118076164 Gravity Separation of Particulate

8/22/2019 118076164 Gravity Separation of Particulate

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Gravity Separation of Particulate Solids

in Turbulent Fluid Flow

JU RGEN TOMAS

QUERY SHEET

Q1 Au: Is bullet list constructed correctly?

Q2 Au: Should this be Table 4. Not otherwise referred to


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Gravity Separation of Particulate Solidsin Turbulent Fluid Flow

JU RGEN TOMAS

5Mechanical Process Engineering

Otto-von-Guericke-University Magdeburg

Magdeburg, Germany

The separation characteristics of particle settling velocity, size, density, and shapeare introduced, and the equivalent settling condition for laminar, transition, and

10turbulent flow are explained. A similarity model of particle transport in a turbulentflow field is brief ly discussed. Typical operation principles in separation apparatusesfor counter current and cross-flow separation are presented. The separationfunction, cut point, sharpness, and separation stage utilization coefficient aredetermined to assess the efficiency for process sequences for multistage turbulent

15cross-flow separation. Satisfactory to very good results were achieved in the difficultseparation of a partially liberated aggregate consisting of hardened cement pasterubble with sharpness from 0.66 to 0.94 at separation stage utilization coefficients of7 to 87%. Specific mass flow rates of 3 to 16 t=(m2h) and mass related energyconsumption of 0.2 to 8 kWh=t were obtained.

20Keywords: Cross-flow gravity separation model, separation efficiency, wasterecycling

Introduction

Typical unit operations of particle separation are introduced to explain the operation

principles like current, counter current, and cross-flow patterns with their physically

25determined separation characteristics, i.e., settling velocity vs,i,j, particle size di,

density rs,j, and shape. These processes are assessed by the separation function Ti,j,

or grading efficiency curve, as the ratio of product to feed mass increments of the

separation characteristic fractions i, j. The ratio of secant points of this function near

the cut point, the so-called separation sharpness k, indicates directly the process30quality; see Schubert (1989, 1996, 2003) for particle separation processes and

Smigerski (1993) and Leschonski (2003) for air classification.

Wet and dry separations have differing advantages and disadvantages. Dry

separation is more cost-effective in terms of its energy requirement, since with wet

separation problems regarding the treatment of process water and its disposal need to

35be considered, and dry separation is especially suitable for semi-mobile processing

3b2 Version Number : 7.51c/W (Jun 11 2001)File path : p:Santype/Journals/Taylor&Francis/Upst/22(2)/22(2)-18467/Upst22(2)-18467.3dDate and Time : 2 8/4/04 and 16:07

Presented at the 4th International Conference for Conveying and Handling of Particulate Solids,

Budapest, Hungary, May 2730, 2003.

Address correspondence to Ju rgen Tomas, Mechanical Process Engineering, Otto-von-Guericke-

University Magdeburg, P.O. Box 4120, D-39106 Magdeburg, Germany. E-mail: juergen.tomas@vst.

uni-magdeburg.de

Particulate Science and Technology, 22: 119, 2004

Copyright # Taylor & Francis Inc.

ISSN: 0272-6351 print/1548-0046 online

DOI: 10.1080/02726350490457222

1


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plants. Wet separation is also useful for the removal of pollutants from contaminated

building waste (Kalck & Werther, 1990). The liberation of building rubble by com-

minution produces a predominantly mineral mixture with a density distribution of

rs 1.82.7 g=cm3 (Tomas et al., 1998; Tomas & Grger, 1999). As a result of the

40relatively narrow density range, the requirements regarding the sharpness of the

process employed for the separation of partially liberated aggregate and concrete-

brick rubble are very high. The separation processes currently employed in the

recycling of building materials remove mainly the lightweight impurities such as

paper, wood, films, insulating materials, and pieces of plastic (rs 0.11.2 g=cm3)

45by wet or dry separation. In such cases, the range of unsharpness beyond the cut

point can be defined in the intermediate range (rs 1.21.8 g=cm3), so that equip-

ment with relatively low separation efficiency is still adequate for these applications.

