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Aerosol collection in granular beds Kennard, Malcolm L. 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 t h i s thesis as conforming to the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA August, 1978  © M a l c o l m L. Kennard, 1978  In p r e s e n t i n g t h i s  thesis  an advanced degree at the L i b r a r y s h a l l I  in p a r t i a l  fulfilment of  the requirements f o r  the U n i v e r s i t y of B r i t i s h Columbia,  make i t  freely available  f u r t h e r agree t h a t p e r m i s s i o n  for  I agree  r e f e r e n c e and  f o r e x t e n s i v e copying o f  this  that  study. thesis  f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s of  this  representatives. thesis  It  is understood that copying o r p u b l i c a t i o n  f o r f i n a n c i a l gain s h a l l  written permission.  Department of The U n i v e r s i t y o f B r i t i s h  2075 Wesbrook Place Vancouver, Canada V6T 1W5  Date  /JU/  Columbia  not be allowed without my  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 e f f i c i e n c y p a r t i c l e c o l l e c t o r s . Based on the experimental data, i t was predicting  attempted to derive expressions for  the aerosol removal e f f i c i e n c y of the granular  bed.  Granular beds composed of f a i r l y uniform, spherical n i c k e l shot were employed i n a 7.4  cm diameter copper column to c o l l e c t s o l i d , monodispersed,  polystyrene latex aerosols. was  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  determined as a function of several variables, v i z . , aerosol diameter  (0.109 to 2.02  urn);  bed  p a r t i c l e diameter (100  to 19 cm);  s u p e r f i c i a l gas v e l o c i t y  (upflow and  downflow).  to 600 ym);  (5 to 67 cm/sec);  bed  and  depth  (0.3  flow d i r e c t i o n  The monodispersed, latex aerosols were generated by atomizing d i l u t e hydrosols of aerosol p a r t i c l e s . measured at the i n l e t and  The aerosol number concentrations were  outlet of the granular bed  techniques), from which the bed  (using l i g h t  c o l l e c t i o n e f f i c i e n c y was  Using the concept of an isolated bed  determined.  p a r t i c l e i t was  quantitatively 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. of an aerosol by an isolated bed mechanisms:-  p a r t i c l e can be attributed  i n e r t i a l impaction, direct interception,  g r a v i t a t i o n a l deposition and  electrostatic effects.  scattering  possible to The  collection  to the  following  d i f f u s i o n a l deposition, In the present study  e l e c t r o s t a t i c effects were eliminated by grounding the equipment and i z i n g the aerosol.  ii  neutral-  Equations based on individual c o l l e c t i o n mechanisms and combinations were f i t t e d to the experimental data by multiple regression analysis.  An  empirical model was developed, which gave good predictions of the experimental bed c o l l e c t i o n e f f i c i e n c y .  The single c o l l e c t o r e f f i c i e n c y (EB) was  calcu-  lated using the following empirical equation: EB = 1.0 St + 150,000 NR ^ 4  3  Pe~ / 2  3  + 1.5 NG  and 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) 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 e f f i c i e n c i e s were  generally less than ten percentage points. Experimental results indicate that high c o l l e c t i o n e f f i c i e n c i e s can be achieved with r e l a t i v e l y shallow fixed beds of granular material.  Inertial  impaction was considered to be the dominant c o l l e c t i o n mechanism at high gas v e l o c i t i e s , whilst d i f f u s i o n and, to a lesser extent, gravity were considered dominant at low gas v e l o c i t i e s . interception  For a l l the experimental conditions studied,  was shown to be i n s i g n i f i c a n t .  iii  TABLE OF CONTENTS  ABSTRACT  '-. ... ... ..... . . . ..  LIST OF TABLES  x  Chapter 1. INTRODUCTION  1.5 2.  2.5 2.6 2.7 2.8 2.9 3.  3.3 3.4 3.6  i  v  The Need for Particulate Control 1 Conventional Dust Removal Equipment 2 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 Background Information on Granular Bed Behaviour . . . . 6 1.4.1 Individual c o l l e c t i o n mechanisms pertinent to an isolated, spherical c o l l e c t o r 6 1.4.2 The single p a r t i c l e c o l l e c t i o n e f f i c i e n c y . . . . 11 1.4.3 Limitations of the single c o l l e c t o r e f f i c i e n c y approach . . . 11 1.4.4 Interference effect 12 1.4.5 Total c o l l e c t i o n e f f i c i e n c y of the granular bed . 12 Scope of the Present Work 13 14  Introduction 14 Effect of F l u i d Velocity on Collection E f f i c i e n c y . . . 14 Effect of Aerosol Size on Collection E f f i c i e n c y . . . . 15 E f f e c t of Collector Size and Bed Depth on Collection E f f i c i e n c y 18 Effect of the Direction of Gas Flow on Collection Efficiency 18 Bounce-off and Re-entrainment 18 Review of Experimental and Industrial Studies Carried out on Granular Beds 20 Empirical Equations 26 Theoretical Work on the Flow F i e l d Within a Granular Bed 26  THEORY 3.1 3.2  i  1  PREVIOUS WORK 2.1 2.2 2.3 2.4  l  xii  ACKNOWLEDGEMENTS  1.4  i i i v  LIST OF FIGURES  1.1 1.2 1.3  •  32  Introduction 32 The Overall Bed Collection E f f i c i e n c y (EBT) as a Function of the Single Collector E f f i c i e n c y (EB) . . . 32 Calculation of Single Collector E f f i c i e n c y from Basic Design and Operating Variables 34 Multiple Regression 36 Pressure Drop through the Granular Bed 38 iv  4.  EXPERIMENTAL WORK  39  4.1 4.2 4.3  39 40 40 43 43 46 50 50 56 56  4.4 4.5 4.6 4.7 4.8 5.  6.  PRELIMINARY EXPERIMENTS  61  5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8  61 61 64 64 65 66 66 68 68 69 70  6.1 6.2  70  6.4 6.5 6.6 6.7 6.8  Introduction The Effect of S u p e r f i c i a l Gas Velocity on Bed Collection Efficiency The Effect of Flow Direction on Bed C o l l e c t i o n Efficiency The Effect of Aerosol Diameter on Bed Collection Efficiency The E f f e c t of Collector Size on Bed C o l l e c t i o n Efficiency The Effect of Bed Depth on Collection E f f i c i e n c y . . . Pressure Drop across the Granular Bed Summary of Experimental Results  STATISTICAL ANALYSIS 7.1 7.2 7.3 7.4  7.5 8.  The Effect of Humidity on Collection E f f i c i e n c y ... Bed Ageing or Loading Collection by the Empty Column and Bed Support . . . . Background Count Sampling Counts and Changeover Time Reproducibility Errors Experimental Programme 5.8.1 Procedure 5.8.2 Programme  EXPERIMENTAL RESULTS AND DISCUSSION  6.3  7.  Objectives of the Experimental Work. . . . . Range of Variables Studied . . . . . . . . . . . . . . Experimental Apparatus 4.3.1 The column 4.3.2 Sampling Aerosol P a r t i c l e s Granular Bed P a r t i c l e s Aerosol Generator Aerosol Detector Minor Modifications and Additional Equipment  70 81 81 82 82 89 89 92  Introduction 92 Evaluation of Various Empirical Equations 92 I d e n t i f i c a t i o n of the Best Empirical Equation . . . . 92 Interpretation and Modification of Equation 7.1 . . . 102 7.4.1 Modification of the Second Term i n Equation 7.1 103 Conclusion 106  CONCLUSIONS  . . . . . .  v  109  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 . . . . . . . C.l Introduction C.2 Empirical Equations Developed by Other Workers . . . . C.3 Parameter Equations C. 4 Polynomial Equations  142 142 142 151 154  DEVELOPMENT OF THE BEST EMPIRICAL EQUATION  156  D.  D. l D.2 D.3 D.4 D.5 D.6  Introduction 156 Development of the Best Equation for Predicting EB . . 156 Comparison of Predicted and Experimental Bed Penetrations using Equation D.5 . 160 Comparison of Predicted Bed Penetrations Using Equation D.5 and the Experimental Results of Other Studies 160 Regression T r i a l s of the Modified Form of Equation D.5 160 Regression T r i a l s with the Equation of Schmidt . . . . 174  vi  LIST OF TABLES I. II. III. IV. V. VI. VII. VIII. IX. X. XI. XII. XIII. XIV. XV. XVI. XVII. A.l A.2 A.3 A.4 A.5 A.6 A.7 A.8 A.9 A.10 A.11 A.12  Comparison of a Granular Bed with Conventional P a r t i c l e C o l l e c t i o n Equipment Experimental Studies I n d u s t r i a l Studies Empirical Equations f o r Single Collector E f f i c i e n c y Based on One C o l l e c t i o n Mechanism Empirical Equations for Single Collector E f f i c i e n c y Based on Combinations of C o l l e c t i o n Mechanisms Range of Variables Studied Purchased Equipment P a r t i c l e s and Collectors Properties of P a r t i c l e s Used Characteristics of Nickel Shot C o l l e c t i o n Efficiency, of 598.1 ym Nickel Shot at Various Humidities C o l l e c t i o n E f f i c i e n c y of 511.0 ym Nickel Shot at Various Humidities Bed Ageing Tests on 598 ym Nickel Shot Bed Ageing Tests on 216.0 ym Nickel Shot C o l l e c t i o n by the Empty Column Background Counts f o r the Empty Column Summary of Experimental Tests Penetrations for Nickel Shot 598.1 ym Diameter (Downflow; bed depth = 4.536 cm) Penetrations for Nickel Shot 598.1 ym Diameter (Upflow and downflow; bed depth = 4.536 cm) Penetrations for Nickel Shot 598.1 ym Diameter (Downflow; varying bed depth; aerosol d i a m e t e r " 0.5 ym) Penetrations for Nickel Shot 598.1 pm Diameter (Downflow; bed depth = 2.268 cm) Penetrations for Nickel Shot 511.0 ym Diameter (Downflow; bed depth = 4.536 cm)....... Penetrations f o r Nickel Shot 511.0 ym Diameter (Upflow and downflow; bed depth = 4.536 cm) Penetrations for Nickel Shot 511.0 ym Diameter (Downflow; varying bed depth; aerosol diameter = 0.5 ym) Penetrations for Nickel Shot 511.0 ym Diameter {Downflow; bed depth = 2.268 cm) Penetrations for Nickel Shot 363.9 ym Diameter (Downflow; bed depth = 4.536 cm) Penetrations f o r Nickel Shot 363.9 ym Diameter (Upflow and downflow; bed depth = 4.536 cm) Penetrations for Nickel Shot 363.9 ym Diameter (Downflow; varying bed depth; aerosol diameter =0.5 ym) Penetrations for Nickel Shot 363.9 ym Diameter (Downflow; bed depth = 2.268 cm)  vii  5 21 23 27 30 40 42 42 50 51 62 62 63 63 64 65 69 118 118 118 118 119 119 119 119 120 120 120 120  Penetrations f o r Nickel Shot 216.1 \xm Diameter (Downflow; bed depth = 2.268 cm) A.14 Penetrations f o r Nickel Shot 216.1 ym Diameter (Upflow and downflow; bed depth == 2.268 cm) A.15 Penetrations f o r Nickel Shot 216.1 ym Diameter (Downflow; varying bed depth; aerosol diameter =* 0.5 ym) A.16 Penetrations f o r Nickel Shot 216.1 ym Diameter (Downflow; bed depth =* 1.134 cm) A.17 Penetrations f o r Nickel Shot 126.0 ym Diameter (Downflow; bed depth =* 2.268 cm) A.18 Penetrations f o r Nickel Shot 126.1 ym Diameter (Upflow and downflow; bed depth = 2.268 cm) A. 19 Penetrations f o r Nickel Shot 126.1 ym Diameter (Downflow; varying bed depth; aerosol diameter - 0.5 ym) A.20 Penetrations f o r Nickel Shot 126.1 ym Diameter (Downflow; bed depth = 1.134 cm) A.21 Penetrations f o r Lead Shot 1800 ym Diameter (Downflow; aerosol diameter =•= 0.5 ym) A.22 Pressure Drop (MM.HG) across Beds of Nickel Shot 598.1 ym Diameter A.23 Pressure Drop (MM.HG) across Beds of Nickel Shot 511.0 ym Diameter A.24 Pressure Drop (MM.HG) across Beds of Nickel Shot 363.9 ym Diameter A. 25 Pressure Drop (MM.HG) across Beds of Nickel Shot 216.1 ym Diameter A.26 Pressure Drop (MM.HG) across Beds of Nickel Shot 126.0 ym Diameter A. 27 Pressure Drop (MM.HG) across Beds of Lead Shot 1800 ym Diameter B. 1 Dimensionless Groups and Single Collector E f f i c i e n c y Corresponding to Tests on Beds of Nickel Shot 598.1 ym Diameter (Downflow) B. 2' Dimensionless Groups and Single C o l l e c t o r E f f i c i e n c y Corresponding to Tests on Beds of Nickel Shot 598.1 ym Diameter (Upflow) B. 3 Dimensionless Groups and Single Collector E f f i c i e n c y Core responding to Tests on Beds of Nickel Shot 511.0 ym Diameter (Downflow) B. 4 Dimensionless Groups and Single Collector E f f i c i e n c y Corresponding to Tests on Beds of Nickel Shot 511.0 ym Diameter (Upflow) B. 5 Dimensionless Groups and Single Collector E f f i c i e n c y Corresponding to Tests on Beds of Nickel Shot 363.9 ym Diameter (Downflow) B. 6 Dimensionless Groups and Single Collector E f f i c i e n c y Corresponding to Tests on Beds of Nickel Shot 363.9 ym Diameter (Upflow) B. 7 Dimensionless Groups and Single Collector E f f i c i e n c y Corresponding to Tests on Beds of Nickel Shot 216.0 ym Diameter (Downflow) B. 8 Dimensionless Groups and Single Collector E f f i c i e n c y Corresponding to Tests on Beds of Nickel Shot 216.0 ym Diameter (Upflow)  A. 13  viii  121 121 121 121 122 122 122 122 123 124 124 124 125 125 125 127 129 130 132 133 135 136 138  B. 9  B. 10 C. 1 C. 2 C. 3 C. 4 C. 5 C. 6 C. 7 C. 8 C. 9 C.10 C.ll C.12 C.13 C.14 C.15 C.16 C.17 C. 18 D. 1 D. 2 D. 3 D. 4 D. 5 D. 6  Dimensionless Groups and Single Collector E f f i c i e n c y Corresponding to Tests on Beds of Nickel Shot 126.1 um Diameter (Downflow) Dimensionless Groups and Single Collector E f f i c i e n c y Corresponding to Test on Beds