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 R12: Granular Flows: Fluctuations and Instabilities |
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Chair: Nathalie Vriend, University of Cambridge Room: 200 |
Tuesday, November 24, 2015 12:50PM - 1:03PM |
R12.00001: Avalanches in a V-shape: inverted roll-waves and a curved free surface Nathalie Vriend, Jim McElwaine In this work, we create avalanches in a V-shaped channel at different apertures and flowrates. For deep flows (at high apertures and flowrates), roll waves are triggered that have surprising features due to the chosen V-shape geometry. For shallower flows (low to medium apertures), the effects of roll waves are reduced and/or eliminated and the base flow appears. This background base flow is characterized by a curved free surface and recirculation cells whose structure and position is a strong function of the flowrate. An alternative rheology is proposed which accounts for this background base flow in terms of second-order stress differences. [Preview Abstract] |
Tuesday, November 24, 2015 1:03PM - 1:16PM |
R12.00002: Continuum modelling of piston driven shock waves through granular gases and ensuing pattern formations Nick Sirmas, Matei Radulescu Two-dimensional event-driven Molecular Dynamics (MD) simulations were previously completed to investigate the stability of piston driven shock waves through dilute granular gases. By considering viscoelastic collisions, allowing for finite dissipation within the shock wave, instabilities were found in the form of distinctive high density non-uniformities and convective rolls within the shock structure. This work is now extended to the continuum level. Euler and Navier-Stokes equations for granular gases are modelled with a modified cooling rate to include an impact threshold necessary for inelastic collisions. The shock structure predicted by the continuum formulation is found in good agreement with the structure obtained by MD. Non-linear stability analyses of the travelling wave solution are performed, showing a neutrally stable structure and responding only to fluctuations in the upstream state. Introducing strong perturbations to the incoming density field, in accordance with the spacial fluctuations in upstream state seen in MD, yields similar instabilities as those previously observed. While the inviscid model predicts a highly turbulent structure from these perturbations, the inclusion of viscosity yields comparable wavelengths of pattern formations to those seen in MD. [Preview Abstract] |
(Author Not Attending)
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R12.00003: Plane shock waves and Haff's law in a granular gas Lakshminarayana Reddy, Meheboob Alam The Riemann problem of planar shock waves is analyzed for a dilute granular gas by solving Euler- and Navier-Stokes-order equations numerically. The density and temperature profiles are found to be asymmetric, with the maxima of both density and temperature occurring within the shock-layer. The density-peak increases with increasing Mach number and inelasticity, and is found to propagate at a steady speed at late times. The granular temperature at the upstream end of the shock decay according to Haff's law [$\theta(t)\sim t^{-2}$], but the downstream temperature decays faster than its upstream counterpart. The Haff's law seems to hold inside the shock up-to a certain time for weak shocks, but deviations occur for strong shocks. The time at which the maximum temperature deviates from Haff's law follows a power-law scaling with upstream Mach number and the restitution coefficient. The continual build-up of density inside the shock is discussed, the origin of which seems to be tied to a pressure instability in granular gases. It is shown that the granular energy equation must be `regularized' to arrest the maximum density, and the regularized hydrodynamic equations should be used for shock calculations (Reddy \& Alam, 2015, J. Fluid Mech., to be published). [Preview Abstract] |
(Author Not Attending)
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R12.00004: Rarefaction effects in dilute granular Poiseuille flow: Knudsen minimum and temperature bimodality Achal Mahajan, Meheboob Alam The gravity-driven flow of smooth inelastic hard-disks through a channel, analog of granular Poiseuille flow, is analysed using event-driven simulations. We find that the variation of the mass-flow rate ($Q$) with Knudsen number ($Kn$) can be non-monotonic in the elastic limit (i.e.~the restitution coefficient $e_n\to 1$) in channels with very smooth walls. The {\it Knudsen minimum effect} (i.e.~the minimum flow rate occurring at $Kn\sim O(1)$ for the Poiseuille flow of a molecular gas) is found to be absent in a granular gas with $e_n\leq 0.99$, irrespective of wall roughness. Another rarefaction phenomenon, the {\it bimodality} of the temperature profile, with a local minimum at the channel centerline and two symmetric maxima ($T_{\max}$) away from the centerline, is studied. We show that the inelastic dissipation is responsible for the onset of temperature bimodality [i.e.~the excess temperature, $\triangle T= (T_{\max}/T_{\min}-1)\neq 0$] near the continuum limit ($Kn\sim 0$), but the rarefaction being its origin (as in molecular gas) holds beyond $Kn\sim O(0.1)$. The competition between dissipation and rarefaction seems to be responsible for the observed dependence of both mass-flow rate and temperature bimodality on $Kn$ and $e_n$. [Alam etal. 2015, JFM (revised)]. [Preview Abstract] |
