9-3-D numerical simulations of cylindrical pleated filter pa.pdf

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Chemical Engineering Science 58 (2003) 49654973

www.elsevier.com/locate/ces

3-D numerical simulations of ows in a cylindrical pleated lterpacked with activated carbon cloth

A. Subrenat, J. Bellettre, P. Le Cloirec

Ecole des Mines de Nantes, GEPEA UMR CNRS 6144, DSEE, 4 rue A. Kastler, BP 20277, 44 307 Nantes Cedex 3, France

Received 24 June 2002; received in revised form 12 November 2002; accepted 4 July 2003

Abstract

This paper focuses on activated carbon cloths used for VOC treatment. The studied device is a cylindrical pleated lter that is developedfor the implementation of these materials in dynamic systems. 3-D numerical simulations of ows have been performed to determine

the ow structure in this kind of geometry. The analysis of the ow structure reveals preferential ow directions in the pleated medium.

The local velocity range near the fabric could be 10 times higher than the average velocity calculated for the whole developed surface of

the lter, but even the maximal value of the velocity (0:3 m s1) is acceptable for adsorption. Overlap phenomena are revealed and dead

zones estimated. The inuence of the number of pleats in such a device on the aerodynamic performance is also studied.

? 2003 Elsevier Ltd. All rights reserved.

Keywords: Adsorption; Fluid mechanics; Porous media; CFD; Pleated lter; Activated carbon cloths

1. Introduction

Environmental regulations demand the design and devel-

opment of increasingly ecient VOC treatment processes.

Several processes use the adsorption phenomena of organic

molecules onto a porous material. It is thus essential to

improve and optimise this type of installation in terms of

porous material and reactor geometry. In this context, acti-

vated carbon cloths, recent forms of adsorbent, have been

developed. Previous studies have shown their eciency in

terms of adsorption capacities and kinetics (Brasquet & Le

Cloirec, 1997; Subrenat & Le Cloirec, 2000). Moreover,

the Joule eect heating of these cloths could be used as a

regenerative process because of their interesting electrical

properties (Subrenat, Baleo, & Le Cloirec, 2001). Their tex-

ture promotes new implementations in dynamic systems of

these media and the design of new adsorbent reactor and

lter geometries. The aerodynamic behaviour of these sys-

tems is one of the most important considerations in the de-

sign and the sizing of such an air treatment process, in terms

of pressure drops and ow structure. Indeed, it is important

to limit the preferential ow directions of the uid into the

Corresponding author. Tel.: +33-2-51-85-82-93;

fax: +33-2-51-85-82-99.

E-mail address: [email protected] (A. Subrenat).

adsorbent fabric in order to avoid a premature breakthrough

point of the lter, and thus to guarantee an emission level inaccordance with future standards (increasingly low). Cylin-

drical pleated lters using activated carbon cloths have al-

ready been designed and used to perform pressure drops and

adsorption capacity measurements. Experimental results re-

veal the eciency of such a geometry and the diculty of

sizing the pleat number in this kind of device (Subrenat,

Baleo, & Le Cloirec, 2000). 2-D numerical simulations of

ow have already been performed to describe and envis-

age the ow structure and the pressure drop in such reactors

(Chen, Pui, & Liu, 1995; Baleo, Subrenat, & Le Cloirec,

2000). In this description of the reactor, the pleated medium

is modelled overall by a porous zone, taking into accountthe material permeability and the pleating eects. Thus, it

does not allow the precise study of the ow structure near

the adsorbent and, more particularly, the preferential ow

directions into the pleated medium. This is a very important

consideration for the eciency of the lter.

The objective of the present study is to evaluate in three di-

rections the ow characteristics in such a cylindrical pleated

lter. With this intention, the computational uid dynamic

is used. The geometry of the lter is precisely described by

a 3-D representation of the system. The physical proper-

ties of the medium are rst experimentally determined. Nu-

merical simulation pressure drop results are then compared

0009-2509/$ - see front matter? 2003 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ces.2003.07.012
mailto:[email protected]:[email protected]


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4966 A. Subrenat et al. / Chemical Engineering Science 58 (2003) 4965 4973

Fig. 1. Cylindrical pleated lter geometry.

