CC BY
29
SOME WAYS TO CONTROL SEGREGATION AND MIXING IN GRAVITY FLOWS OF PARTICULATE SOLIDS V.N. Dolgunin, A.N. Kudy, O.B. Yushkova, A.N. Ananyev
Department “Technological Equipment and Food Technologies”, TSTU Represented by a Member of the Editorial Board Professor V.I. Konovalov
Key words and phrases: aeration; hydromechanical segregation; migration; segregation; vibration.
Abstract: Experimental and analytical investigation of segregation in particulate media at various conditions of a gravity flow are carried out in this paper. Basic segregation effects for the particles differing on size and density and parameters of rapid shear flows flow to control the segregation are explored. The most effective methods to control the segregation in gravity flows of particulate solids are suggested.
Symbols
c - the test component concentration, kg-kg-1; AM - nonuniformity parameter, N-m;
Djf - coefficient of quasidiffusional mixing, S - mean distance between particles, m;
t - time, s;
v - the mean velocity, m-s-1; v - the mean fluctuation velocity, m-s-1; x, y - cartesian coordinates; a - the indination angle, grad;
A - driving forces of segregation processes; s - flow dilatation; p - particles density, kg-m-3;
P - analog gidrostatic pressure in a particulate medium, N- m-2.
1 Introduction
The segregation phenomenon takes place in many circumstances within solids process and handling plants and gives rise to a wide range of unwanted effects in many industries handling and processing solids. The influence of the practical effects of segregation on the product quality and process kinetics may be both negative and positive. Thus it is necessary to control segregation intensity and as a result to decrease separation of nonuniform particles if the ideal mixture is needed or to increase separation if the nonuniform particulate medium is being optimum for technological process.
Segregation tends to occur whenever bulk materials flows are accompanied by the movement of particles relatively to each other.
2 Theoretical aspects of particle segregation in a shear flow
The recently developed [1] general model of segregation dynamics in a shear flow of particulate solids takes into account convection, quasidiffusional mixing and two fluxes of segregation. For a steady two-dimensional shear flow such model is formulated as follows:
2 -1 m2-s 1;
Dm - coefficient of migration, m2-s-1; d - diameter of particle, m;
F - the collision frequency, s-1; j - the particles flux, kg-(m2-s)-1;
Ks - coefficient of segregation, m-s-1; k - coefficient of relative velocity of segregation, N-1-s-1; m - the particle mass, kg;
where c = c(t, x, y) is the test component concentration, t - time, u - velocity towards
shear direction x, s - mean distance between particles, AM is the local nonuniformity parameter; Ddif , Dm, K are the coefficients of quasidiffusional mixing, migration and
hydromechanical segregation respectively, pb - bulk density.
The flux of hydromechanical segregation is proportional to the degree of local nonuniformity of a medium. The nonuniformity parameter is a total excess moment of friction forces AM f, gravity forces AMg , and impact momenta AMc, acting on a test
particle in a conventionally homogeneous medium relative to a certain instantaneous axis of rotation as follows
where k - is the kinetic constant of segregation, defined by the experimental method [2]; c - is the concentration of test particles; AM = AMf + AMg + AMc - is the total excess sum of moments of frictional, gravity forces and impact momenta [3].
When the AM value is positive the particle is more likely moved towards overlying layers of the bed, and on the other hand, if the value of the AM is negative - the particle is more likely to descent to the underlying bed.
The flux value of migration, caused by spatial nonuniformity of particulate medium, is defined as a relative velocity of the quasidiffusional displacement of nonuniform particles. The migration flux is proportional to the degree of spatial nonuniformity of particulate medium. Such nonuniformity degree is defined as a rate of change of the mean distance between particles in the direction of migration Flux as follows
where Dm is the migration coefficient, calculated by analytical method [4] using the traditional physical and mechanical constants of particles and shear flow parameters.
The migration coefficient for spherical cohesionless particles, having diameters d1 and d2, and densities pi and p2 respectively, is defined as
where m(c) is the mean particle mass; F, V ’ are the mean collision frequency and the mean fluctuation velocity respectively.
