ANALYSIS OF PLEATED AIR FILTERS USING COMPUTATIONAL FLUID DYNAMICS

Chang Ming Tsang

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science

Graduate Department of Mechanical and Industriai Engineering University of Toronto

O Chang Ming Tsang 1997

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Abstract

A nurnencai study was performed to investigate factors influence pressure drop

and flow pattern across pleated air filten. Simulations were done using FLUENT, a

commercial available Computational Fluid Dynarnics (CFD) code. The objectives of this

work were: first, to develop CFD models for different pleated filter configurations;

second, to examine the effect of pleat geometry (shape, height and spacing). approaching

air velocity. and filter configuration (panel filters and cylindrical filters) on the flow

pattern and pressure drop across the pleated filters; third, to obtain a generalized

correlation curve for the design of tnangularly pleated air filters; and finally, to develop a

three-dimensional CFD mode1 for a multiple panel filter configuration and investigate the

dependence of the filter pressure drop and filter medium face velocity distribution on the

gap spacing between each panel filter.

Results showed that the pressure &op vs. pleat count per unit length c u v e has a

characteristic U-shape curve for all filter configurations studied. The optimal pleat count

(which corresponding to the minimum filter pressure &op) depends on the pleat height,

pleat shape, and filter configuration, but not on the approaching velocity. For rectangular

pleats. the optimal ratio of the upstrearn channel spacing to the downstream channel

spacing was one. By scaling the inertia and viscous terms in the rnomenturn equation, a

generalized correlation curve was obtained for the design of triangularly pleated air

filters. For the multiple panel fiiter configuration, medium face velocity was highly non-

uniform along the flow channel; decreasing the gap spacing reduced the average medium

face velocity but increased the total filter pressure drop.

Acknowledgments

1 would like to thank my supervisor Professor Sanjeev Chandra for his invaluable

advice and guidance on this work. 1 thank Val Cnstescsn and Alex Lempp for their

support and input. Val Cristescsn has been particularly helpfül to my work. and the

cylindrical filter pressure drop experimental data were provided by him. A special thanks

is also in order for David Atkinson for his hiendship and moral support.

This work has been financially supported by Vent Master Ltd., Mississauga. Ont.

Table of Contents

Abstract

Acknowledgements

List of Figures

List of Tables

1.0 Introduction

1.1 What 1s Computational Fluid Dynamics?

1.2 Why Use Compuatational Fluid Dynamics?

1.3 Motivation

1.4 Literature Review

1.5 Objectives

2.0 Model Development

2.1 introduction to FLUENT

2.1.1 The Finite Volume Method

2.1.2 The Solution Techniques

2.2 Model Description

2.2.1 Panel Filter Model

2.2.2 Cylindrical Filter Model

3.0 Experimental Validation

3.1 Flat S heet Testing

3.2 Rectangular Panel filter

3.3 Cylindrical Filter

4.0 Results and Discussion

iii

4.1 Analysis of Optimization Parameters

4.1.1 Effect of Pleat Geometry

4.1.1.1 Effect of Pleat Shape

4.1 - 1 -2 Effect of Pleat Height

4.1.1.3 Effect of Variation of Pleat Channel Spacing

4.1.2 Effect of Air Velocity

4.1.3 Effect of Filter Configuration

4.2 Nondimensional Anaiysis

5.0 Three-dimensional Simulation of the Multiple Panel Filter Configuration

5.1 Introduction

5.2 Three-Dimensional Mode1 Description

5.3 Simulation Results and Discussion

5.3.1 Solution Procedure

5.3.2 Flow Field

5.3.3 Medium Face Velocity Distribution

5.3.4 Filter Pressure Drop

6.0 Summary and Conclusions

6.1 Motivation

6.2 Essential Findings

6.2.1 Experimental Validation

6.2.2 Pleating Analysis

6.2.3 Multiple Panel Filter Configuration

References

List of Figures

Figure 1.1 Panel and cylindncal cartridge filters

Figure 1.2 Schematic of the Ultra filter design arrangement

Figure 1.3 Typical section of the filter medium, showing the air streamline and electric field

Figure 1.4 Kiosk Ventilation System

Figure 1.5 Geometry details of Kiosk Ventilation System

Figure 2.1 Grids, nodes and control volumes in FLUENT

Figure 2.2a Computational domain for the rectangularly pleated filter medium

Figure 2.2b Typical mesh distribution for the rectangularly pleated filter medium

Figure 2.3a Computational domain for the triangularl y pleated filter medium

Figure 2.3b Typical mesh distribution for the triangularly pieated filter medium

Figure 2.4 Modeled cylindrical filter configuration

Figure 2.5a Computational domain for the cylindrical filter

Figure 2.5b Typical mesh distribution for the cylindrical filter

Figure 3.1 Schematic of the experimental apparatus used for the panel filter

Figure 3.2 Flow charactenstics of the selected filter medium

Figure 3.3a Expenmental results vs. simulation results, triangular pleated panel filter. pleat height 1.3 cm, at 1.5 pleatskm

Figure 3.3 b Experimental results vs. simulation results, triangular pleated panel filter, pleat height 1.3 cm, at 2.4 pleatskm

Figure 3 . 3 ~ Experimental results vs. simulation results, triangular pleated panel filter, pleat height 1.3 cm, at 3 pleatskm

Figure 3.3d Experimental results vs. simulation results, tnangular pleated panel filter, pleat height 1.3 cm, at 4 pleatskm

Figure 3.4

Figure 3 -5

Figure 3.6

Figure 4.1 a

Figure 4.1 b

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Figure 4.7

Figure 4.8

Figure 4.9

Figure 4.10

Figure 4.1 1

Figure 4.12

Experimental results vs. simulation results, triangular pleated panel fiiter, pleat height 1.3 cm, at 1 mis

Schematic of the experirnental apparatus used for the cylindrical filter

Experimental results vs. simulation results, cylindrical filter, pleat height 1.3 cm, 2.44 pleatdcm

Velocity vector diagrams for rectangular pleats, pleat height 1.3 cm. inlet velocity at I m/s

Velocity vector diagrams for triangular pleats, pleat height 1.3 cm. inlet velocity at 1 m/s

Effect of pleat shape on medium face velocity distribution, rectangular pleats, pleat Iength 1 -3 cm, inlet velocity 1 m/s

Effect of pleat shape on medium face velocity distribution. triangular pleats, pleat length 1.3 cm, inlet velocity 1 rn/s

Effect of pleat shape on pressure drop, pleat length 1.3 cm. inlet velocity 1 m/s

Effect of pleat height. rectangularly pleated panel filter, inlet velocity 1 m/s

Effect of pleat height. triangularly pleated cylindrical filter. inlet velocity 1 rn/s

Effect of pleat height, cylindrical filter, inlet velocity 1 rnls

Variations in rectangular pleat spacing, pleat length 2.0 cm, inlet velocity 1 m/s

Effect of approaching velocity, rectangularly pleated panel filter, pleat height 2.0 cm

Effect of approaching velocity, tnangularly pleated panel filter, pteat length 2.0 cm

Pressure &op ratio vs. velocity ratio, panel filter, pleat length 2.0 cm, velocities : 0.5 m/s and 1 mis

Effect of filter configuration, triangularly pleated, pleat length 2.0 cm, inlet velocity 1 mis 56

Figure 4.13

Figure 4.14

Figure 4.15

Figure 5.1

Figure 5.3

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7a

Figure 5.7b

Figure 5 . 7 ~

Figure 5.7d

Figure 5.7e

Figure 5.7f

Figure 5.7e

Figure 5.8a

Channel with varying cross-sectional areas

Schematic for medium face velocity calculation

Generalized correlation curve for triangularly pleated panel filter

Schematic of the multiple panel filter configuration

Computational domain

Sirnplified computational domain

Grid outline and typical mesh distribution

lsometnc view of the velocity vector field

Velocity vectors viewed in two-dimensional planes

Filter medium face velocity distribution. 2 cm gap spacing configuration

Filter medium face velocity distribution, 4 cm gap spacing configuration

Filter medium face velocity distribution. 6 cm gap spacing configuration

Filter medium face velocity distribution, non-uniform gap spacing configuration with 8 cm upstream channel spacing and 4 cm downstream channel spacing

Fiiter medium face velocity distribution, comparison between 6 cm gap spaicng configuration with 8 cm upstream channel spacing and 4 cm downstream channei spacing

Filter medium face velocity distribution, non-uniform gap spacing c ~ ~ g u r a t i o n with 4 cm upstream channel spacing and 8 cm downstream channel spacing

Filter medium face velocity distribution, comparison between 6 cm gap spaicng configuration with 4 cm upstream channel spacing and 8 cm downstream channel spacing

Normalized static pressure distribution, 2 cm gap spacing configuration 78

vi i

Figure 5.8b Normalized static pressure distribution, 4 cm gap spacing configuration 78

Figure 5 . 8 ~ Normalized static pressure distribution, 6 cm gap spacing configuration 79

Figure 5.8d Normaiized static pressure distribution, non-uniforrn gap spacing configuration with 8 cm upstream channei spacing and 4 cm downstream channel spacing

Figure 5.8d Normalized static pressure distribution, non-uniforni gap spacing configuration with 4 cm upstream channel spacing and 8 cm downstream channel spacing

viii

List of Tables

Table 3.1 Physical properties of selected filter medium

Table 3.2 Expenmentai results

1.0 Introduction

1.1 What is Computational Fluid Dynamics?

The physical aspects of any fluid flow are govemed by three fundamental principles:

(1) mass is conserved; (2) Newton's second Iaw (force = mass , acceleration); and

(3) energy is conserved. niese fundamental physical principles can be expressed in

terms of basic mathematical equations, which in their most general form are either

integral equations or partial differential equations. Computational Fluid Dynamics

(CFD) is the process of replacing the integrals or the partial denvatives in these

equations with discretized algebraic foms. which in tum are solved to obtain

numbers for the flow field values at discrete points in tirne andor space.

