COMPARATIVE EVALUATION OF COOLING TOWER

DRIFT ELIMINATOR PERFORMANCE

by

Joseph K. Chan

and

Michael W. Golay

Energy Laboratory

and

Department of Nuclear Engineering

Massachusetts Institute of Technology

Cambridge, Massachusetts 02139

Final Report for Task #3 of theWaste Heat Management Research Program

Sponsored by

New England Electric SystemNortheast Utilities Service Co.

under the

MIT Energy Laboratory Electric Power Program

Energy Laboratory Report No. MIT-EL 77-004

June 1977

COMPARATIVE EVALUATION OF COOLINGTOWER DRIFT ELIMINATOR PERFORMANCE

byJoseph K. Chan andMichael W. Golay

Energy Laboratory Report No. MIT-EL 77-004

June 1977

ABSTRACT

The performance of standard industrial evaporative

cooling tower drift eliminators is analyzed using experiments

and numerical simulations. The experiments measure the

droplet size spectra at the inlet and outlet of the elimi-

nator with a laser light scattering technique. From these

measured spectra, the collection efficiency is deduced as

a function of droplet size. The numerical simulations use

the computer code SOLASUR as a subroutine of the computer

code DRIFT to calculate the two-dimensional laminar flow

velocity field and pressure drop in a drift eliminator. The

SOLASUR subroutine sets up either no-slip or free-slip

boundary conditions at the rigid eliminator boundaries. This

flow field is used by the main program to calculate the elimi-

nator collection efficiency by performing trajectory calcu-

lations for droplets of a given size with a fourth-order

Runge-Kutta Numerical method.

The experimental results are in good agreement with the

collection efficiencies calculated with no-slip boundary

conditions. The pressure drop data for the eliminators is

measured with an electronic manometer. There is good agree-

ment between the measured and calculated pressure losses.

The results show that both particle collection efficiency

and pressure loss increase as the eliminator geometry becomes

more complex, and as the flowrate through the eliminator

increases.

Acknowledgements

This work was begun in recognition of the growing

concern regarding the possible environmental effects of

cooling tower drift in central power station cooling. The

literature in this area has been very sparse, in regard to

the aerodynamic performance and basic physics of drift elimi-

nators, as well as in the related areas of field measurement

of drift transport and field data regarding the environmental

effects of salt exposures. The goal of this work has been to

improve this situation by providing a basic experimental and

theoretical understanding of drift eliminator performance,

spanning the range of designs in current industrial use.

This work has been conducted since 1974 with the

generous support of the New England Electric System and of

Northeast Utilities, through the MIT Energy Laboratory's

Waste Heat Management Program.

The work has been carried out by Joseph K. Chan and

myself, with the doctoral thesis research of Joseph being

derived from the project. The success of this project has

been greatly aided by the generous cooperation of the Ceramic

Cooling Tower Company, Ecodyne Cooling Products, and the

Marley Cooling Tower Company in donating eliminators for

testing and in providing critical reviews as the work has

progressed. In addition, special thanks are due to Thermo-

Systems Inc. for the loan of a Berglund-Liu Monodisperse

3

Droplet Generator, and to Spray Engineering Co. for supplying

SPRACO spray nozzles for use in the Drift Elimination

Experimental Facility.

At MIT, Professors Warren M. Rohsenow and S. H.

Chen have contributed valuably to the work in consultative

discussions regarding the design of the experiments and in

the interpretation of the results. Graduate students Ralph

Bennett and Yi Bin Chen have also provided valuable assistance

to the work in a similar fashion.

In conclusion, the competent typing of this report

by Ms. Marsha Myles also deserves grateful recognition.

Michael W. Golay

Associate Professor

of Nuclear Engineering

W

4

TABLE OF CONTENTS

Abstract 1

Acknowledgments 2

List of Figures 8

List of Tables 14

Chapter 1. Introduction 15

1.1 Background 15

1.2 Previous Theoretical Studies of DriftEliminator Performance 23

1.2.1 Roffman's Analytical Formulation 24

1.2.2 Foster's Model 24

1.2.3 Yao and Schrock's Model 25

1.3 Survey of Drift Measurement Techniques 25

1.3.1 Droplet Size DistributionMeasurement Techniques 26

1.3.1.1 Sensitive Paper 26

1.3.1.2 Coated Slide or Film 27

1.3.1.3 Laser Light Scattering 28

1.3.1.4 Laser Light Imaging 29

1.3.1.5 Holography 30

1.3.1.6 Photography 31

1.3.2 Total Drift Mass Measurement Techniques 31

1.3.2.1 Isokinetic Systems 31

1.3.2.2 High Volume Sampler 33

1.3.2.3 Airborne Particulate Sampler

1.3.2.4 Deposition Pans

1.3.2.5 Chemical Balance

1.3.2.6 The Calorimetric Technique

1.4 Industrial Efforts in Drift EliminatorEvaluation

1.5 Present Approach

1.6 Organization of this Report

Chapter

2.1

2.2

2.3

2.4

2.5

Chapter

3.1

3.2

3.3

3.4

3.5

Chapter

4.1

4.2

2. Theoretical Evaluation of DriftEliminator Performance

Introduction

Assumptions

Calculation of Air Flow Distributions

Pressure Loss Calculations

Droplet Trajectory and CollectionEfficiency Calculations

3. Results of Theoretical Calculations

Introduction

Air Velocity Distributions

Droplet Trajectories

Collection Efficiencies

Pressure Drops

4. Experimental Techniques

Introduction

Drift Elimination Facility

5

33

34

34

34

34

40

41

43

43

43

45

51

52

59

59

59

75

95

99

110

110

111

4.3 Drift Measurement Techniques

4.4 Calibration of the Drift MeasurementInstrumentation

4.5 Data Acquisition and Analysis Techniques

4.6 Pressure Loss and Air Speed MeasurementTechniques

4.7 Sources of Experimental Error

Chapter

5.1

5.2

5.3

5.4

Chapter

6.1

6.2

5. Comparison of Experimental Resultswith Theoretical Calculations

Introduction

Pressure Drop Across Eliminators

Collection Efficiency Results

Estimation of Experimental Error

6. Conclusions and Recommendations

Discussion of Results

Recommendat ions

References

Appendix A DATANA Program

A.1 Introduction

A.2 Description of the Programs

A.3 Description of Input Parameters

A.4 Listing of the DATANA Code

A.5 Sample Problem

6

114

119

125

132

134

139

139

141

144

150

153

153

172

179

186

186

186

191

195

223

Appendix B DAMIE Program 239

B.1 Introduction 239

B.2 Description of the Program 240

B.3 Description of the Input Parameters 241

B.4 Listing of the DAMIE Code 243

B.5 Sample Problem 251

LIST OF FIGURES

No.

1.1.1 Installation Schemes of Drift Eliminatorsin Cooling Towers 19

1.1.2 Some Common Drift Eliminator Geometries 21

1.1.3 Some Modern Industrial Drift Eliminators 22

2.3.1 General Mesh Arrangement in SOLASUR.Fictitious Boundary Cells are Shaded 47

2.3.2 Arrangement of Finite Difference Variablesin a Typical Cell 48

2.3.3 Flow Chart of the SOLASUR Code 50

2.5.1 Flow Chart of the DRIFT Code 58

3.2.1 Velocity Distribution of Air Flow in Single-Layer Louver Eliminator Using Free-SlipConditions at Upper and Lower Boundaries 62

3.2.2 Velocity Distribution of Air Flow in Single-Layer Louver Eliminator Using No-SlipConditions at Upper and Lower Boundaries 63

3.2.3 Velocity Distribution of Air Flow in Double-Layer Louver Eliminator Using Free-SlipConditions at Upper and Lower Boundaries 64

3.2.4 Velocity Distribution of Air Flow in Double-Layer Louver Eliminator Using No-SlipConditions at Upper and Lower Boundaries 65

3.2.5 Velocity Distribution of Air Flow in Sinus-Shaped Eliminator. (A) Free-Slip Conditionsat Upper and Lower Boundaries. (B) No-SlipConditions at Upper and Lower Boundaries 67

3.2.6 Velocity Distribution of Air Flow in Hi-VEliminator. (A) Free-Slip Conditions at Upperand Lower Boundaries. (B) No-Slip Conditionsat Upper and Lower Boundaries 68

9

No.

3.2.7 Velocity Distribution of Air Flow in Zig-Zag Eliminator Using Free-Slip Conditionsat Upper and Lower Boundaries 69

3.2.8 Velocity Distribution of Air Flow in Zig-Zag Eliminator Using No-Slip Conditions atUpper and Lower Boundaries 70

3.2.9 Velocity Distribution of Air Flow in E-EEliminator Using Free-Slip Conditions atUpper and Lower Boundaries 73

3.2.10 Velocity Distribution of Air Flow in E-EEliminator Using No-Slip Conditions atUpper and Lower Boundaries 74

3.3.1 Droplet Trajectory Plot for Single-LayerLouver Eliminator with Droplets Enteringthe Eliminator at Left of Figure . DropletSize is 40 pm 77

3.3.2 Droplet Trajectory Plot for Single-LayerLouver Eliminator with Droplets Enteringthe Eliminator at Left of Figure . DropletSize is 100 m 78

3.3.3 Droplet TrajectOry Plot for Double-LayerLouver Eliminator with Droplets Enteringthe Eliminator at Left of Figure . DropletSize is 40 um 80

3.3.4 Droplet Trajectory Plot for Double-LayerLouver Eliminator with Droplets Enteringthe Eliminator at Left of Figure . DropletSize is 100 m 81

3.3.5 Droplet Trajectory Plot for Sinus ShapedEliminator with Droplets Entering theEliminator at the Left of Figure . DropletSize is 40 m 82

3.3.6 Droplet Trajectory Plot for Sinus ShapedEliminator with Droplets Entering theEliminator at the Left of Figure . DropletSize is 100 m 8383

10

No.

3.3.7 Droplet Trajectory Plot for Asbestos-Cement Eliminator with DropletsEntering the Eliminator at Left of Figure .Droplet Size is 40 m 85

3.3.8 Droplet Trajectory Plot for Asbestos-Cement Eliminator with DropletsEntering the Eliminator at Left of FigureDroplet Size is 100 pm 86

3.3.9 Droplet Trajectory Plot for Hi-V Elim-inator with Droplets Entering the Elimi-nator at Left of Figures.

(A) 40 pm Droplet Size(B) 100 m Droplet Size 87

3.3.10 Droplet Trajectory Plot for Zig-ZagEliminator with Droplets Entering theEliminator at Left of Figure . DropletSize is 30 m 89

3.3.11 Droplet Trajectory Plot for Zig-ZagEliminator with Droplets Entering theEliminator at Left of Figure . Droplet 90Size is 60 m 90

3.3.12 Droplet Trajectory Plot for Two-LayerZig-Zag Eliminator with Droplets Enteringthe Eliminator at Left of Figure . DropletSize is 30 m. 91

3.3.13 Droplet Trajectory Plot for Two-LayerZig-Zag Eliminator with Droplets Enteringthe Eliminator at Left of Figure . DropletSize is 60 m 92

3.3.14 Droplet Trajectory Plot for E-E Elimi-nator with Droplets Entering the Elimina-tor at Left of Figure . Droplet Size is30 m 93

3.3.15 Droplet Trajectory Plot for E-E Elimi-nator with Droplets Entering the Elimi-nator at Left of Figure . Droplet Sizeis 50 m 94

11

No.

3.4.1 Collection Efficiency of Droplets as aFunction of Droplet Size

(a) DRIFT Calculation(b) Roffman Calculation 96

3.4.2 Collection Efficiency of Droplets as aFunction of Droplet Size

(a) Sinus-Shaped Eliminator(b) Double-Layer Louver

Eliminator of Same Dimensions.(Air Inlet Velocity=l m/s) 98

3.5.1 Pressure Drop Distribution Along theLength of Sinus-Shaped Eliminator 102

3.5.2 Pressure Drop Distribution Along theLength of Asbestos-Cement Eliminator 103

3.5.3 Pressure Drop Distribution Along theLength of E-E Eliminator 104

3.5.4 Pressure Drop Distribution Along theLength of Double-Layer Louver Eliminator 106

3.5.5 Pressure Drop Distribution Along theLength of Hi-V Eliminator 107

4.2.1 Schematic Diagram of Drift EliminationFacility 112

4.3.1 Schematic Diagram of Light ScatteringDrift Measurement Instrumentation 116

4.3.2 Scattered Light Intensity Versus DropletSize Calculated by DAMIE 117

4.4.1 Schematic Diagram of the Model 3050Vibrating Orifice Monodisperse AerosolGenerator 121

4.4.2 Schematic Diagram of the Droplet GeneratingSystem 122

4.5.1 Intensity Distribution Across the LaserBeam Cross Section 126

12

No.

4.5.2 Measured Pulse Height Distribution forMonodispersed Water Droplets of 80 mDiameter 127

4.5.3 Calibration Curve - the Peak Voltage ofPulse Height Distribution Versus DropletSize 128

5.1.1 Drift Eliminator Geometries. (A) Belgian-Wave Eliminator, (B) Hi-V Eliminator, (C)Zig-Zag Eliminator 140

5.3.1 Predicted and Measured Droplet CollectionEfficiency Functions for Belgian-WaveDrift Eliminator at 1.5 m/s Air Speed 145

5.3.2 Predicted and Measured Droplet CollectionEfficiency Functions for Hi-V Eliminatorat 1.5 m/s Air Speed 147

5.3.3 Predicted and Measured Droplet CollectionEfficiency Functions for Zig-Zag Eliminator at1.5 m/s Air Speed 148

5.3.4 Predicted and Measured Droplet CollectionEfficiency Functions for Commercial DriftEliminators at 2.5 m/s Air Speed

(A) Belgian Wave Eliminator(B) Hi-V Eliminator(C) Zig-Zag Eliminator 149

6.1.1 Terminal Velocities of Water Droplets 157

6.1.2 Flow Visualization Photograph of theBelgian-Wave Eliminator. (Dye BeingInjected at the Right Side of the Picture) 160

6.1.3 Flow Visualization Photograph of theBelgian-Wave Eliminator (Paper ChipTrajectories) 161

6.1.4 Flow Visualization Photograph of the Hi-VEliminator. (Dye Being Injected at theRight Side of the Picture) 162

13

No.

6.1.5 Flow Visualization Photograph of the Hi-VEliminator (Paper Chip Trajectories) 163

6.1.6 Flow Visualization Photograph of theZig-Zag Eliminator. (Dye Being Injectedat the Right Side of the Picture) 164

6.1.7 Flow Visualization Photograph of the Zig-Zag Eliminator (Paper Chip Trajectories) 165

6.2.1 Schematic Diagram of the Proposed Experi-mental Setup for Studying Droplet Traject-ory and Air Velocity Distribution in DriftEliminators 173

A.2.1 Flow Chart of the DATANA Code 188

Approximation of the Calibration CurveA,3.1 193

14

LIST OF TABLES

No.

1.4.1 Field Work of the Environmental SystemsCorporation 39

3.1.1 Physical Dimensions of the EliminatorsUnder Study 60

3.4.1 Collection Efficiency Calculated by DRIFTat 1.5 m/s Air Velocity for Double-LayerLouver Eliminator and E-E Eliminator 100

3.5.1 Calculated Pressure Loss Across SomeCommon Drift Eliminators 108

4.4.1 Droplet Diameter as a Function of TypicalDroplet Generator Parameters 124

4.5.1 Sensitivity Analysis of the CollectionEfficiency Results 131

5.2.1 Pressure Drop Across Eliminator at LowFan Speed 142

5.2.2 Pressure Drop Across Eliminator at HighFan Speed 143

5.4.1 Measured Collection Efficiencies of theZig-Zag Eliminator at 1.5 m/s Air Speed 151

6.1.1 Pressure Drop and Calculated CollectionEfficiency Results of Some DriftEliminators at an Air Speed of 1.5 m/s 171

A.5.1 Input Data for DATANA Sample Problem 224

Output for DATANA Sample ProblemA.5.2 228

15

CHAPTER 1

INTRODUCTION

1.1 Background

Current practice in the design and operation of new electric

power stations selects a single method of waste heat disposal

and then designs the cooling apparatus to meet the worst sta-

tion heat load throughout the year (Di). This is an outgrowth

of past trends, in which once-through cooling was virtually the

universal method of power station waste heat disposal in the

United States. In the late 1960's waste heat disposal suddenly

became a controversial topic with the introduction of unprece-

dentedly large (>800MWe) and thermally inefficient nuclear

power stations. In 1973 the Environmental Protection Agency

(EPA) added impetus to the use of cooling towers when it took

under advisement a Burns & Roe study indicating that evaporative

cooling towers may well be the only closed circuit cooling option

available in the near future. Based on this study, the EPA

recommended the evaporative cooling tower as the best practical

technology under the Water Pollution Control Amendments. Sub-

sequent concern for protection of the aquatic environment, and

a desire to avoid costly licensing delays has motivated many

utilities to design their new, large power stations using cool-

ing towers rather than once-through cooling. As recently as

October, 1973, a complete listing of all operating or committed

nuclear generating units revealed that 48% of the generating

capacity was to be served by cooling towers. The participation

by fossil-fueled plants is not as great as this, and projections

16

indicates that about 50% of the newly added power generating

installations at early 1980's will be using cooling towers.

The major cooling tower vendors in the United States are

Ecodyne, Inc., Santa Rosa, Calif.; The Marley Co., Mission,

Kansas; Research Cottrell, Inc., Bond Brook, N.J.; Ceramic Co.,

Fort Worth, Texas, and Zurn Industries, Erie, Pa. Other large

corporations which are either entering the field or considering

doing so are Westinghouse Electric Corp., General Electric

Corp., and the Babcock and Wilcox Co.

To meet the increasing demand for electricity in the United

States, the utilities are planning to build a large quantity of

new, large power stations with more emphasis on nuclear power

plants. With the prospect of rapidly increasing cooling require-

ments due to these plants, special attention has been paid to

the environmental effects of cooling methods. The major areas

of concern related to the environmental effects of cooling

towers are fog, icing, and drift deposition.

Drift consists of the water droplets that are mechanically

entrained in the cooling tower's exhaust air stream from the

station's cooling water. Drift particles contribute very little

to the visibility of cooling tower plumes because the quantity

of drift is very small compared to the other forms of water

present. The following order of magnitude numbers for the mass

concentration of typical cooling tower effluents illustrates

this point (S3):

X(vapor) 20 g/m3

X(fog) " 1 g/m3

X(drift)\ 0. 01 g/m3

17

Drift has several important deleterious effects on the

local environment. When the mixture of water vapor and drift

particles in the cooling tower plume, mixed with the ambient

cold air,is carried away, the drift particles may form nuclea-

tion sites for condensation. Also, the mixing of the cooling

tower plume with the stack plume may form acids through chemical

reactions.

In order to meet future electric power requirements and

because of the scarcity of cooling water, it will be necessary

for many of the new power generating plants to utilize cooling

water that contains various concentrations of salt, e.g.,

brackish inland waters, estuarine water, or sea water. There-

fore the drift will contain salt as well as chemicals from the

coolant water chemistry. The main concern about drift is its

potential for damage to nearby facilities, transmission lines

and biota. In some instances, drift has caused serious prob-

lems in electric distribution systems; the drift deposits

being responsible for equipment failures. Cases involving

corrosion and fouling of nearby structures have been reported

from both fresh and sea water cooling towers (L3). Drift can

also be a considerable nuisance when it spots cars, windows,

and buildings.