In the course of migration the heavier particles move towards the gradient of fraction volume of solid phase, whereas the light particles are forced into the area with a greater fraction of void volume.
The analysis of the model of segregation dynamics (1) shows, that the segregation intensity may be controlled by the influence of kinematic and structural characteristics of shear flow of particulate solids.
Therewith the important factors influencing hydromechanical segregation and
du
migration are shear rate — and the gradient of the fraction of void volume
Js = к AMc pb ,
(2)
d In S ~^~c P
(3)
-' 2 ( 7 2 7 2 ^
„ m(c)(V )2 d2 d22
Dm
(4)
respectively.
3 Experimental and analytical investigations of segregation on size and density
In our experimental investigation we used a test unit that consists of an inclined open channel with a rough perforated bottom [3].
The experimental procedure is as follows. When the steady flow is achieved the particles go into receiving tray. To determine the particle distribution along the bed depth the tray contains cells.
To analyze the segregation dynamics we determined the profiles of particle velocity and fraction of void volume. We defined such profiles on the basis of the experimental data including bed depth, channel inclination angle and particle distribution along the tray. Besides we took into account the function of the interrelation
y102, m
dt / db = 0,505
2.0
1.6
1.2
0.8
0.4
0
0.075
y-102,m
0.125
c, kg/kg
0.175
0.225
a)
dt / db = 1,52
6)
Fig. 1 Concentration profiles in the gravity flow of glass beads mixture consisting of the bulk material ( db = 3,4 mm, pb = 2500 kg/m3, cb = 88 %) and the test component:
a - dt = 1,7 mm, pt = 2500 kg/m3, ct = 12 %;
b - dt = 5,1 mm, pt = 2500 kg/m3, ct = 12 %
1.6
0.8
0.4
7-102, m
0.1
0.2
0.3
а)
C, kg/kg
0.4
0.5
.^-0, Dm^0
6)
Fig. 2 Concentration profiles in the gravity flow of glass beads mixture consisting of the bulk material ( db = 3,4 mm, Pb = 2500 kg/m3, Cb = 88 %) and the test component:
a - dt = 3,4 mm, pt = 1000 kg/m3, ct = 12 %;
b - dt = 3,4 mm, pt = 10000 kg/m3, ct = 12 %
1.2
0
0
ship between the bed dilatation, total pressure and shear rate, which is formal analogy between a particulate medium at a rapid shear flow and a dense gas, as follows
= y v , (5)
where p is the total pressure in a particulate medium, e is the shear flow dilatation [3], v is the granular material “temperature”, expressed as a function of the shear rate [3], y is the coefficient of the physical and mechanical properties of the particles.
The analytical investigations of segregation on size and density for varies dt and pt of test component of particulate mixture using Eqv. (1) and the profiles of velocity and fraction of void volume are shown on Figs. 1, 2.
The analysis of this results testify to the fact that the main mechanism for segregation on density is migration and for segregation on size it is hydromechanical segregation. So, in order to control segregation on size we must change the shear rate and in case of segregation on density we must influence the gradient of the fraction of void volume.
4 The methods to control segregation in particulate media
The most wide-spread type of particulate solids movement taking place at the various manufacturing processes is the gravity flow. Segregation control in the gravity flow of particulate solids may be realized in the way to change the geometrical flow parameters such as the chute angle and the bed depth. The experimental investigation show that the segregation efficiency is being maximum at the chute angle close to the angle of repose of the material (Fig. 3) and the bed depth equal 4 - 6d (Fig. 4). The segregation efficiency is evaluated as the variation coefficient, which is calculated as a percentage ratio of the standard of concentration distribution of the test component ci to its mean concentration c
where mi is the material mass in i - cell, n is the total number of cells.
On the other way the aeration and vibration of the bed are used as a methods to control the segregation in particulate media. The above mentioned technique and apparatus were adapted taking into account the specific character of the particulate material flow on an inclined chute during the transverse aeration and vibration.
