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Aerosol collection in granular beds 1978

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AEROSOL COLLECTION IN GRANULAR BEDS MALCOLM L. KENNARD B.Sc, University of Nottingham, Nottingham, England, 1974 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department of Chemical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1978 ©Malcolm L. Kennard, 1978 In presenting th i s thes is in pa r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i l ab le for reference and study. I further agree that permission for extensive copying of th is thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of this thesis for f inanc ia l gain sha l l not be allowed without my writ ten permission. Department of The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date /JU/ ABSTRACT The f i l t r a t i o n of aerosols using granular beds was studied to determine the f e a s i b i l i t y of using such devices as high efficiency particle collectors. Based on the experimental data, i t was attempted to derive expressions for predicting the aerosol removal efficiency of the granular bed. Granular beds composed of f a i r l y uniform, spherical nickel shot were employed in a 7.4 cm diameter copper column to collect solid, monodispersed, polystyrene latex aerosols. The collection efficiency of the granular bed was determined as a function of several variables, viz., aerosol diameter (0.109 to 2.02 urn); bed particle diameter (100 to 600 ym); bed depth (0.3 to 19 cm); superficial gas velocity (5 to 67 cm/sec); and flow direction (upflow and downflow). The monodispersed, latex aerosols were generated by atomizing dilute hydrosols of aerosol particles. The aerosol number concentrations were measured at the inlet and outlet of the granular bed (using light scattering techniques), from which the bed collection efficiency was determined. Using the concept of an isolated bed particle i t was possible to quantitatively predict the collection efficiency of the bed. The collection of an aerosol by an isolated bed particle can be attributed to the following mechanisms:- i n e r t i a l impaction, direct interception, diffusional deposition, gravitational deposition and electrostatic effects. In the present study electrostatic effects were eliminated by grounding the equipment and neutral- izing the aerosol. i i Equations based on individual collection mechanisms and combinations were fitt e d to the experimental data by multiple regression analysis. An empirical model was developed, which gave good predictions of the experimental bed collection efficiency. The single collector efficiency (EB) was calcu- lated using the following empirical equation: EB = 1.0 St + 150,000 NR4^3 Pe~ 2/ 3 + 1.5 NG and the overall bed collection efficiency (EBT) was calculated using the following theoretical equation: EBT - 1 - exp(- 1.5 ( 1 " £) ^- EB) e a c The difference between the experimental and calculated bed efficiencies were generally less than ten percentage points. Experimental results indicate that high collection efficiencies can be achieved with relatively shallow fixed beds of granular material. Inertial impaction was considered to be the dominant collection mechanism at high gas velocities, whilst diffusion and, to a lesser extent, gravity were considered dominant at low gas velocities. For a l l the experimental conditions studied, interception was shown to be insignificant. i i i TABLE OF CONTENTS ABSTRACT '-. ... ... ..... . . . .. • i i i LIST OF TABLES v l i LIST OF FIGURES x i i ACKNOWLEDGEMENTS x i v Chapter 1. INTRODUCTION 1 1.1 The Need for Particulate Control 1 1.2 Conventional Dust Removal Equipment 2 1.3 The Granular Bed F i l t e r 3 1.3.1 Advantages of granular bed f i l t e r s 4 1.3.2 Disadvantages of granular bed f i l t e r s 4 1.4 Background Information on Granular Bed Behaviour . . . . 6 1.4.1 Individual collection mechanisms pertinent to an isolated, spherical collector 6 1.4.2 The single particle collection efficiency . . . . 11 1.4.3 Limitations of the single collector efficiency approach . . . 11 1.4.4 Interference effect 12 1.4.5 Total collection efficiency of the granular bed . 12 1.5 Scope of the Present Work 13 2. PREVIOUS WORK 14 2.1 Introduction 14 2.2 Effect of Fluid Velocity on Collection Efficiency . . . 14 2.3 Effect of Aerosol Size on Collection Efficiency . . . . 15 2.4 Effect of Collector Size and Bed Depth on Collection Efficiency 18 2.5 Effect of the Direction of Gas Flow on Collection Efficiency 18 2.6 Bounce-off and Re-entrainment 18 2.7 Review of Experimental and Industrial Studies Carried out on Granular Beds 20 2.8 Empirical Equations 26 2.9 Theoretical Work on the Flow Field Within a Granular Bed 26 3. THEORY 32 3.1 Introduction 32 3.2 The Overall Bed Collection Efficiency (EBT) as a Function of the Single Collector Efficiency (EB) . . . 32 3.3 Calculation of Single Collector Efficiency from Basic Design and Operating Variables 34 3.4 Multiple Regression 36 3.6 Pressure Drop through the Granular Bed 38 iv 4. EXPERIMENTAL WORK 39 4.1 Objectives of the Experimental Work. . . . . 39 4.2 Range of Variables Studied . . . . . . . . . . . . . . 40 4.3 Experimental Apparatus 40 4.3.1 The column 43 4.3.2 Sampling 43 4.4 Aerosol Particles 46 4.5 Granular Bed Particles 50 4.6 Aerosol Generator 50 4.7 Aerosol Detector 56 4.8 Minor Modifications and Additional Equipment 56 5. PRELIMINARY EXPERIMENTS 61 5.1 The Effect of Humidity on Collection Efficiency . . . 61 5.2 Bed Ageing or Loading 61 5.3 Collection by the Empty Column and Bed Support . . . . 64 5.4 Background Count 64 5.5 Sampling Counts and Changeover Time 65 5.6 Reproducibility 66 5.7 Errors 66 5.8 Experimental Programme 68 5.8.1 Procedure 68 5.8.2 Programme 69 6. EXPERIMENTAL RESULTS AND DISCUSSION 70 6.1 Introduction 70 6.2 The Effect of Superficial Gas Velocity on Bed Collection Efficiency 70 6.3 The Effect of Flow Direction on Bed Collection Efficiency 81 6.4 The Effect of Aerosol Diameter on Bed Collection Efficiency 81 6.5 The Effect of Collector Size on Bed Collection Efficiency 82 6.6 The Effect of Bed Depth on Collection Efficiency . . . 82 6.7 Pressure Drop across the Granular Bed 89 6.8 Summary of Experimental Results 89 7. STATISTICAL ANALYSIS 92 7.1 Introduction 92 7.2 Evaluation of Various Empirical Equations 92 7.3 Identification of the Best Empirical Equation . . . . 92 7.4 Interpretation and Modification of Equation 7.1 . . . 102 7.4.1 Modification of the Second Term in Equation 7.1 103 7.5 Conclusion 106 8. CONCLUSIONS . . . . . . 109 v NOMENCLATURE . . . . I l l REFERENCES 113 Appendix A. EXPERIMENTAL RESULTS FOR THE REMOVAL OF AEROSOL PARTICLES BY GRANULAR BEDS 117 B. CALCULATIONS OF EB AND DIMENSIONLESS GROUPS 126 C. REGRESSION ANALYSIS OF EQUATIONS SUGGESTED BY OTHER WORKERS . . . . . . . 142 C.l Introduction 142 C.2 Empirical Equations Developed by Other Workers . . . . 142 C.3 Parameter Equations 151 C. 4 Polynomial Equations 154 D. DEVELOPMENT OF THE BEST EMPIRICAL EQUATION 156 D. l Introduction 156 D.2 Development of the Best Equation for Predicting EB . . 156 D.3 Comparison of Predicted and Experimental Bed Penetrations using Equation D.5 . 160 D.4 Comparison of Predicted Bed Penetrations Using Equation D.5 and the Experimental Results of Other Studies 160 D.5 Regression Trials of the Modified Form of Equation D.5 160 D.6 Regression Trials with the Equation of Schmidt . . . . 174 v i LIST OF TABLES I. Comparison of a Granular Bed with Conventional Particle Collection Equipment 5 II. Experimental Studies 21 III. Industrial Studies 23 IV. Empirical Equations for Single Collector Efficiency Based on One Collection Mechanism 27 V. Empirical Equations for Single Collector Efficiency Based on Combinations of Collection Mechanisms 30 VI. Range of Variables Studied 40 VII. Purchased Equipment 42 VIII. Particles and Collectors 42 IX. Properties of Particles Used 50 X. Characteristics of Nickel Shot 51 XI. Collection Efficiency, of 598.1 ym Nickel Shot at Various Humidities 62 XII. Collection Efficiency of 511.0 ym Nickel Shot at Various Humidities 62 XIII. Bed Ageing Tests on 598 ym Nickel Shot 63 XIV. Bed Ageing Tests on 216.0 ym Nickel Shot 63 XV. Collection by the Empty Column 64 XVI. Background Counts for the Empty Column 65 XVII. Summary of Experimental Tests 69 A.l Penetrations for Nickel Shot 598.1 ym Diameter (Downflow; bed depth = 4.536 cm) 118 A.2 Penetrations for Nickel Shot 598.1 ym Diameter (Upflow and downflow; bed depth = 4.536 cm) 118 A.3 Penetrations for Nickel Shot 598.1 ym Diameter (Downflow; varying bed depth; aerosol diameter" 0.5 ym) 118 A.4 Penetrations for Nickel Shot 598.1 pm Diameter (Downflow; bed depth = 2.268 cm) 118 A.5 Penetrations for Nickel Shot 511.0 ym Diameter (Downflow; bed depth = 4.536 cm)....... 119 A.6 Penetrations for Nickel Shot 511.0 ym Diameter (Upflow and downflow; bed depth = 4.536 cm) 119 A.7 Penetrations for Nickel Shot 511.0 ym Diameter (Downflow; varying bed depth; aerosol diameter = 0.5 ym) 119 A.8 Penetrations for Nickel Shot 511.0 ym Diameter {Downflow; bed depth = 2.268 cm) 119 A.9 Penetrations for Nickel Shot 363.9 ym Diameter (Downflow; bed depth = 4.536 cm) 120 A.10 Penetrations for Nickel Shot 363.9 ym Diameter (Upflow and downflow; bed depth = 4.536 cm) 120 A.11 Penetrations for Nickel Shot 363.9 ym Diameter (Downflow; varying bed depth; aerosol diameter =0.5 ym) 120 A.12 Penetrations for Nickel Shot 363.9 ym Diameter (Downflow; bed depth = 2.268 cm) 120 v i i A. 13 Penetrations for Nickel Shot 216.1 \xm Diameter (Downflow; bed depth = 2.268 cm) 121 A.14 Penetrations for Nickel Shot 216.1 ym Diameter (Upflow and downflow; bed depth == 2.268 cm) 121 A.15 Penetrations for Nickel Shot 216.1 ym Diameter (Downflow; varying bed depth; aerosol diameter =* 0.5 ym) 121 A.16 Penetrations for Nickel Shot 216.1 ym Diameter (Downflow; bed depth =* 1.134 cm) 121 A.17 Penetrations for Nickel Shot 126.0 ym Diameter (Downflow; bed depth =* 2.268 cm) 122 A.18 Penetrations for Nickel Shot 126.1 ym Diameter (Upflow and downflow; bed depth = 2.268 cm) 122 A. 19 Penetrations for Nickel Shot 126.1 ym Diameter (Downflow; varying bed depth; aerosol diameter - 0.5 ym) 122 A.20 Penetrations for Nickel Shot 126.1 ym Diameter (Downflow; bed depth = 1.134 cm) 122 A.21 Penetrations for Lead Shot 1800 ym Diameter (Downflow; aerosol diameter =•= 0.5 ym) 123 A.22 Pressure Drop (MM.HG) across Beds of Nickel Shot 598.1 ym Diameter 124 A.23 Pressure Drop (MM.HG) across Beds of Nickel Shot 511.0 ym Diameter 124 A.24 Pressure Drop (MM.HG) across Beds of Nickel Shot 363.9 ym Diameter 124 A. 25 Pressure Drop (MM.HG) across Beds of Nickel Shot 216.1 ym Diameter 125 A.26 Pressure Drop (MM.HG) across Beds of Nickel Shot 126.0 ym Diameter 125 A. 27 Pressure Drop (MM.HG) across Beds of Lead Shot 1800 ym Diameter 125 B. 1 Dimensionless Groups and Single Collector Efficiency Corresponding to Tests on Beds of Nickel Shot 598.1 ym Diameter (Downflow) 127 B. 2' Dimensionless Groups and Single Collector Efficiency Corresponding to Tests on Beds of Nickel Shot 598.1 ym Diameter (Upflow) 129 B. 3 Dimensionless Groups and Single Collector Efficiency Core responding to Tests on Beds of Nickel Shot 511.0 ym Diameter (Downflow) 130 B. 4 Dimensionless Groups and Single Collector Efficiency Corresponding to Tests on Beds of Nickel Shot 511.0 ym Diameter (Upflow) 132 B. 5 Dimensionless Groups and Single Collector Efficiency Corresponding to Tests on Beds of Nickel Shot 363.9 ym Diameter (Downflow) 133 B. 6 Dimensionless Groups and Single Collector Efficiency Corresponding to Tests on Beds of Nickel Shot 363.9 ym Diameter (Upflow) 135 B. 7 Dimensionless Groups and Single Collector Efficiency Corresponding to Tests on Beds of Nickel Shot 216.0 ym Diameter (Downflow) 136 B. 8 Dimensionless Groups and Single Collector Efficiency Corresponding to Tests on Beds of Nickel Shot 216.0 ym Diameter (Upflow) 138 v i i i B. 9 Dimensionless Groups and Single Collector Efficiency Corresponding to Tests on Beds of Nickel Shot 126.1 um Diameter (Downflow) 139 B. 10 Dimensionless Groups and Single Collector Efficiency Corresponding to Test on Beds of Nickel Shot 126.1 ym Diameter (Upflow) 141 C. 1 Results of Fitting Equation C.l to the Experimental Data by Multiple Regression 144 C. 2 Results of Fitting Equation C.2 to the Experimental Data by Multiple Regression 145 C. 3 Results of Fitting Equation C.3 to the Experimental Data by Multiple Regression 145 C. 4 Results of Fitting Equation C.4 to the Experimental Data by Multiple Regression 146 C. 5 Results of Fitting Equation C.5 to the Experimental Data by Multiple Regression 146 C. 6 Results of Fitting Equation C.6 to the Experimental Data by Multiple Regression 147 C. 7 Results of Fitting Equation C.l to the Experimental Data by Multiple Regression (intercept set to zero) . . . . 148 C. 8 Results of Fitting Equation C.3 to the Experimental Data by Multiple Regression (intercept set to zero) . . . . 148 C. 9 Results of Fitting Equation C.4 to the Experimental Data by Multiple Regression (intercept set to zero) . . . . 149 C.10 Results of Fitting Equation C.5 to the Experimental Data by Multiple Regression (intercept set to zero) . . . . 149 C . l l Results of Fitting Equation C.6 to the Experimental Data by Multiple Regression (intercept set to zero) . . . . 150 C.12 Comparison of the Coefficients of Equation C.4 with those from Doganoglu's Work 151 C.13 Comparison of the Coefficients of Equation C.5 with those from Doganoglu's Work . 151 C.14 Results of Fitting Equation C.7 to the Experimental Data by Multiple Regression 152 C.15 Results of Fitting Equation C.8 to the Experimental Data by Multiple Regression 152 C.16 Results of Fitting Equation C.7 to the Experimental Data by Multiple Regression (intercept set to zero) . . . . 153 C.17 Results of Fitting Equation C.8 to the Experimental Data by Multiple Regression (intercept set to zero) . . . . 154 C. 18 Results of Fitting Equation C.9 to a l l the Experimental Data by Multiple Regression 155 D. 1 Results of Fitting Equation D.l to the Experimental Data by Multiple Regression 157 D. 2 Results of Fitting Equation D.2 to the Experimental Data by Multiple Regression 158 D. 3 Results of Fitting Equation D.3 to the Experimental Data by Multiple Regression 158 D. 4 Results of Fitting Equatioir D.4 to the Experimental Data by Multiple Regression 159 D. 5 Results of Fitting Equation D.4 to a l l the Experimental Data by Multiple Regression (04 set to zero) 159 D. 6 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 598.1 ym Diameter (aerosol diameter = 0.5 ym; bed depth = 4.536 cm) 161 ix D. 7 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 598.1 ym Diameter (aerosol diameter =* 0.804 ym; bed depth == 4.536 cm) 161 D. 8 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 598.1 ym Diameter (aerosol diameter = 1.011 ym; bed depth = 4.536 cm) 162 D. 9 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 598.1 ym Diameter (additional downflow comparisons; bed depth = 4.536 cm) 162 D.10 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 511.0 ym Diameter (aerosol diameter = 0.5 ym; bed depth = 4.536 cm) 163 D. l l Comparison Between Predicted and Experimental Penetrations for Nickel Shot 511.0 ym Diameter (aerosol diameter = 0.804 ym; bed depth = 4.536 cm) 163 D.12 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 511.0 ym Diameter (aerosol diameter =* 1.011 ym; bed depth = 4.536 cm) 164 D.13 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 511.0 ym Diameter (additional downflow comparisons; bed depth =» 4.536 cm) 164 D.14 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 363.9 ym Diameter (aerosol diameter = 0.5 ym; bed depth = 4.536 cm) 165 D.15 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 363.9 ym Diameter (aerosol diameter = 0.804 ym; bed depth = 4.536 cm) 165 D.16 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 363.9 ym Diameter (aerosol diameter = 1.011 ym; bed depth = 4.536 cm) 166 D.17 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 363.9 ym Diameter (additional downflow comparisons; bed depth = 4.536 cm) 166 D.18 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 216-.1 ym Diameter (aerosol diameter = 0.5 ym; bed depth = 2.268 cm) 167 D.19 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 216.1 ym Diameter (aerosol diameter = 0.804 ym; bed depth = 2.268 cm) 167 D.20 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 216.1 ym Diameter (aerosol diameter =* 1.011 ym; bed depth = 2.268 cm) 168 D.21 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 216.1 ym Diameter (additional downflow comparisons; bed depth = 2.268 cm) 168 D.22 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 126.0 ym Diameter (aerosol diameter = 0.5 ym; bed depth - 2.268 cm) . . . . 169 D.23 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 126.0 ym Diameter (aerosol diameter = 0.804 ym; bed depth = 2.268 cm) 169 D.24 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 126.0 ym Diameter (aerosol diameter = 1.011 ym; bed depth = 2.268 cm) 170 x D.25 Comparison Between Predicted and Experimental Penetrations f o r N i c k e l Shot 126.0 Vm Diameter (a d d i t i o n a l downflow comparisons; bed depth = 2.269 cm) 170 D.26 Comparison Between Predicted and Experimental Penetrations f o r Lead Shot 1800 ym Diameter (downflow; aerosol diameter = 0.5 ym; bed depth = 4.536 cm) 171 D.27 Comparison Between Predicted Penetrations and the Results of A. Figueroa ( c o l l e c t o r diameter = 7000 ym; bed depth ="= 2 cm) 171 • D.28 Comparison Between Predicted Single C o l l e c t o r E f f i c i e n c y and the Results of Y. Doganoglu ( c o l l e c t o r diameter =•= 596.0 ym; l i q u i d D.O.P. aerosol) 172 D.29 Comparison Between Predicted Single C o l l e c t o r E f f i c i e n c y and the Results of Y. Doganoglu ( c o l l e c t o r diameter = 108.5 cm; l i q u i d D.O.P. aerosol) 172 D.30 Results of F i t t i n g Equation D.6 to the Experimental Data by M u l t i p l e Regression 173 D.31 Results of F i t t i n g Equation D.6 to the Experimental Data by M u l t i p l e Regression (013 set at 1.25) 174 D.32 Results of F i t t i n g Equation*D.8 to the Experimental Data by M u l t i p l e Regression 175 x i LIST OF FIGURES 1. 1 Inertial Impaction 7 1. 2 Direct Interception 7 1. 3 Diffusional Interception . . . . . . 7 1. 4 Gravitational Settling 10 2. 1 The Effect of Gas Velocity on Collection Efficiency . . . . 16 2. 2 Velocity Penetration Curve 17 2. 3 Efficiency of a Glass Fibre Mat as a Function of Particle Size and Flow Rate 17 2. 4 Velocity Penetration Curve for 1.1 aerosol and 10-14 Mesh Sand 19 2. 5 Velocity Penetration Curve for 1.1 ym aerosol and 20-30 Mesh Sand 19 3. 1 Schematic Diagram of the Granular Bed . . 33 4. 1 Schematic Diagram of Equipment 41 4. 2 Column Support for Granular Bed . . . . . . . . . 44 4. 3 Velocity Reducer 45 4. 4 Upflow and Downflow Operation of the Column 45 4. 5 Electron Micrograph of 0.109 ym diameter Latex Particles . . 47 4. 6 Electron Micrograph of 0.50 ym diameter Latex Particles . . 47 4. 7 Electron Micrograph of 0.60 ym diameter Latex Particles . . 48 4. 8 Electron Micrograph of 0.804 ym diameter Latex Particles . . 48 4.. 9 Electron Micrograph of 1.011 ym diameter Latex Particles . . 49 4.10 Electron Micrograph of 2.02 ym diameter Latex Particles . . 49 4.11 Electron Micrograph of 598 ym diameter Nickel Shot 52 4.12 Close up of a 598 ym diameter Nickel Shot 52 4.13 Electron Micrograph of 511 ym diameter Nickel Shot 53 4.14 Electron Micrograph of 363 ym diameter Nickel Shot 53 4.15 Electron Micrograph of 216 ym diameter Nickel Shot 54 4.16 Electron Micrograph of 126 ym diameter Nickel Shot 54 4.17 Block Diagram of Aerosol Generator 55 4.18 Layout of Optics for Aerosol Analyser 57 4.19 Schematic Diagram of Modified Equipment 58 4.20 Humidifying Equipment 60 6. 1 Collection Efficiency as a Function of Gas Velocity (Bed depth = 4.54 cm; collector diameter » 598.1 ym) . . 71 6. 2 Collection Efficiency as a Function of Gas Velocity (Bed depth = 4.54 cm; collector diameter = 511 ym) . . . 72 6. 3 Collection Efficiency as a Function of Gas Velocity (Bed depth = 4.54 cm; collector diameter =* 363 ym) . . . 73 6. 4 Collection Efficiency as a Function of Gas Velocity (Bed depth =•= 2.27 cm; collector diameter =- 216 ym) . . . 74 6. 5 Collection Efficiency as a Function of Gas Velocity (Bed depth = 2.27 cm; collector diameter = 126 ym) . . . 75 6. 6 Collection Efficiency as a Function of Gas Velocity (Bed depth =* 4.54 cm; collector diameter = 598 ym) . . . 76 6. 7 Collection Efficiency as a Function of Gas Velocity (Bed depth = 4.54 cm; collector diameter =» 511 ym) . . . 77 6. 8 Collection Efficiency as a Function of Gas Velocity (Bed depth =• 4.54 cm; collector diameter = 363 ym) . . . 78 x i i 6. 9 Collection Efficiency as a Function of Gas Velocity (Bed depth = 2.27 cm; collector diameter = 216 ym) . . . . 79 6.10 Collection Efficiency as a Function of Gas Velocity (Bed depth = 2.27 cm; collector diameter =* 126 ym) . . . . 80 6.11 Collection Efficiency as a Function of Aerosol Diameter at a Superficial Gas Velocity of 5.24 cm/sec 83 6.12 Collection Efficiency as a Function of Bed Depth (Collector diameter = 598 ym, aerosol diameter = 0.5 ym) . 84 6.13 Collection Efficiency as a Function of Bed Depth (Collector diameter = 511 ym, aerosol diameter = 0.5 ym) . 85 6.14 Collection Efficiency as a Function of Bed Depth (Collector diameter = 363 ym, aerosol diameter = 0.5 ym) . 86 6.15 Collection Efficiency as a Function of Bed Depth (Collector diameter = 216 ym, aerosol diameter = 0.5 ym) . 87 6.16 Collection Efficiency as a Function of Bed Depth (Collector diameter = 126 ym, aerosol diameter = 0.5 ym) . 88 6.17 Pressure Drop as a Function of Gas Velocity 90 7.1 Comparison of Experimental and Calculated Collection Efficiencies (Collector diameter =- 598.1 ym) 95 7. 2 Comparison Between Experimental and Calculated Collection Efficiencies (Collector diameter = 511.0 ym) 96 7. 3 Comparison Between Experimental and Calculated Collection Efficiencies (Collector diameter = 363.9 ym) 97 7. 4 Comparison of Experimental and Calculated Collection Efficiencies (Collector diameter =* 216.0 ym) 98 7. 5 Comparison of Experimental and Calculated Collection Efficiencies (Upflow and downflow; aerosol diameter = 0.804 ym; collector diameter = 511.0 ym) 99 7. 6 Comparison of Experimental and Calculated Collection Efficiencies (Upflow and downflow; aerosol diameter = 1.011 ym; collector diameter = 511.0 ym) 100 7. 7 Scatter Plot of Experimental and Calculated Collection Efficiencies (using Eqs. 3.6 and 7.1) 101 7. 8 Diffusion Coefficent as a Function of Aerosol Diameter . . . 104 7. 9 Scatter Plot of Experimental and Calculated Collection Efficiencies (using Eqs. 3.6 and 7.3) 105 7.10 Scatter Plot of Experimental and Calculated Collection Efficiencies (using Eqs. 3.6 and 7.5; aerosol diameters in the range 0.1 to 5.0 ym) 107 x i i i ACKNOWLEDGEMENT S I would l i k e to thank my supervisor, Dr. Axel Meisen, for h i s considerate supervision and guidance throughout the course of t h i s work. Thanks are also due to the personnel i n the Department of Chemical Engineering workshop for t h e i r cooperation and assistance. The manuscript was typed by Mrs. Nina Thurston, whose work i s much appreciated. F i n a l l y , I would l i k e to thank the B r i t i s h Columbia M i n i s t r y of the Environment and the University of B r i t i s h Columbia for f i n a n c i a l assistance. x i v CHAPTER 1 INTRODUCTION 1.1 The Need for Particulate Control In recent years the need to limit the emissions of pollutants has become a matter of increasing concern. Thus numerous new laws on emission standards have been introduced in an attempt to reduce the amount of these pollutants. Air pollution and especially air borne dusts and fumes, which are by-products of most process industries, constitute a d i f f i c u l t and expensive control problem. The need to control the emissions of these particulates is based on the following factors. a) Health hazard. Inhalation of excessive dust, irrespective of i t s chemical composition can produce serious pulmonary diseases, with s i l i c o s i s and asbestosis being the most common. Particles in the 0.1-1.0 ym range can readily reach the innermost portions of the lung and may be retained there. Many dusts act as irritants to the eyes and nose causing allergic responses, dermatitis and other skin disorders. Certain metal particles such as lead, beryllium and chromium may cause fever and nausea when inhaled. b) Effect on the environment. Particulates may affect the atmos- pheric properties in the following ways: i) v i s i b i l i t y reduction, and discolouration i i ) fog formation and precipitation, i i i ) solar radiation reduction 1 2 iv) temperature and wind distribution alteration. Industrial dusts may settle on nearby fields and bodies of water with deleterious effects on the fauna and flora. c) Effect of materials. Particulates can affect materials by soiling or chemical deterioration. For example, corrosion is enhanced by the deposition of acidic particles. d) Explosion risk. Fine dusts of combustible materials dispersed in air at certain concentrations may burn rapidly or even explosively. Dusts such as grain, sugar, coal, plastics, sulphur, aluminium, and other dusts of light metals are the most explosive. The explosion risk increasing with decreasing particle size. e) Commercial value. In some cases such as metal refining or smelting, the emitted dust may have a considerable economic value. 1.2 Conventional Dust Removal Equipment There is increasing evidence that submicron particles are most hazardous and thus legislation should not only be based on the quantity but also the size of particulates. Most conventional control devices are, unfortunately, rather inefficient collectors of submicron particles. Hence there is a need to improve the existing methods and/or to develop new devices for the removal of fine particulates. The conventional equipment available can be divided into the following groups. a) Electrostatic precipitators. Here the particles are charged by passing them through a highly ionized region and subsequently removing them from the gas stream by electrostatic forces. Precipitators are able to collect fine particles but the power requirements are high and increase with mass loading. Furthermore, precipitators are generally large and therefore have high capital and maintenance costs. 