~ ) Pergamon
0021-8502(95)00052-6
J. AerosOl Sci., Vol. 27, No. t, pp. 41 59, 1996
Copyright © 1996 Elsevier Science Ltd
Printed in Great Britain. All rights reserved
0021 8502/96 $15.00 + 0.00
GAS-SOLID FLOW WITH THE SLIP VELOCITY OF PARTICLES
IN A HORIZONTAL CHANNEL
Medhat Hussainov, Alexander Kartushinsky, Anatoly Mulgi and tJlo Rudi*
Institute of Energy Research, Estonian Academy of Sciences, Paldiski Rd, 1, EE-0001, Tallinn, Estonia
(First received 22 February 1994; and in final form 5 June 1995)
Abstract--The behavior of solid inertia particles carried with significant slip velocity in turbulent
gas-solid flow in a horizontal channel is investigated. Our mathematical analysis shows that, for
such motion, particles have substantial transversal velocity and so they interact intensively with the
walls when the Stokes number exceeds a threshold value. The mathematical description of such
motion of particles is based on consideration of two particle flows moving towards each other from
opposite walls and traversing through the center of the channel. The transport equations of particle
mass and linear and angular momenta are integrated along the whole width of the channel. It was
found that the Magnus lift force (in addition to the drag force) plays a significant role in the
transversal motion of particles. The calculations on the motion of particles with various size in
channels of different width for different velocities of the carrier flow show that the model presented
does describe a two-phase flow with the slip velocity. Regardless of the fact that our experimental
results were obtained for a pipe and the calculations, by contrast, were carried out for a fiat channel,
the numerical results for the velocity distribution of both phases, as well as that for the slip velocity,
are in good agreement with experimental ones. Some discrepancy is found only for the description of
particle mass concentration. Our model for a fiat channel describes almost uniform distribution of
particle mass concentration while our experiments, by contrast, show a gradient distribution fading
towards the pipe wall. Apparently this results from the influence of the wall curvature of the pipe.
NOMENCLATURE
B channel width
Cb drag coefficient for dispersed phase
d particle diameter
d nondimensional particle diameter
D pipe diameter
f7 numerical code in finite difference
Fo drag force
Fra Magnus force
hb grid step of buffer layer
ha grid step of laminar sublayer
ht grid step of turbulent core
k turbulent energy
k, restitution coefficient
k~ friction coefficient
l interparticle distance
mp particle mass
N number of particles
Nb number of calculating points in buffer layer
N~ number of calculating points in laminar sublayer
Nt number of calculating points in turbulent core
P pressure
r generator of a cone
Re Reynolds number
Re. friction Reynolds number
Res Reynolds number for dispersed phase
Ret turbulence Reynolds number
Stk. Stokes number
TL Lagrangian integral time scale
u streamwise mean velocity
Up particle streamwise velocity after collision
v transversal mean velocity
v. friction velocity
* Corresponding author.
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