The aeration influence on segregation in aerated gravity flows of particulate solids was analyzed by means of determination of a test component distribution in the moving bed of particulate mixtures (table 1) on a rough chute.
Fig. 5 describes experimental results of the investigation on the efficiency of segregation in gravity flows of mixtures of particulate solids during their aeration in the direction from the bed bottom to its free surface during this experiment. Bed depth was equal to 6-8 particle diameters.
The results testify to the fact that the aeration process in the direction of the free surface reduces the efficiency of segregation on size (mixtures 1, 2, 3) and increases its efficiency for particles differing in density (mixture 4). It should be pointed out that the
(6)
Q
Es, %
, Es, %
0,95
1,05 1,1 1,15 1,2
0 2 4 6 8 10
Fig. 3 The segregation efficiency as a dependence of the chute angle for varies mixtures (tabl. 1)
Fig. 4 The segregation efficiency as a dependence of bed depths for mixture M7 (tabl. 1)
Table 1
Characteristics of particulate material mixtures
mixture materials d-103 , m Pb > kg/m3 a0 , deg wm ,m/s
1 Silicagel (high porosity) +3.5-3.75-50% +4.25-4.5-50% 610 30 0.94
2 Superphosphate +2.2-2.5-50% +2.8-3.0-50% 1080 35 0.959
3 Porcelain 5.5-50% 7.0-50% 1100 30.5 1.71
4 Superphosphate Silicagel (low porosity) +3.75-4.0-85% +3.75-4.0-15% 1000 35 1.18
5 Superphosphate +2.0-2.2-50% +2.6-2.8-50% 1080 35 0.88
6 Superphosphate +3.5-3.75-50% +4.0-4.25-50% 1080 35 1.27
7 Silicagel (high porosity) +3.5-3.75-50% +4.0-4.25-50% 610 30 0.919
8 Silicagel (low porosity) Silicagel (high porosity) +4.0-4.25-10% +4.0-4.25-90% 470 30 0.94
Fig. 5 Influence of aerating air velocity w / wm towards the free bed surface on
segregation efficiency Es of various particulate mixtures (table 1)
Fig. 6 Influence of aerating air velocity w/ wm towards the bed bottom on
segregation efficiency Es of various particulate mixtures (table 1)
influence of the aeration intensity on segregation is relatively small unless the minimum fluidization rate is achieved. Obviously it is connected with the prevailing influence of air separation at high air velocities.
Fig. 6 describes experimental results of the influence of the aeration intensity in the direction from the free bed surface to its bottom on particle segregation on size (mixtures 5, 6, 7) and density (mixture 8). The results testify to the fact that the efficiency of segregation increases with the increase of the aeration intensity (up to relative rate values w/wm « 0,45). The relative velocity being further increased, the
efficiency of segregation decreases, but it is still high enough as compared to the efficiency in the non-aerated flow even at w/wm = -1. These results demonstrate the prevailing influence of the segregation effects in the granular medium as compared to the air separation within a wide range of aeration rate variations.
The experimental investigation of the vibration influence on particle segregation was performed on an inclined vibrated chute under various vibration parameters (frequency and acceleration) and inclination angles. The experiment consisted in determination of the distribution of large particles along the depth of the bed of glass beads mixture of fractions (3,25...3,5 mm - 88 % and 3,6...3,75 mm - 12 %) by analyzing experimental information obtained during the particle free-fall phase using experimental unit. [3]
As a result of the experimental investigation the influence of the slope angle of vibrated chute on segregation during gravity flow of beads differing in size were explored. It was found out that the segregation efficiency Es had a maximum value at
the inclination angle « 28o approximating the angle of repose of the material (Fig. 7) at the various vibration accelerations.
Besides the investigation results, presented in Figs. 8-13, show that the features of functions characterising the influence of vibration acceleration (Figs. 8, 10, 12) and vibration frequency (Figs. 9, 11, 13) on segregation efficiency essentially depended on the angle the of chute slope.