3 b) Fabric filters. These are generally more effective than precipitators in the micron and submicron ranges. Unfortunately.,, most f i l t e r media have limited resistance to chemical attack, mechanical vibra- tion and high temperatures. The media may be d i f f i c u l t or impossible to clean and f i l t e r s therefore often have high operating costs. c) Wet scrubbers. These devices operate on the principle of bringing the dusty gas stream into contact with a liquid phase. Numerous devices of different designs, sizes and performance characteristics are available and some of them are highly effective in the removal of submicron particles. However, scrubbers tend to have high pressure drops and power requirements. A further major disadvantage is that they cannot operate at high temper- atures . d) Centrifugal collectors. Here the particles are collected by i n e r t i a l effects and cyclones are the most common devices of this type. They are cheap to operate and build since they have no moving parts. High collection efficiencies are achievable for particles greater than about 5 ym in diameter. Thus the development of an efficient and low cost device for fine particulate removal is a pressing demand in industry. 1.3 The Granular Bed F i l t e r The granular bed, or packed bed f i l t e r , consists of fixed beds of solid granules through which the dusty gas flows. The dust particles are collected mainly by impaction on the granules and, to a lesser extent, by sieving. Although beds of granular materials have been used for the removal of particulates from gas streams for some time, they have not achieved the same degree of acceptance as other devices. This could be due to the fact that past research efforts have provided l i t t l e reliable data which could 4 be systematically analysed and related to industrial needs. Until recently packed beds were operated batchwise. However, develop- ment of devices such as the panel bed f i l t e r (Baretsky"*") and the fluidized 2 bed f i l t e r (Black and Boubel ) have shown that relatively high removal efficiencies of submicron particles can be achieved with continuous opera- tion. This demonstrates the f e a s i b i l i t y of using beds to remove fine particulates from gases in industrial processes such as coal gasification. 1.3.1 Advantages of Granular Bed Filters Apart from simplicity of design and ruggedness, granular bed f i l t e r s have the a b i l i t y to treat gases which:- i) are at high temperatures i i ) undergo large changes in temperature and volume i i i ) contain abrasive dusts iv) have a wide range of particle sizes and concentrations v) contain corrosive chemicals and moisture. Packed bed f i l t e r s may have low maintenance costs, depending on the efficiency of bed regeneration, and are more compact than some other types of conventional equipment. They can also remove particular matter simul- taneously with gaseous pollutants provided a suitable absorbent material is 3 used (Squires and Pfeffer ). 1.3.2 Disadvantages of Granular Bed Filters In terms of particle removal efficiency granular f i l t e r s are generally less effective than fibre f i l t e r s . They also tend to have rather high pressure drops which are comparable with wet scrubbers of similar efficiency. A major drawback is the d i f f i c u l t y of separating the collected dust from the f i l t e r medium to prevent clogging. Several methods have been developed such as isolating a section of the bed and:- i) dislodging the deposited particles by "puff back", i.e., flushing with 5 4 a pulse of air in the reverse direction to the dusty gas flow (Kalen ; 3 Squires ) i i ) using mechanical vibration of the bed (Englebrecht^), or i i i ) continuous removal of the partially clogged section of bed and replacing i t with fresh material (Egleson^). This method is relatively simple in case of fluidized beds (Meissner^) or spouted beds (Meisen and g Mathur ). The removed granular material may be either washed for re-use or discarded depending on the particular circumstances. Further problems may arise when very high concentrations of dusty gas are fi l t e r e d . This causes rapid clogging and an increase in pressure drop. A simple remedy is to operate the bed in conjunction with a cyclone or bag f i l t e r to remove the majority of large particles. A qualitative comparison of granular beds with conventional f i l t e r s is given in Table I. TABLE I. COMPARISON OF A GRANULAR BED WITH CONVENTIONAL PARTICLE COLLECTION EQUIPMENT Electro- static Wet Bag Precip- Granular Scrubbers Filters itators Cyclones Beds High temp. VP VP G VP VG Gas capacity G VP G VG G Removal efficiency for fine particles P VG G VP VG Capital cost VP P P VG VG Operating cost P P G VG VG Reliability P P P VG VG Key: VP—very poor VG—very good P —poor G —good 6 1.4 Background Information on Granular Bed Behaviour The study of a granular bed as a particle collection device requires a knowledge of the mechanisms which contribute to the collection process. It is also necessary to predict the relative magnitude of these mechanisms in order to develop models of collection performance. Most particle removal theories are based on the simple assumption that particles are captured upon touching the collector surface and that 9 re-entrainment is absent (Dahneke ). Particles stick to surfaces mainly due to short range van der Waals and electrical f o r c e s ^ I t is there- fore necessary to develop a mechanism whereby a particle travelling in a moving f l u i d is able to move across the fl u i d streamlines to a point close enough to the collector surface for these captive forces to come Into effect. 1.4.1 Individual collection mechanisms pertinent to an Isolated, spherical collector In order to explain the different collection mechanisms, which may arise in granular beds, i t is convenient to consider a single isolated collector particle. Calculation of the collection efficiency (or capture efficiency) of a single collector may then be reduced to the calculation of the efficiencies of the individual collection mechanism. The primary collection mechanisms are i i h e r t i a l impaction, direct interception, d i f f u - sional deposition, gravitational sedimentation, and electrostatic deposition. In order to determine which collection mechanisms are predominant in a f i l t e r medium, i t is useful to introduce dimensionless parameters which characterize the interaction between the f l u i d , particles, and collectors. The separate collection mechanisms are discussed below. a) Inertial collection. As shown in Fig. 1.1, the presence of a collector causes the gas streamlines to curve. Since the inertia of the 7 Eig. 1.-3 Diffusional Interception 8 aerosol particles is greater than an equivalent volume of gas, their trajec- tories deviate from the streamlines and approach the collector surface. Two factors determine the collection efficiency:- i) the velocity distribution of the gas around the collector, which is governed by the collector Reynolds number, Re = p_ U d fix , and t c i i ) fhe trajectory of the particle, which is the result of the interaction between the flu i d and particle. The interaction may be characterized by the Stokes number defined as St = d 2 U p_/9 y d a F c The i n e r t i a l mechanism is usually dominant for particles greater than 1 to 2 ym in diameter. The mechanism increases with increasing fl u i d velocity, aerosol diameter and density, and decreasing collector size. b) Direct interception. In this case i t is assumed that the particles do not appreciably disturb the flu i d flowfield and their trajectories coincide with the streamlines.. A particle is captured when i t s centre approaches the collector surface within one particle radius (see Fig. 1.2). Capture is due solely to the size of the particle. This mechanism can be characterized by the parameter NR = d /d a c This effect is usually small in the case of submicron aerosol particles treated by beds of individual collector particles greater than 100 ym diameter. c) Diffusional deposition. Because of Brownian movement the trajec- tories of submicron particles do not usually coincide with the gas stream- lines'. Thus a particle may migrate to the collector surface purely as a result of random diffusion (see Fig. 2.3). The Peclet number Is used to describe this effect. Pe = d U/ D c a where D is the effective diffusivity of the aerosol particle. Some workers 3. prefer the dimensionless group -2/3 ND = Pe • This group changes the magnitude of the diffusional parameter making i t more comparable to the other dimensionless groups. The diffusional effect increases with decreasing particle size and is usually the dominant collection mechanism for particles smaller than about 0.5 ym in diameter at low velocities. d) Gravitational deposition. This represents sedimentation or settling of a particle due to gravity. In most cases the effect is only significant for particles greater than about 2 ym in diameter or at very low gas velocities. Gravitational deposition can be characterized by the parameter NG = U /U s where U g is the terminal velocity of the aerosol particle. If the particle obeys Stokes1 law, U g is given by U s = df g p a/l8 y Depending on the direction of gas flow, the effect of gravity on collection may be either positive or negative (see Fig. 1.4). The collec- tion efficiency increases with aerosol size and density and decreases with Increasing gas flow. e) Electrical effects. The aerosol particles and the collectors may carry electrostatic charges which can affect the motion of the aerosol around a collector and hence their collection. There are four types of 12 electrical forces resulting from these charges which may have to be considered. (i) The coulombic force between a charged collector and a charged aerosol particle, ( i i ) the electrical image force between a charged 10 Fig. 1.4 Gravitational.Settling 11 collector, and a neutral particle, ( i i i ) the image force between a charged particle and a neutral collector, and (iv) the space charge repulsion force effect. 1.4.2 The single particle collection efficiency Each f i l t r a t i o n mechanism described above is based on collection by an 13 isolated collector particle. This approach was developed by Langmuir who assumed that every f i l t e r element (e.g., bed particle) experiences similar f i l t r a t i o n phenomena and therefore a single f i l t e r element efficiency may be defined. Consequently, the f i l t r a t i o n efficiency of an actual f i l t e r can be calculated by summing the effects of a l l the elements of the f i l t e r . In the case of a granular bed each element is assumed to be a sphere and the single collector efficiency may be defined as E = Number of particles Impacting per unit time Number of particles that could impact per unit time i f their trajectories were straight Thus the theoretical calculation of f i l t e r efficiency of a granular bed is usually divided into two parts, i.e., prediction of the single collector efficiency and the summation of a l l the collector efficiencies by integration. (Further details are given in Chapter 3.) It i s also usually assumed that steady state f i l t r a t i o n i s taking place where any structural changes caused by the depositing particles are too small to be of any influence to the collection efficiency of the f i l t e r . 1.4.3 Limitations of the single collector efficiency approach The various assumptions in this approach are rarely met in practice such as (i) the bed granules are completely spherical, ( i i ) that particles 14 colliding with a collector are always retained , i.e., no bounce-off, ( i i i ) that there is no re-entrainment, and (iv) that already deposited particles do not affect the collection efficiency of a collector. There- fore the method is oversimplified and is only useful when the individual mechanisms are small or one is dominant. According to Fuchs^"' the total single collector efficiency is greater than any of the individual e f f i c i e n - cies but smaller than their sum. Thus the problem is how to combine the individual effects, especially when the aerosol diameter is in the range of 0.1-1.0 ym and the effects caused by the various mechanisms are comparable. 1.4.4 Interference effect There is also the problem that the flow f i e l d round an isolated collec- tor particle i s obviously different from that of a collector particle inside a granular bed and therefore i t s collection efficiency is also changed. The flow differs because:- i) The i n t e r s t i t i a l gas velocity in the bed i s higher than a superficial gas velocity. i i ) The gas streamlines around the collector are different due to the close proximity of the neighbouring collectors. Thus the 'interference effect' tends to increase the collection efficiency. However, there is disagreement as to how to account for this effect, especially because i t may be different for the various collection mechanisms. The most plausible parameter to describe the interference effect is the bed porosity (e). To determine the true collection e f f i c - iency of a collector, empirical or semi-empirical corrections must be intro- duced. The single collector efficiency of a collector within a granular bed may therefore be written as EB = f(e, EI, ER, ED, EG ...) where EI, ER, ED, and EG are the collection efficiences of the single collector due to inertia, interception, diffusion and gravity, respectively. 1.4.5 Total collection efficiency of the granular bed Finally the single collector efficiency (EB) must be related to the o v e r a l l c o l l e c t i o n e f f i c i e n c y of the whole bed (EBT). By invoking a s i m p l i f i e d model of the f i l t e r bed, i . e . , assuming a l l the c o l l e c t o r s are spherical.and r e g u l a r l y packed, a simple equation can be developed to r e l a t e EB and EBT. This w i l l be discussed i n greater d e t a i l i n Chapter 3. 1.5 Scope of the Present Work The main objectives of t h i s work were to investigate the removal of submicron aerosols by granular beds and to use the r e s u l t s for the develop- ment of an empirical equation for p r e d i c t i n g the c o l l e c t i o n e f f i c i e n c y of the granular bed. To investigate the f i l t r a t i o n process, the e f f e c t of the following variables on c o l l e c t i o n e f f i c i e n c y were considered: ( i ) aerosol s i z e , ( i i ) c o l l e c t o r s i z e , ( i i i ) gas v e l o c i t y , (iv) d i r e c t i o n of gas flow, and (v) granular bed depth. Other factors observed were:- i) pressure drop across the bed as a function of gas flow rate, and i i ) the e f f e c t of humidity on c o l l e c t i o n e f f i c i e n c y . E l e c t r i c a l e f f e c t s were minimized by using m e t a l l i c bed p a r t i c l e s and grounding the equipment. Thus only i n e r t i a , i n t e r c e p t i o n , d i f f u s i o n and gravity needed to be considered i n developing an equation to predict the c o l l e c t i o n e f f i c i e n c y of the bed. CHAPTER 2 PREVIOUS WORK 2.1 Introduction P a r t i c u l a t e separation from a gas stream by means of granular bed f i l t e r s has been the subject of several t h e o r e t i c a l and experimental studies. The experimental investigations deal mainly with the o v e r a l l performance and methods of improvement. The t h e o r e t i c a l work ranges from the analysis of the flow f i e l d and c o l l e c t i o n e f f i c i e n c i e s of a s i n g l e f i l t e r element to the o v e r a l l c a l c u l a t i o n of the c o l l e c t i o n e f f i c i e n c y of the whole bed. Although a substantial amount of work has been ca r r i e d out, there i s considerable disagreement and inadequate understanding of the f i l t r a t i o n mechanisms. This i s probably due to the fact that previous work i s rather fragmentary and often presented i n a way which precludes systematic a n a l y s i s . Several comprehensive reviews are a v a i l a b l e on p a r t i c u l a t e removal using granular beds (Fuchs^, Davies"*"^, Dorman"^, Strauss"*"^, Silverman"*"^, 20 21 22 Figueroa , Tardos , Pich ). Rather than repeating t h e i r reviews, the e f f e c t of various operating and design variables w i l l be discussed i n t h i s chapter. 2.2 E f f e c t of F l u i d V e l o c i t y on C o l l e c t i o n E f f i c i e n c y I t has been noted by most workers that increasing the v e l o c i t y through the f i l t e r causes the c o l l e c t i o n e f f i c i e n c y to decrease and then increase again. The minimum (see Figs. 2.1 and 2.2) i s caused by d i f f u s i o n a l e f f e c t s becoming les s important and i n e r t i a l e f f e c t s becoming dominant. The 14 velocity resulting in the minimum collection increases the smaller the aerosol. A typical plot of collection efficiency as a function of super- f i c i a l gas velocity is shown in Fig. 2.1 and the following statements can be made about the resulting curve. For diffusion: As the aerosol diameter increases the curve moves to the l e f t . As the collector diameter increases the curve moves to the right. For inertia: As the aerosol diameter increases the curve moves to the le f t and up. As the collector diameter increases the curve moves to the right and down. For interception: As the aerosol diameter increases the curve moves up. As the collector diameter increases the curve moves down. The ordinate of Fig. 2.2 is the penetration of the f i l t e r which is defined as (1 - collection efficiency). Very l i t t l e is known about the combined effects of inertia and d i f f u - sion, which are of particular importance for particles between 0.1-1.0 ym diameter. There i s , also, considerable disagreement on which collection mechanism becomes dominant in a given size range. For instance, for the 23 aerosol size range 1-2 ym diameter, Doganoglu reported that gravity and 24 inertia are dominant whereas Knettig , stated that only inertia is signif- 25 icant. For the same range and comparable gas velocities, McCarthy concluded that interception and diffusion are dominant which is in direct disagreement with Doganoglu. 2.3 Effect of Aerosol Size on Collection Efficiency It has been well established experimentally and theoretically that for fine particles the collection efficiency decreases with decreasing particle size. Further, i'tiis generally accepted that this trend continues down to 16 Fig. 2.1 The Effect of Gas Velocity on Collection Efficiency 0 4 0 - 8 0 120 160 2 0 0 2 4 0 280 3 0 0 v cm/sec 26 Fig. 2.2 Velocity Penetration Curve (Ramskill and Anderson ) 5 2 1 0-5 0-2 0-1 0-05 0-02 0-0. ! j i ' : 1 1 0-94 cm/sec i N J ! ! ' i • A ^v!. i s . 0-42 cm/sec i / ^ x , 1 j V / ' < 0 • 21 cm/sec^ * / i ; K i i / 1 ; ! 1 0-0 ?4cn • « / ! iAec\ | j i ! j 0 005 0-10 0:'5 0-20 0-25 O30 0-JS 0-40 C-45 0-50 0-55 0-60 Panicle radius,/* Fig. 2.3 Efficiency of a Glass Fibre Mat as a Function of Particle Size and Flow Rate (Thomas and Yoder27) Note: Penetration = (1 - collection efficiency) 18 about 0.3 Vm a f t e r which the d i f f u s i o n a l e f f e c t becomes dominant and increases the c o l l e c t i o n e f f i c i e n c y once again. 28 Fruendlich showed that minimum c o l l e c t i o n occurred with aerosols 29 between 0.2-0.4 ym i n diameter. Chen , i n experiments with 0.15 ym diameter 30 aerosols, observed a minimum only for v e l o c i t i e s below 4 cm/sec and La Mer found no minimum c o l l e c t i o n e f f i c i e n c y even down to aerosols of 0.02 ym 27 diameter. Thomas and Yoder pointed out that the p a r t i c l e s i z e producing the minimum c o l l e c t i o n e f f i c i e n c y increased with decreasing gas v e l o c i t y (Fig. 2.3). Thus, once again, there i s disagreement. 2.4 E f f e c t of C o l l e c t o r Size and Bed Depth on C o l l e c t i o n E f f i c i e n c y Most workers, who used c o l l e c t o r s of various s i z e s , have shown that the c o l l e c t i o n e f f i c i e n c y increases with decreasing c o l l e c t o r s i z e . Also the e f f i c i e n c y increases exponentially with bed depth obeying Eq. 3.4 (see Chap- ter 3), i . e . , EBT i s proportional to 1 - exp(^b.H) where 'b' i s a constant. 2.5 E f f e c t of the D i r e c t i o n of Gas Flow on C o l l e c t i o n E f f i c i e n c y 31 32 27 20 Work by Paretsky , Gebhart , Thomas , and Figueroa , demonstrated that gravity plays a small r o l e i n c o l l e c t i o n , by comparing bed e f f i c i e n c i e s for upflow and downflow. However, Thomas showed that gravity can be important i n c o l l e c t i o n of aerosols down to 0.3 ym i n diameter for v e l o c i t i e s between 1 and 4 cm/sec (see Figs. 2.4 and 2.5). At higher v e l o c i t i e s the e f f e c t of the d i r e c t i o n of flow on the c o l l e c t i o n of submicron p a r t i c l e s reduces and can be assumed n e g l i g i b l e at a v e l o c i t y greater than 20 cm/sec. 2.6 Bounce-off and Re-entrainment Bounce-off may occur with s o l i d aerosols due to e l a s t i c c o l l i s i o n s between the aerosol and c o l l e c t o r surface and thus presents a problem i n p r e d i c t i n g the o v e r a l l c o l l e c t i o n e f f i c i e n c y . Furthermore, there i s the 19 ICO I 1 — i — i — i i 1111 1 — i — i — i i i 111 1—i—i—i i 111 31 ; : i • • i i : : i • • i i • ; 1 . i 0.1 0.2 0.4 0.7 1 2 4 7 10 20 40 100 Superficial velocity, cm/sec F i g . 2.4 V e l o c i t y Penetration Curve f or 1.1 ym aerosol and 10-14 Mesh Sand (Paretsky 3 1) 100r 8 0 - t£ -j 60 - f 4 0 - o. 20- I Upshot 0 Downshot 20-30 mesh Bed thickness-8.2 cm 1 0.2 0.7 1 2 4 7 10 Superficial velocity, cm/sec 100 F i g . 2.5 Vel o c i t y Penetration Curve for 1.1 ym aerosol and 20-30 Mesh Sand (Paretsky 3!) 20 33 possibility that re-entrainment may occur i f the gas velocity is high enough 34 to detach deposited particles. Jordan noted that velocities of 100 m/sec were needed to dislodge individual aerosols 2 ym in diameter from a glass slide and up to 4.5 m/sec to dislodge 10 ym diameter particles. Thus re- entrainment should be negligible in granular bed f i l t r a t i o n where i n t e r s t i t i a l velocities are generally below 1-10 m/sec. There i s , however, the phenomena 35 observed by Leers where particles deposit on one another to form "trees" and "chains". In this case much weaker forces are needed to break the adhesion of these chains. 36 Walkenhorst concluded from his experiments on layers of wire gauze that i) particles below 0.5 ym diameter adhere well after c o l l i s i o n and are not removed even at gas velocities exceeding 6 m/sec i i ) for particles with diameters up to 1 ym, bounce-off may occur, as the velocity is increased the effect decreases due to enhanced i n e r t i a l deposition i i i ) for particles with diameters greater than 1 ym, increased i n e r t i a l deposition outweighs any increased failure of adhesion. The chances of bounce-off and re-entrainment can be reduced by coating the surface of the collectors with a non-volatile liquid such as dioctyl phthalate (D0P). Furthermore, retention may be improved by electrostatic 37 38 charging of the aerosol (Balasubramanian , Mazumder ). 