of Nickel Shot 126.1 ym Diameter (Upflow) Results of F i t t i n g Equation C.l to the Experimental Data by Multiple Regression Results of F i t t i n g Equation C.2 to the Experimental Data by Multiple Regression Results of F i t t i n g Equation C.3 to the Experimental Data by Multiple Regression Results of F i t t i n g Equation C.4 to the Experimental Data by Multiple Regression Results of F i t t i n g Equation C.5 to the Experimental Data by Multiple Regression Results of F i t t i n g Equation C.6 to the Experimental Data by Multiple Regression Results of F i t t i n g Equation C . l to the Experimental Data by Multiple Regression (intercept set to zero) . . . Results of F i t t i n g Equation C.3 to the Experimental Data by Multiple Regression (intercept set to zero) . . . Results of F i t t i n g Equation C.4 to the Experimental Data by Multiple Regression (intercept set to zero) . . . Results of F i t t i n g Equation C.5 to the Experimental Data by Multiple Regression (intercept set to zero) . . . Results of F i t t i n g Equation C.6 to the Experimental Data by Multiple Regression (intercept set to zero) . . . Comparison of the Coefficients of Equation C.4 with those from Doganoglu's Work Comparison of the Coefficients of Equation C.5 with those from Doganoglu's Work Results of F i t t i n g Equation C.7 to the Experimental Data by Multiple Regression Results of F i t t i n g Equation C.8 to the Experimental Data by Multiple Regression Results of F i t t i n g Equation C.7 to the Experimental Data by Multiple Regression (intercept set to zero) . . . Results of F i t t i n g Equation C.8 to the Experimental Data by Multiple Regression (intercept set to zero) . . . Results of F i t t i n g Equation C.9 to a l l the Experimental Data by Multiple Regression Results of F i t t i n g Equation D.l to the Experimental Data by Multiple Regression Results of F i t t i n g Equation D.2 to the Experimental Data by Multiple Regression Results of F i t t i n g Equation D.3 to the Experimental Data by Multiple Regression Results of F i t t i n g Equatioir D.4 to the Experimental Data by Multiple Regression Results of F i t t i n g Equation D.4 to a l l the Experimental Data by Multiple Regression (04 set to zero) Comparison Between Predicted and Experimental Penetrations for Nickel Shot 598.1 ym Diameter (aerosol diameter = 0.5 ym; bed depth = 4.536 cm) ix  139 141 144 145 145 146 146 147 . 148 . 148 . 149 . 149 . 150 151 . 151 152 152 . 153 . 154 155 157 158 158 159 159 161  D. 7 D. 8 D. 9 D.10 D.ll D.12 D.13 D.14 D.15 D.16 D.17 D.18 D.19 D.20 D.21 D.22 D.23 D.24  Comparison Between Predicted and Experimental Penetrations for Nickel Shot 598.1 ym Diameter (aerosol diameter =* 0.804 ym; bed depth == 4.536 cm) 161 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 598.1 ym Diameter (aerosol diameter = 1.011 ym; bed depth = 4.536 cm) 162 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 598.1 ym Diameter (additional downflow comparisons; bed depth = 4.536 cm) 162 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 511.0 ym Diameter (aerosol diameter = 0.5 ym; bed depth = 4.536 cm) 163 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 511.0 ym Diameter (aerosol diameter = 0.804 ym; bed depth = 4.536 cm) 163 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 511.0 ym Diameter (aerosol diameter =* 1.011 ym; bed depth = 4.536 cm) 164 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 511.0 ym Diameter (additional downflow comparisons; bed depth =» 4.536 cm) 164 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 363.9 ym Diameter (aerosol diameter = 0.5 ym; bed depth = 4.536 cm) 165 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 363.9 ym Diameter (aerosol diameter = 0.804 ym; bed depth = 4.536 cm) 165 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 363.9 ym Diameter (aerosol diameter = 1.011 ym; bed depth = 4.536 cm) 166 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 363.9 ym Diameter (additional downflow comparisons; bed depth = 4.536 cm) 166 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 216-.1 ym Diameter (aerosol diameter = 0.5 ym; bed depth = 2.268 cm) 167 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 216.1 ym Diameter (aerosol diameter = 0.804 ym; bed depth = 2.268 cm) 167 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 216.1 ym Diameter (aerosol diameter =* 1.011 ym; bed depth = 2.268 cm) 168 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 216.1 ym Diameter (additional downflow comparisons; bed depth = 2.268 cm) 168 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 126.0 ym Diameter (aerosol diameter = 0.5 ym; bed depth - 2.268 cm) . . . . 169 Comparison Between Predicted and Experimental Penetrations for Nickel Shot 126.0 ym Diameter (aerosol diameter = 0.804 ym; bed depth = 2.268 cm) 169 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  D.26  D.27  D.28  D.29  D.30 D.31 D.32  Comparison Between P r e d i c t e d and E x p e r i m e n t a l P e n e t r a t i o n s 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) Comparison Between P r e d i c t e d and E x p e r i m e n t a l P e n e t r a t i o n s f o r Lead Shot 1800 ym Diameter (downflow; aerosol diameter = 0.5 ym; bed depth = 4.536 cm) Comparison Between P r e d i c t e d P e n e t r a t i o n s and t h e R e s u l t s of A. F i g u e r o a ( c o l l e c t o r diameter = 7000 ym; bed depth = " = 2 cm) Comparison Between P r e d i c t e d 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 t h e R e s u l t s 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. a e r o s o l ) Comparison Between P r e d i c t e d 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 t h e R e s u l t s 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. a e r o s o l ) R e s u l t s o f F i t t i n g E q u a t i o n D.6 t o t h e E x p e r i m e n t a l Data by M u l t i p l e R e g r e s s i o n R e s u l t s o f F i t t i n g E q u a t i o n D.6 t o t h e E x p e r i m e n t a l Data by M u l t i p l e R e g r e s s i o n (013 s e t a t 1.25) R e s u l t s of F i t t i n g Equation*D.8 t o t h e E x p e r i m e n t a l Data by M u l t i p l e R e g r e s s i o n  xi  170  171  171  172  172 173 174 175  •  LIST OF FIGURES 1. 1. 1. 1. 2. 2. 2.  1 2 3 4 1 2 3  2. 4 2. 5 3. 1 4. 1 4. 2 4. 3 4. 4 4. 5 4. 6 4. 7 4. 8 4.. 9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 6. 1 6. 2 6. 3 6. 4 6. 5 6. 6 6. 7 6. 8  I n e r t i a l Impaction Direct Interception D i f f u s i o n a l Interception . . . . . . Gravitational Settling The Effect of Gas Velocity on Collection E f f i c i e n c y . . . . Velocity Penetration Curve E f f i c i e n c y of a Glass Fibre Mat as a Function of P a r t i c l e Size and Flow Rate Velocity Penetration Curve for 1.1 aerosol and 10-14 Mesh Sand Velocity Penetration Curve for 1.1 ym aerosol and 20-30 Mesh Sand Schematic Diagram of the Granular Bed . . Schematic Diagram of Equipment Column Support for Granular Bed . . . . . . . . . Velocity Reducer Upflow and Downflow Operation of the Column Electron Micrograph of 0.109 ym diameter Latex P a r t i c l e s . . Electron Micrograph of 0.50 ym diameter Latex P a r t i c l e s . . Electron Micrograph of 0.60 ym diameter Latex P a r t i c l e s . . Electron Micrograph of 0.804 ym diameter Latex P a r t i c l e s . . Electron Micrograph of 1.011 ym diameter Latex P a r t i c l e s . . Electron Micrograph of 2.02 ym diameter Latex P a r t i c l e s . . Electron Micrograph of 598 ym diameter Nickel Shot Close up of a 598 ym diameter Nickel Shot Electron Micrograph of 511 ym diameter Nickel Shot Electron Micrograph of 363 ym diameter Nickel Shot Electron Micrograph of 216 ym diameter Nickel Shot Electron Micrograph of 126 ym diameter Nickel Shot Block Diagram of Aerosol Generator Layout of Optics f o r Aerosol Analyser Schematic Diagram of Modified Equipment Humidifying Equipment Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 4.54 cm; c o l l e c t o r diameter » 598.1 ym) . . Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 4.54 cm; c o l l e c t o r diameter = 511 ym) . . . C o l l e c t i o n E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 4.54 cm; c o l l e c t o r diameter =* 363 ym) . . . Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth =•= 2.27 cm; c o l l e c t o r diameter =- 216 ym) . . . Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 2.27 cm; c o l l e c t o r diameter = 126 ym) . . . Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth =* 4.54 cm; c o l l e c t o r diameter = 598 ym) . . . C o l l e c t i o n E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 4.54 cm; c o l l e c t o r diameter =» 511 ym) . . . C o l l e c t i o n E f f i c i e n c y as a Function of Gas Velocity (Bed depth =• 4.54 cm; c o l l e c t o r diameter = 363 ym) . . . xii  7 7 7 10 16 17 17 19 19 33 41 44 45 45 47 47 48 48 49 49 52 52 53 53 54 54 55 57 58 60 71 72 73 74 75 76 77 78  6. 9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 6.17 7.1 7. 2 7. 3 7. 4 7. 5 7. 6 7. 7 7. 8 7. 9 7.10  Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 2.27 cm; c o l l e c t o r diameter = 216 ym) . . . . C o l l e c t i o n E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 2.27 cm; c o l l e c t o r diameter =* 126 ym) . . . . C o l l e c t i o n E f f i c i e n c y as a Function of Aerosol Diameter at a S u p e r f i c i a l Gas Velocity of 5.24 cm/sec C o l l e c t i o n E f f i c i e n c y as a Function of Bed Depth (Collector diameter = 598 ym, aerosol diameter = 0.5 ym) C o l l e c t i o n E f f i c i e n c y as a Function of Bed Depth (Collector diameter = 511 ym, aerosol diameter = 0.5 ym) C o l l e c t i o n E f f i c i e n c y as a Function of Bed Depth (Collector diameter = 363 ym, aerosol diameter = 0.5 ym) C o l l e c t i o n E f f i c i e n c y as a Function of Bed Depth (Collector diameter = 216 ym, aerosol diameter = 0.5 ym) C o l l e c t i o n E f f i c i e n c y as a Function of Bed Depth (Collector diameter = 126 ym, aerosol diameter = 0.5 ym) Pressure Drop as a Function of Gas Velocity Comparison of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (Collector diameter =- 598.1 ym) Comparison Between Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (Collector diameter = 511.0 ym) Comparison Between Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (Collector diameter = 363.9 ym) Comparison of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (Collector diameter =* 216.0 ym) Comparison of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (Upflow and downflow; aerosol diameter = 0.804 ym; c o l l e c t o r diameter = 511.0 ym) Comparison of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (Upflow and downflow; aerosol diameter = 1.011 ym; c o l l e c t o r diameter = 511.0 ym) Scatter Plot of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (using Eqs. 3.6 and 7.1) D i f f u s i o n Coefficent as a Function of Aerosol Diameter . . Scatter Plot of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (using Eqs. 3.6 and 7.3) Scatter Plot of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (using Eqs. 3.6 and 7.5; aerosol diameters i n the range 0.1 to 5.0 ym)  xiii  79 80 83 .  84  .  85  .  86  .  87  .  88 90 95 96 97 98 99 100  101 . 104 105 107  ACKNOWLEDGEMENT S  I would l i k e t o thank my s u p e r v i s o r , Dr. A x e l Meisen, f o r h i s c o n s i d e r a t e s u p e r v i s i o n and guidance throughout the course o f t h i s work. Thanks a r e a l s o due t o t h e p e r s o n n e l i n t h e Department E n g i n e e r i n g workshop f o r t h e i r  o f Chemical  c o o p e r a t i o n and a s s i s t a n c e .  The m a n u s c r i p t was typed by Mrs. Nina T h u r s t o n , whose work i s much appreciated. Finally,  I would l i k e t o thank t h e B r i t i s h Columbia M i n i s t r y o f t h e  Environment and t h e U n i v e r s i t y o f B r i t i s h Columbia f o r f i n a n c i a l assistance.  xiv  CHAPTER 1 INTRODUCTION 1.1  The Need for Particulate Control In recent years the need to l i m i t the emissions of pollutants has  become a matter of increasing concern.  Thus numerous new laws on emission  standards have been introduced i n an attempt to reduce the amount of these pollutants.  A i r p o l l u t i o n and especially a i r 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 i s based on the following factors. a)  Health  hazard.  Inhalation of excessive dust, i r r e s p e c t i v e 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.  P a r t i c l e s i n the 0.1-1.0  ym range can readily reach the innermost portions of the lung and may retained there.  be  Many dusts act as i r r i t a n t s to the eyes and nose causing  a l l e r g i c responses, dermatitis and other skin disorders. p a r t i c l e s such as lead, beryllium and chromium may  Certain metal  cause fever and nausea  when inhaled. b)  Effect  on the environment.  