0
TECHNICAL PAPERS

Complex Flow Dynamics in Dense Granular Flows—Part I: Experimentation

[+] Author and Article Information
Piroz Zamankhan, Mohammad Hadi Bordbar

Laboratory of Computational Fluid and BioFluid Dynamics,  Lappeenranta University of Technology, Lappeenranta 53851, Finland

J. Appl. Mech 73(4), 648-657 (Nov 11, 2005) (10 pages) doi:10.1115/1.2165234 History: Received January 03, 2005; Revised November 11, 2005

By applying a methodology useful for analysis of complex fluids based on a synergistic combination of experiments, computer simulations, and theoretical investigation, a model was built to investigate the fluid dynamics of granular flows in an intermediate regime where both collisional and frictional interactions may affect the flow behavior. In Part I, the viscoelastic behavior of nearly identical sized glass balls during a collision have been studied experimentally using a modified Newton’s cradle device. Analyzing the results of the measurements, by employing a numerical model based on finite element methods, the viscous damping coefficient was determined for the glass balls. Power law dependence was found for the restitution coefficient on the impact velocity. In order to obtain detailed information about the interparticle interactions in dense granular flows, a simplified model for collisions between particles of a granular material was proposed to be of use in molecular dynamic simulations, discussed in Part II.

FIGURES IN THIS ARTICLE
<>
Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 5

Variations of the component of normal stress σyy (contact pressure) of the node located at the point of initial contact as a function of time. Six point star, five point star, diamond, box, left triangle, right triangle, inverted triangle, triangle, asterisk, and circle represent collisions of impact velocities of 0.01, 0.03, 0.05, 0.07, 0.5544, 0.9538, 2.5, 3.5, 4.0, and 5.0m∕s, respectively.

Grahic Jump Location
Figure 6

(a) Maximum of contact pressure ∣σyy∣ at the initial point of contact as a function of impact velocity. Stars and triangles are the analytical and the numerical results, respectively. (b) Variations of collision time with impact velocity. Crosses and squares represent the analytical and the numerical results.

Grahic Jump Location
Figure 7

Contour plots of σyy for two spheres during a collinear impact. (a) At the middle of compression period. (b) At the maximum compression. (c) At the middle of restitution period. (d) At separation. The impact velocity is 0.55m∕s.

Grahic Jump Location
Figure 8

Contour plots of (a) σyy and (b) σeff (Von Mises stress) at the maximum compression of a collision with an impact velocity of 5m∕s

Grahic Jump Location
Figure 9

(a) Three-dimensional view of a collinear collision of two identical glass balls used in experiments. (b) Normalized kinetic energy for the balls versus time. The relaxation time is set to τ=1.676×10−5s. The solid and dashed lines represent the viscoelastic and elastic collision, respectively. Ktotal is the total kinetic energy of the system. (c) The same as (b) but using a value of 9.87×10−6s for the relaxation time. (d) Time evolution of contact pressure experienced by the node located at the initial point of contact. Box and triangle represent elastic and viscoelastic collision, respectively. (e) Numerical results for deformation history of a node located at the initial point of contact in a collision between two glass balls. Spheres and squares represent elastic and viscoelastic collision, respectively. (f) Typical deformation history proposed by Goldsmith (21).

Grahic Jump Location
Figure 10

(a) The coefficient of restitution versus impact velocity for viscoelastic glass beads with the properties given in Table 1. Squares indicate the numerical results obtained using finite element approach and circles represent experimental data obtained using Newton’s cradle device depicted in Fig. 9. (b) The results in (a) are presented on a log-log scale. The solid line indicates the power law 15. Distribution of en is seen to follow the power law distribution.

Grahic Jump Location
Figure 11

The coefficient of restitution versus impact velocity for a binary collision of viscoelastic glass beads with the properties as given in Table 1. Deltas and squares indicate the numerical results obtained using simplified model 17 for η=1, and η=1∕2, respectively. Gray circles represent experimental data obtained using Newton’s cradle device. The values obtained for the parameter K for η=1 and η=1∕2 are 143 and 1.67, respectively. The Kelvin-type model for η=1∕2 does not seem to predict the behavior of glass balls during a collision at the low velocity limit accurately.

Grahic Jump Location
Figure 1

Schematic of apparatus used for the Newton’s cradle experiments. The balls used were nearly identical, spherical glass particles suspended from very thin threads. Here, the positions of the balls before, at, and after a collision are shown.

Grahic Jump Location
Figure 2

The model consists of auxiliary spring in series with the Kelvin model

Grahic Jump Location
Figure 3

Free-body diagram of a single pendulum in a spherical coordinates (r,θ,φ)

Grahic Jump Location
Figure 4

Three-dimensional view of a collinear collision of two identical spheres. (a) The left sphere with velocity of 0.56m∕s approaches the right sphere, which is initially stationary. To obtain better visualizations one-fourth of the particles are removed. (b) Grid used in the numerical treatments. Note that finer meshes are used in the vicinity of contact area where the gradient of stresses and strains are high. (c)–(f) Time evolutions of the local velocities of the balls during the collision process. (g) Variations of velocities of center of mass of the particles with time. Here velocity and time are normalized with impact velocity and collision time, respectively. Squares and diamonds represent the right side and the left side particles, respectively.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In