The solution methods are mesh-based. where the equations are discretized in either

finite-difference, finite-volume or finite-element form. The mesh itself must be

defined by the user so that it represents the geometry of the flow domain of interest.

Equations for velocity components. pressure. temperature and contaminant

concentration are solved at each of the small volumes (called cells or elements)

defined by the mesh.

1.2 Why Use Computational Fluid Dynamics?

In the 705, due to the limitation of the algorithms and the high cost of cornputers,

CFD was used almost exclusively in aircrafi and nuclear power industries. Also, the

storage and speed capacities of digital computers were not sufficient to allow CFD to

simulate any complicated three-dimensionai geometry. Today, however, this story

had changed substantially due to the developments in areas of numerical analysis and

in faster and lower-cost computers. In today's CFD, three-dimensional flow field

solutions are abundant; they may not be routine in the sense that a great deal of

human and computer resources are still frequentiy needed to successfully cany out

such three-dimensional solutions, but such solutions are becoming more and more

prevalent within industry. Indeed. modern CFD cuts across d l disciplines where the

flow of fluid is important, and is increasingly becoming a vital cornponent in the

design of industrial products and processes.

One such area is concerned with the design of cartridge air filters. Cartridge air

filters are used in a variety of industry applications. including automobile air inlet,

home furnaces and air conditioners, etc. Cartridge air filters corne in a variety of

shapes; the two most popular configurations found in prlctice are tie rectangular

panel filter and the cylindrical filter (Figure 1.1). In general, cartridge air filters have

several features which distinguish them from other types of air filters. They have two

basic components: a housing and a module. The housing holds the filter module and

fluid being filtered. It may be permanently mounted ont0 a piece of equipment or

disposable. In contras to some other types of filters, the filter module is removable.

The module consists of filter medium, seals, and related support matenals. The filter

medium is the hem of the cartridge filter since it perfoms the actual separation.

Pleated filter medium is often used to increase the effective area of filtration, so

reducing the filter medium face velocity and thus the pressure drop across the filter

Figure 1.1 - Panel and Cylindrical canridge filters [ I ]

medium. Seals ensure that unfiltered fluid is not allowed to bypass the filter

medium. Additional support material is ofien required to maintain the physical

integrity of the medium.

Through the years the design of cartridge air filters has usually been based on

laboratory testing: prototypes are built, tested and modified until a 'best' design is

obtained. Although laboratory testing is an invaluable tool of the designer, it suffers

a number of drawbacks. Building and testing prototypes is in most cases expensive,

time consurning, and often the testing results do not tell the engineer why a design

change is having the observed eEect on performance.

CFD techniques have the potential to allow the effect of a proposed design change

to be evaluated relatively quickly. A computational investigation can be performed

with remarkable speed. and the cost of a cornputer nui is, in most applications. lower

than the cost of a corresponding expenmental investigation. The output fiom CFD

codes gives detailed and complete information. It can provide the values of al1 the

relevant variables (such as velocity, pressure, temperature, concentration, turbulence

intensity) throughout the domain of interest. A designer can study the implications

of hundreds of different configurations in a short period of time and choose the

optimum design.

1.3 Motivation

Of particular interest to this study is the Ultra Filter, which uses a non-ionizing

electric field to trap air-borne particdate in an electncally enhanced filter material

[2]. Electrostatic forces are set up within a fibrous mat without intentional charging

of the particles; particle capture is enhanced by the combination of polarization

forces with inertial forces due to air fiow around the fibers. The design arrangement

of the Ultra-Filter is shown in Figure 1.2. Air is introduced into a filter assembly

compnsing of three wire meshes held parallel to each other and separated by a 1.3

cm spacing. Pleated fibrous filter matenal is sandwiched between the second and the

third meshes. An electric field is maintained within the filter medium by applying 3

kV to 9 kV between the meshes. The important quality about this field is that it is, in

general, directed radially inward or outward at the fiber surfaces and that the field is

more intense at the fiber surfaces than the intervening spaces [3,4,5,6]. Figure 1.3 is

a typical magnifird section of the filter medium showing air streamlines and the

electric field. Since the field is nearly radial at the fiber surface, the direction of its

most rapid change will be nearly radial, and the polarization force on particles near

the fiber will be approximately radial, directed toward the fiber. Particles will thus

migrate across streamlines more rapidly than they would fiom inenial effects alone,

and have a higher probability of capture than when no field is present. Consequently,

the filter matenal captures particles much smaller than its pore size, and this

minimizes clogging of the filter. The electrical properties of air at the input and

wire rieshes

medium

Figure 1.2 - Schematic of the ULTRA-Filter design arrangement

Figure 1.3 - Typical section of a charged filter medium, showing air streamlines and electric field

output of the filter assembly are the same, namely "neutral" (no ionized particles are

emitted) .

The invention of Ultra-Filter overcomes the common problems found in

conventional electrostatic air filters and mechanical filters including the High

Efficiency Particdate air filters (HEPA) and the Ultra Low Penetration air filters

(tJLPA). Conventional electrostatic air filters operate at very high voltages, which

require expensive insulation and safety precautions as well as substantiai power, and

they produce ozone which constitutes a health hazard. Mechanical air filters are

unable to capture particles smaller than their pore size, and they are also subject to

rapid clogging by captured particles. Furthemore, the clogging takes place mostly

on the inflow surface of the filter, and the thickness of the filter material for holding

particles is not utilized.

The constraint on Ultra-Filter? however, is that at high air velocities, the inertial

force of the particles may overcome the polarization force and thus the particles may

bypass the field. Therefore, the air flow through the filter medium must be

maintained at a low velocity to ensure good particle capture efficiency; low velocity

also has the advantage of lower pressure drop. High particle capture eficiencies

were found for filter medium face velocities in the range fiom 1 cmk to 5 crn/s.

Face velocities higher than this range resulted in a dramatic &op in the capture

efficient y.

A ventilation equiprnent Company, VentMaster Ltd., Mississauga, Ont., developed

an indoor electric cooking ventilation system called Kiosk Ventilation System (KVS)

using the Ultra-Filter technology (Figure 1.4). This system is a completely self

Figure 1.4 - Kiosk Ventilation System

REAR VlRN L E R StDE V l F N

IEMIZED PAMS UST 1 j C:eaned exhaus: discharge grill 1 10 1 Fan wheeVinlet wne 2 ( 40% Pre-filter / 11 l Drive motor

3 1 95% Medium filter / 12 1 Fan shaftheanngs 4 1 99% HE?A filter 1 13 1 Conml mnel S 1 Fire damoer 1 14 1 Acoustic silencer

, 6 1 Odor control sgray system (optionaO 1 15 1 Cooking aouliance c imi t breaker 7 1 Pressure sensor swctc!es/firesat 1 16 ( Coaking a~oliance terminal blcck

8 1 Hinged acctss doars 1 17 ) Cycio Glean grease filter 9 1 Fre suppression q s e m 1 18 ( Mctncai connedon

Figure 1.5 - Geometry details o f the Kiosk Ventilation System

9

contained exhaust & make-up air system; it is designed for cooking in buildings

where standard exhaust ducthg is not practicd, such as food kiosks in shopping

malls and office building. The detailed geometry of the complete system is shown in

Figure 1 S. Due to the space constraint and the complexity of the effects of pleating,

this Company has experienced certain difficulties in optimizing the filter geometry

design in order to achieve the required medium face velocity and to attain minimum

filter pressure drop. In order for the filter of this invention to accomplish its

objectives, a detailed optimization parametric study on the pleating effect and the

filter configuration was necessary.

1.4 Literature Review

Most of the early studies of porous media flow were based on Darcy's law [7].

Darcy observed that the pressure drop across a flat filter medium is directly

proportional to the rate of fluid flow through them. In its simplest fom, Darcy's law

is:

I,

Where p is the fluid viscosity, v is the velocity vector, and k is a constant of

proportionality depending on the filter medium structure. Several models based on

Stoke's equation of creeping flow have been proposed to justifi Darcy's law.

Stoke's equation is:

These included the ce11 models of Kuwabara [8]. He developed the classical 'cell'

model which provided an approximate method of calculating the forces experienced

by randornly distributed spheres or parallel circuiar cylinders in Stoke's flow. The

ce11 model was evaluated by Henry and Ariman [9]. They solved StokeTs equation

over an array of cylinders and the results agreed well with Kuwabara's model. Fardi

and Liu [10,11] also modeled Stoke's flow over a staggered array of rectangular

fibers.