Particulates may affect the atmos-  pheric properties i n the following ways: i) ii) iii)  v i s i b i l i t y reduction, and discolouration fog formation and p r e c i p i t a t i o n , solar radiation reduction  1  2 iv)  temperature and wind d i s t r i b u t i o n a l t e r a t i o n .  Industrial dusts may  s e t t l e on nearby f i e l d s and bodies of water with  deleterious effects on the fauna and c)  Effect  of materials.  or chemical deterioration.  flora.  P a r t i c u l a t e s can affect materials by s o i l i n g For example, corrosion i s enhanced by the  deposition of a c i d i c p a r t i c l e s . d)  Explosion  risk.  Fine dusts of combustible materials dispersed i n  a i r at c e r t a i n concentrations may burn rapidly or even explosively.  Dusts  such as grain, sugar, coal, p l a s t i c s , sulphur, aluminium, and other dusts of l i g h t metals are the most explosive.  The explosion r i s k increasing with  decreasing p a r t i c l e size. e)  Commercial  value.  In some cases such as metal r e f i n i n g or  smelting, the emitted dust may have a considerable economic value. 1.2  Conventional Dust Removal Equipment There i s increasing evidence that submicron p a r t i c l e s are most  hazardous and thus l e g i s l a t i o n should not only be based on the quantity but also the size of particulates.  Most conventional control devices are,  unfortunately, rather i n e f f i c i e n t c o l l e c t o r s of submicron p a r t i c l e s .  Hence  there i s 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 p a r t i c l e s are charged by  passing them through a highly ionized region and subsequently from the gas stream by e l e c t r o s t a t i c forces.  P r e c i p i t a t o r s are able  c o l l e c t fine p a r t i c l e s but the power requirements mass loading.  removing them to  are high and increase with  Furthermore, precipitators are generally large and therefore  have high c a p i t a l and maintenance costs.  3 b)  Fabric  filters.  These are generally more e f f e c t i v e than  p r e c i p i t a t o r s i n the micron and submicron ranges.  Unfortunately.,, most  f i l t e r media have limited resistance to chemical attack, mechanical tion and high temperatures.  vibra-  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 p r i n c i p l e of bringing  the dusty gas stream into contact with a l i q u i d phase.  Numerous devices of  d i f f e r e n t designs, sizes and performance c h a r a c t e r i s t i c s are available and some of them are highly e f f e c t i v e i n the removal of submicron p a r t i c l e s . However, scrubbers tend to have high pressure drops and power requirements. A further major disadvantage  i s that they cannot operate at high temper-  atures . d)  Centrifugal  collectors.  Here the p a r t i c l e s 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  c o l l e c t i o n e f f i c i e n c i e s are achievable for p a r t i c l e s greater than about 5 ym in  diameter. Thus the development of an e f f i c i e n t and low cost device for f i n e  p a r t i c u l a t e removal i s a pressing demand i n industry. 1.3  The Granular Bed  Filter  The granular bed, or packed bed f i l t e r , consists of fixed beds of s o l i d granules through which the dusty gas flows.  The dust p a r t i c l e s 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 e f f o r t s have provided l i t t l e r e l i a b l e data which could  4  be systematically analysed and related to i n d u s t r i a l needs. U n t i l recently packed beds were operated batchwise. ment of devices such as the panel bed f i l t e r  However, develop-  (Baretsky"*") and the f l u i d i z e d  2 bed f i l t e r  (Black and Boubel ) have shown that r e l a t i v e l y high removal  e f f i c i e n c i e s of submicron p a r t i c l e s can be achieved with continuous operation.  This demonstrates the f e a s i b i l i t y of using beds to remove f i n e  particulates from gases i n i n d u s t r i a l processes such as coal g a s i f i c a t i o n . 1.3.1  Advantages of Granular Bed F i l t e r s  Apart from s i m p l i c i t y of design and ruggedness, granular bed  filters  have the a b i l i t y to treat gases which:i) ii) iii) iv) v)  are at high  temperatures  undergo large changes i n temperature  and volume  contain abrasive dusts have a wide range of p a r t i c l e sizes and concentrations contain corrosive chemicals and moisture. Packed bed f i l t e r s may have low maintenance costs, depending on the  e f f i c i e n c y of bed regeneration, and are more compact than some other types of conventional equipment.  They can also remove p a r t i c u l a r matter simul-  taneously with gaseous pollutants provided a suitable absorbent material i s 3 used (Squires and P f e f f e r ). 1.3.2  Disadvantages  of Granular Bed F i l t e r s  In terms of p a r t i c l e removal e f f i c i e n c y granular f i l t e r s are generally less e f f e c t i v e than f i b r e f i l t e r s .  They also tend to have rather high  pressure drops which are comparable with wet scrubbers of similar e f f i c i e n c y . A major drawback i s 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 i s o l a t i n g a section of the bed i)  and:-  dislodging the deposited p a r t i c l e s by "puff back", i . e . , flushing with  5 4 a pulse of a i r i n the reverse d i r e c t i o n to the dusty gas flow (Kalen ; 3  Squires ) ii) iii)  using mechanical v i b r a t i o n of the bed (Englebrecht^), or continuous removal of the p a r t i a l l y clogged section of bed and replacing i t with fresh material (Egleson^).  This method i s r e l a t i v e l y  simple  in case of f l u i d i z e d beds (Meissner^) or spouted beds (Meisen and g Mathur ).  The removed granular material may be either washed f o r  re-use or discarded depending on the p a r t i c u l a r  circumstances.  Further problems may a r i s e when very high concentrations of dusty gas are f i l t e r e d .  This causes rapid clogging and an increase i n pressure drop.  A simple remedy i s to operate the bed i n conjunction with a cyclone or bag f i l t e r to remove the majority of large p a r t i c l e s . A q u a l i t a t i v e comparison of granular beds with conventional f i l t e r s i s given i n Table I. TABLE I. COMPARISON OF A GRANULAR BED WITH CONVENTIONAL PARTICLE COLLECTION EQUIPMENT  Wet Scrubbers High temp. Gas capacity Removal e f f i c i e n c y for fine p a r t i c l e s Capital cost Operating cost Reliability Key:  VP—very poor P —poor  Bag Filters  Electrostatic Precipitators  Cyclones  Granular Beds  VP G  VP VP  G G  VP VG  VG G  P VP P P  VG P P P  G P G P  VP VG VG VG  VG VG VG VG  VG—very good G —good  6 1.4  Background Information on Granular Bed  Behaviour  The study of a granular bed as a p a r t i c l e c o l l e c t i o n device requires a knowledge of the mechanisms which contribute to the c o l l e c t i o n process.  It  i s also necessary to predict the r e l a t i v e magnitude of these mechanisms i n order to develop models of c o l l e c t i o n performance. Most p a r t i c l e removal theories are based on the simple assumption  that  p a r t i c l e s are captured upon touching the c o l l e c t o r surface and that 9  re-entrainment i s absent  (Dahneke ).  P a r t i c l e s s t i c k to surfaces mainly  due to short range van der Waals and e l e c t r i c a l f o r c e s ^ I t  i s there-  fore necessary to develop a mechanism whereby a p a r t i c l e t r a v e l l i n g i n a moving f l u i d i s able to move across the f l u i d streamlines to a point close enough to the c o l l e c t o r surface for these captive forces to come Into effect. 1.4.1  Individual c o l l e c t i o n mechanisms pertinent to an Isolated, spherical c o l l e c t o r  In order to explain the different c o l l e c t i o n mechanisms, which may arise i n granular beds, i t i s convenient to consider a single collector particle.  isolated  Calculation of the c o l l e c t i o n e f f i c i e n c y (or capture  e f f i c i e n c y ) of a single c o l l e c t o r may  then be reduced to the calculation of  the e f f i c i e n c i e s of the individual c o l l e c t i o n mechanism.  The primary  c o l l e c t i o n mechanisms are i i h e r t i a l impaction, direct interception, d i f f u sional deposition, gravitational  sedimentation, and e l e c t r o s t a t i c deposition.  In order to determine which c o l l e c t i o n mechanisms are predominant i n a f i l t e r medium, i t i s useful to introduce dimensionless parameters which characterize the interaction between the f l u i d , p a r t i c l e s , and c o l l e c t o r s .  The separate  c o l l e c t i o n mechanisms are discussed below. a)  Inertial  collection.  As shown i n F i g . 1.1, the presence of a  c o l l e c t o r causes the gas streamlines to curve.  Since the i n e r t i a of the  7  Eig. 1.-3  Diffusional  Interception  8 aerosol p a r t i c l e s i s greater than an equivalent volume of gas, their t r a j e c tories deviate from the streamlines and approach the c o l l e c t o r surface.  Two  factors determine the c o l l e c t i o n e f f i c i e n c y : i)  the v e l o c i t y d i s t r i b u t i o n of the gas around the c o l l e c t o r ,  which i s  governed by the c o l l e c t o r Reynolds number, Re = p_ U d fix t c ii)  and  ,  fhe trajectory of the p a r t i c l e , which i s the r e s u l t of the interaction between the f l u i d and p a r t i c l e .  The interaction may be characterized  by the Stokes number defined as St = d  2  a  U p_/9 y d F c  The i n e r t i a l mechanism i s usually dominant for p a r t i c l e s greater than 1 to 2 ym i n diameter.  The mechanism increases with increasing f l u i d  v e l o c i t y , aerosol diameter and density, and decreasing c o l l e c t o r size. b)  Direct  interception.  In this case i t i s assumed that the p a r t i c l e s  do not appreciably disturb the f l u i d f l o w f i e l d and their t r a j e c t o r i e s coincide with the streamlines..  A p a r t i c l e i s captured when i t s centre approaches the  c o l l e c t o r surface within one p a r t i c l e radius (see F i g . 1.2). solely to the size of the p a r t i c l e .  Capture i s due  This mechanism can be characterized by  the parameter NR = d /d a c This effect i s usually small i n the case of submicron aerosol p a r t i c l e s treated by beds of i n d i v i d u a l c o l l e c t o r p a r t i c l e s greater than 100 ym diameter. c)  Diffusional  deposition.  Because of Brownian movement the t r a j e c -  tories of submicron p a r t i c l e s do not usually coincide with the gas streamlines'.  Thus a p a r t i c l e may migrate to the c o l l e c t o r surface purely as a  result of random d i f f u s i o n (see F i g . 2.3). describe t h i s e f f e c t .  The Peclet number Is used to  Pe = d where D  U/ D  c  a  i s the e f f e c t i v e d i f f u s i v i t y of the aerosol p a r t i c l e .  Some workers  3.  prefer the dimensionless group ND = Pe  -2/3 •  This group changes the magnitude of the d i f f u s i o n a l parameter making i t more comparable to the other dimensionless groups. The d i f f u s i o n a l effect increases with decreasing p a r t i c l e size and i s usually the dominant c o l l e c t i o n mechanism for p a r t i c l e s smaller than about 0.5 ym i n diameter at low v e l o c i t i e s . d)  Gravitational  deposition.  This represents sedimentation or  s e t t l i n g of a p a r t i c l e due to gravity.  In most cases the effect i s only  s i g n i f i c a n t for p a r t i c l e s greater than about 2 ym i n diameter or at very low gas v e l o c i t i e s .  Gravitational  deposition can be characterized by the  parameter NG = U /U s where U  g  i s the terminal v e l o c i t y of the aerosol p a r t i c l e .  obeys Stokes  1  law, U  g  If the p a r t i c l e  i s given by U  s  = df  g p /l8 y a  Depending on the d i r e c t i o n of gas flow, the effect of gravity c o l l e c t i o n may be either positive or negative (see F i g . 1.4).  on  The c o l l e c -  t i o n e f f i c i e n c y increases with aerosol size and density and decreases with Increasing gas flow. e)  Electrical  effects.  The aerosol p a r t i c l e s and the collectors  may  carry e l e c t r o s t a t i c charges which can affect the motion of the aerosol around a c o l l e c t o r and hence their c o l l e c t i o n .  There are four types of  12 e l e c t r i c a l forces considered.  resulting from these charges which may have to be  ( i ) The coulombic force between a charged c o l l e c t o r and a  charged aerosol p a r t i c l e , ( i i ) the e l e c t r i c a l image force between a charged  10  Fig. 1.4  Gravitational.Settling  11 collector, and p a r t i c l e and  a neutral p a r t i c l e , ( i i i ) the image force between a charged a neutral c o l l e c t o r , and  (iv) the space charge repulsion force  effect. 1.4.2  The  single p a r t i c l e c o l l e c t i o n e f f i c i e n c y  Each f i l t r a t i o n mechanism described above i s based on c o l l e c t i o n by  an  13 isolated c o l l e c t o r p a r t i c l e .  