Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session M2: Granular Flows III |
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Chair: Richard Lueptow, Northwestern University Room: 302 |
Tuesday, November 22, 2011 8:00AM - 8:13AM |
M2.00001: Granular convection in a spherical tumbler Zafir Zaman, Umberto D'Ortona, Julio M. Ottino, Richard M. Lueptow We have performed DEM simulations and experiments for monodisperse particles in partially-filled spherical tumblers to better understand the flow of bidisperse particles in spherical tumblers, which display segregation patterns that result from differential axial migration of the two species. Particle tracking in DEM simulations for a 30{\%} full tumbler suggests that there is a convection pattern in the monodisperse system that could play a role in the bidisperse system. Particles near the surface of the flowing layer move slowly toward the poles while particles lower in the flowing layer move toward the equator. The convection is quite slow, taking O(100) passages through the flowing layer to complete one convection orbit. Experiments in an 8 cm diameter spherical tumbler with 1 mm monodisperse particles having a band of particles of a different color confirm the convection pattern. [Preview Abstract] |
Tuesday, November 22, 2011 8:13AM - 8:26AM |
M2.00002: Instabilities in a Freely Cooling Granular Gas: A Quantitative Comparison of DEM simulations and Kinetic-Theory-based models Peter Mitrano, Andrew Hilger, Christine Hrenya Experiments, discrete element method (DEM) simulations, and kinetic-theory-based predictions have demonstrated the existence of clustering instabilities in flows of solid, inelastic grains. Such instabilities have also been studied via stability analyses of the continuum balances for rapid granular flows. Spurred by discrepancies between DSMC-based and kinetic-theory-based transport coefficients in extremely dissipative systems, previous work has shown that a modified Sonine approximation reduces this disagreement. However, the quantitative accuracy of this modified kinetic theory with respect to predicting instabilities has not been addressed. In this work, hard-sphere, event-driven DEM simulations of the homogenous cooling system are used to study instabilities in granular systems. Detection of instabilities is determined via Fourier analysis. The aim is to determine the critical system size at which clustering appears over a wide range of dissipation. By comparing the critical size from DEM with the predictions based on standard (Garz\'{o} 2005) and modified (Garz\'{o} 2007) Sonine approximations, this work aims to assess the quantitative ability of each model to predict instabilities for monodisperse granular flows. [Preview Abstract] |
Tuesday, November 22, 2011 8:26AM - 8:39AM |
M2.00003: Sudden Chain Energy Transfer Events in Vibrated Granular Media Rodrigo Soto, Nicolas Rivas, Suomi Ponce, Basile Gallet, Dino Risso, Patricio Cordero, Nicolas Mujica In a mixture of two species of grains of equal size but different mass, placed in a vertically vibrated shallow box, there is spontaneous segregation. Once the system is at least partly segregated and clusters of the heavy particles have formed, there are sudden peaks of the horizontal kinetic energy of the heavy particles, that is otherwise small. Together with the energy peaks the clusters rapidly expand and the segregation is partially lost. The process repeats once segregation has taken place again, either randomly or with some regularity in time depending on the experimental or numerical parameters. An explanation for these events is provided based on the existence of a fixed point for an isolated particle bouncing with only vertical motion. The horizontal energy peaks occur when the energy stored in the vertical motion is partly transferred into horizontal energy through a chain reaction of collisions between heavy particles. [Preview Abstract] |
Tuesday, November 22, 2011 8:39AM - 8:52AM |
M2.00004: Packing and stability of geometrically cohesive granular media Nick Gravish, Scott V. Franklin, David L. Hu, Daniel I. Goldman Granular particles with concave shapes may entangle with neighboring particles creating an effective cohesion controlled by particle geometry. We study the packing and stability of vertical columns formed from geometrically cohesive u-shaped particles (staples) of varying barb length, $l$. We prepare cohesive columns by packing particles in a confining cylindrical tube under vertical vibration at fixed frequency of $f = 30$ Hz and peak acceleration (in units of $g$) of $\Gamma = 2$. The initial and final volume fraction vary with $l$ and volume fraction increases for decreasing $l$. Once packed, the tube is removed and columns are subjected to vertical vibration at fixed $f$ and variable $\Gamma$. We monitor column height, $h(t)$, during collapse and find that $h(t)$ is described by a stretched exponential $h(t)/h_0 = \exp[-(\frac{t}{\tau})^\beta]$. The characteristic collapse time, $\tau$, is governed by an Arrhenius law with $\tau = \tau_0 \exp(\Gamma_0/\Gamma)$ where $\Gamma_0$ is a measure of the column's resistance to collapse. We find that $\Gamma_0$ is a non-monotonic function of $l$ and exhibits a maximum at intermediate $l$. We explain this effect through a model considering packing and entanglement. [Preview Abstract] |
Tuesday, November 22, 2011 8:52AM - 9:05AM |
M2.00005: Numerical model for the motion of large object in fluidized bed Takuya Tsuji, Kyohei Higashida, Toshitsugu Tanaka The motion of large object in fluidized beds is quite complex because it is influenced by the fluid force, buoyant force in addition to the contact force from emulsion particles, other immersed objects and walls. Its behavior is expected to change depending on its shape, density and size along with the condition of fluidized bed. It is a physically interesting problem and it also has a practical importance in several engineering applications such as gasification, mixing, separation and granulation. In the present study, a numerical model which predicts the motion of large object in fluidized bed is developed. We concentrate on objects larger than surrounding emulsion particles by one order of magnitude at least. The basic concept of a proposed numerical model is presented and its performance is tested for fundamental problems such as sedimentation of single spherical object in a bubbling fluidized bed. [Preview Abstract] |
Tuesday, November 22, 2011 9:05AM - 9:18AM |