Estimates of drift from cooling towers range from 0.001%

of the circulating water to more than 3%. The industry practice,

until early 1970, was for cooling tower vendors to guarantee

drift release to be less than 0.2%. At the American Power

Conference in Chicago (April, 1970) a new performance standard

18

of 0. 03% was introduced,and in November, 1970, a further

reduction was proposed, leading to the estimate that future

cooling towers may be certified for drift release less than

0.002%.

Drift from cooling towers is traditionally reduced by

passing the exhaust flow through drift eliminators installed

in the cooling towers. These eliminators operate by passing

the two-phase flow stream through a curved duct, with the heavy

water droplets becoming trapped on the duct walls due to

centrifugal acceleration. The accumulated water on the walls

flows back into the cooling tower.

There are many different ways to install the drift elim-

inators in a cooling tower, depending upon the type and geometry

of the cooling tower. All cooling towers are either crossflow

or counterflow types, which is determined by the flow direction

of he cooling air relative to the downward travel of the water

to be cooled. In general, eliminators are installed either

horizontally or vertically. The horizontal scheme is commonly

used in crossflow type cooling towers and the vertical scheme

in counterflow type cooling towers, as shown in Fig. 1.1.1.

The horizontal installation scheme is easier and more sturdy

in construction. It can also be used to adjust the air flow

pattern within the tower. The main problem with the horizontal

installation scheme is the inefficient drainage of water from

the eliminator walls: a thick water film forms on the elimi-

nator walls and reduces the drift collection effectiveness.

The vertical installation scheme has little water drainage

19

I AIR I OUTLET I

FAN

WATER

INLET

N i _ ___ ___ _ _AIR x = AIR

INLET -- _ INLET

i i i rli tw

Countcr-Flow tower

WATEROUTLET

Cross-Flow tower

Fig. 1.1.1 Installation Schemes of Drift

Eliminators in Cooling Towers

DRIFT'-ELIMINATORS

DISTRIBUTION- SYSTEM

r�I

- - - -"1

=--_--.--

I------------------- ,

20

problem due to the enhanced film flow by gravity.

There are many different types of drift eliminators sold

by cooling tower vendors. The common ones are shown in Fig.

1.1.2. The single and double-layer louvre eliminators are

generally made with wood.The sinus-shaped eliminator is made

from asbestos cement. The Hi-V eliminator is made of polyvinyl

chloride (PVC) plastic. The zig-zag eliminator is made from

fiber. Some other industrial eliminators are also shown in

Fig. 1.1.3.

The performance of drift eliminators can be quantified by

two factors: the droplet collection efficiency and the pressure

drop across the eliminator. The collection efficiency is gen-

erally defined as the ratio of drift mass collected by the

eliminator to the total drift mass entering the eliminator.

For environmental protection, this factor should be high. The

pressure drop across the eliminator represents the resistance

of the eliminator to the exhaust air flow. The presence of an

eliminator will reduce the air flow within the cooling tower,

thus decreasing the tower's cooling capacity. This particular

effect can be very detrimental in natural draft cooling towers,

since they pass only the small draft caused by the air density

difference at the entrance and exit. For mechanical draft

cooling towers, a high pressure drop will cause a high horse-

power requirement in the fans. Therefore, for inexpensive

cooling tower performance, the pressure drop across the elimi-

nators should be as low as possible.

Eliminators operate on the principle of centrifugal

separation caused by turning of the flow in the duct. In

5,0 cm-l 5.0 cm ... q .-

cm

(A)

cm

(B)

-- X

(CH(E)

(F)

Some Common Drift Eliminator Geometries

21

4,3 cm -I rcm

(C)

(D)

Fig. 1. 1. 2

Herringbone

Eliminat or

AIR

FLOW SD

FILL SIDE

1ArDuplex Eliminator

DISCH. SIDE.

PVC Chevron Type

Eliminator

Fig. 1.1.3 Some Modern Industrial Drift Eliminators

22

AIR 3

FLOW V

FILL SIDE DISCH. SIDE

11-1

-11 a;-O-

-- r

Ii

.-

-. _we

II.

*%ON! " *`

040-

23

general, more turning results in a higher collection efficiency,

but a higher pressure drop. In order to achieve a high

collection efficiency and a low pressure drop, the design of

drift eliminators calls for an optimization between these two

factors. In current industrial practice, there is no standard

design procedure for doing this. That is, all existing drift

eliminators are generated through random innovation, experience,

and experiments. This thesis develops a numerical technique

to study the cooling tower drift eliminator performance, which

can eventually be used to evaluate and design drift eliminators.

1.2 Previous Theoretical Studies of Drift EliminatorPerformance

Studies of eliminator performance have been carried out

mainly with experiments. However, the experiments suffer from

the difficulties encountered in-measuring the drift quantity

and distribution. None of the drift measurement techniques

has yet been proven to be generally satisfactory to the point

of their being adapted for general use (Al). Theoretical

studies are rarely performed because it is feared that such

studies would be unreliable due to a number of uncertainties.

These include the possibility of flow turbulence within the

eliminator, the droplets rebounding from or being generated

in the water film on the eliminator walls, and the water film

drainage system design. Despite this, a theoretical model is

still a very useful tool in evaluating the relative performances

of different drift eliminators, and in designing improved drift

eliminators. Recently a few attempts have been made in this

24

direction; the approaches are briefly described next.

1.2.1 Roffman's analytical formulation

An analytical formulation for the estimation of drift

eliminator collection efficiency has been developed by Roffman

et al. (R4). In this model it is assumed that the drift drop-

lets flow longitudinally at the assumed-constant vertical air

velocity within the eliminator, and that it experiences trans-

verse viscous drag due to the transverse air velocity component.

This component is obtained by assuming that the air velocity at

any point in the eliminator is locally parallel to the eliminator

wall. For complex geometries the model uses a Fourier series

expansion of the transverse velocity component in terms of the

duct contour. By using these assumptions an explicit form of

the equation describing the droplet transverse displacement

can be obtained as a function of longitudinal location of the

droplet. From the displacement information it can be determined

which of the entering droplets will hit the eliminator walls.

The collection efficiency of the eliminator can be determined

as a function of droplet size, The results are claimed to be

satisfactory when overall collection efficiencies are compared

with the experimental data obtained by Chilton (C4).

1.2.2 Foster's Model

Foster, et al. (F3) have developed a potential flow

numerical simulation model for theoretical investigations of

drift eliminators. The model defines the effective eliminator

boundaries with experimental flow visualization photography,

25

and it is assumed that all droplets entering this region are

eliminated. The main stream flow fields are obtained by solving

the Laplace equation for the velocity potential within an

experimentally defined laminar flow region. Using this inform-

ation the collection efficiency for any droplet size is esti-

mated from numerically computed droplet trajectories by solving

the droplet equation of motion using a Runge-Kutta-Gill pro-

cedure. However, the estimated efficiencies are much greater

than those observed experimentally. This is thought to be due

to the improper treatment of the turbulent wake region. It has

been found that results obtained from direct calculation of the

flow field without definition of the turbulent wake region

provide better agreement with experiments (F2).

1.2.3 Yao and Schrock's model

Yao and Schrock (Y2) also developed a numerical model

for evaluating the eliminator collection efficiency. The

flow field is calculated by a relaxation method for iterative

solution of the Laplace equation for the stream function.

The droplet trajectories are calculated step by step in space,

with the droplet drag-induced acceleration assumed constant

within a given mesh interval. In this model the pressure drop

across the eliminator is also calculated by using a boundary

layer analysis.

1.3 Survey of Experimental Evaluation of Drift Eliminator

Performance

Experimental evaluations- of drift eliminator performance

are performed by measuring the drift at the exhaust side of the

26

eliminator in a particular cooling tower or a simulated cooling

tower facility. In most cases only the drift rate (defined as

the drift mass flowrate escaping the tower divided by the re-

circulating water flowrate in the tower) is measured. The drop-

let size-dependent collection efficiency of the eliminator is

generally never measured. Many methods exist for measuring

drift in these two ways. Most of them stem from droplet

measurement techniques in cloud physics. Those that are widely

used are summarized below.

1.3.1 Droplet Size Distribution Measurement Techniques

The following methods measure the drift droplet size

distribution. The total drift rate can be determined by inte-

grating the distribution over the droplet size.

1.3.1.1 Sensitive Paper

This method has been used extensively to measure the

liquid water content and size distribution in clouds and fog.

Recently this method was adapted for cooling tower drift measure-

ments (F1,R3,S3,S4,W2). In this method filter paper is sensi-

tized by soaking it with a 1% solution of potassium ferricyanide.

The paper is dried thoroughly and dusted with finely ground

ferrous ammonium sulfate. The treated paper is pale yellow

in color. When a water droplet falls on the paper, it dissolves

both chemicals and forms an insoluble blue precipitate known as

Turnbull's blue which is easily identifiable against the pale

yellow background. The area of the stain is related to the

droplet diameter. Adjustments must be made for the speed of

27

impingement and porosity of the paper. The best method of

obtaining calibration factors for these variables and various

droplet sizes is to use a monodisperse droplet generator to

form stains from a known droplet size, speed of impingement,

and porosity of the paper. The calibration is independent of

sensitizing agent (C4).

There are two types of sensitive paper sampling methods.

The most common method exposes the paper briefly in the air

stream with the paper normal to the air flow. However, in this

method, the impingement speeds are different for different

droplet sizes. A second method (S3) moves the sensitive paper

through the air by a rotating head machine with the axis of

rotation parallel to the air flow. The head velocity is perpen-

dicular to the average air flow and droplet trajectory, there-

fore the droplet impingement speed is always equal to the

rotational speed of the heads.

The collection efficiency of sensitive paper depends on

the droplet sizes and velocities. Calibration of this method

should include consideration of the dynamics of particle motion

and impingement: particles can impinge at an angle, producing

elongated stains, and at higher velocities droplets will produce

larger stains. The collection efficiency decreases for smaller

droplets. For these reasons calibration and data reduction are

time-consuming in the sensitive paper technique.

1.3.1.2 Coated Slide or Film

The measurement technology for this method was also

established by cloud physics investigators. This technique is

28

easily adaptable to field measurements of cooling tower drift

droplet size distribution (R3,S4,W2). In this method a glass

slide or photographic film is coated with a material that

preserves the shape of impinging droplets against coalescence

and evaporation. Of all the slide coatings evaluated, a liquid

plastic coating called FORMVAR gives the clearest and most

distinct representation of the drift droplets. When a water

droplet impacts the coating, it is encapsulated as the plastic

solvent evaporates. The water in the droplet eventually evap-

orates through the thin FORMVAR skin,but the exact shape of the

impacting droplet is preserved by the plastic film for future

size analysis with a microscope. Calibration involves correct-

ions for the flattening of droplets on the slide, and for

evaporation, which is a function of time and droplet mineral

concentration.

This technique has an upper droplet size limitation in

the range of 200 to 300 microns. When droplets larger than

this impinge on the slides, the droplets tend to shatter, making

a size determination impossible. As with the sensitive paper

method, data reduction is lengthy and tedious.

1.3.1.3 Laser Light Scattering

In the laser light scattering technique for drift

measurement (S2,S4,S5,S7), droplets are illuminated by coherent,

monochromatic laser light. Light scattered by a particle within

the sampling volume (defined by the intersection of the laser

beam and the detector acceptance cone) is detected by a photo-

detector, producing a current pulse which is related uniquely

29

to the droplet size. The current pulses are analyzed and

stored in a pulse height analyzer and the data can be processed

by a minicomputer. The size of the sampling volume should

be small, so that lengthy sampling times can be avoided, and

so that the probability of having more than one particle pres-

ent in the volume is small.

The system is calibrated by noting the response of the

instrument to droplets of known size that are generated by

a monodisperse droplet generator. However, this method is

complicated by the variation of the laser light intensity

across the laser beam and by an edge effect.

The main advantage of the laser light scattering system

is that it can operate on-line, providing fast results.

1.3.1.4 Laser Light Imaging

This method has not been used in cooling tower drift

measurement but appears in principle to have some advantages

over the laser light scattering system (K1). In this method

a linear array of photodetectors spaced equally measures the

droplet shadow diameter. The droplet passes between a He-Ne

laser and the detector array of fiberoptics. An optical

system focusses the laser beam to cast the droplet's shadow

at the desired magnification on the detector array. A volt-

age drop across a given detector in the array due to shadowing

is compared to the quiescent voltage of the unshadowed detectors.

Since the ambient light level is always used as a reference,

this method has an increased sensitivity to soiling of its

optics. The size of particle is determined by the number of

30

occulted fibers. Only shadows lying fully within the array

are used, which eliminates the unavoidable edge effects of

scattering or extinction methods.

The device operates on-line and samples particles in situ.

However, it is expected that considerable experimentation and

possibly modification would be required before an imaging

instrument was developed to the point of practical applications

for drift measurement.

1.3.1.5 Holography

The principle of this method is that light from coherent

laser light source scattered by the droplet interferes at

the film plane with light which proceeds unscattered and forms

the hologram interference pattern. The photographic film is

then processed and replaced in the electromagnetic wave. The

diffraction by the interference pattern density variations in

the film is such as to produce a focusing of light to produce

a real image of the hologram of the droplet. This can be

viewed with a closed circuit television system. If the record-

ing and reconstruction light waves have the same properties

the reconstructed image will be at the same distance as the

recording distance and the cross-section of the droplet under

reconstruction will be the same as the cross-section of the

original scattering droplet. In this way, one may therefore

map out a dynamic droplet field with respect to both position

and size distribution.

The method has been used in measuring fog droplets in

the size range of 5 to 35 microns (T3). The system has the

31

disadvantage that the reconstruction necessitates a two-step

process and is therefore lengthy. This method is expensive

and is shown to be inferior to the light scattering method (S4).

1.3.1.6 Photography

Droplets can be filmed using a high-speed cine camera,

with the droplets being diffusely illuminated from the opposite

direction. Droplets down to a diameter of 50 microns have

been measured. The films are studied frame by frame using an

analyzing projector, and the diameter, velocity, and trajectory

of the.droplets that are clearly in focus can be analyzed. This

method has been used in studying drift eliminator collection

efficiency (F3). However, the data reduction is lengthy.

1.3.2 Total Drift Mass Measurement Techniques

In most experimental work drift eliminators are evaluated

by measuring the total drift mass flux escaping cooling towers.

Some of these methods are described below.

1.3.2.1 Isokinetic Systems

In isokinetic systems air is drawn into the collector

with a kinetic energy identical to that of a fluid element at

that position, had the collector not been there. If the

density and temperature of the air do not change as the air

is drawn into the collector, isokinetic sampling requires

only that the velocity of the air flow into the collector

being equal to that in the absence of the collector at the

point of measurement. In an isokinetic system, the mean

air flow within the collector is adjusted by a blower to be

32

equal to the mean air flow outside the collector. There are

many different isokinetic systems which use various collectors.

One of them is cyclone collector (R1,W2), where droplets

entering the cyclone collector are separated from the air

stream by centrifugal force and are collected in a container.

The collection efficiency of the collector is determined in a

fog chamber. Drift droplets collected are analyzed by atomic

absorption spectroscopy for dissolved mineral concentration.

Since the collected water contains not only drift water, but

also condensed water, the drift mass flux cannot be determined

simply from the quantity of the collected water. Rather, the

drift mass flux is determined from the dissolved mineral con-

centration by assuming that the mineral concentration in the

drift is the same as in the makeup water source. This consti-

tutes. the greatest uncertainty in this method.

Another kind of collector is the isokinetic sampler

tube (H4,M1,S3,S4) in which a heated glass tube filled with

glass beads is used to collect drift mineral residue. The

heating element evaporates all of the liquid water sampled.

Only the mineral residues are retained for subsequent chemical

analysis. This method also suffers from the uncertainty in

assuming an equality of mineral concentration in the drift and

the makeup water source.

The mineral background in a real cooling tower is generally

high, and this introduces even more error into either of these

methods.

33

1.3.2.2 High Volume Sampler

The high volume sampler method measures the drift mineral

concentration per unit volume of air (L1,R2). Air is pumped

through a filter and particles in the air are trapped. The air

flow rate through the filter is recorded continuously to give

the total volume of air sampled. The filter is heated to keep

it dry, Data reduction of the drift mineral concentration is

performed with atomic absorption spectroscopy and by comparing

the results to a clean filter background count, This method is

affected by ambient humidity, wind, and background airborne

particulate concentration.

1.3.2.3 Airborne Particulate Sampler

The airborne particulate sampler (APS) was originally

developed for monitoring atmospheric salt loading at coastal

locations. It operates on the principle of collection by

impaction. Two woven polyester meshes mounted on rotating arms

sweep out a known volume of air per revolution. By counting

the number of revolutions, the total volume of air sampled

can be determined. A fan maintains the air flow past the

meshes and keeps it parallel to their plane. A wind vane

rotates the entire system about the vertical axis so that it

always faces into the wind. Calibration can be done with a

monodisperse droplet generator. Data reduction is performed

by a spectroscopic analysis of the meshes for salt content.

The main advantage of the APS over the high volume sampler is

that the APS system does not require as much power, and can be

34

run on a car battery at remote locations,

1.3.2.4 Deposition Pans

In this method petri dishes or polyethylene ars are

put at various locations in the horizontal plane surrounding

the cooling tower to measure the quantity of drift residue that

settles on the ground. Residue is collected for a known length

of time and is analyzed by atomic absorption spectrophotometry.

1.3.2.5 Chemical Balance

This method measures the rate of decrease in concentration

of a chemical such as sulfate or other tracer chemicals added to

the circulating water (C2). The drift rate is calculated from

the amount of change in the concentration of the tracer with

time. The disadvantages of this method are that a long test

period is required and that circulating water systems invariably

have other leaks that deplete the chemical tracer.

1.3.2.6 The Calorimetric Technique

The calorimetric technique incorporates special thermo-

dynamic and hydrodynamic principles by utilizing a calorimeter

with a throttling nozzle (R3). The droplets passing through

the throttle point evaporate because of a pressure drop, and

in doing so, they remove heat from the surrounding air. This

in turn causes a detectable air temperature drop which is used

to determine the drift rate.

1.4 Industrial Efforts in Drift Eliminator Evaluation

The first extensive investigation of drift eliminator

35

performance was done by Chilton (C4) in the late 1940's and

early 1950's. The test apparatus included a closed loop

experimental tower which simulated a natural draught cooling

tower. The drift droplets were collected by a Calder Fox

Scrubber at the tower exit. By measuring the water collected

for a certain period of operating time at different velocities,

the collection efficiencies of various eliminators for several

ranges of droplet size were determined. The pressure drop was

measured by pitot static tubes leading to a Chattock Fry tilting

micro-manometer. Many different eliminator geometries were

tested, and a double-layer louvre eliminator was recommended,

which was subsequently adopted on many cooling towers in England.

Measurements of precipitation from the cooling towers after

installation of the recommended eliminator were then performed

using the sensitive paper technique. The sensitive paper used

was Whatman No. 1 filter paper.

The experiment was considered to be a great success.

Since then, not much work on eliminator performance evaluation

has been reported until recently. In 1969, drizzle from two

modern 2000 MW stations was detected by the Central Electricity

Generating Board Regional Scientific Service Staff. Research

work on drift eliminators was subsequently rekindled by the

Central Electricity Research Board. Tests similar to those by

Chilton were performed on some eliminator geometries (Gl),with

a recommendation for a closer pitched (1.75 in.) asbestos-

cement eliminator. Droplet size measurements were made on water

sensitive papers exposed inside cooling towers at various levels

36

including both under and over the eliminators (M3). Droplet

removal efficiencies were found for conventional louvre elim-

inators. The sensitive paper technique described in this work

is the same as the one reported in Chilton's paper except that

the calibration was extended to smaller droplet sizes (25-400pm).