Fig. 2. Geometry of the reactor.

with experimental data. Finally, an analysis of ow struc-

ture through the pleated lter is presented and discussed.

Particular attention is given to the possibility of accurately

predicting quantitative pressure losses and distribution of

the ow rates in the lter device. The design and sizing of

such a lter is carried out taking into account the optimisa-

tion in terms of pressure drop, residence time of the uid in

the adsorbent and also industrial constraints, such as the ad-

sorbent mass per lter, width of the manufactured cloth and

pleat techniques. So, a rst empirical geometry is proposed

and studied taking into account most of the industrial con-

straints. Then, other geometries are simulated with dierentnumbers of pleats to examine the pleat angle eect on the

ow velocity distribution in the medium.

2. Materials and methods

A cylindrical pleated lter using activated carbon cloth

was built and set up in a pilot plant for pressure drop exper-

imental measurements. The precise geometry of this lter

was also used to perform a numerical simulation of ows.

In this way, calculated and measured pressure drops could

be compared to validate the simulation method.

2.1. Filter device

The lter is made of pleated activated carbon cloth

(Fig. 1). It is positioned between an open and closed ange.

The geometrical characteristics of this lter are the inner

diameter (noted d11), the outer diameter (noted d12), the

length of the lter (noted L1) and the number of pleats (N).

The lter is enclosed in a cylindrical reactor. The geomet-

rical characteristics of the reactor (see Fig. 2) are the inner

diameter (noted d21), the external diameter (noted d22) and

its length (noted L2).

Table 1

Characteristics of the studied lters

Filter reference P-10 P-30 P-45 P-60

Number of pleats 10 30 45 60

Pleat angle () 36 12 8 6

Developed surface (m2) 0.18 0.51 0.77 1.02

Adsorbent mass (g) 78.65 225.64 337.42 449.42

Table 2

Main characteristics of the material used

Cloth reference RS-1301

Weave 3-ply serge

Carbonisation temperature (C) 1300

Activation process H2O

Activation temperature (C) 1300

Porous volume (cm3 g1) 0.743

Microporous volume (cm3 g1) 0.506

Median pore diameter ( A) 7.3

Specic surface (BET) (m2 g1) 1300

Thickness (mm) 0.60

External porosity (%) 87

Specic weight (g m2) 220

In this study, the dimensions of the system are the fol-

lowing:

d11 = 0:05 m, d12 = 0:1 m, N = 45 pleats, L1 = 0:34 m,

d21 = 0:036 m, d22 = 0:16 m, L2 = 0:41 m.

Hence, the total developed surface of the lter (noted

Slter) is about 0:76 m2. This lter geometry (named P-45)

is a realistic design in terms of industrial manufacturing and

constitutes an interesting device to study. Other geometries

will also be studied. All the dimensions of these lters are

the same as the P-45 lter previously described, except forthe number of pleats. The main characteristics of the studied

lters are summarised in Table 1.

2.2. Medium used

This lter has been especially designed for VOC treatment

but may also be used for water applications. Hence, the pleat

is made of a recent form of adsorbent well known for its

interesting adsorption capacities, activated carbon cloth. The

main physical characteristics of the material used in this case

are given in Table 2, although only geometrical parameters

are required to perform the present work.


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A. Subrenat et al. / Chemical Engineering Science 58 (2003) 4965 4973 4967

The medium used in the studied lter is composed of two

RS-1301 activated carbon cloth layers with a total thickness

(denoted e) of 1:2 mm, pleated together.

3. Model description

3.1. Equations governing turbulent ow

The uid dynamics core model used has been described

in detail elsewhere (Bellettre, Bataille, & Lallemand, 1999;

Baleo et al., 2000). It consists respectively of mass (1) and

momentum (2) conservation equations where the Reynolds

decomposition has been applied:

@

@xi( ui) = 0; (1)

@

@xj( ui uj) =

@p

@xi+

@ij

@xj+ gi

@

@xj(ui u

j) + Si (2)

and of a turbulence quantities transport equation. The choiceof a turbulence regime is made because of the Reynolds

numbers involved in the range of the studied uid velocities

(Re = 24009100 at the device inlet).