Although Darcy's law is well established for flow through fibrous filters, it has two

major limitations: (1) the flow rate has to be low; (2) Darcy's law is a first order

differential equation, in contmst to Stoke's equation which is a second order

differential equation; it is dificult to match the solutions of the two equations at the

boundary of the free fluid and the porous medium. To rernove the second limitation,

Brinkman 1121 developed a semiempincal equation by adding a body darnping force

proportional to the velocity in addition to viscous and pressure forces in DarcyTs

equation:

Where p, is defined as the effective viscosity, which is a fitting parameter to be

used for fluid inside the porous medium. Brinkman's equation accounted for the

interaction of the fluid with the porous medium, and hence was known as the

modified Darcy's law. Numerous experimental works have been done to establish

the validity of the Brinkman's equation [1 jT14,1 51. To remove the first limitation

and make it applicable to higher flowrates, Darcy's law was M e r modified [16,17]

by incorporating a convective term:

Where E is the porosity of the filter medium.

Obviously, more complexities are presented for pleated filter medium. The

pressure drop across a pleated filter medium is different fiom that across a flat sheet

medium. It is a function of pleat height. pleat shape, filter medium charactenstics,

filter configuration, and air velocity. Currently, there is limited information on the

design of pleated air filters available in the literature.

Yu and Goulding [18,19] developed a semi-analytical method to model

rectangularly pleated panel filters. They modeled the flow field in the pleat spacing

as channel flow with suction or injection prescnbed at the bounding walls. The pleat

height was divided into finite elements with uniform mass addition and extraction

applied to each. The pressure drop across the wall was calculated using Darcy's law,

and then the flow velocity at the wall was calculated based on the filter media flow

characteristics. The final solution was obtained by applying a numerical iterative

method dong the pleat channel. Because Darcy's law is only valid at a low

Reynolds number, i.e., the viscosity dominated region, this model c m be used only

to analyze panel filters operating at a low flow rate. Furthemore, the effects of

developing flow, flow contraction, flow expansion, and reduced permeability at the

corner of the pleat were neglected.

Chen and Pui [20,21] also developed a finite element model to calculate the total

pressure &op across rectangularly pleated filter panels. The model included al1 the

effects that were neglected by Yu and Goulding's model. The upstream and

downstream flow fields were modeled as steady laminar flows, and a uniform

velocity profile was assumed at the far upstream. The flow passing through the filter

media was modeled by the Darcy-Lapwood-BBnkman equation (equation 1.4). The

governing equations were solved using a numencal fmite element method with a

nine-node Lagrangian element. The numencal results agreed well with the

expenmental data and the analytical model of Yu and Goulding [19]. No numerical

rnodel has been developed for triangularly pleated panel air filters and cylindncal air

filters.

1.5 Objectives

The objectives of this snidy can be summarized as follows:

1) To demonstrate the use of a commercial available computational fluid dynamics

code, FLUENT, in simulating flow through pleated air filters.

2) To examine the eEects of air velocity, pleat geometry (length, spacing), pleat

shape (triangular, rectangular), filter configuration (panel, cylindncal) on the filter

pressure &op.

3) Use nondimension analysis and information gained in (2) to obtain a correlation

design curve for triangularly pleated air filten.

4) To develop a three-dimensional cornputer model for a multiple panel filter

configuration and investigate the dependence of filter medium face velocity and

pressure drop on the filter geometry.

2.0 Mode1 Development

2.1 Introduction to FLUENT

The simulations were done using FLUENT, a commercial CFD code for modeling

fluid flow, heat transfer, and chemical reaction. FLUENT can mode1 a wide range of

physical phenomena, including: 2D/3D geometries in Cartesian, cylindncal or

general curvilinear coordinates; steady state or transient flow; incompressible or

compressible flow; laminar or turbulent fiow; conduction/convection/radiation heat

transfer, and flow through porous media.

FLUENT models b i s wide range of phenomena by solving the conservation

equations for m a s , momentum, energy, and chemical species using the finite volume

method. The goveming equations are discretized on each finite volume or grid. A

nonstaggered system is used for storage of discrete velocities and pressures.

Interpolation is accomplished via a first-order, Power-Law scheme or optionally via

higher order upwind schemes. The equations are solved using the SIMPLEC

algorithm with an iterative line-by-line matrix solver and multignd acceleration.

A basic understanding of the above techniques will be helpful here, and in later

chapters as well. Hence, the following section contains a brief outline of the relevant

principles of the finite volume method.

2.1.1 The Finite Volume Method

FLüENT employs what could be termed a grid-based geometry, in which the

geometry of the mode1 is detemined by control volumes defined by the grid [22].

Figure 2.1 illustrates the grid definition and ce11 nurnbering system used by

FLUENT. The grid lines define the boundaries of control volumes or cells. The ce11

center 0,J) is located at the geornetrk center of the control volume or ce11 (I,J). This

ce11 center is the storage for al1 dependent variables, such as: pressure, temperature,

velocity, etc.

Iine I I

(1-1 )'h lm gnd grid line line

Figure 2.1 - Grid lines, nodes and control volumes in FLUENT

FLUENT solves the goveming partial differential equations for the conservation of

mas, momenhim, energy and chernical species in a general form which can be

written in cartesian tensor notation as :

where + is the conserved quantity, and the first term on the left hand side of diis

equation signifies the rate of change of the total arnount of property t$ in the control

volume (zero for steady flow). The second term is the convection term which

represents the net rate of decrease of property 4 due to convection. The fust term on

the right hand side of the equation is the diaision term which represents the net rate

of increase of property 4 due to diffusion, and the last term is the source t e m which

gives the rate of increase of property t$ as a result of sources inside the fluid element.

The equations are reduced to their finite-difference analogs by integration over the

computational ceils into which the domain is divided. M e r the integration of

equations of the form of Equation 2.1. the resulting algebraic equations can be

written in the following common fom:

where the summation is over the neighboring finite difference cells. The A's are

coefficients which contain contributions fkom the convective and diffusive fluxes and

Sc and S, are the components of the linearized source term, Sa = Sc +

Each control volume in a FLUENT mode1 has a cell type. Ce11 types are assigned

as part of the probiem setup procedure, which defines the way in which the ce11 is

treated during the solution process. In other words, the ce11 type tells FLUENT

whether the control volume is filled with fluid, or if the control volume defines a

wall, inlet, outlet, etc.

2.1.2 Solution Techniques

The set of simultaneous algebraic equations is solved by a semi-implicit iterative

scheme:

1) The u,v, and w momennim equations are each solved in tum using current values

for pressure, in order to update the velocity field.

2) Since the velocities obtained in step 1 may not satisfy the mass continuity

equation locally, a pressure correction equation is derived fiorn the continuity

equation and the linearized momentum equations. This equation is then solved to

obtain the necessary corrections to the pressure and velocity fields such that

continuity is achieved.

3) Any auxiliary equations (e.g., enthalpy. species conservation, or any additional

quantities) are solved using the previously updated values of the other variables.

4) The fluid properties are updated.

5) A check for convergence of the equation set is made.

These steps are continued until the error has decreased to a required value.

The accuracy of the solution is govemed by the number of cells in the grid. In

general, the larger the number of cells the better the solution accuracy. Both the

accuracy of a solution and its cost in terms of necessary computer hardware and

computing time are dependent on the fineness of the grid. It is the usual practice to

start the problem using coarse gnd and refine the grid until no further change is seen

in the converged solution.

2.2 Mode1 Descriptions

The assurnptions made in both panel filter model and cylindrical filter mode1 for

filter pleating analysis were:

1. two-dimensional geometrical configuration

2. steady-state laminar flow

3. the fluid has the properties of air

4. unifonn velocity profile at the inlet of the flow domain

The filter medium was modeied using FLUENT'S porous ceil model, which solves

the mornentum equation augmented by a general momentwn sink:

where k and C2 are defined as the permeability and the inertial factor of the porous

medium, respectively. The inertial factor provides a correction for inertial losses in

the porous medium at high flow velocity. Both constants have to be determined

empiricaliy .

This equation contributes to the pressure gradient in the porous ceil, creating a

pressure drop that is in proportion to the flow velocity (or velocity squared). In

addition, the porous cells are 100% open, so the fluid-medium interaction is not

modeled; this may have a significant impact in transient flows since it irnpiies that

the transit time for flow through the medium is not correctly represented by

FLUENT.

2.2.1 Panel filter model

Panel filters were modeled as a series of channels with either triangular or

rectangular cross-section. Because of geometrical symrnetry, the computational

domains for both rectangular and tnangular pleats c m be simplified as shown in

Figure 2.2a and 2.3a. The symrnetry boundary conditions were imposed on the flow

boundaries, and a uniform velocity profile was specified at the idet boundary. Note

that for the mangular pleat model, the thickness of the filter medium in the flow

direction varies with the pleating angle. A typical rrsh for each pleat shape is

shown in Fig 2.2b and 2.3b.