2.7 Review of Experimental and Industrial Studies Carried out on Granular Beds Tables II and III provide a summary of work reported in the literature on the f i l t r a t i o n of aerosols using granular beds. The information was obtained from the given references and converted into consistent units. TABLE II. EXPERIMENTAL STUDIES Aerosol Collector Gas Column Researcher Type Diameter urn Type Diameter urn Velocity cm/sec Diameter cm Bed depth cm Dominant Collection Mechanisms; Remarks KaCz and Macrae-" D.O.P. mist 0.3 Granular charcoal 470-910 16 10.6 2.8 Diffusion; work based on gas mask studies Meissner and Mickley 7 Sulphuric acid mist 2-14 Aluminum silicate Silica gell Glass beads 45-147 57 254 32-62 35-78 37-85 5 5 5 8-25 8-25 8-25 Inertial impaction; efficiency independent of mist concentration and bed age; study on fluidized beds Rams k i l l and Anderson2^ Sulphuric acid mist D.O.P. 0.3 0.2-0.8 Fibrous f i l t e r — 5-280 5-280 — 81 Diffusion and inertia; determined an aerosol size with a minimum collection efficiency Thomas and Yoder 2 7 D.O.P. Polystyrene latex 0.24-1.8 0.6-1.2 Lead shot Sand 1500 360-1600 0.75-1.5 0.1-2.2 3.8 3.8 90 3.6-7.6 Diffusion and gravity; studied upflow and downflow; electrical effects; determined an aerosol size with, minimum collection efficiency Anderson and Silverman 4 0 Genetian violet 0.5 Polystyrene beads 323 25.4 3.5 2.54 Inertia; studied electrical effects; based on a fluidized bed Yoder and Empson4! D.O.P. Polystyrene latex 0.2-2.0 0.5-1.2 Sand 360-1600 ' / 0.1-2.2 — 3.6 Diffusion; determined an aerosol size with a minimum collection efficiency, the size decreases with increasing velocity Scott and Guthrie 4 2 D.O.P. 0.5-1.1 Silica gel. 89 3-15 5.1 19.3-36 Diffusion; efficiency not affected by aerosol concentration Silverman 4 3 Uranine 0.25,0.97 7.03 Epoxy • resin 102 2.5-6 — 1 Diffusion, inertia and interception; velocity for minimum collection found for each aerosol, where diffusion and inertia are weakest Jackson and Calvert 4 4 Fuel o i l mist 6 Glass spheres Berl saddles 12700 12700 183-762 183-762 35.6 35.6 15.2 15.2 Mainly inertial impaction; flow in the horizontal direction Raschig rings 12700 183-762 35.6 15.2 Incalex 12700 183-762 35.6 15.2 saddles Mazumder and Uranine Thomas38 0.16 Polystyrene spheres Copper spheres Epoxy resin 1000 3000 2000 6-36 6-36 6-36 1.5-3 Mainly inertial impaction, studied improvement in collection efficiency due to electrical effects Table II (continued) Aerosol Collector Gas Column Diameter Diameter Velocity Diameter Bed depth Researcher Type wm Type W» cm/sec cm cm Dominant Collection Mechanisms; Remarks Calvert* 5 Fuel o i l 1-1.8 Raschig rings 12700 900 35.6 15 Inertial impaction Bed saddles 12700 900 35.6 Black and Boubel2 Ammonium chloride 0.52 Glass shot 25 4-12 5.1 12.3 Interception and diffusion; studies on a fluldized bed; bed age and aerosol concentration play no effect on collection efficiency Paretsky 3 1 Polystyrene latex 1.1 Sand 841-1650 0.3-8.0 2.5-5 3-7-1.9 Mainly due to inertia and diffusion; upflow and down-flow tests indicate gravity plays a role in collection Yankel, Jackson and Patterson 4 6 D.O.P. 0.67-1.4 Alumina 260 2.5-25 5.1 2.5-10 Interception, some diffusion; efficiencies decreased with increasing gas velocity; fixed and fluldized beds, upflow only Gebhart, Roth and Stahlhofen 3 2 Polystyrene 0.1-2.0 Glass beads 185-4000 0.7-14.2 8 10-40 Diffusion dominant for aerosols less than 0.7 ym diameter, gravity dominant for aerosols greater than 0.7 um diameter; studies on upflow and downflow Kneetig and Beeckmans2* Methylene blue 0.8-2.9 Glass beads 425 8.8-24.6 12.7 1-12 Inertia; studies on fixed and fluldized beds Doganoglu23 Methylene blue D.O.P. 1.1-1.75 Glass beads 110-600 2-45 15 8-12 Gravity dominant for gas velocity less than 8 cm/sec, inertia dominant for gas velocity greater than 8 cm/sec; studies on fixed and fluldized beds Figueroa 2 0 Polystyrene 0.5-2.0 Plastic 305-495 3-18.5 10 3-9 Inertia and diffusion; studies on fixed and fluldized latex beads beds, upflow and downflow; high collection on plastic Methylene 1-2.0 Sand 680 beds due to electrical effects blue First and D.O.P. 0.8 Fibreglass 100-600 254-1524 7.6 1-95 Diffusion at low velocities, inertia at high velocities; Hinds47 Polystyrene 0.36-1.1 mat _ ' bounce-off at high velocities latex Doganoglu, D.O.P. 0.6-3.0 Glass 108-596 10-70 15 3-5 Inertia at high velocities, interceptions and gravity Jog and ballotini at low velocities C l i f t 4 8 Glass spheres 546 60-300 Copper shot 214 60-300 Azaniouch49 Na„S0, 5.2 Granular 3300 60-180 5 5-50 Mainly due to gravity and inertia; bounce-off occurs Nj 2 4 CaCO, ^ TABLE III. INDUSTRIAL STUDIES Researcher Aerosol Collector Type Diameter ym Type Diameter ym Gas Velocity cm/sec Remarks Fairs and Godfrey 5 0 Sulphur 80-10 Graphite 3000-13000 64 Panel bed f i l t e r used in removing fumes from an acid plant burning sulphur Egleson^ Coal dust and ash Coke 3175-10160 particles 5-12 Filtration of dust residue from a coal gasification pilot plant, continuous operation of a packed bed f i l t e r ; column diameter 30.5 cm and bed depth 259 cm Englebrecht 5 Dust Steel 1000-6000 25-80 turnings Sand 1000-6000 Study of a 'Lurgi' M.B. gravel bed f i l t e r ; continuous operation with filtered dust removed by vibration of the bed, operation at 660°F Black and Boubel 2 NH.C1 4 0.52 Glass shot 250 4-12 Fluidized bed operating continuously; collection due to interception, diffusion and electrostatic forces; column diameter 5 cm, bed depth 10-30 cm Squires and Pfeffer 3 Power station f l y ash Sand 760 Study of a panel bed f i l t e r ; contin- uous operation using a "puff-back" method to clean the f i l t e r U> Table III (continued) Researcher Aerosol Collector Type Diameter ym Type Diameter ym Gas Velocity cm/sec Remarks Strauss and Thring 5 1 Fumes Crushed brick 2500-8000 25-100 Horizontal granular f i l t e r for fumes from oxygen-lanced open hearth steel furnace Cook, Swany and . Colpitts52 j Rush and Russ'el 5 4 Fluoride particles Alumina Combination of granular bed (f l u i d - ized) and a f i l t e r bag for removal of fluorides in waste gases from aluminium smelting Kalen and Zenz 4 Catalyst 2-60 Sand 760 Filtering effluent from a cat cracker using a 'Ducon' granular bed f i l t e r ; continuous operation using puff-back for cleaning Dumont 5 5 Radioactive Carbonaceous particles Alumina Sand Fluidized bed operation of a granula bed BBhm and Jordan 5^ Na 20 2 1.4 Sand 280-9700 2-5 Studies on a multilayer sandbed f i l t e r for use with a liquid metal fast breeder reactor Table III (continued) Aerosol Collector Gas Diameter Diameter Velocity Researcher Type ym Type ym cm/sec Remarks Reese5^ Fly ash — Sand 3000-6000 — A dry packed bed scrubber for removal of f l y ash from flue gas from lumber mill operation; continuous recycling of the sand 26 2.8 Empirical Equations Based on experimental and theoretical studies a large number of empirical equations have been suggested to predict the single collector efficiency. These equations, which account for one or more collection mechanisms, vary considerably in accuracy and range of application. Tables IV and V summarize these equations. 2.9 Theoretical Work on the Flow Field Within a Granular Bed In the analysis of the f i l t r a t i o n p r o c e s s , t h e granular bed f i l t e r i s usually assumed to be a homogeneous bed of spherical particles of uniform size through which the dusty gas flows. The f i r s t step in the cal- culation of the f i l t e r efficiency is to determine the flow f i e l d in the f i l t e r . The almost universally used model is to describe the gas flow round a single cylinder or sphere and then to extend this to calculate flow patterns and particle trajectories in a complex of spheres or fibres. However, to describe the geometrical structure of a granular bed Is an extremely complex problem. Some idea of the complexity can be gained by considering the ordered packing of monosized spheres. There are six d i f - ferent ways in which the spheres may be packed, each with i t s own unique porosity. Although these packings have regular geometrical arrangements on which calculations may be based, one is really concerned with the void space through which the carrier gas w i l l flow. These void spaces are so complex that any attempt at a geometrical description must introduce con- siderable simplification. One model considers the spheres as obstacles to an otherwise straight flow of fl u i d without taking into account the effect of neighbouring spheres. 72 This i s called the 'loose' f i l t e r model . However, this model gives a rather poor approximation for the flow f i e l d in an actual granular bed. 73 Another approach is the concept of a 'unit c e l l ' developed by Happel TABLE IV. EMPIRICAL EQUATIONS FOR SINGLE COLLECTOR EFFICIENCY BASED ON ONE COLLECTION MECHANISM Collection Mechanism Researcher Equation Remarks Equation No. Inertia Paretsky 3 1 EI = 2.0ST 1.13 St < 4.4 x 10 2 2000 ym < d < 700 c 2.1 Langmuir and Blodgett 1 3 = 1 + 0.75 ln(2St) -2 St - 1.214 For creeping flow 2.2 EI St' (St + 0.05)2 For potential flow, St > 0.02 2.3 Knettig and EI = 3.76 x 10 3 - 0.464St + 9.68St2 - 16.2St3 Beeckmans24 0.3 > St > 0.0416, based on the experi- mental data of Heme 58 2.4 Landahl and „_ 59 E 1 = HermannJ J St j •.St3 + 0 . 7 7 S t 2 + 0.22 Re = 10 2.5 Behie and Beeckmans^O EI = 0 EI = 3.6 x 10"3 - 0.232St + 2.42St2 - 2.03St3 EI = {St/(St + 0.5)2} St < 0.083 0.6 < St < 0.083 St > 0.06 2.6 l-o Table IV (continued) Collection Mechanism Researcher "Equation Remarks Equation No. Intercep- tion ER = 2NR St -> so, inertia of the particles causes them to travel In a linear direction 2.7 ER - ̂  NR2 St -y 0, particles with no inertia follow the gas streamlines 2.8 Friedlander 6 1 ER = 2Re2 NR2 2.9 Natanson 6 2 NR2 (2 - In Re) 2.10 Diffusive Langmuir X J deposition ED 1.71 Pe~ 2/ 3 (2 - In Re)l/3" 2.11 Johnstone and Roberts 6 3 ED = 8Pe _ 1 + 2.3 Re 1 / 8 Pe~ 5 /* Based on the analogy between heat and mass transfer 2.12 Stairmarid 64 ED = 2.83 Pe 2 Potential flow 2.13 Bousinesque 6 5 ED = 3.15 Pe" Potential flow 2.14 Table IV (continued) C o l l e c t i o n Mechanism Researcher Equation Remarks Equation No. T a r d o s 6 6 ED = 3.96 Pe -2/3 Creeping flow 2.15 Natanson 62 ED = 2.92 Pe -2/3 (2 - In Re)1/3 Pe >> 1, creeping flow 2.16 Gravita- Ranz and Us 2.17 67 EG = — = NG t i o n a l Wong D / U deposition >̂5 TABLE V. EMPIRICAL EQUATIONS FOR SINGLE COLLECTOR EFFICIENCY BASED ON COMBINATIONS OF COLLECTION MECHANISMS Collection Mechanisms Researcher Equation Remarks Equation No. Diffusion and Interception Friedlander f il 1/6 EDR = 6 Re Pe2/3 + 3 NR2 Re2 2.17 Inertia and Davies 6^ Interception EIR = 0.16 [NR + (0.5 + 0.8 NR) St - 0.105 NR St 2] Re = 0.2 2.18 Diffusion, Daviesfi8 Inertia and Interception EDIR =0.16 [NR + (0.5 + 0.8 NR) (j^ + St) - 0.105 NR + St) 2] Pe 2.19 Gravity and Doganoglu Inertia 23 EIG = 2.89 St + 6.87 NG EIG = 5.83 x 10~2 Re St + 1.42 NG d -110 m c d = 600 m c 2.20 2.21 Inertia, Diffusion, Interception and Gravity Schmidt 69 E = 3.97 St + (8 Pe 1 + 2.3 Re 1 / 8 Pe 5 / 8 ) + 1.45 NR + NG Where E EI + ED + ER + EG 2.22 u> o 74 and Kuwabara . It assumes the spheres are homogeneously distributed and the fl u i d may be divided up into spherical regions or cell s , each corres- ponding to one solid sphere. The volume of the c e l l is related to the porosity in such a way that the vol. of fluld/vol. of c e l l equals the porosity (e). It is assumed the flow i s purely viscous thus enabling the velocity of the streamlines and their direction at any point to be calcu- lated. . The ideas of this concept have been used theoretically and experi- mentally by many workers"'">75,76,77 ^ e m o c i e l h a s been extended to 72 higher Reynolds numbers by le Clair and Hamielec 78 Neale and Nader approached the problem from a slightly different point of view. They assumed that the sphere is surrounded by a spherical flu i d envelope whose dimension is computed in the same way as in the Happel- Kuwabara model with a modification that considers the entire sphere swarm as one large exterior porous mass. A different approach is to consider the bed of granules as a random cloud of Identical particles and to use statis- 79 t i c a l methods of analysis. For example, Tarn ^Interpreted the flow as the most probable one around one of the spheres. Creeping flow and no particle/ particle interaction were assumed. Stati s t i c a l and unit c e l l models are s t i l l in their infancy,and, although they describe reasonably well the flow through a packed bed, their complexity w i l l probably preclude their use in engineering designs. Simpler and more easily applied models are s t i l l preferred. CHAPTER 3 THEORY 3.1 Introduction The p r e d i c t i v e model of the c o l l e c t i o n of aerosols by a granular bed i s based on a sing l e granule within the bed. The o v e r a l l bed c o l l e c t i o n e f f i c i e n c y (EBT) i s f i r s t r elated to the si n g l e c o l l e c t o r e f f i c i e n c y (EB). The l a t t e r i s then expressed i n terms of dimensionless groups, which charac- t e r i z e the design and operating conditions of the bed. In d e f i n i n g the f i l t r a t i o n process of aerosol removal by granular beds three sets of factors have to be considered, ( i ) the dispersed aerosol p a r t i c l e s , ( i i ) the dispersion medium or f l u i d , and ( i i i ) the c o l l e c t i o n medium. In t h i s study only s p h e r i c a l aerosols and c o l l e c t o r s are considered. The dispersion medium i s a i r at atmospheric temperature and pressure, the ef f e c t s of temperature and pressure v a r i a t i o n s being assumed n e g l i g i b l e . 3.2 The Overall Bed C o l l e c t i o n E f f i c i e n c y (EBT) as a Function of the Single C o l l e c t o r E f f i c i e n c y (EB) In order to determine the r e l a t i o n s h i p between EBT and EB a s i m p l i f i e d model of the bed i s used. The bed consists of a three dimensional array of uniform granules (diameter d c) of a depth H. The voidage f r a c t i o n of the bed i s e and each c o l l e c t o r exhibits a c o l l e c t i o n e f f i c i e n c y of EB. The analysis i s based on an aerosol p a r t i c l e balance over a very small element of bed (see F i g . 3.1). 32 33 U Cout H U/e, C dh U Cin Figure 3.1. Schematic Diagram of the Granular Bed The rate of aerosol removal is equal to the rate of change of the number of aerosol particles entering and leaving, the element. Therefore for a unit cross section of bed i t can be written where U = superficial gas velocity U/e = i n t e r s t i t i a l gas velocity C = aerosol concentration in the element As = projected area of a collector into the direction of flow x = number of collectors per unit volume of bed = 6(1 - e)/(tt- The rate of removal of aerosol particles by the element for a unit cross-section of bed can be derived in the following manner. The total area of collector available for f i l t r a t i o n i s EB x As dh and therefore the volume of gas swept clean by the collectors per unit time is (U/e) EB x As dh. Since the concentration of the aerosol is C, the rate of removal of aerosol is given by C(U/e) EB x As dh. Integrating equation 3.1 over the whole bed we have U dC = - C(U/e) EB x As dh [3.1] 34 Cout/Cin = exp (- x As EB H/e) [3.2] where C = Cin at h = 0 C = Cout at h = H Since x = 6 (1 - e)/(M d c 3 ) and As = M d 2/4 i t follows that c Cout/Cin = exp {- 1.5(1 - e)H EB/e d'} [3.3] The o v e r a l l bed e f f i c i e n c y i s then given by EBT = (Cin - Coiit)/Cin = 1 - exp {- 1.5(1 - e)H EB/e d^} [3.4] Some workers prefer to use the bed penetration (P) to express the performance of a granular bed, which i s defined as P = 1 - EBT = Cout/Cin [3.5] Equation 3.4 can be rearranged to give EB = - l n ( l - EBT) d^ e / 1 . 5 ( l — e)H [3.6] Equation 3.6 allows the s i n g l e c o l l e c t o r e f f i c i e n c y to be calculated once EBT, e, H and dC are either known or measured. 3.3 Ca l c u l a t i o n of Single C o l l e c t o r E f f i c i e n c y from Basic Design and Operating Variables In order to ca l c u l a t e the si n g l e c o l l e c t o r e f f i c i e n c y (EB) an equation based on the design and operating variables of the f i l t e r must be developed. In t h i s study two methods of producing t h i s equation were considered. The f i r s t assumes that the i n d i v i d u a l c o l l e c t i o n mechanisms act independently of one another. Therefore the c a l c u l a t i o n of EB consists of c a l c u l a t i n g the contribution of the i n d i v i d u a l e f f e c t s of each c o l l e c t i o n mechanism and summing them i n some manner. The second method considers the i n d i v i d u a l c o l l e c t i o n mechanisms are i n t e r r e l a t e d and EB i s calculated d i r e c t l y from the basic v a r i a b l e s . In the f i r s t method the i n d i v i d u a l c o l l e c t i o n e f f i c i e n c i e s are based on the dimensionless groups describing the i n d i v i d u a l c o l l e c t i o n mechanisms. 35 Thus c a l c u l a t i o n of the i n d i v i d u a l e f f i c i e n c y f o r : i n e r t i a (EI) i s based on Re and St, inte r c e p t i o n (ER) i s based on Re and NR, d i f f u s i o n (ED) i s based on Re and Pe, and gravity (EG) i s based on Re and NG. If e l e c t r i c a l e f f e c t s are ignored, then si n g l e c o l l e c t o r e f f i c i e n c y can be estimated by simple summation. E = EI + ER + ED + EG [3.7] However, t h i s summation i s an approximation and i s only v a l i d when one mechanism dominates. Furthermore, as mentioned i n Chapter 1, the e f f i c i e n c y of an i s o l a t e d c o l l e c t o r d i f f e r s when i t i s surrounded by other c o l l e c t o r s . Therefore the value of E must be modified by some cor r e c t i o n factor to obtain the true s i n g l e c o l l e c t o r e f f i c i e n c y within the bed (EB). For example, Eq. 3.7 may be rewritten as EB = ai ED + a 2 ER + a 3 ED + a 4 EG [3.8] or EB = a E [3.9] Using these methods many equations (see Chapter 2) have been developed with varying degrees of accuracy and a p p l i c a b i l i t y . Several forms of these equations were f i t t e d by multiple regression techniques to the experimental r e s u l t s of t h i s study and w i l l be discussed i n Chapter 7. The alternate method i s to develop equations from basic v a r i a b l e s such as gas v e l o c i t y , aerosol and c o l l e c t o r properties. The si n g l e c o l l e c t o r e f f i c i e n c y (EB) was calculated d i r e c t l y from these variables and avoided the problem of having to combine the e f f e c t s of the i n d i v i d u a l mechanisms. In th i s case the value of EB was determined using an equation of the form: EB = f ( d . , d U) [3.10] Equations of t h i s type were also f i t t e d to the experimental r e s u l t s 36 using multiple regression. 3.4 Multiple Regression A l l regressions were carried with the aid of computer programmes called MREG and CONREG developed by the Forestry Department at U.B.C. Multiple regression i s a s t a t i s t i c a l technique for analysing a relation between a dependent variable Y and a set of independent variables X±, X 2 , X 3 . . . X ^ where n is the number of independent variables. A relation of the form Y =a 0+ a i X x + a 2 X 2 + a 3 X 3 ... a n X n [3.11] is chosen where the intercept of the regression equation is a 0 and the co- efficients 04, a 2 ... are estimated by the least squares method. In the present work the dependent variable is the single collector efficiency EB and the independent variables are either the dimensionless groups St, ND, NR etc. or combinations of the basic variables, i.e., d a 2/U. The programme reads m sets of data in the form of EB and the corres- ponding independent variables and places them in a matrix of the form Xl x 2 x 3 X n Y X l l x21 X 31 X n l Yi x 1 2 X 2 2 x3 2 Xn2 Y 2 Xlm x2m x3m X nm Y m The linear regression of Y on two or more independent variables i s called the multiple linear regression. The general form of a multiple linear regression 1s:- V,T , = a n + a-, Xi-•• + a? Xo-» + ... a X . [3.12] Y . X 1 1J- n m 37 where V i s the mean of Y calculated from the regression, and Y • X a0> a l > a ••• a a r e described as population parameters To i n d i c a t e that the i n d i v i d u a l values of Y vary about the mean, i t can be written as Y = a n + a - i X i i + a ? Xoi ... a X . + e i [3.13] x n nx Equation 3.13 implies that/any Y value i s due to the regression mean (V ) plus a deviation from the mean ( e i ) . Y. X i_ The values of c t n , c t i . . . a cannot be obtained unless the whole popu-u n l a t i o n i s measured. From a sample, taken from the population, the best estimates of these parameters are gg, 3i ••• 3 • BY the l e a s t squares p r i n c i p l e these estimates are chosen to produce the l e a s t possible value for the sum of the squares of e i ( i = 1, 2 ... n) when substituted for a 0 , a i . . . a , i . e . , 1 n n n E e i 2 = min E (Yi - g0 - ex X i i - g2 X 2 i ... 3 X . ) 2 [3.14] 1=1 1=1 n n l From Eq. 3.14 one can determine the approximate values of a n , 04 . . . a by d i f f e r e n t i a t i n g the equation f i r s t with respect to g0, and then to 3];» 3 2 ••• a n c ^ 3 • Solving for the values of g0, ĝ  ... ĝ  i s done by matrix inversion c a r r i e d out by the programme. The programme has the f a c i l i t y to eliminate v a r i a b l e s i f the inversion causes the matrix to become singular. The programme also eliminates v a r i - ables i f t h e i r regression c o e f f i c i e n t causes t h e i r contribution to the value of Y^ to be n e g l i g i b l e . In order to s e l e c t the best equation for p r e d i c t i n g values of Y_̂  the programme provides c a l c u l a t i o n s of the standard error of the estimate, r e s i d u a l variance, multiple c o r r e l a t i o n c o e f f i c i e n t and variance r a t i o t e s t s . n 38 3.6 Pressure Drop through the Granular Bed For a complete model of the granular bed It Is necessary to be able to 80 predict the pressure drop across i t . Generally an equation of the Ergun form has been found acceptable, where AP _ (1-e) 2 yU : (1-e) P F U c c a and b are constants which l i e in the ranges 710 > a > 120 4 > b > 0.8 The exact values of a and b depend on the shape of the collector particles and randomness of packing. CHAPTER 4 EXPERIMENTAL WORK 4.1 Objectives of the Experimental Work The experimental programme was designed to investigate the removal of aerosols suspended i n a moving gas by a fixed granular bed and to generate data which could be r e a d i l y analysed. Furthermore, i t was hoped to develop equations from t h i s data that could be used for future scale-up and design. The s p e c i f i c objectives were to determine the e f f e c t on c o l l e c t i o n e f f i c i e n c y of (i) bed depth, ( i i ) gas v e l o c i t y , ( i i ) aerosol s i z e , (iv) c o l l e c t o r s i z e , and (v) d i r e c t i o n of gas flow. Objective ( i ) i s use- f u l f o r t e s t i n g the v a l i d i t y of Eq. 3.6, which can be written as l n ( l - EBT) = - 1.5(1 - e) EB H/e d [4.1] c Therefore a graph of l n ( l - EBT) versus H should be l i n e a r because for a given gas v e l o c i t y voidage, s i n g l e c o l l e c t o r e f f i c i e n c y and c o l l e c t o r diameter a l l remain constant for varying bed depths. Objective (v) would show whether gravity was a s i g n i f i c a n t c o l l e c t i o n mechanism. Many workers believed that e l e c t r i c a l e f f e c t s play a s u b s t a n t i a l r o l e i n 20 28 3(7 c o l l e c t i o n ' ' , but were not sure how to quantify i t . The present experiments were therefore designed to minimize a l l e l e c t r i c a l e f f e c t s by f i r s t passing the aerosol through a charge n e u t r a l i z e r . In addition, a column of copper was used to support the granular bed made up of m e t a l l i c spheres. In t h i s way the whole apparatus could be earthed. The e l e c t r i c a l e f f e c t s were therefore considered n e g l i g i b l e and ignored. 39 40 4.2 Range of Variables Studied The range of variables studied are summarized in Table VI. TABLE VI. RANGE OF VARIABLES STUDIED Variable Range Aerosol diameter 0.1 - 2.0 ym Collector diameter 126 - 598 ym Gas velocity 5 - 7 0 cm/sec Bed depth 0.3 - 18 cm 4.3 Experimental Apparatus Figure 4.1 gives a flow diagram of the equipment used for carrying out the experiments at superficial gas velocities ranging from 5 to 27 cm/sec. Details of purchased equipment are given in Table VII and of the particles and collectors in Table VIII. After leaving the generator the aerosol was mixed with f i l t e r e d bench air to produce the required gas flow through the granular bed. Because of the overall pressure drop throughout the system and the much higher flow of bench air, i t was found that a back pressure was produced which prevented the flow of aerosol into the column. To remedy this, a small diaphragm pump was used to pass the aerosol into the main air flow. The dusty gas was then passed through a neutralizer to remove residual electrical charges from the aerosol particles. The neutralizer was simply a chamber containing a radioactive source (1 millicurle of Krypton 85 gas). The Krypton gas was sealed in a stainless steel tube at atmospheric pressure. The aerosol then passed through copper tubing to the column. To vary the flow rate through the bed, air could be bled off via a flow control valve before reaching the column. This removed the necessity of adjusting flow EXCESS AIR 1 - COLUMN 2 - AEROSOL GENERATOR 3 - AEROSOL PUMP 4 - AEROSOL ANALYSER 5 - SAMPLE PUMP 6 - AIR FILTER 7 - CHARGE NEUTRALIZER 8 - GAS VELOCITY REDUCER 9 - GAS ROTAMETER 10 - GRANULAR BED 1 1 -FLOW CONTROL VALVE 12 - > SAMPLE VALVE 12 SAMPLE AIR 1 -1 8 1 9 FILTERED AIR Fig. 4.1 Schematic Diagram of Equipment 42 TABLE VII. PURCHASED EQUIPMENT Equipment Manufacturer Model Aerosol particle generator Roy co 256 Aerosol particle sensor Royco 241 Aerosol particle monitor Roy co 225 Digital display Royco 264 Charge neutralizer Sierra Instruments 7330 Hygrometer Panametrics 2000 Oilless diaphragm pump Gast Mfg. Corp. DAA110 Vacuum pump Gast Mfg. Corp. 0522-V4-G180DX TABLE VIII. PARTICLES AND COLLECTORS Aerosol Particle Size ym Supplier Material 0.109 0.500 0.600 0.804 1.011 2.020 Dow Chemical Co. Dow Chemical Co. Dow Chemical Co. Dow Chemical Co. Dow Chemical Co. Dow Chemical Co. Polystyrene Polystyrene Polystyrene Polystyrene Polystyrene Polyvinyltoluene Collector Size ym Supplier Material 598.1 511.0 363.9 216.1 126.0 1800.0 Sherritt Gordon Mines Ltd. Sherritt Gordon Mines Ltd. Sherritt Gordon Mines Ltd. Sherritt Gordon Mines Ltd. Sherritt Gordon Mines Ltd. Rona-B Lead Shot Ind. Nickel powder Nickel powder Nickel powder Nickel powder Nickel powder Lead shot 43 rates at the aerosol generation section and ensured a constant aerosol con- centration throughout each experiment. Prior to venting, the gas flow was measured by a rotameter located downstream of the bed. Provisions were also made to measure the humidity of the vented gas. 4.3.1 The Column This was basically a 7.6 cm diameter copper tube which could be easily separated into sections for introducing and removing the collector particles. The entering dusty gas was passed through a calandria to produce a uniform flow of gas before i t entered the bed. The bed particles were supported on a fine wire mesh (approximately 64 ym aperture), which offered negligible resistance to the gas flow at the measured gas velocities. A l l the tubing from the neutralizer to the column was made of copper and the whole apparatus was earthed. Pressure taps were placed at the inlet and outlet of the bed and the pressure drop across the bed was measured by a mercury manometer. At the same level, but on the opposite side of the column, were placed the inlets for the sample probes,(see Fig. 4.2). The column was suspended at i t s centre and could easily be rotated in a vertical plane (see Fig. 4.4). This allowed the column to be operated in either the upflow or downflow mode by making some minor adjustments. These consisted of changing the position of the gauze bed support, rotating the column through 180° and altering the sampling and manometer tubing. 4.3.2 Sampling The gas was sampled before and after the bed. Samples were removed in the direction of the gas flow via 0.9 cm diameter sharp edged probes located in the centre of the column. The gas was continuously removed at a low rate into small chambers and out into the atmosphere via rotameters. From these chambers the gas could 44 h» 76 »H All Dimensions In cm Fig. 4.2 Column Support for Granular Bed All Dimensions In cm. Fig. 4.3 Velocity Reducer JL UPFLOW If L DOWNFLOW An i Fig. 4.4 Upflow and Downflow Operation of the Column 46 be sampled when necessary and directed to the particle counter. Samples could be obtained from either the gas entering the bed or exiting by opening the appropriate sample valve. The counter contained i t s own pump which allowed a larger volume of sheath air to be mixed with the sample before i t entered the analyser c e l l . The discharge from the sample pump was measured by a rotameter and represented the sample flow. No attempts were made to sample isokinetically as calculations suggested that the sampling rate had a negligible effect on the aerosol concentration for particles less than about 5 ym diameter"*"^. This was also confirmed by a series of simple experiments. The purpose of the velocity reducers (Fig. 4.3) was to dampen the varia- tions in aerosol concentration within the column. These variations were caused by the aerosol generator and/or by deposited particles breaking away from the equipment walls. The lines and probes were made as identical as possible for the inlet and outlet gas sampling trains. Errors inherent in the system would there- fore be automatically eliminated when comparing aerosol counts. 