This approach was  developed by Langmuir  who  assumed that every f i l t e r element (e.g., bed p a r t i c l e ) experiences similar f i l t r a t i o n phenomena and be defined.  therefore a single f i l t e r element e f f i c i e n c y  Consequently, the f i l t r a t i o n e f f i c i e n c y of an actual  can be calculated  by summing the effects of a l l the elements of the  In the case of a granular bed and  the single c o l l e c t o r E = Number of Number of unit time  may  filter filter.  each element i s assumed to be a sphere  e f f i c i e n c y may be defined as p a r t i c l e s Impacting per unit time p a r t i c l e s that could impact per i f their t r a j e c t o r i e s were straight  Thus the theoretical calculation of f i l t e r e f f i c i e n c y of a granular bed  i s usually  divided  into two  c o l l e c t o r e f f i c i e n c y and integration.  3.)  assumed that steady state f i l t r a t i o n i s taking place  influence to the c o l l e c t i o n e f f i c i e n c y of the  filter.  Limitations of the single c o l l e c t o r e f f i c i e n c y approach  The various assumptions i n t h i s approach are rarely met such as  single  s t r u c t u r a l changes caused by the depositing p a r t i c l e s are too small  to be of any 1.4.3  of the  the summation of a l l the c o l l e c t o r e f f i c i e n c i e s by  (Further d e t a i l s are given i n Chapter  It i s also usually where any  parts, i . e . , prediction  (i) the bed  granules are completely spherical,  i n practice  ( i i ) that p a r t i c l e s  14 c o l l i d i n g with a c o l l e c t o r are always retained ( i i i ) that there i s no re-entrainment, and  , i . e . , no bounce-off,  (iv) that already deposited  p a r t i c l e s do not affect the c o l l e c t i o n e f f i c i e n c y of a c o l l e c t o r . fore the method i s oversimplified  and  i s only useful when the  There-  individual  mechanisms are small or one i s dominant.  According to Fuchs^"' the t o t a l  single c o l l e c t o r e f f i c i e n c y i s greater than any of the individual cies but smaller than their sum.  efficien-  Thus the problem i s how to combine the  individual effects, especially when the aerosol diameter i s i n the range of 0.1-1.0 ym and the effects caused by the various mechanisms are comparable. 1.4.4  Interference effect  There i s also the problem that the flow f i e l d round an isolated c o l l e c tor p a r t i c l e i s obviously different from that of a c o l l e c t o r p a r t i c l e  inside  a granular bed and therefore i t s c o l l e c t i o n e f f i c i e n c y i s also changed.  The  flow d i f f e r s because:i)  The i n t e r s t i t i a l gas v e l o c i t y i n the bed i s higher than a s u p e r f i c i a l gas v e l o c i t y .  ii)  The gas streamlines around the c o l l e c t o r are different due to the close proximity of the neighbouring c o l l e c t o r s . Thus the 'interference e f f e c t ' tends to increase the c o l l e c t i o n  efficiency.  However, there i s disagreement as to how to account for t h i s  e f f e c t , especially because i t may be different mechanisms.  for the various c o l l e c t i o n  The most plausible parameter to describe the interference  effect i s the bed porosity (e).  To determine the true c o l l e c t i o n e f f i c -  iency of a c o l l e c t o r , empirical or semi-empirical corrections must be i n t r o duced. The single c o l l e c t o r e f f i c i e n c y of a c o l l e c t o r within a granular bed may therefore be written as EB = f ( e , EI, ER, ED, EG  ...)  where EI, ER, ED, and EG are the c o l l e c t i o n efficiences of the single c o l l e c t o r due to i n e r t i a , interception, 1.4.5  d i f f u s i o n and gravity,  respectively.  Total c o l l e c t i o n e f f i c i e n c y of the granular bed  F i n a l l y the single c o l l e c t o r e f f i c i e n c y  (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 s i m p l i f i e d model of  the  spherical.and r e g u l a r l y EB  and  1.5  EBT.  following variables  and i) ii)  ( i i ) collector  (v)  g r a n u l a r beds and  g r a n u l a r bed  effect  to use  gravity  are relate  3.  ( i i i ) gas  depth.  Other f a c t o r s bed  equipment.  (iv) direction  gas  the  (i) aerosol of  flow r a t e ,  using m e t a l l i c  bed  interception,  c o n s i d e r e d i n d e v e l o p i n g an bed.  e f f e c t of  gas  flow,  and  efficiency.  Thus o n l y i n e r t i a ,  c o l l e c t i o n e f f i c i e n c y of the  of  observed were:-  as a f u n c t i o n of  collection  develop-  collection efficiency  f i l t r a t i o n p r o c e s s , the  velocity,  removal of  f o r the  c o l l e c t i o n e f f i c i e n c y were c o n s i d e r e d :  of humidity on  needed to be  the  results  on  size,  the  the  the  investigate  E l e c t r i c a l e f f e c t s were minimized by grounding the  developed to  To  p r e s s u r e drop a c r o s s the the  collectors  t h i s work were to i n v e s t i g a t e  empirical equation f o r p r e d i c t i n g  g r a n u l a r bed.  size,  be  a  P r e s e n t Work  submicron a e r o s o l s by  the  invoking  d i s c u s s e d i n g r e a t e r d e t a i l i n Chapter  main o b j e c t i v e s of  ment of an  By  i . e . , assuming a l l the  packed, a simple e q u a t i o n can  T h i s w i l l be  Scope of the The  f i l t e r bed,  (EBT).  particles  diffusion  equation to p r e d i c t  and and  the  CHAPTER 2  PREVIOUS  2.1  WORK  Introduction P a r t i c u l a t e s e p a r a t i o n from a gas stream by means o f g r a n u l a r bed  f i l t e r s has been the s u b j e c t o f s e v e r a l t h e o r e t i c a l and e x p e r i m e n t a l s t u d i e s . The e x p e r i m e n t a l i n v e s t i g a t i o n s d e a l mainly w i t h the o v e r a l l performance methods o f improvement.  and  The t h e o r e t i c a l work ranges from t h e a n a l y s i s 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  t o the  o v e r a l l c a l c u l a t i o n of t h e 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 s u b s t a n t i a l amount of work has been c a r r i e d o u t , t h e r e i s c o n s i d e r a b l e disagreement  and inadequate u n d e r s t a n d i n g of t h e f i l t r a t i o n  mechanisms.  T h i s i s p r o b a b l y due t o the f a c t t h a t p r e v i o u s work i s r a t h e r  fragmentary  and o f t e n p r e s e n t e d i n a way which p r e c l u d e s s y s t e m a t i c a n a l y s i s .  S e v e r a l comprehensive  reviews a r e a v a i l a b l e on p a r t i c u l a t e  removal  u s i n g g r a n u l a r beds ( F u c h s ^ , Davies"*"^, Dorman"^, Strauss"*"^, Silverman"*"^, Figueroa  20  , Tardos  21  , Pich  22  ).  Rather than r e p e a t i n g t h e i r r e v i e w s , the  e f f e c t of v a r i o u s o p e r a t i n g and d e s i g n v a r i a b l e s w i l l be d i s c u s s e d 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  Efficiency  I t has been noted by most workers t h a t i n c r e a s i n g the v e l o c i t y the f i l t e r again.  through  causes t h e c o l l e c t i o n e f f i c i e n c y t o decrease and then i n c r e a s e  The minimum  (see F i g s . 2.1 and 2.2) i s caused by d i f f u s i o n a l  becoming l e s s important and i n e r t i a l e f f e c t s becoming dominant. 14  The  effects  v e l o c i t y r e s u l t i n g i n the minimum c o l l e c t i o n increases the smaller the aerosol. ficial  A t y p i c a l plot of c o l l e c t i o n e f f i c i e n c y as a function of super-  gas v e l o c i t y i s shown i n F i g . 2.1 and the following statements can  be made about the r e s u l t i n g curve. For d i f f u s i o n :  As the aerosol diameter increases the curve moves to the left.  As the c o l l e c t o r diameter increases the curve  moves to the r i g h t . For i n e r t i a :  As the aerosol diameter increases the curve moves to the l e f t and up.  As the c o l l e c t o r diameter increases the  curve moves to the right and down. For interception:  As the aerosol diameter increases the curve moves up. As the c o l l e c t o r diameter increases the curve moves down.  The ordinate of F i g . 2.2 i s the penetration of the f i l t e r which i s defined as (1 - c o l l e c t i o n e f f i c i e n c y ) . Very l i t t l e i s known about the combined effects of i n e r t i a and d i f f u sion, which are of particular importance for p a r t i c l e s between 0.1-1.0 ym diameter.  There i s , also, considerable disagreement on which c o l l e c t i o n  mechanism becomes dominant i n a given size range.  For instance, f o r the  23 aerosol size range 1-2 ym diameter, Doganoglu reported that gravity and 24 i n e r t i a are dominant whereas Knettig , stated that only i n e r t i a i s s i g n i f 25 icant.  For the same range and comparable gas v e l o c i t i e s , McCarthy  concluded that interception  and d i f f u s i o n are dominant which i s i n direct  disagreement with Doganoglu. 2.3  Effect of Aerosol Size on Collection  Efficiency  It has been well established experimentally  and t h e o r e t i c a l l y that for  f i n e p a r t i c l e s the c o l l e c t i o n e f f i c i e n c y decreases with decreasing  particle  size.  down to  Further, i'tiis generally accepted that this trend continues  16  Fig. 2.1  The Effect of Gas Efficiency  Velocity on  Collection  0  40  -80  120  160 v  200  240  280  300  cm/sec  26 Fig. 2.2  Velocity Penetration Curve (Ramskill and Anderson  j  !  5  0-94 cm/sec i  2  '  1  i  A  •  0-42 cm/sec  0-5  0 • 21 cm/sec^ i i  0-05  *  005  0-10  0:'5  /  /  is.  i  ;  1 !  ; 1  j  i  K  j 0-20  0-25  Panicle  Fig. 2.3  1  <  ! 0  1  1  •«/! 0-0 ?4cn iAec\ |  0-02  : !  ,  V / '  0-1  ' ! ^v!.  x  i/^ j  0-2  0-0.  i  NJ  O30  0-JS  0-40  C-45  0-50  0-55  0-60  radius,/*  E f f i c i e n c y of a Glass Fibre Mat as a Function of P a r t i c l e Size and Flow Rate (Thomas and Yoder27) Note:  Penetration = (1 - c o l l e c t i o n e f f i c i e n c y )  )  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 a g a i n . 28 Fruendlich  showed t h a t minimum c o l l e c t i o n o c c u r r e d w i t h a e r o s o l s 29 between 0.2-0.4 ym i n diameter. Chen , i n experiments w i t h 0.15 ym diameter 30 a e r o s o l s , observed a minimum o n l y f o r 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 a e r o s o l s of 0.02  ym  27 diameter.  Thomas and Yoder  p o i n t e d out  the minimum c o l l e c t i o n e f f i c i e n c y ( F i g . 2.3). 2.4  Effect  of C o l l e c t o r  collection efficiency  S i z e and  Bed  Depth on C o l l e c t i o n  used c o l l e c t o r s  Effect  gas  increases with decreasing  Efficiency  collector size.  depth obeying Eq.  of the D i r e c t i o n of Gas  3.4  31  , Gebhart  32  Flow on C o l l e c t i o n , Thomas  27  , and  Figueroa  20  of the d i r e c t i o n  reduces and  2.6  4 cm/sec (see F i g s . 2.4  Bounce-off may  2.5).  (see Chapconstant.  efficiencies be  i n diameter f o r v e l o c i t i e s At h i g h e r v e l o c i t i e s  of flow on the c o l l e c t i o n of submicron  can be assumed n e g l i g i b l e  Bounce-off and  and  ym  the  , demonstrated  However, Thomas showed t h a t g r a v i t y can  i n c o l l e c t i o n of a e r o s o l s down to 0.3  between 1 and effect  downflow.  at a v e l o c i t y  the  particles  g r e a t e r than 20 cm/sec.  Re-entrainment occur w i t h  between the a e r o s o l and  solid  a e r o s o l s due  c o l l e c t o r s u r f a c e and  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 .  the  Efficiency  t h a t g r a v i t y p l a y s a s m a l l r o l e i n c o l l e c t i o n , by comparing bed f o r upflow and  Also  i s p r o p o r t i o n a l to 1 - exp(^b.H) where 'b' i s a  Work by P a r e t s k y  important  velocity  of v a r i o u s s i z e s , have shown t h a t  i n c r e a s e s e x p o n e n t i a l l y w i t h bed  t e r 3 ) , i . e . , EBT  2.5  increased with decreasing  producing  Thus, once a g a i n , t h e r e i s disagreement.  Most workers, who  efficiency  t h a t the p a r t i c l e s i z e  to e l a s t i c c o l l i s i o n s  thus p r e s e n t s  a problem i n  Furthermore, t h e r e i s the  19  ICO I  F i g . 2.4  1 — i — i — i i 1111  31  ;  0.1  0.2  :  i• • ii 0.4  1 — i — i — i i i 111  :  :  i • •i i•  1 — i — i — i i 111  1  ;  0.7 1 2 4 7 10 Superficial velocity, cm/sec  20  . i 40  100  V e l o c i t y P e n e t r a t i o n Curve f o r 1.1 ym a e r o s o l and 10-14 Mesh Sand ( P a r e t s k y ) 3 1  100r I Upshot 0 Downshot 20-30 mesh Bed thickness-8.2 cm  80t£  -  j  60 -  f  40-  o. 20-  1  0.2  0.7 1  2  4  7  10  100  Superficial velocity, cm/sec  Fig.  2.5  V e l o c i t y P e n e t r a t i o n Curve f o r 1.1 ym a e r o s o l and 20-30 Mesh Sand ( P a r e t s k y ! ) 3  20 p o s s i b i l i t y that re-entrainment  33  may occur i f the gas v e l o c i t y i s high enough 34  to detach deposited p a r t i c l e s .  