2.2.2 Cylindricai Filter Mode1

The cylindrical filter configuration modeled is shown in Figure 2.4. Air flows into

the filter through the open end and exits circumferentially through the pleated filter

medium. Since the purpose of this analysis was to shidy the effect of filter

configuration on the pleating design, the flow through the pleated filter medium was

assumed uniform. This also reduced the problem to two-dimensions.

pleated f i l t e r m e d i u m

/

O ppr OQ c hi1713

ve loc i t y

t--- r1 + Figure 2.4 - Schematic of the modeled cylindrical

----- ups t rean channel

downstrean chonne(

- - - - - , - ,

-1

W : p lea t spocing L : p ( e a t height h : channel h o t f - w i d t h t : f i l t e r m e d i u m thickness

figure 2.2a - Computational domain for the rectangularly pleated filter medium

Figure 2.2b - Typical mesh distribution for the rectangularly pleated filter medium

Opproa ching

v e t o c ~ t y

W : p l e a t spacing L : p l e o t height t : f i l t e r medium thickness

Figure 2.3a - Computational domain for the ûiangularly pleated filter medium

Figure 2.3b - Typical mesh distribution for the triangularly pleated filter medium

For cylindrical filter codiguration, the downstream pleat spacing is relatively

larger than the upstream pleat spacing. This was modeled using polar coordinates,

and since the flow repeats every pleat, our mode1 needed only a sector angle equai to

one pleat spacing with cyclic boundary conditions imposed at the circumferential

flow boundaries. The computationai domain and a typical mesh are shown in Figure

2.5a and 2.5b. There is no special coding within FLUENT to cope with the case of a

two-dimensional flow in which the axial coordinate is neglected. Therefore,

symmetry boundary conditions were imposed at the axial flow boundaries to perfonn

pseudo two-dimensional R-8 calcuIations, i.e., there are only three cells in the axiai-

direction. ï he symmetry cells apply a zero-gradient boundary condition which is

equivalent to a two-dimensional domain.

Perlodic boundaries

approaching veiocity

Figure 2.5a - Computational domain for the triangularly pieated filter medium with cylindricai filter configuraiton

Figure 2.Sb - Typicd mesh distribution for the triangularly pleated filter medium with cylindrical f i l ter configuration

3.0 Experimental Validation

In order to validate the FLUENT models, pressure drop expenments were perfonned for

a rectangular panel filter and a cylindrical filter. Both filters were triangularly pleated

with a 1.3 cm pleat height. The filter medium used was the DID0/4/40 filter medium,

obtained fiom Vent Master Ltd. The specification of this filter medium is shown in Table

TYPE BASIC WEIGHT ( d m 3

100 % cellulose

Table 3.1 - Physicai Properties of Selected Filter Medium

PERMEABILITY c d s at 125 pa

122

3.1 Flat Sheet Testing

-

THICKNESS mm

The flow characteristics of the filter medium was obtained by flat sheet testing. The

apparatus used is s h o w in Figure 3.1 (note that apparatus was also used for the pleated

panel filter testing). The flat filter medium was mounted at the idet of the plexiglas duct

which has a cross-section of 30 cm x 30 cm. An elecuic blower (KG-XL, Kanalflakt Inc.,

Sarasota, FL) was used to draw air into the duct through the filter medium. The pressure

drop across the filter panel was measured by a pressure gauge (Magnehelic Gage, N D

46360, Dwyer Instruments Inc., MICH) mounted downstrearn of the filter. The

approaching air velocities were varied by manually adjusting the speed of the electric

Figure 3.1 - Schematic of the panel filter pressure drop measurement setup

blower. Velocity measurements were performed at nine grid points at the panel filter face

using a hot wire anemometer (Kun Ltd.). and the average of the nine rneasurements was

taken as the filter medium face velocity. Figure 3.2 shows the measured pressure drop

across the filter medium as a function of medium face veiocity. The data were c w e

fitted to a second order polynornial with zero constant term to obtain k and Ci

(permeability and inertial factor, see Equation 2.3) for input to FLUENT models. The

resulting fitted equation is:

AP = 1 3 . 3 2 ~ ' + 190.79~

and k and C2 were found to be 4.17 x 1 O-' ' rn2 and 4.45 x 1 o4 rn-', respectively.

3.2 Rectangular Panel Filter

ï h e apparatus used for testing the pleated rectangular panel filter is the same as for the

flat sheet testing (Figure 3.1). The filter panel was mounted at the inlet of the plexiglas

duct. Gaskets were designed to hold and suaport the pleated filter medium. Again, the

Figure 3.2 - Filter medium flow characteristics

pressure drop across the pleated filter panel was rneasured by the sarne pressure gauge

meter mounted downstream, and the velocity measurernents were performed at nine grid

points at the filter panel face using the hot wire anemometer, with the average value taken

as the approaching air velocity. The pleat count was varied from 0.9 pleatskm to 4.5

pleatskm, and 4 to 7 pressure drop readings were taken for each pleat count with

approaching velocities varied fiom 0.5 m/s to 2.0 d s (shown in Table 3.2). Figure 3.3

shows the cornparison of the experimental results (pressure &op vs. velocity at each pleat

count) with the FLUENT mode1 results. It can be seen that both results agreed very well.

Because the approaching velocities were varied by manually adjusting the speed of the

elecûic blower, it was dificult to obtain the same velocity reading for each pleat count.

For the purpose of comparing the experimental results with the FLUENT mode1 results

with regard to filter pressure &op vs. pleat count per unit Iength. the measured data were

fitted to a curve for each pleat count. Pressure drop was then calculated from this curve

with the corresponding velocity used in FLUENT models and compared with the pressure

drop calculated fiom the FLUENT models. It is interesting to noted that for al1 pleat

counts measured, the resulting data were best fitted to a power curve.

Figure 3.4 shows a cornparison between the results of simulation and experiment (filter

pressure drop vs. pleat count). Both results agreed quite well and demonstrate the

charactenstic 'U' shape curve. Pleating reduces the medium face velocity and thus, the

pressure drop through the filter medium; however, excessive pleating causes the pressure

drop to rise again resulting from the viscous drag in the pleat channel. The optimal pleat

count occurs when the combination of the pressure drop through the filter medium and

velocity ( d s ) OS9

pressure &op @a) 30

f

1.19 1.54 1.64 2 pleatkm velocity ( d s )

L

0.7 1 0.8 1 0.9 1.5 pleatkm velocity (ds) 0.52 0.89

0.52 0.98

velocity (mis) 0.63 1 .O6 1.35 1.5 1.75 3.5 pleatlcm velocity (m/s) 0.57

' 42 45 6Q

pressure drop (pa) 25 40 60 75 82

pressure drop @a)

Table 3.2 - Expenmental resufts

pressure drop @a) 21 50 56 65

1

75

pressure drop @a) 20

20 40

1 ' 1.09 1.25 1.39 1.67 1.90 2.4 pleatkrn velocity (m/s) 0.5 1

velocity (mk) 0.69

0.84 1.18 1.51 1.68 4 pleaUcrn

pressure drop @a) 25

4

27 45 55 62

\

velocity (m/s) 0.43

45 50 55 65 70

pressure drop @a) 15

pressure drop @a) 25

0.94 1.35 1.56 1.75 4.5 pleatkm velocity (rn/s) 0.46 0.76

40 67 80 87

4

pressure drop @a) 38 65

Y -

O 0.5 1 1.5 2

velocity (mis)

Figure 3.3a - Experimental results vs. simulation results, triangularly pleated panel filter, pleat height 1.3 cm, at 1.5 pleatdcm.

velocity (m/s)

80 - 70 - l

60 -. 50

40 - ,

30 - 20 - I O -

O ,

Figure 3.3 b - Experimental results vs. simulation results, triangularly pleated panel filtcr, pleat height 1.3 cm, at 2.4 pleatdcm.

I

s i m u l a t i o n

A 7 1 I

O 0.5 1 1.5 2

velocity (m/s)

Figure 3 . 3 ~ - Experimenta! resuits vs. simulation results, triangulariy pleated panel filter, pleat height 1.3 cm, at 3 pleatdcm.

O OS 1 1.5 2

velocity (m/s)

Figure 3.3d - Experirnental resuits vs. simulation results, triangularly pleated panel filter, pleat height 1.3 cm, at 4 pleats/cm.

2 3 4 5 pleat countlcm

4

Figure 3 .? - Experimentai results vs. simulation results, triangularly pleated panel filter, pleat height 1.3 cm, at 1 d s .

I I I T

mediun resistanco viscous Force doninated region donina t e d region

-

0

--,-

A

experiment -simulation

the viscous drag in the pleat channel is a minimum. The discrepancy between the

experimental results and numerical predictions in the high pleat count region is mainly

due to the pleat bunching eEect. It was observed during the experirnent that pleat

bunching occurred at approximately 3 pleatskm, which caused a highly non-uniform

velocity distribution at the filter medium face. The effect of pleat punching becarne more

senous with increasing pleat count; at 4.5 pleatdcm, the pressure drop rise rapidiy. This

reveais the thickmess and the flexibility of the filter medium are d s o important factors in

pleat optirnization.

Other possible causes of the discrepancy are: (1) the error associated with the readings

from the pressure gauge, which was taken as one half the smallest division on the scale;

in our case it was 2.5 Pa. (2) the error associated with the readings from the hot wire

anemometer, also taken as one half of the smdlest division on the scaie, and in our case it

was 2.6 cm/s (- 2.4 Pa, obtained from the filter medium characteristics curve. see Figure

3.2). Also, the gaskets holding the filter medium created an additional pressure drop

(flow expansion downstrearn of the filter panel) which was not accounted for in the

FLUENT models.

3.3 Cylindrical Filter

Figure 3.5 shows a schematic diagram of the apparatus used to test the cylindrical filter.