In Eqs. (1) and (2), is the uid density, ui is the velocity

component in the i direction, p is the pressure, ij is the

viscous stress tensor and gi is the gravitational acceleration

in the i direction. Inside the porous medium, momentum

(2) is augmented by a source term, Si, incorporating the

additional pressure gradient in the porous medium (dened

later by Eq. (5)). This source term is valid whatever the ow

regime is (Baleo et al., 2000; Fluent, 1998). In practice, its

value makes the other terms of Eq. (2) negligible except the

pressure one. This leads to a computation equivalent to the

replacement of the momentum equation by a pressure drop

law. In the present study, the ow is considered as steady and

isothermal while the porous material properties are isotropic.

The thermophysical properties of the uid are set constant

( = 1:225 kg m3 and = 1:7894 kg m1 s1). Constant

density is assumed because the expected pressure drops are

low compared to the absolute atmospheric pressure.

Momentum equations (2) are closed by the standard k

model (Jones & Launder, 1972) because no complex ow

structures (such as recirculations) are expected. Hence, there

is no need to use a higher order closure turbulence model.

3.2. Boundary conditions

Close to the solid walls, the standard law of the wall

(Launder & Spalding, 1974) accounts for the no-slip condi-

tion eect:

U

U=

1

ln(Ey+); (3)

where U =

w=w, w is the wall shear stress, is the

von-Karmans constant and E is an empirical constant set

equal to 9.0 (smooth wall). y+ is the wall unit (it is a di-

mensionless coordinate dened by relation (4)).

The assumption of an equilibrium turbulent boundary

layer is adopted, and the wall unit y+ is computed as

y+ =U

=

C1=4 k

1=2p

; (4)

where is the distance from the wall and kp is the near wall

value of the turbulent kinetic energy (C being a constantof the turbulence model).

Boundary conditions for k and values can be found in

Bellettre et al. (1999).

At the inlet of the device, a constant velocity value is

imposed. At this location, the turbulence intensity, I, and

the hydraulic diameter, dh, are set respectively at 10% and

0:16 m (i.e. d22), leading to the boundary conditions for

k and equations. The reference pressure is xed at the

inlet. Its value is 101325 Pa. It may be added to the relative

static pressure deduced from the ow calculation in order

to determine the absolute pressure. Finally, at the outlet of

the device, the diusion ux normal to the exit surface isassumed to be zero. This corresponds to an outlet boundary

condition of a developed ow.

3.3. Numerical method

The numerical procedure is based on a nite volume ap-

proach with quadrilateral control volumes and structured

meshes. The diusion terms are discretised according to

a central dierence method and the convective terms us-

ing a power law scheme (Patankar, 1980). Pressure ve-

locity coupling is calculated with the SIMPLE cell-centred

scheme (Patankar, 1980). The discrete algebraic equationsare solved using a line-by-line tri-diagonal matrix (Fluent,

1998).

Furthermore, the convergence of the results is tested ac-

cording to two criteria. First, all the normalised residuals

must be less than 103. Secondly, supplementary iterations

do not change the calculation results (the evolution is less

than 0.5%).

3.4. Computational domain and grid

The geometrical symmetry of the system enables only a

small part of the lter to be described, that is to say a volumeincluding only one half pleat (Fig. 3). The three directions

are indicated in Fig. 3, the origin of the positions being

located at the inlet on the device axis.

The mesh is unstructured and is composed of 350,000

nite volumes with a higher density close to the porous

media. Inside the porous media, seven nodes occur along

the thickness. The law of the wall (Launder & Spalding,

1974) is used only for the rst point over the solid walls.