Fig. 7 The s egregation efficiency Es as a dependence of the chute angle at different vibration accelerations:
1 - 2 g; 2 - 4 g; 3 - 7 g (for the frequency 50 Hz)
Fig. 8 The segregation efficiency Es as a dependence of the vibration acceleration A at different frequencies:
1 - 35 Hz; 2 - 50 Hz; 3 - 100 Hz;
4 - 150 Hz (for the chute angle 26°)
Fig. 9 The segregation efficiency Es as a dependence of frequency f at different vibration accelerations A :
1 - 2 g; 2 - 4 g; 3 - 7 g; 4 - 10 g (for the chute angle 26°)
Fig. 10 The segregation efficiency Es as a dependence of the vibration acceleration A at different frequencies (for the chute angle 28°)
Fig. 11 The segregation efficiency Es as a dependence of the vibration frequency f at different vibration accelerations:
1 - 2 g; 2 - 3 g; 3 - 7 g (for the chute angle 28°)
Fig. 12 The segregation efficiency Es as a dependence of the vibration acceleration A at different frequencies:
1 - 35 Hz; 2 - 50 Hz;
3 - 100 Hz; 4 - 150 Hz (for the chute angle 30°)
Fig. 13 The segregation efficiency Es as a dependence of the vibration frequency f at different vibration accelerations:
1 - 2 g; 2 - 4 g; 3 - 7 g (for the chute angle 30°)
Also it was found out that at inclination angles 26o and 28o the segregation efficiency decreases, when the frequency of vibration increases. Figs. 8, 10 present experimental results, characterizing the influence of the vibration acceleration on segregation of the glass beads in their gravity flow. The results testify to the fact that the segregation efficiency has a maximum at the acceleration of vibration equal approximately to 4-5 g. When the inclination angle is equal to 30o the influence of vibration conditions on segregation in gravity flow was variegated. At the constant frequencies 50, 100 Hz, as Fig. 12 shows, segregation decreases and at the frequency 150 Hz increases with increase in acceleration. Fig. 13 shows the tendency of segregation efficiency to increase with the increase in the frequency of vibration.
The experimental results allow to draw the following conclusions. The vibration parameters exert the essential influence on the granular material segregation in gravity flows.
As the results of investigation of the above mentioned methods, the optimum conditions for segregation and mixing in gravity flows of mixtures, consisting of particles differing in size and density are determined.
1. Dolgunin V.N., Ukolov A. A, Ivanov O.O. Research on particle segregation during rapid gravity flow // The 3-rd Israel conference for conveging and bulk solids handling. Proceeding. Jerusalem. 2000: Pp. 8.67 - 8.73.
2. Dolgunin V.N., Kudy A.N., Ukolov A.A., Tyalin A.G. Segregation kinetics in moving granular media // The forum for Bulk Solids Handing, Proceedings, Jerusalem, 1997, p. 11.75 - 11.81.
3. Dolgunin V.N., Ukolov A.A. // Powder Technology. V.83 (1995). Pp. 95-103.
4. Dolgunin V.N., Kudy A.N., Ukolov A.A. // Powder Technology. V.96 (1998). Pp. 211-218.
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В.Н Долгунин, А.Н Куди, О.Б. Юшкова, А.Н. Ананьев
Кафедра «Технологическое оборудование и пищевые технологии», ТГТУ
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Verfahren der Steuerung von Segregation und Mischung in den Gravitationsstromen des Kornigmediums
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Moyens de la gestion de la segregation et du melange dans les courants de gravitation du milieu granule
Resume: Dans cet article est realisee l’etude experimentale et analytique de la segregation dans les milieux granules avec les etats differents du milieu granule. Pour la gestion de la segregation sont etudies les effets essentiels de la segregation pour les particules qui se distinguent par les dimensions, par la densite et par les parametres du courant rapide du decalage. Sont proposees les methodes les plus efficaces pour le controle de la segregation dans les courants rapides des particules solides.
