Open Journal of Applied Sciences, 2013, 3, 21-26

doi:10.4236/ojapps.2013.31B1005 Published Online April 2013 (http://www.scirp.org/journal/ojapps)

Numerical Simulations of the Equations of

Particle Motion in the Gas Flow

Kelong Zheng1*, Liuxiang Zhang2, Haiyan Chen2

1School of Science, Southwest University of Science and Technology, Mianyang, China

2School of Environment and Resource, Southwest University of Science and Technology, Mianyang, China

Email: zhengkelong@swust.edu.cn

Received 2013

ABSTRACT

Under the assumption of considering the gravity and without gravity, two different acceleration models to describe par-

ticle’ motion in the gas flow are formulated, respectively. The corresponding numerical simulations of these models do

not only show the trend of the velocity o f the particle in different density and particle diameter sizes, but also the rela-

tionship between the maximum particle velocity and its diameter size.

Keywords: Numerical Simulation; Particle Motion; Acceleration; Jet Grinding

1. Introduction

The principle of jet grinding is that solids particles are

accelerated by high-speed gas flow and fragmented due

to multiple particle-particle collisions in interacting gas-

particle jet. The development of jet grinding technology

mainly includes the development of basic theory of jet

grinding and its device, and the former is the foundation

of the latter. According to the principle of jet grinding,

the grind energy of particles comes from high-speed gas.

Therefore, the analysis on the particle acceleration pro-

gress is a key point in the design of jet grinding device.

Whether the particles in the gas flow can be effectively

accelerated and collided at its maximum velocity is the

important condition to improve the efficiency of jet

grinding. Researches of particles’ acceleration in nozzles

have been reported in some literatures [1-3], but there

have not any reports about particles’ acceleration in flu-

idized bed. If the accelerated distance is too far, when the

particle is accelerated to the maximum velocity, it will be

affected by the gas flow and solid s, an d slow down ; if the

accelerated distance is too close, particle can not be ac-

celerated enough. So, to determine the optimal injection

distance is very important to improve the efficiency of jet

grinding. Reference [4,5] pointed out that it was a pref-

erable choice that the accelerated distance of nozzles was

as 10 - 20 times as the dimensionless distance, but the

result is too wide. On the other hand, although many pa-

pers on the analysis of particle motion do not consider

the influence of gravity, for tough particle, the gravity, as

well as the angle of inclination of the nozzle, has great

influence on the efficiency of the fluidized bed.

To investigate the particle motion in the high-speed gas

flow better, this paper establishes some different mathe-

matical models to describe particle acceleration with and

without considering gravity, respectively. Meanwhile,

numerical simulations show the trend of the velocity of

the particle under different conditions and the relation-

ship between the maximum particle velocity and its di-

ameter size.

2. Particle Acceleration Model without

Gravity

2.1. Mathematical Model

Without considering gravity, the equation of a single

particle motion [6] is as follows

2

0.75 (() )

sd s

ss

duC ut u

dt d

(1)

where

u is the velocity of particle, is the veloc-

ity of gas, ()ut

is the gas density,

is the particle den-

sity,

d is the particle diameter size and is the

particle drag force coefficient. d

C

Equation (1) indicates the velocity of particle

u is a

function in t. By transformation, it can be rewritten to an

equation about th e particle velocity and the jet distance,

2

0.75 (() ),

sde

ss

ss

duC d

uu

dx d

xu

(2)

Where

is the dimensionless distance which equals to

the ratio of the distance of jet stream section to the nozzle

*Corresponding author.

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