Table 1 provides an overview of the state-of-the-art with respect to separation for

recycling building materials and domestic waste (Bilitewski, 1995; Friedrichs &

50Tomas, 1996; Hanisch et al., 1991; Melchiorre et al., 1994; G. Schubert, 1999;

Tra nkler, 1992).For the separation of building rubble, classifiers are mainly used in practice. The

upward flow or single-stage cross-flow separators commonly employed for dry

separation in an airflow separate the material feed according to the respective settling

55velocities of the different components. The separation behavior is influenced deci-

sively by the particle size, particle shape, and particle density of the components to

be separated. An air classifier can separate the materials, according to one of these

parameters, providing that the influence of the other two variables is minimized.

The separation of totally or partially liberated aggregate particles in the size

60range of d 216 mm, therefore, presents a challenge to the separation sharpnessand efficiency of the equipment. Tests were carried out in a zigzag channel to

establish whether the high separation sharpness required can be achieved in a

multistage turbulent cross-flow separation apparatus.

Table 1

Selected separation processes for the recycling of building and domestic waste

Wet separation Dry separation

*

Float and sink cleaning (Tra nkler,1992; Schu tze, 1987)

*

Classification (Greschner, 1994)

* Hand sorting (Hanisch et al., 1991)* Aquamator (Rohr, 1987; Schu tze, 1987) * Automatic sorting (Schubert, 1996)

* Countercurrent and cross-flow

aeroseparation (Schubert, 1999)* Upward flow (Kalck & Werther, 1990) * Pneumatic table (Gu ldenpfennig &

Lohr, 1995)* Jig (Breuer, 1988; Kellerwessel, 1993) * Sloping separating belt

(Schubert, 1996)* Slinger (Hanisch et al., 1991)

* Washing drum (Hentzschel, 1990) * Eddy current separator(Schubert, 1994)

2 J. Tomas


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Fundamentals of Aeroseparation of Building Rubble

65The basis for studying a separation process in a fluid cross flow is the balance of the

forces of buoyancy, weight, and fluid resistance of a particle. With this balance, it is

possible to obtain a correlation between particle size and the quasi-stationary settling

velocity vs in a gravitational field:

v2s 2

cWrs rf

rf

Vp

Ap g 1

70where Ap is the side-fed cross-sectional area, cW the drag coefficient of the fluid flow

pattern around the particles, Vp the particle volume, and rf the fluid density. The

density of the solid particles rs depends on the inner porosity (up to 95% for

insulating materials) and pore saturation with a liquid.

75In the separation of particles of varying density rs the principle of what is termed

equivalent falling classes, i.e., classes with equal settling velocity, can be for-

mulated as follows. If the particle shape is constant, large and lightweightparticles settle just as fast as small and heavy particles. With d i to di 1 as the

particle size of the class i to i 1 as well as rs,S and rs,L, as the particle densities of80the heavy fraction (index S) and the lightweight fraction (index L), the following

applies:

vsdi1; rs;L vsdi; rs;S 2

Depending on the particle flow patterns vs / da, (Schubert et al. 1986), and with

85the relationship

cW / Re1

2

a

3 3

and the particle Reynolds number Re vs d rf=Zf, then for the size fractions thefollowing holds:

di1di

rs;S rfrs;L rf

!a13a

4

90

and for the settling velocity vs related to cut point vsT (Table 2):

vsvsT

d

dT

a

rs rfrs;T rf

!a13

5

Table 2

Equivalent-falling condition dependent on the particle flow-around pattern

Exponent a a 13 a

Flow pattern Reynolds number Drag coefficient

2 1=2 Laminar (Stokes) Re < 1 cw / Re1

2 < a< 1=2 1=2 . . .1 Transition 1 < Re < 103 cw / Re1 . . .01=2 1 Turbulent (Newton) 103 < Re < (24)105 cw / Re

0

Gravity Separation of Particulate Solids in Turbulent Fluid Flow 3


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First, the counter current particle separation in a field of gravity has been described

95by Molerus (1967), Molerus and Hoffmann (1969), Schubert et al. (1986), Schubert

