Numerical study of aerosol dust behaviour in aspiration bunker

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European Conference on Computational Fluid Dynamics ECCOMAS CDF 2006 P. Wesseling, E. Onate, J. Periaux (Eds)

NUMERICAL STUDY OF AEROSOL DUST

BEHAVIOUR IN ASPIRATION BUNKER

Konstantin I Logachev, Aleksei I Puzanok, Violetta U Zorya Belgorod State Technological University named after Shukhov (BSTU)

Kostyukova st. 46, 308012, Russia e-mail: kilogachev@intbel.ru http://www.bstu.ru/ru/faculties/iem.kafs/pm/

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Konstantin I Logachev, Aleksei I Puzanok, Violetta U Zorya

_____________________________________________________________________________________________________________________________________________________________________________________

1 INTRODUCTION

In order to correctly choose aspiration dust collecting devices it is necessary to possess in-formation on dispersion composition and dust concentration in the aspirated air. Besides, while using aspiration bunkers in practice the goal is to reduce dust entrainment in aspiration system. For instance, double wall bunkers are used with this aim. The less is the dust concen-tration in the suction inlet of the aspiration bunker the smaller are the costs for aspirated air cleaning in the dust collecting device.

In order to reduce dust entrainment in the aspiration system it is better to use rotating suc-tion cylinder.1_{Aerodynamic calculation of this local suction was based on the method of} boundary integral equations (BIE) and correspondingly vortex flows emerging in the aspira-tion bunker as a result of the interacaspira-tion between the inflowing induced jet and sucaspira-tion jet were ignored. The behavior of a single particle was studied. Its maximum diameter dimin-ishes with the increase of the suction cylinder rotation speed in the range from 1 to 3m/s by 30-30mcm.

Vortex type flow record is possible with the use of the discrete vortex method (DVM).2 It is necessary to note that the use of BIE and DVM methods made it possible to solve a number of new problems in industrial ventilation3.

The goal of the given paper is to study the behavior of dust aerosol in aspiration bunker equipped with rotating suction cylinder and to work out recommendations on designing effi-cient aspiration bunkers with the function of the dust precipitation chamber.

2 NUNERICAL ALGORITHM OF COMPUTATION

Let there be given the field of flat airflow containing inflow opening with the width a and the outflow opening with the width b (Figure1). The depth of the flow field is 1m. There be given the speed of the air in the inflow opening and the suction –

v

and

v

correspondingly, with v a v b⋅ = ⋅ .

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Figure1: Aspiration bunker: a) ordinary design; b) design with rotation suction cylinder.

Fraction limits

_d

₁

_{– d}

₁

_d

₂

_{– d}

₂

_{… d}

_i

_{– d}

_i

_{… d}

_n

_{– d}

_n

Fractions

_l

₁

_l

₂

_…

_l

_i

_…

_l

_n

Table 1: Dispersion composition determined by the lower and upper limits of fractions Note: there is an assumption that the sum of fractions is equal one in the table 1.

In order to determine the speed field at a random moment of time t=τ∆t numerical

algo-rithm of computation was used base on the combination of BIE and DVM methods. Along-side with this the border of the bunker was digitized by vortexes and control points where the normal speed component was known. Vortex sheet separation was exercised in three points of the flat surface between the calculated points with different signs of speed tangential compo-nent. The cylinder border was divided into sections on which run-off sources were continu-ously situated. In the center of the cylinder there was a vortex with the circulation

0

=

2 R v

π

, (1) where R – cylinder radius,

v

– linear speed of its rotation.