This point is set in order to stay in the validity domain of the

law without going into the laminar sublayer (y+ 11:2, as

explained in detail in Bellettre et al., 1999). In the present

case, a minimum distance between the solid walls and the


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Fig. 3. Computational domain.

rst cells set at 0:5 mm enables the condition y+ 11:2 to

be respected.

3.5. Determination of porous medium properties

The pressure drop due to the porous medium is introduced

in the source term of the momentum equations (5). It is

expressed as

p =

V + C

1

2V|V|

; (5)

where is the porous medium permeability, C is an

inertial factor and V is the supercial velocity close to the

medium.

The physical parameters ( and C) of the medium may

be deduced from experimental pressure drops performed in

planar conguration (Fig. 4).

The pressure drop due to the two layer medium is a func-

tion of the supercial velocity (which is also the mean ve-

locity in the device), and is tted by the following classical

polynomial expression:

p = a1V + a2V2 = 2340:8V + 3192:2V2; (6)

where a1 is a viscous term coecient and a2 is the inertial

coecient.

Fig. 4. Planar device.

One may write, integrating in the ow direction (noted

Ox):

p =

e0

p dx =

e0

V +

C

2V2

dx

=e

V +Ce

2

V2: (7)

By identication of Eqs. (4) and (5) one obtains

=e

a1; (8)

C =2a2

e: (9)

The numerical values for the two layer medium (referred to

as RS-1301) are

= 1:07 1011 m2 and C = 7:30 m1:

4. Results and discussion

4.1. Validation of the numerical simulations in the case

of the 45 pleats lter

In order to validate the simulations, the computational

pressure gap between the inlet and the outlet of the device is

compared with the measured ones (Fig. 5). The lter device

described in Part 2 is used to perform experimental pressure

drop measurements. Satisfactory agreement is obtained be-

cause the discrepancy is always less than 200 Pa. This dis-

crepancy between numerical and experimental results is sig-

nicant only in the case of the lowest volumetric ow rate. It

is important to note that the pressure drop due to the porousmedia is less than 10% of the total pressure drop in the de-

vice (for example, 140 Pa against 1750 Pa for the highest

studied ow rate, 2:86 102 m3 s1). Thus, not only theporous pressure jump but also all the pressure losses due to

singularities and wall friction are well predicted.

Validation of the numerical method is also carried out

by testing the eect of a mesh modication on the com-

putational results. A slightly dierent mesh is tested by

increasing the cell number by 10%. Results are shown in

Figs. 5 and 6 regarding, respectively the total pressure drop


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0

500

1000

1500

2000

0 5.10-3

10.10-3

15.10-3

20.10-3

25.10-3

30.10-3

Q (m3.s

-1)

p(P

a)

Experiments

Simulation 2Simulation 1

Fig. 5. Comparison of predicted and measured pressure drops.

and the map of the velocity component that is normal to theupstream side of the porous medium (dened Un later). No

signicant gap is observed. Thus, the rst mesh is kept for

the following simulations.

4.2. Analysis of the ow structure in the case of the 45

pleats lter

An example of stream lines is plotted in Fig. 7. The

ow coming inside the device seems to be rather uniformly

Fig. 6. Un velocity (component that is normal to the surface) on the upstream side of the porous layer ( Q = 2:86 102 m3 s1).

Fig. 7. Stream lines inside the device (Q = 2:86 102 m3 s1).

distributed when it crosses through the porous layer. Thus,

the surface of the porous medium seems to be correctly used.

In contrast, if the ow direction is reversed, the useful sur-

face of the medium becomes very small (as shown in Fig. 8).

Flow direction is thus kept as in the rst conguration in

the following work.

Present simulations provide the characteristics of the owinside the device. The relative pressure eld is rst given in

Fig. 9. Before analysing this relative pressure eld, it could

be interesting to note that the total applied force of the whole

device is around 10 N in the case of the highest volumet-

ric ow rate. This force is essentially due to the pressure

force (resulting from the integration of the dierences be-

tween internal and external pressure), the viscous force be-

ing negligible in the present case. The pressure (plotted in

Fig. 9) normally decreases from the inlet to the outlet ex-

cept for just before the upper part of the bottom wall where

the kinetic energy of the ow is changed into static pres-

sure. This increase in pressure above the last part of the lter

favours the passage of uid. This will now be analysed in

detail.