(1989), and Bhme (1989) and centrifugal forces by Husemann (1990) and Husemann

and May (1998). Numerical simulations on basis of computational fluid dynamics

(CFD) models were performed by Heiskanen (2002). But the models of counter

current separations formulated by Gorzitzke (1982) and Bhme (1989) to date have

100proven unsuitable or too complex (Senden, 1979) for the evaluation of the multistage

cross-flow separation in order to describe the process efficiency. The separation

tapping model of a turbulent cross-flow hydroclassification derived by Schubert and

Neee (1973), Neee (1969, 1978), and Neee and Schubert (1975, 1976, 1977, 1977)

was used to develop a model for multistage turbulent cross-flow aeroseparation

105(Tomas & Grger, 1999, 2000). The good separation characteristics of a zigzag

separator, invented by Stebbins (1930), are based on the series arrangement of

several such stages (Kaiser, 1963; Tomas & Grger, 1999, 2000, 2001).

The separation efficiency is influenced by the turbulent flow pattern in the

process chambers (Schubert & Neee, 1973; Neee, 1969, 1978; Neee & Schubert,1101975, 1976, 1977). This effective dimensionless turbulence variable can be roughly

described by the averaged apparatus Reynolds number Re ub=n 103106, degreeor intensity of turbulence Tu 0.010.15, and turbulent diffusion coefficient of fluidDt 12000 cm

2=s (Table 3). Because of the comparably high degree of turbulence inthe zigzag channel the turbulent particle diffusion or eddy diffusion coefficient of

115fluid Dt,s % Dt % (45 cm)2=s(63 cm)2=s measures high also. Additionally, the

amounts in brackets can be physically correctly interpreted as the local particle

position shift squared, averaged, and related to a time increment, i.e., a second

statistical momentum of particle concentration distribution.

The ratio of convective to diffusive transport expressed by the Bodenstein

120number Bo ub=Dt 1103 is large. Hence the particle separation may be described

by a model for random or turbulent mass transport with following prerequisites:

The particle hold up probability distributions (concentration per number cn,i,j)

versus height y are independent of each other, i.e., for every particle size fraction i as

well as density fraction j the one-dimensional Fokker-Planck-Equation is assumed to

125be valid:Q1

@cn;i;j@t

vs;i:j

1

1!@cn;i;j@y

Dt;s 1

2!@2cn;i;j@y2

6

For homogeneous field of turbulence in the process chamber the turbulent dif-fusion coefficient Dt % Dt,s and the particle diffusion coefficient are assumed to be

130equivalent. The turbulence intensification by the free turbulent particle flow-around

pattern is larger than damping by particle concentration caused by inelastic particle-

particle or particle-wall collisions:

L

ffiffiffiffiffiffiu02x

q% const: Dt 7

The macrodimension of turbulence (diameter of largest eddies dW,max L=2)135depends on the characteristic dimension of a turbulence generating tool, i.e., the

width of process channel L/ b. The root-mean-square of turbulent flow ratefluctuations across the principal flow direction is proportional to the eddy

circumferential speed uf and to the averaged fluid flow rate

ffiffiffiffiffiffiu02

x

q/ uj / uu.

4 J. Tomas


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The particle size is small compared with the channel width d < 0.1L< b. The particle140size should also be small compared with the microdimension of turbulence (dW,min

diameter of smallest eddies with circular laminar flow) d < dW,min % 10lD with theKolmogorov dimension of microturbulence lD n

3=e 0;25

.

For steady-state condition @cn,i,j

= @t 0 (at bottom y 0, cn,i,j

cn,0,i,j

) an

exponential particle number concentration distribution versus height h is obtained

145from Equation (6), (Molerus, 1967):

cn;i;j cn;0;i;j exp vs;i;j

Dt;s h

!8

This function is the basis of models that describe the stochastic process

efficiency. The so-called separation function or grade efficiency curve is used to

150assess the accuracy of gravity separation of any narrow particle size fraction Ddi, as

shown in Figure 1. This figure shows the incremental probability distribution of

particles that are discharged as heavy product. As limits for this S-shaped function,

a step function indicates the ideal or perfect separation and a horizontal line

characterizes the undesired feed mass splitting without any effect related to the

155separation property, i.e., particle density rs (or particle size d in terms of classifi-

cation). The difference between the step function and the S-curve characterizes the

amount of misplaced product. Hence, the steeper the S-function, the better is the

separation effectiveness, i.e., sharpness. Generally, this sharpness can be evaluated as

k 0.30.6 being sufficient, k 0.60.8 being good, and k 0.80.9 being very good,160which is shown in Figure 1 (Rumpf, 1975).