Theoretical evaluation was also carried out to calculate the

collection efficiency as a function of droplet size (F3). The

theoretical efficiencies were found to be much greater than

the observed efficiencies from their experiments which was done

with a photographic method.

In 1971, Fish and Duncan at Oak Ridge National Laboratory

developed an isokinetic sampling sensitive paper technique

using Whatman No. 41 filter paper (F1). The technique was

used to measure the drift size distribution above drift elimi-

nators of a counterflow hyperbolic cooling tower. The drift

rate was found to be 0.002-0.006%.

The Marley Company has established a strong program in

drift measurement and drift eliminator development since late

1960's. In 1968, a chemical balance method was used in the

Marley Laboratory to check drift levels with and without drift

eliminators in the testing tower. The technique was also used

in drift determinations on an operating mechanical draft in-

dustrial crossflow tower at a Municipal Power Plant. n 1970,

the Marley Co. was interested in operating a cooling tower on

salt water makeup, which required an accurate knowledge of

drift rate. Since that time they have sponsored and cooperated

with the Environmental Systems Corporation (ESC) to develop

37

reliable drift measurement instruments that include the

Particulate Instrumentation by Laser Light Scattering (PILLS)

system, the Isokinetic Sampling (IK) system, and sensitive

paper techniques. Later the Marley Co. added a special drift

test cell to the Marley Laboratory exclusively for drift elim-

inator development. Drift measurements were mostly done with

the isokinetic sampling system developed by ESC. Many different

eliminators have been tested. Some of the important conclusions

are listed here (H4):

(1) Numerous observations have shown that the

circulating water rate has little effect on

the drift level. Specific tests on the Duplex

eliminator revealed, within the limits of test

accuracy, that there was no change in drift

rate with circulating water rates ranging from

12 GPM/ft 2 to 22 GPM/ft 2.

(2) Theoretically, drift eliminator collection

efficiency increases with air velocity. However,

the water load on the eliminator also increases

with the air velocity, but at a greater rate than

the increase in efficiency. Altogether it was

found that drift increases with air velocity.

The rate of this increase can be drastic with

an inefficient eliminator, with the failure to

control the pattern of the water on the fill

side of the eliminator, or with inadequate

provision for draining the eliminator.

38

(3) The effect of efficient air handling in the

tower by the eliminators seriously changes the

tower performance and drift release rate.

The Environmental Systems Corporation was first sponsored

by the Marley Co., but later established itself as an inde-

pendent organization providing services to parties of every

interest. In 1971 ESC received grants from Environmental

Protection Agency to further develop drift measurement tech-

niques, particularly on the PILLS system. Other techniques

to be evaluated were isokinetic sampling using filter papers,

cyclone collector and glass wool fill material, sensitive

paper using milli-pore membrane filter paper, and on-line

holography. APS was developed later for airborne particulate

measurement. Numerous drift measurements at operating cooling

towers by ESC using these techniques have been performed.

Some of them are listed in Table 1.4.1.

In the early 1970's, Ecodyne developed several drift

measurement techniques for field testing. These include the

isokinetic sampling system using a cyclone separator, assembled

and calibrated by Meteorology Research, Inc., the impaction

method using FORMVAR coated slides, and sensitive paper tech-

niques. As of 1973, more than twenty types of drift tests had

been conducted on industrial towers. The tests included towers

equipped with both the standard two pass drift eliminator config-

urations typical of the industry for the past twenty years, and

a new drift eliminator developed by Ecodyne, the Hi-V eliminator.

Test results showed that drift rates for the standard two pass

39

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40

designs varied from 0.02% to 0.12% with a typical value of

0.05%. The Hi-V drift eliminator drift rates varied from 0.001%

to 0.008% with a typical value of 0.004%.

Other companies that are involved in cooling tower drift

measurements are Research Cottrell, Inc., who uses the High

Volume Air Sampling Method (L1), and the Balcke Co., who uses

the cyclone separator (R3), etc.

Although much progress has been made recently in drift

measurement techniques, disagreements and unreconciled differ-

ences frequently show up, which often involve factors of two or

three in the value of certain results. Reliable methods should

be developed soon in order to accurately access the environmental

effects of cooling towers.

1.5 Present Approach

In the present study, an analysis of the performance of

standard industrial drift eliminator devices using both theo-

retical and experimental techniques is carried out. The

theoretical approach makes use of the code SOLASUR (H2) to cal-

culate the air velocity distribution within a drift eliminator

and the pressure loss through the eliminator, using both free-

slip and no-slip boundary conditions at the eliminator walls.

This information is used to perform trajectory calculations

with a fourth order Runge-Kutta numerical technique for droplets

of a given size injected into the eliminator in a uniform

transverse distribution.

In the experimental approach, the laser light scattering

technique is used to measure the droplet size spectra both at

41

the inlet section and outlet section of the eliminator. This

drift measurement technique is selected because of its on-line

data acquisition and reduction capacity, and because of its

successful application in the PILLS system by the Environmental

Systems Corporation. The main differences between the present

technique and the PILLS system are that the laser presently

used is a steady-state laser instead of a pulsed laser as in

the PILLS system (S4), and that there is no fog problem in this

laboratory scale work. The pressure drop across the eliminator

is measured with a differential electronic manometer.

Comparison of the calculated results and the experimental

data for several drift eliminators is presented.

1.6 Organization of this Report

Chapter 2 describes the numerical model for theoretical

evaluation of drift eliminator performance. The assumptions

made in the theoretical model are also listed in Chapter 2.

The results of this calculation for some common cooling tower

drift eliminators are presented in Chapter 3.

In Chapter 4, the details of the experimental measurement

techniques in this work are described. The experimental data

is displayed in Chapter 5, where it is compared with the calcu-

lated results. The sources of experimental error, and efforts

to quantify this error are included in both Chapters 4 and 5.

Chapter 6 discusses the discrepancies between the measured

and calculated results, the validations of the assumptions

42

made in the theoretical calculations, and the usefulness

of the theoretical model. The overall performances of many

drift eliminators are compared, and future improvements are

recommended for drift eliminator design.

43

CHAPTER 2

THEORETICAL EVALUATION OF

DRIFT ELIMINATOR PERFORMANCE

2.1 Introduction

Despite the fact that many of the important parameters

which affect the performance of drift eliminators cannot be

easily accounted for, a theoretical model remains very useful

in evaluating the relative performances of different drift

eliminators, and in designing improved devices.

In order to do this, a computer program, DRIFT, has

been written to numerically simulate the performance of

drift eliminators. This chapter describes the theory of

the calculations performed by the code and the assumptions

that are made in the analysis. A detailed discussion of

the use of the code can be found in Ref. C5.

2.2 Assumptions

There are many parameters that affect eliminator per-

formance that cannot be easily included in a theoretical

model. Therefore, the following assumptions have to be

made in the numerical analysis:

(1) The air flow within the eliminator is laminar.

It was demonstrated (F3) experimentally that the

flow in a typical drift eliminator is laminar

throughout most of the eliminator volume, with

44

Reynolds numbers lying in the range 2000 to 4000.

(2) The exhaust flow field is not affected by the

presence of the drift since the drift density is

low.

(3) The flow is two dimensional.

(4) The flow is incompressible since the flow Mach

number Is low.

(5) Any water film effects on the air flow are

neglected.

(6) The initial velocity of the droplet at the inlet

of the eliminator is the vector sum of the exhaust

flow velocity at the inlet and the vertical droplet

terminal velocity.

(7) The probability of a droplet of a given size

entering the eliminator inlet at any location is

uniform.

(8) There is no droplet mass loss due to either

evaporation or friction.

(9) Interactions among the droplets can be neglected

since the drift density is low.

(10) The drift is eliminated if it impinges on the

eliminator walls, i.e., the "bounce" effect and

any water film effects are neglected. Re-entrain-

ment of water droplets from the water film on wall

into the exhaust flow can be neglected if the

drainage is properly designed and if the film

45

thickness is sufficiently small so that film

surface instabilities do not develop over the

anticipated range of exhaust speeds.

Further discussion of the validity of some of these

assumptions is presented in Chapter 6.

2.3 Calculation of Air Flow Distributions

In order to calculate the droplet trajectory within an

eliminator, it is necessary to know the air velocity distri-

bution within the eliminator. In all previous studies

either a uniform flow distribution (R3), or potential flow

(F3,Y2) is assumed. In this study, the flow distribution is

calculated by the SOLASUR code (H2) which is included in the

DRIFT code as a subroutine. In the original SOLASUR code a

free-slip boundary condition is used at the rigid boundaries

of the eliminators. In this work the option of a no-slip

boundary condition at the rigid boundaries has been added to

the code so that the mass-averaged total pressure drop between

the inlet phase and the outlet phase of the eliminator can

be evaluated. It is found that the flow distributions calcu-

lated with no-slip boundary conditions look more realistic

than those with free-slip boundary conditions. Also, the

collection efficiencies calculated with these more realistic

flow distributions agree better with measured values. All of

these results are shown in later chapters.

The SOLASUR code is a modified version of the SOLA

code for calculating confined fluid flows having curved

rigid or free surfaces as boundaries. It solves the two-

dimensional, transient Navier-Stokes equations for an incom-

pressible fluid using an implicit finite difference tech-

nique. This technique is based on the Marker-and-Cell (MAC)

method (Hl, W). The description of a flow transient pro-

ceeds step by step from an assumed initial velocity field to

an asymptotically steady final exhaust flow distribution.

The time step size is determined from numerical stability

considerations (H2). The fluid region is made up of uniform

rectangular cells, and is surrounded by a single layer of

fictitious cells as shown in Fig. 2.3.1. Fluid velocities

and pressures are located at cell positions as shown in Fig.

2.3.2; horizontal velocities at the middle of the vertical

sides of a cell, vertical velocities at the middle of the

horizontal sides, and pressure at the cell center.

The procedures involved in one calculational cycle

(one time step) consist of:

(1) Computing guesses for the new velocities for the

entire mesh from the difference form of the Navier-

Stokes equations, which involve only the previous

values of contributing pressures and velocities

in the various flux contributions. The velocities

at boundary cells are adjusted so that the boundary

conditions are satisfied.

47

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49

(2) Adjusting these velocities iteratively to

satisfy the continuity equation by making

appropriate changes in the cell pressures. In

the iteration, each cell is considered successively

and is given a pressure change that drives its

instantaneous velocity divergence to zero, thus

satisfying the continuity equation.

(3) When convergence has been achieved, the velocity

and pressure fields are at the advanced time level

and are used as starting values in the next calcu-

lational cycle.

The above procedures are repeated in each time step

until an asymptotic distribution is reached. The results

are then used for droplet trajectory calculations in the

main program. The flow chart of the SOLASUR subroutine is

shown in Fig. 2.3.3.

In the original code, free-slip boundary conditions

are used at the rigid boundaries (the top and bottom bound-

aries), where-in each top surface cell the u-velocity in the

top fictitious cell (the cell above the surface cell) is set

equal to the u-velocity in the top surface cell, and for

each bottom surface cell the u-velocity in the bottom

fictitious cell (the cell below the bottom cell) is set

equal to the u-velocity in the bottom surface cell. In the

DRIFT code, no-slip boundary conditions were added as an

50

SET INITIALCONDITIONS FOR

PROBLEM

.COMPUTE INITIALGUESS VELOCITIES

. SET BOUNDARY1"r T 'T T - fnN I

I .IJ1lJJ I

/HAVE PRESSRRESCONVERGED. _ F

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NO

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UPDATE FREEURFACE POSITION

ADVANCE TI ME]AND CYCLE

IPRINT & PLOTI

IHtbUKt ROPCCUL TION!

(TIME TO STOP?>

IYES

STOP

Fig. 2.3.3 Flow Chart of the SOLASUR Code

v.

I i II 11

rs _ _ -

I V 114 I? I JSET SPECIA

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_ I... i I

II I II

II

. Ir-_^ ^. .,I;C ~A~I

NO -

I-

A . .I

I

option, where the u-velocity in the fictitious cells at the

top and bottom boundaries are set equal to the negative u-

velocity in the top and bottom surface cells.

A detailed discussion of the SOLASUR code is given in

Ref. H2. Results of air velocity distribution calculations

are presented in Chapter 3.

2.4 Pressure Loss Calculations

The pressure loss of the air stream flowing through an

eliminator is an important factor in designing a drift elim-

inator. A large pressure drop will reduce the tower cooling

capacity and will thus either increase the capital cost or the

operating cost of the tower. An estima.te (Gl) reveals that

a flow resistance of three velocity heads (=AP/½ pV2 ) will

increase the final temperature of the condensate by approxi-

mately 0.20C. This seems to be a very small increase, yet it

is significant in terms of overall station economics, bearing

in mind that 10C is valued at about $3M over the life of a

2000MW station. The flow resistances of current industrial

drift eliminators range from two to ten velocity heads.

Prediction of the pressure drop across an eliminator is

complicated by the fact that flow separation occurs in most

eliminator geometries, and this induces a large pressure drop.

Yao and Schrock (Y1, Y2) calculated the pressure drop across

drift eliminators using the method of Lieblein and Roudebush

(L2), in which the total pressure loss is expressed as a

52

function of boundary layer thickness, provided that no flow

separation occurs in the eliminator. The hydrodynamic boundary

layer thickness is determined by an approximation method

proposed by Thwaites (T5).

In the SOLASUR code values of pressure are calculated

at all cells. Using no-slip boundary conditions at the

rigid walls, the pressure drop can be calculated. Assuming

equal air density at the inlet and outlet regions of the

eliminators, the mass averaged pressure loss is defined as

JT JT

U2j P2,j E ;IBAR,j , PIBAR,jAP = j=JB - JJB (2.4.1.)

JT JT

EJ Buj E UIBAR,j

where the summation is from the bottom boundary cell (JB) to

the top boundary cell (JT). i=IBAR is the outlet region,

and i=2 is the inlet region. uij and Pi j are horizontal

velocity component and pressure at cell (i,j), respectively.

This pressure loss calculation is performed at each time step

until a steady state value is reached. Results of this calcu-

lation are presented in Chapter 3.

2.5 Droplet Trajectory and Collection Efficiency Calculations

The droplet collection efficiency of an eliminator is

generally defined as the ratio of drift mass collected by the

eliminator to the drift mass entering the eliminator. It is

customary to study eliminator efficiency only in terms of its

effect on the total mass of droplets leaving the cooling

53

tower. However, it is currently known that the droplet size

distribution also plays an important part in determining the

nature of drift deposition. Therefore it is necessary in

evaluating an eliminator to investigate the variation of

eliminator efficiency as a function of droplet size. The

collection efficiency is defined as

N (d)n(d) = , (2.5.1)

where NC(d) represents the number of droplets of diameter d

being-captured by the eliminator, and Ni(d) represents the

number of droplets of diameter d entering the eliminator.

In the numerical simulation process, a certain number

of droplets of a given size are injected into the eliminator

with a uniform transverse distribution. By calculating their

trajectories within the eliminator, the number of droplets

that encounter the eliminator boundaries and are then assumed

to be captured can be found. The collection efficiency of

the eliminator for this droplet size is then determined from

Eq. 2.5.1.

The drift trajectory is calculated by solving the droplet

equation of motion. For a sphere moving in a flow field, the

general solution is governed by the momentum equation (M4)

dVd CdRedV

md = 6 aR( Va -Vd 24 + md , (2.5.2)

dt

where

= 1 + 0.197Re0 ' 6 3 + 2.6xl0-4Re 38 (2.5.3)

2 V-Vd lRpV-Vd RPa (2.5.4)

pa

For a spherical water droplet, Eq. 2,5.2 can be

dVd = 9 "a

dt 2 pwR2

Cd Re

21 (V a-Vd ) (2.5.5)

The symbols appearing in the above equations are:

md = droplet mass

Vd = droplet velocity

t = time

air viscosity

R = droplet radius

air velocity

Cd = drag coefficient

Re = Reynolds number

g = gravitational acceleration

Pa = air density

Pw= water density

Equation 2.5.5 is a nonlinear differential equation.

A fourth-order Runge-Kutta numerical analysis is applied to

54

C dRe

24

and

Re =

fied;

simpli-

1a

Va =

55

determine the droplet trajectory. At any time step, the

position of the droplet and its velocity are found. At each

location the air velocity is interpolated from the cell values

calculated by the SOLASUR code. The air velocity at the

beginning of each time step is used throughout that time step,

and the local drag coefficient and droplet acceleration are

calculated from these velocities and from the local values

of the remaining parameters.

A variable time step size is used in the calculation.

The step size is determined from a consideration of the

propagation of errors in the following manner: For a differ-

ential equation of the form

dVd = f(t,Vd), (2.5.6)dt

the error at time step i + 1 in the fourth order Runge-Kutta

method is (C1)

af hi+1-l d' (.5.7)ti ,c

where a is a velocity value somewhere in the interval between

ti and ti+l, E is a time value somewhere in the interval be-

tween ti and ti+l, and h is the time step size.

The first term on the right hand side of Eq. 2.5.7

represents the propagation error, and the second term is the

local truncation error, which is generally small for small

values of h. Then, if av is negative, a value of hvalues o h. Thend tia

56

afcan be found which will make (l+hav )<1 , and thedterror will tend to diminish or die away, so the solution will

be stable. For the cases considered, aV is always found to

be negative, so by specifying a proper value for the step

factor, h , a stable solution can be obtained. A large

value for this step factor will yield a smaller propagation

error but a larger truncation error. A small step factor will

result in too small a step-size, thus prolonging the compu-

tation. A step factor of 0.1 has been found to be satis-

factory for the cases under study. In the present model,

af/aVd is determined at the beginning of each time step

using the local values of droplet velocity and air velocity.

The step size of this time step is then the constant step

factor divided by af/ Vd.

If the eliminator is installed in a vertical scheme, the

droplets are assumed to enter the eliminator at a velocity

which is the difference between the air velocity and their

terminal velocities. The terminal velocity of a droplet of

radius R is determined from Eq. 2.5.5 by requiring dVd/dt

to be zero. Thus

2 Pw gR

Vt V- - 2 pgRif (2.5.8)Vt Va-Vd -9 1IaCdRe

24

57

This nonlinear algebraic equation is solved by Newton's

method of tangents with a calculational accuracy of 0.1%.

If a droplet enters the eliminator other than vertically

(as in a horizontal scheme), then the initial velocity of the

droplet will have a vertical component which equals the

difference between the vertical component of the air velocity

and the droplet terminal velocity, and a horizontal component

which equals the horizontal component of the air velocity.

Droplets of a certain size are introduced uniformly

across the inlet of the eliminator. The trajectory of each

droplet is calculated until it either hits the eliminator walls

or passes through the eliminator. The collection efficiency

for this droplet size is then the ratio of the number of

captured droplets to the number introduced at the entrance.

The number of droplets introduced at the entrance determines

the accuracy of the collection efficiency calculation. If Nd

droplets are introduced uniformly at the entrance, then the

error in the collection efficiency calculation will be

proportional to 1/Nd. In the DRIFT code, a provision is

made for testing a finer distribution of droplets at the

locations where the condition of trap and escape changes

between two adjacent droplets. This method greatly improves

the accuracy but does not demand too much computation time.