4.4 Aerosol Particles The aerosols used were of polystyrene latex with the exception of the 2.02 ym diameter aersol which was of polyvinyltoluene (provided by the Dow Chemical Company) and were generated by atomizing dilute suspensions of the latex"particles. These particles were chosen because: i) they are available in uniform sizes with low standard deviations (see electron micrographs Figs. 4.5 to 4.11) i i ) they could be generated and handled easily i i i ) they could be generated at low concentrations which minimizes particle agglomeration and bed loading. 47 Fig. 4.5 Electron Micrograph of 0.109 ym diameter Latex Particles (Mag. 30,000 x) Fig. 4.6 Electron Micrograph of 0.50 ym diameter Latex Particles (Mag. 8,000 x ) Fig. 4.8 Electron Micrograph of 0.804 ym diameter Latex Particles (Mag. 8,000 x) Fig. 4.10 Electron Micrograph of 2.02 ym diameter Latex Particles (Mag. 4,000 x) From the electron micrographs i t can be seen that the p a r t i c l e s are sp h e r i c a l , smooth and f a i r l y uniform. However, i n some cases (Figs. 4.8 and 4.10) a few very much smaller p a r t i c l e s are also present. Properties of p a r t i c l e s used are summarized i n Table IX. TABLE IX. PROPERTIES OF PARTICLES USED Diameter Standard Density Material ym Deviation gm/cc Polystyrene 0.109 0.0027 1.05 Polystyrene 0.500 0.0027 1.05 Polystyrene 0.600 0.0030 1.05 Polystyrene 0.804 0.0048 1.05 Polystyrene 1.011 0.0054 1.05 Polyvinyltoluene 2.020 0.0135 1.027 4.5 Granular Bed P a r t i c l e s I n i t i a l tests were c a r r i e d out with 1.8 mm diameter lead shot. However, most experiments were performed with n i c k e l shot obtained from S h e r r i t t Gordon Mines Ltd. The sizes used are given i n Table X. Figures 4.11 to 4.16 are electron micrographs of each c o l l e c t o r . It can be seen that they are f a i r l y uniform and s p h e r i c a l . The surfaces are quite smooth but the larger c o l l e c t o r s exhibit some surface i r r e g u l a r i t i e s which may increase t h e i r a b i l i t y t o c c o l l e c t aerosols by providing more surface area. 4.6 Aerosol Generator The aerosol was generated from a purchased hydrosol of latex p a r t i c l e s a f t e r d i l u t i o n with d i s t i l l e d water (about 0.1 ml of hydrosol to 30 ml of d i s t i l l e d water). The d i l u t e d hydrosol was atomized with clean a i r i n a Royco aerosol generator model 256. The atomizer consisted e s s e n t i a l l y of a 51 TABLE X. CHARACTERISTICS OF NICKEL SHOT Sieve Analysis % Material Retained on ym- the Sieve Collector 1 2 3 4 5 +600 45.8 9.7 0.1 -600 + 500 54.1 90.1 10.7 -500 + 300 0.1 0.2 86.1 0.8 -300 + 150 3.1 97.8 6.0 -150 + 106 1.9 89.2 - 106 4.8 Vol. Av. diameter ym 598.1 511.0 363.9 216.1 126.0 Voidage 0.416 0.398 0.425 0.415 0.425 small neutralizer (or jet pump) (see Fig. 4.17). The input air causes a partial vacuum over the jet that protrudes into the diluted hydrosol, so that water is forced out of the jet to be dispersed into vapour. The water vapour and standard particles then flow out of the atomizer into the aerosol mixer tube. The aerosol then has to be dried to remove any water droplets. In the mixer tube air, which has been dried over anhydrous calcium sulphate and f i l t e r e d , i s added at two points in a direction that causes the air to flow in a helical pattern around the humid air from the atomizer. The tube has a number of constrictions so that the atomizer air and drier air are thoroughly mixed. At the end of the tube dehumidified air and suspended particles are drawn off. For normal operation of the aerosol generator the drier air flow rate was set at ^ 20 1/min and the atomizer air pressure at 5 p.s.i. Thus the maximum aerosol supply pressure was only 5 p.s.i. The aerosol concentra- 7 3 tion was set to about 10 partlcles/M but could easily be varied by changing F i g . 4.11 E l e c t r o n Micrograph of 598 ym diameter N i c k e l Shot (Mag. 15 x) F i g . 4.12 Close up of a 598 ym diameter Nickel Shot (Mag. 80 x) 53 Fig. 4.14 Electron Micrograph of 363 ym diameter Nickel Shot (Mag. 20 x) g. 4.15 Electron Micrograph of 216 ym diameter Nickel Shot (Mag. 40 x) Fig. 4.16 Electron Micrograph of 126 ym diameter Nickel Shot (Mag. 80 x) 55 ATOMIZER FILTER ATOMIZER PRESSURE GAGE ATOMIZER PRESSURE VALVE DILUTE HYDROSOL OF LATEX PARTICLES AND DISTILLED WATER FILTER AIR DRIER DRIER FLOW METER DRIER AIR VALVE ;<Js) M 11 11 11 AEROSOL MIXER TUBE EXHAUST AEROSOL OUTPUT Fig. 4.17 Block Diagram of Aerosol Generator 56 (i) the drier air flow, ( i i ) the atomizer pressure, or ( i i i ) the hydrosol concentration. 4.7 Aerosol Detector It was necessary to be able to count the number of aerosol particles in a given volume of gas in order to determine the collection efficiency of the granular bed. The counter used was a Royco sensor model 241, which operates on the principle of forward light scattering. A sharply defined beam of light is focused onto a small sensitive volume called the sample c e l l (̂ 0.5 x 1.0 x 4 mm). A l l aerosol particles entering the sensor are passed through the c e l l (see Fig. 4.18). If no particles are present, a l l the light passes through to the light trap where i t is absorbed. If a particle is present, light is scattered and is able to by-pass the light trap. By means of two collecting lenses the forward scattered light is focused onto a photomultipller which generates a current pulse to drive a d i g i t a l counter. Coincidence errors arise when more than one particle enters the c e l l at any one time. In the case of the Royco counter this occurs at aerosol 10 3 concentrationsv;greater than about 10 particles/m . 4.8 Minor Modifications and Additional Equipment After several experiments had been carried out i t was realized that i t would be necessary to increase the gas flow through the column. This required changing the rotameter floats and recalibrating them. Further modifications were made when i t was noted that the aerosol diaphragm pump was acting as a f i l t e r and prevented the passage of sufficient amounts of 1 and 2 ym aerosol particles. Hence, instead of pumping the air through the system, the air was drawn through i t by means of a vacuum pump (see Fig. 4.19). This arrangement presented some sampling problems and a l l REFLECTOR 1 COLLECTING LENSES FORM RELAY LENS FORMS SHARP ' IMAGE OF PARTICLE ON IMAGE OF APERTURE IN PHOTOMULTIPLIER CATHODE FROM THE SENSITIVE VOLUME THE LIGHT THAT MISSES LIGHT TRAP Fig. 4.18 Layout of Optics for Aerosol Analyser EXCESS AIR INLET AIR txH 2 I -COLUMN 2 - A E R O S O L GENERATOR 3 —GRANULAR BED 4 - A E R O S O L ANALYSER 5 —SAMPLE PUMP 6 - AIR FILTER 7 - CHARGE NEUTRALIZER 8 - GAS VELOCITY REDUCER 9 - GAS ROTAMETER 10 - V A C U U M PUMP I I-FLOW CONTROL VALVE 1 2 - S A M P L E VALVE Fig. 4.19 Schematic Diagram of Modified Equipment 59 the outlet lines had to be connected to the pump. As the sample pump in the aerosol counter was not powerful enough to draw samples from the equipment, it s discharge line was also connected to the vacuum pump. Set up in this manner, the operation of the equipment was virtua l l y the same as before. Additional equipment was used to generate humidified air. To vary the humidity a simple spray nozzle was added to the inlet gas supply. Water was sprayed into the main air flow and the damp air and water droplets passed into a cyclone. Water droplets were removed from the base of the cyclone and the humidified air passed through a f i l t e r before being mixed with the aerosol flow (see Fig. 4.20). The humidity of the gas was measured by a Panametrics hygrometer (model 2000) with the probe inserted into the gas leaving the column. 60 AEROSOL AIR - B H INLET AIR SPRAY CHAMBER T H FILTER CYCLONE DRAIN Fig. 4.20 Humidifying Equipment CHAPTER 5 PRELIMINARY EXPERIMENTS A series of experiments was carried out to develop a consistent experimental procedure and to become familiarized with the equipment. 5.1 The Effect of Humidity on Collection Efficiency If electrical charges were present in the equipment or on the aerosol particles, then changes in humidity should affect the collection efficiency. For instance, i f electrical charges were helping collection then damp air, which would more easily disperse these charges, would produce a lower collec- tion efficiency than dry air. However, based on several tests (see Tables XI and XII) no significant difference in collection efficiency could be detected by changes in humidity. These results suggest that the aerosols and collectors are electrically neutral and that the electrical effects may be ignored. It was realized that humidity could also affect the retention forces between the particle and the collector by altering the nature of the absorbed film of water on the collector surface. The humidity was therefore recorded at the beginning and end of a l l subsequent experiments. 5.2 Bed Ageing or Loading 23 It has been reported that a build up of dust in the interstices of granular beds increases the collection efficiency as well as the pressure drop across the bed. These effects usually occur at aerosol concentrations very 61 62 TABLE XI. COLLECTION EFFICIENCY OF 598.1 ym NICKEL SHOT AT VARIOUS HUMIDITIES (Bed depth = 4.5 cm; Aerosol diameter = 0.5 ym) Gas Collection Humidity Velocity Relative Humidity cm/sec 38% 45% 70% 5.24 38.2 37.9 34.6 11.16 29.6 28.2 27.4 16.97 28.8 28.0 27.8 22.37 26.9 28.4 27.4 27.08 26.5 23.9 26.4 TABLE XII. COLLECTION EFFICIENCY OF 511.0 ym NICKEL SHOT AT VARIOUS HUMIDITIES (Bed depth = 9.1 cm; Aerosol diameter = 0.5 ym) Gas Collection Efficiency Velocity Relative Humidity cm/sec 18% 38% 64% 5.24 43.0 41.9 42.1 11.16 32.9 35.1 35.0 16.97 31.9 32.3 32.8 22.37 31.2 31.9 32.0 27.08 30.3 32.5 31.5 63 7 3 much higher than 1.0 particles/m , which were used in the present work. Thus in a l l experiments the bed loading was extremely small. For example, i t would take about two years for one gram of 2.02 ym particles to be deposited assuming typical operating conditions and a 100% removal efficiency. Nevertheless, long term tests were conducted on each collector and Tables XIII and XIV summarize the results performed with two collectors. As can be seen, no significant change in collection efficiency was observed. TABLE XIII. BED AGEING TESTS ON 598 ym NICKEL SHOT (Bed depth = 9.1 cm; Aerosol diameter = 0.500 ym) Gas Collection Efficiency Velocity cm/sec 0 3 5 Time Hours 8 9.5 12 14 16 18 5.24 46.3 44.7 40.9 40.2 41.9 43.5 41.3 43.0 45.2 11.16 37.1 37.8 36.1 35.3 34.5 35.7 32.8 32.9 39.2 16.97 36.7 38.3 31.3 32.3 32.9 33.0 32.8 32.9 35.0 22.37 32.1 34.4 32.9 30.7 31.5 30.9 35.7 31.2 31.0 27.08 33.7 38.0 32.5 32.6 33.0 32.8 33.7 30.3 33.4 TABLE XIV. BED AGEING TESTS ON 216.0 ym NICKEL SHOT (Bed depth = 2.27 cm; Aerosol diameter = 0.500 ym) Gas Collection Efficiency Velocity Time Hours cm/sec 0 3 6 5.24 88.2 86.5 85.5 86.2 11.16 80.1 77.2 78.0 80.5 16.97 76.3 75.9 74.9 75.9 22.37 72.3 71.8 71.4 74.3 27.08 71.6 68.1 69.0 70.1 64 5.3 Collection by the Empty Column and Bed Support Several empty column tests were carried out to determine the removal of particles on the bed support and walls of the column. As can be seen from Table XV, the removal was found to be less than 1%. TABLE XV. COLLECTION BY THE EMPTY COLUMN Gas Collection Efficiency Velocity Aerosol diameter ym cm/sec 0.109 0.500 0.600 0.804 5.24 0.80 1.00 0.90 0.60 11.16 0.40 0.90 0.80 0.80 16.97 0.33 0.80 0.80 0.50 22.37 0.35 0.25 0.80 0.90 27.08 0.00 0.35 0.40 0.65 Since the aerosol removal of the empty column was so low, no correction to the measured bed collection efficiency was made. 5.4 Background Count The background counts were readings recorded by the aerosol counter during normal operation of the equipment but with no aerosol generation. The background count could be caused by dust in the system from (i) particles depositing in the inlet tubing and subsequently breaking away, ( i i ) incomplete f i l t r a t i o n of the bench and aerosol drier a i r , ( i i i ) impure d i s t i l l e d water (used in dilution of the latex hydrosol), (iv) leaks of air into the equip- ment , or (v) electrical noise generated within the aerosol detection equip- ment. Prior to each experiment background counts were therefore determined. The counts usually varied between 20-40 particles/minute which is negligible in comparison with counts of about 2,000-8,000 recorded when the aerosol generator was operating. 65 It was also possible that during normal operation of the equipment water droplets (caused by atomization of the diluted latex hydrosol) were carried into the column. If this was the case, then the presence of the droplets would modify the measured collection efficiency of the bed. Tests were therefore performed to determine i f this was taking place. This was simply done by running the aerosol generator with d i s t i l l e d water only. Table XVI shows some of the recorded counts and i t can be seen there is no detectable difference from the background count. TABLE XVI. BACKGROUND COUNTS FOR THE EMPTY COLUMN (Gas velocity = 27 cm/sec) Aerosol generator not used Aerosol generator used with only d i s t i l l e d water 39 42 40 27 21 34 28 29 33 30 Av. 32 Av. 32.4 5.5 Sampling Counts and Changeover Time Due to the unsteady performance of the aerosol generator several counts had to be taken before reproducible counts could be recorded. Once the system was reasonably steady (i.e., the several successive counts f e l l within ± 5% of each other) then 4-8 readings were taken and averaged. After sampling the inlet gas flow to the bed, the aerosol concentration was determined for the outlet flow. However, i t was necessary to decide how long to wait for the system to stabilize before counts could be recorded after each changeover. Waiting for 1, 2, 5 and 10 minutes between each changeover gave no noticeable difference in measured counts. A waiting time 66 of one minute between changeovers was therefore adopted. 5.6 Reproducibility Several tests were repeated three to four months later and were found to agree well within ± 5%. Also with the changeover of pumping to drawing the gas through the equipment (which allowed tests with 1 and 2 ym diameter aerosols to be performed), tests with 0.8 and 0.5 ym diameter aerosols were repeated. Again the results obtained were in good agreement with those of previous tests. When the equipment was modified for higher gas flows, several measurements were repeated to check for consistency. This was done by overlapping the two velocity ranges with the low velocity tests covering 5 to 27 cm/sec and the high velocity tests covering 16 to 67 cm/sec. 5.7 Errors These were very d i f f i c u l t to quantify owing to the nature of the equip- ment and the f i l t r a t i o n process. The largest single source of errors was probably the aerosol generator which tended to behave rather erratically. For example, counts of the sampled gas flow could jump from 2,000 to 4,000 counts per minute for no apparent reason and remain there for the rest of the experiment. Alter- natively the counts would increase steadily from 2,000 to 6,000 over the course of the experiment and later perhaps f a l l back to 4,000. Thus errors were introduced by the aerosol generator which could not be overcome. Re-entrainment and bounce-off could substantially affect the overall aerosol deposition and hence the collection efficiency of the bed. If these effects were taking place, then the recorded efficiencies would be lower than their true value. It was possible to check to see i f re- entrainment was occurring by shutting off the aerosol generator at the end of an experiment and measuring the aerosol concentration of the gas 67 downstream from the bed. It was noted that the counts rapidly f e l l to the background value after the aerosol generator was shut off which implies that l i t t l e , i f any, re-entrainment was taking place. However, bounce-off is a different phenomena. It occurs when a particle collides with a collector but is not retained. This effect is usually only observed with dry, solid aerosols. Using sticky, liquid aerosols such as dloctyl phthalate (D.O.P.) bounce-off could be eliminated. Thus i t would be possible to determine i f bounce-off was occurring by comparing results of tests conducted with dry and liquid aerosols. This was not done in this study as the available aerosol generator was not capable of producing liquid aerosols. Further small errors are summarized below, i) Aerosol counter:-As mentioned before, errors could be introduced by the 'interference' effect or by particles depositing on the optical surfaces of the analyser. This would usually occur at high aerosol concentrations. The period for counting the aerosols was set electronically with the d i g i t a l counter being stopped automatically after one minute and therefore timing errors were negligible. i i ) Gas flow-:-Small errors could be caused by incorrectly reading the rotameters. Also fluctuations in the bench air supply could cause errors and could contribute to the erratic behaviour of the aerosol generator, i i i ) Non isokinetic sampling:-This could cause a small error in the measured counts but is most unlikely, especially with aerosols below 2 ym in diameter. Errors within the sampling equipment were minimized by making the inlet and outlet sampling trains as identical as possible. 68 5.8 Experimental Programme 5.8.1 Procedure From the preliminary experiments a test procedure was developed. Each experiment involved the measurement of collection efficiency for various superficial gas velocities at different bed depths and was repeated for a range of aerosol and collector sizes. Details of a typical run, which took about 2-3 hours are presented below. i) The aerosol counter was switched on and allowed to warm up for about half an hour. i i ) A measured volume of specific collector particles was charged to the column and fluidized to give a loosely packed bed. If necessary the surface was levelled without compressing the bed. i i i ) The column was set up in an upflow or downflow mode (see Chapter 4). iv) A dilute hydrosol mixture of a specific aerosol was charged to the aerosol generator, v) With the aerosol generator isolated, a l l pumps and gas flows were turned on and adjusted to give maximum flow, vi) Particle counts were taken to measure the background count, v i i ) The aerosol generator and pump were turned on and the humidity of the exit gas from the column was measured. Also the air temperature was noted. v i i i ) The particle counts/minute were monitored for the inlet air un t i l steady and then 4 to 8 readings were taken, ix) The sample flow was then changed to the outlet gas and one minute allowed for stabilization. Further 4 to 8 readings were taken, x) The sample flow was changed back to the Inlet gas to check the counts for consistency. 69 xi) The pressure drop across the column was measured for each.gas velocity, x i i ) The gas velocity was then reduced and steps ( v i i i ) to (xii) repeated. 5.8.2 Programme For each collector the tests summarized in Table XVII were carried out. TABLE XVII. SUMMARY OF EXPERIMENTAL TESTS Aerosol diameter ym Test 0.109 0.500 0.600 0.804 1.011 2.020 Downflow: Low velocity High velocity X X X X X X X X X Upflow: Low velocity High velocity X X X X X Bed depth X X X X Humidity test X Ageing test X Low velocity configuration•:—5 to 27 cm/sec High velocity configuration:-16.33 to 67.0 cm/sec Bed depth test-:-For aerosols 0.109, 0.600 and 0.804 ym in . diameter only two depths were used; for 0.500 ym aerosol four to five depths were used. Humidity test •:-This involved comparing the collection of 0.500 ym aerosol with dry and damp air. A l l other tests were carried out at ^ 30-40% relative humidity. Ageing test :-This involved runs of up to 18 hours duration and measuring the collection efficiency every two hours for each gas velocity. CHAPTER 6 EXPERIMENTAL RESULTS AND DISCUSSION 6.1 Introduction A summary of a l l experimental conditions and results can be found in Appendix A. When tests were duplicated, the shown results are averaged values. Unless otherwise stated, a l l the figures in this section show results for experiments conducted in the downflow mode. 6.2 The Effect of Superficial Gas Velocity on Bed Collection Efficiency Figs. 6.1 to 6.10 show the collection efficiency of the granular beds as a function of superficial gas velocity for various collectors and aerosol particles. Figs. 6.1 to 6.5 refer to the low velocity tests only. Figs. 6.6 to 6.10 refer to both the high and low velocity tests for upflow and downflow. The characteristic shape of the efficiency curve (see Fig. 2.1) was not observed in the i n i t i a l low velocity tests. Figs. 6.1 to 6.5 show a steady decrease in collection efficiency with no subsequent rise due to increasing i n e r t i a l effects. Therefore, additional high velocity tests were performed in order to study particle collection in the inertia domin- ated region. From Figs. 6.6 to 6.10, which cover the f u l l range of velocities tested, i t i s clear that the efficiency curves can be divided into two regions. At low velocities the collection efficiency decreases with increasing gas velocity due to the reduced diffusional effect and, perhaps, gravitational 70 71 0 10 20 30 SUPERFICIAL GAS VELOC ITY cm/sec Fig. 6.1 Collection Efficiency as a Function of Gas Velocity (Bedcdepth = 4.54 cm; collector diameter = 598.1 ym) 72 10 20 30 SUPERFICIAL GAS VELOCITY cm/sec Fig. 6.2 Collection Efficiency as a Function of Gas Velocity (Bed depth = 4.54 cm; collector diameter = 511 ym) 73 0 10 20 SUPERFICIAL GAS VELOCITY cm/sec 30 Fig. 6.3 Collection Efficiency as a Function of Gas Velocity (Bed depth = 4.54 cm; collector diameter =• 363 ym) Fig. 6.4 Collection Efficiency as a Function of Gas Velocity (Bed depth = 2.27 cm; collector diameter = 216 ym) 75 Fig. 6.5 Collection Efficiency as a Function of Gas Velocity (Bed depth = 2.27 cm; collector diameter = 126 ym) SUPERFICIAL GAS VELOCITY cm/sec Fig. 6.6 Collection Efficiency as a Function of Gas Velocity (Bed depth = 4.54 cm; collector diameter = 598 ym) ON COLLECTION EFFICIENCY % LL COLLECTION EFFICIENCY % (TO ON 00 w o fD h-1 & h-1 fD n fD rt TJ H" rt O 11 W hh -P- i-h • H- Ui O -f> H- fD Q 3 B o n w o t_> ft) M fD trj o c rt 0 o o i-i rt CL O H. 3 0>3 o ro H I rt ro en i-i cu co ll < W fD ON I—1 u> o o B rt o ro o c t J m o OJ > o r~ > < m r~ o o 4* O o 3 o ° O 3 21  100 h- 10 20 30 40 SUPERFICIAL GAS VELOCITY 50 cm/sec 60 70 Fig. 6.10 Collection Efficiency as a Function of Gas Velocity (Bed depth = 2.27 cm; collector diameter = 126 ym) CO o 81 effect for the larger aerosol particles. Minimum collection occurs at gas velocities between about 15 and 20 cm/sec where both the diffusional and i n e r t i a l effects are weak. As the gas velocity increases the collection efficiency starts to rise again because the i n e r t i a l effect becomes domin- ant. It may be noted that, as the aerosol size increases, the velocity of minimum collection decreases. For example, in case of 598.0 ym diameter nickel shot the velocity for minimum collection is about 12 cm/sec for 2 ym diameter aerosol particles and 25 cm/sec for 0.5 ym diameter aerosol particles. At velocities greater than about 45 cm/sec the collection efficiency was usually found to level off or decline. This phenomena may be caused by bounce-off because re-entrainment is unlikely for reasons mentioned in Section 5.8. 6.3 The Effect of Flow Direction on Bed Collection Efficiency Figs. 6.6 to 6.10 also show the results for the upflow (dashed lines) as well as downflow (solid lines) experiments. There is a substantial decrease in collection efficiency at the lower velocities in the upflow mode especially for the 1.01 ym aerosols. The difference in collection becomes negligible at high gas velocities. Also, the smaller the aerosol particle the smaller the difference between upflow and downflow results. Since the direction of flow only influences the gravitational collection mechanism i t can be concluded that gravity is playing a significant role in collection especially at low gas velocities and for large aerosols. 6.4 The Effect of Aerosol Diameter on Bed Collection Efficiency As seen from Figs. 6.1 to 6.10, the collection efficiency usually 27 28 29 decreases with aerosol size. Many workers ' ' have pointed out that this trend stops at a certain aerosol size after which the collection 82 efficiency starts to increase again due to the enhanced diffusional effect. Figure 6.11 shows that no minimum in the efficiency-aerosol size curves was detected in this work. This may have been due to the lack of experimental 29 results at low gas velocities and small aerosols. Chen has pointed out that the minimum only occurs at gas velocities less than about 4 cm/sec. 6.5 The Effect of Collector Size on Bed Collection Efficiency As expected the collection efficiency increases with decreasing collector diameter due to the reduced i n t e r s t i t i a l spaces. The smaller void spaces increase the effects of inertial, diffusional and gravitational collec- tion because the aerosol particles need to travel smaller distances to reach the collector surface. It is unlikely that sieving plays a significant role in collection even for the larger.: aerosol particles (2.02 ym in diameter) and the smallest collector particles (126 ym in diameter). 6.6 The Effect of Bed Depth on Collection Efficiency Figs. 6.12 to 6.16 summarize the results of varying the bed depth for 0.5 ym diameter aerosol particles and different gas velocities. As suggested by Eq. 3.6, the data are plotted as log(100 - % collection efficiency) versus bed depth (H). The results follow straight lines, which pass approximately through the point of zero collection efficiency at zero bed depth. This is in agreement with Eq. 3.6 whose validity is therefore confirmed. At large bed depths some deviation from the straight line behaviour occurs and Eq. 3.6 overpredicts the collection efficiency. The deviation is accentuated by the log scale and only occurs when the efficiencies exceed about 90%. The effect may be due to the presence of a small fraction of undersize aerosol particles in the aerosol. The electron micrographs (Figs. 4.8 and 4.10) show that several smaller particles are found together with the larger aerosol. The collection efficiency for these smaller sized 0.5 1.0 AEROSOL DIAMETER /JLm 2.0 Fig. 6.11 Collection Efficiency as a Function of Aerosol Diameter at a Superficial Gas Velcoity of 5.24 cm/sec. 0 5 10 15 20 BED DEPTH cm. 6.12 Collection Efficiency as a Function of Bed Depth (Collector diameter = 598 urn, aerosol diameter =0.5 ym) 85 5 10 15 20 BED DEPTH cm. Fig. 6.13 Collection Efficiency as a Function of Bed Depth (Collector diameter = 511 ym, aerosol diameter =0.5 ym) Fig. 6.14 Collection Efficiency as a Function of Bed Depth (Collector diameter = 363 ym, aerosol diameter = 0.5 ym) Fig. 6.15 Collection Efficiency as a Function of Bed Depth (Collector diameter = 216 ym, aerosol diameter = 0.5 ym) 00 88 Fig. 6.16 Collection Efficiency as a Function of Bed Depth (Collector diameter = 126 ym, aerosol diameter = 0.5 ym) 89 aerosols would be much lower than that of the main aerosol. Thus their presence would result in a reduced, overall collection efficiency especially at high removal rates. 