When one balances the particle flow in one cross-flow element or stage, i.e., asingle channel bend, of the zigzag channel and takes into account the turbulent

particle flow-around pattern in the zL overflow separation stages or zS in the

underflow, respectively, the normalized separation function is as follows ( _VVL,_VVS

165total volume flow rates of lightweight and heavy particles; Tomas & Grger, 2000):

TzL;zS

rs;j rfrs;T rf

!dconst:

1

1 _VVL_VVS

1 ffiffiffiffiffiffiffiffiffi ffiffirs;jrfrs;Trf

q 9

This fractional grade function (Equation (9)) corresponds to a probabilitydistribution of a class j of the measurable density of the porous particles rs,j (the pore

170space in hardened cement paste measures around 2030%) being discharged in the

heavy fraction S. In his case, the cut point (average separation density) is defined

with TzL,zS(rs,T) 0.5 probability. For equal fractional grade efficiencies of the zLlightweight fraction separation stages and zS heavy fraction separation stages, the

component mass balance of all stages (apparatus elements) returns the total

175separation probability (feed index A):

Ttot;j _mm

S;j_mmA;j

Rm;S qS rs qA rs 1

1 1TzL;j

zL

TzS;j zS

10



7/20

Table3

Separatorswith

turbulentfluidflow(Schube

rtetal.,

1986),re-calculatedfromseparationresults

Cross-flow

separation

appara

tus

Apparatus

Reynoldsno.

Re

uD=n

Degr

eeof

turbu

lence

Tu

ffiffiffiffiffiffiu02

p

=u

T

urbulent

diffusion

coeffi

cient(cm)2=s

D

t

L

ffiffiffiffiffiffi

u02

p

Bodenstein

number

B

os

vL=D

t;s

Screw

classifier

nS

D2 S

n

Recrit%

104

104

51

05

0.05

0.15

0;014n

SD2 S

0;48_VV

F

B

550or%

(2)2(

7)2

nS

D2 S

Dt

%

100

Rakeclassifier

nR

L2 R

n

104

51

04

0;31n

RL2 R

0;48_VV

F

B

301

00o

r%

(5.5

)2(

10)2

nR

L2 R

Dt

%

1:5

3

1.3Cyclones

uD

Cn

Recrit%

103

105

106

0.01

0.05%

0.1

atinput

Hydrocyc

lone:8

10

4uD

C

Aerocyclone:0:0035uD

C

120or%

(1)2(

4,5)2

uD

C

Dt

%

103

6


8/20

1.4Zigzagseparatora

)

ub n

104

61

05

Tu%

Dt

ub

%

0.110.13

(0.110.13)ub

20004

000

or%

(45)2

(63)2

ub

Dt

%

1

15

2.Coun

tercurrentclassifier

uD n

103

106

0.02uD

2002000or%

(14)2

(45)2

0.550

aSchubettetal.,

1986

.

7


9/20

For a symmetrical separation with the same number of stages in the lightweight and

heavy particle flow (zL zS z), the total separation function can be simplified with180Equations (9) and (10) to:

Ttot;j 1

1 _

VVL_VVS

1 ffiffiffiffiffiffiffiffiffiffiffirs;jrfrs;Trf

q z 11

An increasing number of stages z results in a steeper rising separation function

characterized by a essentially higher sharpness (Figure 2). Hence, the slope of the

185separation function can be characterized by an elegant analytical formulation of the

overall separation sharpness ktot for the ratio of secant points rs,25=rs,75 of 25% and75% separation probability:

ktot rs;25

rs;75

z ln _VVL= _VVS

ln 3

z ln_

VVL=_

VVS

ln 3" #

2

1 12

Separation in the turbulent particle flow pattern can be achieved with appropriate

190separation sharpness only if the separator has a comparably high number of

separation stages and if a sufficiently high ratio between the lightweight and heavy

material volume flow rates _VVL= _VVS can be maintained. This is commensurate withpractical experience gained with classification (Kaiser, 1963). Because of this fact, the

multistage separation model is generalized for a wide range of flow patterns

195concerning the characteristic particle settling velocity (Table 2).Q2With the effective total number of separation stages ne (the feed stage both in the

overflow and the underflow is included in this number),

ne 2 ze 1 13

Figure 1. Assessment of gravity separation of a particle size fraction Ddi.