A flow chart of the DRIFT code is presented in Fig. 2.5.1.

Trajectory plots and calculated collection efficiencies

are presented in Chapter 3.

58READ INPUTAR

READ INPUT PARAMETERS

CALCULATE THEAIR VELOCITYDISTRIBUTION BYSOLASUR SUBROUTINE

/TO CALCULATECOLLECTION

NO \FICIENCY? / YES

NO OES USER SUPPLY\THE AIR VELOCITY _1 I;RIBUTION? /

YES

INPUT AIR VELOCITYI DISTRI BUTION I

J CALCULATE DROPLET i1 TERMINATE VELOCITYI

FOR ALL GIVENDROPLET SIZES IFIND INITIAL CONDITIONS-

CALCULATE THE- IS THE ENTRANCE POINTCOLLECTION YES OF THE ELIMINATOR?EFFICIENCY

NO

FIND CONDITIONS AT BE GINNING OF TIME STEP

CALCULATE TIMEL - I DECREASE ENTRANCE ISTEP SIZE DIVISION SIZE FOR -

IMORE ACCURATE RESULTI

YESiCALCULATE CONDITIONSAT END OF TIME STEP I

DETERMINE THE ELIMINATOR BOUNDARY

IS DROPLET OUT OF \ELIMINATOR BOUNDARY?/ NO

lT C ThDDI CT AT DD\ITfIIC \NO

I.0 . L C~ u 1 Ml F I v iv uo I O %ENTRANCE POINT TRAPPED?--

YE

IS DROPLET OUT OF NOTOP OF ELIMINATOR?

EIS DROPLET AT PREVIOUS N I "I-"". "'l tNTRANCE POINT TRAPPED? MORE ACCURATE RESULT

[RECORD TRAPPED DROPLE

RECORD TRAPPED DROPLET-

I nFrFDAF F:NKITDAAIIc I

Fig. 2.5.1 Flow Chart of the DRIFT Code

YES

I

I B I

- i

Jl

I

,i II

B i I II L

s, i , i

. .

.. 1

I

!

I ...... I m ! i ~ .............. I

I1

:s _._ _._ _. - - ---- --;-.1

1

59

CHAPTER 3

RESULTS OF THEORETICAL CALCULATIONS

3.1 Introduction

This chapter presents the results of the calculations

performed with the DRIFT code. The air velocity distributions

in some common cooling tower drift eliminators are calculated

by the SOLASUR subroutine. The calculations employ both

free-slip and no-slip boundary conditions at the eliminator

walls, and results are compared and discussed in Section 3.2.

The calculated droplet trajectories within these eliminators

are presented in Section 3.3. The collection efficiencies

calculated from these trajectories are compared with those

obtained from other sources in Section 3.4. The last section

of this chapter presents the calculated pressure loss across

some common industrial drift eliminators.

Table 3.1.1 tabulates the physical dimensions of the

eliminators under study. The case numbers in the table will

be referred to throughout this thesis.

3.2 Air Velocity Distributions

In this section, ir velocity distribution plots for

some drift eliminators are presented and discussed. In the

plots, the length of the line segments are proportional to

the magnitudes of the velocities at the mesh points, and the

directions of the lines represent the directions of the

flow at the mesh points. In all of the cases presented here

II-% 0 0)--T 0 o

cN 0

r- coH r

C(m

01-.I

IO-4

I Iin i n

I JI ~ x

O0 co l r0 0 0rH - - r- H rH

C\j 'IO 0 0 0 1O t-- Ln U Lf Ln

a) at) )

0 0 0

a) a) a a

Cd Cd Cd 4-)

I II,) a) 0 4)

H H HCdbD a a Ql]

0)

d

a) a I

ar-co CdC) C) boI I H

CO COO)0

4)

a,)c)

4)U)

CO¢,

bOCd

II bO

Lnb--

Hm m0

-T CY)

Wrw

r-I ,J r- r-IH~5 H H H H

0o

Cd

HH0 UIH'z

60

E4)

,1)

.I

o-

E0.r-r

HC

'I)

CCO

r-4 O01)04-Cd

-HE-Hr-A

0CO

tq)d

C)

r-IC(

I

Cl C)QI a

61

the air flow direction at the inlet of the eliminator is

normal to the flow channel cross section. The gravity

effect on the air flow is negligible; therefore the air

velocity fields will be assumed to be the same whether the

eliminators are installed horizontally or vertically.

Figures 3.2.1 and 3.2.2 display the air velocity distri-

butions for a single-layer louver eliminator as calculated

by the SOLASUR subroutine using free-slip and no-slip

boundary conditions at the eliminator walls, respectively.

With the free-slip condition, the calculated velocity is

quite uniform ( see Fig. 3.2.1). With the no-slip boundary

condition, the calculated velocity field,shown in Fig. 3.2.2,

is more realistic. Near the lower boundary a wake region

can clearly be seen. Such a wake region is expected in the

real flow. Note that the velocity in both cases is mainly

parallel to the duct boundary, thus, the collection efficiency

can be expected to be low for this type of eliminator.

Figures 3.2.3 and 3.2.4 show similar air velocity fields

for a two-layer louver eliminator. The free-slip prediction,

Fig. 3.2.3, shows a nearly uniform distribution except at

the turn in the eliminator where the velocity decreases as

the radius of curvature increases. With the no-slip condition,

the velocity distribution plot, Fig. 3.2.4, shows very small

velocities at the lower boundary in the first half of the

eliminator, and at the upper boundary in the second half of

the eliminator. In fact, these are the regions where a wake

is expected.

62

-_\An\\\~\\\ \\\ \\\ \\\\\

~-`\\\\\\\\\Ad\\\\ \\\\\\

\\\\\\\ \\\ \e\\\\\

\\\\

Fig. 3.2.1 Velocity Distribution of Air Flow in Single-

Layer Louver Eliminator Using Free-Slip

Conditions at Upper and Lower Boundaries

63

\

NNN-\\\`% '\\

% \\% %

Fig. 3.2.2 Velocity Distribution of Air Flow in Single-

Layer Louver Eliminator Using No-Slip Conditionsat Upper and Lower Boundariesat Upper and Lower Boundaries

~ \ \ \ \ \ \ \ \\\\\\\\\\

\\\\\\\\\\\\\\\\\\\\ E\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ ~~~~~~~~\\\\\\\\\\\\\\\\\\\\ \ \\\\\\\\\\\\\\\\\\\\ 0)\\\\\\\\\\ \\\\ \\\\\\\

\\\\\\\\\\\\\\\\\\\\\ 0

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ 0 c

\\\\\\\\\\\\\\\\\\\\

\ll I rlI 0)

/ I I I I I I Ir I I Il r lr I I I j ,,, o r

//////11 1 t! / t/ / / /////!/!!Illlrii c .¢

/111/11II~~~~~~ // / / /// /. ¢ 0///11I!!!t~//////// / = o-P0I~~//11/!/ / / /I / / / / / / .a

Iii1111./ / / / ~~/ ., ./.,/., / / //¢ -P riHI0~ )///////////// /., /., h /

IIII!!!!11I //.I / / r / °

I!11!!!!!1/~/I/.,,/ o bC

0l d//111/1 1 / //./ / // / , / I / /1i1II!I!!I / / / / / / / / / / /

C-'J///1///lt ! / //// ////I!/////ll/ c,, ,,11 ////1111! ! // /////11//111!!1111//

111111111111111 11111 //Il1111111I I J I I I ! I I ! Z / o s

.. ,,rrrrir\\\\..\\\\, ' \\\\\\\\\\\\\\..\\\\\\\\\\\\\\\\ %\\\\\\\\\\\\\\\\\ E

ii/IIIIIIItI//

I/ //I//I ///////////////// ////

I//I//I//I,,/ /1///f//I/f//I///// / / / 114

It11////f//1//f/Il/f////1/ /i / ,.1/f/I/f//f,,/ I/I/u, f//f//Il/Il///////,,./I \/\ \/\ \/\\\\\/11111 \ //\\ \\\\\/I/1111111////////,.

/1111ll~ II I I I I !I 11/

11I/111l111111111111

IIIII1111111111111 I.,.\\ \ \ \\\\ \ \ \ \\\\

.\\\ \ \ \ \\ \I \ \ \ \ \,

, \ \ \ 1 18 \ 1 / I \I I II ~I II

I I t I /I If I II

///////////// / /

///////////// / /,,

////////////,X, . .

/////// / / / // /,. . .

//// / / / / / / / ,/,...

J//// / / / // / / ,/,. ..

/ //// // IIIIl/ / / . ..

///// /IIII {III/f/,,

1 | | 1 | 1 1 1 1 | |1 1

65

\\'

\\\\

III1%

111

IIIItIll,

IIIII

II,,,ffI

I,

I .a ..

f .

0o

r4-

-CH

: O0-i¢)

O 0H d

O C

0

o 0

I

...-- t

0c a --H

'ItI I

It

66

Figure 3.2.5 compares the air velocity fields for a sinus-

shaped eliminator calculated with free-slip and no-slip

boundary conditions. In the free-slip case, A,the velocity

distribution is approximately uniform. At the mid-length of

the eliminator the velocity decreases as the radius of

curvature increases. Also, at the high pressure sides of the

eliminator the velocity is slightly greater than that at the

low pressure sides. It can also be observed at each trans-

verse cross section that the maximum velocity always occurs

at the wall. This is not true in the no-slip case, B, where

the maximum velocities occur at short distances away from the

high pressure walls, and approach a value of zero at the walls.

At the mid-length of the eliminator the maximum velocity

occurs close to the center of the cross section. Note that

the velocities shown at the upper and lower boundaries of

the eliminator do not represent the velocities exactly at

the walls, but rather at short distances away from the walls.

It can also be seen from these plots that the no-slip results

predict a more realistic flow because they show the wake

regions. This will be illustrated with the help of flow

visualization photographs in Chapter 6.

Similar observations can be made regarding the velocity

fields of the Hi-V and Zig-Zag type eliminators shown in

Figs. 3.2.6 through 3.2,8. For these more complicated

geometries it is anticipated that significant recirculating

eddies and turbulent wake regions exist at and near the bends

67

... \\\\\\., \\\\\\, / \ \ \ \ \ \\\./\\/ \\\\\ \\

I.\\\\\\\ I

i\ \ \\\\\\\.

C li

////////,, , . H oH

Kr , 0 _d 0 II I I I I I I

/ II I I I C O

H 4 -/1////,/,/. U) 0

l////l/ //, , o ///////I,,

'Cl

0 CO Z

//I//I"" ' t 4-

/ HlI!1~ I I4 U \ I I

\I I \\ \I I , * . . H I O0\ I\ \ \ \ I. I \ ,, 4 Z;

a: ( l I I 1 * . . .

it II>/ I I I I , .I//I/, " ",

/ I / I I I I t , . .: ,

f//// / -.///l I / I /-

68

... \\..\\O 0.. .. ,), .~ ~ \\\\.. . \\\\\.. ~ \\\\\\. \\\\\

aIItI ,0 E ./l/I/cl ·0 4i ,..////, , ... C //////, . ! 0

* Billies. ,

///0 *IoH O 0. , * , I I, , I 4 )

\\\ \\\\ I U)...x

Cdo C IoI It I I C iI Q O

//1 / / / .//I I/ / / //I I @ I I *

' ///'/'/I ,

I gI1ll1 |~~ ~~~ /

/I/ / II // / / / * , , .

/ / / / / / / / ///// / / / / /

/ / / / / / / / /

/ / / / / / / / /

// z / / //-/ I, 1,11, , I I I I I /

, ,. , , , I ~ \ \

% 4' ' 4' 4 '\ \\ \ \ \ \ \ \ \

\ \ \ \ \ \ \ \ \

\ \ \ \ \ \ \ \ \\ \ \ \ \ \ \ N N\ \ \ \ \ \ , \\\ \ \I \\\ \ '4' 9,

\ I I ,

/ / I I I , , ,

// / / i /// / / / / ,

// / // / I I I I I,,

/ I / I I I I///////I///f/ // /

I I I I I I I I I

69

bO

0

C03 C i)

haS

o0t0 Cb- 00

ro

4 00 z)

0i i

r-trk4

/ /

/ / /

''1/ / / /

.. iI / / / // / I I / /

* * *

* I I I I /

* · . , , I \ \ \* . X 8 \ \\* S S 8 \ \ \\\* . % \\ \ · ~~ . . \ \ \ \.~~ ., \ \ \ \

.~~ . \ \ \\· \ \ '.,\

~~ fI//lI,I////////I//

//////,///////,

///////, / / .~~~~~~~- -

/ / / / I, I / I I

/ I t , . .

, . ./ I, o

I

I

II

II

I

I

II

IU

U0

a

I* SS *. .

70

0

a)r d

CI

o 0oH C0

0

0 D

D CO4H4) CO

.0

CD

H a

o H0 c.

q) 0

CO

-H

0 71

in the flows, From the distributions shown it is concluded

that the no-slip results predict more realistic distributions

than the free-slip results, which will also be discussed in

Chapter 6.

For the Zig-Zag eliminator with no-slip boundary condi-

tions, the calculation fails to achieve a steady-state value.

Or, if a small mesh size is used for a more accurate determi-

nation of the actual flow, the calculation fails, These

effects are due to the fact that in the actual flow, turbu-

lence is very significant for this eliminator. This will be

shown in Chapter 6. The effects of turbulence are not taken

into account in the current calculation. The recirculating

eddies in interior corners are not fully resolved in the

solution. This could be done by using a finer calculational

mesh. However, this was not done since the mesh size already

is in a range for which the calculated droplet capture

efficiencies are relatively insensitive to the choice of mesh

size. In addition, the droplet capture dynamics are relatively

insensitive to whether the calculation of an eddying region-;is

exact or if the region is treated as being approximately stagnant-

which is what occurs with an inadequate spatial resolution of

the calculated flow field.

The flow structure of any turbulent wake flow cannot be

resolved by simply using a finer mesh, but it could be treated

explicitly with a "turbulence model" calculation (for which

several different computer programs are available). However,

72

in view of the success of DRIFT in predicting the experiment-

ally observed behavior of the drift eliminators, it was

decided that a turbulence model calculation would not be

required. Effectively, the error introduced into the capture

efficiency prediction by a failure to describe turbulent

eddy regions is relatively small. This is mainly true because

the devices examined have droplet trajectories that result in

captures lying far from these wake regions. This will be

discussed further in the following section and in Chapter 6.

Figures 3.2.9 and 3.2.10 show the results for the E-E

eliminator designed by Yao and Schrock (Yl, Y2). The criterion

for the design is that in order to minimize the air stream

total pressure loss, any flow separation of the hydrodynamic

boundary layer from the walls is to be avoided. Separation

can be avoided if the air velocity increases monotonically

along the flow direction. This is done by making the cross

section of the flow channel decrease monotonically. After

using this criterion and examining several geometries, it

was found the E-E eliminator performs satisfactorily. Looking

at the velocity distribution calculated by the SOLASUR sub-

routine using a free-slip boundary condition (Fig. 3.2.9), it

is found that the velocity increases monotonically along the

flow direction except near the outlet of the eliminator.

However, the result predicted with a no-slip calculation

(Fig. 3.2.10) indicates that separation does occur and that

a wake region exists at the upper boundary just after the

73

/s

//

////

////////////////-- /t///1 /

Fig. 3.2.9 Velocity Distribution of Air Flow in E-EEliminator Using Free-Slip Conditions atUpper and Lower Boundaries

* a

Ill//f/I//, / ////I// ////

v - *% -e *~ * , / //////

4 4 4 4 4 4 i s 4 4 A- - - - - - - - . - - //////// / -

__________________________ofcrrrr~)l/// / / I

/4 / //111111

Fig. 3.2.10 Velocity Distribution of Air Flow in E-E

Eliminator Using No-Slip Conditions at

Upper and Lower Boundaries

75

sharp turn. As a result of this, the pressure loss calculated

by the DRIFT code is much higher than that predicted by Yao

and Schrock (Y1 and Y2). The collection efficiency calcu-

lated by the DRIFT code using the free-slip condition has a

velocity distribution that is very close to that calculated

by Yao and Schrock. Using a no-slip condition, the collection

efficiency calculated by the DRIFT code is not significantly

different. These results will be developed in the following

sections.

3.3 Droplet Trajectories

The collection efficiency of a drift eliminator at a

certain droplet size is determined theoretically by uniformly

injecting droplets of that size into the inlet of the elim-

inators and observing their trajectories inside the elimina-

tors. If the trajectory of a droplet ends at an eliminator

wall, then that droplet is assumed to be captured. If the

trajectory exits the eliminator without touching the walls,

then the droplet is assumed to have escaped the eliminator.

By comparing the numbers of escaped and captured droplets,

the collection efficiency can be determined.

Droplet trajectories are calculated by solving numeric-

ally the droplet equation of motion within the eliminator

flow field as described in Chapter 2. Figs. 33.1 through

3.3.13 illustrate the droplet trajectory plots for seven

different eliminator geometries, with all eliminators assumed

76

to be in vertical scheme, and droplets entering the eliminators

at the left of the figures. For each geometry the trajectories

for two droplet sizes are shown. It can be seen in all of the

eliminator geometries that larger droplets are more easily

captured. In fact, it will be shown in a later section that

for any eliminator and any air speed, the calculated droplet

collection efficiency increases monotonically with droplet

size. This occurs because the net acceleration on a drop varies

approximately as l/R, where R is the droplet radius. To see

this, note that at a given air speed, the aerodynamic drag

force increases approximately as R2 (see Fig. 2.3.1), while

the particle mass varies in proportion to R3, and the time

during which the particle is affected by drag is approximately

constant. Thus, the net acceleration on a particle, and the

resulting displacement vary approximately as R, resulting in

easier capture for larger droplets.

Figures 3.3.1 and 3.3.2 show the droplet trajectories

within a single-layer louver eliminator determined by using

a free-slip air velocity distribution. It is observed that

the paths of the droplets are essentially parallel to the duct

boundary except at the entrance where the inertial motion of

the droplets carries them towards the duct boundary. It is

because of this inertial effect that the droplets are trapped,

and it can be expected that they will be trapped at the

boundary towards which they are initially directed, in this

case being the upper boundary. Thus, it is concluded that as

77

DRBOPLET D IA= 40 MICRON

Fig. 3.3.1 Droplet Trajectory Plot for Single-Layer

Louver Eliminator with Droplets Entering

the Eliminator at Left of Figure. Droplet

Size is 40 pm

78

DROPLET DI R= 100 MICRON

Fig. 3.3.2 Droplet Trajectory Plot for Single-Layer

Louver Eliminator with Droplets Entering the

Eliminator at Left of Figure. Droplet Size

is 100 m

-'

ji

I:

0

k"

S<

I

79

the duct boundary steepness increases the collection efficiency

will also increase since the area of the boundary towards

which the droplets are initially directed is increased.

Figures.3.3.3 through 3.3.6 display similar sets of data

for the two-layer louver and sinus-shaped geometries. In

these two cases the length, pitch, and entrance conditions

are the same in each of the two geometries in order to compare

their drift collection efficiencies. The trajectories are

calculated using free-slip boundary conditions in the air

velocity determination. Their collection efficiencies are

tabulated in Table 3.3.1 as a function of droplet size. The

fact that the sinus-shaped geometry has a higher collection

efficiency can be explained with the fluid velocity vector

and droplet trajectory plots. Comparing these figures, it is

seen that the sinus-shaped geometry has a steeper slope at the

entrance than does the two-layer louver eliminator, and this

is where most of the smaller droplets are trapped (see Figs.