Jordan  noted that v e l o c i t i e s of 100 m/sec  were needed to dislodge individual aerosols 2 ym i n diameter from a glass s l i d e and up to 4.5 m/sec to dislodge 10 ym diameter p a r t i c l e s .  Thus re-  entrainment should be negligible i n 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 v e l o c i t i e s are generally below 1-10 m/sec.  There i s , however, the phenomena  35 observed by Leers where p a r t i c l e s deposit on one another to form "trees" and "chains". In t h i s case much weaker forces are needed to break the adhesion of these chains. 36 Walkenhorst  concluded from h i s experiments on layers of wire gauze  that i)  p a r t i c l e s below 0.5 ym diameter adhere well after c o l l i s i o n and are not removed even at gas v e l o c i t i e s exceeding 6 m/sec  ii)  for p a r t i c l e s with diameters up to 1 ym, bounce-off may occur, as the v e l o c i t y i s increased the effect decreases due to enhanced i n e r t i a l deposition  iii)  for p a r t i c l e s with diameters greater than 1 ym, increased i n e r t i a l deposition outweighs any increased f a i l u r e of adhesion. The chances of bounce-off and re-entrainment can be reduced by coating  the surface of the c o l l e c t o r s with a non-volatile l i q u i d such as d i o c t y l phthalate (D0P).  Furthermore, retention may be improved by e l e c t r o s t a t i c 37  charging of the aerosol (Balasubramanian 2.7  38 , Mazumder  ).  Review of Experimental and Industrial Studies Carried out on Granular Beds Tables II and III provide a summary of work reported i n the l i t e r a t u r e  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 I I . Aerosol Researcher  Type  KaCz and Macrae-"  D.O.P. mist  Meissner and Mickley  Sulphuric acid mist  2-14  Rams k i l l and Sulphuric Anderson ^ acid mist D.O.P.  0.3 0.2-0.8  Thomas and Yoder  0.24-1.8 0.6-1.2  7  0.3  2  D.O.P. Polystyrene latex  27  Diameter urn  Gas Velocity cm/sec  Granular charcoal  470-910  16  10.6  2.8  Aluminum silicate S i l i c a gell Glass beads  45-147  32-62  5  8-25  57 254  35-78 37-85  5 5  8-25 8-25  Collector Diameter urn  Fibrous filter  Lead shot Sand  Genetian violet  Yoder and Empson !  D.O.P. Polystyrene latex  0.2-2.0 0.5-1.2  D.O.P.  0.5-1.1  Uranine  0.25,0.97 Epoxy • resin 7.03  4  Scott and Guthrie  0.5  Type  Anderson and Silverman 40  EXPERIMENTAL STUDIES  Polystyrene beads Sand  5-280  —  —  Bed depth cm  81  1500 360-1600  43  Jackson and Calvert 44  Fuel o i l mist  Mazumder and Uranine Thomas 38  Diffusion;  Remarks  work based on gas mask studies  Inertial impaction; efficiency independent of mist concentration and bed age; study on fluidized beds  Diffusion and inertia; determined an aerosol size with a minimum collection efficiency  323  360-1600  90 3.6-7.6  3.8 3.8  25.4  3.5  2.54  Inertia; studied e l e c t r i c a l effects; fluidized bed  —  3.6  Diffusion; determined an aerosol size with a minimum collection efficiency, the size decreases with increasing velocity  0.1-2.2  /  89  102  Diffusion and gravity; studied upflow and downflow; electrical effects; determined an aerosol size with, minimum collection efficiency  0.75-1.5 0.1-2.2  3-15  5.1  19.3-36  42  Silverman  Dominant Collection Mechanisms;  5-280  '  Silica gel.  Column Diameter cm  2.5-6  183-762 183-762 183-762 183-762  6  Glass spheres Berl saddles Raschig rings Incalex saddles  12700 12700 12700 12700  0.16  Polystyrene spheres Copper spheres Epoxy resin  1000  6-36  3000 2000  6-36 6-36  —  1  35.6 35.6 35.6 35.6  15.2 15.2 15.2 15.2  1.5-3  based on a  Diffusion; efficiency not affected by aerosol concentration Diffusion, inertia and interception; velocity for minimum collection found for each aerosol, where diffusion and inertia are weakest Mainly i n e r t i a l impaction; direction  flow i n the horizontal  Mainly i n e r t i a l impaction, studied improvement i n collection efficiency due to e l e c t r i c a l effects  Table I I (continued) Aerosol Researcher Calvert*  Type  Diameter wm  Collector Type  Fuel o i l  1-1.8  Black and Boubel  Ammonium chloride  0.52  Glass shot  Paretsky  Polystyrene latex  1.1  Sand  5  2  31  Raschig rings Bed saddles  Diameter W» 12700 12700 25  841-1650  Gas Column Velocity Diameter cm/sec cm 900 900 4-12  0.3-8.0  Bed depth cm  35.6 35.6  15  5.1  12.3  2.5-5  Dominant Collection Mechanisms; Remarks Inertial impaction  Interception and diffusion; studies on a fluldized bed; bed age and aerosol concentration play no effect on collection efficiency  3-7-1.9  Mainly due to inertia and diffusion; upflow and downflow tests indicate gravity plays a role in collection  2.5-10  Interception, some diffusion; with increasing gas velocity; beds, upflow only  efficiencies decreased fixed and fluldized  2.5-25  5.1  0.7-14.2  8  425  8.8-24.6  12.7  1-12  Inertia;  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  Polystyrene latex Methylene blue  0.5-2.0  305-495  3-18.5  10  3-9  Inertia and diffusion; studies on fixed and fluldized beds, upflow and downflow; high collection on plastic beds due to electrical effects  First and Hinds47  D.O.P. Polystyrene latex  0.8 Fibreglass 0.36-1.1 mat  100-600 '  254-1524  7.6  1-95  Diffusion at low velocities, inertia at high velocities; bounce-off at high velocities  Doganoglu, Jog and Clift  D.O.P.  0.6-3.0  108-596  10-70  15  3-5  Inertia at high velocities, interceptions and gravity at low velocities  546 214  60-300 60-300  Azaniouch49  Na„S0,  3300  60-180  5-50  Mainly due to gravity and inertia;  Yankel, Jackson and Patterson  D.O.P.  0.67-1.4 Alumina  Gebhart, Roth and Stahlhofen  Polystyrene  0.1-2.0  Glass beads  Kneetig and Beeckmans *  Methylene blue  0.8-2.9  Glass beads  Doganoglu  Methylene blue D.O.P.  260  46  10-40  32  2  Figueroa  185-4000  23  20  1-2.0  4 8  2  4  5.2  Plastic beads Sand  680  _  Glass ballotini Glass spheres Copper shot Granular CaCO,  5  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 studies on fixed and fluldized beds  bounce-off occurs  Nj ^  TABLE I I I . Aerosol Researcher  Type  INDUSTRIAL STUDIES  Collector Diameter  Gas Velocity cm/sec  Diameter ym  Type  80-10  Graphite  3000-13000  64  5-12  ym  Fairs and Godfrey  Sulphur  Egleson^  Coal dust and ash  Coke particles  3175-10160  Dust  Steel turnings Sand  1000-6000  50  Englebrecht  5  Black and Boubel  NH.C1 4  Squires and Pfeffer  Power station f l y ash  2  3  0.52  25-80  1000-6000  Glass shot  250  Sand  760  4-12  Remarks Panel bed f i l t e r used i n removing fumes from an acid plant burning sulphur  F i l t r a t i o n of dust residue from a coal g a s i f i c a t i o n p i l o t plant, continuous operation of a packed bed f i l t e r ; column diameter 30.5 cm and bed depth 259 cm Study of filter; filtered the bed,  a 'Lurgi' M.B. gravel bed continuous operation with dust removed by v i b r a t i o n of operation at 660°F  Fluidized bed operating continuously; c o l l e c t i o n due to interception, d i f f u s i o n and e l e c t r o s t a t i c forces; column diameter 5 cm, bed depth 10-30 cm  Study of a panel bed f i l t e r ; continuous operation using a "puff-back" method to clean the f i l t e r U>  Table I I I  (continued) Aerosol  Researcher  Type  Diameter ym  Collector Diameter Type ym  Strauss and Thring  Fumes  Crushed brick  Cook, Swany and . Colpitts52 Rush and Russ'el  Fluoride particles  Alumina  Kalen and Zenz  Catalyst  Dumont  Radioactive Carbonaceous particles  5 1  2500-8000  Gas Velocity cm/sec 25-100  Remarks Horizontal granular f i l t e r for fumes from oxygen-lanced open hearth s t e e l furnace Combination of granular bed ( f l u i d ized) and a f i l t e r bag for removal of fluorides i n waste gases from aluminium smelting  j  54  2-60  Sand  F i l t e r i n g effluent from a cat cracker using a 'Ducon' granular bed f i l t e r ; continuous operation using puff-back for cleaning  760  4  5 5  BBhm and Jordan ^ 5  Na 0 2  2  Alumina Sand  1.4  Sand  Fluidized bed operation of a granula bed  280-9700  2-5  Studies on a multilayer sandbed f i l t e r for use with a l i q u i d metal fast breeder reactor  Table III (continued) Aerosol Researcher Reese ^ 5  Type F l y ash  Diameter ym —  Collector Diameter Type ym Sand  3000-6000  Gas Velocity cm/sec —  Remarks A dry packed bed scrubber for removal of f l y ash from f l u e gas from lumber m i l l operation; continuous recycling of the sand  26 2.8  Empirical Equations Based on experimental and t h e o r e t i c a l studies a large number of  empirical equations have been suggested to predict the single c o l l e c t o r efficiency.  These equations, which account for one or more c o l l e c t i o n  mechanisms, vary considerably i n accuracy and range of application.  Tables  IV and V summarize these equations. 2.9  Theoretical Work on the Flow F i e l d 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 p a r t i c l e s of uniform size through which the dusty gas flows.  The f i r s t step i n the c a l -  culation of the f i l t e r e f f i c i e n c y i s to determine the flow f i e l d filter.  i n the  The almost universally used model i s to describe the gas flow  round a single cylinder or sphere and then to extend this to calculate flow patterns and p a r t i c l e t r a j e c t o r i e s i n a complex of spheres or f i b r e s . 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 s i x d i f -  ferent ways i n which the spheres may be packed, each with i t s own porosity.  unique  Although these packings have regular geometrical arrangements  on which calculations may be based, one i s r e a l l y concerned with the void space through which the c a r r i e r gas w i l l flow.  These void spaces are so  complex that any attempt at a geometrical description must introduce considerable s i m p l i f i c a t i o n . One model considers the spheres as obstacles to an otherwise straight flow of f l 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 i n an actual granular bed. 73 Another approach i s the concept of a 'unit c e l l ' developed by Happel  TABLE IV.  Collection Mechanism  Researcher  Inertia  Paretsky  EMPIRICAL EQUATIONS FOR SINGLE COLLECTOR EFFICIENCY BASED ON ONE COLLECTION MECHANISM  Equation  EI = 2.0ST  31  Langmuir and Blodgett 13  EI = 3.76 x 10  - 0.464St + 9.68St - 16.2St  3  2  24  Landahl and Hermann59 JJ  Behie and Beeckmans^O  E  „_ 1  St < 4.4 x 10 2000 ym < d < 700 c  2.1  For creeping flow  2.2  For potential flow, St > 0.02  2.3  0.3 > St > 0.0416, based on the experimental data of Heme 58  2.4  Re = 10  2.5  2  St' (St + 0.05)2  EI  Knettig and Beeckmans  1.13  -2 0.75 ln(2St) St - 1.214  = 1 +  Equation No.  Remarks  St •.St + 0 . 7 7 S t 2 + 0.22  3  j  =  3  EI = 0  St < 0.083  EI = 3.6 x 10" - 0.232St + 2.42St - 2.03St 3  2  EI = {St/(St + 0.5) } 2  3  0.6 < St < 0.083 St  2.6  > 0.06  l-o  Table IV (continued) Collection Mechanism  Researcher  "Equation  Interception  Remarks  ER = 2NR  ER - ^ NR  2  Friedlander  Diffusive deposition  Natanson  62  Langmuir  XJ  61  ER = 2Re  2.7  St -y 0, p a r t i c l e s with no i n e r t i a follow the gas streamlines  2.8  2.9  2  NR (2 - In Re)  2.10  2  ED = 8 P e  Stairmarid 64  ED = 2.83 Pe  _1  3  + 2.3 R e  63  65  2.11  1.71 Pe~ / (2 - In Re)l/3" 2  ED  Johnstone and Roberts  Bousinesque  St -> so, i n e r t i a of the p a r t i c l e s causes them to travel In a linear direction  NR  2  ED = 3.15 Pe"  2  Equation No.  1 / 8  Pe~ * 5/  Based on the analogy between heat and mass transfer  2.12  Potential  flow  2.13  Potential  flow  2.14  T a b l e IV  (continued)  Collection Mechanism  Researcher  Tardos  6 6  Natanson 62  Gravitational deposition  Ranz and 67 Wong D/  Equation  -2/3 ED = 3.96 Pe  ED =  -2/3 2.92 Pe  Remarks  Equation No.  flow  2.15  Pe >> 1, c r e e p i n g flow  2.16  Creeping  (2 - In Re)1/3  Us EG = — U  = NG  2.17  >^5  TABLE V.  Collection Mechanisms  EMPIRICAL EQUATIONS FOR SINGLE COLLECTOR EFFICIENCY BASED ON COMBINATIONS OF COLLECTION MECHANISMS  Researcher  Equation  Diffusion and Interception  Friedlander l  Inertia and Interception  Davies ^  fi  6  EDR =  1/6 6 Re Pe2/3 + 3 NR  Remarks  Re  2  Equation No.  2.17  2  EIR = 0.16 [NR + (0.5 + 0.8 NR) St  2.18  Re = 0.2  - 0.105 NR S t ] 2  Diffusion, Inertia and Interception  Gravity and Inertia  Inertia, Diffusion, Interception and Gravity  Davies 8 fi  EDIR =0.16  [NR + (0.5 + 0.8 NR) (j^ + St)  - 0.105 NR  Doganoglu 23  + St) ] 2  Pe  EIG = 2.89 St + 6.87 NG  d  EIG = 5.83 x 10~ Re St + 1.42 NG  d  2  Schmidt 69  2.19  E = 3.97 St + (8 Pe + 1.45 NR + NG  1  + 2.3 R e  1 / 8  Pe  5 / 8  )  c c  -110  m  2.20  = 600  m  2.21  EI + ED + ER  2.22  Where E  + EG  u> o  and Kuwabara  74  .  It assumes the spheres are homogeneously distributed and  the f l u i d may be divided up into spherical regions or c e l l s , each corresponding to one s o l i d sphere.  