8 J. Tomas


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An additional degree of freedom z ze is obtained, which, on the one hand, can200be used to fit the measured values to a physically valid separation function (Equation

(11)) especially with regard to their S-shape. On the other hand, the so-called

separation stage utilization coefficient represents an additional parameter to assess

separation efficiency in the case of small density differences:

ZT ne=n 14

205Setup of the Test Rig

For the separation of mineral materials, a test rig, consisting of a zigzag channel

measuring 173 200 mm2, a feed unit, a fan, a cyclone, and a cloth filter was set upas shown in Figure 3. The separation process can be observed through the glass side

walls of the channel. The mass flow rates of the feed materials and the separation

210products are determined by means of weight cells. In addition, during the tests, the

air volume flow rate, the average channel velocity, the pressure drop versus the

zigzag apparatus, the pressure drop versus the filter, and the temperature and relative

humidity at significant points can be measured (Friedrichs & Tomas, 1996).

Zigzag classifiers are usually classed as counter current classifiers (Bhme, 1989).

215The separation process in the zigzag channel can also be understood, however, as a

series arrangement of cross-flow separation stages. In each stage, so-called vortexrolls are formed, to which one fractional grade can be assigned in the ideal case

(Senden, 1979).

Figure 2. Influence of stage number z on total separation function Ttot of normalized particle

density rs=rs,T of a multistage cross-flow (zigzag) apparatus.



11/20

Usually, the feed material is added to the separation process at the center

220relative to the number of stages in the zigzag channel. In each stage of the apparatus,

separation into lightweight and heavy fractions takes place. The heavy particles slide

along the downward sloping channel walls and the lightweight particles are swept up

with the airflow at the two upward sloping channel walls. At the bends of the zigzag

channel, these two currents cross the channel so that a cross-flow separation takes

225place. The good separation characteristics of a zigzag separator are based on theseries arrangement of several such stages (Kaiser, 1963; Senden, 1979; Gorzitzke,

1982; Bhme, 1989; Friedrichs & Tomas, 1996; Tomas & Friedrichs, 1997; Tomas

et al., 1999; Tomas & Grger, 1999, 2000, 2001).

Assessing the Separation Model for Air Classification

230As part of preliminary studies, the separation model in Equation (11) was applied for

the classification of glass beads, sand=splits, and gravel (Table 5). In Figures 4 and 5,the measured values for the four separation experiments with the cut particle size

dT 2.1, 4.6, 5.4, and 6.7 mm are shown. Despite reduction by particle shape impact,

the quasi-stationary settling velocity of spheres vsT at this cut point is higher than235the averaged channel airflow rate u, which is a characteristic of the predominant

cross-flow separation principle.

Figure 3. Setup of the test rig.

10 J. Tomas


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Table4

Assessmentcharacteristicsformultistagecross-f

lowseparationin

asymmetricalapparatuswithzo

zu

znumberofseparationstages

andtheexponent

a

accordingtoTable1

Separationfunction

Ttot(

x=xT

)

Cutcharacteristic

xT

x50

(Ttot

0.5)

Separationsharpness

ktot

x25

=x75

Fluidflowseparationx

vs

1

1

_VVo

_VVu

1

vzd;rs

vsTd

T;rsT

h

i

z

vsT

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2r

sT

rf

VP

;T

g

cW;

Trf

AP

;T

s

z

ln_VV

o=

_VV

u

ln3

z

ln_VV

o=

_VV

u

ln3

Classificationx

d

rsc

onst.