3.3.3 and 3.3.5). For larger droplets, the number trapped

near the turn in the duct becomes significant. However, the

number is about the same for both geometries, as shown in

Figs. 3.3.4 and 3.3.6. Therefore, in order to collect small

droplets a geometry that has a steep slope at the entrance

should be used, while for large droplets both slopes are

important. Thus, if the drift size distribution is known, an

optimal drift eliminator for that distribution can be indicated

in this manner.

4

zIEiT"O

80

Q4

o

o 0

O

0

cti

H .0QdO O

.4-

a) vo v

4-)

04 IO S

a~ r.~·r

.i

b Bc

II

CC

LLJ

tL-

EDCr

ci

4.9'

;L

I:

81

4)

0

r. O

O H

H 4-

. oa)aH 00

H O

0O CO 4

0 -Pa

bO

a) -H O

a)

.aIe

0CE

t-LIr-

E

a

ZID

DI

82

o o

oC''

o 4.r4 N

EdH a

0

coa)

a bo

I C

O

0 0

r 40) 0

E

o -

o aH 4-3

O ·,r\ Ca, I0)

0.U-

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83

o.)H OO r

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I Hr 0

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4) ~U)

H

04)

\9z

(m~

Z:

I'C)

O

II

CD

r-D

CDOS

84

Figures 3.3.7 and 3.3.8 show the droplet trajectory plots

for the asbestos-cement eliminator using a free-slip air

velocity distribution. Trajectory plots for those using no-

slip air velocity distributions in a Hi-V eliminator are

shown in Fig. 3.3.9. By observing the results of all of the

essentially two-layer type eliminator geometries (two-layer

louver, sinus-shaped, asbestos-cement, Hi-V), it is concluded

that in the first half of those eliminators, the droplets

are trapped on the upper duct boundaries, while for the

second half of the eliminators, the droplets are trapped on

the lower duct boundaries. It can therefore be expected

that most of the water loading on these eliminators will occur

at these two regions. In designing an effective drainage

technique for this water loading, special attention must

be paid to these two regions. One drainage technique is

to put small grooves on the eliminator surfaces at these two

regions to direct the water away.

Another point can be made by observing the traject-

ories in these two-layer eliminators. The droplet trajector-

ies shown in Fig. 3.3.9 for the Hi-V eliminator are a good

example. It is seen that few water droplets enter the two

regions where turbulent wakes are expected to occur as

discussed in the previous section. These two regions are

near the lower boundary for the first layer of the eliminators

.85

r- rao E

r-I4 i

I0HU a

4 COH) o

r Oco 0

q)

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O O

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E-4

4, C

0.,

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IIFI

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86

4O3a)

o04

r9-

-

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ll

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cc

I-o=r

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0.CDE3

88

and near the upper boundary for the second layer of the elim-

inators. This means that the turbulent wakes will not have

a great effect on the droplet trajectories. Therefore, even

if these wake regions are not described exactly, the calcu-

lated collection efficiency results may approximate the results

of an exact flow field, as long as the velocity distribution

is calculated using no-slip boundary conditions which will

show the general pattern of the flow field. Further discussion

will be made in Chapters 5 and 6.

Figures 3.3.10 and 3.3.11 show the droplet trajectories

in the Zig-Zag eliminator, using no-slip boundary conditions

for the air velocity calculation. It is seen that all droplets

that are captured were trapped in the first two layers of the

eliminator. Therefore it is doubtful that a third layer is

necessary. Figs. 3.3.12 and 3.3.13 display similar data,

but with the third layer of the Zig-Zag eliminator removed.

It is observed that the capture efficiencies are about the

same for the two droplet sizes shown. This is in fact true

for all droplet sizes, though the Zig-Zag eliminator has a

slightly higher efficiency at smaller droplet sizes. It is

expected that the drift collection efficiency for the two

cases will not differ significantly,and therefore it is

suggested that two layers of the Zig-Zag eliminator will

probably suffice. If this is done, then the pressure loss

will be significantly reduced.

Figures 3.3.14 and 3.3.15 display the trajectory plots

89

4;3

Cdo4o

o )h N

Cd

4-3 -p

0 0a

cr-

CCd 0

h 4 OH ob O

0 0

0 .So

EbO4o

C4 o

r.

Z

_

IICE

I

JD

o0Dr

90

E

o

o tae0 a)

O N

2 -HH a)

CO

I4 0

oN

O ObO

C)

o IO 0

h C

E-4bO

a)

HC

-H

zC)

Z

(D

cE:

LJI

-

cD

91

DROPLET DIR= 30 MICRON

Fig. 3.3.12 Droplet Trajectory Plot for Two-Layer

Zig-Zag Eliminator with Droplets Entering

the Eliminator at Left of Figure. Droplet

Size is 30 m

92

DROPLET DIR= 60 MICRON

Fig. 3.3.13 Droplet Trajectory Plot for Two-Layer

Zig-Zag Eliminator with Droplets Entering

the Eliminator at Left of Figure. Droplet

Size is 60 pm

93

DROPLET DI R= 30 MICRON

Fig. 3.3.14 Droplet Trajectory Plot for E-E Eliminator

with Droplets Entering the Eliminator at Left

of Figure. Droplet Size is 30 m

94

DROPLET D I AR= 50 MICRON

Fig. 3.3.15 Droplet Trajectory Plot for E-E Eliminator

with Droplets Entering the Eliminator at Left

of Figure. Droplet Size is 50 m

95

for the E-E eliminator. It is seen that the capture efficiency

of this eliminator is indeed very high, as predicted by Yao

and Schrock (Y1, Y2). However, it will be shown in Sec. 3.5

that the pressure drop across this eliminator calculated by

the DRIFT code is much higher than that predicted by Yao and

Shrock.

3.4 Collection Efficiencies

The droplet collection efficiencies of drift eliminators

are calculated from the droplet trajectories through the

eliminators. These trajectories are obtained by using either

no-slip or free-slip predictions of the air velocity field.

Figure 3.4.1 compares the collection efficiency results

calculated by the DRIFT code using a free-slip air velocity

field with those calculated by Roffman et al. Roffman et al°.

used an analytical formulation for the estimation of drift

eliminator efficiency by assuming that the drift flows longi-

tudinally at the assumed-constant vertical air velocity within

the eliminator, and that it experiences transverse viscous

drag due to the transverse air velocity component which is

obtained by assuming that the air velocity at any point in

the eliminator is locally parallel to the eliminator wall.

For complex geometries the model uses a Fourier series expansion

of the transverse velocity component in terms of the duct

contour. Results obtained by the DRIFT code using free-slip

boundary conditions for air flow field calculations are shown

100

DROPLET DIAMETER (MICRON)

Fig. 3 .4.1 Collection Efficiency of Droplets as

a Function of Droplet Size

(a) DRIFT Calculation

(b) Roffman Calculation

1.0

96

L)

L)-4-

U-U-LL

.I

CD

-C)_J-J

.0110 1000

97

in Fig. 3.4.1 as the curves A and Roffman's results are the

curves B. The solid curves are the results for the double-

layer louver eliminator, Case D1 as identified in Table 3.1.1.

The broken curves are for the sinus-shaped eliminator, Case

N2 as identified in Table 3.1.1 For both geometries there is

a fair agreement between the two calculations over the range

of droplet sizes considered. However, at small droplet sizes,

the results deviate from each other. The reason for this is

that for small droplets, the trajectory depends strongly on

the air velocity distribution. Therefore, for an air

velocity distribution that is mainly parallel to the duct

walls, even near the entrances and turns as assumed by Roff-

man's model, the smaller droplets will follow the air stream

and escape the eliminator. In this way, a smaller collection

efficiency than the real value is predicted.

It is found from these comparisons that the calculated

results are quite sensitive to the assumptions regarding the

air-stream velocity distribution. It is noted that the

numerical simulation model in this work is physically more

realistic than others which are available.

Figure 3.4.2 shows the drift collection efficiencies for

the two-layer louver and sinus-shaped type geometries of the

same length, pitch, and entrance conditions. The comparisons

of their air velocity distributions and trajectory plots were

given in previous sections. The fact that the sinus-shaped

geometry has a higher collection efficiency can be explained

)

%W

DROPLET n, r.-_ V 100ICRON)

P19- 3.4.2Ri *.3 CO1lection Efficienc

Untlon of Droplet roplets a(a ) Snus-Shaped ze(b) DUble-Layer Eliminato

Of SamrD Louver Eliminator(Air e DimensiOns

Inlet Velocty_ l/s)

98

U.

(

LU

(-

C3

Lj

CD

0.0

_

- " t FER (f,

99

by the fluid velocity vector and droplet trajectory plots as

explained in the previous section.

The comparison of collection efficiency results will be

discussed in Chapter 5. Generally, for simple geometries like

the one or two-layer louver eliminators, and sinus-shaped

eliminator, the difference in the calculated collection

efficiency using a no-slip or free-slip velocity distribution

is not significant. This is demonstrated by the results

shown in Table 3 .4.1 for the two-layer louver eliminator at

a 1.5 m/s air velocity. For more complicated geometries,

this difference becomes significant, and will be shown in

Chapter 5.

Also shown in Table 3.4.1 is the capture efficiency

comparison of the DRIFT code calculation with Yao's calcu-

lation for the E-E eliminator. It is seen that with free-

slip conditions in the DRIFT calculation, the results are

very close to Yao's results. This is expected because po-

tential flow is assumed in Yao's calculation. Using a no-

slip condition in the DRIFT calculation, the results are

different, but not significantly. However, the difference

in the pressure drop results is very great, and is demon-

strated in the net section.

3.5 Pressure Drops

The SOLASUR subroutine determines the pressure at each

nodal point. From this information the total mass-averaged

Ln LCn

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L\ Lf

C) C

OC)

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C)i

L' in CH zz t- C

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100

il

OHU)II01

ZI

0)

a)aE4

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a)

co

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04-,JO

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Ca)a)

E:1

4oa) 4-H a)

.a E0 4

w

101

pressure drop across the eliminator can be determined if a

no-slip boundary condition is assumed at the eliminator walls.

The results of such calculations will be compared with experi-

mental data in later chapters. In this section the pressure

drop distribution along some of the eliminators will be

presented to get some insight into the effect of the geometry

upon pressure loss across eliminators. The pressure drop

distributions presented here are normalized as the ratio of

the pressure drop at any location in the eliminator to the

total pressure drop across the eliminator.

Figure 3.5.1 shows the pressure drop distribution for

the sinus-shaped eliminator. It can be seen that most of the

pressure loss occurs near the inlet and outlet regions of the

eliminator. This is due to the fact that the slope of the

duct boundaries is steeper at these regions. Similar results

are obtained for the asbestos-cement eliminator (Fig.3.5.2)

which has a shape similar to the sinus-shaped eliminator except

that the slope at the entrance and exit regions is not as

steep while it is steeper at other regions. These regions of steeper

slope extends farther along the eliminator length than in

the sinus-shaped eliminator. It will be shown later that the

total pressure loss across the asbestos-cement eliminator is

larger than that of the sinus-shaped eliminator.

Figure 3.5.3 shows the results for another smooth geometry,

the E-E eliminator designed by Yao and Schrock (Y1,Y2). The

flow channel cross-sectional area decreases along the eliminator

102

O ~ ~ ~ O

rl ~ ~ ~ r

4Q 0) ~~o i

E~~~~~~~~~~0 .-~~~~~~~~~~~~~~~~~~.c,~~~~~~~~~~~~~~~~~~~~~~~~

TJ· EL X.

0 .dP Q,~~~~~~~~~~~

rZ~~~~~~~~~~~.C~~~~~~~~~cd j~~~~~~~~~~~~~.

o 1';o

v '

4-4

m olhOo) 4a) C;_ a

r-nLr\

b.D

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'dV/ (1)d-XCDd

dV/((I)d-(X)d)

FI

103

z o4U

.C 0o4 4.

rl

E

0H

0 U)

i3 0 ·

4-)Uo bh¢

-bOLCh vD

C) C)

IdV/((I)d-(X)d)

104

CD

O

0

0

4-'CH

01

r-l~3 ·rf

Ln C

I d((O)d-(X)d)idV/( (q)d- (X)d)

105

length, which causes the pressure loss to increase steadily

along the eliminator length. The pressure loss increases

sharply near the outlet region of the eliminator. This is

probably due to the occurrence of flow separation as discussed

in Sec. 3.2.

Figures 3.5.4 and 3.5.5 show the results of the two

eliminators with sharp corners, the double-layer eliminator

and the Hi-V eliminator. For both of these eliminators, the

pressure distribution curves exhibit a complicated behavior.

For the double-layer louver eliminator in Fig. 3.5.4, the first

discontinuity occurs near the inlet region, and is probably

due to the occurrence of flow separation. The maximum

pressure loss occurs at the turn in the eliminator, where it

decreases sharply in a very short length. It then increases

again to the outlet of the eliminator. Similar results are

obtained for the Hi-V eliminator in Fig. 3.5.5. These

distributions are not physically reasonable. Therefore, the

pressure drop results for geometries with sharp corners are

not reasonable, and should be used with care.

Table 3.5.1 lists the calculated pressure losses across

some common drift eliminators. They are expressed in terms

of the velocity head, which is AP/pV2. It can be seen

from this table that the pressure loss increases as the

eliminator geometry becomes more complex. Since the collection

efficiency also increases in this manner, it is necessary to

compromise between these two parameters in the design of a

106

0a,

bo0

0H,-

0Ca)Xla)4

*-o

Fl4 D

_ r--C CVdV/((1)d-(X)d)1

107

0,~~~S 4

04-)

.rC

4U)Ert

0H4-:O

.C

C

U)hOfr-t5-4,C

X.oo3

LfonC

oC- CD

'dV/( (I)d-(X)d)

CI--

108

Table 3.5.1

Calculated Pressure Loss Across Some CommonDrift Eliminators

EliminatorGeometry

Case No. inTable 3.1.1

Single-layerLouver

Double-LayerLouver

Sinus

Asbestos-Cement

Hi-V

Zig-Zag

E-E

E-E(Yao's result)

S1

AP4 2fpV

2.35

D2 0.97

N2 2.82

Al

H1

Z1

El

3.91

3.43

2.54

14.61

El 1.20

109

drift eliminator with low pressure loss and high collection

efficiency,

The pressure loss across the E-E eliminator calculated

by Yao and Schrock (Y1,Y2) is also found in the table. Its

value is much lower than the one calculated by the DRIFT code.

This is because Yao and Schrock assumed that there was no

flow separation. This was, however, shown not to be true in

Sec. 3.2. If this is true, then this eliminator will be nsuit-.

able for use in cooling towers despite its high capture efficiency.

As mentioned earlier, for eliminators with sharp turns,

the pressure loss calculation will not yield reasonable

results. This is illustrated in Table 3.5.1; for the double-

layer louver, Hi-V, and Zig-Zag eliminators, the results are

unreasonably low. The experimental values of the pressure

loss are higher, and are reported in Chapter 5.

110

CHAPTER 4

EXPERIMENTAL TECHNIQUES

4.1 I' ntroduction

Experimental evaluations of drift eliminator performance

are usually performed by measuring the drift distribution at

the exhaust side of an eliminator which is installed in a

particular cooling tower or in a simulated cooling tower

facility. In most cases only the drift rate (defined as the

drift mass current divided by the recirculating water flowrate

in the tower) was measured. Very limited experimental work

has been done on the droplet size-dependent collection

·efficiencies of drift eliminators.

Recently it has been realized that the droplet size

distribution plays an important part in determining the nature

of any drizzle which may arise from the drift (M3). Investi-

gations have therefore been made into the droplet capture

efficiency of drift eliminators as a function of droplet

size. This data can also validate the calculations performed

by the DRIFT code.

This chapter describes the drift elimination facility,

the drift measurement techniques, the methods for analyzing

the measured data, and the technique for pressure loss measure-

ments. Results obtained from the experiments will be presented

and discussed in Chapter 5.

I

i

111

4.2 Drift Elimination Facility

In order to perform comparative performance studies of

cooling tower drift eliminators experimentally, a Drift

Elimination Facility has been constructed. The facility

simulates a cooling tower fill-outlet environment in which

drift eliminators can be installed for testing. A schematic

diagram of the facility is presented in Fig. 4.2.1.

This facility is a low-speed wind tunnel, 0.8 m by 0.8 m

(2.5' x 2.5') with plexiglass walls, supported by a Dexion

angle skeleton. Chrome felt gaskets are placed between the

plexiglass and Dexion angles to prevent leakage. In order to

have access to various regions, most of the plexiglass plates

can be removed. Air speeds are adjusted by means of a two-

speed exhaust fan at either 1.5 m/s or 2.5 m/s, which simulates

natural-draft or mechanical-draft cooling tower conditions,

respectively. The fan is placed at the inlet of the tunnel

and forces air into the tunnel. To dampen the flow turbulence,

some soda straws and honeycomb sheets have been installed

downstream from the fan. The turning vanes are made of plastic

sheets, and are spaced in such a way that the air flow will

remain uniform after turning out of the horizontal section of

the facility into the vertical section of the facility. The

air is recirculated continuously through a 0.46 m (18") diameter

flexible air duct to insure that water vapor saturation is

maintained. Recirculating droplets are thought to contribute

only an insignificant amount to the drift generated in the

1 I2

F--

ILLt;E

H

Q

CCd

0

C-H

m4.)cri

0r-q

w

Cd

bO

C)4-)

Cd

S0C)H

CMQ

bC.1-f

113

tunnel and are neglected.

Water droplets are injected into the flow by a spray

head which consists of 20 full-cone center-jet nozzles (SPRACO

Model 3B), each delivering about 0.3 gallons per minute of

water (S8). The drift quantity and droplet size spectrum

can be controlled by means of the spray flowrate valve located

above the pump. The valve is a PVC ball valve and the pump

is rated at two horsepower. The droplets produced by the nozzles

lie mainly in the 5 to 200pm diameter range. A Fulflo

water filter with a cellulose acetate honeycomb cartridge

that has a removal rating of 20 m filters out any solid

particles in the circulating water that might plug the spray

nozzles. The facility is slightly tilted so that water will

run down to a drain and be collected in the water tank. This

recirculating water is changed to fresh, clear water before

an experiment is performed.

The vertical test section in which the eliminators are

installed is shown in Fig. 4.2.1. Eliminators could also

be installed horizontally in the horizontal test section of

the facility. However, in the work reported in this thesis

the eliminators have all been installed in the vertical test

section. This is done so that no significant water film can

accumulate on the eliminator walls; also the droplet entrance

conditions are simpler and are consistent with the theoretical

calculations.

Three types of industrial drift eliminators have been

114

received from cooling tower vendors. They are the following:

(A) Belgian-Wave (sinus-shaped) eliminator

(B) Hi-V eliminator

(C) Zig-Zag eliminator

The eliminators are cut into suitable lengths so that

they can be fitted into the test section of the facility.

These eliminators are secured by special eliminator holders,

which can hold eliminators of different lengths. The holders

can adjust the pitch of the eliminators and the angle inclined

to the air flow direction. The holders are made of aluminum to

resist corrosion in the humid environment of the facility.

4.3 Drift Measurement Techniques

There are many methods for measuring the water droplet

size distribution of water entrained in an air flow stream.

In the work reported here, the laser light scattering technique

is used because of its capability to measure very small water

droplets online. This technique is' similar to the PILLS

system developed by the Environmental Systems Corporation

(S2,S4).