Experiment procedures were similar to the panel filter measurement. Velocity

measurements were performed at the HEPA filter face using the hot wire anemometer;

the obtained velocity was convened to the approaching velocity at inlet of the cylindrical

filter housing using the area ratio (the cross-section area of the duct to the cross-section

p r e s s u r e diFferentirii

cylindricaî fil t e r

--- exhoust ---

air blower

HfPA fi l t<lr

Figure 3.5 - Schematic of the cylindrical filter pressure drop measurement setup

area of the cylindrical filter). Pressure drop across the filter was measured by the

pressure gauge meter. Experiments were performed for one pleat count only (2.4

pleatskm). As stated previously, we were only interested in the effect of filter

configuration on pleating design, not the flow pattern inside the cylindrical filter. Since

the only effect was the change in pleat geometry, measurements of more pleat counu

were not necessary.

Figure 3.6 shows the cornparison of the simulation results with the experimental

results. It c m be seen that the pressure drop fiom expenment was higher than the mode1

prediction throughout the whole velocity range. This was expected since the pressure

drop reported fiom the experiment included the additional losses resulting &om 80w

contraction and flow expansion at the filter inlet.

velocity (rn/s)

Figure 3.6 - Expenmental results vs. simulation results, cylinàrical filter, pleat height 1.3 cm. 2.44 pleatskm.

4.0 Results and Discussion

This chapter provides a detailed parametric study of the air filter pleating design

using the FLUENT models descnbed in Chapter 2. The first section examines the

effects of factors that influence pressure &op and the flow pattern across a pleated

filter medium. The factors studied were: pleat geomeüy (pleat shape, pleat height,

pleat spacing); air velocity; and filter configuration (panel filter and cylindrical

filter). The second section presents a general correlation design curve for the design

of triangularly pleated air filters.

4.1 Anaiysis of Optimization Parameters

Cases were simulated for both panel filters (triangularly pleated and rectangular

pleated) and cylindrical filters (triangularly pleated). Approaching air velocities

were set at 0.5 m/s and 1 mk; Pleat heights investigated were 1.3 cm and 2 cm.

Dm0 - 4/40 filter medium properties were used for the entire analysis. Note that the

design pleat height for the ULTRA-Filter is about 1.3 cm (OS"), other pleat heights

and velocities used in the analysis were chosen for convenience.

4.1.1 Effects of pleat geometry

4.1.1.1 Effect of pleat shape

Air filters are usually pleated using corrugated separators, spacer threads, or forrning

techniques [23]. Generally, pleats are either rectangular or tnanguiar. The flow field

36

The

In the

in a rectangular pleat channel is different fiom that in a triangular pleat channel, and

this difference in flow pattern may significantly influence the filter pressure drop and

particle capture eficiency.

F1o.w Pattern

Figure 4. la-b show some typical flow diagrams at different pleat count for both

pleat shapes. It can be seen that with a rectangular pleat configuration, the fluid

contracts as it reaches the pleated medium. Most of the fluid enters the upstream

pleat channel while a srnall fiaction passes through the front end of the pleat directly.

The fluid entenng the upstream channel is accelerated and separates fiom the inner

surface of the pleat channel because of the reduction in the flow cross sectional area.

The intensity of fiow separation increases wirh higher pleat count. Following this,

the flow gradually spreads and as a result of fiuid viscosity, the velocity drops

steeply to nearly zero at the fluid-medium interface, i.e., there fonns a thin boundary

layer whose thickness increases with distance fiom the inlet. Since the rnass of the

fluid decreases dong the pleat channel, and pleat channel cross sectional area is

constant, the flow decelerates dong the pleat channel. Upon exiting the filter

medium, the flow then enters the downstrearn channel, and the process is repeated in

reverse. The flow acceleration, in this case, is due to the mass injection from the

fluid-medium interface. Flow recirculation can be seen at the channel exit resulting

fiom flow expansion. The intensity of flow expansion also increases with higher

pleat count.

, triangular pleat has the maximum cross-sectional area at the inlet and outlet.

upstream channel, the cross-sectional area in the direction of the air flowing

Figure 4. la - Velocity vector diagrams for rectangular plats, pleat height 1.3 cm, iniet velocity at 1 mls

Figure 4.1 b - Velocity vector diagrams for trianguiar pleats, pleat height 1.3 cm, idet velocity at I m/s

through it decreases, resulting in nearly inviscid flow through the pleat channel.

Upon exiting the pleat, the cross-sectional area increases, which minirnizes the flow

acceleration and thus the pressure drop in the downstrearn channel.

As already discussed in Chapter 1, the particle capture efficiency of the ULTRA-

Filter varies significantly with the medium face velocity (the air velocity crossing the

filter medium). One concem in this study is whether the pleat shape affects the

distribution of the medium face velocity, and thus the particle capture eficiency.

Plots of medium face velocity along the pleat channel at different pleat count for the

two pleat shapes (rectangular and triangular) are shown in Figure 4.2 - 4.3. It can be

seen that for both types of pleats. the medium fâce velocity increases along the pleat

channel. For trianguia. pleats (see Figure 4.3 , the velocity variation is relatively

smdl (within 1040% of the average value). However for rectangular pleats, the

velocity variation is 60-100% of the average value for the three pleat counts

examined (see Figure 4.2). Also, the non-uniformity of velocity is seen to increase

with higher pleat count for both pleat shapes, probably due to the higher inertial

effect resulting fiom the reduction of flow channel area.

Pressure drop

The pressure drop through both types of pleat channels is caused by three

mechanisms: the entrance loss resulting fiom flow separation at the inlet and the

subsequent flow deceleration; the pressure drop dong the pleat channel resulting

from viscous drag; and the exit loss resulting from flow separation at the edge of the

exit. Clearly, fiom the velocity vector diagrams. the triangular pleat shape is more

aerodynamically favorable over the rectangular pleat shape: it has more srnoother

0.325 0.65 0.975

distance along pleat channel (cm)

Figure 4.2 - Effect of pleat shape on medium face velocity, rectangular pleats, pleat height 1.3 cm, inlet velocity 1 d s .

8

8 ( - - 2.7 pleatslcrn 1 8 - - - 3.85 pleatslcrn

I b

I

0.325 0.65 0.975

distance along pleat channel (cm)

Figure 4.3 - Effect of pleat shape on medium face velocity, triangulsr pleats, pleat length 1 -3 cm, inlet velocity 1 m/s.

streamlines at the idet and outlet, so the entrance and exit losses are rninirnized; also

the flow does not accelerate in the downstream channel which fiirther reduces

pressure loss. However, note that the rectangular pleats provide a larger filter

medium area than aiangular pleats at the same pleat count, which means rectangular

pleats have lower medium face velocity and thus lower pressure drop through the

filter medium. Figure 4.4 is a cornparison of the two pleat shapes with regard to

filter pressure drop. As expected, the rectangular pleats have a lower pressure drop

than niangular pleats in the medium resistance dominated region resulting fiom

lower medium face velocity, and a higher pressure drop in the viscous dominated

region resulting from the higher viscous drag in the flow channels.

4.1.1.2 Effect of pleat height

This section examines the effect of pleat height on the optimal pleating design for

both panel filters and cylindncal filters. For rectangularly pleated panel filters (see

Figure 4 3 , with a larger pleat height, the optimal pleat count and the pressure drop

decrease whereas the pressure drop in the viscous force dominated region (i.e., the

region where the viscous drag is more important than the pressure drop through the

fiiter medium) rises more dramatically. This is because in the medium resistance

dorninated region (i.e., the region where the pressure drop through the filter medium

is more important than the viscous drag), increasing the pleat height increases the

effective filter medium area, which further reduces the medium face velocity and

thus the pressure drop. However, the viscous drag also increases due to the longer

3 4 5

pleat countlcm

Figure 4.4 - Effect of pleat shape on pressure drop, pleat height 1.3 cm, iniet velocity 1 m/s

2 3 4

pleat countkm

Figure 4.5 - Effect of pleat height, rectangularly pleated panel filter, inlet velocity 1 m/s.

flow channel; this resuits in a lower optimal pleat count and a higher pressure &op

in the viscous dominated region.

The effect of pleat height on the triangularly pleated panel filter is show in Figure

4.6. It can be seen that for the two pleat lengths simulated (1.3 cm and 2.0 cm),

increasing the pleat height reduces the pressure drop throughout the entire pleat

cour& and only a slight decrease of the optimal pleat count. This again indicates that

the viscous drag in a triangular pleat channel is smaller than that in a rectangular

pleat channel. So for long pleats, triangular pleats could provide a higher optimal

pleat count and a lower pressure drop than rectangular pleats.

The effect of pleat height on the cylindrical filter is shown in Figure 4.7. The trend

is similar to the tnangularly pleated panel filter.

4.1.13 Effect of variation of pleat channel spacing

Yu [19] showed that for a rectangularly pleated channel, the pressure loss in the

downstream spacing is significantly larger than that in the upstream spacing due to

the increase of momentum resulting fiom mass addition and flow acceleration. He

suspected a funher reduction of pressure drop is possible by increasing the

downstream pleat spacing and simultaneously reducing the upstream pleat spacing.

In order to test this hypothesis, simulations were performed for rectangular pleats at

4.5 pleatskm with difierent channel spacing ratio (i.e., the ratio of downstream

channel spacing to upstream channel spacing). The result is shown in Figure 4.8.

Clearly the optimal channel spacing ratio is one (when downstream channel spacing

equals the upstream spacing, in this case 0.375 mm). The reason is that although the

pleat count/cm

Figure 4.6 - Effect of pleat height, triangularly pleated panel filter, inlet velocity 1 d s .

