Clara Salueña

Dissipative properties of vibrated granular materials

We investigate collective dissipative properties of vibrated granular materials by means of moleculardynamics simulations. Rates of energy losses indicate three different regimes or ‘‘phases’’ in the amplitudefrequency plane of the external forcing, namely solid, convective, and gaslike regimes. The behavior of effective damping decrement in the solid regime is glassy. Practical applications are discussed. @S1063-651X~99!07304-3# PACS number~s!: 83.70.Fn, 05.40.2a, 45.05.1x The dominating approach in the world of vibration control and suppression by granular systems has been mainly practical @1#. Granular motion relaxes rapidly once the energy supply is switched off, and dampers can efficiently absorb energy released by shocks of external forcing. Engineers classify granular dampers as passive ones. For the case of ‘‘granular gases,’’ i.e., particulate systems in a state where the mean free path is large as compared with particle sizes, the cooling rate, which is the dissipation rate of the system, has been investigated @2#, and applications of this work require an analysis of granular gas ~hydro!dynamics in a given experimental setup. Damping in dense granular arrangements is a much more difficult problem which is mostly studied experimentally. In this work, by using molecular-dynamics simulations, we show that granular systems reveal different damping regimes indicating collective dissipation modes. Our study of these regimes leads to a ‘‘phase diagram’’ of horizontally vibrated granular systems ~see Fig. 4!. By using this diagram along with the presented estimates for damping decrements, practitioners may accelerate the design and testing procedures. In simulations we focus on two-dimensional containers which are partially filled with granular material and shaken horizontally. The motion of the container is sinusoidal, x(t) 5A sin(vt); it mimics practical situations where dampers are tested in the vicinity of the eigenmodes of the vibrating mechanism. We study the reaction of the system to the choice of parameters of shaking A and v, keeping all other parameters ~size, roughness and hardness of particles, filling factor, and size and shape of the apparatus! fixed@3#.

Transient structures in a granular gas.

A force-free granular gas is considered with an impact-velocity-dependent coefficient of restitution as it follows from the model of viscoelastic particles. We analyze structure formation in this system by means of three independent methods: molecular dynamics, numerical solution of the hydrodynamic equations, and linear stability analysis of these equations. All these approaches indicate that structure formation occurs in force-free granular gases only as a transient process.

Scaling properties of granular materials

Given an assembly of viscoelastic spheres with certain material properties, we raise the question how the macroscopic properties of the assembly will change if all lengths of the system, i.e. radii, container size etc., are scaled by a constant. The result leads to a method to scale down experiments to lab size.

Dissipative properties of granular ensembles

We investigate collective dissipative properties of vibrated granular materials by means of molecular dynamics simulations. The rate of energy loss indicates three different phases in the amplitude-frequency plane of the external forcing, namely solid, convective and gas-like regimes. The behavior of the effective damping decrement is consistent with the glassy nature of granular solids. The gas-like regime is most promising for practical applications.

Granular hydrodynamics and pattern formation in vertically oscillated granular disk layers

The goal of this study is to demonstrate numerically that certain hydrodynamic systems, derived from inelastic kinetic theory, give fairly good descriptions of rapid granular flows even if they are way beyond their supposed validity limits. A numerical hydrodynamic solver is presented for a vibrated granular bed in two dimensions. It is based on a highly accurate shock capturing state-of-the-art numerical scheme applied to a compressible Navier–Stokes system for granular flow. The hydrodynamic simulation of granular flows is challenging, particularly in systems where dilute and dense regions occur at the same time and interact with each other. As a benchmark experiment, we investigate the formation of Faraday waves in a two-dimensional thin layer exposed to vertical vibration in the presence of gravity. The results of the hydrodynamic simulations are compared with those of event-driven molecular dynamics and the overall quantitative agreement is good at the level of the formation and structure of periodic patterns. The accurate numerical scheme for the hydrodynamic description improves the reproduction of the primary onset of patterns compared to previous literature. To our knowledge, these are the first hydrodynamic results for Faraday waves in two-dimensional granular beds that accurately predict the wavelengths of the two-dimensional standing waves as a function of the perturbations amplitude. Movies are available with the online version of the paper.