Soon after the laser was developed, it was recognized

to be extraordinarily useful for light scattering studies

because of its monochromaticity, high power density, spatial

coherence in the TEMoO mode, temporal coherence, and the small

divergence of a laser beam. The laser used in the present

study is a steady-state, Helium-Neon gas laser (Spectra-

115

Physics Model 125A) which provides 50 milliwatts of single

transverse mode optical power at 632.8 nm. The schematic

diagram of the droplet measuring instrument shown in Fig. 4.3.1

illustrates the general principle of this light scattering

technique for sensing flowing droplets. The laser light

source illuminates a narrow beam in the medium where the water

droplets are flowing. The illuminated water droplets scatter

light in all directions. The scattered light intensity is

related to the parameters of the scattering medium and to

the geometry of the apparatus through the familiar Mie theory

(M5, V1). It has been found that the scattered light intensity

Is, at any angle can be related to the size of the spherical

water droplet by the relation

Is = Kd 2 (4.3.1)

where K is the proportionality constant and d is the droplet

diameter. Fig. 4.3.2 shows a plot of scattered light

intensity versus droplet size calculated by the DAMIE code.

A description of the code is given in Appendix B. It can be

observed from this figure that Eq. 4.3.1 holds. A scattering

volume, designated V in Fig. 4.3.1, is defined by the inter-

section of the laser beam and a collimated photodetector

acceptance cone, The acceptance cone is defined by the two

1000 m diameter apertures in front of the detector. The

photodetector is an RCA Model 7265 photomultiplier tube. This

is a 14-stage, head-on type detector having an S-20 spectral

response. It is placed at an angle of approximately 30° to

116

cn

SL4

cin0a)

-4 cW ; > ¢ ( C 4 ;

bO

-' 0d 4H-

CO0 O

e: Eb :j

'H SI)H

r.,-tQ a)

bC

CL

I

117

e_ _ _ __

105

wL-4

z-4

103

103

101 102 10 3

DROPLET DIAMETER (m)

Fig. 4.3.2 Scattered Light Intensity Versus Droplet

Size Calculated by DAMIE

118

the laser beam, which was found to be optimum. When a droplet

passes through the scattering volume, light is scattered and

detected by the photomultiplier tubes,producing a voltage

pulse. The height of the pulse represents the scattered intens-

ity. The pulse is amplified and recorded in a multichannel

analyzer. The multichannel analyzer determines the pulse

height and records each pulse in an appropriate channel. The

analyzer used in this work is an NS 900 pulse height analyzer

with 1024 channels. It can record pulse heights of zero to

eight volts. In the current work, only 256 channels are used.

It has been demonstrated,by using a standard pulse generator,

that this analyzer is capable of analyzing the typical pulse

shapes encountered in the experiments. The spectrum being

recorded represents the droplet size spectrum of the droplets

passing through the scattering volume.

This measuring technique was developed from the PILLS

system (S2). Limitations of the PILLS system due to fog-

induced background signals havebeen reported in field measurements

of drift in cooling towers, but are nonexistent in this lab-

oratory work since cold water is used in the experiments.

Multi-particle scattering can be avoided by controlling the

size of the scattering volume and by adjusting the drift density

appropriately. A single droplet is never counted more than

once because a steady-state laser is used rather than a pulsed

laser as in the PILLS system, where a slow moving particle may

remain in the scattering volume during more than one laser pulse.

119

Other background signals are derived from the high-voltage

power supply, photomultiplier tube, amplifier, and from any

surrounding light sources. These contribute very little to

the measured signal and are neglected.

4.4 Calibration of the Drift Measurement Instrumentation

A calibration is necessary in order to find the voltage

response of the drift measurement instrumentation versus the

droplet size. The instrument is calibrated by introducing

monodisperse water droplets of certain sizes into the scatter-

ing volume and noting the output signals. Monodisperse means

that the droplets all have the same size. Monodisperse drop-

lets are generated by a Berglund-Liu Monodisperse Aerosol

Generator, on loan from Thermo Systems, Inc. This generator

produces water droplets of a certain uniform size by utilizing

a vibrating orifice. Its operation is based on the instability

and uniform breakup of a cylindrical water jet under mechanical

disturbances (B1). When these mechanical disturbances are

generated at a constant frequency and with sufficient amplitude

in a liquid jet of constant velocity, the jet will break up into

equally sized droplets. To form a source of monodisperse drop-

lets, these uniform droplets must be dispersed and diluted

before they recombine. The generator is unique in that it can

produce droplets of a known size, the droplet size being calcu-

lable from the generator operating conditions to an accuracy

of 2%. The droplets generated are exceedingly uniform in size-

the standard deviation is approximately 1% of the mean droplet

diameter (B1).

120

A schematic diagram of this generator is shown in

Fig. 4.4.1 . It consists of four major parts :the liquid

feed system, the droplet generator, the droplet dispersion

system, and the wave generator. The liquid feed system is a

syringe pump which forces water through a membrane filter at

a constant rate into the droplet generator. The rate is

determined by noting the time (using a stop watch) in which

a known volume of liquid is forced into the droplet generator.

The droplet generator pictured in Fig. 4.4.2 consists of a

stainless steel cup with a 1.15 in. diameter flange and a

hole in the bottom. A 0.375 in. O.D. orifice disc is placed

in a groove inside the bottom of the cup, a Teflon O-ring is

placed on top of the orifice disc, and a stainless steel cap

is tightened onto the O-ring holding the orifice disc in

place. A ring-shaped piezoelectric ceramic with two silvered

faces is epoxied to the flange on the cup with conductive

epoxy. The liquid from the liquid feed system is fed through

the cap into the cup and is then sprayed through the orifice.

An A.C. voltage from the wave generator is applied to the

piezoelectric ceramic which vibrates the cup and disturbs the

liquid et at a constant adjustable frequency. Because the

syringe pump delivers the liquid at a constant rate, the liquid

Jet breaks up into uniform droplets at the frequency of the A.C.

voltage. The uniform droplet stream then enters the dispersion

system. The droplet dispersion system consists of a stainless

steel holder and cover for the droplet generator, a pressure

13~ ZO O0 0

onw ww~~~zZ a-

< CD _) ,,~:~~ <.

0J <c: Z .(, Z.-.~ L.

Z.cr

w: w

W .

121

w

I(n Zr ,--- _

CLIJ

w

a

Q,

O

0

a)

,-IoObO

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-J wC) -,

< LL.

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Cd

r-O0

S~4

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CnLn

a.00-U <

122

DISPERSEDDROPLETS

DISPERSIONCOVER .. .. DISPERSION

Fig. 4.4.2 Schematic Diagram of the Droplet Generating

System

.

123

regulator, a flow meter, and an absolute filter. The cover

has a dispersion orifice through which both the droplet stream

and a turbulent air Jet pass. When the droplet stream mixes

with this air Jet, it is dispersed into a conical shape. The

dispersed droplets are then ready to enter the wind tunnel flow

stream. The droplet generator is placed under the laser light

beam at an appropriate distance so that the droplets are well

enough dispersed to avoid multiple scattering, yet it is close

enough to avoid significant evaporation of the droplets. The

droplets are carried up to the scattering volume by the

normal air flow in the Drift Elimination Facility described in

Sec. 4.2. The scattered light from these droplets is detected

and recorded by the drift measuring instrument in the manner

described in Sec. 4.3.

The water droplet size produced by the vibrating orifice

monodisperse aerosol generator is deduced from a knowledge of

the orifice size, the liquid feed system flowrate, and the wave

generator frequency by

6Q 1/3d (-) , (4.4.1)

f

where Dd is the droplet diameter, Q is the liquid feed flowrate

and f is the disturbance frequency. Table 4.4.1 tabulates some

droplet sizes under typical operating parameters. The droplet

sizes generated in this work range from 50 m to 100 m

diameter. More detailed information on this generator is

contained in Refs. B and T1.

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124

125

4.5 Data Acquisition and Analysis Techniques

Because the laser light intensity is not uniform across

the beam cross section, monodisperse water droplets passing

through the beam will emit different scattered intensities.

The laser light has the Gaussian intensity distribution along

its diameter shown in Fig. 4.5.1, where the laser light

intensity was measured across the beam cross section using a

Spectra-Physics Model 404 laser power meter. Because of this,

the pulse heights recorded in the multichannel analyzer will

not yield a single sharp peak as would be expected from a beam

of uniform intensity if the edge effect is negligible (which is

true when the beam size is much greater than the droplet size).

Figure 4.5.2 shows a typical measured monodisperse

droplet pulse height distribution using 80 m diameter drop-

lets. The location of the peak in the distribution is unique

to this droplet size. This measurement is repeated for several

monodisperse droplet sizes. Fig. 4.5.3 plots the heights of

the peaks versus the droplet sizes. The slope of the curve

in this logarithm plot is very close to two, which verifies

the correlation of Eq. 4.3.1.

Since the measured relationship between an output voltage

pulse and an input droplet size is not unique, a complicated

matrix operation must be used to analyze the measured voltage

distribution. To transform the measured voltage distribution

data into a droplet size distribution the following transform-

ation procedure is used.

126

-2,0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2r0

DISTANCE (MM)

Fig. 4,5.1 Intensity Distribution Across the Laser Beam

Cross Section

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128

129

If the matrix R (v;d) represents the voltage response

function for droplets of diameter d, and if vector A(d) is

the actual size spectrum of the drift, then the measured

voltage distribution vector, M(v), is given as

M(v) = R (v;d) A(d) (4.5.1)

So the actual size spectrum can be determined as

A(d) = R-l(v;d) M(v), (4.5.2)

where R and M are found by calibration and field measurements,

respectively

For 256 channels, the R matrix is a 256 by 256 square

matrix, This matrix is determined from calibration measurement

with the relationship in Eq. 4.3.1. The matrix inversion for Eq.

.4.5.2 is done by the LEQT1F subroutine of the IMSL Library

(I2). A description of the subroutine is given in Appendix A.

To determine the collection efficiency of the eliminators

as a function of droplet size, the droplet size spectra should

be measured at the inlet and outlet of the eliminators. In

the present experiment, the scattering volume is fixed in

space while the eliminators are either placed below the volume

or above it. By placing the eliminators above the scattering

volume the spectrum measured represents the inlet droplet

spectrum, Pin(d), and similarly the spectrum measured when the

eliminators are below the scattering volume is the outlet

spectrum, Pout(d). From these two spectra, the collection

efficiency as a function of droplet size, n(d), can be

130

calculated by

P (d)n(d) = 1 (4.5.3)

Pin(d)

The measured spectra are recorded on paper tape and analyzed

by a computer program called DATANA which performs the response

matrix multiplication and calculates the collection efficiency

if a pair of measured spectra are provided. A description of

this code can be found in Appendix A.

A sensitivity analysis of the effect of the response

function R(v;d) on the collection efficiency calculation was

performed. This was done by using a typical set of measured

voltage distributions at the inlet and outlet of the eliminator,

and the calibration curve. By changing the parameters in the

calibration curve, the sensitivity of the collection efficiency

results are recorded. The parameters include the size of the

monodisperse droplets used for calibration, DC, and NC1, NC2,

and CC1, which are three parameters that specify the cali-

bration curve (as explained in Appendix A). Table 4.5.1 lists

the maximum changes in the calculated collection efficiency

from its mean value as the parameters are individually changed

by 10% from their mean values. It is observed that the only

parameter that yields a significant change in the collection

efficiency is DC, and this change is only significant at small

droplet sizes. It is concluded that the collection efficiency

results are not very sensitive to the response function, and

131

Table 4.5.1

Sensitivity Analysis of the Collection

Efficiency Results

Parameter whosevalue is changedby 10%

Maximum Changein Collection Efficiency

17% at 40 pm

8% at 50 m

4% at 60 m

8% at 40 m

3% at 50 m

No significant change

No significant change

DC

NC2

NC1

CC1

132

the error introduced by the calibration will not amplify the

error in the collection efficiency results.

4.6 Pressure Loss and Air Speed Measurement Techniques

The pressure loss across the eliminators is measured with

a differential electronic manometer (D4). Two static pressure

pitot tubes monitor the static pressure at the inlet and

outlet of the eliminators. The tubes are made of 1/16" ID,

18" long, stainless steel. One pitot tube is located 6"

downstream of the eliminators and the other is located 10"

upstream. They are 21" apart overall. The pressures are

measured at these two points, and averaged over a certain time

period. The differential pressure is first set to zero with

the air flowing, but without the eliminators. In this way

the pressure loss due to other structures will not be included

in the pressure loss measurement of the eliminators.

The sensor is a Barocell differential pressure trans-

ducer (Datametrics Model 570D). The pressure range that can

be measured by this sensor is from zero to 10 torr(i.e., zero

to 0.1934 psi). The pressure-sensing element in this unit is

a high-precision stable capacitive potentiometer; its

variable element is a thin, highly prestressed metal diaphragm

positioned between two gas-tight enclosures which are connected

to the external pressure ports. A difference in pressure

between the two enclosures produces a deflection of the dia-

phragm which varies the capacitance of the diaphragm and the

'133

fixed capacitor plates. The Barocell is wired into a 10 KHz

carrier-excited bridge so that the variable capacitance un-

balances the bridge and produces a 10 KHz signal whose ampli-

tude is proportional to the applied pressure. This A.C. volt-

age is measured by a high-precision electronic manometer

(Datametrics Model 1173), which gives a zero to 1.0 volt D.C.

output. This D.C. voltage is read by a digital voltmeter.

The accuracy of the system is about 0.5% of the reading.

-6The sensitivity of the system is 3 x 10 torr.

The pressure difference can be accurately measured, but

there are other errors in the interpretation due to pressure

fluctuations in the flow turbulence and pressure loss contri-

butions by the eliminator holder structure, which have been

found to be significant. The measured results will be

presented in Chapter 5.

The air velocity is measured with a hot wire anemometer

(Datametrics Series 800-VTP Flowmeter- (D5)). It measures the

average and instantaneous velocities in the flow of air by

considering the cooling effect of the stream on a very thin

electrically-heated wire filament. The probe that holds the

flow-sensing wire filaments is a 3/8" diameter stainless

steel wand. It is inserted into the drift measurement facility

at any point to measure the local, time-averaged air velocity.

The velocity range metered by this system is from zero to

6000 ft/min (0-30 m ). It has a two volt D.C. output connection

for a digital voltmeter. The voltage reading can be converted

.,, I

134

to a velocity with a calibration curve. The accuracy of this

unit is about 2% of the reading. However, due to flow turbulence

and a non-uniform flow distribution, an error of about 10% is

introduced.

The results of these measurements will be presented and

compared with calculations in Chapter 5.

4.7 Sources of Experimental Error

It is difficult to analyze the contributions of the

experimental uncertainties in the final drift measurement

results. In this work, the approach is to repeat the measure-

ments several times, so that the experimental accuracy is

indicated by the variations in the final results. These

measurements include the calibration measurement and the

measurements of voltage distributions at the inlet and outlet

of the eliminators. The results of this test are presented

in Chapter 5. In this section, all possible sources of

experimental error are identified.

(1) The position of the laser beam moves in the first

few hours after it is turned on. Therefore,

a warm up period of at least one hour should be

allowed before any measurement. Movement of

other drift measuring components is not significant

throughout the experiment, which takes about

ten to fifteen hours.

135

(2) Calibration is the most difficult measurement

in the experiment. The droplet generator

orifice is frequently plugged, and sometimes

may be partially plugged, which decreases the

pumping flow rate and thus changes the droplet

size and the uniformity of generated droplets.

Therefore, the flow rate should be constantly

checked throughout a measurement.

One important uncertainty in the calibration

is that the chance of more than one droplet

appearing in the scattering volume is signifi-

cant, although efforts have been made to reduce

this. However, the final results are found not

to be very sensitive to the calibration curve

except at small droplet sizes, as discussed before.

Since the monodisperse droplets are carried by

the flow up to the scattering volume a few inches

away from the droplet generator, the droplet

size will decrease due to evaporation. It was

estimated that this decrease can be as large as

5% for 100 m droplets. This error could intro-

duce an error of 10% in the final results for

small droplet sizes, as was shown previously.

(3) Statistical counting errors are difficult to

estimate because they are not uniform for all

136

droplet sizes, but become larger for bigger

droplets. In the data analysis, the distribu-

tion is smoothed, and this will eliminate some

of this error. Dead time in the pulse height

analyzer contributes another uncertainty to the

results. Since the drift rate is much higher

at the eliminator inlet than at the outlet, the

dead time is very different for the two distri-

butions, and it is found that the analyzer used

in this work cannot account for this very well.

(4) There is a possibility that more than one drop-

let may appear in the scattering volume and cause

the analyzer to record a wrong signal. This

possibility cannot be avoided but can be reduced

by decreasing the size of scattering volume and

by reducing the quantity of drift. This error is

thought to be small.

(5) The quantity of drift fluctuates with time due

to the pumping power fluctuations and changing

conditions within the Drift Elimination Facility.

However, if the data acquisition time is long

(three to five hours in the present experiment),

this fluctuation will average out in the measured

results.

137

The pressure drop across the filter in the

circulating water system increases with time

because of the gradual plugging of the filter

by foreign particles in the circulating water.

This affects the quantity of the drift generated

by the facility. But the effect is small during

one test.

(6) Signal noises that may contribute to the measure-

ment uncertainty consists of electronic noise

in the amplifier and high voltage supply, the

dark current of the photomultiplier tube, and

scattered light from other sources. It is found

that these noises contribute about 10% to the

lowest recordable signal and become insignificant

for larger signals.

(7) The laser light intensity at the measuring

point depends on the drift concentration which

shadows some of the laser light. However, by

measuring the intensity at the scattering volume

with a power meter for different drift concen-

trations, this effect was found to be almost

undetectable.

138

The above discussion gives possible sources of

experimental uncertainties. In Chapter 6, a quantitative

analysis of experimental errors is developed.

139

CHAPTER 5

COMPARISON OF EXPERIMENTAL RESULTS

WITH THEORETICAL CALCULATIONS

5.1 Introduction

In this chapter the experimental results for the drift

collection efficiency and pressure loss across some industrial

cooling tower drift eliminators are presented. These results

are compared with the calculations from the DRIFT code. The

experimental measurement techniques are discussed in Chapter 4,

and the numerical simulation techniques in the DRIFT code are

described in Chapter 2.

Three industrial drift eliminators were donated for this

study by cooling tower vendors. These are the Belgian-wave elim-

inator, the Hi-V eliminator, and the Zig-Zag eliminator. Their

geometries and dimensions are shown in Fig. 5.1.1. The Belgian-

wave eliminator is made of sinusoidally shaped asbestos cement

board, and it has a uniform flow channel cross section. The Hi-

V eliminator is made of polyvinyl chloride. Its flow channel

cross section is not uniform, as shown in Fig. 5.1.1. The

Zig~Zag eliminator is made of fiberglass. Its flow channel

cross section is uniform, except at the corners.

The measured pressure losses across these eliminators are

compared with calculated pressure losses in Section 5.2, and the

collection efficiency comparisons are presented in Section

5.3, The data is developed at two air speeds, 1.5 m/s and

2.5 m/s.

140

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5.2 Pressure Drop Across Eliminators

Table 5.2.1 is a comparison of the theoretically

calculated pressure losses across the three types of drift

eliminators with the experimentally measured values at an air

speed of 1.5 m/s. Table 5.2.2 presents the same comparison

at an air speed of 2.5 m/s. The true air speeds are slightly

different for each eliminator, since their flow resistances

are different.

