1 Index

1. Introduction ...................................................................................................... 22. Model for electrostatic precipitators ................................................................ 4

2.1. Gas properties................................................................................................................. 4

2.2. Estimating the corona current ........................................................................................ 5

2.3. Electrical properties of the electrostatic precipitator ...................................................... 5

2.4. Particle charging ............................................................................................................. 6

2.4.1. Field charging .............................................................................................................. 6

2.4.2. Diffusion charging .................................................................................................. 7

2.5. Drift velocity and collection efficiency ..................................................................... 8

3. Centrifugal forces in a flow field ................................................................... 114. Process identification using simultaneous heat and mass transfer ................ 145. Inertial separation based on turbulent flows .................................................. 206. The influence of a falling water film.............................................................. 267. Ionic wind Literature review and experiments ........................................... 29

7.1. Literature review .......................................................................................................... 29

7.2. Experimental detection of ionic wind .......................................................................... 31

8. Particle diffusion ............................................................................................ 349. Particle agglomeration.................................................................................... 3610. Properties of dust in the paper industry ....................................................... 3911. Nonspherical particles .................................................................................. 4112. CFD Simulations .......................................................................................... 4313. Experiments .................................................................................................. 52

13.1. Electrostatic collection efficiency .............................................................................. 52

13.2. Determination of a regression model for the new equipment .................................... 53

13.3. Experiments validating the collection efficiency for the new geometry .................... 56

14. Model for combined electrical and centrifugal air cleaning in turbulentflows ................................................................................................................... 57

14.1. MODEL 1 for the air cleaner...................................................................................... 57

14.2. MODEL 2 for the air cleaner...................................................................................... 59

14.3. MODEL 3 for the air cleaner...................................................................................... 59

14.4. Experiments and validation of models ....................................................................... 60

15. Conclusions .................................................................................................. 62References .......................................................................................................... 64Appendix 1 ......................................................................................................... 66

21. Introduction

Air cleaning in the paper industry has its specific problems requiring some extraordinary precau-tions and equipment. For instance, since the dust is inflammable and even explosive, a normal bagfilter has to be placed outdoors, leading to excessive piping etc. A wet scrubber on the other handconsumes significant amounts of water and power.

This is why a concept based on an electrostatic precipitator with a wetted collection surface, wherethe charging electrode consists of rings with needles on, was developed (see figure 1). A project atthe VTT Manufacturing Technology Center was carried out in order to investigate the electrostaticcleaning properties in such an air cleaner. From the beginning the concept was like a normalelectrostatic air cleaner, where the air is lead through the cleaner as calmly as possible. In the paperindustry, however, the air can contain large pieces of paper which eventually lead to the clogging ofthe charging electrode at the centre of the air cleaner. To avoid this clogging, the inlet was changedto a tangential position; see figure 1 for a better description.

This project was started in order to establish whether the conventional model for electrostatic col-lection can be used under such highly turbulent conditions, and how forces other than electrostaticones should be considered. A mathematical model to determine the collection efficiency for differ-ent air cleaner geometries in varying paper production or conversion industries was also set as agoal. A Masters thesis was produced within the project, to determine the properties and distribu-tion functions for the dust present in different industrial environments (Dahlbacka 1999). The projectlasted from 1.2.1998 to 31.5.1999.

3Figure 1: Full scale electrostatic air cleaner. The reactor height is 5 m (see figure 6). Thecharging electrode with its rings can be seen at the center, with the reactor surface actingas the collection surface. The equipment is situated at the Mets-Tissues factory in Mntt,Finland.

The experiments described in chapters 4 and 7 are all conducted on the apparatus in Mntt figure1. Later on during the project a new, slightly different apparatus was built, to be used for experi-mental purposes, by Valmet Corp. Air Systems for the project. The new design was based on mea-surements from the first apparatus, preliminary calculations from this project and the CFD calcula-tions described in chapter 12. The new air cleaner (see figure 36) was built lower, which was onefundamental goal for the development of the cleaner.

In chapter 13 some different experiments are described. One important part is the one certifying theelectrostatic collection efficiency model for a full scale air cleaner.

42. Model for electrostatic precipitators

Electrostatic precipitators are well covered by literature and therefore it should not be necessary todiscuss these things so thoroughly in this context. A mathematical model based on a wire-in-tubeelectrostatic precipitator is presented together with other equations necessary for solving a practicalproblem numerically. For more detailed information see e.g. (Lehtimki 1998a).

2.1. Gas properties

The mobility of a gas ion, Zi , is defined as the ratio of ionic drift velocity i to the electric field E,i.e.

E Z= ii (2.1)

The theory dealing with the mobility of gas ions is complicated. A reasonable approximation for theion mobility can be expressed as follows:

pi

1 )T k (2 )

m

1 +

m

1)(p 16

e 3( = Z 1/21/2ig

i (2.2)

where p is the gas pressure, mg is the mass of the gas molecule, m

i is the ionic mass, e is the

elementary charge (e = 1.6021 10-19 As) and is the mean impact cross section. The mean impactcross section can be determined from the following polynomial fit curve:

c + m b + m a = i2

i (2.3)

where the coefficients a, b and c have the following values: a = 1.94 10 m/amu, b = 3.62 10-21 m/amu and c = 1.01 10-18 m.

The diffusional motion of gas ions is characterised with the diffusion coefficient Di which is re-

lated to the ion mobility Zi by

ii Ze

T k = D (2.4)

where k is the Boltzmann constant (k = l.3807 10-23 J/K) and T is the absolute temperature.

The mean thermal speed of gas ions is calculated from a formula describing the mean thermal speedin the case of an ideal gas. The mean thermal speed is given by

5)m

T k 8( = c 1/2i

ipi (2.5)

2.2. Estimating the corona current

The electrostatic cleaning efficiency, calculated as described in the following sections, requires asan input parameter the corona current. If the calculations are performed for an existing air cleaner,a measured value for the corona current is normally used, but in the design phase, at least an ap-proximate value for the corona current has to be calculated. The corona current depends, naturally,on several factors e.g. the design of the discharge electrode and high voltage. The expression pre-sented here can be used for the electrode configuration as seen in figure 1 (Lehtimki 1998b):

( )2

3x2

2i0 U

rr

LrZKI

= pi (2.6)

In equation (2.6) r2 is the radius of the air cleaner, rx is the radius of the discharge electrode and Uis the onset voltage. The factor K is based on experiments . A set of data points for K is graphicallypresented by Lehtimki, and to these points a curve can be fitted. Here the following expression forK is suggested:

468.0

x2

r

rr

n/L6278.1K

= (2.7)

In this equation L is the length of the electrostatic collection section and nr is the number of elec-trode rings. At high voltages, or with a small distance between the electrode rings, it would seemthat (2.6) would give somewhat too low values for the corona current but the expression is anyhowused to estimate the corona current.

2.3. Electrical properties of the electrostatic precipitator

The electric field between the discharge electrode and the collection electrode plays an importantrole in the particle charging and collection processes. The electric field depends on the voltageapplied between the electrodes. The electric field and ion concentration are modelled by assuminga simple wire and pipe geometry, i.e. a thin corona wire on the centre line of the cylindrical collec-tion tube.

