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STUDIES ABOUT THE INFLUENCED OF THE
SURFACE STATE ON A BEHAVIOR OF SOLID
PARTICLES FINDED INTO AN AIR FLOW
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Panainte Mirela
University of Bacau
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Retrieved on: 01 July 2016

7th INTERNATIONAL MULTIDICI PLINARY CONFERENCE
Baia Mare, Romania, May 17-18, 2007
ISSN-1224-3264

STUDIES ABOUT THE INFLUENCED OF THE SURFACE STATE ON
A BEHAVIOR OF SOLID PARTICLES FINDED INTO AN AIR FLOW

Moșneguțu Emilian, Nedeff Valentin, Panainte Mirela, Savin Carmen, M ăcărescu Bogdan
Lecturer dr. eng., Prof. dr. eng., Lectur er drd. eng., Lecturer drd. eng., Dr. eng.
University of Bacău, Str. M ărășești nr. 157

Abstract : An important factor in the aerodynamic sorting process represents the surface state of solid particle.
In this work the results of studies concerning the influence of the surface state of solid particle over behaviour of
particle in ascendancy vertical air flow, respectively the value of the floating speed of solid particle are
presented. The experimental determinations proved that the turbulence intensity of the air flow obtained “behind” of the
solid particle is direct proportional w ith the value of the air flow speed and with the value of friction coefficient
of the respective particle.
Key words: friction coefficient, perimeter, the floating speed of particle, turbulence intensity.

1. INTRODUCTION
The choosing of the sorting method and sorting equipment is made taking into
consideration the characteristic af ter which the particle mixture may be differentiate [4, 6, 10].
When the components of the mixture of solid particles are distinguished after their
behavior in air flow, the sorting process can be realized after the aerodynamic properties,
which are characterized mainly by the floating speed. This can be determinate analytically
(for ideal particles, spherical, isotropic and which have a stable pos ition in air flow) and
experimental (with help of a special equipment) [3, 7]
The floating speed of solid particles is influe nced by different factor s: the density of the
particle, shape of the particle, the dimensions of the particle and the surface state of the
particle [2, 9]
The researches made to set off the influence of the surface state (the friction coefficient) on
the floating speed of the particle are very poor , presenting just the va lue of these, without
correlating these factors [5, 8].

2. THE EXPERIMENTAL PART
To determine the floating speeds of differen t types of the particles it was used a
laboratory installation (fig. 1). Air flow is produced by the axial fan 1. On the aspiration
pipeline of the fan is connected the sedimentation room 2, seal ed on the inferior side by the
487

seeds box 3. In the extension of the sedimentation room is the vertical channel 4 built with
glass walls for the visualization of the particles. The upset jump room of fan is connected to a
compartment which contains a filter element 5 from cloth, which has the role to retain the fine
particles of dust which, possibly, were aspirated together w ith the work particles. The flow
capacity is measured with help of tow rotame ters 6 positioned behind the filter element 5, and
by closing the evacuation connections 7 it is r ealized the adjustment of air quantity which
flows through the installation (lar ge adjustment and fine adjustme nt). For the determination of
the floating speed of a particle the air flow capacity from installation is regulated until the
particle is in a stable position in the channel with the glass walls. The value of the air flow
capacity is read with the help of two rotameters 6 and knowing the section of the glass
pipeline, the floating speed of the so lid particle can be found out [1].
3 6 7 4 21
5
Fig.1. The scheme of equipment fo r determination of the float ing speed of the particles:
1 – axial – radial fan; 2 – sedi mentation room; 3 – box of seed s; 4 – vertical air channel; 5 –
filter elements; 6 – rotameter; 7 – nozzle for air evacuation from installation

The surface state of the solid particles is characterized by the friction coefficient. The
values of friction coefficient μf were determined indirectly, by computation, using the relation
presented the in specialty literature [10]:
ftgμϕ= , ( 1 )

where ϕ is the friction angle between the particle and material on which the particle moves
(friction)( fig. 2) [10], in which:
– G weight of the particle;
– N reaction force;
– m mass of particle;
– ϕ friction angle.

488

N Ff

Fig. 2. The scheme of the device for determination the friction angle ϕ Gm g=⋅
In labo ratory the determ ination of friction ang le (for sliding a nd for rollin g) it was rea lized
on a m etallic plate, having a plane surface and a roughness R a = 3, 2 μ m.
It was chosen particles with the sam e density, respectively ρ = 1200 kg/m3; the same
equivalent diam eter, respectively d e = 3 mm ; for which it was determ ined and estab lished:
– the friction coefficient;
– the pe rimeter of the par ticle;
– the f loating speed;
– the intens ity of the turb ulence.
These determ inations were realized five tim es and below are presented the average v alues,
in order to obtain the relations of dependenc y between the following two factors: the floating
speed and th e friction co efficient.