2 3 4 5

pleat count/cm

Figure 4.7 - Effect of pleat height, cylindrical filter, inlet velocity 1 ds.

I I l downs trean Chonnet

0.125 0.25 0.3 75 0.5 0.625 0.75 downstream spacing

Figure 4.8 - Variations in nctangular pleat spacing, pleat height 2.0 cm, inlet velocity 1 m/s

downstream channel has a higher pressure drop, any reduction of the upstream

channel spacing will increase not only the viscous drag in the upstream channel, but

also the hc t ion of fluid passing directly through the front end of the pleat, resulting

in a higher pressure drop through the filter medium.

4.1.2 Effect of air velocity

The effect on pressure drop of varying approaching velocity for rectangulariy pleated

filter is shown in Figure 4.9, and for triangularly pleated filter is s h o m in Figure

4.10. With a higher face velocity, the pressure drop through the filter medium and

the viscous drag in the pleat channel both increase, which increases the pressure drop

at al1 pleat count.

For a flat sheet of filter medium. the pressure drop ratio at two different

approaching air velocities is the same as the velocity ratio at low velocities, because

the inertial correction t e m s in equation (2.3) can be neglected and reduced to

Darcy's equation (equation 1.1 ). However, Chen et al. [2 1 ] pointed out that based on

their numerical results, the pressure drop ratio for a rectangularly pleated filter

medium should also be the same as the velocity ratio at low velocities (the velocity

range they investigated was fkom 0.125 m/s to 1.255 d s ) . Figure 4.1 1 compares the

prcssure drop ratio for two approaching air velocities ( 0.5 m l s and 1 d s ) with the

approaching air velocity ratio (2.0) as a function of pleat count. It c m be seen that

for both pleat shapes, the pressure drop ratios were higher than the velocity ratio

throughout the entire pleat count. This may be explained by considerinp the flow in

1 2 3 4 5 pleat countkm

Figure 4.9 - Effect of approaching veiocity, rectangularly pieated filter, pleat height 2 cm.

2 3 4 pleat count/cm

Figure 4.1 O - Effect of approaching velocity, tnangularly pleated panel filter, pleat height 2 cm.

both pleat channel as intemal channel flows; there is an entrance region where the

inviscid upstrearn flow converges and enters the channel [24]. Viscous boundary

iayers grow downstream as a result of fluid viscosity. At a finite distance from the

entrance (called entrance 1engt.h) the boundary layen merge and the channel flow is

then entirely Mscous; the flow is then said to be fùlly developed. Downstream of this

region, the wall shear is constant, and the pressure &op is proportional to the

velocity and decreases linearly with distance in the flow direction. However, within

the entrance length, the pressure drop is significantly higher than that in the fully

developed region. This is because additional pressure forces are needed to acceferate

the center-core flow in order to maintain the incompressible continuity requirement.

For laminar flow, the entrance length Le takes the form [24]:

where d is the channel spacing, and Re is the Reynolds number which is proportional

to the flow velocity. Therefore, the entrance length increases with increasing

approaching flow velocity, resulting in a larger pressure drop ratio than the

corresponding velocity ratio. Also, the viscous drag along the pleat channels is

proportional to velocity squared.

From Figure 4.1 1, the discrepancy between the pressure drop ratio and the velocity

ratio is seen more significant for rectangular pleats; this is because the pressure

losses at the rectangular pleat channel inlet and exit are also proportional to the

velocity squared [24]. Whereas these losses are minimized for triangular pleat

channels (as discussed in section 4.1.1.1).

4.1.3 Effect of filter configuration

The effect of filter configuration (panel filter vs. cylindrical filter) on pleating design

is shown in Figure 4.12. It c m be seen that with the increase in the downstream

channel spacing (as mentioned previously, the cylindncal filter medium face velocity

is assurned uniform in this analysis, so the only difference between the pleats in

cylindrical and panel filter configuration is the downstream pleat spacing), the

pressure drop vs. pleat count curve for the panel filter configuration shifts to die

right, Le., cylindrical filter provides a higher optimal pleat count. This is expected

since the increase in downstream channel spacing M e r reduces the flow

acceleration and viscous drag in the viscous dominated region, but the reduction of

filter medium area results in a higher pressure drop in the medium resistance

dominated region.

4.2 Nondimensional Analysis

As mentioned previously, the optimal- pleat count exists when the pressure drop

through the filter medium is the same as the pressure drop through the pleat channel.

If an expression cm be obtained for each of these two pressure drop in terms of pleat

count, pleat height, filter medium thickness, and filter medium characteristics, then

the ratio of these two pressure drop can be used to normalize al1 the points in the x-

axis in the pressure drop vs. pleat count curve, and the Y-axis c m be normalized by

dividing the pressure drop by the minimum pressure drop. The resulting

- O O cylindrical

- panel k 2 3 4 5

pleat countkm

Figure 4.12 - Effect of filter configuration, triangularly pleated, pleat height 2.0 cm, inlet velocity I d s .

dimensionless correlation c w e c m be used to assess the pressure drop performance

of a pleated air filter with different combinations of parameters @lest count, p h

height, filter medium thickness, filter medium cbaracteristics).

Chen et al. [20] obtained a design c w e for rectangdarly pleated panel filtea. For

the purpose of this snidy, we will perform dimensional analysis to obtain a

generalized correlation design c w e for triangularly pleated panel air filters. The

pressure diop through the filter medium can be approximated as:

where u, is the medium face velocity and t is the medium thickness. Note that this is

an approximation of Darcy's equation (equation 1.1). The inertial correction factor

in equation 2.3 is neglected since o d y low medium face velocity cases were

investigated in our study (in the order of 0.1 m/s or less).

The flow through the triangular plear channei can be approximated as flow through

a channel with varying cross-sectional areas (see Figure 4.13). Assuming the

channel has Iength L which the pressure drop Q is imposed, allowed the width w to

Vary slowly w(x), while the channel has a characteristic width W.

w(?O

Figure 4.13 - Channel with varying cross-sectional areas

The velocity scale for the x direction is assurned to be thal for flow in a straight

channel [25], that is:

The transverse velocity v which is much srnaller and can be estimated h m the fiom

the continuity equation as follows:

Denoting thev velocity scale by v , , and assuming the length scale in the x and y

directions are L and W respectively, the terms can be estimated as

The vertical velocity scale is then:

Consider the y-momentum equation. From this equation we c m estimate the size of

the y pressure gradient.

The terms have the following sizes:

W With the assumption that - is small, then the largest term above is the viscous terni

L

a 2 v w p- . Al1 the other terms of order - are negligible. Hence, by using equation

ay2 L

4.3, we have:

w The y pressure gradient will be smaller than the x pressure gradient by a factor - ;

L

therefore, we c m take p as a function of x done.

The x-momenhun equation is considered next. The equation is:

Estimates for the size of each term are:

p u p pu, w AP + P%W + pu., +-=- - L~ L* L L~ w 2

W Again, assuming - is very small, the dominant terms are:

L

Therefore, with the assumption of a small wall slope. Le., srna11 pieat spacing, the

dominant pressure drop across the triangular pleat channel is due to viscous drag.

Let the approaching air velocity be u , (refer to Figure 2.3a). the characteristic

velocity in the pleat channel, uscm be estimated as:

and the characteristic medium face velocity, u,,,, c m be estimated using mas

consemation principle (see Figure 4.14):

IB = pleat spacing

L = pleat height

t = filter medium thickness

-L-- I

Figure 4.14 - Schematic for medium face velocity calculation

Using equations (4.2), (4.12). (4.13) and (4.14), the ratio of the viscous drag. Ap, to

the pressure drop through the filter medium, Ap,, is:

Since W-L. equation 4.15 becomes:

K = a constant defined as the pressure drop per unit medium face velocity,

f/k. which is cornrnonly used in filtration industry [20].

E = inlet flow width = (W-2t)

The pressure drop results for the triangular pieats at different pleat heights (1.3 cm,

2.0 cm and 3.6 cm) were plotted using the nondimensional parameter (equation 4.16)

as the abscissa and normalizing the total pressure drop with the minimum pressure

drop. The resulting correlation c w e is shown in Figure 4.15 together with a

logarithmic plot to show the details of low value data. This c w e can be used to

obtain the optimum combination of pleat length and pleat count for triangularly

~L*/(KYV~E) Figure 4.15 - Generalized correlation c w e for triangular pleated panel filter

pleated air filters using the DDO-4/40 filter medium.