The corona current per unit length of the corona electrode, jL ,is given by

r E(r) n(r) Ze2 = LI

= j iL pi (2.8)

6For high corona currents and for r >> r1 , the electric field can be estimated by

2/1

i0

L0 Z2

jE

pi

(2.9)

An approximate solution for the average ion concentration, n , between the electrodes can be calcu-lated:

r

1

Ze2

j 2 n

2i2

L01/2

pi

(2.10)

This solution can be used in the idealised case, i.e. the space charge due to aerosol particles isassumed to be zero. It has also been assumed that there is no dust layer on the collection electrodethat could affect the electrical behavior of the system. This, naturally, is always the case when thewalls are constantly washed with water.

2.4. Particle charging

Particle charging has been studied for several decades and therefore relatively good models areavailable. There are two basic mechanisms responsible for the charging of aerosol particles. Theseare referred to as field and diffusion charging. Particle charging in an electric field is assumed to bedue to the ordered motion of ions under the influence of an electric field. This approach is appli-cable predominantly for large particles (dp > 0.5 m). Diffusion charging is due to ion attachment toparticles caused by the random motion of the ions. Particle charging in an electrostatic precipitatortakes place in a strong electric field and at high ion concentration. Thus both charging mechanismsmust be taken into account.

2.4.1. Field charging

Particle charging in a strong electric field can be described by the classical field-charging theory(Hinds 1982). According to the field charging theory the mean charge number of a particle is givenby

+=

s0F tt

ts)t(s (2.11)

where the saturation charge number is given by

702

pr

r00 Ed2e

3s

+=

pi(2.12)

and the time constant ts is given by

i

0s Zen

4t

= (2.13)

and t is the particle charging time calculated from the geometry and the mean flow-velocity. Theconstant r is the dielectric constant for the particle material.

2.4.2. Diffusion charging

Ion attachment to aerosol particles can also be caused by the thermal motion of ions (Brownianmotion). This is called diffusion charging and it is the dominating process for particles smaller than0.2 0.5 m (depending on source). Due to diffusion charging, the maximum charging predictedby (2.12) can be slightly exceeded.

The so-called White equation gives the particle charge as a function of charging time t:

+= tncdd

41ln

dd)t(s i0p

0

pW

pi(2.14)

where the coefficient d0 is given by

Tk2ed

0

20 pi

= (2.15)

When modeling particle charging by corona discharge, both field and diffusion charging have to betaken into account. The simplest way of doing this is by combining the two mechanisms:

)t(s)t(ss FW += (2.16)

This equation can be used to estimate the total particle charge in an electrostatic precipitator.

82.5. Drift velocity and collection efficiency

Electrostatic force and aerodynamic forces govern the motion of a charged aerosol particle in a gas.The electrostatic force FE caused by the electric field E0 is given by

0E E e s=F (2.17)

where s is the particle charge number and e is the elementary charge. This force causes a particledrift in the direction of the electric field. The electrostatic force is balanced by the gas resistanceforce or drag force, which is given by

p22

pgDD dw3w d 8 C = F pipi = (2.18)

(the middle part of which, is the general form of Newtons resistance equation and the right handpart is known as Stokes law) where CD is the drag coefficient, g is the gas density, dp is the particlediameter and w is the velocity of the particle (Hinds l982). The drag coefficient can be approxi-mated by

6Re

+ 1 Re24

Cp

2/3

pD (2.19)

where Rep is the particle Reynolds number given by

d w

= Repg

p (2.20)

At mechanical equilibrium the forces FE = F

D and the drifting velocity w for a charged particle in an

electric field can be calculated by

1p

2/3

p

c

6Re

+ 1 d 3CE e s

= w

pi (2.21)

where Cc is the Cunningham slip correction factor (Hinds l982) the value of which is given by

9

d

C -exp B + A d

+ 1 = C pp

c (2.22)

where is the mean free path of the gas molecules (for air = 6.53 10-8 m). The values of thecoefficients A, B and C are A = 2.5l4, B = 0.8 and C = 0.55 (values for A, B and C vary slightlydepending on the source). The Cunningham slip correction factor extends the range of Stokes lawto below 0.01 m (without correction it is valid only down to 1 m). Thus small particles, using theslip correction, settle faster by a factor of Cc than predicted by Stokes law. This correction isneeded when the size of a particle approaches the mean free path of the gas molecules because theparticle is so small that it starts slipping between the gas molecules.

In order to predict the collection (or cleaning) efficiency of the electrostatic precipitator the as-sumption of the complete mixing of air in the collection system is made, i.e. that no gradients existin the particle concentration. This should, for a totally turbulent flow, be rather a good assumption.The collection efficiency is then given by

VA w

exp - 1 =

&

(2.23)

where A is the collecting area (i.e. the area of the collecting electrode at the length of the chargingelectrode) and V& is the air flow. The equation is known as the Deutsch formula (Hinds 1982). Theequation (2.23) is based on the assumption that no particle re-entrainment takes place. This as-sumption is valid for liquid particles or if a falling water film wets the collection surface. As thedrifting velocity w depends on particle size, the collection efficiency is of course also different fordifferent particle sizes. As several phenomena are examined in this context, the collection effi-ciency given by (2.23) is hereafter referred to as e and the corresponding velocity as we. A typicalcollection efficiency curve is shown below:

10

Collection efficiency (%) as a function of particle size

0 %

20 %

40 %

60 %

80 %

100 %

0.001 0.010 0.100 1.000 10.000 100.000Particle diameter [m]

Effi

cien

cy [%

]

Figure 2: Collection efficiency for an electrostatic precipitator as a function of particlesize. The calculations have been made for a system with the following dimensions:

Flow rate V& =3.0 m/s Length of collection section L=2.6 m Diameter of the collector tube d=1.6 m Corona current I=3.2 mA

11

3. Centrifugal forces in a flow field

A rotational air flow will invoke a centrifugal force throwing airborne particles outwards in theflow field. This property is commonly utilised in, for example, cyclones. The airflow is broughtinto rotation by, for instance, bringing the air tangentially into a larger vessel. The vessel studied inthis particular case could well be described as a cylindrical reactor (for cyclones it would then be aconical reactor). A tangential inlet, as described earlier, is assumed in this study (see figure 1).

In order to determine the centrifugal collection efficiency, the centrifugal particle velocity wc has tobe determined. Assuming that the centrifugal force acting on a particle is equal to the drag forceacting on the same particle (see equation 2.18) the radial velocity of the particle is calculated by(Ogawa 1984)

( )

18

rdw

2gp

2p

c

= (3.1)

where is the angular velocity, g and p are the gas and particle densities respectively and r is theradius of the particle path in the flow. This radius is growing with time since the particle is slungoutwards by the centrifugal force. Assuming that no other forces tend to drag the particle towardsthe center of the reactor, a simplification is done by using an average value for the particle pathradius, r, calculated from the centerline of the reactor to the centerline of the tangential inlet. Sincethe measure of the inlet is rather small compared to the reactor radius, using an average value for rdoes not drastically affect the result of equation (3.1).

Equation (3.1) should be completed with the Cunningham slip correction factor

( )

18

Crdw

c2

gp2

pc

= (3.2)

The meaning of this correction factor was discussed in chapter 2.