At the moment of time t=τ∆t the system for determining the circulations of the attached

vortexes and sources (run-offs) will have the following form: 0 1 1 1 1 1 1 1

;

0,

N M B pi i pk k p p pab ab i k b a M B k ab k a b

F q

G

v

G

τ

G

τ = = = = = = =

+

+ Λ =

−

+

=

(2)

where qi – intensity of sources (run-offs) continuously situated on the i section of the cylinder;

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M – number of control points and attached vortexes along the border of the bunker;

1 1 1 2 2 2 2 2 1 1 2 2

1 (

)

(

)

( , )

( )

2 (

)

(

)

i pi p i S

x

n

x

n

F

F x

dS

x

ξ

π

_∆

ξ

−

+

−

=

−

+

−

(3) 1 2

( , )

i

ξ ξ ξ

− random point of the section

∆

S

_i, on which sources (run-offs) are continuously situated ( );

1 2

( , )

p

x x x

− middle of the pn-section of the cylinder boundaries, or pn control point of the

bunker boundary;

1 2

{ , }

n

=

n n

− unit vector of the normal; formula

2 1 1 1 2 2 2 2 1 1 2 2

(

)

(

)

( , )

2 [(

)

(

) ]

n x

G x

x

−

=

⋅

−

+

−

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is used to calculate quantities

G

pab,

G

pk,

G

p, which express vortexes influence on the point

1 2

( , )

p

x x x

at the current moment of time;

1 2

( , )

ξ ξ

− the point of free vortex circulation ab_{, attached vortex by the circulations} k_{, or}

the vortex situated in the center of the cylinder with the circulation ₀ ;

− the number of points of vortex sheet separation;

ab _{− circulation of the free vortex run off at the point of time a from b}

n point of vortex sheet

separation;

Λ

− regularizing variable of I.K. Lifanov4_.

At the next moment of time there occurs the run off of new free vortexes from all points of separation (points 1, 2, 3 in Figure 1). The new position

( , )

x x

₁

′ ′

₂ of all free vortexes situated in the flow is determined:

1 1 x

,

2 2 y

x

′

= + ∆

x

v t

x

′

= + ∆

x

v t

(5) Speed components as well as the speed in any point of our interest along the unit direction

1 2

{ , }

n

=

n n

is determined from the expression:

0 1 1 1 1 1

( )

N i i M k k B ab ab L l l n i k b a l

v x

F q

G

τ

G

= = = = =

=

+

, (6)

where in the formula in order to determine functions F and G instead of

( , )

x x

₁ ₂ coordinates of the given point are substituted.

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Figure 2: Function of the dust particles diameters distribution

On the basis of the dispersion composition of dust in the inflow opening we build the function P for the distribution of the dust particles diameters (Figure 2). The area of each rec-tangle is equal to the part of the corresponding fraction. The inflow opening is divided into k equal parts and at each moment of time generate k random numbers (diameters of particles), distributed according to the law determined by function P. Thus at each model moment of time the bunker is entered by k dust particles. The dust mass, which came into the given area during the time ∆t:

t

C

_∆

=

km

=

Cv a t

∆

, (7) where the average mass of the dust particle in accordance with the distribution function P:

(

)

(

)

3 2 2 1

6(

)

24

1 i i d n n i i i i i i i d i i i

x l

m

dx

l d

d

π

_ρ

πρ

= =

=

+

−

(8)

Whence the time interval of the dust particles arrival in the bunker:

(

)

(

2 2

)

1

24

n i i i i i i

k

t

l d

d

Cv a

π ρ

=

∆ =

+

(9) In order to calculate the dust concentration in the suction opening we set the number n of the moments of time arrival in the bunker of the composition k of dust particles. We are mod-eling the movement n⋅k of particles until they all lodge or are caught by the aspirator. In the

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where V = v ⋅a⋅∆t⋅n.

In the process of modeling we memorize the diameters of the dust particles caught by the suction and determine the percentage composition of dust fractions in the aspirated air.

The real concentration of dust in the inflow air differs from the set one due to the model discretion. In order to determine the real inflow concentration Cr we calculate mr − aggregate

mass n⋅k of particles, arrived in the bunker from the inflow opening and correspondingly

/

r r

C

=

m V

(11) With the increase of the number of particles n⋅k concentration Cr approaches C with any

set accuracy.