6.7 Pressure Drop across the Granular Bed Pressure drops across the granular beds were measured for each gas velocity and the detailed results are given in Appendix A. From Fig. 6.17 i t can be seen that there is a good linear relationship between AP/H and gas 80 velocity. The results f i t an Ergun type equation of the following form: — = ,316 —p + 1.73 — — [6.1] c c where the variables have the following units: AP/H = dynes/cm2 cm d c = cm U = cm/sec P F = gm/cc y = gm cm/sec 80 The coefficients 316 and 1.73 l i e within the range observed by others For the velocity range tested, viscous force dominates in the granular bed as compared to in e r t i a l effects. The pressure drop was attributable mainly to viscous energy losses. 6.8 Summary of Experimental Results i) At low gas velocities (less than about 10 cm/sec) the collection e f f i c - iency decreases with increasing gas velocity, probably due to decreasing diffusional and gravitational effects, i i ) A minimum is observed in collection efficiency versus gas velocity curves when diffusional and in e r t i a l effects are both weak, i i i ) The larger the aerosol size the lower the gas velocity at which this minimum collection occurs. 06 91 iv) At higher gas velocities (greater than about 20 cm/sec) collection efficiency increases with gas velocity because i n e r t i a l effects become dominant. v) The collection efficiency increases with increasing aerosol size and decreasing collector size, vi) The collection efficiency increases with bed depth as predicted by Eq. 3.6. v i i ) As the collection efficiency for downflow is always greater than upflow at low gas velocities, i t is evident that gravitational settling was playing a role in the f i l t r a t i o n , v i i i ) For the range of conditions studied, direct interception played no role in the f i l t r a t i o n . CHAPTER 7 STATISTICAL ANALYSIS 7.1 Introduction From the experimental results i t was hoped to develop an empirical and, possibly, a theoretical model to predict aerosol collection in granular beds. The model would be based on variables such as bed depth, gas velocity, aerosol properties and collector dimensions. The overall bed collection efficiencies (EBT), which were determined experimentally, were f i r s t reduced to single collector efficiencies (EB) by means of Eq. 3.6. Since EB is independent of bed depth, the single particle efficiencies calculated for different bed depths, but otherwise identical conditions, could be averaged. As discussed in Chapter 1, the following dimensionless groups govern particle collection in granular beds and were calculated for each set of experimental conditions: Reynolds number (Re); Stokes number (St); Interception number (NR); Peclet number (Pe); and Gravity number (NG). These dimensionless groups and single collector efficiencies are tabulated in Appendix B. 7.2 Evaluation of Various Empirical Equations Most workers have concentrated on calculating the individual collection efficiencies due to inertia, diffusion, gravity and interception, and summed them to give an overall single collector efficiency. Others have calculated the various dimensionless numbers and combined them in such a manner as to 92 93 produce the single particle efficiency. As pointed out before, neither method i s entirely correct, especially when working in a region where the magnitude of the effects of several collection mechanisms are comparable. The equations developed by other workers were fitt e d to the present experimental data using a multiple regression programme. Other equations, such as polynomials based on the gas velocity, as well as aerosol and col- lector diameters were also tested. The results of a l l regression analyses are summarized in Appendix C. In general, these equations gave relatively good f i t s when predicting the collection efficiency for a single collector or aerosol size. However, the overall f i t for a l l the experimental data was quite poor. Consequently there was a need to develop a more general equation. 7.3 Identification of the Best Empirical Equation The best f i t of the experimental data was obtained with an equation of the type: d d d 2 EB = aC-r3-) (d U) + b (d U) / / J + c [7.1] d a d a U c c with constants a = 660, b = 0.0148, c = 400,000, and a multiple correlation coefficient (R) of 0.972. (The development of this equation i s given in Appendix D together with a comparison of the experimental and predicted collection efficiencies.) Equation 7.1 satisfactorily predicts the minimum in the collection efficiency versus gas velocity curves and the effect of gravity. Some dis- agreement, however, arises at high velocities, which could be due to bounce- off which is not taken into account. The f i t is worst for the 0.109 ym diameter aerosols which suggests that the diffusive effect is not properly represented. However, i t should be noted that the experimental results obtained with 0.109 ym diameter aerosols 94 may be somewhat unreliable since the particle counter was used as i t s limit of detection. (The manufacturer recommends i t s use only for particles greater than 0.3 ym in diameter.) Figs. 7.1 to 7.6 provide a comparison between some predicted (using Eqs. 3.6 and 7.1) and experimental bed collection efficiencies. Fig. 7.7 is a scatter plot of a l l calculated efficiencies versus experimental e f f i c - iencies and the agreement is within ± 10% for most cases. The i n i t i a l experimental results obtained by using granular beds of lead shot were not used i n the development of Eq. 7.1. However, the collec- tion efficiencies predicted by Eq. 7.1 agree with the lead shot results to within ± 1.5%. Also listed in Appendix D are comparisons of the predicted bed collection efficiencies and the experimental results of other researchers. 20 Comparisons were made with Figueroa's data based on experiments with 7000 ym diameter sand. His other experimental results were not compared since they were obtained with plastic bed particles susceptible to electrical effects. The predictions of Eq. 7.1 agree well with Figueroa's results and especially the measurements made with 0.5 ym diameter aerosols. 23 Further comparisons were made with the results of Doganoglu. . He used 110 and 600 ym diameter glass beads as collector particles and D.O.P. aerosol particles. Equation 7.1 is rather poor in predicting the collection efficiencies of the 600 ym collectors, except at the higher velocities of 30 cm/sec. The predictions are better for the 110 ym collectors especially for the removal of 1.75 ym diameter aerosols. The poor predictions of Doganoglu's results could be due to the fact that he used liquid D.O.P. aerosol particles whereas Eq. 7.1 is based on dry, solid aerosol particles. However, this does not explain why in general the prediction of Eq. 7.1 are higher than the experimental values; using liquid aerosols should in fact improve the collection efficiency of the bed. 10 20 30 40 50 60 70 SUPERFICIAL GAS VELOCITY cm/sec Fig. 7.1 Comparison of Experimental and Calculated Collection Efficiencies (Collector diameter = 598.1 ym) Calc. Downflow Experimental A - I .ON fJLm • — .804/i.m O - .500/1 m 0 10 Fig. 7.2 20 30 SUPERFICIAL GAS 40 VELOCITY 50 cm/sec 60 70 Comparison between Experimental and Calculated Collection Efficiencies (Collector diameter = 511.0 ym) 100 50 Calc. Downflow Experimental A-I.OII Ltm O — .804 Li m O — .500/Jm • - J 0 10 Fig. 7.3 20 30 40 50 SUPERFICIAL GAS VELOCITY c m / s e c 60 70 Comparison Between Experimental and Calculated Collection Efficiencies (Collector diameter = 363.9 ym) 10 20 30 40 50 60 70 SUPERFICIAL GAS VELOCITY cm/sec Fig. 7.4 Comparison of Experimental and Calculated Collection Efficiencies (Collector diameter = 216.0 ym) 30 40 50 SUPERFICIAL GAS VELOCITY cm/sec 60 70 Fig. 7.5 Comparison of Experimental and Calculated Collection Efficiencies (Upflow and downflow; aerosol diameter = 0.804um; collector diameter = 511.0 ym) SUPERFICIAL GAS VELOCITY cm/sec Fig. 7.6 Comparison of Experimental and Calculated Collection Efficiencies (Upflow and downflow; aerosol diameter = 1.011 ym; collector diameter = 511.0 ym) o o 101 Fig. 7.7 Scatter Plot of Experimental and Calculated Collection Efficiencies (using Eqs. 3.6 and 7.1) 102 7.4 Interpretation and Mbdlficatibri of Equation 7.1 By considering the f l u i d properties of the dispersion medium i t is possible to reduce Eq. 7.1 to dimensionless form. Thus the f i r s t term on the right hand side becomes a Stokes number (St) and the third term becomes a gravity number (NG). 1st term: d 2 p d 2 c c 3rd term: d 2 p g d 2 U _§_ = (_§_) = — = NG TJ 18y V U ' U The second term is more d i f f i c u l t to simplify and does not reduce easily to dimensionless form. Thus Eq. 7.1 becomes EB = 1.018 St + 0.0148 NR(d U ) ~ 2 / 3 + 1.25 NG [7.2] The efficiency equation therefore consists of three terms. The f i r s t and third terms represent the i n e r t i a l and gravitational effects, respec- tively. The gravity term being positive for downflow and negative for upflow. The contribution of the gravity term to EB is usually very small and only becomes significant for low gas velocities and large or dense aerosols. The contributions of the f i r s t and second terms are highly dependent on gas velocity. The main contribution to EB is due to the second term at low velocities and the f i r s t (inertial) term at high veloc- i t i e s . It is interestingito note that the interception term was eliminated from a l l the equations by the regression analysis. Thus i t can be concluded that direct interception was playing a negligible role in the aerosol f i l - tration of this work. It i s rather d i f f i c u l t to explain the second term in Eq. 7.1, which may be due to diffusion even though i t cannot be reduced to a Peclet number or a similar dimensionless group. It is probably a combination term reflecting both diffusion and inertia. 103 7.4.1 Modification of the Second Term in Equation 7.1 An attempt was made to introduce the Peclet number into the second term of Eq. 7.1. It is simple to show that i (d u)"2/3 = (%1/3 (d ur 2 / 3 d a d c c c Now the Peclet number is defined as (d U/D ) where the diffusivity c a -2/3 of the aerosol particle i s denoted by D . Fig. 7.8 shows that D is proportional to d for the range 0.1 < d < 2.02 jjm. Hence / d a N l / 3 . .-2/3 d a ,da,.l/3 .-2/3 (j-) (d c U) - (—) (d c U) c a c j 4/3 d a d c U.-2/3 c a d 4 / 3 a .-2/3 c To render the term completely dimensionless, i t could be divided by d or d . Dividing by d was found to give the best results for predicting SL C C EB. Thus Eq. 7.1 could be rewritten as EB = a.St + b.NR4,/3 Pe~ 2 / 3 + c.NG [7.3] and fit t e d to the experimental data by regression analysis. The following values were found for the constants: a = 1.0; b = 150,000; and c = 1.5. Equation 7.3 gave equally good predictions of EB as Eq. 7.1, having a multiple correlation coefficient (R) of 0.94. Fig. 7.9 shows a scatter plot of the calculated versus experimental collection efficiencies using Eq. 7.3. 4/3 In the present experiments NR >> 1, and the second term in Eq. 7.3 may be rewritten as: b Pe 2 / 3 [1 - exp {- NR 4 / 3}] or b Pe 2 / 3 - b Pe 2 / 3 exp {- NR 4 / 3} -2/3 The term b Pe represents the diffusional effects whereas b Pe 2 ^ 3 exp {- NR4^3} reflects the interaction between diffusion and inertia.  105 Fig. 7.9 Scatter Plot of Experimental and Calculated Collection Efficiencies (using Eqs. 3.6 and 7.3) 106 Although Eq. 7.3 adequately predicts the collection efficiencies obe served in the present experimental work, i t does not predict a minimum collection efficiency with respect to aerosol diameter. However, as noted by several workers, this minimum collection efficiency i s only observed at low gas velocities, i.e., less than 4 cm/sec. Therefore Eq.7.3's only limitation i s i t cannot be used for prediction of EB at gas velocities below about 5 cm/sec. For lower gas velocities aerosol capture is dominated by the diffusional mechanism and equations developed for purely diffusional , 63,32,81 , A • *. A deposition may be used instead. 69 A recent paper by Schmidt discusses the use of an equation of the., type: EB = 3.97 St + (8 Pe" 1 + 2.3 Re 1 / 8 P e ~ 5 / 8 ) + 1.45 NR + NG [7.4] This equation predicts a minimum in EB with respect to aerosol diameter and i t was therefore fit t e d to the present experimental data. The following equation was obtained by multiple regression: EB = 0.8 St + 8 ;(8 Pe" 1 + 2.3 Re 1 / 8 P e " 5 / 8 ) + 1.25 NG [7.5] However Eq. 7.5 proved only applicable to aerosols in the 0.5 to 1.0 ym diameter range; the f i t for 0.109 and 2.02 ym diameter aerosols was considerably poorer. Fig. 7.10 shows a scatter plot for aerosols in the 0.5 to 1.0 ym diameter range. It is clear that the f i t is much poorer than that obtained by Eq. 7.1 or 7.3. 7.5 Conclusion An equation (Eq. 7.3) has been developed which predicts the collection of 0.1 to 2.02 ym latex aerosols by beds of spherical collectors in the range of 100 to 600 ym in diameter. The predictions of this equation match the present experimental results better than expressions proposed by previous workers. Equation 7.3 has the advantage of simplicity and wide range of 107 Fig. 7.10 Scatter Plot of Experimental and Calculated Collection Efficiencies (using Eqs. 3.6 and 7.5; aerosol diameters in the range 0.1 to 5.0 ym) applicability. By comparison with other experimental data the equation is capable of predicting collection efficiencies for beds of spherical collec- tors up to 7000 ym in diameter. Unfortunately the equation is unable to determine an aerosol size which gives a minimum collection efficiency for a given gas velocity. Thus use of Eq. 7.3 should therefore be limited to gas velocities greater than about 5 cm/sec. CHAPTER 8 CONCLUSIONS i) Granular beds of particles 100 to 600 ym in diameter were found to be highly efficient aerosol collectors. For example, at least 95% of 0.1 ym and greater diameter aerosols were collected by a 2.27 cm deep bed of 126 ym diameter nickel shot, having a pressure drop across the bed of 2.5 cm of mercury. i i ) At superficial gas velocities below 10 cm/sec aerosol removal was found to be mainly due to diffusional deposition, and, to a lesser extent, gravitational settling, i i i ) At superficial velocities greater than about 20 cm/sec, aerosol removal was mainly due to in e r t i a l impaction. iv) For a l l experimental conditions tested, interception was found to be insignificant. v) Aerosol collection was found to be unaffected by bed loading and to take place i n an electrically neutral environment, vi) Bounce-off probably occurred at superficial gas velocities greater than about 50 cm/sec causing the theoretical predictions to over- estimate collection efficiencies, v i i ) The present experimental results agreed f a i r l y well with the results of other studies although conclusions on collection mechanisms differed. v i i i ) An empirical equation (Eq. 7.3) was developed which was able to predict the single collector efficiency of a bed particle for the 109 110 experimental conditions chosen in this work, ix) The theoretical expression (eq. 3.4) relating the single collector efficiency to the overall bed efficiency was confirmed by the results of this study. x) The difference between the experimental and calculated (using Eqs. 7.3 and 3.4) bed collection efficiencies was within ten percentage points). xi) The pressure drop through the bed was adequately described by an equation of the Ergun form (Eq. 3.15). I l l NOMENCLATURE Symbol Explanation arid Typical Units a,b,c Constants used in empirical equations 2 D Diffusivity coefficient of aerosols, cm /sec SL d & Diameter of aerosol particle, cm or ym d c Diameter of collector particle, cm or ym D.O.P. Dioctyl phthlate E Single collector efficiency of an isolated collector EB Single collector efficiency of a collector in a granular bed EBT Total collection efficiency of a granular bed ED Single collector efficiency due to diffusion EDR Single collector efficiency due to diffusion and interception EDIR Single collector efficiency due to diffusion, inertia and interception EG Single collector efficiency due to gravity EI Single collector efficiency due to inertia EIR Single collector efficiency due to inertia and interception ER Single collector efficiency due to interception 2 g Gravitational acceleration, cm/sec H Bed depth, cm -2/3 ND Dimensionless diffusion parameter (Pe ) ND Dimensionless gravitational parameter(U 7U) NR Dimensionless interceptional parameter (d /d ) P Penetration, (1 - EBT) AP Pressure drop across the granular bed, mm Hg Pe Peclet number (d U/D ) c a R Multiple correlation coefficient 112 Symbol Explanation and Typical Units Re Reynolds number (p p U / u) St Stokes number (d 2 U p„/9 y d ) a F c U Superficial gas velocity, cm/sec U g Settling velocity of aerosol particle, cm/sec Greek Symbols a,3 ,Y jO Constants used in empirical equations ctg ,ai ,oi2 ,<X3 , Constants used in empirical equations ai+ ,015 e Bed voidage y Viscosity of gas, gm/cm sec p Density of aerosol particle, gm/cm3 p Density of dispersion.medium, gm/cm3 113 REFERENCES 1. Paretsky, L. C , Theodore, L. , Pfeffer, R. , and Squires, A. M., J. Air Polln. Control Assoc., 21, 204 (1971). 2. Black, C. H., and Boubel, R. W., Ind. Eng. Chem. Proc. Des. S. Dev., 8, 573 (1969). 3. Squires, A. M., and Pfeffer, R., J. Air Polln. Control Assoc., 20, 523 (1970). 4. Kalen, B., and Zenz, F. A., Chem. Eng. Prog., 69(5), 67 (1973). 5. Engelbrecht, H. L., J. Air Polln. Control Assoc., 15(2), 43 (1965). 6. Egleson, G. C., Simons, H. P., Kane, L. J., and Sands, A. E., Ind. Eng. Chem., 46(6), 1157 (1954). 7. Meissner, H. P., and Mickley, M. S., Ind. Eng. Chem., hi, 1238 (1949). 8. Meisen, A., and Mathur, K. B., Inst. Chem. Engrs. Symp. Ser., 38(K3), (1974). 9. Dahneke, B. , J. Colloid and Interface Sci., 37., 342 (1971). 10. Corn, M., J. Air Polln. Control Assoc., 11, 523 (1961). 11. Corn, M. , and Silverman, L. , Am. Ind. Hyg. Assoc. J., 22_, 337 (1961). 12. Kraemer, H. F., and Johnstone, H. F., Ind. Eng. Chem., 47, 2426 (1955). 13. Langmuir, I., and Blodgett, K., U.S. Army Air Force Tech. Report 5418, (1946). 14. Gillespie, T., J. Colloid Sci., 10, 281 (1951). 15. Fuchs, N. A., "The Mechanics of Aerosols", Pergamon Press, Oxford (1964). 16. Davies, C. N., Ed. of "Aerosol Science", Academic Press, London (1966). 17. Dorman, R. G., "Dust Control and Air Cleaning", Pergamon Press, Oxford, (1974). 18. Strauss, W. , "Industrial Gas Cleaning", Pergamon Press, Oxford (1966). 19. Silverman, L., Am. Ind. Hyg. Assoc. J., 25(6), 529 (1964). 20. Figueroa, A., Ph.D. Thesis, Univ. Cincinnati (1975). 21. Tardos, G. I., Abuaf, N., and Gutfinger, C., Paper from Dept. Mectu Eng. Technion, Israel Inst, of Tech., Haifa (1977). 114 22. Pich, J., From "Aerosol Science", Ed. C. N. Davis, (1966). 23. Doganoglu, Y., Ph.D. Thesis, McGill Univ. (Aug. 1975). 24. Knettig, P., and Beeckmans, J. M., Can. J. Chem. Eng., 5JZ, 703 (1974). 25. McCarthy, D., Yankel, A. J., Patterson, R. G., and Jackson, M. L., Ind. Eng. Chem. Proc. Des. S. Dev., _15, 266 (1976). 26. Ramskill, E. A., and Anderson, W. L., J. Colloid Sci., 6_, 416 (1951). 27. Thomas, J. W., and Yoder, R. E., A.M.A. Archives Ind. Health, 13, 545 (1956). 28. Freundlich, H., "Colloid and Capillary Chemistry", Methuen Press, London (1926). 29. Chen, C. Y., Chem. Rev., 55, 595 (1955). 30. La Mer, V. K., A.E.C. Rep. NYO-512 Tech. Info. Serv., (1951). 31. Paretsky, L. C , Ph.D. Thesis, The City Univ. of N.Y., (1972). 32. Gebhart, J. , Roth, C. , and Stahlhofen, W. , J. Aerosol Sci., 4_, 371 (1973). 33. Cleaver, J. W., and Yates, B., Chem. Eng. Sci., 31, 147 (1976). 34. Jordon, D. W., Brit. J. App. Phys., Suppl. No. 3, 5194 (1966). 35. Leers, R., Staub., 50, 402 (1957). 36. Walkenhorst, W., Staub., 32(6), 256 (1972). 37. Balasubramanian, M., Meisen, A., and Mathur, K. B., Can. J. Chem. Eng., (1976). 38. Mazumder, M. K., and Thomas, K. T., Filt r a t i o n and Sepn., 25 (Jan/ Feb. 1967). 39. Katz., S. H., and Macrae, D. J., J. Phys. Colloid Chem., 52, 695 (1948). 40. Anderson, D. M., and Silverman, L., Proc. of 5th Air Cleaning Conference, A.E.C. 140 (1957). 41. Yoder, R. E., and Empsom, F. M., Am. Ind. Hyg. Assoc. J., 19, 107 (1958). 42. Scott, D. S., and Guthrie, D. A., Can. J. Chem. Eng., 37, 200 (1959). 43. Silverman, L., Proc. of U.S. Tech. Conf. on Air Polln., Ed. L. C. McCabe (1952). 44. Jackson, S., and Calvert, S., A. I. Ch. E. J., 12, 1075 (1966). 115 45. Calvert, S. P., "Air Pollution", Stern (Ed.) Vol. 3, Academic Press (1968). 46. Yankel, A., Jackson, M., and Patterson, R., Presented Air Polln. Control Assoc., (Nov. 1972). 47. First, M. W. , and Hinds, W. C , J. Air Polln. Control Assoc., 26, 119 (1976). 48. Doganoglu, Y., Jog, V., Thambimuthu, K. V., and C l i f t , R., to be published (1978). 49. Azaniouch, M. K., Can. J. Chem. Eng., (in print 1978). 50. Fairs, G. L., and Godfrey, E., From "Dust in Industry", Soc. of Chem. Ind., London (1948). 51. Strauss, W., and Thring, M. W., J. Iron and Steel Inst. (London), 196 (1960). 52. Cook, C. C , Swany, G. R. , and Colpitts, J. W. , J. Air Polln. Control Assoc., 21, 479 (1971). 53. Rubin, Yu M., and Margolin, Y. A., Coke and Chem. (USSR), 3, 15 (1974). 54. Rush, D., Russel, J. C., and Iverson, R. E., J. Air Polln. Control Assoc., 23, 75 (1973). 55. Dumont, G., Goossens, W., Taeymans, A., and Balleux, W., Het. Ingesieusblad, 103 (1973). 56. Bohm, L. , and Jordan, S., J. Aersol Sci., ]_, 311 (1976). 57. Reese, R. G., Proc. (P. 76) of the Conf. Energy and Wood Product Industry, Forest Product Research Society, Atlanta, Georgia (1976). 58. Heme, H. , "Aerodynamic Capture of Particles", Ed. by E. G. Richardson, Pergamon Press, Oxford (1960). 59. Landahl, H. , and Hermann, K. , J. Colloid Sci., 4̂, 103 (1949). 60. Behie, S. W., and Beeckmans, J. M., Can. J. Chem. Eng., 51, 430 (1973). 61. Friedlander, S. K., Ind. Eng. Chem., 50, 1161 (1958). 62. Natanson, G. L., Dokl. Akad. Nauk. SSSR, 112, 100 (1957). 63. Johnstone, H. F., and Roberts, M. H., Ind. Eng. Chem., 41, 2417 (1949). 64. Stairmand, C. J., Trans. Inst. Chem. Engrs. (London), 28_, 130 (1950). 65. Boussinesque, J., "Theorie Analytique de Chaleur", Vol. II, 224, Paris (1903). 66. Tardos, G. I., Gutfinger, C., and Abuaf, N., A.I. Ch. E.J., 22(6), 1147 (1976). 116 67. Ranz, W. E., and Wong, J. B., Ind. Eng. Chem., 44(6), 1371 (1952). 68. Davles, C. N., Proc. Inst. Mech. Engrs., 1, 185 (1952). 69. Schmidt, E. W., Gieseke, J. A., Gelfand, P., Lugar, T. W., and Furlong, D. A., J. Air Polln. Control Assoc., 28(2), 143 (1978). 70. Rajagopalan, R. , and Tien, C , A.I. Ch. E. J. , 22(3), 523 (1976). 71. Tardos, G. I., Gutfinger, C. , and Abuaf, N. , Israel J. of Tech., 12_, 184 (1974). 72. Le Clair, B. P., and Hamielec, A. E., Can. J. Chem. Eng., 49, 713 (1971). 73. Happel, J., A.I. Ch. E. J., 4-, 197 (1958). 74. Kuwabara, S., J. Phys. Soc. Japan, 144, 527 (1959). 75. Davies, C. N., "Air Filt r a t i o n " , Academic Press, London (1973). 76. Spielman, L. A., and Fitzpatrick, J. A., J. Coll. Interface Sci., 42, 607 (1973). 77. Fitzpatrick, J. A., Ph.D. Thesis, Harvard Univ. (1972). 78. Neale, G. H., and Nader, W. K., A.I. Ch. E. J., 20(3), 531 (1974). 79. Tam, C. K. W., J. Fluid. Mech., _38, 537 (1969). 80. Ergun, S., Chem. Eng. Prog., 48, 89 (1952). 81. Wilson, E. J., and Geankoplis, C. J., Ind. Eng. Chem. Fund., _5, 9 (1966). 117 APPENDIX A EXPERIMENTAL RESULTS FOR THE REMOVAL OF AEROSOL PARTICLES BY GRANULAR BEDS For each set of conditions the aerosol removal by the granular bed is expressed as percentage penetration. The relationship between bed penetration (P) and bed collection efficiency (EBT) i s : P = 1 - EBT or %P = 100 (1 - EBT) A l l the results were obtained with the apparatus set up in the low velocity configuration unless otherwise stated. Tables A.l to A.21 give the measured penetrations for each set of conditions. Tables A.22 to A. 27 give the results of pressure drop measurements across beds of each collector for varying superficial gas velocity. 118 TABLE A . l PENETRATIONS FOR NICKEL SHOT 598.1 UH DIAMETER. i DOWNFLOW; BED DEPTH = 4.536 CM ) GAS V E L . AEROSOL DIAMETER UM CM/SEC D .109 0 . 5 0 0 0 .600 0. 804 1.011 2. 020 5.24 82 . 50 6 6 . 90 61 . 30 4 9 . 3 0 3 9 . 6 0 11 .88 8 .30 8 3 . 7 0 7 0 . 10 6 5.60 5 2 . 3 0 4 2 . 6 0 14 .09 11. 16 85. 10 72. 70 6 7 . 0 0 5 6 , 7 0 4 6 . 0 3 15.50 16 .97 8 3 . 7 0 72.3 0 6 9 . 8 0 6 0 . 7 0 51 . 20 1 3 . 5 0 22.37 8 6 . 0 0 7 5 . 8 0 7 0 . 4 0 6 0 . 7 0 5 3 . 20 7 .88 27 . 08 I 84. 40 75. 80 7 0 . 5 0 61 .33 5 2 . 5 0 1 .95 rABLE A.2 PENETRATIONS FOR N ICKEL SH3T 5 9 8 . 1 UM DIAM5 TER. ( UPFLOW AND DOWNFLOW; 3ED DEPTH = 4 .536 CM ) GAS V E L . AEROSOL DIAMETER UM CM/SEC 0 . 5 0 0 0 .804 1 .011 UP DOWM UP DOWM UP DOWN 5.24 7 1 . 0 0 66. 90 5 3 , 2 0 49 .33 4 3 . 8 3 3 6 . 9 0 8 .30 7 4 . 2 0 70 . 10 54 . 50 52. 30 52. 00 4 2 . 6 0 11 .16 7 5 . 3 0 7 2 , 7 0 5 7 . 5 0 5 6 . 7 0 5 3 . 5 0 4 6 . 0 0 1 6 . 9 7 7 6 . 6 0 7 2 . 3 0 62. 40 6 0 . 7 0 5 6 . 8 0 51 .20 22 .3 7 7 9 . 9 0 7 5 . 8 0 6 3 . 60 60. 70 5 7 . 80 53.2 0 2 7. 08 7 8 . 2 0 7 5 . 8 0 6 0 . 1 0 61 .80 55 .20 52 .50 1 6 . 3 3 * 7 6 . 4 0 7 1 . 8 0 60. 90 58 .90 - 5 0 . 8 9 2 2 . 5 7 * 7 7 . 6 0 7 4 . 5 0 6 4 . 4 0 59 .00 - 52. 70 3 5 . 4 6 * 73. 60 6 9 . 70 5 4 . 9 0 54 .10 - 4 7 . 7 7 5 0 . 7 5 * 7 2 . 0 0 6 6 . 5 0 5 2 . 5 0 48 . 10 - 3 7.20 67 . 00* - 6 6 . 6 0 - 48 .60 - 3 4 . 1 2 * APPARATUS IN HIGH VELOCITY CONFIGURATION TABLE A.3 PENETRATIONS FOR N ICKEL SHOT 598. 1 UM DIAMETER. ( DOWNFLOW; VARYING BED DEPTH; AEROSOL DIAMETER = 0.5 UM } GAS VEL . BED DEPTH CM CM/SEC 4 , 5 3 6 9,071 13.607 18. 142 5.24 66 . 90 44. 60 3 0 .20 20 .50 8 .30 7 0 . 1 0 46 . 30 3 2 . 2 0 23. 00 11. 16 7 2 , 7 0 5 0 . 8 0 3 6 . 5 0 26.50 1 6 . 9 7 7 2 . 3 0 5 4 . 4 0 4 0 . 60 3 1 . 00 2 2 , 3 7 7 5 . 8 0 5 6 . 9 0 4 5 . 3 0 35 .00 2 7 . 0 8 75 .80 6 0 , 50 4 7 . 5 0 37 .53 TABLE A.4 PENETRATIONS FOR NICKEL SHOT 598. 1 UM DIAMETER, i DOWNFLOW; BED DEPTH = 2.2 6 8 CM > GAS V E L . CM/SEC AEROSOL DIAMETER UM 0 .109 0 .500 0 .600 0.804 5.24 27. 