Since the inlet and outlet not are necessarily equal in size and shape, it is therefore justifiable toassume that the angular velocity varies with the length (or height) of the reactor. Calculating theangular velocities in and out for the inlet and outlet from the velocities in the connecting pipes(depending on geometry it might be necessary to use only the tangential velocity component) from

r

inin

r

w= and

r

outout

r

w= (3.3)

gives the angular velocity as a function of reactor height:

12

hh

)h(r

inoutin

+=

(3.4)

where rr marks the total reactor radius (3.3) and h

r the reactor height (3.4). In a later section these

assumptions can be compared to the results from CFD simulations. Equations (3.l) and (3.2) hold,only if the Reynolds particle number is small (equation 2.20), i.e. if the relative velocity betweenthe particle and the fluid is small enough, whilst only then the drag force C

D can be given by the

simpler form

pD Re

24C (3.5)

Considering that Rep might be significantly higher than one, equation (2.19) should be used. Thusequation (3.2) has to be modified to:

( )

12

h

h p2/3

c2

gp2

p

c hh

dh

6Re

+ 118

Crd

w

2

1

=

(3.6)

A mean value for the velocity wc is obtained from equation (3.6). In equation (3.6) the equation for

(3.4) is inserted. An expression similar to the Deutsch formula can be used to calculate thecentrifugal collection efficiency

VA w

exp - 1 = cc

&

(3.7)

Since the centrifugal particle velocity wc depends on the square of the particle diameter, the result of

equation (3.7) will depend heavily on the particle size. A typical collection-efficiency curve isshown below (figure 4).

These calculations, as well as the equations presented above, are made under the assumption thatthe angular velocity changes linearly through the collector. The angular velocity at the inlet iscalculated from the mean velocity win in the inlet pipe ( 2.11.1ww inmax K ), see figure 3, usingthe total radius of the collector rr instead of the actual radius of the particle path r (assuming wmax atthe centre line of the inlet). The same principle goes for the outlet. The value for win obtained thisway is smaller than it would be using wmax and the radius r. Thus a compensation for wall losses isautomatically obtained, giving a flow profile more according to the somewhat hypothetical oneinserted in Figure 3. The profile can be compared with the ones given by the CFD calculations(chapter 12).

13

rr

r

wmax win

Figure 3: A drawing describing the assumptions made when calculatingthe collection efficiency for the centrifugal flow.

Collection efficiency (%) as a function of particle size

0 %

20 %

40 %

60 %

80 %

100 %

0.001 0.010 0.100 1.000 10.000 100.000

Particle diameter [m]

Effi

cien

cy [%

]

Figure 4: Collection efficiency in a rotating flow field as a function of particle size.The calculations have been made using the following values: Length of collection section L=5 m Diameter of collection section d=1.6 m w

in=12.3 m/s in a 0.60.4 m duct

wout

=0.5 win

Particle density rp=1000 kg/m

Air properties at 25C

14

4. Process identification using simultaneous heat and mass transfer

This chapter explains how a regression model giving heat- and mass-transfer coefficients for thestudied air cleaner is obtained. The coefficients are needed later when calculating the collectionefficiency for the air cleaner. A more detailed description can be found in (Berg and Altner 1999).

The studied process is described with the following differential energy balance for the controlvolume a, b, c and d in figure 5, and gives:

1wwa0wv0wwac tcm)dii(mtcmdtcmimqd &&&&&& ++=+++ (4.1)

The numerical differentiation of equation (4.1) requires governing equations for both turbulent heatand mass transfer.

2.

i x i0 x0t

t

5. di/dx i/ x

3. h0 +tcv

BA

4.

6.

dqc.

ix

t

.

ma

i+dix+dxt+dt

dmvt

d

b

c

a

1.

6.t0

.

t1

mv.

mv.

dmv+.

1.

dq.

i1 x1

2.

Figure 5: Heat and mass transfer through the boundary layer in the cylinder with a falling waterfilm. The air state change during evaporation is also described by including a principal picture ofa perspectively transformed humidity chart (Soininen 1994), often named the i,x-chart. The controlvolume and control surface are described by the dotted lines connecting a,b,c and d.

Heat transfer

Heat-flow through a boundary layer is usually defined by the following expression, see figure 5:

dAttqd

=dAtt=qd )( )( &

& (4.2)

We may, in principle, define an average mass flow Amn& perpendicular to the surface and consider

that the measured heat flow is the difference between the enthalpies of mass flow away from thesurface, at surface temperature t, and mass flow of the same magnitude towards the surface, at themain flow temperature t. This gives:

15

)()( ttA

Cttc

Am

tcA

mtc

Am

=

dAqd n

pn

pn

pn

==

&&&&&(4.3)

From a comparison of equations (4.2) and (4.3), we obtain:

AC

cA

m np

n&&

== (4.4)

Mass transfer

If the surface in contact with air is the surface of a drying material, the humidity of the flow awayfrom the surface is higher than that of the flow towards the surface. Denoting the temperature of thesurface with t, the humidity of saturated air at that temperature with x and the humidity of themain flow with x and replacing A

mn& combined with a more accurate definition of the specific heat cpone may write (Berg and Karlsson 1998):

va

nv

cxc

xxxx

Am

dAmd

)()(+

==

&&(4.5)

where the content of moisture in the air, also known as air humidity x, is defined as:

v

v

a

v

ppp

MM

x

= (4.6)

and the air humidity x (kgH2O/kgda) is the saturation moisture content defined by the local controlvolumes mass content of water vapour divided by the mass content of dry air.

The content of moisture in the air is defined using Daltons law for ideal gas combined with Antoineswater vapour equilibrium curve. Here the notation is used for the mass-transfer coefficient in-stead of , that is, the heat-transfer coefficient. The stress mark indicates that we now refer to themass transfer which occurs simultaneously to heat transfer. Equation (4.5) is known in the literatureas the Lewis equation when k

1 in equation (4.7) equals one.

kk 11 = 1 when (4.7)

Let us now examine the experimental process by looking at figures 5 and 6. Convective heat trans-fer is the product of the heat capacity mass flow rate of air and the temperature drop of the air.Whereas mass transfer takes place at the same time, we write that this convective heat flow is

dAtt )( . Further, when we consider that dxma& represents evaporation vmd & , equation (4.1) can

16

be rewritten as:

)21()()()( dt

dAmd

dAm

c=ttkttdAmd

cttch vwwccvwv0&&&

+++ (4.8)

It is now possible to solve equation (4.8) numerically when assuming k1=1 and solving an approxi-mate value kc 4 W/m

2C from the free convection theory (Jakob 1949).

Surface temperature t according to the Lewis analogy

During heat and mass transfer, the state of the air is changed from point 1 to point 6 shown as the di/dx line B in figure 5. The Lewis analogy surface temperature t is obtained, if the difference be-tween curve A and curve B in figure 5 is neglected. This is the case when k1=1 and thus along thisline the direction of the air state change is indicated by the ratio i/x and can be expressed with thefollowing statement.

xx

iix

idxdi

x

i

=

=

(4.9)

The Lewis analogy surface temperature t, is therefore, always different from the measured surfacetemperature when 11 k . The assumptions that are related to equations (4.8 and 4.9) are consid-ered, at this stage of the work, as the method basis when determining . It is often veryinformative to critically analyse the process by drawing the experimental wet and dry bulb tempera-tures in an i,x-diagram, and thereby obtain a figurative description showing if the assumed air statechanges differ from the experimental ones.

The experiments were carried out on a full-scale apparatus, shown in figure 6. In order to obtain theheat- and mass-transfer coefficients ( and ) for the apparatus using the theory presented, someprocess variables were measured (see table 1 below): dry and wet bulb temperatures of both theinlet and outlet air flows, as well as flow velocities. The flow velocities were measured with a Pitottube and a digital micromanometer. The inlet temperatures were measured in the vertical duct (seefigure 6) about 2 metres before the duct entered the cylinder body and outlet temperatures at a pointabout 2 metres from the cylinder exit. The temperature of the surrounding hall was measured onseveral occasions, and it could be considered constant (tc=25 C). The heat-transfer coefficientfrom the surrounding hall air to the water film was calculated as 4 W/mC. Table 1 also shows theair humidity, calculated from dry and wet temperatures.