3

2.5 4,

A

2 ; r - 4 b

0 2 1.5 5 C, d

1

0.5

3

- 2.5

2 -

w r a 1.5 s s 1 - 0.5

- - -- - -

O 1 I 1

O 1 2 3 4

41.3 cm 2.0 cm

r 3.6 cm

O

0.001 0.1 1 O - ZL~/(I(KW'E)

5.0 Three-dimensional Simulation of the

Multiple Panel Filter Configuration

5.1 Introduction

As rnentioned previously, the particle capture efficiency of the ULTRA filter varies

greatly with the filter medium face velocity. A multiple panel filter configuration

incorporating the ULTRA-Filter technology has been proposed to be used in the

Kiosk Ventilation System (see Figure 5.1). This configuration is meant to minimize

the medium face velocity by fully utilizing available space inside KVS, and this

configuration has die advantage of being easy to manufacture. The space available

for the overall multiple panel filter assembly is 61 cm x 61 cm x 30 cm. Each panel

filter has a dimension of 2.54 cm x 61 cm x 30 cm. and is composed of three wire

meshes held parallel to each other and separated by a 1.3 cm space. Triangularly

pleated filter medium is secured between the second and the third meshes. The gap

spacing between each panel filter determines the number of panel filters to be used

depending on the design flowrate and the design pressure drop. Increasing the

number of panel filters reduces the medium face velocity and thus the pressure drop

through the filter medium; however, the reduction in gap spacing also increases the

pressure loss fiom flow contraction and subsequent expansion at the dead ends due to

larger flow obstruction.

panel FiI t e r \

\9( approaching II\ veiocit y

pleoted fil t e r nediun

* ire neshes

panel f iHer cross-section

Figure 5.1 - Schematic of the multiple panel filter configuration

Assuming the medium face velocity is unifonn dong the flow direction, and the

medium face velocity is uniform along the pleat channels (fiom the results in section

4.1.1.1, the variation of medium face velocity in a triangular pleat channel is small),

then the required gap spacing cm be calcdated using the mass conservation

principle. However, fiom the results presented in section 4.1.1.1 with the case of

rectangular channel flow, the medium face velocity is expected to distributed non-

uniformly along the flow channel, and this flow variation, as well as the filter

pressure &op will depend on the gap spacing.

In order to optimize the geometrical design of this filter configuration so that it can

attain high capture efficiency with minimal energy cost, a simplified three

dimensional FLUENT mode1 has been developed to investigate the dependence of

the medium face velocity distribution and the filter pressure drop on the gap spacing.

5.2 Three-dimensional Mode1 Description

The flow field in the multiple panel filter is syrnmetric about the center line of the

flow channel, thus the computational domain can be simplified as s h o w in Figure

5.2. This configuration, however, still imposed some difficulties in modeling: (1)

because the length of the computational cells in the =-direction is limited to the order

of 0.1 mm (due to the small thichess of the filter medium) , and the length of the

computational domain in the y-direction and x-direction are on the order of 10 mm

and 100 mm respectively, there is a large scale difference between the z and y,x

directions; (2) the flow is three-dimensional and large flow gradients are expected

near the dead ends which requires very fine grids to model. Hence, a large grid size

(in the order of 200,000 cells) was needed to obtain a mesh that has adequate ce11

aspects ratio (e.g. Wh) and fine enough cells near the dead ends. With our current

computing hardware, this requires tremendous man hours and CPU time in building

the mesh and simulating the problem; this would significantly increase the cost of the

project and slow down other users working in the same computing system.

In order to minimize this problem and yet undertake useful simulations of such

flows, a simplified geometry (see Figure 5.3) was employed in our model. By

removing the first wire mesh and the associated half inch spacing, the flow gradient

near the dead ends and the length of the computational domain in the y-direction are

both reduced; this resulted in a more adoptable grid size. Note that this simplified

model would underpredict the flow recirculations near the dead ends, but the trend of

the dependence of medium face velocity distribution and filter pressure drop on the

gap spacing would be similar to that of the actual filter assembly. Non-uniform ce11

distribution was also used to minimize gnd usage such that the grids are more

densely clustered near the dead ends; the resulting gnd size was on the order of

100,000 cells. Figure 5.4 show the computational domain outline and a typical mesh

distribation. The fluid was assumed to be incompressible larninar flow, and a

uniform velocity profile was imposed at the inlet boundary. The dead ends were

modeled using FLUENT'S wall cells with the no slip boundary condition. Syrnrnetry

boundary condition was imposed on the x-y and x-z plane boundaries. The filter

medium was modeled using FLUENT'S porous cells with the D/DO-4/40 filter

f r o c t view

Figure 5.2 - Computationd domain

synne f r y boundary

opproaching - veloci t y .-,

c r o s s ssc t ion

pieatsd f i t t e r nediun /

f r o n t view C î O S S section

Figure 5.5 - Simplified cornputational domain

Figure 5.4 - Grid outline and typical mesh distribution

medium charactenstics. The two wire meshes were dso modeled using porous cells

but with the penneability term eliminated and used a small inertial loss factor (a

guessed vaiue) aione; the choice of the inertial loss factor vaiue would not effect the

solution since the porosity of the wire meshes is very high. The outlet section was

placed at about 3 - 4 gap spacing from the filter to ensure the velocity profile to

become fully developed and purely axial at the cutlet plane (due to outiet boundary

conditions).

5.3 Simulation Results and Discussions

5.3.1 Solution Procedure

Cases were simulated for gap spacing of 2 cm, 4 cm, 6 cm, and non-unifom gap

spacing with 8 cm upstream channel spacing and 4 cm downstream channel spacing,

and 4 cm upstream channel spacing with 8 cm downstream channel spacing. Inlet

flow velocity was set at 1 rnk for al1 five cases. Multigrid and small underrelaxation

factors (0.5 for velocities and 0.2 for pressure) were used to accelerate convergency

and ensure solution stabilities. Nonetheless, gradually refining the grids manually

near the dead ends was necessary to improve solution convergency. The

convergency cnterion was set such that when the total residuals (the normalized

relative changes in the variables from one iteration to the next) were of the order of

O Typically, each simulation required about 300 to 400 iterations (about 20

hours).

5.3.2 Flow Field

The main features of the flow can be seen fiom Figure 5.5, which shows the

isometric view of the velocity vectors distribution throughout the domain of the

simplified mode1 for a 6 cm gap spacing configuration. Front views and cross-

section side views of the velocity vectors are aiso shown in figure 5.6. It can be seen

that a flow recirculation zone foms at a relatively large distance downstrearn of the

inlet cross section (- 1.5 gap spacing); this zone constricts the idet jet, increasing its

velocity and reducing even more the static pressure in the given zone. As a result.

very little flow passes through the filter medium in this zone and the effective length

of the panel filter is reduced. Following this. the flow gradually spreads and

decreases along the channel. Due to inertia the flow approaching the filter medium is

at angles smaller than 90' from the axis of the flow channel. These angles increase

and become close to 90' only just upstream of the dead end. Flow recirculation zone

is aiso seen near downstrearn of the outlet dead end due to flow expansion.

5.3.3 Medium Face Velocity Distribution

The medium face velocity distribution along the flow channel was examined by

plotting the velocity magnitude reported at the center of the porous cells. Face

velocity distribution for gap spacing 2 cm, 4 cm, and 6 cm are shown in Figure 5.7a-

c along with the hand calculated design face velocity. It is clearly seen that the face

velocity distribution is highly non-unifom with the higher velocity near the end of

Figure 5.5 - Isomeuic view of the velocity vectors in the pleat center plane

velocity vectors viewed in the x-y plane

velocity vecton at different cross-section: (a) near channel inlet (b) at mid-channel

section (c) near channel outlet

Figure 5.6 - Velocity vectors viewed in NO-dimensional planes

the flow channel, and more than half of the panel filter has higher face velocity than

the design vaiue.

It was suspected that the use of a non-uniform gap spacing configuration, such

that we increase the upstream channel spacing and simultaneously reduce the

downstream channel spacing, would reduce the inlet 80w recirculation, hence

increasing the effective filtration area and perhaps the uniformity of the face velocity

distribution. A simulation was done for a filter configuration with 8 cm upstrearn

channel spacing and 4 cm downstream channel spacing. The resulting face velocity

distribution is shown in Figure 5.7d. A cornparison with the uniform 6 cm gap

spacing face velocity distribution is shown in Figure 5.7e. It can be seen that the

non-uniform gap spacing configuration has a more uniform face velocity distribution

in the flow developing region (downstream of the channel inlet). This is because of

the smoother pressure gradient resulting fiom the reduction of flow obstruction at the

inlet. Following this, however, the face velocity of the non-uniform gap spacing

conf~guration nses more dramatically, and exceeds that of the uniform gap spacing

configuration at approximately the channel mid-section. This may be explained as

the flow acceleration in the downstream channel resulted a pressure drop which

increases progressively in the flow direction; with the reduction of channel spacing

the 80w acceleration increases, and thus a higher pressure differential across the

filter medium which magnifies the non-uniformity of the face velocity distribution.

A simulation was also done for non-uniform gap spacing configuration with 4 cm

upstrearn channel spacing and 8 cm downstream channel spacing. The resulting face

Figure 5.7a - Filter medium face velocity distribution, 2 cm gap spacing configuration

Figure 5.7b - Filter medium face velocity distribution, 4 cm gap spacing configuration

6 c m r p i o n g Aug 05 1997 Ccll Vatucl Along EPozition = 22. K-Poriùon = 13 Ruurr 432 Vciooty M a ~ n i t d c (MIS) Va. 1-Oircccion (M Fîucnt Inc.

Figure 5 . 7 ~ - Filter medium face velocity distribution, 6 cm gap spacing configuration

Figure 5.7d - Filter medium face velocity distribution, non-uniform gap spacing configuration with 8 cm upstream channel spacing and 4 cm downstrearn channel spacing

1-DIRECTION LENCM M 8-4 cm spacing Ccll Valucc Along J-Position = 28. K-Posiuon = 12 Vclocity Magnitude (MIS) Vc. 1-Directton Lcngth (M)

Aug 05 1 997 Fiucnr 432 nucni Inc.