Tuesday, November 24, 2015 1:42PM - 1:55PM |
R12.00005: Transition in a granular chute flow due to periodic and aperiodic perturbations Bharathraj S, Kumaran V Granular flow down an inclined plane exhibits a transition from a disordered,random state to an ordered state with layers of particles with in-layer hexagonal order, when there is a small change in the roughness of the base. In earlier studies,a rough base was created using a random arrangement of frozen particles at the base,and the roughness was varied by varying the ratio of the frozen and moving particle diameters.Here,the effect of a different form of base roughness,which is sinusoidal perturbations of varying amplitude and wavelength,is also examined. The transition from an ordered to disordered state is also observed when a sinusoidal base is used, when the amplitude of the sine wave increases beyond a critical value.The critical amplitude initially increases as the wavelength is increased, reaches a maximum and then decreases as the wavelength is further increased. The critical amplitude also increases as the height of the flow increases.The states induced by the sinusoidal base have peculiar transient features, where there is a tendency to order at intermediate times in disordered states, unlike the rough base where no such tendency is observed.We also formulate a boundary layer theory for the ordered state, which develops in two distinct stages of shear propagation [Preview Abstract] |
Tuesday, November 24, 2015 1:55PM - 2:08PM |
R12.00006: Nonlinear instability and convection in a vertically vibrated granular bed Priyanka Shukla, I.H. Ansari, D. van der Meer, Detlef Lohse, Meheboob Alam The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis. Under a quasi-steady ansatz, the base state temperature decreases with increasing height away from from the vibrating plate, but the density profile consists of three distinct regions: (i) a collisional dilute layer at the bottom, (ii) a levitated dense layer at some intermediate height and (iii) a ballistic dilute layer at the top of the granular bed. For the nonlinear stability analysis, the nonlinearities up-to cubic order in perturbation amplitude are retained, leading to the Landau equation. The genesis of granular convection is shown to be tied to a supercritical pitchfork bifurcation from the Leidenfrost state. Near the bifurcation point the equilibrium amplitude is found to follow a square-root scaling law, $A_e\sim \sqrt{\triangle}$, with the distance ${\triangle}$ from bifurcation point. The strength of convection is maximal at some intermediate value of the shaking strength, with weaker convection both at weaker and stronger shaking. Our theory predicts a novel {\it floating-convection} state at very strong shaking [Shukla etal, JFM (2014), vol. 761, p. 123-167]. [Preview Abstract] |
Tuesday, November 24, 2015 2:08PM - 2:21PM |
R12.00007: Low-frequency oscillation in a narrow vibrated granular system Loreto Oyarte Gálvez, Devaraj van der Meer The analogy of the behaviour of granular materials with that of fluids has motivated much appealing research. An important example is a vertically shaken granular bed which exhibits fluid-like behavior, such as the Leidenfrost effect where a dense layer of grains floats on top of a gaseous layer, just like when a liquid droplet floats on its own vapour above a hot plate. When the shaking energy is increased the granular bed transits from the Leidenfrost to the convection state, for which a precursor is expected in the form of an oscillation of the bed as a whole. This precursor was observed numerically like an oscillation in the motion of the dense part, where the frequency of this oscillation is much lower than the frequency of the injected energy, and appears more relevant when the system is getting closer to the convective state. We built a setup that permits the observation of the granular Leidenfrost effect for a wide range of driving parameters. More specifically, a monodisperse granular material is contained in a transparent box and vertically shaken, and a fast camera is used to study its dynamics. The presence of a LFO is directly measured by images analysis and shows a good agreement with the previous numerical and experimental works. [Preview Abstract] |
Tuesday, November 24, 2015 2:21PM - 2:34PM |
R12.00008: Motion of a Short Granular Polymer in Vibrations P.C. Huang, Jack Wu, C.Y. Tao, Y.Y. Chen, J.C. Tsai Using both numerical simulations and laboratory experiments, we investigate the movements of a short granular polymer driven by vibrations. Surprisingly, our minimal models of constrained point masses with a simple assumption on the momentum transfer not only reproduce the rapid ratcheting motion in prior experiments [Phys. Rev. Lett. 112, 058001 (2014)], but also reveal the crucial role of random noises in triggering the spontaneous switching of bouncing modes in our previous report [http://meetings.aps.org/link/BAPS.2014.DFD.H24.1]. Subsequent experiments with a bead chain vibrated in an annular channel allow uninterrupted observations on the granular polymer. From the long-time statistics, we correlate the horizontal displacements to the different modes of response and identify the characteristic timescales for the transitions. Cross examinations of the numerical models and the statistical experiments suggest certain generic ratcheting and mode transitions that are insensitive to the mechanical details of such polymer. [Preview Abstract] |