The modeling of the dust particles movement is done on the basis of integration of their movement according to Runge-Kutt equation method5

3 CALCULATION RESULTS AND THEIR DISCUSSION

Input data for the computation: bunker height h = 0,7m; bunker width H = 1m; bunker depth − 1 m; distance between the inflow opening and left wall e = 0,05m; inflow opening

width = 0,3m; dust particles density ρ₁ =3500 kg/m3_{; air dynamic viscosity coefficient}

µ =0,0000178Pa/sec; dust particles dynamic shape coefficient χ =1; dust particle restoration coefficient at hitting k = 0,5; dust particle slip friction coefficient f = 0,5. The quantity of dust particles at each of 200 moments of time of their arrival in the bunker − 20. Particles

percent-age by their fractions are presented in Table.2. The set concentration of dust particles in the inflow air: _{30 mg/m}3_.

Fraction limits, mcm 10 – 30 30 – 50 50 – 70 70 – 90 90 − 110

Percentage 0,2 0,2 0,2 0,2 0,2

Table 2: Dispersion composition of dust in the inflow air

The behavior of dust aerosol inside the bunker is determined by the aerodynamic field (Figure 3).

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a)

b) v = 0 m/sec, (0,7; 0,5) c) v = 2 m/sec, (0,7; 0,5)

d) v = 16 m/sec, (0,7;0,5) e) v = −8 m/sec, (0,7; 0,5) f) v = 8 m/sec, (0,45; 0,3)

Figure 3. Current lines in different configurations of the bunker (points – free vortexes)

) b)

c) d)

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In case of the bunker equipped with suction cylinder concentration and dispersion compo-sition of the suppressed aerosol depend on the initial pocompo-sition of the suction opening of the cylinder. Due to this calculations were done several times with its different positions5 then the received quantities were averaged. It should be noted that with certain speeds of rotation cir-culation of dust particles around the suction cylinder was registered with particles not sup-pressed by it. It this case the computation was stopped due to the supposition that in the very end the particles would coagulate and fall on the bottom of the bunker.

Parameters Speeds, m/s Fractions, mcm

C(x,y) b R v v v 10−30 30−50 50−70 70−90 90−110

Outflow

concentra-tion mg/m3 Ordinary bunker (without suction cylinder)

− 0,1 − − 1,5 0,5 0,78 0,22 0 0 0 0,1981

− 0,1 ₋ ₋ 3 1 0,591 0,367 0,042 0 0 0,6765

− 0,1 − − 6 2 0,438 0,384 0,177 0,001 0 1,8290

− 0,1 − − 12 4 0,390 0,403 0,203 0,005 0 2,5316 Increase of the cylinder rotation speed

(0,8;0,5) 0,1 0,1 0 3 1 0,567 0,398 0,037 0 0 0,6849 (0,8;0,5) 0,1 0,1 1 3 1 0,580 0,388 0,032 0 0 0,5795 (0,8;0,5) 0,1 0,1 2 3 1 0,586 0,379 0,035 0 0 0,5045 (0,8;0,5) 0,1 0,1 4 3 1 0,742 0,255 0,003 0 0 0,1770 (0,8;0,5) 0,1 0,1 8 3 1 0,972 0,028 0 0 0 0,0163 (0,8;0,5) 0,1 0,1 16 3 1 0,987 0 0,013 0 0 0,0057 (0,63;0,5) 0,1 0,1 1 3 1 0,575 0,361 0,064 0 0 0,7161 (0,63;0,5) 0,1 0,1 2 3 1 0,542 0,424 0,034 0 0 0,4485 (0,63;0,5) 0,1 0,1 4 3 1 0,994 0,006 0 0 0 0,0600 (0,63;0,5) 0,1 0,1 8 3 1 1 0 0 0 0 0,0008

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Note: actual inflow concentration in all cases: 29.82mg/m3, counter clock rotation of the cylinder; speed in the aspiration − v₀; speed in the inflow opening − v ; rotation speed − v ;

cylinder radius − R ; aspiration width − b.