The component of the velocity which is normal to the

lter surface is directly linked to the local volumetric ow

rate. Its calculation leads to an accurate knowledge of the

ow rate distribution across the lter. The velocity normal

to the porous layer, Un, is directly deduced from the angle

of the lter pleats (5) according to Eq. (10):

Un =0:087Ux 0:996Uy: (10)


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Fig. 8. Stream lines in the opposite ow direction (Q = 2:86 102 m3 s1).

Fig. 9. Relative static pressure eld (Q = 2:86 102 m3 s1).

Fig. 10. Flow distribution in the upstream side of the medium with the 45 pleats lter.

Fig. 10 presents this distribution on the upstream and

downstream side of the porous layer for a ow rate of

2:86 102 m3 s1. We can observe a uniform and lowvalue (around 5 102 m s1) of the normal velocity inthe major part of the medium, which constitutes the useful

zone. Higher values of the velocity can be observed in

the bottom right corner of the lter, because of the slight

increase in the static pressure above this part that we previ-

ously observed. However, this higher value of the velocity

(close to 0:3 m s1 with the highest volumetric ow rate)

constitutes a preferential ow zone (but it is small). We can

also observe a very low velocity zone (close to 0 m s1)

at the bottom of the pleats of the two sides of the medium

which constitute dead zones due to the overlap phenom-

ena.

Fig. 11 presents this distribution on the upstream side of

the porous layer (in front view) for the four ow rates stud-

ied. We can observe that the preferential ow decreases with

the volumetric ow rate. It must also be noted that the de-

tailed analysis of the simulation results did not reveal a high


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Fig. 11. Flow distribution in the upper side of the medium in front view (Un in m s1).

0

0.05

0.1

0.15

0.2

0.25

0.05 0.1 0.15 0.2 0.25 0.3 0.35

X = 0.048 mX = 0.041 m

Normalvelocity(m.s

-1

)

Z position (m)

X = 0.035 m

Fig. 12. Un curves at dierent distances from the axis (Q =

2:86 102 m3 s1).

sensitivity of some calculated elds to the most important

parameter in the study: the volumetric ow rate.

Fig. 12 gives some curves of the normal velocity calcu-

lated at dierent distances from the device axis when the

highest ow rate is simulated. The increase in the ow near

the end of the lter is again observed. We can also notice

that the normal velocity is higher when the distance from

the axis is decreased. This is partially due to the reduction of

the cross-section experienced by the ow when approaching

the axis.

Fig. 13 shows velocity curves at dierent longitudinal

positions. The major part of the uid ows through the lowerpart of the lter (X less than 0:042 m).

The normal velocity range observed in Figs. 12 and 13 is

compared with the calculated average velocity (noted Uaver)

taking into account the total developed surface of the lter.

This is given by

Uaver =Q

Slter 4 102 m s1;

where Q is the ow rate (m3 s1) and Slter the total devel-

oped surface of the lter (m2).

The discrepancy between Uaver and those observed in

Figs. 12 and 13 can essentially be explained by the larger

Fig. 13. Un curves at dierent longitudinal positions (Q =

2:86 102 m3 s1).

thickness of the lter in its highest part. The thickness of the

lter is indeed greater in its upper part when two sides are

joined. Consequently, the porous medium allows very low

passage of uid in this upper zone, which has previously

been called a dead zone. However, the values of veloc-

ity in the central part of the media are always low enough

to perform adsorption eciently. The surface of the use-

ful zone is estimated by analysing the ow structure given

by the numerical simulations. It is about 0:29 m2, which is

37% of the total developed surface of the lter. Hence, the

average velocity in the preferential ow zone is given by

Uaver 101 m s1:

This value could be correlated with the normal velocity

curves described in Figs. 12 and 13. Hence, this analysis of

the computational uid dynamic simulations reveals that, in

this kind of geometry, the average ow velocity across the

medium is much higher than the velocity estimated for the

total developed surface of the lter. Thus, the quantity of

adsorbent actually used for adsorption phenomena is about

60% lower than the total amount of material used in the

lter. This fraction of useful media could be increased by

using wider pleats.


