Granular Dynamics Model of Explosive Particle Dispersal

Summer Undergraduate Research in Engineering Poster Presentation 2012

Mélanie Tétreault-Friend

Event-Driven Granular Dynamics time

t0

t1*

t2*

• We model the collisions between the particles by solving the conservation of momentum equations for each particle simultaneously.

• Each iteration corresponds to an event, i.e. the time at which the next collision occurs. Hence, there is no fixed time step.

Creating Dense Distributions ∆t

First particle

Second particle

Third particle

Recalculate Recalculate

In granular dynamics, random distributions are normally created by placing particles one-by-one in a given geometry. This method is computationally intensive for dense particle distributions.

Very dense “random” particle distributions are created by distributing them in a grid and allowing them to disperse for some time. The resulting particle cloud becomes our new initial distribution which can be used in different simulations. This method significantly reduces runtime.

Geometry and Initializing Particles

Cylindrical expanding piston

R

ro

Vr

r ro R

The particles are distributed in a cylindrical geometry in order to compare with experimental results.

The cloud is set in motion by initializing an inner core of particles with a radially proportional velocity profile, or by “pushing” them with an expanding cylindrical piston.

Background • Explosive particle dispersal

is a type of granular flow.

• Pattern formation within granular media is observed in a variety of experimental settings.

Objective To numerically investigate particle kinematic interactions during explosive particle dispersal using an event-driven granular dynamics model.

Hydrophopbic particles are dispersed over water and are accelerated outward by dipping a needle at the centre. [2]

A rigid container containing particles is vibrated vertically, causing the particles to form a regular pattern. The number of peaks depends on the vibrating frequency. [1]

Conclusion

A method to numerically investigate the effects of kinematic interactions during explosive particle dispersal was successfully implemented. Instabilities have been observed in the numerical results, however further investigations are required to determine if these instabilities evolve into jets.

Acknowledgements: Prof. David Frost, Dr. Oren Petel, Dr. Zouya Zarei

Analysis

0

1

2

3

4

5

6

7

8

0 100 200 300 400 500 600 700 800

Standard deviation

time (microseconds)

Standard deviation of number per sector of particles versus time

eps=1

ϵ=1

ϵ=0.21

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

0 10 20 30 40 50 60 70

fraction of total kinetic

energy

Time (s)

Radial Kinetic Energy (fraction of total) versus time

The standard deviation in number of particles indicates how much particle density within a cloud is varying over time.

The initial kinetic energies of the particles is a combination of radial and transverse kinetic energy. Over time, it becomes fully radial.

Sample Results

Expansion of particles initialized by a core of moving particles.

Expansion of particles initialized with a piston.

References: [1] K. M. Aoki and T. Akiyama (1996), Phys. Rev. Lett. 77 4166-4169 [2] M. M. Bandi, T. Tallinen and L. Mahadevan (2011), EPL 96 36008

Introduction

• Instabilities form within a cloud of explosively dispersed particles.

• These instabilities often evolve into jets.

• The mechanism causing their formation remains unknown.