The calculated and measured results are in good agreement,

and are within the bounds of experimental error. It is clear

from the data that as the geometry of the drift eliminator

becomes more complex, the pressure loss increases. Since the

drift collection efficiency also increases with increasing

.geometrical complexity (shown in Section 5.3), it is necessary

to strike a compromise in designing an eliminator that will

achieve an acceptable pressure loss and an acceptable collec-

tion efficiency. The values in brackets are the resistances

of the eliminators to the air flow expressed in terms of

velocity heads corresponding to the nominal air speed. This

is an advantageous way to report the data since its numerical

value for a particular eliminator is independent of the air

speed and the working fluid if the flow is fully turbulent.

The theoretical pressure loss calculations for the Zig-

Zag eliminator have been unsuccessful because of the complex

eliminator geometry and because of the limitations of the

calculational method in describing turbulence (see Chapter 3).

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However, the agreement of the calculated and measured results

for the other two, more simple geometries, demonstrates that

the calculations are valuable in reasonably smooth geometries

for predicting pressure loss.

Comparing Table 5.2.1 and Table 5.2.2, it is found that

the pressure loss increases approximately as the square of the

air speed for all three eliminators. The observations made

about Table 5.2.1 also apply to Table 5.2.2.

The pressure losses for these eliminators quoted by their

vendors are higher than the values presented here (H6, S9).

The reason is that in their measurements, the pressure differ-

ences with no eliminators installed were not set to zero.

This means that their measured data include the pressure loss

due to other structures, which are considerable in comparison

with just the pressure loss across the eliminators.

5.3 Collection Efficiency Results

In this section, the calculated and measured collection

efficiency results are presented. Fig. 5.3.1 shows the drop-

let collection efficiency as a function of droplet size for

the Belgian wave eliminator at an air speed of 1.5 m/s. The

measured data are presented as a broken line in the figure.

The experimental technique is described in Chapter 4. The

calculated results using both no-slip and free-slip boundary

conditions are compared with the experimental results. It

is found that the calculated and measured droplet capture

145

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efficiences agree well for this smooth eliminator geometry,

with the no-slip boundary results providing more accurate

predictions. It is also found that droplets smaller than 60

um in diameter can easily escape from the eliminator.

The calculated and measured collection efficiency data

for the Hi-V eliminator are shown in Fig. 5.3.2. It is found

that this eliminator is more efficient in capturing droplets

of any size than the Belgian wave eliminator. Also, the agree-

ment between the no-slip prediction and the measurement is

reasonably better than the agreement between the free-slip pre-

diction and the measurement. The no-slip result predicts a high-

er collection efficiency than the measured data, while the free-

slip prediction is generally lower than the measured data.

Figure 5.3.3 displays the data for the Zig-Zag eliminator.

The calculation of the air velocity distribution for this elim-

inator failed to achieve asymtoptic values using no-slip

boundary conditions, as discussed in Chapter 3. By using the

calculated distribution of the nonasymtoptic solution, approx-

imate results of droplet collection efficiency for this elim-

inator were obtained. This is compared with the free-slip

prediction and the measured data in Fig. 5.3.3.. This approx-

imate result predicts a higher collection efficiency than the

free,slip prediction, and agrees with the measured data better

than the free-slip prediction in general.

Figure 5.3.4 shows the data at high fan speed,

where the calculated results are no-slip prediction. Similar

conclusions can be made from this figure.

147

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150

5.4 Estimation of Experimental Error

A qualitative discussion of the sources of experimental

errors is given in Chapter 4. It was mentioned that the quanti-

tative contributions of those uncertainties in the data are

not easily accounted for. In this work only the repeatability

of the measured data is established. This is done for each

eliminator by repeating the measurements several times under

similar conditions.

Table 5,4.1 shows the results of four measurements on the

Zig-Zag eliminator at an air speed of 1.5 m/s . The measure-

ments included the calibration run and the droplet size

distribution measurements at the inlet and the outlet of the

eliminator. The data was taken on different days. From

these results it can be seen that the data is repeatable with

a maximum standard deviation of about 10% at the smallest

droplet size.

The results for the Zig-Zag eliminator are the most

consistent among the three eliminators tested in this work.

The reason is that this eliminator is constructed in one block

so that the pitch and the inclination of the louvres always

remains the same even though it was taken out after each

measurement, The other two eliminators are furnished in

pieces which are installed by using the eliminator holders

described in Chapter 4. When taking these eliminators in and

out of the test section, it is difficult to repeat the exact

pitch and angle of inclination. Therefore, for the Belgian

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152

wave and the Hi-V eliminators the results are not very

repeatable; the maximum standard deviation is as high as 20%.

The discrepancy between the calculated and measured

results is discussed further in Chapter 6.

153

CHAPTER 6

CONCLUSIONS AND RECOMMENDATIONS

6,1 Discussion of Results

It was demonstrated in previous chapters that predictions

of collection efficiency and pressure drop for some drift

eliminators by the DRIFT code agreed fairly well with measured

results. The discrepancies are due to the experimental un-

certainties and the calculational and experimental assumptions.

The results are discussed in this section.

It was indicated earlier that both the calculated and

measured pressure drop results of this work are significantly

lower than the values quoted by cooling tower vendors. This

is due to a difference in the definition of pressure drop.

The vendors include in their definition the pressure loss due

to structures other than the eliminators themselves, and this

contributes a significant amount to the measured pressure loss.

The collection efficiency results reported in this study

are higher than expected because these results generally

show 100% efficiency for droplets larger than 100 m, yet

droplets much larger than this have been found to escape

actual cooling towers. This is probably due to the assumpt-

ions made in the calculations and the simplified conditions

in the experiments. Droplet growth effects,water film

effects, and flow turbulence are thought to be the main

factors. These effects are discussed here.

154

(1) Water film effects

The droplet collection efficiency calculations have

ignored the possible effects of the water film on the elimi-

nator walls. Two effects arise from the drag of the exhaust

flow on the water film, and another effect arises from the

impacting of captured water droplets on the film. The

presence of the water film modifies the exhaust flow boundary

conditions from simple no-slip conditions to those of matching

the air-water velocities at the gas-liquid interface. Except

in the case of a thick film, the effect of this complicated

boundary condition on the velocity distribution within the

eliminator should be small. Also, drag on the liquid film

can lead to droplet generation because water can be drawn off

of the trailing edge of the eliminator, or droplets can be

stripped from the film surface through the formation of Helm-

holtz instability waves.

The work of Yao and Schrock (Y1) indicates that at an air

speed of 2.0 m/s in a smooth drift eliminator geometry the

minimum film thickness required for droplet stripping is 0.2

mm, and that substantially higher air speeds are required for

droplet generation via pickup from the peaks of Helmholtz

instability waves for a film of this thickness. In the present

work, the water film thickness on the eliminator walls was

not measured, however, visual observations were unable to

detect either droplet stripping at the trailing edge of the

eliminator or droplet generation on the interior walls. The

155

absence of droplet stripping at the outlet is implicit

evidence for the absence of wave generated droplets in the

interior (Y1).

With sufficiently thick films and with droplets impacting

at sufficiently acute angles and high velocities, it has been

observed that a droplet can rebound from the film, or "bounce"

back into the exhaust flow (J2). This droplet bouncing

problem is thought to be significant for drift eliminator

performance in actual cooling towers where the water loading

on the eliminator is high and the water film is thick.

Foster et al. (F3) studied this problem and observed that this

effect is indeed significant, however, they found that many

droplets meeting the impact conditions established by Jayar-

atne and Mason (J2) did not bounce. It was concluded that

it is not possible to estimate the true importance of droplet

bouncing in a real tower environment due to the lack of

information about the surface water coverage. Further work

on this effect is being carried on by Foster in the Central

Electricity Research Laboratories (F5).

(2) Droplet growth effect

It was mentioned that droplets as large as several

hundred microns could escape commercial cooling towers out-

fitted with the drift eliminators being tested in this work.

According to the collection efficiency results for these

eliminators, these droplets should have been trapped. It is

156

suggested that the droplets might bypass the eliminators

through the openings around the tower structure. It might

also be due to the stripping and rebounding effects in the

water film as discussed earlier. Another possibility that

has so far been overlooked in the literature is droplet

growth in cooling towers. It has been suggested that droplet

growth is not significant in a cooling tower because a small

drift droplet, moving at a velocity approaching that of the

air stream, might leave the top of the tallest natural draft

tower in less than one minute from the time it passes through

the eliminators. If that is true, then even though the air

in the surrounding air stream is generally saturated, the time

span is too short for any significant droplet growth. However,

this is not true for some droplets in cooling towers. Large

droplets (>100 pm) do not travel at the air stream speed

because their terminal velocities approach that of the air

stream speed as shown in Fig. 6.1.1. Therefore they will

stay in the tower for a long time. Another factor that causes

some water droplets to reside in a cooling tower for a long

time is the air flow pattern inside the cooling tower. The

turbulent effect, the quiescent region, and the variation of

air velocity at the throat of the shell (in the case of a

hyperbolic cooling tower) can prolong the residence time of

water droplets inside the tower, thus making the growth effect

significant. This effect will not only change the size dis-

tribution of the escaping drift, it will also change the

10 100 1000

DROPLET SIZEj MICRON

Fig. 6.1.1 Terminal Velocities of Water Droplets

157

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158

drift chemical concentrations.

(3) Turbulence effects

In the theoretical calculation of the performance of a

drift eliminator, it is assumed that the air flow is laminar,

and that the turbulent wake region is neglected. However,

for some eliminator geometries, this wake region extends

over a large portion of the eliminator cross section. In this

work, flow visualization is performed for three eliminators:

the Belgian wave eliminator, the Hi-V eliminator, and the Zig-

Zag eliminator. The flow is established in a long, two foot

wide free surface flume. The working fluid is water, instead

of air. The water depth is about three inches and the water

flow velocity was adjusted to be about 0.1 m/s so that the

Reynolds number matches that of a flow of air whose velocity

is 1.5 m/s. Blue dye was injected at the eliminator entrance

and at the middle of the water deptjh to get away from the

free-surface and boundary layer regions, each of which is

about half an inch thick. The dye was injected at the elim-

inator boundaries so that wake regions could be observed.

Photographs were taken of these dye traces for the three

eliminators. To observe the general flow pattern within these

eliminators, tiny paper chips were sprinkled on to the water

surface and time-exposure pictures recorded the trajectories

of these chips. The results of these simple experiments were

159

quite satisfactory.

Figure 6.1.2 displays the wake regions in the Belgian

wave eliminator by injecting dye into the flow. The water

enters at the right side of the picture where the dye inject-

ion tubes are shown. It can be seen that a significant

wake region exists at the lower boundary and another wake

region exists in the second half of the upper boundary. Fig.

6.1.3 shows the flow pattern by using paper chips. The water

enters at the right side of the picture where the dye inject-

ion tubes are shown. This picture also shows the wake region

at the central portion of the lower boundary where recircu-

lation occurs. The calculated velocity distribution using

no-slip boundary conditions shown in Fig. 3.2.5b simulates

these regions with almost stagnant regions. These regions

are poorly represented if free-slip boundary conditions are

used (see Fig. 3.2.5a).

Similar observations can be made for the Hi-V elimina-

tor. Figs. 6.1.4 and 6.1.5 show the wake regions and flow

pattern respectively. Again,the wake regions exist at the

lower boundary and the second half of the upper boundary.

These wake regions are larger than those in the Belgian wave

eliminator. In the calculation these regions are represented

by stagnant regions if no-slip boundary conditions are used,

as shown in Fig. 3.2.6b. Again, the free-slip result cannot

account for these regions very well.

Figures 6.1.6 and 6.1.7 show the same set of pictures

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166

for the Zig-Zag eliminator. It is seen that the wake regions

are very large for this eliminator. In fact, the third layer

of this eliminator is so turbulent that the dye is well-mixed.

Since the flow is so turbulent in this layer, the pressure

drop in this layer will be greater than the pressure drop in

either of the other two layers. As discussed in Chapter 3

the third layer has little effect on the capture efficiency

of this eliminator, and by taking off this layer great

savings can be realized in cooling tower operation without

producing additional drift.

The calculated velocity distributions using either no-

slip or free-slip boundary conditions, as shown in Figs.

3.2.7 and 3.2.8, cannot account for these turbulent wake

regions. However, the no-slip prediction gives a better

approximation than the free-slip prediction, and the no-slip

results predict the flow pattern quite well in the first two

layers where most droplets are captured. Therefore, the

collection efficiency calculated using these results should

be close to the actual result.

For this eliminator it can also be seen that at the

entrance of the upper boundary there is flow diversion. This

is caused by a pressure difference above and below the elimi-

nator boundary. It is expected that this would not affect

the-collection efficiency of the eliminator but would certainly

increase the pressure drop, and thus it is not desirable. In

order to avoid this flow diversion, the eliminator walls at

167

the entrance should be more parallel to the inlet flow.

From these flow visualization photographs it is con-

cluded that turbulent wake and eddy regions occur in all the

eliminators investigated. These effects are especially sig-

nificant in complex geometries. In the calculations, the

turbulence effects are not accounted for and the wakes are

not completely resolved. In order to achieve an exact

solution, the mesh size should be reduced enough so that re-

circulating eddies can be fully resolved, and a turbulence

model must be included in the equations. However, in view

of the success of the present calculation for predicting

the experimentally observed behavior of the drift eliminators,

it was decided that this more expensive and complicated

approach would not be required. The reason for the success

of present approximation is that by using no-slip boundary

conditions, the calculated velocity distributions represent

the actual flow patterns quite well as observed by comparing

the flow pattern photographs in this section with the velocity

distribution plots in Chapter 3. Although the eddy and turb-

ulent wake regions are not exactly described in the calculated

velocity distribution, these regions are approximated by

stagnant regions. Moreover, the water droplets seldom travel

into these regions as seen in the droplet trajectory plots

displayed in Section 3.3. Therefore, using this approach,

the collection efficiency can be fairly accurately calculated.

However, the pressure drop depends greatly on the existence

168

of turbulence, and thus it cannot be accurately predicted

by these calculations if significant turbulence occurs in the

eliminator. For smooth geometries the predictions agree quite

well with measurements, but for complicated geometries (such

as the Zig-Zag eliminator), the calculation predicts a much

smaller pressure drop than the measurement.

Another factor that the calculation does not take into

account is the air turbulence inside cooling towers. In order

to solve this problem, it is necessary to have a turbulence

code to calculate the air velocity distribution inside elimi-

nators, and also to have quantitative information about the

nature of air turbulence inside cooling towers. However, this

quantitative information is not well known. Martin and Barbar

(M3) have indicated the possible variations in the velocity

of air approaching an eliminator, but it is also important

to know the frequency with which this variation occurs. Some

idea of the variation in flow direction was obtained using

an ammonium chloride smoke generator (F3). It was suggested

that the variation was sensitive to the ambient wind conditions,

fluctuating approximately 100 about the vertical with a one

second period when the wind was gusting strongly, and remaining

steady when the ambient conditions were calm. However, these

observations were made close to the tower center, and larger

variations would be expected towards its perimeter. The

positioning of towers relative to other constructions might

also be an important factor in this respect.

169

The following conclusions are made in this study:

(1) The calculational method can accurately predict the

collection efficiencies of cooling tower drift

eliminators

(2) The pressure drop calculations are reasonably good

for smooth eliminator geometries. For eliminator

geometries with sharp corners the calculation pre-

dicts much smaller pressure drops than the actual

values.

(3) The design of the Zig-Zag eliminator is economically

unsound, The third layer of this eliminator should

be removed. By doing this, the drift collection

efficiency will not be significantly affected, yet an

appreciable savings from the reduced pressure drop

will be obtained.

(4) The E-E eliminator designed by Yao and Schrock

collects droplets very efficiently as predicted by

the designers, yet the pressure drop is much higher

due to the occurrence of flow separation. Therefore,

this eliminator does not appear as promising as its

collection efficiency shows.

(5) In order to achieve a high drift collection efficiency

the drift eliminator geometry should be as complex

as possible. However, the pressure drop will also

increase as the geometry becomes more complex. It

is found that an eliminator yielding a higher collection

170

efficiency will always have a higher pressure

drop. Table 6,1,1 demonstrates this point. The

table shows the calculated collection efficiency

(using no-slip boundary conditions) for some

common drift eliminators at an air speed of 1.5 m/s.

The values of pressure drop presented in the table

are either experimental results, where available,

or calculated results. The calculated pressure

drop results for complicated geometries with sharp

corners might not be reliable. This table shows

that more complex geometries have better collection

efficiencies yet higher pressure drops.

Up to now, there is no available technique for designing

drift eliminators that optimizes between the collection

efficiency and the pressure drop. It is therefore suggested

that in designing a drift eliminator for a particular cooling

tower, a pressure drop limit across the eliminator that can

be tolerated should be set first. Then an eliminator geometry

should be chosen that has a pressure drop lower than the set

limit, yet has the best collection efficiency. This can be

done theoretically with the DRIFT code, After selecting the

eliminator geometry in this way, it should be constructed and

tested in an experimental facility to check that the overall

drift emission is lower than the environmental standard set

by the Environmental Protection Agency. This approach will

171

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certainly save a lot of unnecessary effort and money while a

better eliminator is designed.

6,2 Recommendations

The results from the DRIFT code in this paper suggest

that this code is very useful in the evaluation and design of

cooling tower drift eliminators. The following future work

on this numerical technique is recommended:

(1) It has been shown that the air velocity distribution

inside an eliminator calculated by the SOLASUR sub-

routine using no-slip boundary conditions approximates

the actual flow pattern quite well. In order to

further validate this calculation, a spatial

measurement of the air velocity distribution inside

the eliminator would be appropriate. There are

many such measurement techniques; a suitable one

would be the Laser Doppler Anemometer (LDA) tech-

nique which is commercially available. Fig. 6.2.1

shows a recommended test section for this purpose

and for the droplet dynamics experiments which

are described later. The LDA technique will not

only measure the velocity values but also the turb-

ulent flow parameters. These will be very useful

for investigating the eliminator performance.

(2) The droplet trajectory calculation performed by the

173

AIR

MONODISPER'DROPLETGENERATOR

t

INATOR

T WIRE

EMOMETER

AIR

Fig. 6.2.1 Schematic Diagram of the Proposed ExperimentalSetup for Studying Droplet Trajectory and AirVelocity Distribution in Drift Eliminators

174

DRIFT code can be checked by a simple experiment.

The suggested experimental setup is shown in Fig.

6.2,1. A small exhaust fan will induce the required

air flow. Drift eliminators are installed in a

test section that consists of plexiglass walls

and a flow channel that is several inches thick.

The nominal air speed can be measured by hot wire

anemometer at the inlet region of the eliminator.

Colored water droplets generated by a monodisperse

droplet generator are introduced below the elim-

inator . Their trajectories can be observed with

a high-speed cine camera, These trajectories can

be compared with calculated results. This experi-

ment can also study the droplet rebounding effect

at the walls. Water film effects can also be

studied by introducing a water film at the elimi-

nator walls. Since the test section is small, it

can be placed either horizontally or vertically.

As mentioned in (1), the air velocity distribution

inside the eliminator can also be measured by an

LDA technique with the eliminators installed in

this test section. This basic experiment could

validate the present calculation as well as provide

improvements to the code concerning the droplet

rebounding and water film effects,

175

For the design of drift eliminators, the following

recommendations are made:

(1) It is found from the present calculation that the

third layer of the Zig-Zag eliminator serves no

purpose in capturing drift droplets, and thus should

be removed to reduce the pressure drop across the

eliminator. Also, to avoid flow diversion at the

eliminator entrance, the boundaries should be reshaped

so that they are parallel to the flow. An experimental

test of the performance of the Zig-Zag eliminator

with only two layers and a smoothed entrance is

recommended.