The experiments were carried out during the cold season, with very dry air. In this range of dry andwet temperatures, the influence of daily variations in total air pressure can, in some cases, be con-sidered negligible when calculating differences in air humidities, x. The influence of the absolutepressure p

0 on the experimental results should, however, be checked before continuing with or

without correction.

17

windin=0.5 m

woutdout=0.4 m Starting point of

falling water film

See figure 1 forenlargement

Tangential inlet

h4.4 m

dc=1.6 m

Figure 6: Drawing showing the principles of the apparatus used forexperiments.

Table 1: Experimental data.

Mea

sure

d in

let

Velo

city

[m/s]

.M

easu

red

Dry

Tem

pera

ture

at

inle

t [C]

Mea

sure

d W

et

Tem

pera

ture

at

inle

t [C]

Mea

sure

d Dr

y Te

mpe

ratu

re a

t outle

t [C]

Mea

sure

d W

et

Tem

pera

ture

at

outle

t [C]

Psyc

hrom

etri

c Ai

r Hum

idity

at

inle

t [kg

H 2O

/kgd

a]Ps

ychr

om

etri

c Ai

r H

umid

ity a

t outle

t [kg

H 2O

/kgd

a]15.1 26.2 14.4 21.9 14.2 0.00538 0.006937.5 26.5 14.2 22.2 14 0.00504 0.0065910.6 26.3 13.8 22.5 13.9 0.0047 0.0063614.6 26.1 13.5 22 13.8 0.00447 0.006467.3 26.6 14 22.3 13.8 0.00479 0.006346.4 24.5 12.1 20.1 11.8 0.0037 0.005214.8 23.6 11.1 20.2 12.1 0.0031 0.0054610.8 24.5 12.2 20.1 11.8 0.0038 0.00526.9 24.6 12.5 20.6 12.9 0.00406 0.006114.7 24.5 12.9 20.6 13.1 0.00451 0.00631

Using the numerical data, together with the equations presented, gives the possibility of calculating. Iterative calculations are carried out as follows: is given a value, after which the outlet drytemperature and the outlet air humidity are calculated. The calculated values are then comparedwith the measured ones, and the -value adjusted until a satisfactory result is obtained. The maingoal is to match the dry temperatures, as the measured dry temperature values can be expected to bethe most reliable ones. As one can see from the results in table 2, the agreement of the measure-ments is good, and even the calculated air humidity values (which were mentioned as being ofsecondary interest at this point) give good agreement. In addition, the inlet temperature of thefalling water film had to be adjusted (note: water inlet in the upper region of the cylinder).

18

Table 2: Experimental and calculated values. The transfer coefficients are adjustedto an accuracy of 0.5 W/mK.

Mea

sure

d Dr

y Te

mpe

ratu

re at i

nlet

[C]

Mea

sure

d Dr

y Te

mpe

ratu

re a

t out

let [

C]

Calcu

late

d Dr

y Te

mpe

ratu

re a

t out

let [

C]

Diff

erence

[%]

Psyc

hrom

etri

c Ai

r H

umid

ity at o

utle

t [kg

H 2O

/kgd

a]

Calcu

late

d Ai

r Hum

idity

at

outle

t [kgH

2O/k

gda]

Diff

erence

[%]

Res

ultin

g Tr

ansf

er

coeffi

cient

[W

/mK

]

26.2 21.9 21.86 -0.19 0.00693 0.00691 -0.34 69.526.5 22.2 22.18 -0.1 0.00659 0.00656 -0.55 32.526.3 22.5 22.5 0 0.00636 0.00635 -0.24 42.526.1 22 21.95 -0.21 0.00646 0.00643 -0.59 67.526.6 22.3 22.31 0.04 0.00634 0.00631 -0.57 30.524.5 20.1 20.13 0.15 0.0052 0.00519 -0.22 27.523.6 20.2 20.19 -0.05 0.00546 0.00544 -0.33 6924.5 20.1 20.12 0.08 0.0052 0.0052 0.01 45.524.6 20.6 20.61 0.05 0.0061 0.00608 -0.43 33.524.5 20.6 20.57 -0.16 0.00631 0.00627 -0.57 70

When looking at the small differences between the measured and the calculated values for the drytemperatures and air humidity, the conclusion is that the agreement seems to be acceptable. Therelation between heat and mass transfer can be expressed as = 1k where, in this particular case,k11. From the resulting heat- and mass-transfer coefficients presented in table 2 the Nusselt andReynolds numbers are calculated from their respective characteristic equation:

dNu = (4.10)

dwRe m= (4.11)

For separate flow geometries, the characteristic flow velocity (w) and the characteristic length unit(d) will be defined differently. Here wm is defined as the mean axial velocity in the cylinder and d isthe cylinder diameter (dc in figure 6). The experimentally obtained Nusselt numbers, as a functionof Reynolds numbers, can be seen in figure 7. A curve is, thereafter, fitted to the experimentallyobtained Nusselt numbers. As can be seen, a fairly good agreement is reached using a straight line.This would give the relation:

Re027.0Nu = (4.12a)

which can be transformed into a more familiar form:

45.01 PrRe032.0Nu = (4.12b)

19

Equation (4.12a) is presented graphically in figure 7. The tangential flow pattern seems to give highNusselt numbers compared to Reynolds numbers.

Nusselt number as a function of Reynolds number

0

1000

2000

3000

4000

5000

0 50000 100000 150000 200000Re

Nu

Figure 7: The experimentally obtained Nusselt numbers as a function ofReynolds numbers. The dotted line marks the equation (4.12a).

The values of in the cylinder might be considered to be higher than expected. One could, how-ever, compare these values with the values calculated for the inlet pipe diameter and the flowvelocity of the air. The expression for Nu in turbulent flow is (VDI-Wrmeatlas 1953):

cm

bm

3/2PrRe

ld1aNu

+= (4.13)

where a = 0.024, b = 0.786 and c = 0.45 for turbulent flows in straight circular tubes. In equation(4.13) the physical properties of air should be calculated using arithmetic mean values, i.e. tm=(t1+t2)/2, xm=(x1+x2)/2. For the cylinder under observation the ratio l/d is 4.2 m/1.6 m 2.6. Noting that theconstant in front of Re in (4.12a and 4.12b) describes the development of the temperature or veloc-ity profile, where in this case thermal entrance effects are significant, the same constant togetherwith the mentioned l/d, should be used in (4.13) when comparing the levels of heat- and mass-transfer coefficients.

Thus the level of turbulence (i.e. the level of heat and mass transfer) in the cylinder, depends bothon the inlet geometry and the kinetic energy of the flow in the inlet pipe. Hence, this is the mostplausible explanation for the remarkably high exponent b in Reb. Values of b=0.80.95 can befound in the pertinent literature for turbulent flows over rough surfaces and impingement drying(e.g. Nunner 1956 and Mujumdar 1987, pp. 461-474).

Some more experiments and thoughts around regression models for the studied air cleaner can befound in chapters 7 (same geometry as here) and in 13 (a new geometry).

20

5. Inertial separation based on turbulent flows

The deposition of particles in turbulent flows has been discussed by many authors (for instanceOgawa 1984 and Friedlander 1977). One physical interpretation of the deposition is that fine solidparticles with a large inertial force caused by the fluctuating velocity of the turbulent flow, in thefully turbulent flow region, penetrate the quiescent region near the wall and reach the wall surface.In other words, the stopping distance of a particle is compared with the thickness of the laminarsublayer.

