collisionally charged and experience Saturn's dipolar magnetic field and Lorentz forces as they orbit. The experimental setup includes a closed ring-like track where granular matter is forced to circulate driven by compressed air. The structure sits between two electromagnets so that a portion of the track experiences up to a 0.2 T magnetic field. We vary the strength of the field and the speed of the particles. We report the voltage differences between two conducting plates on opposite sides of the track. If Saturn's rings do experience the Hall Effect, the inside and outside of the rings will develop a charge separation that can lead to a radial electric field and various phenomena including orbital effects due to the additional electric forces. Observational evidence from Cassini suggests that Saturn's rings exhibit lighting, supporting the notion that they are electrically charged. [Preview Abstract] |
Sunday, November 19, 2017 3:46PM - 3:59PM |
D20.00008: Abstract Withdrawn
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Sunday, November 19, 2017 3:59PM - 4:12PM |
D20.00009: New Instability Mode in A Driven Granular Gas: Athermal and Thermal Convection Priyanka Shukla, Meheboob Alam For a thermally-driven granular gas confined between two plates under gravity, we report a new instability mode which is found to be active at very small values of the heat-loss parameter. We show that the origin of this new mode is tied to the ``thermal'' mode of the well-studied Rayleigh-Benard convection. This is dubbed {\it purely elastic instability} since it survives even for perfectly elastic collisions ($e_n=1$). The distinction of this new instability mode from its dissipative/athermal counterpart is clarified for the first time. Furthermore, a weakly nonlinear analysis using Stuart-Landau equation has been carried out for both instability modes, and the underlying bifurcation scenario (supercritical/subcritical) from each mode is elucidated. The resulting linear and nonlinear patterns with respect to inelasticity and gravity are compared. [Preview Abstract] |
Sunday, November 19, 2017 4:12PM - 4:25PM |
D20.00010: On the granular fingering instability: controlled triggering in laboratory experiments and numerical simulations Nathalie Vriend, Jonny Tsang, Matthew Arran, Binbin Jin, Alexander Johnsen When a mixture of small, smooth particles and larger, coarse particles is released on a rough inclined plane, the initial uniform front may break up in distinct fingers which elongate over time. This fingering instability is sensitive to the unique arrangement of individual particles and is driven by granular segregation (Pouliquen et al., 1997). Variability in initial conditions create significant limitations for consistent experimental and numerical validation of newly developed theoretical models (Baker et al., 2016) for finger formation. We present an experimental study using a novel tool that sets the initial fingering width of the instability. By changing this trigger width between experiments, we explore the response of the avalanche breakup to perturbations of different widths. Discrete particle simulations (using MercuryDPM, Thornton et al., 2012) are conducted under a similar setting, reproducing the variable finger width, allowing validation between experiments and numerical simulations. A good agreement between simulations and experiments is obtained, and ongoing theoretical work is briefly introduced. [Preview Abstract] |
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