(2) The performances of many common drift eliminator geom-

etries have been evaluated in this work either by

numerical simulation or experiments. However, there

are still many other eliminator designs that have been

used commercially, and some potential designs that are

worth investigating. These include the Chevron-type

eliminator used by French cooling tower vendors, a

helical flow channel design with smooth inlet and outlet

nozzles, a "polisher" eliminator design, and many others.

(3) Total drift emission is the most important parameter

of the environmental acceptance of cooling tower

drift. Therefore, after selecting a particular

eliminator design, it is necessary to test the

176

design for its total drift emission. However,

none of the available drift measurement techniques

has been proven to be generally satisfactory-,to

the point of being adopted for general use (Al).

A reliable technique for drift emission measurement

is needed.

It is proposed that future work should be

performed to demonstrate the feasibility of using

a radioactive tracer for absolute drift rate measure-

ments, The suggested candidate tracer is Na24

(T1 = 15 hr.; Ey's = 2.75 Mev and 1.37 Mev) which

23can be produced from irradiating stable Na (in

NaOH form) in a nuclear reactor. After irradiation,

the activated solution will be neutralized with

HC1, and injected into the recirculating water flow

in the experimental drift facility. Because the

air flow in the wind tunnel is recirculated and

rapidly becomes saturated, it is expected that drop-

let evaporation will be negligible. Thus, the salt

concentration in the entrained droplets should be

the same as in the recirculating water, making

possible a direct comparison of drift rates measured

by drop-size spectra methods, and by deducing the

total salt current using the radioactive tracer.

This point has been a problem in the past in inter-

comparisons between various drift measurement methods -

177

those methods which observe total salt flow rate

(e.g., isokinetic samplers, cyclone samplers, etc.)

do not provide a measure of the droplet spectra,

and those methods which observe the droplet spectra

(e.g., the PILLS systems sensitive paper sampling)

do not provide information regarding the total

salt current without some assumption being made

regarding the salt concentration in the droplets

due to evaporation or growth. This is difficult to

provide since evaporation and growth rates vary

with droplet sizes.

In the test the salt current will be sampled

with an array of NaI detectors that scans a trans-

verse section of the experimental drift facility

so that the total amount of radiation observed will

be directly proportional to the amount of salt that

flows past the measurement station.

For a reasonably accurate (2%) experiment

it is estimated that the laboratory demonstration

will require approximately 10 mCi of activity

injected into the recirculating water. For a field

test roughly 10 Ci of activity would be required,

depending upon the desired accuracy and the extent

of the NaI detector array, It is envisioned that

this measurement technique would be used sparingly

for absolute drift measurements,and that less accurate

178

methods would be sufficient for routine drift

monitoring. In field applications the total amounts

of released activity would be no greater than those

currently encountered on a chronic basis with

boiling water reactors.

In conclusion, the DRIFT code is quite capable of

predicting the performance of cooling tower drift eliminators,

although some care should be taken in the pressure drop

calculations for complex (sharp-cornered) eliminator geom-

etries. This code should be very useful in evaluating drift

eliminator performance to aid in the design of drift elimi-

nators for any cooling tower. Provisions for the effect of

water film on the eliminator walls, of flow turbulence within

the eliminator, and of droplets rebounding from the elimina-

tor walls should be investigated and developed to supplement

the DRIFT code.

179

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M6 Marguardt, D.W., "An Algorithm for Least-Squares Esti-mation of Nonlinear Parameters," Journal of the Societyfor Industrial and Applied Mathematics, Vol. 11, No. 2,June 1963, pp. 431-441.

R1 Reisman, J.I., and Ovard, J.C., "Cooling Towers andthe Environment - An Overview," presented at theAmerican Power Conference 35th Annual Meeting, Chicago,Illinois, May 1973.

R2 Roffman, A., "Drift Loss from Saltwater Cooling Towers -Some Atmospheric Considerations," Amer. GeophysicalUnion, 54th Annual Meeting, Washington, D.C., April 16-20, 1973.

R3 Roffman, A., et al., "The State of the Art of SaltwaterCooling Tower for Steam Electric Generating Plants,"WASH-1244, Feb, 1973, U.S. Atomic Energy Commission,pp. E.1-E.21.

183

R4 Roffman, A., and VanVleck, L.D., "The State-of-theArt of Measuring and Predicting Cooling Tower Driftand Its Deposition," Paper No. 73-140, presentedat the 66th Air Pollution Control Assoc. Annual Meeting,Chicago, Illinois, 1973.

S1 Schrecker, G.O., Wilber, K.R., Shofner, F.M., "Pre-diction and Measurement of Airborne ParticulateConcentrations from Cooling Device Sources and in theAmbient Atmosphere," presented at the 'Cooling TowerEnvironment-1974' Symposium, March 4-6, 1974.

S2 Shofner, F.M., "Explicit Calibration of the PILLS IISystem," EPA Project No. 16130GNK, EnvironmentalProtection Agency, Sept. 1973.

S3 Shofner, F.M., Schrecker, G.O., Carlson, T.B., andWebb, R.O., "Measurement and Interpretation of DriftParticle Characteristics," presented at the 'CoolingTower Environment-1974' Symposium, March 4-6, 1974.

S4 Shofner, F.M., and Thomas, C.O., "Development andDemonstration of Low-Level Drift Instrumentation,"Environmental Protection Agency Report No. 16131GNK,Oct. 1971.

S5 Shofner, F.M., and Thomas, C.O., "Drift Measurementin Cooling Towers," Cooling Tower, AIChE, New York,N.Y., 1971.

S6 Shofner, F.M., Thomas, C.O., Schrecker, G.O., Lyon,C.R., Carlson, T.B., and Bishop, A.O., "Measurementof the Drift and Plume Characteristics of PEPCO'sChalk Point Unit #3 Cooling Tower, Phase One:Experimental Design," Final Report submitted to Mary-land Department of Natural Resources, Baltimore,Maryland, August, 1973.

S7 Shofner, F.M., Watanabe, Y., and Carlson, T.B.,"Design Considerations for Particulate Instrumentationby Laser Light Scattering (PILLS) Systems," ISATransactions 12, 1973, pp. 56-61.

S8 "SPRACO Spray Nozzles and Industrial Finishing Equip-ment," Catalog 73, Spray Engineering Company, Burling-ton, Mass.

S9 Stewart, Paul B., Personal Communication, CeramicCooling Tower Company, Fort Worth, Texas, Jan. 20, 1977.

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185

APPENDICES

186

APPENDIX A

DATANA PROGRAM

A.1 Introduction

In the drift measurements by laser light scattering the

voltage distribution, M_(v), recorded by the multichannel analy-

zer is not the true droplet size distribution, P(d), as

mentioned in Chapter 4. However, these two distributions can

be related by

M(v) = R(v;d) P(d) , (4.4.1)

where R(v;d) is the voltage response matrix to droplets of

diameter d.

In order to recover P(d) from the measured distribution

M(v) in Eq. 4.4.1, a system of linear algebraic equations must

be solved. The DATANA program transforms the measured spectra

at the inlet and outlet sections of the eliminator to the true

droplet size spectra so that the collection efficiency as a

function of droplet size can be determined.

This appendix describes this program in detail. The

necessary input parameters are described in Section B.3. A

listing of the program and a sample problem are also given.

A.2 Description of the Program

The DATANA computer code is written in FORTRAN IV and

analyzes the measured voltage pulse height distribution. This

187

distribution represents the scattered light intensity distri-

bution produced when a spectrum of droplets passes through

the scattering volume.

The procedures of the code are listed in the flow chart

in Fig,* A.2.1. The calibration parameters determined from a

calibration check of the drift measuring instrument are used

by the program to determine the calibration factors and

response function. To transform a voltage pulse height dis-

tribution into a droplet size distribution, the measured

distribution is first smoothed by a least-squares fitting in

the LSMARQ subroutine. This subroutine can use any approp-

riate fitting function that is supplied by the user through

the external function YFCN. It is found that a polynomial of

the form8 a

f(x) = i- (A.2.1)i=l x

provides the best fit of the typical measured distributions.

Guessed values of the parameters ai are input by user, and

best fit.values of ai are calculated by the subroutine. The

transformation of the measured distribution to the droplet

size distribution is performed either by backward substitu-

tion method, if the response function is an upper triangular

matrix, or otherwise by the LEQT1F subroutine, which obtains

a solution of a system of linear equations. The backward

substitution method is the simpler approach and takes less

computation time. Collection efficiencies as a function of

188

Ip

(READ CALIBRATION

PARAMETERS

COMPUTE CALIBRATION

FACTORS

READ MEASURED

VOLTAGE PULSE

HEIGHT DISTRIBUTION

/CALCULATE COLLECTION \

EFFICIENCY?

NO

YES

DO LOOP

I=1, IEFF

DETERMINE

COLLECTION

EFFICIENCY

l

Flow 3hart of the DATANA Code

LEAST-SQUARE

FITTING OF

THE DISTRIBUTION

COMPUTE THE

RESPONSE FUNCTION

1 ~~~

, .

L L ~ ~ -

ii

1---~~~~~~

--- ·I . I

w .

--

l_ . .

I

Fig. A.2.1

189

droplet size can be determined when two measured distributions,

one at the inlet and one at the outlet of the eliminator, are

provided,

The DATANA code uses several subroutines. They are

described below.

(A) LSMARQ

The subprogram LSMARQ computes the solutions of non-

linear least-squares curve and surface-fitting problems. That

is, LSMARQ finds values of bl,b2,...,,b p , which minimizes

nE Wi(Y-f(x i,lsXIsx im xi ;bllb2...lbp)), (A.2.2)

i-1

where the fitting function f depends on m> 1 independent varia-

bles ( lxi ,...,xim)' and on the p unknown parameters, bj.i~l' l i,2i .. x,m j

The ith dependent and independent variables, i and xi,l,...Xim'

are known values corresponding to the ith data point or obser-

vation. The number of data points is n, and the wi are para-

meters that weight the errors at each data point.

LSMARQ uses the Levenberg-Marquardt algorithm described

in Refs. B2, L4, and M6. It computes the coefficients of a

partial Taylor series for the fitting function and then uses

the steepest-descent method (or gradient method) to find a

"neighborhood" in parameter-space where the series provides

an adequate approximation to the data.

This subroutine is called by the main program.

190

(B) RSIMQ

This is a subroutine called by LSMARQ. It performs

forward elimination with partial pivoting.

(C) YFCN

This is a user-supplied FUNCTION subprogram, which

computes the function f(x,b) of Eq. A.2.2. This external

function is called from the main program, the LSMARQ, and

RSIMQ subroutines.

(D) LEQTF

This subprogram solves a set of linear equations, AX=B,

for X, given the NxN matrix A in full storage mode.

LEQT1F performs Gaussian elimination (Crout algorithm)

with equilibration and partial pivoting (F4).

This subroutine is taken from the IMSL library (I2), and

is called by the main program.

(E) LUDATF

This subroutine decomposes the N by matrix A into the

matrices U, where L is lower triangular with one's on the

diagonal, and U is upper triangular.

LUDATF is called by LEQT1F. Its algorithm is described

in Ref. I2.

191

(F) LUELMF

LUELMF performs the elimination part of the solution of

a set of simultaneous equations (I2). It is called by LEQT1F.

(G) UERTST

This subprogram prints a message reflecting any error

detected by an IMSL subroutine (2).

A.3 Description of the Input Parameters

Card No 1

I.EFF, IRT

FORMAT (215)

IEFF= 1 for data transformation.only, no collection

efficiency calculation will be performed.

IEFF= 2 for a collection efficiency calculation. In

this.case two spectra, one at the inlet and

one at the outlet of the eliminator, should be

provided.

IRT = 0 if the response function is an upper triangular

matrix where the simpler transformation method

can be used.

IRT 0 if the response function is not an upper triangu-

lar matrix so that the subroutine LEQT1F must be

used.

Card No.2

A,B

FORMAT (2E20.6)

A and B convert the channel number to a voltage pulse

192

height with

voltage = A + B x Channel number.

Card No.3

NC1,NC2,NC3,DC,CC1,CC2

FORMAT (3I5,3F10.3)

These are all calibration parameters and are obtained

from a calibration check of the drift measurement instrument-

ation. DC is the monodisperse droplet size used in the cali-

bration, which is about 80 pm in this work. The meanings of

other parameters are found in Fig.A.3.1, which is a calibra-

tion curve recorded by the multichannel analyzer for mono-

disperse droplets.

Card No.4

NC

FORMAT (I5)

NC is the maximum channel number of the data.

Card No. 5 and Card No. 6

(PARAM(I), I = 1, NPARAM)

FORMAT(4E20.6)

PARAM(I) are the guessed values of the least-square

fitting parameters. They can be set to be 1.0, however,

values closer to the true values will save a lot of computation

time.

NPARAM is the number of parameters. It is 8 in the

present work.

CI-

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193

194

Card No. 7 to Card No. (6+NC/5)

(PV(I), I=1, NC)

FORMAT (4X,5F7.0)

PV(I) is the voltage pulse height distribution measured

at the outlet of the eliminator if a collection efficiency

calculation is to be performed.

If IEFF equals 2 in Card No. 1, the following insertions

are made in the input deck:

Card No. 4A (If IEFF=2)

NC

FORMAT (I5)

NC = the maximum channel number for the distribution

measured at the inlet of the eliminator

Card No, 5A and Card No. 6A (If IEFF=2)

(PARAM(I), I = 1, NPARAM)

FORMAT(4E20.6)

PARAM(I) are the guessed values of the least-square

fitting parameters for the distribution measured at the

inlet of the eliminator.

Card No, 7A to Card No. (6+NC/5)A (If IEFF=2)

(PV(I), I=1,NC)

FORMAT (4X,5F7.0)

PV(I) is the distribution measured at the inlet of the

eliminator.

195

A.4 Listing of the DATANA Code

196

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Table A.5.1 lists the input' data for a sample problem,

and Table A.5.2 displays the output from the DATANA code.

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NG a 0\ ej~C 0 QCV ~ r0rQr0t-C000000000000000000000

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COl "T 0 m ar m 0I- T r- iur a % M w0 r %O n Ln Un t n m n 3 V 4 N N OCO OOOOOOOoOOOOO00000 C O O0 C0000000 O O O O OO O OOO OO O OOOO

0o ; (4 (N 7-0 t - ICa 0) oY r- N m ) OC 0 -a ) en w L 0w 0 i M - C - rj w (N - N _v- OD I C V-m cr a C Cn N 0 >O 0 C = CP0 Co r o 0 ut a : > 0) 0 0

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o o o o o o N o o o o o o o o o o o N a o N C,. W , 1 o 0

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0 00 0000 000 000 000 06000 0000 0000 000

F K" " M I M a M 01 K K U -K K K - - - - - K K K K Uov-o0 oe0'00IAN0'o *0 N 0 00 00 00 0000000

O M I- . a 0 N 1- IA _ I A N O O 2, C0 0 0 t 0000000000000000000000000000000000*p1 NN N N NNN _ _ _ _ _ _0_ 00_ 0000000000000C000000000000000 00

0000 00 00 000000 000 0 00 000 00 00 000 0

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239

APPENDIX B

DAMIE PROGRAM

B.1 Introduction

DAMIE (D2) is a FORTRAN subroutine which computes the

so-called "Efficiency Factors" and Stokes parameters for

electromagnetic radiation scattered by a sphere. The form-

ulas calculated in this subroutine were first derived by

G. Mie (M5), and thus this scattering process is referred

to as Mie scattering.

Mie's expressions for the radiation scattered by a

sphere are valid when the radius of the sphere is comparable

to or greater than the wavelength of the incident radiation.

The index of refraction of the material of the sphere is

assumed to have the form nl-in2. In the DAMIE subroutine,

all functions are computed with an upward recurrence pro-

cedure. This procedure is stable for non-absorbing (n2=0),

moderate or large-sized spheres. For partially-absorbing

(n2>0) spheres, the DBMIE subroutine (D2), which uses a

downward recurrence procedure, gives more reliable results.

In the present study, the scattered intensity of water

droplets is found as a function of droplet size. Since water

is essentially a non-absorbing medium, and the droplet sizes

under consideration are large, the DAMIE subroutine is used,

requiring much less computer storage.

240

This appendix describes the part of the DAMIE code that

finds the relationship between the scattered light intensity

and droplet size. Other features of the subroutine will not

be presented here. They are described in Ref. D2. A listing

of the program and a sample problem are included at the end

of this appendix.

B.2 Description of the Program

The expressions for Mie scattering can be written as

I F' I. (B.2.1)s -i

where I and I respectively represent the Stokes parameters

of the incident and scattered radiation, and F' is a

four-by-four matrix referred to as a "transformation matrix".

It has the following form:

F' =

M2 0 0 0

0 M 1 0 0

0 0 S21 -D21

o 0 D2 1 S21_L

(B.2.2)

The DAMIE subroutine calculates the elements in this

transformation matrix at any scattering angle. The scattered

intensity, Is, at any scattering angle, can simply be expressed

asas1 /2(Ml ( e ) + M2 (e ))

Is 2 2 ik ·

where

-01

I

241

k = 2 (B.2.4)

where X is the wavelength of the incident radiation, and L is

the distance from the scattering location. In the program out-

put, the value of (1/2)(Ml+M2) is also given under the heading

"INTENSITY" for each scattering angle, as shown in Section

B.5. The only purpose of using this subroutine in the present

study is to find this value as a function of droplet size.

All of the necessary information for this computation

are input through the main program. These include the

refractive index of water, the wavelength of the incident

radiation, the scattering angle, and the droplet size. The

subroutine is called to compute the transformation matrix

elements, which are then used to compute the scattered

intensity factor.

B.3 Description of the Input Parameters

Card No. 1

RFR, RFI, ALAM

FORMAT (4D15.5)

RFR is nl, the real part of the refractive index of

the material of the sphere. RFR equals 1.341 for water.

RFI is n2, the imaginary part of the refractive index of

the material of the sphere. RFI equals 0.0 for water.

ALAM is the wavelength of the incident light source

expressed in microns.

242

Card No. 2

THETD(1), AJX, JX

FORMAT(2D15.5, I5)

THETD(1) is 01, the smallest angle between the

direction of the scattered light and the direction of the

incident light in the calculations. It is expressed in

degrees, and its value should not exceed 900° .

AJX is AO, the interval between successive O's for calcu-

lations.

JX is the total number of O's for calculations of a

scattered intensity. Its value should not exceed 100, unless

the dimensions in all related statements are appropriately

changed. It must be greater than or equal to 1.

Card No. 3 and Onward

X

FORMAT (D15.5)

X is the water droplet radius expressed in microns, for

the calculations. Execution will be terminated when there

are no more data cards.

243

B.4 Listing of the DAMIE Code

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B.5 Sample Problem

A sample problem is given here to demonstrate the

use of the DAMIE code. The material of the scattering

medium is pure water which has a refractive index of 1.34-i0.

The wavelength of the incident light source is 0.6328 pm. The

scattering angle is set to be 26.50. The radii of the

water droplets for this computation are listed in the input

section of the sample problem.

The output of the code gives the input information

as well as the elements of the transformation matrix for

the input scattering angle and its complementary angle. In

the present study only the values of the intensity are used.

All of this information is repeated for each input droplet

size.

252

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