3. EXPE RIMENTAL RESULTS.

After the experim ental determ ination s the f ollowing variation s of the f loating speed o f the
solid particles were obtained f unction of the s olid p article mass (fig. 3). The values were
measured with help of laboratory equi pment which is presented in figure 1.
33.544.555.56
0.02 0.03 0.04 0.05 0.06
Particle mass (g)Floating speed
(m/s)

Fig. 3. The v ariation o f the floa ting s peed func tion of the so lid partic le mass

For the same particles w as determ ined, experim entally, the variations of friction co efficien t
μf depending on the particle m ass (fig. 4). cos Gϕ⋅ sinGϕ⋅
ϕ
489

0.20.40.60.81
0.02 0.03 0.04 0.05 0.06
Particle mass (g)Friction coefficient

Fig. 4 . The variation of friction coeffici ent function of the particle mass
Both in the case of solid particles movement into an air flow and in the case of solid
particles movement on a plane, their motion is influenced by the friction force, respectively
by the surface state of particle.
To differentiate two particles from their surface state (roughness) point of view we
consider that they are differentiated by the to tal size of surface. The rough particle has an
unfolded total surface bigger than smooth partic le. By eliminating is analyzed just the
difference between the circumferences (the perimete rs) of the particles (a coarse particle has a
bigger perimeter than a smooth particle).
For the determination of perimeter of a solid particle we used the Solidworks software,
respectively the function Measure, to measure the perimeter of solid particle. Further, for the studied particles, the variations of the speed floating and the fr iction coefficient depending on
the perimeter of solid particle ar e presented (fig. 5 and fig. 6).
33.544.555.5
9.9 10.7 11.5 12.3 13.1 13.9 14.7
Perimeter (mm)Floating speed (m/s)

Fig. 5. The variation of floating speed functi on of the perimeter of solid particle
00.20.40.60.81
9.35 10.45 11.55 12.65 13.75 14.85
Perimeter (mm)Friction coefficient

Fig. 6. The variation of friction coefficient f unction of the perimeter of solid particle

490

In a process of aerodynamic sorting, the particle behaves differe ntly in air flow because of
friction which appears between their surfaces a nd air flow. Because, practically the intensity
of the air flow turbulence obtained in the behind of solid particle it can not be measured, the
simulation program FLUENT was utilized. In fi gure 7 is presented, with help of FLUENT
program, the distribution of th e flow lines (turbulence) around of solid particle with the
smooth surface and around of particle with the rough surface for an air flow with speed equal
with value of the floating speed of respective particles. It was considered that the smooth
particle has the perimeter 1, in this case the coarse particle, presented in the figure 6, have the
perimeter bigger by 1,69, respectively 3,2 times (it was measured with help of the function
Measure from Solidworks software).
a)
b)
c)
Fig. 7. Form of the air flow turbulence for different particles:
a) Particle with the smooth surface (the perimeter 1); b) particle with the rough
surface (the perimeter 1,69); c) particle with the rough surface (the perimeter 3,2)

Taking into account the values of the turbulence intensity of the air flow, in figure 8 is
presented the variation of this factor depending on the friction co efficient of the solid particle.
8595105115125135145155165
0.26 0.36 0.46 0.56 0.66 0.76 0.86
Friction coefficientTurbulence
intensity of the air
flow (%)

Fig. 8. The variation of turbulence intensity of the air flow depending on the friction
coefficient

The variation of the turbulence of the air flow depending on floating speed of the solid
particles is presented in the figure 9.
491

8595105115125135145155165
3.3 3.8 4.3 4.8 5.3
Floating speed (m/s) Turbulence intensity
of the air flow (%)

Fig. 9. The variation of turbulence intensity of the air flow depending on the floating speed

4. MATHEMATICAL MODELATION

As in any process, in this case it was looke d up to obtain an equivalent mathematical
model of process.
Starting from the values obtai ned on experimental way, with the help of the generating
linear and nonlinear equation soft ware, TableCurve 3D, it was de termined the equation of the
frictional coefficient variation of the solid particles depending on the particle mass and on its
perimeter (see table 1.a), as well as the correlation between floating speed, the friction coefficient and the perimeter of solid par ticle (see table 1.b). The dependency between
turbulence intensity of the air flow around each particle, the friction coefficient and floating
speed was also determined (see table 1.c).
Table 1. Mathematical models
a) ()
() ()
()2
34
5
237114,8214 10533, 385 ln 0217, 3155 ln
1830, 0012 ln 268, 57755 ln
15, 723033 ln 1, 6189338
0,13762953 0, 003764544fp
pp
pe
eemm
mm
mP
PPμp =+⋅ +⋅
+⋅ +⋅ +
+⋅ +⋅ −
−⋅ + ⋅+
, (2)
b) 2
34
5212, 505204 107, 94986 393, 75147
690, 2027 574, 92575
183,1513 0, 68336123 0, 021122558pf
ff
fev
PPμμ
μμ
μf
e=−+⋅ −⋅
+⋅ − ⋅ ++⋅ + ⋅ − ⋅+
, (m/s)
(3)
492

c)2
34
233755, 5261 820, 35344 1788, 6542
1304,8774 221, 5177
2817,1036 662,17222 51, 687849tf
ff
ppI
vvμμ
μμf
pv=−−⋅ +⋅
−⋅ + ⋅ ++⋅ −⋅ +⋅−
, (%) (4)

The corresponding mathematical equati on was made the next notations:
– m p – mass of the solid particle, g;
– Pe – perimeter of solid particle, mm.
– It – the turbulence intensity of the air flow.

The correlation coefficients of the equations (2), (3) and (4), generated with the program
Table Curve 3D, are: 0,985, 0,99 and 0,989.

5. CONCLUSION

Analyzing the experimental data it was established that bo th the floating speed and the
friction coefficient vary directly proportional with mass of solid particle.
With Solidworks software it could be measured the perimeter of solid particles, and it is
observed that both floating speed of the solid particle and the friction coefficient are
influenced directly by this.
Both the current lines and the turbulence inte nsity of the air flow are influenced by the
perimeter of the particle.
Both speed of the air flow, in this case represented through floating speed of the solid
particle, and friction coefficient of the solid par ticle influences significan tly the distribution of
the current lines, respectively the tu rbulence intensity of the air flow.

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