Onset of fluidization in vertically shaken granular material

When granular material is shaken vertically one observes convection, surface fluidization, spontaneous heap formation, and other effects. There is a controversial discussion in the literature as to whether there exists a threshold for the Froude number Gamma=A(0)omega(2)(0)/g, below which these effects cannot be observed anymore. By means of theoretical analysis and computer simulation we find that there is no such single threshold. Instead, we propose a modified criterion that coincides with the critical Froude number Gamma(c)=1 for small driving frequency omega(0).

A numerical study of the Navier–Stokes transport coefficients for two-dimensional granular hydrodynamics

A numerical study that aims to analyze the thermal mechanisms of unsteady, supersonic granular flow by means of hydrodynamic simulations of the Navier–Stokes granular equation is reported in this paper. For this purpose, a paradigmatic problem in granular dynamics such as the Faraday instability is selected. Two different approaches for the Navier–Stokes transport coefficients for granular materials are considered, namely the traditional Jenkins–Richman theory for moderately dense quasi-elastic grains and the improved Garzo–Dufty–Lutsko theory for arbitrary inelasticity, which we also present here. Both the solutions are compared with event-driven simulations of the same system under the same conditions, by analyzing the density, temperature and velocity field. Important differences are found between the two approaches, leading to interesting implications. In particular, the heat transfer mechanism coupled to the density gradient, which is a distinctive feature of inelastic granular gases, is responsible for a major discrepancy in the temperature field and hence in the diffusion mechanisms.

Hydrodynamic fluctuations and averaging problems in dense granular flows

The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such systems and the peculiarities of the sources of noise. We perform a quantitative study by combining analytical methods and numerical results obtained by ensemble-averaging of data on creep during compaction and molecular dynamics simulations of convective flow. We show that numerical integration of the hydrodynamic equations gives the expected evolution for the time-dependent fields.The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such systems and the peculiarities of the sources of noise. We perform a quantitative study by combining analytical methods and numerical results obtained by ensemble-averaging of data on creep during compaction and molecular dynamics simulations of convective flow. We show that numerical integration of the hydrodynamic equations gives the expected evolution for the time-dependent fields.

Hydrodynamics at the Navier-Stokes level applied to fast, transient, supersonic granular flows

We perform two-dimensional hydrodynamic simulations on a paradigmatic problem of granular dynamics, the Faraday instability, using two different approximations to the Navier-Stokes granular equations: the constitutive equations and kinetic coefficients derived from the assumption of vanishing inelasticity (Jenkins-Richman approach) obtained by solving the Enskog equation disks by means of Grads method, and the ones obtained by solving the Enskog equation with the Chapman-Enskog method (Garzo-Dufty-Lutsko approach). The comparison reveals important qualitative and quantitative differences with respect to the hydrodynamic fields obtained by averaging results from particle simulations of the same system.

Contact of granular particles and the simulation of rapid flows using event-driven molecular dynamics

ABSTRACT We discuss several models for granular particles commonly used in Molecular Dynamics simulations of granular materials, including spheres with linear dashpot force, vis-coelastic spheres and adhesive viscoelastic spheres. Starting from the vectorial interaction forces we derive the coefficients of normal and tangential restitution as functions of the vectorial impact velocity and of the material constants. We review the methods of measurements of the coefficients of restitution and characterize the coefficient of normal restitution as a fluctuating quantity. Moreover, the scaling behavior and the influence of different force laws on the dynamical system behavior are discussed. The powerful method of event-driven Molecular Dynamics is described and the algorithmic simulation technique is explained in detail. Finally we discuss the limitations of event-driven MD.