08 9 2 . 3 0 8 5 . 7 0 8 3 . 0 0 77 .70 9 0 , 4 0 7 8 . 4 0 7 6 . 7 0 71.70 119 TABLE A.5 PENETRATIONS FOR NICKEL SHOT 5 1 1 . 0 UM DIAMETER. I DOWNFLOW; BED DEPTH = 4 .536 CM ) GAS V E L . AEROSOL DIAMETER UM CM/SEC 0. 109 0 . 500 0 .600 0.804 1.011 . 2 .020 5 .24 7 5 . 7 6 0 . 0 0 45 . 40 3 6 . 8 0 2 9 . 50 6. 802 8.3 0 7 8 . 5 0 6 5 . 30 5 2 . 7 0 41 .00 3 7 . 5 0 8 . 6 1 4 1 1 . 1 6 8 0 . 5 0 6 9 . 0 0 57. 30 4 5 . 4 0 4 0 . 00 1 0 . 9 0 9 1 6 . 9 7 8 3 . 0 0 7 1 . 3 0 6 1 . 6 0 50 .30 4 4 . 10 8. 387 2 2 . 3 7 8 3. 60 75. 00 6 6 . 6 0 55 .2 0 4 5 . 0 0 1.526 2 7 . 0 8 8 3 . 6 0 73 . 10 67 . 20 5 5 . 5 0 4 3 . 50 0 .096 'ABLE A . 6 PENETRATIONS FOR N ICKEL SHOT 5 1 1 . 0 UM DIAMETER. ( UP FLOW AND DOWNFLOW; BED DEPTH = 4 . 5 3 6 CM ) GAS VEL . AEROSOL DIAMETER UM CM/SEC 0. 500 0. 804 1.011 UP DOWN UP DOWM UP DOWM 5.24 6 2 . 2 0 60. 00 39. 80 36 .80 33 . 80 29 .50 8 .30 6 6 . 8 0 6 5 . 3 0 44 .90 41 .00 3 8 . 7 0 37 . 50 1 1 . 1 6 69. 00 69. 00 4 8 . 9 0 45 .43 42 .50 40 .00 1 6 . 9 7 7 5 . 0 0 7 1 . 3 0 5 3 . 3 0 5 0 . 3 0 48. 70 4 4 . 1 0 2 2 . 3 7 7 5 . 7 0 7 5 . 0 0 5 6 . 2 0 5 5 . 2 0 4 8 . 9 0 45 .00 27 . 08 76. 20 73. 1 0 5 9 . 50 55 .50 4 6 . 0 0 43 .50 16 .3 3* 7 3 . 8 0 72 .30 5 4 . 0 0 51 . 30 - 4 5 . 4 5 22 . 57* 7 6 . 0 0 7 5 . 9 0 5 7 . 4 0 53 .50 — 39 .69 3 5 . 4 6 * 7 3 . 0 0 68 . 40 56. 00 53.6 0 - 3 5 . 2 4 5 0 . 7 5 * 7 0 . 2 0 6 7 . 2 0 5 4 . 0 0 45 .00 3 0 . 0 3 6 7 . 0 0 * - 65. 00 4 5 . 0 0 49 .63 - 2 7 . 4 6 * APPARATUS IN HIGH VELOC ITY CONFIGURATION TA8LE A . 7 PENETRATIONS FOR N ICKEL SHOT 5 1 1 . 0 UM DIAMETER. ( DOWN FLOW; VARYING BED DEPTH; AEROSOL DIAMETER = 0 .5 U*l ) GAS V EL . BED DEPTH CM CM/SEC 2.268 4 .5 36 9.071 13 .607 18.142 5 .24 7 5 . 2 0 60 . 00 37. 20 2 5 . 0 0 1 8 . 3 0 8 .30 7 8 . 2 0 6 5 . 3 0 43 .00 30 .00 2 4 . 3 0 11. 16 82. 20 69. 00 4 6 . 5 0 32 .60 2 7 . 3 0 16 .97 8 2 . 7 0 71 .30 5 1 . 2 0 37 . 50 31 . 50 2 2 . 3 7 8 5 . 2 0 7 5 . 0 0 5 5 . 7 0 44 .00 3 7 . 00 2 7 . 08 8 7. 40 73.1 0 5 9.1 0 45 .00 3 8 . 7 0 TABLE A.8 PENETRATIONS FOR NICKEL SHOT 5 1 1 . 0 UM DIAMETER. { DOWNFLOW; BED DEPTH = 2 .268 CM ) GAS V E L . CM/SEC AEROSOL DIAMETER UM 0 .109 0 . 6 0 0 0 .804 5.24 2 7 . 08 90 .20 8 2 . 8 0 7 3 . 5 0 8 7 . 0 0 66. 80 5 5 . 6 0 120 TABLE A.9 PENETRATIONS FOR NICKEL S.H3T 3 6 3 . 9 UM DIAMETER. ( DOWNFLOW; BED DEPTH = 4 .536 CM ) GAS V E L . AEROSOL DIAMETER UM CM/SEC 0. 109 0.5 00 0.6 00 0 .804 1.011 2.020 5.24 4 0 . 5 0 2 9 . 1 0 2 1 . 9 0 14.80 12. 50 0. 561 8.3 0 48. 20 33. 30 2 6 . 7 0 19.23 19.90 0 . 7 3 6 1 1 . 1 6 5 1 . 2 0 3 6 . 9 0 3 1 . 10 24. 70 22 . 90 1. 129 16. 97 5 7 . 6 0 38*10 3 7 . 3 0 29.00 2 6 . 8 0 0 . 0 5 5 2 2 . 3 7 62.2 0 4 3 . 0 0 39. 90 31 .00 2 6 . 4 0 0 .0016 27 .08 6 5 . 4 0 4 6 . 7 0 44 . 30 30 .80 2 3 . 3 0 0.0003 TABLE A . 1 0 PENETRATIONS FOR NICKEL SHOT 3 6 3 . 9 UM DIAMETER. < UPFLOW AND DOWNFLOW; BED DEPTH = 4 . 5 3 6 CM ) GAS V E L . AEROSOL DIAMETER UM CM/SEC 0 .500 0. 804 1. O i l UP DOWN UP DOWN DOWN 5.24 3 2 . 3 0 2 9 . 1 0 2 1 . 10 14. 80 12. 50 8.3 0 3 6 .00 3 3 . 3 0 2 2 . 1 0 19 .20 19 .90 11 .16 4 0 . 3 0 3 6 . 9 0 25. 60 2 4 . 7 0 22 .90 16 .97 4 3 . 4 0 3 8 . 1 0 2 9 . 4 0 29. 00 2 6 . 8 0 22. 37 4 5 . 6 0 4 3 . 0 0 33 .20 31 .00 2 6 . 4 0 2 7 . 0 8 4 9 . 3 0 4 6 . 70 33 , 90 3 0 . 8 0 2 3 . 3 0 16 .3 3* 4 2 . 5 0 4 0 . 0 0 3 1 , 0 0 2 8 . 1 0 27 . 30 2 2 . 5 7 * 50. 00 4 1 . 60 3 3 . 9 0 31 .10 2 6 . 0 4 3 5 . 4 6 * 4 6 . 7 0 4 4 , 6 0 3 2 . 0 0 29. 20 19. 63 50 . 75* - 3 7 . 8 0 2 4 . 6 0 25.10 13.62 6 7 . 0 0 * 40. 70 - 20.03 1 2 . 6 0 * APPARATUS IN HIGH VELOCITY CONFIGURATION TABLE A .11 PENETRATIONS FOR NICKEL SHOT 3 6 3 . 9 UM DIAMETER. i DOWN FLOW ; VARYING BED DEPTH; AEROSOL DIAMETER = 0 .5 UM > GAS V E L . BED DEPTH CM CM/SEC 2 ,268 4 .5 36 9 .071 13 .607 18.142 5 .24 54.4 0 2 9 . 10 1 0 . 0 0 4 . 2 0 3. 40 8.3 0 5 8 , 0 0 3 3 . 3 0 12 .40 5 .00 3 .90 11. 16 61 . 00 3 6 . 90 14 .00 6 .00 4 . 9 0 16.97 6 3 . 7 0 3 8 . 1 0 1 6 . 5 0 8. 20 6 .40 22 .3 7 6 6 . 0 0 4 3 . 0 0 2 0 . 0 0 11 .40 9 .30 27 .08 6 6 . 4 0 4 6 . 7 0 24. 40 14 .90 1 2 . 0 0 TABLE A.12 PENETRATIONS FOR N ICKEL SHOT 3 6 3 . 9 UM DIAMETER. ( D0WNFL3W; BED DEPTH = 2 .268 CM ) GAS V E L . CM/SEC AEROSOL DIAMETER UM 0 .109 0 .600 0 . 8 0 4 5.24 2 7 . 0 8 8 0 . 8 0 3 5 . 8 0 46 .00 6 6 . 6 0 5 4 . 0 0 6 2 . 8 0 121 TABLE A .13 PENETRATIONS FOR N ICKEL SHOT 215,1 UM DIAMETER, i DOWNFLOW; BED DEPTH = 2. 268 CM ) GAS V E L . AEROSOL DIAMETER UM CM/SEC 0 . 1 0 9 0. 5 00 0. 600 0. 80'* 1.011 2.02 0# 5.24 3 1 . 6 0 1 4 . 3 0 6 .00 5 .45 4 , 5 0 1.891 8 .30 3 5.00 1 6 . 5 0 7. 80 7 .46 6 .90 3 .13 8 11 .16 3 7 . 1 0 2 0 . 9 0 11.40 9 .60 8. 10 1. 218 16. 97 42. 10 2 4 . 3 0 1 3 . 2 0 11.53 10 .20 0 .261 2 2 . 3 7 4 8 . 3 0 2 7 . 6 0 1 6 . 6 0 12.00 9. 20 0. 080 27.0 8 4 8 . 5 0 2 8 . 4 0 19 .02 12.50 5 .80 0. 180 # BED DEPTH = 0. 567 CM TABLE A.14 PENETRATIONS FOR NICKEL SHOT 216 .1 JM DIAMETER. ( UPFLOW AND DOWNFLOW; BED DEPTH = 2 .268 CM ) GAS V E L . AEROSOL DIAMETER UM CM/SEC 0. 500 0 .804 1.011 UP DOWN UP DOWN DOWN 5. 24 14 .90 1 4 . 3 0 7.00 5 .45 4 . 5 0 8 .30 15. 70 16 .50 8.70 7.45 6. 80 1 1 . 1 6 1 7 .90 2 0 . 9 0 10.50 9 .60 8. 10 1 6 . 9 7 24. 70 24. 30 1 2 . 5 0 11 .50 10 .20 22 .37 2 8 . 9 0 2 7 . 6 0 12.20 12.00 9. 20 27 . 08 2 8 . 3 0 2 8 . 4 0 16.20 12.50 5.80 1 6 . 3 3 * 2 5 . 0 0 24. 30 12. 00 9.70 10.51 2 2 . 5 7 * 2 9 . 5 0 2 7 . 2 0 13 .70 12.80 13.01 3 5. 46* 28 . 00 25 . 90 1 2 - 3 0 10.33 2.98 5 0 . 7 5 * 2 1 . 5 0 2 0 . 5 0 6. 50 5.40 0. 20 6 7 . 0 0 * - 18.30 - 4 . 8 0 0.01 * APPARATUS IN HIGH VELOCITY CONFIGURATION TABLE A .15 PENETRATIONS FOR N ICKEL SHOT 216 .1 UM DIAMETER, ( DOWNFLOW; VARYING BED DEPTH; AEROSOL DIAMETER = 0 .5 UM GAS VEL. BED DEPTH CM CM/S EC 0 .567 1.134 2. 268 4. 536 5.24 5 8. 70 38 .3 0 1 4 . 3 0 7.40 8.30 6 4 . 0 0 4 1 . 0 0 16. 50 9.40 1 1 . 1 6 6 8 . 0 0 4 5 . 4 0 20 .90 11 .80 16 .97 70. 80 4 9 . 2 0 24. 30 1 6 . 8 0 2 2 . 3 7 7 3 . 8 0 5 3 . 0 0 2 7 . 6 0 20 .50 2 7 . 0 8 74 . 80 5 6 . 0 0 31 .30 22 .00 TABLE A.16 PENETRATIONS FOR N ICKEL SHOT 216 .1 UM DIAMETER. I DOWNFLOW; BED DEPTH = 1.134 CM ) GAS V E L . CM/SEC AEROSOL DIAMETER UM 0 .109 0 .600 0 ,304 5.24 27 . 08 6 8 . 2 0 4 6 . 2 0 35 .70 5 6 . 4 0 25 .00 21 .50 1 2 2 T A B L E A . 1 7 P E N E T R A T I O N S F O R N I C K E L S H O T 1 2 6 . 0 U M D I A M E T E R . i D O W N F L O W ; B E D D E P T H = 2 . 2 6 8 CM } GAS VEL . AEROSOL DIAMETER UM CM/SEC 0 .109 0 . 5 0 0 0.600 0.804 1.011 2. 020# ' 5.24 3 .50 0 . 8 2 7 0.353 6 0. 2 5 2 7 0. 1 0 1 5 1 . 2 0 3 0 8.3 0 4.9 0 1.612 0 . 5 1 1 0 0 . 4 0 0 0 0 . 1 7 2 1 1. 1700 1 1 . 1 6 5. 70 2. 5 7 6 0 . 6 3 5 0 0 . 5 4 1 5 0 . 3 3 7 0 1.4722 1 6 . 9 7 9.90 3 . 5 8 8 1 . 7 3 9 0 1. 5603 0. 0 9 8 2 1 . 4 4 5 4 22. 3 7 1 3 . 7 0 5 . 0 0 4 2 . 4 2 3 0 2 . 1 6 9 9 0 . 0 1 9 6 1.3170 2 7 . 0 8 15 . 0 0 6. 8 7 6 2 . 6 8 5 0 2. 365 5 0. 0024 1.1041 * BED DEPTH = 0 . 2 8 3 CM T A B L E A . 1 8 P E N E T R A T I O N S FOR N I C K E L SHOT 1 26.1 UM DI A M E T E R . { UPFLOaI AND DOWNFLOW; BED DEPTH = 2 .268 CM ) GAS V E L . AEROSOL DI A M E T E R UM CM/SEC 0. 5 0 0 0 . 6 0 0 0. 8 0 4 1. O i l UP DOWN DOrfN UP DOWN DOWN 5.24 1.352 0 . 8 2 7 0.353 6 2. 151 0 0 . 2 5 2 7 0. 1 0 1 5 8.30 2 . 4 0 0 1.612 0 . 5 1 1 0 1 . 9 9 1 0 0 . 4 0 0 0 0 . 1 7 21 1 1 . 1 6 2 . 8 7 3 2. 5 7 6 0. 6 3 5 0 1. 4 1 7 0 0 . 5 4 1 6 0 . 3 3 7 0 16 . 9 7 3.717 3 . 5 8 8 1 . 7 3 9 0 1.3890 1.5603 0. 0 9 8 2 22.3 7 5. 39 6 5. 004 2 . 4 2 3 0 1.5510 2 . 1 6 9 9 0 . 0 1 9 6 2 7 . 0 8 5.3 52 6 . 8 7 6 2 . 6 8 5 0 1. 6 1 5 0 2. 3 6 5 5 0.0024 16.3 3* — - 2 . 5 0 0 0 - 0 . 4 2 4 4 0 . 1 0 3 4 2 2 . 5 7 * - - 2 . 8 2 8 0 - 0 . 4 2 6 0 0 . 0 3 4 8 3 5 . 4 6 * - - 1 . 3 6 9 0 - 0 . 0 7 6 5 0 . 0 0 1 6 5 0 . 7 5 * - - 0 . 3 9 4 0 - 0 . 0 1 0 0 0 . 0 0 0 5 6 7 . 0 0 * - - 0. 2 4 1 0 - 0.0032 0 . 0 0 0 2 * APPARATUS IN H I G H V E L O C I T Y C O N F I G U R A T I O N T A B L E A . 1 9 P E N E T R A T I O N S FOR N I C K E L SHOT 1 26.1 UM DIAM E T E R . ( DOWNFLOW; V A R Y I N G BED DEPTH; AEROSOL DIAMETER = 0.5 GAS V E L . BED DEPTH CM CM/SEC 0. 5 6 7 1. 1 3 4 2.268 5.24 29 .00 9.00 0 .827 8.30 34. 60 1 2 . 3 0 1 .612 1 1 . 1 6 3 8 . 10 1 5 . 3 0 2. 5 76 1 6 . 9 7 4 1 . 0 0 17.00 3 . 5 8 8 22. 37 43 . 70 19 . 2 0 5.004 2 7 . 0 8 4 7 . 0 0 2 5 . 6 0 6.876 T A B L E A . 2 0 P E N E T R A T I O N S FOR N I C K E L SHOT 1 26.1 UM DIAM E T E R . { D0WNFL3W; BED DEPTH = 1.134 CM ) GAS V E L . CM/SEQ AEROSOL DIAMETER UM 0 . 1 0 9 0.6 0 0 0 . 8 0 4 5.24 2 7 . 0 8 38.60 17. 8 0 1 5 . 5 0 2 0.90 5. 50 5. 80 123 TABLE A.21 PENETRATIONS FOR LEAD SHOT 1800 UM DIAMETER. i DOWNFLOW; AEROSOL DIAMETER = 0 . 5 UM ) GAS V E L . CM/SEC BED DEPTH CM 4 . 5 3 6 9. 071 13 .607 18.142 5 .24 11. 16 16 .97 22. 37 2 7 . 08 9 5 . 8 0 9 2 . 9 0 83 .90 7 8 . 6 0 90 . 20 9 2 . 8 0 86.05 80 .50 8 9 . 5 0 8 7 . 5 0 86.2 0 85.6 0 9 6 . 5 0 8 7 . 7 0 8 6 . 5 0 85 .00 9 2 . 4 0 8 5 . 6 0 88 .30 8^.40 124 TABLE A .22 PRESSURE DROP IMM.HG) ACROSS BEDS OF NICKEL SHOT 598 .1 UM DIAMETER- GAS V E L . CM/SEC 4.53 6 BED 9.071 DEPTH CM 1 3 . 6 0 7 18.141 DP/H MM.HG/CM 5.24 1.4 3 .5 4 . 4 5.5 0 . 3 1 2 8 .30 2 .5 4 . 5 5.0 7.0 0 .416 1 1 . 1 6 3 .0 5.5 8.0 10 .0 0 .602 1 6 . 9 7 5.0 9 . 0 13 .0 15.5 0 . 9 7 4 2 2 . 3 7 6.4 1 3 . 0 16.5 2 1 . 5 1.311 2 7. C8 7.3 1 6 . 0 21 .0 2 9 . 0 1.58 4 16 .33 5.0 - - - 1.102 2 2 . 5 7 6.5 - - - 1. 433 35 . 46 1 0 . 0 - - - 2 . 2 0 5 5 0 . 7 5 14.0 - - - 3 .086 6 7 . 0 0 18 .7 — - - 4 .120 T A B L E A .23 PRESSURE DROP (MM.HGJ ACROSS BEDS OF NICKEL SHOT 5 1 1 . 0 UM DIAMETER. GAS V E L . CM/SEC 4 . 5 3 6 BED 9.071 DEPTH CM 13 .607 18 .141 DP/H MM.HG/CM 5.24 2.5 3 . 5 5*5 6.5 0 .392 8 .30 3 .0 4 . 0 5.5 8.0 0 . 4 2 9 11*16 4. 1 6. 0 9 .5 12 .5 0 . 6 8 3 16 .97 6.5 9 . 5 14 .0 17 .5 1.014 2 2 . 3 7 7.0 13 .5 18 .0 2 5 . 0 1.432 2 7 . 0 8 8 .0 1 5 . 0 2 2 . 5 3 1 . 0 1.695 16.33 5.0 - - - 1. 102 2 2 . 57 7.0 - - - 1.543 3 5 . 4 6 11 .7 - - - 2. 579 50 .75 1 6 . 0 - - - 3.527 6 7 . 0 0 21 .3 - - - 4 . 9 6 0 TABLE A . 2 4 PRESSURE DROP IMM.HG) ACROSS BEDS OF N ICKEL SHOT 3 6 3 . 9 UM DIAMETER. GAS V E L . BED DEPTH CM DP/H CM/SEC 4.53 6 9 .071 13.60 7 18.141 MM.HG/CM 5 .24 4 .3 7 . 0 10 .0 13 .0 0 .741 8 .30 5.1 8 .0 1 3 . 0 1 8 . 0 0 .982 11 .16 7 .0 13.0 18*5 27 .5 1. 49 7 16 .97 10 .3 1 9 . 5 2 8 . 0 4 0 . 0 2 . 2 0 9 2 2 . 3 7 13 .4 2 7 . 0 3 8 . 0 5 4 * 0 2 . 9 6 9 2 7 . 0 8 16.4 3 1 . 0 4 7 . 0 6 8 . 0 3 .496 16 .33 11 .0 - - - 2.425 2 2 . 5 7 14 .3 — - - 3.153 3 5 . 4 6 26 .3 - - - 5.79 8 50 .75 3 5 . 0 - - - 7 . 7 1 6 6 7 . 0 0 4 3 . 0 - - - 9 .480 125 ABLE A -25 PRESSURE DROP (MM. HGJ ACROSS BEDS OF N ICKEL SHOT 216 .1 UM DIAMETER. GAS V E L . BED DEPTH CM DP/H CM/SEC 1.134 2 .268 4 . 5 3 6 6 . 8 0 4 MM.HG/CM 5.24 3.5 7 .0 12 .0 19. 0 3 . 8 7 0 8 .30 5.0 9 .5 1 6 . 0 2 6 . 5 4 .005 11 .16 7.0 1 2 . 5 2 4 . 0 3 7 . 0 5 .413 1 6 . 9 7 11.5 19 .4 3 4 . 0 5 5 . 0 8 .568 2 2 . 4 0 1 4 . 0 2 6 . 0 4 5 . 0 7 3 . 0 10 .563 2 7 . 0 8 16 .5 3 2 . 0 5 6 . 0 9 1 . 0 1 3 . 5 9 5 16 .33 - 2 0 . 5 - - 9 . 0 3 9 2 2 . 5 7 - 2 8 . 0 - - 12 .346 3 5 . 4 6 - 4 4 . 0 - - 1 9 . 4 0 0 5 0 . 7 5 - 5 9 . 0 - - 2 6 . 0 1 4 6 7 . 0 0 — 7 6 . 0 — — 3 3 . 5 1 0 TABLE A . 2 6 PRESSURE DROP (MM.HGJ ACROSS BEDS OF N ICKEL SHOT 1 2 6 . 0 UM DIAMETER. GAS V E L . BED DEPTH CM DP/H CM/SEC 0 . 5 6 7 1. 134 2. 26 8 4 . 5 3 6 MM.HG/CM 5 .24 5 .0 8 .0 1 7 . 0 3 0.0 7 .489 8 .30 7.0 1 2 . 0 2 4 . 0 4 7 . 5 10 .545 1 1 . 1 6 8.5 1 6 . 0 3 3 . 0 6 0 . 0 14 .219 16.<57 12 .0 2 2 . 0 4 6 . 0 8 6 . 0 1 9 . 9 5 0 2 2 . 3 7 1 5 . 4 2 8 , 5 6 1 . 5 114.0 26 . 135 2 7 . C8 18.0 3 4 . 0 7 3 . 0 143.0 3 1 . 8 2 0 TABLE A . 2 7 PRESSURE DROP 1MM.HG) ACROSS BEDS OF LEAD SHOT 1800 UM DIAMETER. GAS V E L . CM/SEC BED DEPTH CM 4 . 5 3 6 9.071 1 3 . 6 0 7 18.141 DP /H MM.HG/CM 5.24 1 1 . 16 1 6 . 97 2 2 . 3 7 2 7 . C 8 0 . 1 3 0 . 2 6 0 . 3 5 0 .44 0 .26 0 .49 0 . 7 6 0.96 0 .44 0 .83 1.20 1.54 0 . 6 6 1.23 1.81 2.32 0 .88 1.75 2.51 3 .14 0.026 8 0 .0551 0 .0905 0 .1322 0 . 1 8 6 0 126 APPENDIX B CALCULATIONS OF EB AND DIMENSIONLESS GROUPS For each set of experimental conditions the value of EB was calculated from the experimentally measured value of EBT using Eq. 3.6. The values of EB are listed with the corresponding dimensionless groups, viz., Re, St, NR, Pe, and NG. Sample calculation of EB: Consider the downflow f i l t r a t i o n of 0.5 ym diameter aerosols by a granular bed of 598.1 ym diameter nickel shot. Bed depth (H) = 4.536 cm Voidage (e) = 0.415 Superficial gas velocity = 5.24 cm/sec Experimental bed collection efficiency (EBT) = 0.331 From Eq. 3.6 i t follows: EB - - l n ( l - 0.0331) 0.05981 1.5 0.415 , 1 0.415; 4.536 2.5184 x 10 -3 TABLE B.1 DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORSESPONDING TO TESTS ON BEDS OF NICKEL SHOT 598.1 UM DIAMETER. ( DOWNFLOW ) a . UM VEL. CM/SEC SE ST NE PE NG EB 0. 109 5.24 2. 176 0.674659E- 05 0.182244E- 03 0.522870E 05 0.719975E- 05 0.119953E- 02 0. 109 8.30 3. 447 0.106864E-04 0.182244E- 03 0.828209E 05 0.454538E- 05 0. 110949E-02 0.109 11.16 4. 635 0.143687E- 04 0. 182244E-03 0. 1 11359E 06 0.338053E- 05 0. 100605E-02 0. 109 16.97 7. 048 0.218492E- 04 0. 182244E-03 0.169334E 06 0.222314E- 05 0.110949E- 02 0. 109 22.37 9. 291 0.288018E- 04 0. 182244E-03 0.223217E 06 0. 168649E-05 0.940452E- 03 0. 109 27.08 11. 248 0.348660E- 04 0. 182244E-03 0.270216E 06 0.139316E- 05 0. 105755E-02 0.500 5.24 2. 176 0.141962E- 03 0,835981E- 03 0.4 892 55E 06 0.151497E- 03 0.251840E- 02 0.500 8.30 3. 447 0.22 486 3E-03 0.835981E- 03 0.774966E 06 0.956440E- 04 0.232389E- 02 0.500 11.16 4. 635 0.302346E- 03 0.835981E- 03 0.104200E 07 0.711331E- 04 0.206494E- 02 0.500 16.97 7.048 0. 45975 1E-03 0.835981E- 03 0. 158448E 07 0.467793E- 04 0. 193148E-02 0.500 22. 37 9. 291 0.606047E- 03 0.835981E- 03 0.208867E 07 0.354870E- 04 0. 171063E-02 0.500 27.08 11. 248 0.733650E- 03 Q..835981E-03 0.252844E 07 0.293148E- 04 0. 161401E- 02 0.500 16.33 6. 783 0. 442412E-03 0.835981E- 03 0.152472E 07 0.486127E- 04 0.206572E- 02 0.500 22.57 9. 374 0.611466E- 03 0. 835981E-03 0.210735E 07 0.351725E- 04 0. 183554E-02 0.500 35.46 14.728 0.96 0681E-03 0.835981E- 03 0.331088E 07 0.223870E- 04 0.225082E- 02 0.500 50.75 21. 079 0. 137492E-02 0.835981E- 03 0.473849E 07 0.156423E- 04 0.254388E- 02 0.500 67.00 27.828 0. 181516E-02 0.835981E- 03 0.6 255 75E 07 0.118484E- 04 0. 253451E-02 0.600 5.24 2. 176 0.204425E- 03 0. 100318E-02 0.613062E 06 0.218156E- 03 0. 305158E-02 0.600 8.30 3.447 0.323803E- 0 3 0. 100318E-02 0.971071E 06 0.1377 27E-03 0. 262884E- 02 0.600 11.16 4. 635 0. 43 5379E-03 0. 100318E-02 0.130568E 07 0.102432E- 03 0. 249717E-02 0.600 16.97 7. 048 0. 66 204 1E-03 0. 100318E-02 0.198543E 07 0.673622E- 04 0.224188E- 02 0.600 22.37 9. 291 0. 872707E-03 0. 100318E-02 0.261721E 07 0.511013E- 04 0.218851E- 02 0.600 27.08 11. 248 0. 105646E-02 0. 100318E-02 0.316826E 07 0.422133E- 04 0.217966E- 02 TABLE B. 1 ( CONTINUED ) da UM VEL. CM/SEC .RE ST Nfi PE NG EB 0.804 5. 24 2. 176 0. 367066E-03 0. 134426E-02 0.869726E 06 0.391721E- 03 0.441002E- 02 0.804 8.30 3. 447 0.581421E- 03 0. 134426E-02 0.137762E 07 0.247303E- 03 0.404167E- 02 0.804 11.16 4. 635 0.7 8176 5 E-03 0. 134426E-02 0. 185232E 07 0. 183926E-03 0.353799E- 02 0.804 16.97 7. 048 0.118876E- 02 0.134426E- 02 0.281665E 07 0.12 0956E-03 0.311292E- 02 0.804 22,37 9. 291 0.156703E-02 0. 134426E-02 0.371293E 07 0. 917576E-04 0.311292E- 02 0.804 27.08 11.248 0. 189697E-02 0.134426E- 02 0.449469E 07 0.757982E- 04 0.300093E- 02 0.804 16.33 6.783 0. 114393E-02 0.134426E- 02 0.271043E 07 0. 125696E-03 0.330062E- 02 0. 804 22.57 9. 374 0. 158104E-02 0.134426E- 02 0.374613E 07 0.909444E-04 0.329004E- 02 0.804 35.46 14.728 0.248400E- 02 0.134426E-02 0.588559E 07 0.578854E- 04 0.383068E- 02 0.804 50.75 21. 079 0.355507E- 02 0, 134426E-02 0.842340E 07 0.404456E- 04 0. 456367E-02 0.804 67.00 27. 828 0.469340E- 02 0.134426E- 02 0.1112 05E 08 0.306361E- 04 0.449919E- 02 1,011 5.24 2. 176 0.580409E- 03 0./169035E-02 0.113349E 07 0.619394E- 03 0.621651E- 02 1.011 8. 30 3. 447 0.919349E- 03 0.169035E- 02 0.179541E 07 0.391039E- 03 0.532083E- 02 1,0 11 11,16 4. 635 0.123614E- 02 0. 169035E-02 0.241408E 07 0.290826E- 03 0.484203E- 02 1.011 16.97 7. 048 0.187968E- 02 0. 169035E-02 0.3.67087E 07 0.191256E- 03 0.417422E- 02 1,011 22.37 9. 291 0.247781E- 02 0.169035E- 02 0.483896E 07 0.145088E- 03 0.393528E- 02 1,011 27.08 11. 248 0.29 9952E- 02 0, 169035E-02 0.585781E 07 0.119853E- 03 0.367137E- 02 1.011 16.33 6. 783' 0. 18 0879E-02 0, 169035E-02 0.353242E 07 0.198752E- 03 0.421209E- 02 1.011 22. 57 9. 3 74 0. 249997E-02 0. 169035E-02 0.488223E 07 0.143802E- 03 0.399416E- 02 1.011 35.46 14. 728 0. 392773E-02 0.169035E- 02 0.767053E 07 0.915291E- 04 0.460568E- 02 1.011 50.75 21. 079 0.562133E- 02 0,169035E- 02 0.109780E 08 0.639531E- 04 0.616603E- 02 1.011 67.00 27.828 0. 742126E-02 0. 169Q35E-02 0.144931E 08 0.484421E- 04 0. 6704 92E-02 2.020 5.24 2. 176 0. 226629E-02 0. 337736 E-02 0.243670E 07 0.241845E- 02 0. 132835E-01 2.020 8. 30 3. 447 0. 358974E-02 0.337736E- 02 0.385966E 07 0.152683E- 02 0.122197E- 01 2.020 11,16 4. 635 0.482668E- 02 0. 337736E-02 0.518962E 07 0.113554E- 02 0. 116250E-01 2.020 16.97 7. 048 0.733950E- 02 0.337736E- 02 0.789138E 07 0.746769E- 03 0..124864E-01 2.020 22.37 9. 291 0.967498E- 02 0. 337736E-02 0.104025E 08 0.566503E- 03 0. 158433E-01 2.020 27.08 11. 248 0.117120E- 01 0. 337736E-02 0.125927E 08 0.467971E- 03 0,245512E- 01 TABLE B.2 DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 598.1 UM DIAMETER. { UPFLOW ) d a VEL. OM CM/SEC 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35. 46 50.75 67. 00 5.24 8. 30 11.16 16.97 22.37 27.08 16.33 22. 57 35.46 50.75 67.00 1.011 5.24 1.011 8.30 1.011 11.16 1.011 16.97 1.011 22.37 1.011 27.08 RE 2. 176 3.447 4.635 7.048 9. 291 11.248 6.783 9. 374 14.728 21.079 27.828 2. 176 3. 447 4. 635 7.048 9. 291 11.248 6.783 9.374 14.728 21.079 27.828 2. 176 3.447 4.635 7.048 9.291 11.248 ST 0. 141962E-03 0.224863E-Q3 0. 302346E-03 0.45 975 1E-03 0.606047E-03 0.73365GE-03 0. 442412E-03 0.611466E-03 0.96 0681 E-03 0. 137492E-02 0. 181516E-02 0.367066E-03 G.581421E-03 0.781765E-03 0. 118876E-02 0. 1567 03E-02 0. 189697E-02 0. 114393E-02 0. 158104E-02 0. 248400E-02 0.355507E-02 G.46 9340E-G2 0.580409E-03 0.919349E-03 0. 123614E-02 0. 187968E-02 0.247781E-02 0.299952E-02 NR 0. 835981E-03 0.835981E-03 0.835981E-03 0.835981E-03 0.8359 81E-03 0.835981E-03 0.835981E-03 0.835981E-03 0. 835981E-03 0.835981E-03 0. 835981E-03 0. 134426E-02 0. 134426E-02 0.134426E-02 0. 134426E-02 0.134426E-02 0. 134426E-02 0. 134426E-02 0. 134426E-02 0. 134426E-02 0. 134426E-02 0. 134426E-02 0.169035E-02 0. 169035E-02 0. 169035E-02 0. 169035E-02 0. 169035E-02 0. 169035E-02 PE 0.489255E 06 0.774966E 06 0. 1 042 00E 07 0.158448E 07 0.208867E 07 0.252844E 07 0.152472E 07 0.210735E 07 0.331088E 07 0.473849E 07 0.625575E 07 0.869726E 06 0.137762E 07 0.185232E 07 0.281665E 07 0.371293E 07 0.449469E 07 0.271043E 07 0.374613E 07 0.588559E 07 0.842340E 07 0.111205E 08 0. 1 133 49E 07 0.179541E 07 Q.241408E 07 0.3 67087E 07 0.483896E 07 0.585781E 07 NG 0.151497E-03 0.956440E-04 0.711331E-04 0.467793E-04 0.354870E-04 0.293148E-04 0.486127E-04 0.351725E-04 0.223870E-04 0.156423E-04 0.118484E-04 Q.391721E-03 0.247303E-03 0. 18 3926 E-03 0.120956E-03 0.917576E-04 0.757982E-04 0.125696E-03 0.909444E-04 O.578854E-04 0.404456E-04 0.306361 E-04 0.619394E-03 0.391039E-03 0.290826E-03 0.191256E-03 0.145088E-03 0.119853E-03 EB 0. 213559E-02 0.186070E-02 0.176894E-02 0.166221E-02 0. 139921E-02 0.153331E-02 0.167851E-02 0. 158133E-02 0. 191133E-02 0.204838E-02 0.187753E-02 0.393528S-02 0. 378475E-02 0.345062E-02 0.294068E-02 0.282191E-02 0.317486E-02 0.309241E-02 0. 274396E-02 0. 373915E-02 0.356002E-02 0.3615 45E-02 0.514760E-02 0.407755E-02 0. 390022E-02 0.352700E-02 0.341818E-02 0.337517E-02 TABLE B.3 DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 511.0 UM DIAMETER. { DOWNFLOW ) Ul! VEL, CM/SEC RE ST NR PE NG EB 0.109 5.24 1. 8 59 0.772358E- 05 0.213307E- 03 0.446725E 05 0.704185E- 05 0.148311E- 02 0. 109 8.30 2. 945 0. 122339E-04 0.213307E- 03 0.707599E 05 0.444570E- 05 0. 128962E-02 0. 109 11.16 3. 960 0, 164495E-04 0. 213307E-03 0.9 51423E 05 0.330639E- 05 0. 1 15559E-02 0.109 16.97 6. 022 0.250132E-04 0. 213307E-03 0.144674E 06 0.217438E- 05 0. 992655E-03 0. 109 22.37 7. 938 0.329726E- 04 0.213307E- 03 0.190711E 06 0.164950E- 05 0.954282E- 03 0. 109 27.08 9. 610 0.399150E- 04 0.213307E- 03 0.2 30865E 06 0. 136260E-05 0. 954282E-03 0.500 5.24 1. 859 0.162520E- 03 0. 9784 74 E-03 0.4 180 06E 06 0.148175E- 03 0,260589E- 02 0.500 8.30 2. 945 0.257426E- 03 0. 978474E-03 0.662109E 06 0.935464E- 04 0.221898E- 02 0.500 11.16 3. 960 0.346130E- 03 0. 978474E-03 0.890258E 06 0.695731E- 04 0.200242E- 02 0.500 16.97 6. 022 0.526328E- 03 0. 978474 E-03 0.1353 73E 07 0.457534E- 04 0. 177579E-02 0.500 22.37 7. 938 . 0.693810E-03 0.9784 74 E-03 0. 178450E 07 0.347088E- 04 0. 151652E-02 0.500 27.08 9. 610 0. 83 989 2E-03 0.978474E- 03 0.216023E 07 0.286719E- 04 0. 149617E-02 0.500 16.33 5. 795 0.506478E- 03 0, 978474E-03 0. 130268E 07 0.475466E- 04 0. 172793E-02 0.500 22.57 8.009 0.700013E- 03 0.97 84 74 E-03 0.1 80046E 07 0.344012E- 04 0. 146905E-02 0.500 35.46 12. 583 0.109980E- 02 0. 978474E-03 0.282872E 07 0.218961E- 04 0.202334E- 02 0.500 50.75 18.009 0.157402E- 02 0. 97 84 74 E-03 0.404844E 07 0.152992E- 04 0.211763E- 02 0.500 67.00 23.776 0.207802E- 02 0.978474E- 03 0.534474E 07 0.115886E- 04 0.229496E- 02 0.600 5.24 1. 859 0.234028E- 03 0. 117417E-02 0..5 237 83E 06 0.213372E- 03 0.420684E- 02 0.600 8. 30 2. 945 0.370694E- 03 0. 117417E-02 0.829656E 06 0. 134707E- 03 0.341250E- 02 0.600 11.16 3. 960 0. 4984 27E-03 0. 117417E-02 0. 1 11554E 07 0. 100185E-03 0.296668E- 02 0.600 16.97 6. 022 0. 757912E-03 0. 117417E-02 0. 169630E 07 0.658849E- 04 0.258118E- 02 0.600 22.3 7 7. 938 0.999086E- 03 0. 117417E-02 0.2 236 07E 07 0.499807E- 04 0.216541E- 02 0.600 27.08 9. 610 0. 120944E-02 0. 117417E-02 0.270688E 07 0.412876E- 04 0.211763E- 02 TABLE B.3 ( CONTINUED } d a VEL. UM CM/SEC 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 1.0 11 1.011 1.011 1.011 1.0 11 1.011 1.011 1.011 1.011 1.011 1.011 5. 24 8.30 11. 16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00 5. 24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00 2.020 5.24 2.020 8.30 2.020 11.16 2.020 16.97 2.020 22.37 2.020 27.08 BE 1, 859 2.945 3.960 6.022 7. 938 9.610 5.795 8.009 12.583 18.009 2 3.776 1.859 2.945 3.960 6. 022 7.938 9.610 5.795 8.009 12.583 18.009 23.776 1 .859 2.945 3.960 6.022 7.938 9.610 ST 0.420221E-03 0.665618E-03 0.894974E-03 0.136091E-02 0.179396E-02 0.217168E-02 0. 130958E-02 0.181000E-02 0.284371E-02 0.406989E-02 0.537306E-02 0.664459E-03 0. 105248E-02 0. 141515E-02 0.215188E-02 0.28 3663E-02 0.343388E-02 0.207073E-02 0.286199E-02 0.449651E-02 0.643536E-02 0.849595E-02 0. 265258E-02 0.420161E-02 0.56 4939E-0 2 0.85 9052E-02 0. 113241E-01 0.137084E-01 NB PE NG 0.157339E- 02 0.743070E 06 0.383130E- 03 0. 157339E-02 0.1 17700E 07 0.2418 80E-03 0. 157339 E-02 0.158257E 07 0.179893E- 03 0.157339E- 02 0.240647E 07 0.118303E- 03 0.157339E- 02 0.317223E 07 0.897453E- 04 0.157339E- 02 0.384014E 07 0.741359E- 04 0. 157339E-02 0.231571E 07 0.122939E- 03 0.157339E- 02 0.3200 59E 07 0.889500E- 04 0. 157339E-02 0.502848E 07 0.566159E- 04 0. 157339E-02 0.719672E 07 0.395586E- 04 0.157339E- 02 0.9501 08E 07 0.299642E- 04 0. 197847E-02 0.968423E 06 0.605810E- 03 0. 197847E-02 0.153395E 07 0.382463E- 03 0. 197847E-02 0.206252E 07 0.284448E- 03 0. 197847E-02 0.313629E 07 0.187062E- 03 0.197847E- 02 0.413428E 07 0.141906E- 03 0. 197847E-02 0.500475E 07 0.117225E- 03 0.1S7847E- 02 0.301801E 07 0.194393E- 03 0.197847E- 02 0.417124E 07 0.140649E- 03 0, 197847E-02 0.655349E 07 0.895218E- 04 0. 197 847 E-02 0.937929E 07 0.625506E- 04 0.197847E- 02 0.123825E 08 0.473798E- 04 0.395303E- 02 0.208185E 07 0.241845E- 02 0.395303E- 02 0.329759E 07 0.1526 83E-02 0.395303E- 02 0.443387E 07 0.1 13554E-02 0.395303E- 02 0.674218E 07 0.746769E- 03 0.395303E- 02 0.888760E 07 0.566503E- 03 0.395303E- 02 0.1075 89E 08 0.467971E- 03 EB 0.532568E-02 0.474992E-02 0.420684E-02 0.366082E-02 0.316559E-02 0. 313672E-02 0.355594E-02 0.333224E-02 0. 332229E-02 0. 425399E-02 0.373548E-02 0.650360E-02 0.522529E-02 0.488146E-02 0. 436161E-02 0.425399E-02 0.4434 59E-02 0.420086E-02 0. 492291E-02 0.555689E-02 0. 640856E-02 0.688537E-02 0. 143198E-01 0. 130617E-01 0.118033E-01 0. 132039E-01 0.222820E-01 0. 370180E-01 TABLE B.4 DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 511.0 tJM DIAMETER. ( UPFLOW ) UM VEL. CM/SEC RE ST NR PE NG EB |0.500 0.500 0.500 0.500 G.500 0.500 0.500 0.500 0.500 0.500 0.500 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00 5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00 1.011 5.24 1.011 8.30 1.011 11.16 1.011 16.97 1.011 22.37 1.011 27.08 1. 859 2.945 3.960 6. 022 7. 938 9.610 5.795 8. 009 12.583 18.009 23.776 1.859 2.945 3.960 6. 022 7.938 9.610 5.795 8.009 12.583 18.009 23.776 1. 859 2.945 3.960 6.022 7.938 9.610 0.162520E-03 0.257426E-03 0.346130E-03 0.526328E-03 0.693810E-03 0.839892E-03 0.506478E-03 0.70 0013E-03 0.109980E-02 0.157402E-02 0.207802E-02 0.420221E-03 0.665618E-03 0.894974E-03 0. 136091E-02 0. 179396E-02 0.217168E-02 0. 130958E-02 0. 181000E-02 0.284371E-02 0.406989E-02 0.537306E-02 0.664459E-03 0. 105248E-02 0.141515E-02 0.215188E-02 0. 283663E-02 0.343388E-02 0. 978474E-03 0. 978474E-03 0. 9784 74 E-03 0. 978474E-03 0.978474E-03 0. 97 8474E-03 0.978474E-03 0.9 7 8474 E-03 0.978474E-03 0. 978474E-03 0. 978474E-03 0. 157339E-02 0. 157339E-02 0. 157339E-02 0. 157339E-02 0.157339E-02 0.157339E-02 0.157339E-02 0. 157339E-02 0.157339E-02 0. 157339E-02 0..157339 E-02 0.197847E-02 0.197847E-02 0.197847E-02 0. 197847E-02 0. 197847E-02 0. 1S7847E-02 0.4180 06E 06 0.148175E- 03 0.662109E 06 0.935464E-04 0.890258E 06 0.695731E-04 0.135373E 07 0.457534E-04 0. 178450E 07 0.347088E- 04 0.2 16023E 07 0.286719E-04 0. 1 30268E 07 0.475466E-04 0. 1800 46E 07 0.344012E-04 0.282872E 07 0.218961E- 04 0.404844E 07 0.152992E-04 0.534474E 07 0. 115886E-04 0.7430 70E 06 0.383130E- 03 0.1 177 00E 07 0.2418 80E-03 0.158257E 07 0. 179893E-03 0.240647E 07 0."̂ ^̂ 18303 E-03 0.317223E 07 0.897453E- 04 0.384014E 07 0.741359E- 04 0.231571E 07 0.122939E- 03 0.320059E 07 0.889500E-04 0.502848E 07 0.566159E- Q4 0.719672E 07 0.395586E- 04 0.950108E 07 0.299642E- 04 0.968423E 06 0.605810E- 03 0.1533 95E 07 0.382463E- 03 0.206252E 07 0.284448E- 03 0.313629E 07 0.187062E- 03 0.413428E 07 0.141906E- 03 0.500475E 07 0.117225E- 03 0.252954E-02 0.214944E-02 0. 197681E-02 0. 153260E-02 0. 148311E-02 0.144804E-02 0. 161853E-02 0. 146204E-02 0. 1676 60E-02 0. 174268E-02 0. 180213E-02 0. 490817E-02 0.426584E-02 0.381120E-02 0.335219E-02 0.306994E-02 0.276596E-02 0. 328268E-02 0.294812E-02 0.251244E-02 0. 