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Fig. 14. Flow distribution in the upstream side of the medium with the 30 and 60 pleats lter.

4.3. Inuence of the pleat number

Other geometries with dierent numbers of pleats

are studied at a total volumetric ow rate equal to

2:86 102 m3 s1. The normal velocity eld upstream ofthe medium is presented in Fig. 14 for the 30 and 60 pleats

lters. The velocity distribution is more homogeneous for

the 30 pleats lter. In this case, the pleat angle is higher

and so overlap phenomena are reduced, thus limiting the

preferential ow area.

In the case of the 60 pleats lter, the two sides of themedium are very close to each other and there is an important

overlap of the medium over the whole length of the pleat.

Hence, we can observe a large dead zone (at the bottom of

the pleat) and a large preferential ow zone in the hollow

of the pleat with very high velocity values up to 0 :3 m s1.

The change in ow structure in relation to the pleat number

is complex. Low and high numbers of pleats generate dead

zones and thus preferential ow. The performance of such

pleated lters in terms of ow structure could also be anal-

ysed in terms of pressure drops (Fig. 15). Between 10 and

30 pleats, the pressure drops decrease due to an increase of

the developed area without a signicant overlap eect. Over

30 pleats, the pressure drops increase due to the increase ofthe dead zone and thus preferential ow. The lowest pres-

sure drops and best ow distribution is obtained with the 30

pleats lter.

5. Conclusion

Activated carbon cloths are well-known adsorbents for

VOC treatments in terms of their physical and chemical

properties and adsorption capacities. The implementation of

these materials in dynamic systems may be done in new

0

500

1000

1500

2000

2500

3000

00 1

Flow rate = 2.86 10-2

m3.s-1

p

(Pa)

Pleat number

706050403020

Fig. 15. Pressure drop as a function of the pleat number (Q =

2:86 102 m3 s1).

reactor designs, such as cylindrical pleated lters. 3-D nu-

merical simulations of ows in this kind of geometry allowthe evaluation of the ow structure in such a lter and the

local ow velocity near the medium. The best ow direction

to increase the eciency of the lter is from outside to inside

the cylindrical lter. An increase in the ow velocity was

observed downstream of the lter due to the local increase

in the static pressure at the end of the pipe. Results also re-

veal overlap phenomena, which lead to dead zones and

thus preferential ows for the lter. With the tested geome-

try, 60% of the medium surface is well used for adsorption

in the case of a 45 pleats lter. Compared to the average ve-

locity estimated for the total developed surface of the lter,

local velocities across the medium are higher. Nevertheless,


9/9


the maximal velocity value (0:3 m s1) in such a geometry

is acceptable for adsorption in a dynamic system. The opti-

misation of cylindrical pleated lters using activated carbon

fabric may be achieved by decreasing the number of pleats.

In fact, the 30 pleats lter shows good results in terms of

velocity distribution and pressure drop. It corresponds to a

pleat angle of around 6

.

Notation

d diameter, m

dh hydraulic diameter, m

I turbulence intensity (I =

u2i=u)

k turbulent kinetic energy, m2 s2

p pressure, Pa

Q volumetric ow rate, m3 s1

Slter total developed cross-section, m2

u velocity mean value, m s

1

u velocity uctuation, m s1

U friction velocity, m s1 (U =

w=)

Uaver average velocity, m s1, Uaver = Q=Slter

Uaver average velocity in the preferential ow zone,

m s1

X distance from the axis, m

y+ wall unit y+ = U=

Z longitudinal position, m

Greek letters

distance from the solid wall, m

turbulent kinetic energy dissipation rate, m2 s3

dynamic viscosity, kg m1 s1

density, kg m3

shear stress, Pa

Subscripts

i, j i, j directions

p close to the wall

w on the wall

x, y X, Y directions

References

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