Considering a pipe flow, as Friedlander did, gives the stopping distance for a particle, based on theradial fluctuating velocity of turbulent flow, w

r:

2f

w9.0wr = (5.1)

The equation is the result of experiments (Laufer 1953). Here w is the mean gas-velocity in the pipeand f is known as the fanning friction factor, which is given by the Blasius equation (Bennett andMeyers 1982)

25.0Re0791.0f = (5.2)

Using the fluctuating velocity wr given by equation (5.1) gives the stopping distance for a particle

according to the Stokes equation

18wd

S r2

pp= (5.3)

Friedlander gives two separate equations for the transport (or migration) velocity of particles in theturbulent flow. When the stopping distance is much smaller than the thickness of the viscous sub-layer, the following expression gives the deposition velocity

2/5

45

52p

2p

2

2f

101.6

Udk

=

(5.4)

where k is the transport velocity, f is the fanning friction factor and U is the average gas velocity.The upper limit of this equation is given as

21

52fUS 2/1

(5.7)

In figure 8 the group of lines denoted as A are calculated with equation (5.4), while those denotedas B represent equation (5.6). The lines B are not drawn to the upper limit S/d < 0.5. Already,before reaching the upper limit the empirical equation (5.6) tends to collapse (i.e. the transportvelocity falls dramatically). The theory, presented above, gives the equations for two extreme situ-ations. The discontinuity of the lines (see figure 8) also causes problems when modelling the clean-ing efficiency for turbulent flows.

22

In order to obtain a continuous function and to be able to secure equations for varying geometries,a slightly different method though based on the same principles as described above is used. Thestopping distance is compared with the thickness of the laminar sublayer (Berg 1998):

1g

21

1w

ky

= (5.8)

where k1=2.5 and w1 gives the flow velocity at the distance y1 from the wall:

g

210

1k

w

= (5.9)

which gives a critical diameter, dp,crit

1pgr

21

2crit,p

ww

k18d

= (5.10)

Particle fractions larger than dp,crit are assumed to deposit totally, and consequently no particlessmaller than dp,crit would deposit. Since this is experimentally verified as being false, the function ismade continuous by proportioning the stopping distance of an observed particle to the stoppingdistance of the critical particle size. A constant kp is introduced:

critp S

Sk = (5.11)

where Scrit

is the stopping distance for the particle having the diameter dp,crit

. The maximum value ofk

p is 1, since the turbulent eddies cannot transport particles faster than the transporting velocity (it

was earlier stated that particles larger than dp,crit

are assumed to deposit totally). See also later sec-tions.

The velocity of the particles towards the collection surface is determined by the flows which arenormal to the pipe surface. The heat- and mass-transfer coefficient for a system is, in fact, theaverage heat-capacity rate of flows occurring in the direction normal to the surface (Soininen 1994).For turbulent flows in pipes is given by (VDI-Wrmeatlas 1953):

dPrRe024.0 45.0786.0

= (5.12)

23

where the physical properties of air (in Re and Pr) should be calculated using arithmetic meanvalues, i.e. tm=(t1+t2)/2, xm=(x1+x2)/2. Thus the velocity for the turbulent flow (i.e. eddies) in thedirection normal to the surface is given by (Soininen 1994):

gpn

cw

= (5.13)

The velocity wn can be said to transport particles towards the collection surface in the air cleaner,whilst the stopping distance is determined by wr (Friedlander 1977). The product np wk is equiva-lent to the transport velocity of the particles. This way, the upper limit of kp given above, alsobecomes natural.

Transport velocity as a function of Reynolds number

1

10

100

1000

1000 10000 100000 1000000

Re

[cm/m

in] 2 m

5 m

8 m

Figure 9: Particle transport velocity in a turbulent pipe flow as a function ofReynolds number. Pipe diameter d=25 mm and particle density r=7800 kg/m.The critical particle size is obtained by comparing equations (5.3) and (5.8).

Since the radial fluctuating velocity wr given by equation (5.1) actually gives the velocity of the gasjust outside the buffer layer, the stopping distance should be compared with the thickness of thelaminar and the buffer layer, not just the laminar sublayer as above. The thickness of the laminarand buffer layer, y2, is given by (Berg 1998)

1g

212

w

kky

= (5.14)

(k2=22.5) and therefore the expression giving the critical particle size becomes

24

1pgr

212

crit,pww

kk18d

= (5.15)

Figures 9 and 10 can be said to describe two extreme situations, the first with S=y1 and the second

with S=y2. The actual case will probably be somewhere between these two values, which also can

be seen from figure 11 showing some experimental results (Ogawa 1984). Unfortunately theseexperimental values are covered by equation (5.4) and never go into the region covered by equation(5.6).

Transport velocity as a function of Reynolds number

1

10

100

1000

1000 10000 100000 1000000Re

[cm/m

in] 5 m

8 m2 m

Figure 10: Particle transport velocity in a turbulent pipe flow as a function ofReynolds number. Pipe diameter d=25 mm and particle density r =7800 kg/m. The critical particle size is obtained by comparing equations (5.3) and (5.14).

Figure 11: The deposition of fine solidparticles. Pipe diameter d = 25 mm.Experiments presented in (Ogawa 1984).

In agreement with the assumption of no re-entrainment, made in the Deutsch formula, equation(2.23), the collection efficiency of the turbulent deposition is given by

25

=

VAwk

exp1 npT & (5.16)

Collection efficiency (%) as a function of particle size

0 %

20 %

40 %

60 %

80 %

100 %

0.001 0.01 0.1 1 10 100

Particle diameter [m]

Effi

cien

cy [%

]

ABC

Figure 12: Collection efficiency in a turbulent flow field as a function of particlesize. Using equation (5.10) for the critical particle size gives (B), using equation(5.15) gives (A and C). The difference between A and C is explained below.The calculations have been made with the following values: Pipe diameter d=0.5 m Flow velocity w=15.1 m/s Particle density r

p=1000 kg/m

Collection area A=25.1 m

Since the velocity of the fluctuating velocity, wr, is given just outside the buffer layer, the transport-ing velocity, wn also should be calculated at the same location. Equation (5.13) gives wn as a func-tion of the overall heat- and mass-transfer coefficient. It can easily be shown (Berg 1998) that theheat- and mass-transfer coefficient for the turbulent core can be expressed as:

tot3 32 K= (5.17)

In figure 12, C is calculated using tot5.2 in equation (5.13).

The maximum level for collection efficiency is consequently determined by the transporting veloc-ity w

n, whereas the point at which the maximum level is reached, is determined by the thickness of

the laminar (y1) or laminar and buffer layer (y

2). Using

3 for (w

n) and y

2 is, at this point, considered

the most logical way since wr is used to determine the stopping distance and by definition w

r is the

fluctuating velocity at the location where 3 describes the heat and mass transfer rate.

The values used to calculate the lines in figure 12 correspond to the inlet pipe in the studied aircleaner (Figure 1). The collection area is the area of the air cleaner. This calculation is made just toget an overall picture of the turbulent collection efficiency. The selection of geometrical parameterswill be discussed more in detail in a later section.

26

6. The influence of a falling water film

The collection surface of the air cleaner is constantly washed with water falling down as a thin film.The water is applied to the uppermost region of the cleaner (see figure 13) along the whole width ofthe wall. To estimate the properties of the falling water film, some equations from (Bird et al l960)are used.