.' non-uniform gap spacing

I I.OOaEOi ZOQOEQi 3.000E4 l 4 ooOEQl s axEOl

I-DIREcrION mm (hl)

6 cm spxing vs. 8-4 cm spacing ~ u g 05 1997 Ccll Valua Along J-Position = 28. K-Parruon = 12 Ruent 4.32

Velocity Magnitude (WS) Vs. 1-DinXfion Luigth ()ci) Ruai tnc.

Figure 5.7e - Filter medium face velocity distribution, cornparison between 6 cm gap spacing configuration and non-uniforni gap spacing configuration with 8 cm upstream channel spacing and 4 cm downstrearn channel spacing

Figure 5.7f - Filter medium face velocity distribution, non-unifom gap spacing configuration with 4 cm upstream channel spacing and 8 cm downstrem channel spacing

Figure 5.7g - Filter medium face velocity distribution, cornparison between 6 cm gap spacing configuration and non-uniform gap spacing configuration with 4 cm upstream channel spacing and 8 cm downsîrearn channel spacing

velocity distribution and a cornparison with that of the uniform 6 cm spacing

configuration are s h o w in Figure 5.6f-g. As expected, higher face velocity gradient

is seen in the flow developing region resulting from the reduction of channel inlet

flow are* and the face velocity becomes more uniform than that of the uniform gap

spacing configuration in the second half of the flow channel.

5.3.4 Filter Pressure Drop

Figure 5.8a-e. show the normalized static pressure distribution from the inlet

boundary to the outlet boundary for the five gap spacing conf~gurations sirnulated.

The pressure was taken at a node in the center line of the upstrearn pleat spacing.

Clearly, the viscous drag dong the flow channel is relatively small. The dominant

pressure drop is comprised of two mechanisms: (1) the flow contraction and

subsequent expansion at the dead ends, and (2) the pressure drop through the filter

medium. Changing the gap spacing has a less significant effect on the second

mechanism, because the resulting change in the medium face velocity magnitude is

relatively small (for the cases investigated). Hence, reducing the gap spacing reduces

the average medium face velocity but increases the overall filter pressure drop.

Figure 5.8a - Nomalized static pressure distribution, 2 cm gap spacing configuration

- 4 cm rpxing Aug OS 1997

NoDc Valucl Along 1-Position r 21. K-Position = 9 fluent 4.32

Staiic Prcssurc fPi) VI. 1-Direciron Lengrh (M) Fiucnt Inc.

Figure 5.8b - Normalized static pressure dis-bution, 4 cm gap spacing configuration

Figure 5.8~ - Normalized static pressure distribution, 6 cm gap spacing configuration

Figure 5.8d - Normalized static pressure distribution, non-uniform gap spacing configuration with 8 cm upstream channe1 spacing and 4 cm downstream channel spacing

Figure 5.8e - Nomalized static pressure distribution, non-uniform gap spacing configuration with 4 cm upstream channel spacing and 8 cm downstream channe1 spacing

6.0 Summary and Conclusions

6.1 Motivation

A ventilation equipment manufacturer, Vent Master Ltd.,Mississauga, Ont., has

developed a Kiosk Ventilation System (KVS) incorporating the Ultra-Filter

technology, which uses a non-ionizing electric field to enhance particle capture. The

constraint on this filter technology is that the flow through the filter medium must be

kept at a low velocity to prevent particles bypassing the electric field. Due to the

complexities of filter pleating design and the space constraint with the KVS, the

Company has expenenced diff~culties in obtaining the desired filter medium face

velocity and pressure drop. In order for the filter of this invention to accomplish its

objectives, a detail pararnetnc snidy on the filter pleating and filter geometry was

necessary.

The objectives of this work c m be summarized as: first, to develop computer

models using a CFD code, FLUENT, for different pleated filter configurations, and

validate the CFD models by comparing with experimental results; second, to

examine the effect of pleat geometry (shape, height, spacing), approaching air

velocity, and filter configuration @anel filters and cylindrical filters) on the filter

pressure drop; third, to obtain a generalized correlation c w e for the design of

triangularly pleated air filters; and finally, to develop a three-dimensional computer

mode1 for the proposed multiple panel filter configuration to be used in the KVS, and

investigate the dependence of the filter pressure &op and filter medium face velocity

on the gap spacing between each panel filter.

6.2 Essential Findings

63.1 Experimental Validation

Pressure drop experiments were conducted for both triangularly pleated panel filter

and cylindrical filter configurations. For the panel filter, the experimental and

simulation results agreed quite well and both demonstrated the characteristic 'U'

shape curve. In the high pleat count region, however, the experimentai pressure drop

nse more dramatically mainly due to pleat bunching. The thickness and the

flexibility of the filter medium are therefore important factors in pleat optimization.

For the cylindncai filter. pressure drop measurements were performed for one pleat

count only. The experimental results were higher than the simulation results

throughout the entire velocity range; this is because the additional pressure drop

(flow contraction and expansion at the inlet of the filter) were not accounted for in

the cornputer model.

6.2.2 Pleating Analysis

Simulations were performed for both rectangular pleats and triangular pleats.

Velocity vector diagrams showed that the floa field inside a triangular pleat channel

is different fiom that in a rectangular pleat channel, with the triangular pleat being

the more aerodynarnic shape; it has a minimum of al1 three pressure drop

mechanisms across the pleat channels (entrance loss, viscous drag along the pleat

channel, and the exit loss). These resulted in a more uniform medium face velocity

distribution along the pleat channels than that of the rectangular pleat channels.

However, keep in mind that the rectangular pleats have a larger medium area than

triangular pleats, and thus have a lower average medium face velocity and pressure

drop through the filter medium.

For rectangular pleats, the optimal pleat count and pressure drop decreased with

increasing pleat height, whereas in the viscous force dominated region, the pressure

drop rises more ripidly. This is because in the medium resistance dominated region,

incrcasing the pleat height ùicreases the effective filter medium area, which M e r

reduces the medium face velocity and thus the pressure &op; however, in the viscous

force dominated region, the viscous drag also increases due to the longer flow

channel. For triangular pleats, increasing the pleat height reduced the pressure drop

throughout the entire pleat count, and with only a slight decrease of the optimal pleat

count. Therefore, for long pleats, triangular pleats could provide a higher optimal

pleat count and a lower pressure drop.

Increasing the rectangular pleat downstream channel spacing and simultaneously

decreasing the upstream chuinel spacing resulted in a higher filter pressure drop; the

optimal ratio of the downstream channel spacing to the upstrearn channel spacing

was found to be one.

With a higher velocity, the pressure drop through the filter medium and the viscous

drag in the

pleat count.

pleat channel both increased, which increased the pressure drop at ail

For both rectangular and triangular pleats, the pressure drop ratio at two

different approaching velocities was higher than the corresponding approaching air

velocity ratio. This is because the channel entrance length (where the pressure drop

is significantly higher than in the 80w developed region) increases with higher

velocity, also, the viscous drag dong the channel is proportional to the velocity

squared. The discrepancy between the pressure drop ratio and the air velocity ratio

was seen more significant for rectangular pleats. This is because the pressure losses

at the rectangular pleat channel inlet and exit are also proportional to the velocity

squared; whereas these losses are minùnized for triangular pleat channels.

Increasing the downstream channel spacing of the triangular pleats, Le., for a

cylindrical filter configuration, the pressure drop vs. pleat count c w e shified to the

nght; the optimal pleat count was increased. This is because the larger pleat

downstream channel spacing M e r reduced the flow acceleration and viscous drag

in the viscous force dorninated region, but the reduction of the ratio of filter medium

surface to volume caused the pressure drop to increase in the medium resistance

dominated region.

By scaling the inertia and visco& stress terms in the rnomentum equations, an

expression was obtained for the pressure drop through the triangular plezt charnel;

the pressure drop through the filter medium waç approximated using Darcy's

equation. The ratio of these two pressure drop was used as a nondimensional

parameter. The pressure drop results of the three cases simulated for the triangularly

pleated filter (with pleat heights of 1.3 cm, 2.0 cm and 3.6 cm) were repiotted

together using the nondimensional parameter as abscissa in the x-axis, and

normalizing the total pressure drop with the minimum pressure drop. The resulting

correlation c-me can be used for the design of triangularly pleated air filten.

6.23 Multiple Panel Filter Configuration

A simplified three-dimensional mode1 was developed for the proposed multiple panel

filter configuration to be used in the KVS. The simulation results showed that flow

recirculation regions formed downstream of the dead ends due to flow expansion; the

size of the flow recirculation region decreased with increasing gap spacing. For al1

cases investigated, the medium face velocity distribution dong the flow channel was

highly non-unifonn with the higher velocities near the end of the channel, and more

than half of the panel filter had a higher velocity than the design value. This was

attributed to inertia effect.

The overall filter pressure drop decreased with increasing gap spacing. This is

because the relative change in the medium face velocity magnitude with gap spacing

was small in the cases we investigated, and thus changing the gap spacing had a

more significant effect on the pressure drop resulting from flow contraction and

subsequent expansion at the dead ends than on the pressure &op through the filter

medium.

For both non-uniform gap spacing configurations investigated (8 cm inlet spacing

with 4 cm outlet spacing, 4 cm inlet spacing with 8 cm outlet spacing), the resulting

medium face velocity distribution was not significantly different from that of the

corresponding 6 cm uniform gap spacing configuration; the overall filter pressure

drop was higher for the non-uniform gap spacing configurations.

85

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