The volume of the c e l l i s related to the  porosity i n such a way that the v o l . of f l u l d / v o l . of c e l l equals the porosity (e).  It i s assumed the flow i s purely viscous thus enabling the  v e l o c i t y of the streamlines and their d i r e c t i o n at any point to be calculated. .  The ideas of this concept have been used t h e o r e t i c a l l y and experi-  mentally by many workers"'">75,76,77  ^  e  m o c  iel h  a s  been extended to  72 higher Reynolds numbers by l e C l a i r and Hamielec 78 Neale and Nader point of view.  approached the problem from a s l i g h t l y d i f f e r e n t  They assumed that the sphere i s surrounded by a spherical  f l u i d envelope whose dimension i s computed i n the same way as i n the HappelKuwabara model with a modification that considers the entire sphere swarm as one large exterior porous mass.  A d i f f e r e n t approach i s to consider the  bed of granules as a random cloud of Identical p a r t i c l e s and to use s t a t i s 79 t i c a l methods of analysis.  For example, Tarn  most probable one around one of the spheres.  ^ I n t e r p r e t e d the flow as the Creeping flow and no p a r t i c l e /  p a r t i c l e i n t e r a c t i o n were assumed. S t a t i s t i c a l and unit c e l l models are s t i l l i n their infancy,and, although they describe reasonably well the flow through a packed bed, their complexity w i l l probably preclude their use i n engineering designs. Simpler and more e a s i l y 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 t h e c o l l e c t i o n of a e r o s o l s by a g r a n u l a r bed i s  based on a s i n g l e granule w i t h i n the bed. efficiency The  (EBT) i s f i r s t  The o v e r a l l bed c o l l e c t i o n  r e l a t e d t o t h e 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 (EB).  l a t t e r i s then expressed  i n terms of d i m e n s i o n l e s s  t e r i z e the d e s i g n and o p e r a t i n g  of a e r o s o l removal by g r a n u l a r beds  t h r e e s e t s o f f a c t o r s have t o be c o n s i d e r e d ,  medium. The  charac-  c o n d i t i o n s of the bed.  In d e f i n i n g t h e f i l t r a t i o n p r o c e s s  particles,  groups, which  ( i ) the dispersed a e r o s o l  ( i i ) t h e d i s p e r s i o n medium or f l u i d ,  and ( i i i ) t h e c o l l e c t i o n  I n t h i s study o n l y s p h e r i c a l a e r o s o l s and c o l l e c t o r s a r e c o n s i d e r e d .  d i s p e r s i o n medium i s a i r a t atmospheric temperature and p r e s s u r e , t h e  e f f e c t s of temperature and p r e s s u r e v a r i a t i o n s b e i n g assumed n e g l i g i b l e .  3.2  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) as a F u n c t i o n of t h e  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 (EB) In order t o determine t h e 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 o f t h e bed i s used. uniform bed  granules  (diameter  The bed c o n s i s t s of a t h r e e d i m e n s i o n a l d ) o f a depth H. c  a r r a y of  The v o i d a g e f r a c t i o n of t h e  i s e and each c o l l e c t o r e x h i b i t s a c o l l e c t i o n e f f i c i e n c y of EB. The  a n a l y s i s i s based on an a e r o s o l p a r t i c l e b a l a n c e  element of bed (see F i g . 3.1).  32  over a v e r y  small  33 U  Cout  U/e,  H  U  Figure 3.1.  dh  C  Cin  Schematic Diagram of the Granular Bed  The rate of aerosol removal i s equal to the rate of change of the number of aerosol p a r t i c l e s entering and leaving, the element.  Therefore  for  a unit cross section of bed i t can be written U dC = - C(U/e) EB x As dh where  [3.1]  U = s u p e r f i c i a l gas v e l o c i t y  U/e  = i n t e r s t i t i a l gas v e l o c i t y  C = aerosol concentration i n the element As = projected area of a c o l l e c t o r into the d i r e c t i o n of flow x = number of c o l l e c t o r s per unit volume of bed = 6(1 - e)/(ttThe rate of removal of aerosol p a r t i c l e s by the element for a unit cross-section of bed can be derived i n the following manner. The t o t a l area of c o l l e c t o r 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 c o l l e c t o r s per unit time i s (U/e) EB x As  dh.  Since the concentration of the aerosol i s C, the rate of removal of aerosol i s given by C(U/e) EB x As  dh.  Integrating equation 3.1 over the whole bed we have  34 C o u t / C i n = exp (- x As EB H/e)  [3.2]  where C = C i n at h = 0 C = Cout a t h = H S i n c e x = 6 (1 - e)/(M d and  3 c  )  As = M d /4 i t f o l l o w s c 2  that  C o u t / C i n = 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 g i v e n by EBT = ( C i n - C o i i t ) / C i n = 1 - exp {- 1.5(1 - e)H EB/e d^} Some workers p r e f e r  t o use t h e bed p e n e t r a t i o n  [3.4]  (P) t o express the  performance o f a g r a n u l a r bed, which i s d e f i n e d as P = 1 - EBT = C o u t / C i n  [3.5]  E q u a t i o n 3.4 can be r e a r r a n g e d t o g i v e EB = - l n ( l - EBT) d^ e / 1 . 5 ( l —  e)H  [3.6]  E q u a t i o n 3.6 a l l o w s t h e 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 t o be c a l c u l a t e d EBT, e, H and dC a r e e i t h e r 3.3  Calculation and  once  known or measured.  of 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 B a s i c Design  Operating Variables  In order t o c a l c u l a t e  the s i n g l e  collector efficiency  based on the d e s i g n and o p e r a t i n g v a r i a b l e s  (EB) an e q u a t i o n  of t h e f i l t e r must be developed.  In t h i s study two methods of p r o d u c i n g t h i s e q u a t i o n were c o n s i d e r e d . first  assumes that  one another. contribution  the i n d i v i d u a l  c o l l e c t i o n mechanisms a c t i n d e p e n d e n t l y o f  T h e r e f o r e the c a l c u l a t i o n  of EB c o n s i s t s  of c a l c u l a t i n g t h e  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 c o n s i d e r s the i n d i v i d u a l  c o l l e c t i o n mechanisms a r e i n t e r r e l a t e d basic  The  and EB i s c a l c u l a t e d  d i r e c t l y from t h e  variables. In t h e 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 a r e based on  the  d i m e n s i o n l e s s groups d e s c r i b i n g  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 : inertia  (EI) i s based on Re and S t ,  interception diffusion gravity  (ER) i s based  on Re and NR,  (ED) i s based on Re and Pe, and  (EG) i s based  on Re and NG.  I f e l e c t r i c a l e f f e c t s a r e i g n o r e d , then 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 can be estimated by simple summation. E  = E I + ER + ED + EG  [3.7]  However, t h i s summation i s an a p p r o x i m a t i o n and i s o n l y v a l i d when one mechanism dominates. of an i s o l a t e d  Furthermore,  as mentioned  i n Chapter 1, t h e e f f i c i e n c y  c o l l e c t o r d i f f e r s when i t i s surrounded by o t h e r  collectors.  T h e r e f o r e t h e v a l u e o f E must be m o d i f i e d by some c o r r e c t i o n f a c t o r t o o b t a i n the t r u e 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 w i t h i n the bed (EB).  F o r example,  Eq. 3.7 may be r e w r i t t e n as EB =  ai  ED + a  2  ER + a  3  ED + a  4  EG  [3.8]  or EB = a E U s i n g t h e s e methods many e q u a t i o n s w i t h v a r y i n g degrees  [3.9] (see Chapter 2) have been developed  of a c c u r a c y and a p p l i c a b i l i t y .  S e v e r a l forms of t h e s e  equations were f i t t e d by m u l t i p l e r e g r e s s i o n t e c h n i q u e s t o the e x p e r i m e n t a l r e s u l t s o f t h i s study and w i l l be d i s c u s s e d i n Chapter 7. The a l t e r n a t e method i s t o develop equations from b a s i c v a r i a b l e s as gas v e l o c i t y , a e r o s o l and c o l l e c t o r p r o p e r t i e s . efficiency problem  The s i n g l e  such  collector  (EB) was c a l c u l a t e d d i r e c t l y from these v a r i a b l e s and a v o i d e d t h e  o f having t o combine the e f f e c t s o f t h e i n d i v i d u a l mechanisms.  t h i s case t h e v a l u e of EB was determined EB = f ( d . , d  In  u s i n g an e q u a t i o n of the form:  U)  E q u a t i o n s of t h i s type were a l s o f i t t e d  [3.10] t o the e x p e r i m e n t a l 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 r e l a t i o n between a dependent variable Y and a set of independent variables X±, X X3  2  ,  . . . X ^ where n i s the number of independent variables. A relation Y =a + 0  a  of the form i  X + a x  2  X + a 2  3  X  3  ... a  n  X  [3.11]  n  i s chosen where the intercept of the regression equation i s a efficients 0 4 , a  2  ...  0  and the co-  are estimated by the least squares method.  In the  present work the dependent variable i s the single c o l l e c t o r e f f i c i e n c y EB and the independent variables are either the dimensionless groups St, ND, NR etc. or combinations of the basic v a r i a b l e s , i . e . , d /U. 2  a  The programme reads m sets of data i n the form of EB and the corresponding independent variables and places them i n a matrix of the form  Xl  x  Xll  x  x  X  lm  x  3  Y  X  n  21  X  1 2  x  2  X 1 3  x 2  2  2m  x  3 2  3m  X  nl  X  n2  Yi Y  2  Y  X  nm  m  The l i n e a r regression of Y on two or more independent variables i s c a l l e d the multiple l i n e a r regression.  The general form of a multiple l i n e a r  regression 1s:V, , = a n + a-, Xi-•• + a? Xo-» + ... a X . Y.X n m T  1  1J  [3.12]  37 where V a  Y •X  0>  a  i s the mean of Y c a l c u l a t e d from the r e g r e s s i o n , and  l>  a  •••  a  a  r  e  d e s c r i b e d as p o p u l a t i o n parameters  To i n d i c a t e t h a t the i n d i v i d u a l v a l u e s of Y v a r y about the mean, i t can be w r i t t e n as Y  x  = a n + a - i X i i + a ? X o i ... a  E q u a t i o n 3.13 (V  Y. X  n  X  . + ei nx  i m p l i e s that/any Y v a l u e i s due  [3.13] to the r e g r e s s i o n mean  ) p l u s a d e v i a t i o n from the mean ( e i ) . i_  The v a l u e s of c t , c t i . . . u  l a t i o n i s measured.  n  a  n  cannot be o b t a i n e d u n l e s s the whole popu-  From a sample, taken from the p o p u l a t i o n , the b e s t  e s t i m a t e s of these parameters are gg,  3i •••  3 •  B  Y  the l e a s t  squares  p r i n c i p l e these e s t i m a t e s a r e chosen to produce the l e a s t p o s s i b l e v a l u e f o r the sum . . .  a i  of the squares  0  , i.e., n n E e i = min 1=1  n E 1=1  (Yi - g  From Eq.  one  can determine the approximate v a l u e s of a  a  1  2  3.14  by d i f f e r e n t i a t i n g 3];» 3  of e i ( i = 1, 2 ... n) when s u b s t i t u t e d f o r a ,  2  matrix  •••  a n c  ^  3 •  0  - e  x  Xii - g  2  X i 2  ... 3 n  the e q u a t i o n f i r s t w i t h r e s p e c t to g , 0  S o l v i n g f o r the v a l u e s of g , 0  g^  ...  X n  .)  [3.14]  2  l  and  n  , 04  ...  a  n  then to  g^ i s done by  i n v e r s i o n c a r r i e d out by the programme. The programme has  the f a c i l i t y to e l i m i n a t e v a r i a b l e s i f the i n v e r s i o n  causes the m a t r i x to become s i n g u l a r . ables i f t h e i r regression c o e f f i c i e n t v a l u e of Y^ to be  The programme a l s o e l i m i n a t e s v a r i causes t h e i r c o n t r i b u t i o n to the  negligible.  In o r d e r to s e l e c t the best e q u a t i o n f o r p r e d i c t i n g v a l u e s of Y_^ programme p r o v i d e s c a l c u l a t i o n s of the standard  e r r o r of the  the  estimate,  r e s i d u a l v a r i a n c e , m u l t i p l e c o r r e l a t i o n c o e f f i c i e n t and v a r i a n c e r a t i o  tests.  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) yU 2  : (1-e) F  c  P  U  c  a and b are constants which l i e i n the ranges 710 > a > 120 4 > b > 0.8 The exact values of a and b depend on the shape of the c o l l e c t o r p a r t i c l e s and randomness of packing.  CHAPTER 4  EXPERIMENTAL  4.1  WORK  O b j e c t i v e s of the E x p e r i m e n t a l Work The  e x p e r i m e n t a l programme was  designed  to i n v e s t i g a t e the removal of  a e r o s o l s suspended i n a moving gas by a f i x e d g r a n u l a r bed data which c o u l d be r e a d i l y a n a l y s e d . equations  and  Furthermore, i t was  to  hoped to  from t h i s data t h a t c o u l d be used f o r f u t u r e s c a l e - u p and  The  s p e c i f i c o b j e c t i v e s were to determine the e f f e c t  e f f i c i e n c y of  ( i ) bed depth,  ( i v ) c o l l e c t o r s i z e , and  ( i i ) gas v e l o c i t y ,  l n ( l - EBT)  on  design.  collection  O b j e c t i v e ( i ) i s use-  which can be w r i t t e n as  - e) EB H/e d  = - 1.5(1  develop  ( i i ) aerosol size,  (v) d i r e c t i o n of gas flow.  