M2.00006: Segregation of Binary Mixtures: Competing Effects of Gravity and Shear Rate Gradients Kimberly Hill, Yi Fan Mixtures of particles tend to segregate when they flow. For example, when a dense binary mixture of different-sized particles flows down an inclined plane, the larger particles tend to go up (toward the free surface), and the smaller particles, down. However, this trend is not as simple as it might first seem. It has recently been demonstrated that under otherwise identical conditions the relative segregation fluxes in a binary mixture of particles are not monotonically dependent on particle size ratio. Further, for a single mixture, larger particles may rise or fall relative to the small particles, depending on subtle differences in local flow conditions. We have recently shown that a shear rate gradient drives segregation in dense flows, and that the direction depends on the partitioning of stress between species. The complicated segregation dynamics in gravity-driven flow may be due to competing effects of gravity and shear rate gradients in segregating particles. We combine a theory for gravity-driven segregation of granular materials (Gray and Thornton, Proc. R. Soc. A, 2005) with our theory for shear-driven segregation (New J Phys, in press) to study how these competing segregation effects can give rise to the variety of trends that have been observed. [Preview Abstract] |
Tuesday, November 22, 2011 9:18AM - 9:31AM |
M2.00007: Kinetic theory based computational approaches for granular flows Prakash Vedula Challenges for efficient computational prediction of granular flows arise particularly due to their nonequilibrium behavior, as a result of which the continuum field assumptions become invalid (especially when the effective Knudsen number is not a small parameter). To address some of these challenges, we present computational methods for treatment of granular flows including particle rotation effects, based on solution of the corresponding Boltzmann equation with full collision operator using fixed-lattice and adaptive quadrature based approaches. Nonequilibrium behavior in dilute granular flows consisting of smooth and rough spheres will be investigated. The effects of inelasticity and mass distribution of the constituent spheres will also be discussed. Detailed treatment of the collision operators in our approaches ensures that the collision invariants are preserved and the functional dependence of evolution of generalized moments (involving linear and angular velocity components) is correctly represented. Semi-analytic representations of the moment contributions due to collision operator, which involve fourteen dimensional integrals, will also be developed. Microscopic dynamics of binary collisions is considered to relate pre-collisional and post-collisional linear and angular velocities of particles. [Preview Abstract] |
Tuesday, November 22, 2011 9:31AM - 9:44AM |
M2.00008: Numerical study of unsteady shear, and gravity-driven granular flows Christos Varsakelis, Miltiadis V. Papalexandris In this talk, we report on the results of a numerical study for unsteady, shear-driven granular flows and granular flows over inclined planes. The numerical simulations have been performed with the application of a new algorithm for two-phase continua that has been recently developed by our team. After a short description of the algorithm, we present representative results of our numerical simulations. Further, we discuss the characteristics of the emerging flow structures and their dependence on certain physical parameters of the granular phase, such as, initial concentration, viscosity coefficient, etc. The talk concludes with a comparison of our numerical predictions at large times with those of previous studies on steady granular flows. [Preview Abstract] |
Tuesday, November 22, 2011 9:44AM - 9:57AM |
M2.00009: Layer Depth Dependence of Shocks and Patterns in Shaken Granular Systems Michael Hollowed, Jon Bougie We simulate shaken granular layers using numerical solutions of continuum equations to Navier-Stokes order and use these simulations to study shocks and patterns in vertically oscillated layers of grains. When the accelerational amplitude of the forced oscillations exceeds that of gravity, the layer leaves the plate at some time during the cycle. When the grains collide with the plate later in the cycle, shocks are formed within the layer. If the accelerational amplitude exceeds a critical value, standing wave patterns also form. We investigate the interactions between shocks and patterns in these systems, as well as their dependence on layer depth. We demonstrate relationships between properties associated with shocks (such as Mach number and pressure gradients across the shock) and properties associated with standing wave patterns (such as pattern wavelength and horizontal flow speed between peaks). Re-scaling these quantities by the depth of the layer yields relationships between dimensionless quantities that are valid across a range of layer depths. [Preview Abstract] |
Tuesday, November 22, 2011 9:57AM - 10:10AM |
M2.00010: The stress profile in a sheared granular column Prabhu Nott, Vishwajeet Mehandia, Kamala Jyotsna Gutam It has been known for several centuries that the normal stress at the base of a column of granular material deviates from the value dictated by the hydrostatic balance. This was explained by Janssen (1895) as being due to the shear stress imposed by the confining walls on the granular column, as a result of grain-wall friction. The question we address in this presentation is, what is the stress field when the column is sheared? Depending on the assumptions on the kinematics, plasticity theories predict that the stress profile is similar either to that in a static column, or to that in a sheared fluid column. Here, we report the results of our experimental study of slow shear of a granular material in a cylindrical Couette cell, in which all components of the stress were measured at the stationary outer cylinder. The stress was measured as a function of distance from the free surface. The results of our experiments are intriguing: the radial normal stress deviates strongly from the predictions of all available theories and previous experimental measurements. The axial shear stress changes sign when a static column is sheared. We describe these results, and speculate as to which type of theory might explain the observations. [Preview Abstract] |
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