1

1

_VVF

_VVG

1

ddT

a

h

i

z

dT%

rf

3r

s

gD

t;s

hln

_VVF

_VVG

!2

forspherescW

0.44

z

ln_VV

F=_VVG

ln3

z

ln_VV

F=_VVG

ln3

"

#1a

Gravityseparation

x

r

sd

const.

1

1

_VVL

_VS

VS

1

rs;

jrf

rs;

Trf

a1

3

"

#z

rsT%

rf

3

d

gD

t;s

hln

_VVL

_VVS

!2

forspherescW

0.44

z

ln_VV

L=

_VVS

ln3

z

ln_VV

L=

_VVS

ln3

"

#

3a

1

_VVo;

_

VV

F;

_VVL

overflow,

fine,orlightweig

htparticlesuspensionvolumeflowrates.

_VVu;

_

VV

G;

_VVS

underflow,

coarse,

orheav

yparticlesuspensionvolumeflowrates.

a

2laminar(Stokes),a

0.5turbulent(Newton)flowpatternacc

ordingtovs/

da

(Schubertetal.,1986).

11


13/20

Table 5

Comparison of classification results with the separation model according to

Equations (11), (12), (13), and (14)

According to Figure 5

According

to Figure 4

m

Sand=Split

*

Split

r

Split=gravel

Particle fraction du,i - do,i, mm 216 0.84 1.616 316

Channel velocity u, m=s 13 7.5 8 10Air volume flow rate _VVg, m

3=s 0.52 0.3 0.32 0.38Particle settling velocity vsT(dT), m=s 18.2 11.5 15.6 18.7Mass flow rate _mms, t=h 0.12 0.34 0.12 0.16Specific mass flow rate _mms;A,

t=(m2h)3.0 8.5 3 4

Particle concentration ms,g, g=kg 82 262 82 94Cut size dT, mm 5.4 2.1 4.6 6.6

Separation sharpness k 0.89 0.75 0.7 0.7

n 7, effective separation stages ne 5.8 1.8 1.2 1.2Utilization of separation

stages ZT, %

83 26 17 17

Pressure drop DpZZ, Pa 440 440 440 700

Specific energy consumption Wm,ZZ,

kWh=t1.25 0.39 1.25 1.72

Figure 4. Classification of log normal distributed glass beads and comparison with the

separation model according to Equation (11), Table 5.

12 J. Tomas


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The best efficiency is obtained for the very sharp separation of ideal-shaped glass

spheres with a steep curve in Figure 4. For the purpose of comparison, the corre-

sponding model curves with fitted, i.e., effective, stage numbers zL zS ze 1.4,2401.1, and 1.1 are also plotted for splits. With this additional degree of freedom z, the

experimental separation processes with the S-shaped curves typical of air classifi-

cation (rs const.) can be reproduced very well. From these, separation efficienciesof k 0.89 for glass beads and 0.70.75 for split is determined, which can be con-sidered good (range k 0.60.8). However, for this classification, effective stage

245numbers in the range ne 1.21.8 results. This means that only seven separationstages of the apparatus are utilized satisfactorily, i.e., ZT ne=n 1726%.Remarkable in technical terms as well are the mass flow rates of 38.5 t=(m2h)related to the apparatus cross-sectional area and the mass-related energy con-

sumption of only 0.41.7 kWh=t, as summarized in Table 5.

250Results of Gravity Aeroseparation

Tests on the separation of concrete-brick mixtures were carried out. Figure 6 shows

the reproducibility of the separation efficiency on the basis of the results of four tests

with a 15-stage unit, all conducted under identical conditions (d 812 mm). It canbe seen that the separation results demonstrate considerable scatter in comparison

255with the classification according to Figure 5. The plotted model curves limit the

range of separation efficiency from k 0.670.91 for ne 17 (Table 6).From comparison of the separation experiments with narrowly fractionated

concrete-brick mixtures d 810 mm (Figure 7), it can be concluded that the scatteris caused by the influence of the particle size. For other tests, Figure 7 shows that the

260separation model Equation (6) can be fitted very well to the measurement results for

narrow particle size ranges. The sharpness of this separation with the seven-stage

Figure 5. Comparison of the classification results with the separation model according to

Equation (11), Table 5.