293886E-02 0.318493E-02 0.577870E-02 0.505750E-02 0. 455850E-02 0.383304E-02 0.381120E-02 0.347351E-02 TABLE B.5 DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 363.9 UM DIAMETER. { DOWNFLOW ) UM VEL. CM/SEC RE ST NR PE NG EB 0.109 5.24 1. 324 0. 108457E-04 0.299533E- 03 0.318128E 05 0.704185E- 05 0.342913E- 02 0. 109 8.30 2. 097 0.171793E-04 0. 299533E-03 0.503905E 05 0.444570E- 05 0.276878E- 02 0. 109 11.16 2. 820 0.230989E- 04 0. 299533E-03 0.677539E 05 0.330639E- 05 0.2539 71E-02 0.109 16.97 4. 288 0.35124 4E-04 0.299533E- 03 0.103027E 06 0.217438E- 05 0.20 9 286E-02 0. 109 22.37 5. 653 0.46 3012E-04 0.2995 33 E-03 0.135811E 06 0.164950E- 05 0. 1801 37E-02 0. 109 27.08 6. 843 0.56 049 9E-04 0. 299533E-03 0.1644 07E 06 0.136260E- 05 0.161104E- 02 0.500 5.24 1. 324 0.228215E- 03 0.137400E- 02 0.297676E 06 0. 148175E-03 0. 455698E-02 0.500 8.30 2. 097 0.361486E- 03 0.137400E- 02 0.471510E 06 0.935464E- 04 0. 408838E-02 0.500 11.16 2. 820 0.486046E- 03 0. 137400E-02 0.633982E 06 0.695731E- 04 0. 375427E-02 0.500 16.97 4. 288 0.739087E- 03 0. 137400E-02 0.964039E 06 0.457534E- 04 0.350035E- 02 0.500 22.37 5. 653 .0.974270E-03 0. 137400E-02 0.127080E 07 0.347O88E-04 0.313599E- 02 0.500 27.08 6. 843 0.1179 40E-02 0.137400E- 02 0.153837E 07 0. 286719E-04 0. 289057E-02 0.500 16.33 4. 127 0.711213E- 03 0.137400E- 02 0.927681E 06 0.475466E- 04 0.347625E- 02 0.500 22.57 5. 704 0.98 2981E-03 0.137400E- 02 0. 128217E 07 0.344012E- 04 0.332746E- 02 0.500 35.46 8.961 0.154437E- 02 0.137400E-02 0.201443E 07 0. 218961E-04 0.306328E- 02 0.500 50.75 12.825 0.221029E- 02 0. 137400E-02 0.288303E 07 0.152992E- 04 0.369087E- 02 0.500 67.00 16. 931 0.291802E- 02 0. 137400E-02 0.3806 16E 07 0.115886E- 04 0.341044E- 02 0.6 00 5.24 1.324 0.328630E- 03 0.164880E- 02 0.373003E 06 0.213372E- 03 0.576163E- 02 0.600 8.30 2. 097 0.520540E- 03 0. 164880E-02 0.590825E 06 0.134707E- 03 0.500978E- 02 0.600 11.16 2. 820 0.699907E- 03 0. 164880 E-02 0.794411E 06 0. 100185E-03 0. 443105E-02 0.600 16.97 4. 288 0.. 106428E-02 0. 164880E-02 0.1207 99E 07 0.658849E- 04 0. 37 4139E-02 0.600 22.3 7 5. 653 0. 140295E-02 0. 164880E-02 0.159238E 07 0.499807E- 04 0. 3477 20E-02 0.600 27.08 6. 843 0.169834E- 02 0.164880E- 02 0.1 92766E 07 0.412876E- 04 0.308888E- 02 134 Q m a SB M 6H ES O U tn # W ' 6M CN CN O O I I w w CO CN CO 00 o at vO CN CN p- vo CN CN 0 o 1 I tO W p~ cn T— (\J IT) VO O Cn oo vo i n at CN CN o o w w p- oo CN CO cn p». at vo at s t at- sx. 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CM/SEC SE ST NR PE NG EB 0.500 5.24 1. 324 0.228215E- 03 0. 137400E-02 0.297676E 06 0. 148175E-03 0.428742E- 02 0.500 8.30 2.097 0.361486E-03 0. 137400E-02 0.4715 10E 06 0. 935464E-04 0. 387597E-02 0.500 11.16 2. 820 0.486046E-03 0. 137400E-02 0.633982E 06 0.695731E- 04 0.344791E- 02 0.500 16.97 4. 288 0.739087E- 03 0.1374 00E-02 0.964039E 06 0.457534E- 04 0.316675E- 02 0.500 22.37 5.653 0.974270E- 03 0. 137400E-02 0.127080E 07 0.347088E- 04 0.297915E- 02 0.500 27.08 6.843 0. 117940E-02 0.137400E- 02 0.153837E 07 0.286719E- 04 0. 268317E-02 0.500 16.33 4.127 0.711213E- 03 0. 137400E-02 0.927681E 06 0.475466E-04 0.324625E- 02 0.500 22. 57 5.704 0.982981E- 03 0.1374 00E-02 0. 128217E 07 0.344012E- 04 0. 262968E-02 0.500 35.46 8.961 0. 154437E-02 0.137400E- 02 0.201443E 07 0.218961E- 04 0.288872E- 02 0.500 50.75 12.825 0.221029E- 02 0.137400E- 02 0.2 883 03E 07 0. 152992E-04 0.283228E- 02 0.500 67.00 16.931 0.291802E- 02 0.137400E- 02 0.380616E 07 0.115886E- 04 0.315802E- 02 0.804 5.24 1.324 0.590088E-03 0. 220940E-02 0.529164E 06 0.383130E- 03 0.590281E- 02 0.804 8.30 2.097 0.934682E- 03 0.220940E- 02 0.838180E 06 0.241880E- 03 0. 572714E-02 0.804 11.16 2.820 0.125675E- 02 0. 220940E-02 0.112700E 07 0.179893E- 03 0.516939E- 02 0.804 16.97 4.288 0.191103E- 02 0. 220940E-02 0.171373E 07 0.118303E- 03 0.464431E- 02 0.804 22.37 5.653 0.251914E- 02 0.220940E- 02 0.225905E 07 0.897453E- 04 0.418315E- 02 0. 804 27.08 6.843 0.304954E- 02 0. 220940E-02 0.273469E 07 0.741359E- 04 0. 410400E-02 0.804 16.33 4. 127 0.183896E- 02 0.220940E- 02 0.164910E 07 0.122939E- 03 0.444327E- 02 0.804 22.57 5.704 0.254166E- 02 0.220940E- 02 0.227925E 07 0.889500E- 04 0. 410400E-02 0.804 35.4 6 8.961 0.399323E- 02 0.220940E- 02 0.358095E 07 0.566159E- 04 0,432282E- 02 0.804 50.75 12. 825 0.571507E- 02 0.220940E- 02 0.512502E 07 0.395586E- 04 0.532056E- 02 0.804 67.00 16.931 0.754"5G2E-02 0. 220940E-02 0.6 766 03E 07 0.299642E- 04 0.541424E- 02 TABLE B.7 DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 216.0 UM DIAMETER. { DOWNFLOW ) d a DM VEL. CM/SEC RE ST NR PE NG EB 0.109 5.24 0.786 0.182635E-04 0. 504396E-03 0.188918E 05 0.704185E-05 0.5190 85E-02 0. 109 8.30 1.246 0.289289E-04 0.504396E-03 0.299241E 05 0.444570E- 05 0.473038E- 02 0. 109 11.16 1. 675 0.388972E-04 0. 504396E-03 0.402353E 05 0.330639E-05 0.446783E-02 0. 109 16.97 2.547 0.591474E-04 0.504396E-03 0.611822E 05 0.217438E-05 0.389815E- 02 0. 109 22. 37 3.357 0.779686E-04 0. 504396E-03 0.806509E 05 0.164950E- 05 0.327911E-02 0. 109 27.08 4. 064 0. 94384 9E-04 0. 504396E-03 0.976319E 05 0.136260E-05 0.326049E- 02 0.500 5.24 0.786 0.384301E-03 0.231374E-02 0.176773E 06 0.148175E- 03 0.900468E- 02 0.500 8.30 1. 246 0.608722E-03 0. 231374E- 02 0.280003E 06 0.935464E-04 0.806578E- 02 0.500 11.16 1,675 0.818474E-03 0.231374E-02 0.376487E 06 0.695731E-04 0.704028E- 02 0.500 16.97 2. 547 0.124458E- 02 0.2313 74E-02 0.572489E 06 0.457534E- 04 0.633001E-02 0.500 22.37 3.357 0.164062E-02 0.231374E-02 0.754660E 06 0.347088E- 04 0.566594E- 02 0.500 27.08 4, 064 0.198605E-02 0.231374E- 02 0.913553E 06 0.286719E- 04 0.52 30 74E-02 0.500 16.33 2.451 0.119764E-02 0. 2313 74 E-02 0.550898E 06 0.475466E-04 0.637446E-02 0.500 22.57 3. 387 0.165528E-02 0.231374E- 02 0.761407E 06 0.344012E-04 0.586646E-02 0.500 35.46 5.321 0.260063E-02 0. 231374E-02 0. 119626E 07 0.218961E- 04 0.608713E- 02 0.500 50.75 7. 616 0.372200E-02 0.231374E- 02 0.171207E 07 0.152992E- 04 0.714069E-02 0.500 67.00 10.055 0.491378E- 02 0.231374E-02 0.2260 27E 07 0.115886E- 04 0.765222E- 02 0.600 5.24 0.786 0.553394E-03 0.277649E-02 0.221506E 06 0.213372E- 03 0. 126769E-01 0.600 8.30 1. 246 0.876560E- 03 0. 277649E-02 0.350858E 06 0.134707 E-03 0. 1149 47E- 01 0.600 11.16 1.675 0.117860E-02 0. 277649E-02 0.471756E 06 0.100185E- 03 0.978480E- 02 0.600 16.97 2.547 0.179219E-02 0.277649E-02 0.717357E 06 0.658849E-04 0. 912422E- 02 0.600 22.37 3.357 0.236248E-02 0.277649E-02 0.945626E 06 0.499807E-04 0. 809154E- 02 0.600 27.08 4.064 0.28599 1E-02 0.277649E- 02 0.114473E 07 0.412876E-04 0.747833E- 02 TABLE B.7 { CONTINUED ) Uti 0.804 0.804 0.804 0.804 0.804 0.804 0,804 0.804 0.804 0.804 0,804 011 011 011 011 011 1.011 1.011 1.011 1.011 1.011 1.011 VEL. CM/SEC 5,24 8.30 11. 16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00 5.24 8.30 11. 16 16,97 22.37 27.08 16.33 22.57 35. 46 50.75 67.00 2.020 5.24 2.020 8.30 2.020 11.16 2.020 16.97 2.020 22.37 2.020 27.08 RE ST 0.786 0.993674E-03 1.246 0.157395E-02 1.675 0.211630E-02 2.547 0.3218G6E-02 3.357 0.424208E-02 4.064 0.513525E-02 2.451 0.309670E-02 3.387 0.428000E-02 5.321 0.672437E-02 7,616 0.962385E-02 10.055 0.127054E-01 0.786 0.157121E-02 1.246 0.248875E-02 1.675 0. 334632E-02 2.547 0.508844E-02 3.357 0.670762E-02 4.064 0.811992E-02 2.451 0.489654E-02 3.387 0.676760E-02 5.321 0.106327E-01 7.616 0. 152173E-01 10.055 0.200899E-01 0.786 0.627241E-02 1.246 0.993531E-02 1.675 0.133588E-01 2.547 0.203135E-01 3.357 0.267775E-01 4.064 0.324154E-01 NS 0. 372050E-02 0.372050E-02 0. 372050E-02 0.372050E-02 0.372050E-02 0. 372050E-02 0.372050E-02 0.372050E-02 0.372050E-02 0.372050E-02 0.372050E-02 0.467839E-02 0.467839E-02 0.467839E-02 0.467839E-02 0.467839E-02 0.467839E-02 0.467839E-02 0.467839E-02 0.467839E-02 0.467839E-02 0.467839E-02 0. 934752E-02 0.934752E-02 0. 934752E-02 0. 934752E-02 0. 934752E-02 0. 934752E-02 PE 0.314241E 06 0.497749E 06 0.669262E 06 0.101769E 07 0.134152E 07 0.162398E 07 0.9 793 06E 06 0.135352E 07 0.212653E 07 0.304346E 07 0.401797E 07 0.409542E 06 0.648703E 06 0.872231E 06 0.132632E 07 0.174837E 07 0.211649E 07 0. 1276 30E 07 0.176400E 07 0.277145E 07 0.396646E 07 0.523651E 07 0.880407E 06 0.139454E 07 0.187507E 07 0.285124E 07 0.375853E 07 0.454989E 07 NG 0.383130E-03 0.241880E-03 0.179893E-03 0.118303E-03 0.897453E-04 0.741359E-04 0.122939E-03 0.889500E-04 0.566159E-04 0.395586E-04 0.299642E-04 0.605810E-03 0.382463E-03 C.284448E-03 0.187062E-03 0. 141906E-03 0.117225E-03 0.194393E-03 0.14064 9E-03 0.895218E-04 0.625506E-04 0.473798E-04 0.241845E-02 0.152683E-02 0.113554E-02 0.746769E-03 0.566503E-03 0.467971E-03 EB 0.131101E-01 0. 116956E-01 0.105591E-01 0.974545E-02 0.955368E-02 0. 936974E-02 0.105124E-01 0.926287E-02 0.102420E-01 0. 131517E-01 0. 136824E-01 0. 139732E-01 0. 121130E-01 0. 113247E-01 0. 102860E-01 0.107509E-01 0. 1282 97E-01 0.101511E-01 0.919128E-02 0. 158303E-01 0. 2794 86E-01 0.424503E-01 0.715000E-01 0.624000E-01 0.794600E-01 0. 107230E 00 0. 128550E 00 0. 113930E 00 138 S3 O co to ca o o Si H Q z o ex. to w 03 03 O u CN CO a. H o o O M CM CO O CO W w u S5 o CO ca szs CO CO 2 : Pu o H — SB O w to ft S O S H W Q PQ — W OS u O o o o O o o o o o o o o o o o o a o o o o S3 W WD VO VO VD VO VO r- p* r- v© vo vo p» r» p» vo p~ r- r- H O O o o O O o o o o o o o o o o o o o o o o U H pa W w w ca pa ca pa pa Pa pa pa pa pa pa pa pa pa ca ca pa ca oo cn r- Ch o 00 00 p- vo r- p> »— cn CN C h CN 00 VO CN no VD r- CM r- o 00 00 VO i n Ch o CN o CN a t a r VO VO i n ON o i n i n a t ON M w r~ o a t a t VO i n 00 a r vo CN o CN p» CN r- no no no VO no r-ft VO o VO CN a T no o T— ON VO a t r» C h r - a t CN ON i n CN a t <W 00 r> r-m i n VO T— r- CN T- ON VO O no VO p- no «— o O o CN no i n r- ON i n p» r » r - CN 00 a r VO r~ ON T— CN no iH CJ • o O O o o o o o O O O o o o o o O o o O o o M as ca H <N CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN CN o w O o O O O o O o O O O O O O O O O o O O O O u 1 1 1 1 1 1 1 i 1 1 1 1 | 1 1 1 1 1 1 1 1 1 pa KJ Pa pa w ca pa pa pa pa pa pa pa pa pa pa pa pa pa Pa pa pa ca M a t a t a r a t a t a t a r a r a t a r o o o o o o o o G o o r- r» r- o r- P* r~ p» p» i n i n i n i n i n i n i n i n i n m m a OS oo 00 oo no no no no no no ro no o o o o o o o o o o o 25 S3 55 ?— r - T~ V r " r - CN CN CN CN CN CN CN CN CN CN CN S3 -• no no CO no m no no rr> no no no p- (-» p- p» !> p* P« p» r- r- r-to CM CN CN CN CN CN CN CN CN CN CN no no no no no no no no no no no Q O- • o O O O o o O O O o o o o o o o o o o o o o U . Pa _3 tO 00 pa \ • > 3?3 c q U pa cn c d s H CN CN O O I I pa Pa vo o no r** oo CN in no oo co CN CN 0 o 1 I Pa.pa o vo 00 no •p** i n oo r- oo r- vo CM fM 0 o 1 I pa ca en 00 CN CD no r» ON CO i n vo i n i n CN CN O O I I pa Pa cn o VO O st O CN cn vo m CN CN CN O O O I I I ca ca w £3* a t ^ 00 CN CN m «~ r» no CN f N f**. f^. m vo vo 1— «—•*- CN 0 o o o 1 i i i ca pa pa pa no r*» a- 5t CN CN i n oo o m ON cn o r- vo T~* V Q ff) T™"- T— ON f N f N O O I I pa ca O s t f N =t ON r ~ r- o a t CN ON oo CN CN CN r - r - O O O O O I I I I I pa pa pa aa pa oo o CN ON r- vo f*» a t Ch CN no vo CN a t O i n in a t co o tn ON o r - Ch co cn r~ r~ o o o o o o o o o o o o o o o o o o o o o o no a r 0 o 1 I ca ca m a t r- vo « - a t oo tn a t no v» Ch a t a r 0 o 1 I ca ca r ™ a f no no r~ i n i n r- ON m ô at a t a r o o ca pa oo cn CO T ~ o r> r> vo a r CO no CN a t a r a t 0 o o 1 I I ca ca Pa VO CN vo T— vo a t o i n a t h- a t <~ a t no CN cn oo a t a t 0 o 1 I ca pa CN VO ON 00 ON 00 t N in i n r~ no no no a o o ' i i i ca ca ca o o no no co cn T- CO oo no T— ch CO a t r*> no CN r - no a r 0 o 1 I Pa ca no no o m no a r oo r- T— cn r ~ 00 a t no O O t I ca ca ON ON in no no o> r~ f N a t CN a t a t 0 o 1 I ca ca o cn o i n i n T- tn vo oo v p oo i n a r a r o o ca ca VO CN oo a r in vo m cn cn cn no CN no no no CN CN CN f N CN CN CN CN no CN CN f N CN CN CN CN CN CN o O o O o O O • O O i O | O O o o 1 O O O o | o 1 O O • o 1 i pa 1 ca 1 ca 1 ca 1 ca 1 pa ca 1 pa } ca pa 1 ca t ca 1 pa 1 ca 1 pa 1 ca 1 ca ca 1 ca 1 pa 1ca 1 Pa CN a t 00 CN i n a t 00 no o oo a t i n o VO oo i n o o i n =t o CN !-» m VO o VO CN vo o r- cn no o o CN o oo CO i n no r-- a r a r O VO i n o CN no VO no CO CN i n VO o a r no o a r 00 00 a r a t 00 ON i n o CN r — no r> T" r - a t no Ch 00 CN CN oo o *— CN vo en VO <o r- Ch ON i n r~ CN CN T— o CN r» vO CN no VO oo CN no a t C h f N no a r m no a t ON o o o o o o o o o o o i O v o i n r - i ^ a f r - i N i - v o i n co=r r * -a r in io incocNT— m r*» CN vo m n o o a r n o o o v o o o o o o o o o o o o o v o v o m r ^ r~-arT - r , ~ ' — v o i n o o a r r ^ s r m v o m o o f M T - v n fN vo in no o ar no no vo o O r - r - C N O O a t C N O O m O O rMnoarrNinoinr-o at o vo r» r» oo no t-vvo in o rsi no 1— cn no o no in =r r>« o a t o ^ o r ^ r ^ c o n o r ^ v o m o CN no r~ cn no o no in ar r> o m o o » ~ v o c N r » v o c N m o f ^ - T - r - f M c N » - ( N n o i n v o o o o o o o o o o o o o o o o o o o o o o o i n m i n in i n mm tn m i n i n m co v O C N f - V Q C N t n o O r - C N C N ' ~ f N n 0 t n v 0 a t a r a T a r a r a r a r a t a r a t a r o o o o o o o o o o o CO CO 00 00 00 00 00 00 CO 00 oo o o o o o o o o o o o o o o o o o o o o o o TABLE B.9 DIMENSION LESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 126.1 UM DIAMETER. ( DOHNFLOW ) UM VEL. CM/SEC RE ST NR PE NG EB 0. 109 5.24 0.458 0.31323 4E-04 0.865079E- 03 0.110151E 05 0.704185E- 05 0.880751E- 02 0. 109 8.30 0.726 0.496153E-04 0. 865079E-03 0.174477E 05 0.444570E- 05 0.792353E- 02 0.109 11.16 0,976 0.667117E- 04 0.865079E- 03 0.234597E 05 0.330639E- 05 0.752621E- 02 0. 109 16.97 1.485 0. 101442E-03 0. 865079E-03 0.356731E 05 0.217438E- 05 0.607580E- 02 0. 109 22.37 1.957 0.133722E- 03 0.865079E- 03 0.470246E 05 0.164950E- 05 0.522232E- 02 0. 109 27.08 2.369 0.161878E- 03 0.865079E- 03 0.569256E 05 0.136260E- 05 0.498415E- 02 0.500 5.24 0. 458 0.659107E-03 0. 396825 E-02 0.1030 70E 06 0.148175E- 03 0. 127530E-01 0.500 8.30 0.726 0.104401E- 02 0. 396825E-02 0.163260E 06 0.935464E- 04 0. 110029E-01 0.500 11.16 0.976 0.140375E-02 0.396825E- 02 0.219516E 06 0.695731E- 04 0.987256E- 02 0.500 16.97 1.485 0.213455E- 02 0.396825E- 02 0.3 337 97E 06 0.457534E- 04 0. 914087E-02 0.500 22.37 1.957 0.281379E- 02 0.396825E- 02 0.4400 14E 06 0.347088E- 04 0.841301E- 02 0.500 27.08 2. 369 0.340623E- 02 0.396825E- 02 0.532660E 06 0.286719E- 04 0. 737581E-02 0.600 5.24 0.458 0.949115E- 03 0.476190E- 02 0.129152E 06 0.213372E- 03 0. 148300E-01 0.600 8.30 0.726 0. 150337E-02 0.476190E- 02 0.204573E 06 0.134707E- 03 0. 138627E- 01 0.600 11.16 0.976 0.202140E- 02 0.476190E- 02 0.275064E 06 0.100185E- 03 0. 132919E-01 0.600 16.97 1.485 0.307375E- 02 0. 476190E-02 0.418265E 06 0.658849E- 04 0.106451E- 01 O.600 22.37 1.957 0.405185E- 02 0. 476190E-02 0.551360E 06 0.499807E- 04 0. 977369E-02 0.600 27.08 2. 369 0.490497E- 02 0. 476190E-02 0.667449E 06 0.412876E- 04 0.950394E- 02 0.600 16.33 1.429 0.29 5783E-02 0.476190E- 02 0.402491E 06 0.684671E- 04 0.969150E- 02 0.600 22.57 1, 975 0.408807E- 02 0. 476190E-02 0.556290E 06 0.495377E- 04 0.936762E- 02 0.600 35.46 3. 103 0.642283E- 02 0. 476190E-02 0.873994E 06 0.315304E- 04 0.112736E- 01 0.6 00 50.75 4.441 0.919228E- 02 0.476190E- 02 0.125085E 07 0.220309E- 04 0.145458E- 01 0.600 67.00 5. 862 0.121356E- 01 0. 4761 90E-02 0.165137E 07 0.166876E- 04 0.158372E- 01 TABLE B.9 { CONTINUED ) d a VEL. UM CM/SEC RE ST NR PE NG EB 0.804 0. 804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 1.011 1.011 1.0 11 1.011 1.011 1.011 1.011 1.011 1.011 1.011 1.011 5.24 8.30 11. 16 16.97 22.37 27.08 16.33 22. 57 35. 46 50.75 67.00 5.24 8.30 11.16 16.97 22. 37 27.08 16.33 22.57 35. 46 50.75 67.00 2.020 5.24 2.020 8.30 2.020 11.16 2.020 16.97 2.020 22.37 2.020 27.08 0.458 0.170423E-02 0.726 0.269945E-02 0.976 0.362962E-02 1.485 0.551923E-02 1.957 0.727550E-02 2.369 0.880735E-02 1.429 6.531108E-02 1.975 0.734055E-02 3. 103 0.115328E-01 4.441 0.165057E-01 5.862 0.217907E-01 0.458 0.269475E-02 0.726 0.426840E-02 0.976 0.573920E-02 1.485 0.872708E-02 1.957 0. 115041E-01 2.369 0.139263E-01 1.429 0.839795E-02 1.975 0.116070E-01 3. 103 0. 182358E-01 4.441 0.260990E-01 5.862 0.344558E-01 0.458 0. 107577E-01 0.726 0.170398E-01 0.976 0.229114E-01 1.485 0.348393E-01 1.957 0.459255E-01 2.369 0.555950E-01 0.638095E-02 0.638095E-02 0.638095E-02 0.638095E-02 0.638095E-02 0.638095E-02 0.638095E-02 0.638095E-02 0.638095E-02 0.638095E-02 0. 638095E-02 0.802381E-02 0.802381E-02 0.802381E-02 0. 802381E-02 0.802381E-02 0.802381E-02 0. 802381E-02 0.802381E-02 0.802381E-02 0.802381E-02 0.802381E-02 0, 160317E-01 0. 160317E-01 0. 160317E-01 0.160317E-01 0. 160317E-01 0. 160317E-01 0. 1832 23E 06 0.383130E- 03 0.290219E 06 0.241880E- 03 0.3 902 22E 06 0.179893E-03 0.5933 76E 06 0. 118303E-03 0.782193E 06 0.897453E-04 0.946884E 06 0.741359E- 04 0.570998E 06 0.122939E- 03 0.789187E 06 0.889500E-04 0.123990E 07 0.566159E-04 0.177453E 07 0.395586E-04 0.2342 73E 07 0.299642E-04 0.238789E 06 0.605810E-03 0.3782 35E 06 0.382463E- 03 0.508566E 06 0.284448E-03 0.773331E 06 0.187062E-03 0.101941E 07 0.141906E-03 0.1234 05E 07 0.117225E-03 0.744166E 06 0. 194393E-03 0.102853E 07 0.140649E-03 0. 161593E 07 0.895218E-04 0.231270E 07 0.625506E-04 0.3 05322E 07 0.473798E- 04 0.513333E 06 0.241845E-02 0.813104E 06 0. 1526 83E-02 0.1 09328E 07 0.113554E- 02 0. 166246E 07 0.746769E- 03 0.219146E 07. 0.566503E- 03 0.265288E 07 0.467971E- 03 0. 157127E-01 0. 145061E-01 0. 137099E-01 0. 109300E-01 0. 100635E-01 0. 983679E-02 0. 143505E-01 0. 143407E-01 0. 188520E-01 0. 241976E-01 0. 271912E-01 0. 181096E-01 0. 167220E-01 0. 149565E-01 0. 181965E-01 0.224270E-01 0.280023E-01 0. 180604E-01 0.209214E-01 0. 2896 34E-01 0. 319150E-01 0.341082E-01 0.929000E-01 0.935000E-01 0.886000E-01 0.890500E-01 0.910000E-01 0.947000E-01 TABLE B.10 DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TEST ON BEDS OF NICKEL SHOT 126.1 UM DIAMETER. { UPFLOB ) da VEL. RE ST NR PE NG EB UB CM/SEC • 0.500 5.24 0. 458 0.659107E-03 0. 396825E-02 0.10 3070E 06 0.148175E- 03 0.113065E- 01 0.50 0 8.30 0.726 0.104401E- 02 0.396825E- 02 0.163260E 06 0.935464E- 04 0.979875E- 02 0.500 11. 16 0.976 0. 140375E-02 0.396825E- 02 0.219516E 06 0.695731E- 04 0.932615E- 02 0.500 16.97 1. 485 0.213455E- 02 0.396825E- 02 0.3337 97E 06 0.457534E- 04 0.864948E- 02 0.500 22.37 1. 957 0.281379E- 02 0.396825E- 02 0.4400 14E 06 0.347088E- 04 0.767020E- 02 0.500 27.08 2.369 0.340623E- 02 0.3S6825E- 02 0.532660E 06 0.286719E- 04 0. 769171E-02 0.804 5.24 0.458 0. 170423E-02 0.638095E- 02 0.183223E 06 0.383130E- 03 0. 100865E-01 0.804 8.30 0.726 0.269945E- 02 0,638095E- 02 0.290219E 06 0.2418 80E-03 0.102896E- 01 0.804 11.16 0.976 0.362962E- 02 0. 638095E-02 0.390222E 06 0.179893E- 03 0. 111831E-01 0.804 16.97 1. 485 0.551923E- 02 0.638095E- 02 0.5 933 76E 06 0.1 18303E-03 0. 112355E-01 0.804 22.37 1.957 0.727550E- 02 0.638095E-02 0.7 82193E 06 0.897453E- 04 0. 1094 57E-01 0.804 27.08 2. 369 0.880735E- 02 0. 63 8095 E-02 0.946884E 06 0.741359E- 04 0. 108395E-01 142 . APPENDIX C REGRESSION ANALYSIS OF EQUATIONS SUGGESTED BY OTHER WORKERS C.l Introduction Equations developed by other workers were tested by f i t t i n g them to the present experimental data to study their a b i l i t y to predict the single collector efficiency (EB). Several other types of equations were also tried in an attempt to improve on the predictions of EB. This section gives the results of the regression analyses. C.2 Empirical Equations Developed by Other Workers EB = a 0 + ctiCE) [C.l] where E = EI + ER + ED + EG 1.13 31 EI = 2 St (Paretsky ) 9 f\~\ ER = 1.5 NR - (Friedlander ) ED = 8 Pe _ 1 +2.3 Pe" 5^ 8 Re 1' 8 (Johnstone and Roberts 6 3) EG = NG (Ranz 6 7) The equation for EI was chosen because other i n e r t i a l type equations could not be applied to the experimental data. For example, the equation 13 of Langmuir and Blodgett (Eq. 2.2) predicts a minimum value of the Stokes number (0.83) below which no i n e r t i a l collection takes place. It was evident this was not the case with the results of this work. Other equa- 59 tions such as that of Landahl and Hermann (Eq. 2.5) gave excessively low collection efficiencies again bearing no relation to this data. 143 -2/3 For the value of ED equations of the type ED = g Pe (Eq. 2.15) would have been satisfactory. However, the equation of Johnstone and Roberts was chosen as i t possibly contains an interactive term which may be 13 62 more r e a l i s t i c . Equations developed by Langmuir (Eq. 2.11) and Natanson (Eq. 2.16) were of l i t t l e use as the limit of Re had to be less than 7.38 which was not the case in this work. The interception term ER was chosen from Eq. 2.7 as most of the experi- ments were conducted in the creeping flow region. Again equations of Langmuir and Natanson suffered due to the limiting value of Re. The other equations tested were:- EB = ct0 + ax St + a 2 NR St + a 3 NR St 2 (Davies 1 6) [C.2] 16 8 31 EB = a 0 + a-i NR + a 2 St (Davies , Meisen , Paretsky ) [C.3] 23 EB = a 0 + ai NG + a 2 St (Doganoglu ) [C.4] 23 EB = a 0 + ai NG + a 2 Re St (Doganoglu ) [C.5] — 2/3 —— — 61 EB = t ag + OLI Sc Re 2 + a 2 NR2 Re2 (Friedlander ) [C.6] Tables C.l to C . l l give the results of f i t t i n g the above equations to the data by multiple regression. The value of the ex's are lis t e d for con- ditions relating to constant aerosol or collector size, i.e., for each aerosol the variables are gas velocity and collector diameter and for each collector the variables are gas velocity and aerosol diameter. Also, the value of the a's were calculated for a l l the data. To compare the degree of f i t of each equation the square of the multiple correlation coefficient (R) was calculated. This is defined as:- n - Z (Yk - Y ) 2 2 = k=3_ R n _ E (Yk - Y ) 2 k=l where Yk = kth calculated value of Y Yk = kth experimental value of Y Y = mean of the experimental values of Y Ideally, the closer R i s to unity the better the model. The actual value of R measures the proportion of total variation about the mean accounted for by the regression. For example i f R2 = 0.9 then the model explains 90% of the total variation within the data. TABLE C.l. RESULTS OF FITTING EQUATION C.l TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d ym c a 0 >< 10 3 ai R2 598.1 0.704 1.590 0.855 511.0 0.102 1.870 0.874 363.9 0.391 2.012 0.935 216.0 0.308 3.411 0.870 126.0 9.396 1.484 0.684 d ym a 0.109 2.467 1.985 0.498 0.500 2.364 0.509 0.397 0.600 2.470 0.289 0.353 0.804 3.990 1.157 0.748 1.011 4.667 0.623 0.755 2.020 10.270 0.967 0.711 A l l results 1.630 1.890 0.692 TABLE C.2. RESULTS OF FITTING EQUATION C.2 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d ym a c o x io 3 a 2 x 10 - 2 a3 x 10"4 R2 598.1 2.46 5.126 0.867 511.1 2.66 - 3.430 1. 5576 0.893 363.9 3.30 4.150 - 0.956 216.1 7.10 - 4.510 - 0.9101 126.1 12.60 - 1.247 - 0.744 d ym a 0.109 2.705 3.330 0.489 0.500 2.749 - 2.654 - 0.425 0.600 4.180 - 1.117 - 0.365 0.804 8.060 - - 1. .724 0.889 1.011 10.800 - 1.005 - 0.801 2.02 0.507 - 1.616 - 0.716 A l l results 7.055 - - 1.700 - 0.513 TABLE C.3. RESULTS OF FITTING EQUATION C .3 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d ym ag x 10 4 aj a 2 R' 598.1 -2.76 2.35 1.03 0.852 511.0 2.36 0.11 0.17 0.870 363.9 6.68 0.86 0.21 0.922 216.0 -78.'62 4.41 2.87 0.903 126.1 -103.70 4.66 0.57 0.887 d ym a 0.109 -2.61 3.31 1.41 0.800 0.500 -2.83 2.69 0.22 0.780 0.600 -=11.24 3.03 0.11 0.808 0.804 12.90 1.60 0.09 0.618 1.011 -19.60 1.05 1.16 0.701 2.020 6.92 1.67 0.63 0.828 A l l results -0.08 1.817 0.66 0.854 TABLE C.4. RESULTS OF FITTING EQUATION C.4 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION •d ym do x 10 d ctj 0-2 R' 598.1 1.11 3.76 1.48 0.947 511.0 0.89 2.97 0.19 0.895 363.9 1.26 3.76 0.22 0.884 216.0 -0.90 21.60 3.66 0.941 126.1 3.06 34.60 1.48 0.960 d ym 0.109 0.62 12.44 2.35 0.774 0.500 1.31 7.85 0.69 0.960 0.600 1.13 9.61 0.65 0.922 0.804 2.70 8.73 0.39 0.899 1.011 2.15 17.80 1.44 0.785 2.020 6.47 19.15 0.89 0.848 A l l results 0.99 15.80 1.24 0.764 TABLE C.5. RESULTS OF FITTING EQUATION C.5 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d ym a 0 x 10 3 ai a 2 x 10 - 1 R2 598.1 1.204 5.51 1.42 0.960 511.0 0.968 5.56 2.19 0.941 363.9 1.512 7.97 3.35 0.943 216.0 0.342 34.20 9.09 0.884 126.1 3.970 43.40 6.26 0.931 d ym a 0.109 1.590 1.93 4.46 0.511 0.500 1.810 8.12 0.25 0.878 0.600 1.730 9.72 0.25 0.796 0.804 3.130 9.08 0.24 0.874 1.011 4.390 20.77 1.52 0.837 2.020 10.560 17.17 1.38 0.682 A l l results 4.250 13.45 0.74 0.204 147 TABLE C. 6. RESULTS OF FITTING EQUATION C. 6 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d ym c a 0 x 10 3 a 2 x 10 - 2 R2 598.1 1.31 4.85 0.904 511.0 0.93 - 0.51 0.848 363.9 1.13 - 4.81 0.910 216.0 -4.17 9.92 7.37 0.953 126.1 4.99 - 2.74 0.882 d ym a 0.109 3.78 7.47 0.764 0.500 1.98 - 2.89 0.573 0.600 1.92 - 2.52 0.533 0.804 3.58 - 1.17 0.402 1.011 2.83 - 3.33 0.605 2.020 6.13 - 1.79 0.792 A l l results 0.80 20.53 2.32 0.837 In general i t was possible to obtain relatively good predictions for equations f i t t e d to the results relating to one collector or aerosol size. However, attempts to produce equations to f i t a l l the data met with l i t t l e 2 success with R values in the range of 0.5 to 0.7. In many cases the value of the intercept ctg was comparable to the single collector efficiency and therefore dominated the equations. This was obviously unrealistic and the regression analysis was repeated by forcing the equations through the origin. Furthermore, the total single collector efficiency, which by definition is made up of the individual efficiencies, should equal zero when a l l these individual efficiencies are zero. Thus setting ag = 0 should probably result in a more precise model. TABLE C.7. RESULTS OF FITTING EQUATION C.l TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO) d ym c cti R̂ 598.1 511.0 363.9 216.0 126.1 1.65 1.79 1.89 3.14 1.64 0.829 0.843 0.872 0.814 0.640 d ym a 0.109 0.500 0.600 0.804 1.011 2.020 17 75 2 64 37 97 0.706 0.490 0.090 0.187 0.661 0.865 A l l results 1.97 0.689 TABLE C.8. RESULTS OF FITTING EQUATION C.3 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO) d ym c cti 0 t 2 R̂ 598.1 511.0 363.9 216.0 126.1 2.12 1.28 1.18 2.19 2.90 0.96 1.51 1.71 2.90 0.84 0.874 0.817 0.832 0.803 0.817 d ym a 0.109 0.500 0.600 0.804 1.011 2.020 7.75 2.57 2.62 2.29 1.70 1.35 0.06 0.72 1.84 0.869 0.884 0.810 0.810 0.903 0.828 A l l results 2.53 1.38 0.757 TABLE C.9. RESULTS OF FITTING EQUATION C.4 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO) d um c ai a2 R2 598.1 4.67 1.52 0.899 511.0 4.11 1.80 0.846 363.9 5.74 1.95 0.865 216.0 24.00 3.13 0.884 126.1 37.10 1.49 0.960 d um a 0.109 48.00 4.10 0.476 0.500 39.70 2.26 0.518 0.600 37.90 1.82 0.533 0.804 22.50 1.39 0.757 1.011 13.90 1.42 0.846 2.020 2.90 2.17 0.846 A l l results 14.00 2.16 0.765 TABLE C. 10. RESULTS OF FITTING EQUATION C.5 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO) d ym c R? 598.1 7.2 0.11 0.781 511.0 9.7 0.15 0.723 363.9 11.4 0.22 6.689 216.0 40.3 0.58 0.740 126.1 49.5 0.50 0.865 d ym a 0.109 67.33 4.04 0.006 0.500 46.30 0.14 0.096 0.600 45.00 0.37 0.075 0.804 27.22 0.10 0.025 1.011 18.80 0.10 0.144 2.020 6.46 0.26 0.576 A l l results 23.20 0.31 0.434 150 TABLE C . l l . RESULTS OF FITTING EQUATION C.6 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO) d c ym cti a 2 x 10 - 2 R2 598.1 3.19 5.35 0.869 511.0 2.66 5.30 0.843 363.9 3.95 4.80 0.891 216.0 3.06 6.60 0.914 126.1 7.09 2.88 0.878 d ym a 0.109 3.06 32.30 0.865 0.500 20.40 2.38 0.895 0.600 32.20 1.85 0.870 0.804 38.70 1.80 0.857 1.011 36.30 2.17 0.899 2.020 42.20 5.62 0.783 A l l results 5.96 3.78 0.750 Once again equations could be fitt e d reasonably well to the data relating to one aerosol or collector size but the f i t to a l l the data was s t i l l poor. Generally there was l i t t l e improvement in forcing the equa- tions (C.l to C.6) through the origin except they are more r e a l i s t i c . Equations of this type are good for predicting EB for a given collector diameter but have limited a b i l i t y for predicting EB over large collector and aerosol size ranges. 