Figure 13: Flow of liquid film under the influence of gravity with no rippling. Sliceof thickness Dx over which the momentum balance is made. The y-axis is pointingoutward from the plane of the paper.

The maximum velocity of the falling film (Figure 13) is the velocity furthest away from the wall,and can be calculated by

2cosg

w2

max = (6.1)

where is the fluid (water) density, is the wall angle and is the film thickness. The integratedaverage velocity is given by

3cosg

w2

z = (6.2)

The film thickness may be calculated from the average velocity, the volume rate of flow or fromthe mass rate of flow per unit width of the wall. Here, the equation for volume rate of flow only, isgiven, for the others please see (Bird et al 1960).

27

3cosgWQ3

= (6.3)

where Q is the volume rate of flow and W is the wall width (perpendicular to the falling direction).

Film velocity as a function of film temperature

0.2

0.3

0.4

0.5

0.6

0.7

0 20 40 60 80Film temperature [C]

Film

v

eloc

ity [m

/s

Q=20 l/min Q=30 l/min

Figure 14: Velocity of the falling water film for two flow rates. Cylinderdiameter d =1.6 m.

For instance, having a wall width W = 5.0 m (i.e. d = 1.6 m) and Q = 20 litres/min would give amaximum velocity wmax = 0.34 m/s (fluid properties at 12 C), with a film thickness = 0.30 mm. Ahigher temperature results in a higher film velocity and a thinner film. Thus it should be consideredwhich property to keep constant in the air cleaner with seasonal temperature changes the flowfield or the film thickness.

When considering the flow profile of the upward flowing air in the air cleaner, the following ques-tion arises: how does a water film with an opposite direction influence the profile? Closest to thewater surface, the air will have the same velocity and direction as the water (the velocity of whichwill slightly diminish from the value given by equation (6.1) under the influence of the air. This is,however, ignored in this context).

Since particles drift towards the collecting surface as they travel through the cleaner, they will, atsome point, enter the region assumed to have a velocity directed downwards. This should, slightly,influence the cleaning efficiency in a positive manner. Particles entering this region can be assumedto be separated since their relaxation time reaches infinity. The thickness of the laminar and bufferlayer (y2) can be diminished to represent only the part of y2 being directed upwards. The followingmodification is suggested to the theory presented in chapter 5: The velocity of the falling waterfilm, equation (6.1) is added to the axial velocity component of the main flow. The critical particlesize is calculated by comparing equation (5.3) with the thickness of the reduced laminar and bufferlayer given by

28

=+

max2

maxmax222

w

wwyy (6.4)

(which is slightly less than y2) where wmax is given by (6.1) and w2max is calculated from the originalw2 increased with wmax.

Changing the thickness of the laminar and buffer layer (from y2 to y2+) will slightly change w2 (and

consequently w2max). The radial velocity component is, however, dominant compared to the axialcomponent considered here. The result is that minor inaccuracies in the value of w2 will not signifi-cantly affect the second factor at the right hand side of equation (6.4). This somewhat simplifiedprocedure results in a minor error of less than 1% in equation (6.4).

29

7. Ionic wind Literature review and experiments

In an electrostatic precipitator a continuous stream of ions is established, due to the potential differ-ence between the charging and collecting electrodes. Because of this stream of ions, surroundinggas molecules are also brought into motion in the same direction. This movement of gas (air mostly)is often called ionic wind (or corona wind, electric wind). In this text a short summary of somepapers on the subject is presented first. Later, some experiments to evaluate ionic wind are re-ported. A more extensive analysis of the experiments in chapter 7.2 is found in (Berg and Altner1999).

7.1. Literature review

As a summation of the papers studied, it can be said that they all imply that ionic wind gives ahigher rate of turbulence in the precipitator. Whether this is a positive or a negative factor whenconsidering collection efficiency, varies from one paper to another.

Zhibin & Guoquan (1994) for instance, reach the conclusion that when increasing the corona cur-rent in relation to the flow velocity, the collection efficiency increases, but when increasing thecurrent over a certain point diminishes the collection efficiency. Furthermore, they state that areduction of turbulence results in a higher collection efficiency. An explanation for this maxi-mum in collection efficiency, when varying the corona current, could be that the ionic wind in-creases the level of turbulence. Increasing the turbulence only a little improves the collection effi-ciency, but when the corona current is further increased, re-entrainment occurs, resulting in a low-ered collection efficiency. Strictly speaking, the statement made by Zhibin & Guoquan, that a re-duction of turbulence gives a higher collection efficiency, would mean that ionic wind is a negativefactor for the collection efficiency.

Leonard et al (1982) found experimentally that the intensity of the corona-induced turbulence wascomparable to or less than the background turbulence present, without an electrical field for gasvelocities exceeding 1.5 m/s, but increased rapidly when compared to background turbulence fordecreasing gas velocities. Generally, it is assumed that there will be a progressive deterioration inthe effective migration velocity at increasing flow velocities due to re-entrainment. According to(Leonard et al 1982), to achieve improved precipitator performance with a negative corona throughturbulence control, the gas velocity should be approximately equal to or larger than 1.5 m/s, i.e. theratio of corona-induced turbulence to background turbulence should become lower. This meansthat the ionic wind could be seen as a negative factor with regard to collection efficiency. Both(Zhibin & Guoquan) and (Leonard et al) seems to have made their experiments with dry collectionsurfaces. The fact that re-entrainment occurs at higher flow velocities is valid only for dry surfaces with a wet surface no re-entrainment occurs.

Kercher (1969) made some interesting observations in his experiments. First of all, in quiescent air,no ionic wind could be observed for a wire discharge electrode. Some needles or points had to bepresent at the electrode before any ionic wind could be measured. For a system with a 43 kV voltage(and needle electrode), increasing the distance, between the charging and collecting electrode, tonot more than 120 mm, decreased the ionic wind to a minor level. For air in motion, a system with50 kV was used. When the flow velocity was 0.5 m/s the ionic wind was still clearly measurable,but when the flow velocity was increased to 1.2 m/s no ionic wind could be detected. Overall theconclusion made by Kercher is that ionic wind has a positive effect on collection efficiency in an

30

electrostatic precipitator because of the corona-induced turbulence pointing towards the collectingsurface. It is especially beneficial when considering small particles that easily form space charge.Due to the turbulence, the space charge is displaced towards the collecting surface leading to onlya minimal reduction in the corona current. The experiments presented by Laufer were carried outwith clean air only.

Liang and Lin (1994) gave a ratio between the flow velocity and the characteristic velocity of ionicwind, described as:

0ew

eV

U = (7.1)

where is the gas density, ew

is the charge density and V0 is the applied voltage. They concluded

that when the ratio was less than 0.2, turbulent kinetic energy increased significantly due to ionicwind, thus diminishing the collecting efficiency. When the ratio was over 0.5 the electric forceacting upon the flow field was not prominent, and the kinetic energy of the flow was near that of afully developed flow without an electric field. Furthermore, the authors stated that under normaloperating conditions, the influence of ionic wind on the flow field was insignificant. Decreasing theflow velocity (i.e. decreasing the ratio mentioned to below 0.2) the ionic wind became more obvi-ous and had a negative effect on the collection efficiency. The results were theoretical only, and thereduction in collection efficiency seemed to be due to re-entrainment caused by turbulence. Againit can be said that this does not apply to wet surfaces.