15/20

Figure 6. Results for the separation of concrete-brick rubble, d 812 mm, n 15, Table 6.

Table 6

Assessment of the gravity separation results

Concrete-brick

rubble

Concrete,

rubber

Figure 8

Particle fraction du,i - do,i, mm

812

Figure 6

810

Figure 7

45 56.3

Channel velocity u, m=s 14 12.5 8.5 8.5Air volume flow rate _VVg, m3=s 0.56 0.51 0.35 0.35

Particle settling velocity vsT(dT), m=s 20.3 21.7 14.3 14.9Mass flow rate _mms, t=h 0.12 0.15 0.15 0.63Specific mass flow rate _mms;A, t=(m

2h) 3.0 3.7 3.7 15.8Particle concentration ms,g, g=kg 50 68 98 417Cut density rs,T, g=cm

3 2.1 2.4 2.1 1.8

Separation sharpness k 0.70.9 0.86 0.80 0.78

Effective separation stages ne 17 3.8 3 3.4

Utilization of separation stages ZT, % 747 54 43 49

Pressure drop DpZZ, Pa 1600 815 350 350

Specific energy consumption Wm,ZZ,kWh=t

8.0 2.75 0.83 0.19

14 J. Tomas


16/20

unit can be rated as very good with k 0.86. The utilization of the seven apparatusstages ZT 54% at an effective number of stages of ne 3.8 is considered satisfactoryto good (Table 6).

265On this basis, the layout for the separation of a light fraction, i.e., rubber

granulate rs % 1.0g=cm3, is relatively non problematic (Figure 8). Because of high

particle concentration ms,g 417 g=kg, a comparably small specific energy con-

sumption Wm,ZZ 0.19 kWh=t is generally obtained for good separation efficiency(Table 6). Satisfactory to very good results were also achieved in the difficult

270separation of a partially liberated aggregate consisting of hardened cement paste

rubble, k 0.660.94 at utilization coefficients of ZT 787%. Generally, specific

Figure 7. Separation of concrete-brick rubble, d 810 mm, n 7, Table 6.

Figure 8. Separation of concrete-brick rubble with rubber granulate, *d 45 mm, md 56.3 mm, Table 6.



17/20

mass flow rates of 3 to 16 t=(m2h) and mass-related energy consumption of 0.2 to8kWh=t were obtained.

Conclusions275To assess the efficiency of multistage turbulent cross-flow separation, the separation

functions were derived and compared with test results. With the effective total

number of separation stages an additional degree of freedom is obtained, which can

be used to fit measured values to the separation function on a physical basis.

A separation stage utilization coefficient represents an additional parameter to assess

280the separation efficiency in terms of small separation characteristic differences. On

the basis of the well-known separation sharpness, a considerable utilization of

separation stages, and geometrical variability of a zigzag apparatus, it was shown

that this multistage cross-flow separation principle is well suited for the gravity

separation of particulate solids including mineral and waste materials.

285Nomenclature

A area, m2

Bo Bodenstein number

cW fluid drag coefficient

d particle size, mm

290D diffusion coefficient, m2=s

g acceleration due to gravity, m=s2

h channel height, m

_mm mass flow rate, t=hn total number of separation stages

295q frequency distribution, (kg=m3)1

R recovery

Re Reynolds number

T separation efficiency function

Tu degree of turbulence

300u fluid velocity, m=sv particle velocity, m=s_

VV volume flow rate, m3

=hW work, energy consumption, J

Wm specific work, kWh=t305z fraction number of separation stages

Greek letters

a exponent

Dp pressure drop, Pa

Z utilization coefficient

310k separation sharpness

m particle concentration, g=kgx physical separation characteristic

r density, kg=m3

16 J. Tomas


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Subscripts

315A cross-sectional area related, feed

e effective

f fluid

F finesg gaseous

320G coarse

i particle size fraction

j particle density fraction

K channel

L lightweight

325m mass related

p particle

o overflow

s solid, settling

S heavy

330t turbulent

tot total

T cut point, separation

u underflow

ZZ zigzag apparatus

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