23 Comparisons of the coefficients from the equations of Doganoglu with those from equivalent equations developed in this work are shown in Tables C.12 and C.13. 151 TABLE C.12. COMPARISON OF THE COEFFICIENTS OF EQUATION C.4 WITH THOSE FROM DOGANOGLU'S WORK d ym This work Doganoglu c " ai ct2 oil a z 110 37.10 1.49 6.89 2.89 600 4.67 1.52 0.97 0.83 A l l 14.00 2.16 8.60 2.69 TABLE C.13. COMPARISON OF THE COEFFICIENTS OF EQUATION C.5 WITH THOSE FROM DOGANOGLU'S WORK This work Doganoglu d ym c ai ot2 04 a 2 110 4.95 0.50 9.27 2.53 600 7.20 0.11 1.42 0.06 A l l 23.2 0.31 9.8 0.15 The coefficients agree in magnitude i f not in actual value and demon- strate equations of this form can adequately predict EB for a given collector diameter. C.3 Parameter Equations Equations were formulated based on single dimensionless groups and were fitt e d by regression analysis to the experimental data. The equations were of the type:- EB = a 0 + ax Re + a 2 St + a 3 ND + ak NR + a 5 NG [C.7] and EB = a 0 + cti Re St + a 2 ND + a 3 NR + ah NG [C.8] Tables C.14 to C.17 give the results of f i t t i n g the above equations to the data by multiple regression. 152 TABLE C.14. RESULTS OF FITTING EQUATION C.7 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION cL ym ag x 103 a\ a.2 «3 «i+ a 5 R2 598.1 1.11 - 1.48 - - 3.76 0.946 511.0 14.10 - 2.09 - 0.869 363.9 1.92 - 2.32 - 0.916 216.0 -0.89 - 3.66 - - 21.60 0.943 126.1 3.06 - 1.48 - - 34.60 0.966 d ym a 0.109 1.07 - 0.66 0.52 2.34 2.56 0.964 0.500 0.27 - 0.49 - 0.96 7.44 0.941 0.600 2.70 - 0.39 - - 8.73 0.903 0.804 2.15 - 1.42 - - 17.7 0.785 1.011 0.69 - 0.63 - 1.67 - 0.824 2.011 -1.95 - 1.02 27.06 0.85 6.44 0.899 A l l results -6.08 - 1.30 9.39 2.62 10.31 0.810 TABLE C.15. RESULTS OF FITTING EQUATION C.8 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d £ ym ctQ x 10^ oq a2 a 3 R 598.1 1.20 0.14 - - 5.51 0.958 511.0 0.97 0.22 - - 5.55 0.941 363.9 1.51 0.33 - - 7.97 0.943 216.0 0.34 0.91 - - 34.20 0.884 126.0 _ _ _ _ _ d ym a 0.109 0.38 0.020 1.53 5.35 0.960 0.500 -0.39 0.015 1.95 5.53 0.935 0.600 2.30 0.020 0.54 7.44 0.903 0.804 0.08 0.117 ± 2.22 - 0.794 1.011 -1.76 0.098 2.47 - 0.819 2.020 -2.06 0.053 9.82 2.61 - 0.810 A l l results -8.77 0.091 9.55 4.91 7.43 0.767 153 These equations had the same problem as the previous equations that the values of oig were too large. Therefore, the regression analysis was repeatedni. a forcing the equations through the origin, i.e., ag was set to zero. L i t t l e improvement was obtained from equations of this form and generally the regression program produced equations similar to those already tested, i.e., equation (C.7) resulted in an equation similar to equation (6 ..4). TABLE C.16. RESULTS OF FITTING EQUATION C.7 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO) d ym oti c a 2 a3 015 R 2 598.1 1.26 2.60 0.755 3.45 0.927 511.0 2.08 4.15 - 0.789 363.9 2.22 5;70 - 0.821 216.0 3.14 - 24.5 0.891 126.1 1.49 5.56 36.4 0.968 d ym a 0.109 _ 4.57 _ 0.762 03500 1.31 25.06 - 0.905 0.600 1.17 37.25 - 0.893 0.804 1.08 47.50 - 0.908 1.011 1.22 50.40 - 0.916 2.020 2.09 104.00 - - 0.846 A l l results - 2.34 15.3 0.740 154 TABLE C.17. RESULTS OF FITTING EQUATION C.8 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO) d ym c ai x 10 2 a 2 a3 R2 598.0 6.70 1.35 1.76 3.62 0.865 511.0 11.32 1.49 1.31 4.53 0.757 363.9 15.90 2.50 1.51 6.23 0.723 216.0 46.5 2.25 1.71 30.60 0.750 126.1 33.0 2.56 1.43 35.00 0.904 d ym a 0.109 4.57 _ 0.762 0.500 1.78 11.57 1.71 - 0.949 0.600 2.40 42.66 - - 0.792 0.804 3.81 - 2.10 5.39 0.828 1.011 4.91 - 2.43 - 0.828 2.020 15.90 - 3.08 - 0.757 A l l results 4.89 — 3.90 5.8 0.689 C.4 Polynomial Equations It was attempted to develop an equation which avoided the problem of combining the dimensionless numhens which was equivalent to combining the collection efficiencies of the individual capture mechanism. The variables were therefore reduced to their simplest form, namely the superficial gas velocity (U), collector diameter (d ) and aerosol diameter (d ). c a Several combinations of these variables were tried, the best results being obtained by a term of the form: C = (/) u n c where n was a variable chosen to obtain the best f i t . The equation tested was of the form EB = a 0 + a-! C + a 2 C 2 + a 3 C 3 + a 4 C 4 [C.9] Table C.18 gives some of the results of f i t t i n g this 'equation to a l l 155 the data using multiple regression. As there was no improvement with this approach, further work with equations of this type were discontinued. Also the equation bore l i t t l e relation to the data as i t could not predict a minimum value for the col- lection efficiency with increasing gas velocity. TABLE C.18. RESULTS OF FITTING EQUATION C.9 TO ALL THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION n a 0 x 10 4 ai a 2 x 10~2 a 3 x 10"3 a t * R2 0.05 4.47 - 25.72 - - 0.712 0.20 5.21 0.89 - 4.79 - 0.803 0.30 4.79 - 7.11 - - 0.756 0.50 47.90 - 0.17 - - 0.717 156 APPENDIX D DEVELOPMENT OF THE BEST EMPIRICAL EQUATION D.1 Introduction This section shows the steps taken to obtain the best empirical equation which could predict the s i n g l e c o l l e c t o r e f f i c i e n c y from the basic v a r i a b l e s (d , d , and U). The equations were tested by f i t t i n g them to the experi- mental data using regression analysis. Having established the best empirical equation, i t s predictions for EB were converted into the o v e r a l l bed e f f i c i e n c y EBT using Eq. 3.4. These calculated values for EBT were then compared with the experimentally measured values. Also the best empirical equation was used to predict the experi- mental r e s u l t s of other workers. D.2 Development of the Best Equation for P r e d i c t i n g EB An equation of the following form was selected. -2/3 -1 EB = a 0 + a-]. NR + a 2 NR U + a 3 NR U + NR U [D.l] where NR = d /d a c This equation i s based on: I n e r t i a being proportional to U -2/3 D i f f u s i o n being proportional to U Gravity being proportional to U ^ and Interception being independent of U. 157 TABLE D.l. RESULTS OF FITTING EQUATION D.l TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d jM c a 0 * 10 3 a 2 x 102 a 3 x lO" 2 R2 598.1 -1.70 4.53 _ 0.803 511.0 -2.78 4.87 - - - 0.672 363.9 -4.30 5.16 - - - 0.656 216.0 -1.97 10.41 - - - 0.740 126.1 -1.52 5.48 - 0.37 — 0.810 d um a 0.109 -0.294 _ 0.884 0.500 -0.017 - - 3.49 - 0.949 0.600 0.336 - 3.95 11.02 - 0.922 0.804 0.192 - 3.95 1.02 - 0.912 1.011 -0.590 0.88 5.23 0.78 - 0.846 2.020 -1.610 6.69 6.53 0.73 - 0.689 A l l results -5.30 5.58 - - - 0.706 As can be seen, the values of ag dominate the equation where the average — 3 value of EB was about 2.0 to 8.6 x 10 and thus these results are unrealistic. Therefore t r i a l s were made forcing the equation through the origin, i.e., using EB = ct! NR + ct2 NR U + ct3 NR u"2^3 + ak NR U _ 1 [D.2] Trials were carried out just with data for constant aerosol size as the f i t appeared better than for constant collector size,(see Table D.2). 158 -TABLE D.2. RESULTS OF FITTING EQUATION D.2 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d ym a1 a 2 x 10 2 a 3 x 10"2 ak x lO" 2 R2 0.109 - - 3.730 - 0.880 0.500 - 4.20 1.006 - 0.953 0.600 - 4.11 1.062 - 0.908 0.804 - 5.47 0.788 - 0.897 1.011 0.593 7.11 - 1.19 0.922 2.020 6.54 - - - 0.689 All-results - 4.92 0.912 - 0.757 It was not-leed that £or aerosols up'to _. 0 um there was a tendency for the value of 0:3 to decrease with increasing aerosol diameter (d ). From a plot of 3. versus d on log paper i t was found that ct3 is roughly proportional to cL -2/3 (d a) . Therefore the equation was modified to EB = 0 4 NR + a 2 NR U + a 3 NR (d U)" 2^ 3 + NR u"1 [D.3] Si TABLE D.3. RESULTS OF FITTING EQUATION D.3 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d a ym a 2 a 2 x 10 2 a 3 x 10 2 R2 0.109 - - 1.79 - 0.876 0.500 - 4.77 1.35 - 0.951 0.600 - 4.79 1.66 - 0.908 0.804 - 6.09 1.45 - 0.897 1.011 - 7.82 1.56 - 0.826 2.011 - 29.20 1.57 - 0.828 This change forced the value of a 3 to be nearly constant for a l l aerosol diameters at ̂  0.0156. It was also noticed that there was an approximate linear relationship between a 2 and d with the exception of 2 ym aerosol. Therefore the inertia term was modified from NR U to NR (d U). a The equation needed a gravitational term to explain the effects of 159 upflow and downflow. Thus d /U and d 2/U were tried in the last term. The c a a best results were obtained with a value of d 2/U for the gravitational term. c l The modified equation was now of the form EB = cti NR + ct2 NR (d U) + a3 NR (d U ) ~ 2 / 3 + on* d /U [D.4] et 3. c l TABLE D.4. RESULTS OF FITTING EQUATION D.4 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d ym ai a a 2 x 10" 2 a 3 x 1 0 2 ai+ x 1 0 - 5 ' R 2 0.109 1.79 _ 0.876 0.500 9.49 1.48 6.7 0.929 0.600 8.11 1.58 7.4 0.910 0.804 7.79 1.17 4.9 0.914 1.011 8.40 1.21 6.3 0.850 2.020 14.45 1.57 — 0.850 After eliminating several experimental results (e.g., those at high velocities, i.e., 67 cm/sec, which are probably affected by bounce-off and the inaccurate results of the collection of 2.02 ym diameter aerosols on 210 and 126 ym diameter collectors), the equation was then fitted to the remain- ing results. In a l l cases, as noted previously, the interception constant 04 was always set to zero and thus i t can be assumed that interception plays no part in the collection. TABLE D.5. RESULTS OF FITTING EQUATION D.4 TO ALL THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (04 SET TO ZERO) a 2 x 1 C T 2 a 3 x 1 0 2 ak x 1 0 - 5 R2 A l l results 12.41 0.916 32.59 0.784 A l l results less results for gas velocity of 67 cm/sec 7.58 1.359 5.84 0.93 A l l results less results for gas velocity of 67 cm/sec and 2.02 ym aerosols on 216 and 120 ym collectors 6.79 1.406 4.87 0.933 160 Using these regression results, further improvements were made by optimization and the f i n a l form of the equation was: d d _?/-} d 1 EB = 660 - j ^ (d U) + 0.0148 (d U) ' + 400,000 [D.5] d a d a U c c where the multiple correlation coefficient (R) was 0.972. Using this f i n a l form of the equation, comparisons were made with the predictions of EB by this equation and the experimental data of this work. D.3 Comparison of Predicted and Experimental Bed Penetrations using Equation D.5 The comparison of predicted and experimental bed penetrations are summarized in Tables D.6 to D.25. Aerosol removal is given in a l l of the tables as percent penetration where the relationship between penetration (P) and bed collection efficiency (EBT) i s : P = 1 - EBT D.4 Comparison of Predicted Bed Penetrations Using Equation D.5 and the Experimental Results of Other Studies The comparison of predicted bed penetrations and the experimental results of other studies are summarized in Tables D.26 to D.29. D.5 Regression Trials of the Modified Form of Equation D.5 In order to make Eq. D.5 dimensionless i t was modified as follows: EB = ctj St + a 2 NR 4 / 3 Pe~ 2 / 3 + a 3 NG [D.6] The results of the regression analysis are given in Table D.30. TABLE D.6 COMPARRISQN BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 598.1 UM DIAMETER. | AEROSOL DIAMETER = 0.5 UM; BED DEPTH = 4.536 CM ) GAS VEL. DOWNFLOW UPFLOW CM/SEC EXP. , CALC, EXP. , CALC. 5. 24 66.90 58,40 71.00 62, 10 8.30 70.10 66.30 74.20 68.90 11. 16 72.70 70. 10 75.30 72.20 16.97 72.30 73.80 76.60 75.20 22.37 75. 80 75.00 79.90 76.10 27,08 75.00 75.30 78.20 76.16 16.33 71.80 73.60 76.40 75.00 22.57 74.50 .. 75.00 77.60 76.10 34.46 69.50 74.60 73.60 75.3 0 50.75 66.50 72. 10 72.00 72.50 67.00 66.60 68.50 - 68.80 TABLE D.7 C0MPAR8IS0N BETWEEN PREDICTED AND EXPERIMENTAL PENET RATIONS FOR NICKEL SHOT 598. 1 UM DIAMETER. { AEROSOL DIAMETER = 0.804 UM; BED DEPTH = 4. 536 CM ) GAS VEL. DOWNFLOW UPFLOW CM/SEC EXP. CALC. EXP. , CALC. 5.24 49.30 49.40 53.20 57.90 8.30 52.30 57.10 54.50 63.10 11. 16 56.70 60.40 57.50 65.10 16.97 60.70 62.30 62. 40 65.50 22.37 60.70 61.70 63.60 64.10 27.08 61.80 60.30 60, 10 62.20 16.33 58. 80 62.30 60.90 65.60 22.57 59.00 61.70 64. 40 64.00 35.46 54. 10 56.90 54.90 58.20 50.75 48. 10 49.80 52.90 50.60 67.00 48.60 ' 42.60 — • 43.10 162 TABLE D.8 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 598.1 DM DIAMETER. ( AEROSOL DIAMETER = 1.011 UM; BED DEPTH = 4.536 CM ) GAS VEL. DOWN FLOW UPFLOW CM/SEC EXP. CALC. EXP. CALC. 5.24 36. 90 43.60 43.80 56.0 0 . 8.30 42. 60 50.90 52.00 59.60 1 1.16 46.00 53.50 53.50 60.20 16.97 51. 00 54.00 56.80 58.30 22.37 53.00 52.00 57.80 55.10 27.08 52.50 49.50 55.20 51.90 16.33 50. 80 54. 10 - - 22.57 52.70 51.80 - -35.46 47.80 44.40 - - 50.75 37.20 35.40 - - 67.00 34. 10 27.30 — — TABLE D.9 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 598.1 UM DIAMETER. ( ADDITIONAL DOWNFLOW COMPARRISONS; BED DEPTH =4.536 CM ) GAS VEL., AEROSOL DIAMETER UM CM/SEC 0. 109 0.600 2.020 EXP. , CALC. EXP. CALC. EXP. CALC. 5.24 82. 50 74.50 61.30 55.30 1 1.90 19.40 8.30 83.70 80.40 6 5.60 63.30 14. 10 23, 10 11.16 85. 10 83.60 6 7.00 66.90 15.50 22.70 16.97 83.70 87. 10 69.80 70.20 13.50 18.30 22.37 86.00 89.00 70.40 70,90 7.90 13. 80 27.08 84.40 90.20 70.50 70.60 1.95 . 10.50 TABLE D.10 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 511.0 UM DIAMETER. ( AEROSOL DIAMETER = 0.5 UM; BED DEPTH = 4.536 CM ) GAS VEL, DOWNFLOW UPFLOW CM/SEC EXP. ., CALC. EXP. CALC. , 5. 24 60. 00 48.20 62.20 51.70 8.30 65.30 57. 10 66.80 59.80 1 1. 16 69.00 61.70 69.00 67,60 16.97 71. 30 66. 10 75.00 67.60 22.37 75. 00 67.50 75.70 68.70 27.08 73.10 67.80 76.20 68.80 16.33 72.30 65.80 73.80 67.30 22.57 75. 90 67.60 76.00 68.70 35.46 68.40 67.10 73. 00 67.80 50.75 67.20 63.90 72. 10 64.30 67.00 65.00 59.60 — 59.90 TABLE D.11 COMPARISSON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 511.0 UM DIAMETER. i AEROSOL DIAMETER = 0.804 UM; BED DEPTH = 4.536 CM ) GAS VEL., DOWNFLOW UPFLOW CM/SEC EXP. .. CALC. EXP. , CALC. 5. 24 36. 80 38.60 39.80 46.50 8.30 41.00 46.90 44. 90 52.70 11. 16 45.40 50.50 48.90 55.10 16.97 50.30 52. 60 53.30 55.70 22.37 55.20 51.80 56.20 54.10 27.08 55.50 50. 10 59.50 52.00 16. 33 51.30 52. 60 54.00 55.80 22.57 53.50 51.80 57.50 54.00 35.46 53.60 46.30 56.00 47.60 50.75 45.00 38.60 54.00 39.30 67.00 49.60 31.10 45.00 31.60 164 TABLE D. 12 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 511.0 UM DIAMETER. ( AEROSOL DIAMETER = 1.011 UM; BED DEPTH = 4.536 CM ) GAS VEL., DOWNFLOW UPFLOW CM/SEC EXP. . CALC. EXP. , CALC. 5.24 29.50 32.80 33.80 44.10 8.30 37.50 40.30 38.70 48.40 11.16 40.00 43.00 42.50 49.30 16.97 44. 10 43.30 48.70 47.40 22.37 45. 10 41.00 48.90 44.6 0 27.08 43.50 38.30 46.00 40.50 16.33 45.40 43.50 - -22.57 39.70 40.90 - -35.46 35.20 33.00 - -50.75 30.00 24. 10 - -67.00 27.50 17.00 - — TABLE D.13 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 511.0 UM DIAMETER. ( ADDITIONAL DOWNFLOW CO MP AS RISO N S; BED DEPTH = 4.536 CM ) GAS VEL., AEROSOL DIAMETER UM CM/SEC 0. 109 0. 600 2.020 EXP. CALC. EXP. , CALC. EXP. CALC. 5.24 75.70 66.85 45.40 44.90 6.80 11.70 8.30 78.50 74.30 52.70 53.70 8.60 14.30 1 1.16 80.50 78.20 57.30 58.00 1 0.90 13.70 16.97 83.00 82.90 61.60 61.80 8.40 10.10 22.37 83.60 85.30 66.60 62.50 1.50 6. 80 27.08 83.60 86.80 67. 20 62.20 0.096 4.70 TABLE D. 14 COHPARBISON BETHEES PREDICTED AMD EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 363.9 UM DIAMETER. { AEROSOL DIAMETER = 0.5 OM; BED DEPTH .= 4. 536 CM ) GAS VEL. DOHNFLOH UPFLOS CM/SEC EXP. CALC. , EXP. CALC. 5.24 29. 10 24.20 32.30 26.70 8.30 33. 30 33.60 36.00 35.70 11, 16 36.90 38.90 40.30 40,80 16.97 38,10 44.50 43.40 45.90 2 2.37 43.00 46.40 45.60 47.50 27.08 46.60 46.60 49.30 47.60 1 6.33 40.00 44. 10 42.50 45.50 22.57 41.60 46.40 50.00 47.50 35.46 44. 60 45.60 46.70 46.30 50.75 37.80 41.40 - 41.80 67,00 40.80 36. 10 36.30 TABLE D.15 COHPARBISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 363.9 UM DIAMETER. ( AEROSOL DIAMETER = 0.804 UM; BED DEPTH = 4.536 CM ) GAS VEL., DOWNFLOW UPFLOW CM/SEC EXP. EXP. CALC. 5.24 14.80 16.20 21.00 21.10 8.30 19.20 23.20 22.10 27.40 11. 16 24.70 26.70 25.60 30.10 16.97 29.00 28.70 29.40 31 .00 22.37 31.00 27.70 33.20 29.40 27.08 30.80 26.00 33.90 27.30 16.33 28. 10 28.60 31.00 31.10 22.57 31.10 27.60 33.90 29.30 35.46 29.20 22. 10 32.00 22.90 50.75 25. 10 15.40 2 4.60 15.80 67.00 20.00 10.00 — 10.20 166 TABLE D. 16 COUPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 363.9 UM DIAMETER. ( AEROSOL DIAMETER = 1.011 UM; BED DEPTH = 4. 536 CM ) GAS VEL. DOWNFLOW CM/SEC EXP. CALC. 5.24 12.50 12. 10 8.30 19.90 17.50 11. 16 22.90 19.70 16.97 26.80 19.70 22.37 26.40 17.60 27. 08 23.30 15.30 16.33 27.30 19.80 22.57 26.00 17.50 35.46 19.60 11. 40 50.75 13.60 6.14 67.00 12. 60 3.04 TABLE D.17 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 363.9 UM DIAMETER. ( ADDITIONAL DOWNFLOW COMPAERISONS; BED DEPTH = 4.536 CM ) GAS VEL. AEROSOL DIAH ETER UM CM/SEC 0. 109 0.600 2.020 EXP. CALC. EXP. CALC. EXP. . CALC. 5.24 40. 50 45.20 21.90 21 .20 0.56 2.03 8. 30 48.20 55.70 26.70 29.90 0.74 2.67 11. 16 51. 20 61.70 31.10 34.60 1.13 2.34 16.97 57.60 69. 10 37.30 39.00 0.06 1.20 22. 37 62.20 73.20 39.90 * 39.90 0.02 0.54 27.08 65.40 75.70 44.30 39.40 0.003 0.2 5 167 TABLE D.18 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 216.1 UM DIAMETER. ( AEROSOL DIAMETER = 0.5 UM; BED DEPTH = 2.268 CM ) GAS ?EL. DOWNFLOW UPFLOW CM/SEC EXP. CALC. EXP. , CALC. 5.24 14. 30 13.70 14.90 14.96 8.30 16.50 21.70 15.70 22.70 11.16 20. 90 26.50 17. 90 27.70 16.97 24.50 32.00 24.70 32.80 22.37 27.60 33.70 2 8.90 34.50 27.08 28.40 34. 10 28.30 34.80 16.33 24.30 31.60 25.00 32.50 22.57 27.20 33.90 29.50 34.60 35.46 25.90 33.00 28.00 33.40 50.75 20.50 28.70 21. 50 29.00 67.00 18.30 23.60 — 23.70 TABLE D,19 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 216.1 UM DIAMETER. ( AEROSOL DIAMETER = 0.804 UM; BED DEPTH = 2.268 CM ) GAS YEL. DOWN FLOW UPFLOW CM/SEC EXP. CALC., EXP. , CALC. 5. 24 5.50 8.16 7.00 10.10 8.30 7.50 13.20 8.70 15.20 11. 16 9.60 15.90 10.50 17.60 16.97 " 11.50 17.40 12.50 18.60 22.37 12.70 16.40 12.20 17.30 27.08 12.50 14.90 16.20 15.60 16.33 9.70 17.40 12.00 18.70 22. 57 12. 80 16.40 13.70 17.30 35.46 10. 30 11.70 12.30 12 .30 50.75 5.40 7. 10 6. 50 7.20 67.00 4. 80 3.90 — 3.90 168 TABLE D.20 CQMPARHISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 216.1 OM DIAMETER. { AEROSOL DIAMETER = 1.011 UM; BED DEPTH = 2.268 CM ) GAS VEL., DOWNFLOW CM/SEC EXP. , CALC. 5.24 4.50 5.60 8.30 6. 80 9.10 11. 16 8.10 10.60 16.97 10.20 10. 40 22.37 9.20 8.76 27.08 5. 80 7. 16 16.33 10.50 10.50 2 2.37 13.01 8.70 35.46 2. 98 4.70 50.75 0.20 1.90 67.00 0.008 0.71 TABLE D.21 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 216.1 UM DIAMETER. { ADDITIONAL DOWNFLOW COMPARRISONS; BED DEPTH = 2.268 CM ) GAS VEL. AEROSOL DIAMETER UM CM/SEC 0. 109 0.600 2. 020 EXP. CALC. EXP. , CALC. EXP. CALC. 5.24 31.60 32.50 6.00 11.60 0.00 0..64 8.30 35. 00 43.60 7.80 18.50 0.00 0.79 11. 16 37. 10 51. 40 11.40 22.70 0.00 0.61 16.97 42. 10 59.40 13.20 26,70 0.00 0.22 22.37 48.30 59.20 16.60 27.40 0.0 0 0.07 27.08 48.50 64.20 19.02 26.90 0.00 0.02 TABLE D.22 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOB NICKEL SHOT 126.0 UM DIAMETER. ( AEROSOL DIAMETER = 0.5 UM; BED DEPTH = 2.268 CM ) GAS VEL. , DOWNFLOW UPFLOW CM/SEC EXP. EXP. CALC. 5. 24 0.35 0. 19 1.35 0.36 8.30 0.51 0.74 2.40 1 .26 11. 16 0.64 1.32 2.87 2.23 16.97 1.74 2.10 3.72 3.72 22. 37 2.42 2. 27 5.39 4.3 0 27.08 2.69 2. 14 5.35 4.4 0 16.33 2.50 2.05 • - - 22.57 2.83 2.27 - - 35.46 1.37 1.65 - - 50.75 0.39 0.81 - - 67.00 0.24 0.32 - • — TABLE D.23 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 126.0 UM DIAMETER. { AEROSOL DIAMETER = 0.804 UM; BED DEPTH = 2.268 CM ) GAS VEL. DOWN FLOW UPFLOW CM/SEC EXP. CALC. EXP. . CALC. 5.24 0. 250 0.072 2.150 0. 105 8.30 0.400 0.280 1.990 0.360 11. 16 0.540 0.470 1.420 0. 570 16.97 1. 560 0.610 1.390 0.680 22.37 2.170 0.510 1.550 0.560 27.08 2.360 0.380 1.615 0.410 16.33 0.420 0.610 - -22.57 0.430 0.510 - -35.46 0.076 0. 190 - -50.75 0.010 0.042 -67.00 0.003 0.007 — • — 170 TABLE D. 24 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 126.0 UM DIAMETER, { AEROSOL DIAMETER = 1.011 UM; BED DEPTH = 2.268 CM ) GAS VEL. DOWNFLOW CM/SEC EXP. CALC. 5.24 0. 100 0.027 8.30 0. 170 0. 100 11.16 0.337 0. 148 16.97 0.098 0. 136 22.37 0.019 0.081 27.08 0.002 0.044 16.33 0. 103 0. 142 22.57 0.035 0.079 35.46 0.0016 0.0125 50.75 0.0005 0.0009 67.00 0.00023 0.00005 TABLE D. 25 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 126.0 UM DIAMETER. ( ADDITIONAL DOWNFLOW COMPARRISONS; BED DEPTH = 2.268 CM ) GAS VEL. AEROSOL DIAMETER UM CM/SEC 0. 109 0. 500 2. 020 EXP. , CALC. EXP. ' CALC. EXP. CALC. 5.24 3. 50 3.68 0.35 0.19 0.0 0.027 8.30 4.90 8.70 0.51 0.73 0.0 0. 100 1 1. 16 5.70 13.30 0.64 1.30 0.0 0.150 16.97 9. 90 21.40 1.74 2.10 0.0 0. 130 22.37 13.70 27.20 2.40 2.27 0.0 0.081 27.08 15.00 31.30 2.69 2.14 0.0 0.040 171 TABLE D.26 COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR LEAD SHOT 1800 UM DIAMETER. ( DOWNFLOW; AEROSOL DIAMETER =0.5 UM; BED DEPTH = 4.536 CM ) GAS VEL. CM/SEC EXP., CALC. 5. 24 11.16 16.97 22.37 27.08 93.76 93.47 94.36 95.89 95.00 96.53 96.29 96.75 96.07 96.80 TABLE D.27 COMPARRISON BETWEEN PREDICTED PENETRATIONS AND THE RESULTS OF A.FIGUEROA. ( COLLECTOR DIAMETER = 7000 UM; BED DEPTH = 2 CM ) GAS VEL. ,. AEROSOL DIAMETER UM CM/SEC 0. 500 1 .099 2. 020 EXP. / CALC. EXP. , CALC. EXP. CALC. 3. 10 80.3 78.5 81.2 67.1 64. 4 47.9 4. 11 81.9 81.8 82.4 71.6 66.9 53.8 5. 14 84.0 84.0 84.6 74.6 68. 9 57.4 6. 17 83.8 85.5 86. 4 76.5 73.9 59.5 7.20 87.1 86.7 84.6 77.8 70. 1 60.8 8.20 87.2 87.6 88.6 78.8 76. 0 61.5 9.30 85. 9 88.3 85.0 79.4 68.8 61.7 10.30 90.0 88.8 88.8 80.0 74.0 61.6 11.30 87.2 89.3 86.4 80.2 69.7 61.3 12.30 89.0 89.7 89.7 80.3 71.3 60.9 13.40 90. 1 90.0 88.5 80.4 67. 6 60.3 14.40 87.5 90. 3 86.0 80.4 67.8 59.6 15.40 88.7 90.5 87.2 80.3 64. 9 58.8 16.50 88.4 90.7 86. 1 80.2 57.7 58.0 17.50 89.8 90.8 87.8 80.0 56.7 57. 1 18.50 90.2 90.9 88.6 79.8 51.6 56.2 TABLE D.2 8 COMPARRISON BETflEEN PREDICTED SINGLE COLLECTOR EFFICIENCY AND THE RESULTS OF Y.DOGANOGLU. ( COLLECTOR DIAMETER = 596.0 UM; LIQUID D.O.P. AEfiOSOL ) GAS VEL., AEROSOL DIAMETER UM CM/SEC 1. 35 1 .75 EXP. CALC. EXP. CALC., 2.86 0. 124E-2 0.935E-2 0.515E-2 0.120E-1 3.83 0.720E-3 0.779E-2 0.417E-2 0.101E-1 6.04 - - 0.297E-2 0.814E-2 12.37 0.100E-3 0.536E-2 0.332E-2 0.762E-2 19.51 0.600E-4 0.593E-2 0.240E-2 0.893E-2 31.46 0.285E-2 0.765E-2 0.632E-2 0.121E- 1 43.80 0.81 IE-2 0.975E-2 0.151E-1 0.158E- 1 TABLE D.29 COMPARRISON BETWEEN PREDICTED SINGLE COLLECTOR EFFICIENCY AND THE RESULTS OF Y.DOGANOGLU. ( COLLECTOR DIAMETER = 10 8.5 CM; LIQUID D.O.P. AEROSOL ) GAS VEL. AEROSOL DIAMETER UM CM/SEC 1. 35 1 .75 EXP. CALC. EXP. CALC 0.98 0.328E- 1 0.784E-1 0.4 89E- 1 0.906E-1 2.02 0.355E- 1 0.489E- 1 0.577E- 1 0.568E- 1 2.69 0.343E- 1 0.413E-1 0.501E-1 0.483E-1 3.83 0.371E- 1 0.342E- 1 0.354E- 1 0.408E- 1 3.83 0.369E- 1 0.342E- 1 0.38 5E-1 0.408E-1 4.92 0.253E- 1 0.306E- 1 0.412E-1 0.374E- 1 6.04 0.259E- 1 0.285E- 1 - - 8.70 0.302E-1 0.26 5E- 1 0.415E- 1 0.349E- 1 10.53 0.278E-1 0.264E- 1 0.441E- 1 0.360E- 1 12.37 0.367E-1 0.268E- 1 0.442E- 1 0.374E- 1 13.20 0.572E- 1 0.271E- 1 0.737E-1 0.382E-1 19.50 0.838E- 1 0.320E- 1 0. 92 7E-1 0.562E- 1 173 TABLE D.30. RESULTS OF FITTING EQUATION D. ,6 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d iim c a 2 x 10 - 5 a 3 x 10 - 1 R2 598.7 1.29 1.76 0.26 0.91 511.0 1.52 1.11 0.27 0.87 363.9 1.64 0.71 0.43 0.84 216.0 2.87 - 2.68 0.93 126.1 1.36 1.43 3.39 0.89 d urn a 0.109 18.90 1.46 24.40 0.92 0.500 1.46 1.36 2.23 0.88 0.600 1.18 1.38 2.24 0.86 0.804 1.11 1.29 1.51 0.89 1.011 1.19 1.31 0.85 0.86 2.020 - - - . . . - A l l results 1.76 1.48 1.15 0.89 The value of a 3 in a l l cases i s too large and therefore Eq. D.6 does not f i t the upflow data. Thus the value for a 3 (i.e., the gravity term constant) was fixed at 1.25 derived from Eq. D.5. Table D.31 gives the results of the regression t r i a l s based on constant aerosol diameter. 174 TABLE D.31. RESULTS OF FITTING EQUATION D.6 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (ct3 SET AT 1.25) d a ym ai a2 x 10 5 R2 0.109 20.79 1.57 0.82 0.500 1.58 1.48 0.86 0.600 1.14 1.55 0.88 0.804 1.12 1.45 0.89 1.011 1.20 1.42 0.94 2.020 1.55 1.89 0.72 A l l results less results of 2.02 ym aerosol* 1.16 1.47 0.91 *the results of 2.02 ym diameter aerosol were ignored owing to their possible Innacuracies By further optimization the fi n a l form of the equation was derived. EB = 1.0 St + 150,000 NR4j/3 Pe"^ 3 + 1.25 NG [D.7] 69 D.6 Regression Trials with the Equation of Schmidt The term for interception (NR) was ignored as interception plays no role in the present work. The equation used was of the form: EB - ai St + a 2 (8 Pe" 1 +2.3 Pe"5''8 Re^ 8) + a 3 NG [D.8] Again the value of a 3 was fixed at 1.25 and the regression t r i a l s carried out only for constant aerosol sizes. TABLE D.32. RESULTS OF FITTING EQUATION D.8 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d um a a 2 R 2 0.109 15.48 0.95 0.81 0.500 1.04 5.98 0.82 0.600 1.07 8.73 0.83 0.804 0.94 11.03 0.86 1.011 1.24 11.40 0.84 2.020 1.41 28.40 0.50 A l l results less the results of 2.02 ym aerosol 1.19 8.06 0.82 further optimization the f i n a l form of the equation was derived EB = 0.8 St + 8.0 (8 Pe" 1 + 2.3 Pe~ 5 / 8 Re~ 1 / 8) + 1.25 NG [D.

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