Shu & Lai (1995) in their paper, studied improved heat transfer due to an electric field. The electricfield results in a secondary air-flow (i.e. ionic wind) directed towards a grounded surface, enhanc-ing the heat-transfer in the system. The net effect of this secondary flow is an additional mixing ofthe flow and destabilisation of the thermal boundary layer leading to raised heat-transfer coeffi-cients. The enhancement is most significant regarding small air-flows, giving a heat-transfer sev-eral times higher than one without electric field. The results of Shu & Lai are theoretical. Theyfurther suggest that the enhancement in heat-transfer is possible due to the oscillatory flow-field.Whenever two flows, being of the same order of magnitude are opposed or perpendicular to eachother, some degree of oscillation is to be expected.

Of the papers cited here discussing ionic wind and particle collection, the only one implying animprovement in particle collection efficiency due to ionic wind is Kercher (1969), and that regard-less of whether it is a wet or dry collecting surface. A wet surface might influence the conclusionsof the other studies.

The paper of Shu & Lai gives an opportunity to consider the results in chapter 4, and also to try tomeasure the ionic wind in the air cleaner studied in this project. The heat- and mass-transfer coef-ficients are measured with and without an electric field, and any difference in levels would then beexplained by the ionic wind. In the following sections some experimental results are presented.

31

7.2. Experimental detection of ionic wind

The experiments were made using the equipment described in chapters 1 and 4. A more detaileddiscussion about regression models and also about ionic wind can be found in (Berg and Altner1999). The regression model presented in this chapter is an improvement to that presented in chap-ter 4. See also chapter 13.

The experimental results were entered into the overall energy balance for the system, giving as aresult, the heat- and mass-transfer coefficient . Thereafter, a regression model of the same type asbefore is generated. The energy and mass balances give the following equations from which t2 and are calculated. Solving the equations, assuming a steady temperature t1 = 6 C and calculatingthe Reynolds and Nusselt numbers in accordance with equations (4.10) and (4.11), we obtained aset of points which are shown in figure 15.

( )ww

totc

w1wtot1

ctotcc1a2ael2

cm2A

ctmA2tAtxmxmq

t&

&&&&

++=

(7.2)

and

( )

tot2121

elv21

aa21

A2

tt

2tt

qc2

xxcmtt

+

+

+

++

=

&&

(7.3)

where t represents the temperature in the vicinity of the evaporating surface, the lower indexes 1and 2 denote the properties at the inlet and outlet, and elq& is a small amount of electrical lossesadded as heat to the system, measured in form of a corona current. In this case, the corona currentcomes from the fact that the air is lead through a passage between two high voltage electrodes(Ogawa 1984). The overall effect of the corona current was in this case measured as elq& 400 W.

Here elq& is added completely to the air since the resistance of air, compared to other resistances isof a different order of magnitude. Anyhow, in this case the influence of elq& 400 W is so small thatit could just as well be omitted. Furthermore using elq& in equation (7.3) assures a maximum influ-ence of the input electrical effect, in the form of ionic wind, on the heat- and mass-transfer coeffi-cient, and yet no measurable differences can be detected.

32

Nusselt number as a function of Reynolds number

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 50000 100000 150000 200000 250000Re

Nu

Experiments (without electricity) Experiments (with electricity) Regression modell

Figure 15: The experimentally obtained Nusselt numbers as a function of theReynolds numbers and a regression model (equation 7.4a, shown as a drawn line)fitted to the Nusselt numbers.

From the data points in figure 15 no significant difference can be seen between those cases with orwithout an electric field, i.e. Nusselt numbers and therefore can be held as equal in both cases.Shu & Lai (1995) amongst others, wrote about an additional mixing of the gas due to the appliedhigh voltage (i.e. ionic wind), resulting in an enhancement in the heat-transfer, but they also statedthat the influence would be greatest at small flow velocities (i.e. low Reynolds numbers). In thecase under study (the system was described earlier in chapters 1 and 4) the level of turbulence isextremely high and even a voltage as high as 130 kV (i.e. elq& 400 W), should not cause measur-able differences in the heat- and mass-transfer coefficients.

From these data points the regression model becomes:

95.0Re032.0Nu = (7.4a)

or, to use a more familiar form

45.095.0 PrRe037.0Nu = (7.4b)

Considering the ratio d/l and using the more general equation (4.13) gives for (7.4b)

45.095.03/2

PrReld1024.0Nu

+= (7.5)

33

When comparing these equations with the equations (4.12a) and (4.12b), one can see that the expo-nent of Re does not equal one, as suggested in the previous section, but is a little bit lower, whichwas already predicted as the most probable case. Some further experiments giving regression mod-els of the same kind as equations (7.4a) and (7.4b) are described in chapter 13.

34

8. Particle diffusion

In order to evaluate the need to consider particle diffusion when modeling an air cleaner of the kindstudied during this project, some equations are presented. The diffusion coefficient for a particle isgiven by (Hinds 1982)

p

c

d3CTk

Dpi

= (8.1)

where k is the Boltzmanns constant, T is the absolute temperature and Cc is the Cunninghamscorrection factor (see chapter 2). The equation is called the Stokes-Einstein equation for aerosolparticle diffusion coefficients.

For deposition on a collecting surface by diffusion from a turbulent flow, the situation is compli-cated, and no explicit solution exists. The customary assumption made, is that the turbulent flowprovides a constant concentration, n0, which is uniform beyond a thin diffusive boundary layer(the same assumption concerning the concentration was made earlier for the Deutsch formula). Inthis thin layer, the concentration decreases from the concentration of the main flow to zero at thesurface. The deposition velocity is given by

DVdep = (8.2)

where is the thickness of the diffusion boundary layer. The value of depends on flow mecha-nisms, the nature of the velocity boundary layer and the size of the particles. One suggestion for found in (Hinds 1982, page 148) is

4/1

g

8/7

4/1t

Re

Dd5.28

=

(8.3)

where dt is the tube diameter. Larger particles get thrown partway into the diffusion boundary layerand have a shorter distance to diffuse, whereas smaller particles, having smaller inertia, have todiffuse the whole distance. To express the diffusive deposition in terms of collection efficiency, thefollowing is given

=

VAV

exp1 depD & (8.4)

35

In the equation (8.4) A is the collection surface area. For decreasing particle sizes the diffusionaleffects become more pronounced, whilst for larger particles, inertial effects increasing with particlesize, govern collection efficiency. In between, a gap appears where neither of the processes workproperly. This gap in the efficiency curve can be seen for particles in the 0.1 to 1.0 m range.

When calculating the collection efficiency for diffusional deposition in a turbulent flow for the aircleaner studied in this project, a circular tube with a flow, giving an equal level of turbulence (i.e.-value) is chosen in order to achieve collection efficiencies of the right magnitude. Therefore apipe of d=0.5 m with the flow velocity w

g=15 m/s is used. To get approximately the same residence

time as in the air cleaner, a tube length L52 m is used, resulting in a collection surface area A82m.

Collection efficiency (%) as a funtion of particle size

0

20

40

60

80

100

0.001 0.01 0.1 1 10 100

Particle diameter [m]

Effi

cien

cy [%

]

Figure 16: Collection efficiency for deposition by diffusion in a turbulent pipe flow.

Analogous to diffusive and field charging, chapter 2, where equations (2.9) and (2.12) were added,equations (5.16) and (8.4) could be combined to one - the error being very small because of theabove-mentioned gap in the collection efficiency. The resulting equation would become

( )

+

=+ VAVwk

exp1 depnpDT & (8.5)

The influence of the diffusional deposition, however, is hereafter neglected since, as seen in figure16, it is significant in a particle size range with very little practical interest to the paper industry.