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,  generate  [4.1] c  T h e r e f o r e a graph of l n ( l - EBT) a g i v e n gas v e l o c i t y v o i d a g e , diameter  v e r s u s H should be l i n e a r because f o r  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  a l l remain c o n s t a n t f o r v a r y i n g bed depths.  show whether g r a v i t y was  a significant  collector  O b j e c t i v e (v) would  c o l l e c t i o n mechanism.  Many workers b e l i e v e d t h a t e l e c t r i c a l e f f e c t s p l a y a s u b s t a n t i a l r o l e i n  20 28 3(7 collection  '  '  , but were not sure how  experiments were t h e r e f o r e designed f i r s t p a s s i n g the a e r o s o l through column of copper was spheres.  The  present  to minimize a l l e l e c t r i c a l e f f e c t s  a charge n e u t r a l i z e r .  used to support  In t h i s way  to q u a n t i f y i t .  by  In a d d i t i o n , a  the g r a n u l a r bed made up of m e t a l l i c  the whole apparatus  c o u l d be e a r t h e d .  e f f e c t s were t h e r e f o r e c o n s i d e r e d n e g l i g i b l e and  39  ignored.  The  electrical  40 4.2  Range of Variables Studied The range of variables studied are summarized i n Table VI. TABLE VI.  RANGE OF VARIABLES STUDIED  Variable  4.3  Range  Aerosol diameter  0.1 - 2.0 ym  Collector diameter  126 - 598 ym  Gas v e l o c i t y  5 - 7 0 cm/sec  Bed depth  0.3 - 18 cm  Experimental Apparatus Figure 4.1 gives a flow diagram of the equipment used for carrying out  the experiments at s u p e r f i c i a l gas v e l o c i t i e s ranging from 5 to 27 cm/sec. Details of purchased equipment are given i n Table VII and of the p a r t i c l e s and collectors i n Table VIII. After leaving the generator the aerosol was mixed with f i l t e r e d bench a i r to produce the required gas flow through the granular bed.  Because of  the o v e r a l l pressure drop throughout the system and the much higher flow of bench a i r , i t was found that a back pressure was produced which prevented the flow of aerosol into the column.  To remedy t h i s , a small diaphragm pump was  used to pass the aerosol into the main a i r flow. The dusty gas was then passed through a neutralizer to remove residual e l e c t r i c a l charges from the aerosol p a r t i c l e s .  The neutralizer was simply a  chamber containing a radioactive source (1 m i l l i c u r l e of Krypton 85 gas). The Krypton gas was sealed i n a stainless s t e e l tube at atmospheric pressure. The aerosol then passed through copper tubing to the column.  To vary  the flow rate through the bed, a i r could be bled o f f v i a 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 PUMP 5 - SAMPLE AIR FILTER 6 7 - CHARGE NEUTRALIZER 8 - GAS VELOCITY REDUCER 9 - GAS ROTAMETER BED 10 - GRANULAR 1 1 - FLOW CONTROL VALVE 12 - SAMPLE VALVE >  12  -  1  1 8 1  FILTERED Fig. 4.1  SAMPLE  9  AIR  Schematic Diagram of Equipment  AIR  42 TABLE VII.  Aerosol p a r t i c l e generator Aerosol p a r t i c l e sensor Aerosol p a r t i c l e monitor D i g i t a l display Charge neutralizer Hygrometer O i l l e s s diaphragm pump Vacuum pump  TABLE VIII.  598.1 511.0 363.9 216.1 126.0 1800.0  Roy co Royco Roy co Royco Sierra Instruments Panametrics Gast Mfg. Corp. Gast Mfg. Corp.  256 241 225 264 7330 2000 DAA110 0522-V4-G180DX  PARTICLES AND COLLECTORS Supplier  Aerosol P a r t i c l e Size ym  Collector Size ym  Model  Manufacturer  Equipment  0.109 0.500 0.600 0.804 1.011 2.020  PURCHASED EQUIPMENT  Dow Dow Dow Dow Dow Dow  Chemical Chemical Chemical Chemical Chemical Chemical  Co. Co. Co. Co. Co. Co.  Supplier  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.  Material  Polystyrene Polystyrene Polystyrene Polystyrene Polystyrene Polyvinyltoluene  Material  Nickel powder Nickel powder Nickel powder Nickel powder Nickel powder Lead shot  43 rates at the aerosol generation section and ensured a constant aerosol concentration 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 b a s i c a l l y a 7.6 cm diameter copper tube which could be e a s i l y separated into sections for introducing and removing the c o l l e c t o r p a r t i c l e s . The entering dusty gas was passed through a calandria to produce a uniform flow of gas before i t entered the bed.  The bed p a r t i c l e s were supported on  a fine wire mesh (approximately 64 ym aperture), which offered n e g l i g i b l e resistance to the gas flow at the measured gas v e l o c i t i e s .  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 i n l e t and outlet of the bed  and the pressure drop across the bed was measured by a mercury manometer. At the same l e v e l , but on the opposite side of the column, were placed the i n l e t s for the sample probes,(see F i g . 4.2). The column was suspended v e r t i c a l plane (see F i g . 4.4).  at i t s centre and could e a s i l y be rotated i n a This allowed the column to be operated i n  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 a l t e r i n g the sampling and manometer tubing. 4.3.2  Sampling  The gas was sampled before and after the bed.  Samples were removed  i n the d i r e c t i o n of the gas flow v i a 0.9 cm diameter sharp edged probes located i n the centre of the column. The gas was continuously removed at a low rate into small chambers and out into the atmosphere v i a rotameters.  From these chambers the gas could  44  h»  All Dimensions In  Fig. 4.2  76  »H  cm  Column Support for Granular Bed  All  Dimensions  Fig. 4.3  In cm.  Velocity Reducer  JL If  L DOWNFLOW  UPFLOW  An  i Fig. 4.4  Upflow and Downflow Operation of the Column  46 be sampled when necessary and directed to the p a r t i c l e 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 a i r 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 i s o k i n e t i c a l l y as calculations suggested that the sampling rate had a n e g l i g i b l e effect on the aerosol concentration for p a r t i c l e s less than about 5 ym diameter"*"^.  This was also confirmed by  a series of simple experiments. The purpose of the v e l o c i t y reducers (Fig. 4.3) was to dampen the v a r i a tions i n aerosol concentration within the column.  These variations were  caused by the aerosol generator and/or by deposited p a r t i c l e s breaking away from the equipment walls. The l i n e s and probes were made as i d e n t i c a l as possible f o r the i n l e t and outlet gas sampling t r a i n s .  Errors inherent i n the system would there-  fore be automatically eliminated when comparing aerosol counts. 4.4  Aerosol P a r t i c l e s 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 d i l u t e suspensions of the latex"particles. i)  These p a r t i c l e s were chosen because:  they are available i n uniform sizes with low standard deviations (see electron micrographs Figs. 4.5 to 4.11)  ii) iii)  they could be generated and handled e a s i l y they could be generated at low concentrations which minimizes p a r t i c l e agglomeration and bed loading.  47  F i g . 4.5  Fig. 4.6  Electron Micrograph of 0.109 ym diameter Latex P a r t i c l e s (Mag. 30,000 x)  Electron Micrograph of 0.50 ym diameter Latex P a r t i c l e s (Mag. 8,000 x )  F i g . 4.8  Electron Micrograph of 0.804 ym diameter Latex P a r t i c l e s (Mag. 8,000 x)  F i g . 4.10  Electron Micrograph of 2.02 ym diameter Latex P a r t i c l e s (Mag. 4,000 x)  From t h e e l e c t r o n micrographs i t can be seen t h a t the p a r t i c l e s a r e s p h e r i c a l , smooth and f a i r l y uniform.  However, i n some cases  4.10) a few v e r y much s m a l l e r p a r t i c l e s a r e a l s o p r e s e n t .  ( F i g s . 4.8 and  P r o p e r t i e s of  p a r t i c l e s used a r e summarized i n T a b l e IX.  TABLE IX.  PROPERTIES OF PARTICLES USED  Diameter ym  Material  4.5  Granular  Standard Deviation  Density 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  Bed P a r t i c l e s  I n i t i a l t e s t s were c a r r i e d out w i t h 1.8 mm diameter l e a d  shot.  However, most experiments were performed w i t h n i c k e l shot o b t a i n e d S h e r r i t t Gordon Mines L t d .  from  The s i z e s used a r e g i v e n i n T a b l e X.  F i g u r e s 4.11 t o 4.16 a r e e l e c t r o n micrographs o f each c o l l e c t o r . can be seen t h a t they a r e f a i r l y u n i f o r m  and s p h e r i c a l .  It  The s u r f a c e s a r e  q u i t e smooth but t h e l a r g e r c o l l e c t o r s e x h i b i t some s u r f a c e  irregularities  which may i n c r e a s e t h e i r a b i l i t y t o c c o l l e c t a e r o s o l s by p r o v i d i n g more surface  4.6  area.  Aerosol The  Generator  a e r o s o l was generated  from a purchased h y d r o s o l o f l a t e x p a r t i c l e s  a f t e r d i l u t i o n w i t h d i s t i l l e d water distilled  water).  (about  0.1 ml o f h y d r o s o l t o 30 ml o f  The d i l u t e d h y d r o s o l was atomized w i t h c l e a n a i r i n a  Royco a e r o s o l generator  model 256.  The atomizer  c o n s i s t e d e s s e n t i a l l y of a  51 TABLE X.  CHARACTERISTICS OF NICKEL SHOT  Sieve Analysis ym-  % Material Retained on the Sieve  Collector  1  2  3  +600  45.8  9.7  0.1  -600 + 500  54.1  90.1  10.7  -500 + 300  0.1  0.2  86.1  -300 + 150  3.1  -150 + 106  4  5  0.8 97.8  6.0  1.9  89.2  - 106  4.8  Vol. Av. diameter ym Voidage  598.1  511.0  363.9  216.1  126.0  0.416  0.398  0.425  0.415  0.425  small neutralizer (or j e t pump) (see F i g . 4.17).  The input a i r causes a  p a r t i a l vacuum over the j e t that protrudes into the diluted hydrosol, so that water i s forced out of the j e t to be dispersed into vapour.  The water  vapour and standard p a r t i c l e s 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 a i r , which has been dried over anhydrous calcium sulphate and f i l t e r e d , i s added at two points i n a d i r e c t i o n that causes the a i r to flow i n a h e l i c a l pattern around the humid a i r from the atomizer.  The tube  has a number of constrictions so that the atomizer a i r and d r i e r a i r are thoroughly mixed.  At the end of the tube dehumidified a i r and suspended  p a r t i c l e s are drawn o f f . For normal operation of the aerosol generator the drier a i r flow rate was  set at ^ 20 1/min  and the atomizer a i r pressure at 5 p . s . i .  maximum aerosol supply pressure was only 5 p . s . i . 7 t i o n was set to about 10  Thus the  The aerosol concentra-  3 partlcles/M  but could easily be varied by  changing  F i g . 4.11  E l e c t r o n M i c r o g r a p h of 598 ym d i a m e t e r N i c k e l Shot (Mag. 15 x)  Fig.  Close up of a 598 ym diameter Nickel Shot (Mag. 80 x)  4.12  53  Fig. 4.14  Electron Micrograph of 363 ym diameter Nickel Shot (Mag. 20 x)  g. 4.15  Fig. 4.16  Electron Micrograph of 216 m (Mag. 40 x) y  diameter Nickel Shot  Electron Micrograph of 126 ym diameter Nickel Shot (Mag. 80 x)  55  DILUTE  HYDROSOL  OF LATEX ATOMIZER  AND  FILTER  ;<Js) AEROSOL MIXER TUBE  DRIER FLOW METER  ATOMIZER PRESSURE GAGE ATOMIZER PRESSURE VALVE  DISTILLED WATER  AIR DRIER  FILTER  PARTICLES  M  11 11 11  DRIER AIR VALVE  AEROSOL OUTPUT  Fig. 4.17 Block Diagram of Aerosol Generator  EXHAUST  56 (i) the drier a i r 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 p a r t i c l e s i n  a given volume of gas i n order to determine 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. The counter used was a Royco sensor model 241, which operates on the p r i n c i p l e of forward l i g h t scattering.  A sharply defined beam of l i g h t i s  focused onto a small sensitive volume called the sample c e l l (^0.5  x 1.0 x 4 mm).  through the c e l l  A l l aerosol p a r t i c l e s entering the sensor are passed  (see F i g . 4.18).  If no p a r t i c l e s are present, a l l the  l i g h t passes through to the l i g h t trap where i t i s absorbed.  If a p a r t i c l e  i s present, l i g h t i s scattered and i s able to by-pass the l i g h t trap.  By  means of two c o l l e c t i n g lenses the forward scattered l i g h t i s focused onto a photomultipller which generates a current pulse to drive a d i g i t a l counter. Coincidence errors a r i s e when more than one p a r t i c l e enters the c e l l at any one time.  In the case of the Royco counter this occurs at aerosol  concentrations ;greater than about 10  10  v  4.8  3 particles/m .  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 f l o a t s and r e c a l i b r a t i n g 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 s u f f i c i e n t amounts of 1 and 2 ym aerosol p a r t i c l e s .  Hence, instead of pumping the a i r  through the system, the a i r was drawn through i t by means of a vacuum pump (see  F i g . 4.19).  This arrangement presented some sampling problems and a l l  REFLECTOR  RELAY LENS FORMS SHARP IMAGE OF APERTURE IN THE SENSITIVE VOLUME  Fig. 4.18  1 '  Layout of Optics for Aerosol Analyser  COLLECTING LENSES FORM IMAGE OF PARTICLE ON PHOTOMULTIPLIER CATHODE FROM THE LIGHT THAT MISSES LIGHT TRAP  EXCESS AIR  INLET AIR  txH  2  I -COLUMN 2 - A E R O S O L GENERATOR 3 —GRANULAR BED 4-AEROSOL ANALYSER 5 —SAMPLE PUMP 6 - AIR FILTER 7 - CHARGE N E U T R A L I Z E R 8 - GAS VELOCITY REDUCER 9 - GAS ROTAMETER 1 0 - V A C U U M PUMP I I-FLOW CONTROL VALVE 12-SAMPLE VALVE  Fig. 4.19  Schematic Diagram of Modified Equipment  59 the outlet lines had to be connected to the pump.  