Parameters Speeds, m/s Fractions, mcm

C(x,y) b R v v v 10−30 30−50 50−70 70−90 90−110

Outflow

concentra-tion mg/m3 Cylinder position change with fixed rotation speed

(0,45; 0,5) 0,1 0,1 4 3 1 0,875 0,125 0 0 0 0,1182 (0,45; 0,43) 0,1 0,1 4 3 1 0,974 0,026 0 0 0 0,0563 (0,45; 0,35) 0,1 0,1 4 3 1 0,967 0,033 0 0 0 0,0558 (0,45; 0,28) 0,1 0,1 4 3 1 0,935 0,065 0 0 0 0,0628 (0,45; 0,2) 0,1 0,1 4 3 1 0,913 0,087 0 0 0 0,0690

Change of the width of the suction opening (0,45; 0,35) 0,05 0,1 4 3 0,5 1 0 0 0 0 0,0033 (0,45; 0,35) 0,075 0,1 4 3 0,75 1 0 0 0 0 0,0170 (0,45; 0,35) 0,15 0,1 4 3 1,5 1 0 0 0 0 0,24

Cylinder radius change (0,45; 0,35) 0,075 0,05 8 3 0,75 0 0 0 0 0 0 (0,45; 0,35) 0,075 0,075 5,34 3 0,75 1 0 0 0 0 0,0035 (0,45; 0,35) 0,075 0,1 4 3 0,75 1 0 0 0 0 0,0160 (0,45; 0,35) 0,075 0,125 3,2 3 0,75 0,997 0,03 0 0 0 0,0433 (0,45; 0,35) 0,075 0,15 2,67 3 0,75 0,837 0,163 0 0 0 0,1374

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With the immobile cylinder dust cloud down flow occurs from different sides, which is determined by the speeds field (Figure 3 b). Aspirated aerosol concentration is even some-what higher than in the standard bunker (Table 3).

) b) c)

d) e) f)

Figure 5: Dust aerosol dynamics in the bunker with the suction cylinder with the center in point (0.45; 0.35) and counter clock rotation speed 8 m/s ( ,b,c,d,e,f − different moments of time).

With cylinder rotation current lines possess spiral character (Figure 3 c-f), which prevents particles inflow in the cylinder. With the growth of the cylinder rotation speed in any direc-tion the concentradirec-tion of the aspirated aerosol decreases (Table 3). In order to decrease dust entrainment counter clock rotation is preferable (Figure 5) due to the fact that the air flow in-duced by the cylinder rotation is aimed in the direction coincided with the dust particles grav-ity at the initial section of their movement (to the left of the cylinder). With the decrease of the cylinder height dust aerosol concentration in the aspirated air decreases. The smallest dust particles entrainment in the aspiration system is registered with the cylinder center position in point (0.45;0.35) (Table 4). Concentration decrease and dispersion composition shift in the direction of small particles occurs with the decrease of the cylinder radius R and the width of the suction opening b.

4 CONCLUSIONS

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systems, make prognosis of concentration and dispersion composition of aerosols in suction openings.

On the basis of research carried out according to the developed program while designing aspiration bunkers with the function of dust suppression chamber the authors propose:

• to use suction cylinder with counter clock rotation;

• linear rotation speed should be high but not causing noise level increase;

• the cylinder radius and suction opening width should be as small as possible with the

air speed in the opening not exceeding 20m/s;

• vertical position of the cylinder should be chosen approximately in the center of the

bunker, its horizontal position – to the right of the inflow opening as close as possible to it, but it shouldn’t interfere with the technological process.

The work was done at financial support of the grant of President of Russia YD-5015.2006.8 and the grant of Russian foundation for basic research 05−08−01252 .

REFERENCES

[1] Logachev K.I., Puzanok A.I. Numerical modeling of dust and air flows in the vicinity of rotating suction cylinder. Higher schools edition. Construction, 2005. No9. pp. 63-70.

[2] Belotserkovsky S.M., Ginevsky A.S. Modeling of turbulent flows and traces on the basis of discrete vortexes method. M.: Fizmatlit, 1995. 365p.

[3] Logachev I.N., Logachev K.I. Aerodynamic foundations of aspiration. St. Petersburg, Khimizdat, 2005. 659p.

[4] Lifanov I.K. Method of singular integral equations and numerical experiment. M. Yanus. 1995. 520p.