Tuesday, November 24, 2015 2:34PM - 2:47PM |
R12.00009: Transverse Diffusion in Bedload Transport Olivier Devauchelle, Anais Abramian, Gregoire Seizilles, Eric Lajeunesse When a fluid flows over a granular bed, it entrains the grains as bedload. This interaction produces a beautiful variety of shapes and landscapes, such as dunes, ripples and meanders. In this context, Coulomb's law of friction translates into a threshold shear stress, above which the grains are entrained. When the flow-induced stress is barely above this threshold, only a small proportion of the superficial grains move. Their trajectory is then strongly influenced by the layer of static grains below them. They mostly move in the flow direction, but the roughness of the underlying bed causes their velocity to fluctuate, and turns their trajectory into a random walk. As a consequence, bedload diffuses in the direction orthogonal to the flow. Laboratory experiments suggest that this diffusion opposes gravity to maintain the banks of a river. However, quantifying the terms of this balance remains an experimental challenge. We propose to use an instability generated by bedload diffusion to do so. [Preview Abstract] |
Tuesday, November 24, 2015 2:47PM - 3:00PM |
R12.00010: On creating macroscopically identical granular systems with different numbers of particles Devaraj van der Meer, Nicolas Rivas One of the fundamental differences between granular and molecular hydrodynamics is the enormous difference in the total number of constituents. The small number of particles implies that the role of fluctuations in granular dynamics is of paramount importance. To obtain more insight in these fluctuations, we investigate to what extent it is possible to create identical granular hydrodynamic states with different number of particles. A definition is given of macroscopically equivalent systems, and the dependency of the conservation equations on the particle size is studied. We show that, in certain cases, and by appropriately scaling the microscopic variables, we are able to compare systems with significantly different number of particles that present the same macroscopic phenomenology. We apply these scalings in simulations of a vertically vibrated system, namely the density inverted granular Leidenfrost state and its transition to a buoyancy-driven convective state. [Preview Abstract] |
Tuesday, November 24, 2015 3:00PM - 3:13PM |
R12.00011: Rare events in granular media: a volcanic-like explosion Evgeniy Khain, Leonard Sander Granular matter is ubiquitous in nature and exhibits a variety of nontrivial phenomena. Within the same system, different regions of granular media can be at a solid or a gas phase. Here we focus on a granular Leidenfrost effect: a solid-like cluster is levitating above the ``hot'' granular gas [1]. This state was observed experimentally, when granular matter was vertically vibrated in a two-dimensional container [2]. This solid-gas coexistence can be described by using granular hydrodynamics, taking into account the viscosity divergence in the solid cluster. The approach is similar to the one employed in investigating solid-fluid coexistence in dense shear granular flows [3]. We performed extensive molecular dynamics simulations of a simple model of inelastic hard spheres driven by a ``thermal'' bottom wall. Simulations showed that for low wall temperatures, the levitating cluster is stable, while for high wall temperatures, it breaks down, and a hot gas bursts out resembling a volcanic explosion. We found a hysteresis: for a wide range of bottom wall temperatures, both the clustering state and the volcanic state are stable. However, even if the system is at the (stable) clustering state, a volcanic explosion is possible: it is a rare event driven by large fluctuations. We propose a special simulation technique that allows investigating such rare events. [1]. B. Meerson, T. P\"{o}schel, and Y. Bromberg, Phys. Rev. Lett. 91, 024301 (2003). [2]. P. Eshuis, K. van der Weele, D. van der Meer, and D. Lohse, Phys. Rev. Lett. 95, 258001 (2005). [3]. E. Khain, Phys. Rev. E 75, 051310 (2007); E. Khain, EPL 87, 14001 (2009). [Preview Abstract] |
Tuesday, November 24, 2015 3:13PM - 3:26PM |
R12.00012: Evolution of injected air stream in granular bed Ritwik Maiti, Gargi Das, prasanta Das An air stream injected through an orifice into a granular bed creates intriguing but aesthetically exotic patterns. The interaction of air with an aggregate of cohesionless granules presents evolution of patterns from stationary bubble to meandering filament and finally to a floating canopy with the increase of air velocity. [Preview Abstract] |
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