36

9. Particle agglomeration

The phenomena studied so far in this text are all collecting particles from the gas flow regardless ofparticle concentration. For particle agglomeration (or coagulation) this is different as agglomera-tion occures due to collisions between particles. No mass is actually separated from the gas flowdue to agglomeration, but the number of particles is reduced.

The theories for particle agglomeration assume that when two particles collide with one anotherdue to a relative motion between them, they attach to each other and form larger particles. The sizeof the particle growing with the collision, is not affected that much, but for the other particle thechange is much more dramatic it vanishes completely. The result is a decrease in number concen-tration, and as the agglomeration is more significant for small particles, the number size distribu-tion is also displaced towards larger particles.

The mechanisms for particle collisions are various, and some idealistic models can be found in thepertinant literature. When the relative motion between particles is due to Brownian motion theprocess is called thermal agglomeration (or coagulation), whereas when external forces are in-volved, the process is called kinetic agglomeration. Such forces are gravity, electrical forces orturbulent eddies.

The simplest case is thermal agglomeration of monodisperse spherical aerosols. The theory is basedon how particles diffuse to the surface of an observed particle. The rate of collisions, which is equalto the rate of change in number concentration, can be given by (Hinds 1982):

2p NDd4dt

dNpi= (9.1)

where D is the diffusion coefficient for particles (equation 8.1). If the change in number concentra-tion with time due to agglomeration is to be described, the following equation is obtained by inte-grating equation (9.1):

tDd4N1N)t(N

p0

0pi+

= (9.2)

where N0 is the number concentration at t=0. The diffusion coefficient D decreases rapidly withincreasing particle size. Therefore N(t) will differ from N0 only for small particles. The same can besaid when the time period is short. As an example, the net result of agglomeration can be neglectedover a 10-minute period if the number concentration is less than 106/cm. Since the residence timein the studied air cleaner is given in terms of seconds rather than minutes, and since the numberconcentration reaches 106/cm only for the smallest particles, the influence of (thermal) agglomera-tion (of monodisperse spherical aerosols) can be neglected in the paper industry. The curve Num-ber distr out in figure 17 represents equation (9.2) with t=5 seconds.

For polydisperse aerosols the rate of agglomeration is significantly higher. Small particles having a

37

large diffusion coefficient D diffuse well to larger particles, having a higher surface area. Thusagglomeration between particles of different size will affect the number size distribution faster. Thebigger difference in size, the faster the agglomeration will proceed. For the mass size distributionshown in figure 17, which should represent a typical distribution curve for paper converting dust,having a total mass concentration of 21 mg/m, the increased agglomeration for polydisperse aero-sols will not significantly change the number size distribution curve coming out of the system.

1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

1.E+00

1.E+02

1.E+04

1.E+06

1.E+08

0.001 0.01 0.1 1 10 100 1000Particle diameter [m]

Nu

mbe

r di

stri

butio

n [1

/cm

]

0.0

0.5

1.0

1.5

2.0

2.5

Mass

di

stri

butio

n [m

g/m

]

Number distr in Number distr out Mass distr

Figure 17: Mass and number distributions for an aerosol (rp=1000 kg/m, spherical

particles). The total mass concentration in this example is 21 mg/m.

When observing an airflow, there will always be velocity gradients which result in different veloci-ties for particles. Equations can be found for both laminar and turbulent flows, only the latter beingof practical interest. As the turbulent eddies result in significant velocity gradients, the followingequation is given:

=

t

3g

2p

dUf2

D64db

ionagglomeratThermalionagglomeratTurbulent

pi (9.3)

where b is a constant of order 10, U is the average velocity in the duct with the diameter dt and f isthe fanning friction factor (equation 5.2). Equation (9.3) gives the ratio of turbulent agglomerationto thermal agglomeration. With U =15 m/s and dt = 0.5 m the ratio becomes one (i.e. turbulentagglomeration exceeds thermal agglomeration) for approximately 0.7 m, and increases rapidlywith increasing particle size. However, as the number concentration decreases rapidly with increas-ing particle size, the conclusion drawn from figure 17 will not change.

For the agglomeration of charged particles, particles of opposite charges would attract each otherand form agglomerates (clusters) more easily. The net result is a minor change compared to theagglomeration of uncharged particles, as the effect is balanced by collisions between particles of

38

same sign repelling each other.

In an electrostatic air cleaner the particles all have a negative (or positive) charge (possibly formingdipoles) and therefore the net result should be, not just equal to agglomeration of uncharged par-ticles, but even lower.

The conclusion is, for the air cleaner studied in this project with paper dust, that the number ofparticles is too low for significant agglometation, no matter which theory for agglomeration isconsidered. The conclusion is the same even when the particles are charged.

39

10. Properties of dust in the paper industry

The different mechanisms for particle collection described in earlier chapters, all to some extent,include properties of the particles, and the material of the particles. The particle size, density, di-electric constant and particle shape for individual particles must be known and since the collectionefficiency depends heavily on particle size, the particle size distribution function for the processeddust must be known in order to properly estimate the final (mass) collection efficiency of the plannedair cleaning system.

Some of the properties are described here in brief, but the shape factor and some aspects concerningthat are presented in a later chapter. The properties presented are based on the Masters thesisundertaken within the project (Dahlbacka 1999).

Particle size distribution can be split up in three separate fractions; the particles with the smallestdiameter are referred to as the nucleous fraction, the next is called the accumulation fraction and thelargest particles are defined as the coarse fraction. Whether the sizes of particles match any defini-tion for the names used is irrelevant. The names are just used to indicate which fraction is beingdiscussed.

Since the physical properties of the particles vary for the different fractions, the collection effi-ciency as a function of particle size will also be different for the different fractions. The threedifferent fractions have to be treated separately and if a final curve giving the collection efficiencyas a function of particle size for the whole particle distribution is desired it can, for example, becalculated from the difference between input and output dust. This might lead to some unlinearitiesin the collection efficiency curve.

The nucleous and accumulation fractions are treated as ideal spheres, the coarse fraction as fibersdescribed as cylinders (Dahlbacka 1999). A study was made in order to determine the particle sizedistribution function for dust from different paper qualities in different paper production or conver-sion processes. The qualities were coated paper, newsprint and tissue paper. The relative size distri-butions are shown in figure 18.

For the different distributions the following values are used (table 3), based on the study mentionedand literature:

40

Table 3 : Particle properties.

Nucle

ous

Accu

mula

tion

Coar

se

r 4 6 2.5 -Tissue paper

p 640 950 800 kg/mk 0.0085 0.261 0.731 - 0.4289 10.9 174.8 m 1.7 2.51 76.9 m

Newsprint p 640 850 800 kg/mk 0.0278 0.255 0.717 - 0.4456 6.55 174.8 m 1.79 2.34 76.9 m

Coated paper p 640 790 800 kg/mk 0.0818 0.567 0.351 - 0.485 6.27 174.8 m 1.81 2.21 76.9 m

Relative particle size distribution for different paper qualities

0.0 %

2.0 %

4.0 %

6.0 %

8.0 %

10.0 %

12.0 %

14.0 %

16.0 %

18.0 %

0.1 1 10 100 1000Particle diameter [m]

Fra

ctio

n [%

]

Tissue paper Coated paper Newsprint

Figure 18: Relative particle size distribution for different paper qualities.