As the sample pump i n the  aerosol counter was not powerful enough to draw samples from the equipment, i t s discharge l i n e was also connected to the vacuum pump.  Set up i n this  manner, the operation of the equipment was v i r t u a l l y the same as before. Additional equipment was used to generate humidified a i r . humidity a simple spray nozzle was added to the i n l e t gas supply.  To vary the Water  was sprayed into the main a i r flow and the damp a i r and water droplets passed into a cyclone.  Water droplets were removed from the base of the cyclone  and the humidified a i r passed through a f i l t e r before being mixed with the aerosol flow (see F i g . 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 -BH  INLET  AIR H  T SPRAY CHAMBER  CYCLONE  DRAIN  Fig. 4.20  Humidifying Equipment  FILTER  CHAPTER 5 PRELIMINARY  EXPERIMENTS  A series of experiments was carried out to develop a consistent experimental procedure and to become f a m i l i a r i z e d with the equipment. 5.1  The Effect of Humidity on Collection  Efficiency  If e l e c t r i c a l charges were present i n the equipment or on the aerosol p a r t i c l e s , then changes i n humidity should affect the c o l l e c t i o n e f f i c i e n c y . For instance, i f e l e c t r i c a l charges were helping c o l l e c t i o n then damp a i r , which would more easily disperse these charges, would produce a lower c o l l e c tion e f f i c i e n c y than dry a i r . However, based on several tests  (see Tables XI and XII) no s i g n i f i c a n t  difference i n c o l l e c t i o n e f f i c i e n c y could be detected by changes i n humidity. These results suggest that the aerosols and collectors are e l e c t r i c a l l y neutral and that the e l e c t r i c a l effects may be ignored. It was realized that humidity could also affect the retention forces between the p a r t i c l e and the c o l l e c t o r by a l t e r i n g the nature of the absorbed f i l m of water on the c o l l e c t o r surface. at the beginning and end of a l l subsequent 5.2  The humidity was therefore recorded experiments.  Bed Ageing or Loading 23 It has been reported  that a b u i l d up of dust i n the i n t e r s t i c e s of  granular beds increases the c o l l e c t i o n e f f i c i e n c y as well as the pressure drop across the bed.  These effects usually occur at aerosol concentrations very 61  62 TABLE XI.  Gas Velocity cm/sec  COLLECTION EFFICIENCY OF 598.1 ym NICKEL SHOT AT VARIOUS HUMIDITIES (Bed depth = 4.5 cm; Aerosol diameter = 0.5 ym)  Collection Humidity Relative Humidity 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.  Gas Velocity cm/sec  COLLECTION EFFICIENCY OF 511.0 ym NICKEL SHOT AT VARIOUS HUMIDITIES (Bed depth = 9.1 cm; Aerosol diameter = 0.5 ym) Collection Efficiency Relative Humidity 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 i n the present work. i n a l l experiments the bed loading was extremely small.  Thus  For example, i t  would take about two years for one gram of 2.02 ym p a r t i c l e s to be deposited assuming t y p i c a l operating conditions and a 100% removal e f f i c i e n c y . Nevertheless, long term tests were conducted on each c o l l e c t o r and Tables XIII and XIV summarize the results performed with two c o l l e c t o r s . As can be seen, no s i g n i f i c a n t change i n c o l l e c t i o n e f f i c i e n c y was observed. TABLE XIII.  Gas Velocity cm/sec 5.24 11.16 16.97 22.37 27.08  0 46.3 37.1 36.7 32.1 33.7  3 44.7 37.8 38.3 34.4 38.0  BED AGEING TESTS ON 598 ym NICKEL SHOT (Bed depth = 9.1 cm; Aerosol diameter = 0.500 ym)  Collection E f f i c i e n c y Time Hours 12 8 9.5 5 40.2 35.3 32.3 30.7 32.6  40.9 36.1 31.3 32.9 32.5  TABLE XIV.  41.9 34.5 32.9 31.5 33.0  43.5 35.7 33.0 30.9 32.8  14  16  18  41.3 32.8 32.8 35.7 33.7  43.0 32.9 32.9 31.2 30.3  45.2 39.2 35.0 31.0 33.4  BED AGEING TESTS ON 216.0 ym NICKEL SHOT (Bed depth = 2.27 cm; Aerosol diameter = 0.500 ym)  Gas Velocity cm/sec  0  5.24 11.16 16.97 22.37 27.08  88.2 80.1 76.3 72.3 71.6  Collection E f f i c i e n c y Time Hours 3 6 86.5 77.2 75.9 71.8 68.1  85.5 78.0 74.9 71.4 69.0  86.2 80.5 75.9 74.3 70.1  64 5.3  C o l l e c t i o n by the Empty Column and Bed Support Several empty column tests were carried out to determine the removal  of p a r t i c l e s 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 Velocity cm/sec  Collection Efficiency Aerosol diameter ym 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 c o l l e c t i o n e f f i c i e n c y 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 i n the system from (i) p a r t i c l e s depositing i n the i n l e t tubing and subsequently breaking away, ( i i ) incomplete f i l t r a t i o n of the bench and aerosol d r i e r a i r ,  ( i i i ) impure d i s t i l l e d water  (used i n d i l u t i o n of the latex hydrosol), (iv) leaks of a i r into the equipment , or (v) e l e c t r i c a l noise generated within the aerosol detection equipment.  Prior to each experiment background counts were therefore determined.  The counts usually varied between 20-40 particles/minute which i s n e g l i g i b l e i n 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.  I f this was the case, then the presence of the droplets  would modify the measured c o l l e c t i o n e f f i c i e n c y of the bed. therefore performed  to determine i f this was taking place.  Tests were 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 i s no detectable difference from the background count. TABLE XVI.  BACKGROUND COUNTS FOR THE EMPTY COLUMN (Gas v e l o c i t y = 27 cm/sec)  Aerosol generator not used  Av.  5.5  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. 32.4  32  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  fell  within ± 5% of each other) then 4-8 readings were taken and averaged. After sampling the i n l e t 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 s t a b i l i z e before counts could be recorded a f t e r each changeover.  Waiting for 1, 2, 5 and 10 minutes between each  changeover gave no noticeable difference i n measured counts.  A waiting time  66 of one minute between changeovers was  5.6  therefore adopted.  Reproducibility Several tests were repeated three to four months l a t e r 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 i n 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 v e l o c i t y ranges with the low v e l o c i t y tests covering 5 to 27 cm/sec and the high v e l o c i t y 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 e r r a t i c a l l y .  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 l a t e r 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 o v e r a l l  aerosol deposition and hence the c o l l e c t i o n e f f i c i e n c y of the bed.  If  these effects were taking place, then the recorded e f f i c i e n c i e s would be lower than their true value.  It was possible to check to see i f re-  entrainment was occurring by shutting o f f 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 l i t t l e , i f any, re-entrainment was  taking place.  shut off which implies that However, bounce-off i s a  d i f f e r e n t phenomena.  It occurs when a p a r t i c l e c o l l i d e s with a c o l l e c t o r  but i s not retained.  This effect i s usually only observed with dry, s o l i d  aerosols.  Using s t i c k y , l i q u i d aerosols such as d l o c t y l phthalate (D.O.P.)  bounce-off could be eliminated. bounce-off was  occurring by comparing results of tests conducted with dry and  l i q u i d aerosols. generator was  Thus i t would be possible to determine i f  This was  not done i n this study as the available aerosol  not capable of producing  l i q u i d aerosols.  Further small errors are summarized below, i)  Aerosol counter:-As mentioned before, errors could be introduced  by  the 'interference' effect or by p a r t i c l e s depositing on the o p t i c a l surfaces of the analyser.  This would usually occur at high aerosol concentrations.  The period for counting the aerosols was  set e l e c t r o n i c a l l y with the d i g i t a l  counter being stopped automatically after one minute and therefore timing errors were n e g l i g i b l e . ii)  Gas flow-:-Small  rotameters.  errors could be caused by i n c o r r e c t l y reading the  Also fluctuations i n the bench a i r supply could cause errors  and could contribute to the e r r a t i c behaviour of the aerosol iii)  Non  generator,  i s o k i n e t i c sampling:-This could cause a small error i n the measured  counts but i s most u n l i k e l y , especially with aerosols below 2 ym i n diameter. Errors within the sampling equipment were minimized by making the i n l e t outlet sampling t r a i n s as i d e n t i c a l as possible.  and  68 5.8  Experimental Programme 5.8.1  Procedure  From the preliminary experiments a test procedure was developed. Each experiment involved the measurement of c o l l e c t i o n e f f i c i e n c y for various s u p e r f i c i a l gas v e l o c i t i e s at different bed depths and was repeated for a range of aerosol and c o l l e c t o r  sizes.  Details of a t y p i c a l 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.  ii)  A measured volume of s p e c i f i c c o l l e c t o r p a r t i c l e s was charged to the column and f l u i d i z e d to give a loosely packed bed.  I f necessary the  surface was l e v e l l e d without compressing the bed. iii) iv)  The column was set up i n an upflow or downflow mode (see Chapter 4). A d i l u t e hydrosol mixture of a s p e c i f i c 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) vii)  P a r t i c l e counts were taken to measure the background  count,  The aerosol generator and pump were turned on and the humidity of the exit gas from the column was measured.  Also the a i r temperature was  noted. viii)  The p a r t i c l e counts/minute were monitored for the i n l e t a i r u n 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 s t a b i l i z a t i o n .  x)  Further 4 to 8 readings were taken,  The sample flow was changed back to the Inlet gas to check the counts for consistency.  xi) xii)  69 The pressure drop across the column was measured for each.gas v e l o c i t y , The gas v e l o c i t y was then reduced and steps ( v i i i ) to ( x i i ) repeated. 5.8.2  Programme  For each c o l l e c t o r the tests summarized i n Table XVII were carried out.  TABLE XVII.  SUMMARY OF EXPERIMENTAL TESTS  0.109  Test Downflow: Low v e l o c i t y High v e l o c i t y  Aerosol diameter ym 0.500 0.600 0.804 1.011  X  X  X  X  Upflow: Low v e l o c i t y High v e l o c i t y Bed depth  X  X X  X  X  Humidity test  X  Ageing test  X  X X  X  X  X  2.020  X  X  X  X  Low v e l o c i t y configuration•:—5 to 27 cm/sec High v e l o c i t y configuration:-16.33 to 67.0 cm/sec Bed depth test-:-For aerosols 0.109, 0.600 and 0.804 ym i n . diameter only two depths were used;  for 0.500 ym aerosol four to f i v e  depths were used. Humidity test •:-This involved comparing the c o l l e c t i o n of 0.500 ym aerosol with dry and damp a i r .  A l l other tests were carried out  at ^ 30-40% r e l a t i v e humidity. Ageing test  :-This involved runs of up to 18 hours duration and measuring the c o l l e c t i o n e f f i c i e n c y 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 i n  Appendix A. values.  When tests were duplicated, the shown results are averaged  Unless otherwise stated, a l l the figures i n t h i s section show  results f o r experiments conducted i n the downflow mode.  6.2  The Effect of S u p e r f i c i a l Gas Velocity on Bed Collection E f f i c i e n c y Figs. 6.1 to 6.10 show the c o l l e c t i o n e f f i c i e n c y of the granular beds  as a function of s u p e r f i c i a l gas v e l o c i t y for various c o l l e c t o r s and aerosol particles.  Figs. 6.1 to 6.5 refer to the low v e l o c i t y tests only.  Figs.  6.6 to 6.10 refer to both the high and low v e l o c i t y tests for upflow and downflow. The  c h a r a c t e r i s t i c shape of the e f f i c i e n c y curve (see F i g . 2.1) was  not observed i n the i n i t i a l low v e l o c i t y tests.  Figs. 6.1 to 6.5 show a  steady decrease i n c o l l e c t i o n e f f i c i e n c y with no subsequent r i s e due to increasing  i n e r t i a l effects.  Therefore, additional high v e l o c i t y  tests  were performed i n order to study p a r t i c l e c o l l e c t i o n i n the i n e r t i a dominated region. From Figs. 6.6 to 6.10, which cover the f u l l range of v e l o c i t i e s i t i s clear that the e f f i c i e n c y curves can be divided  tested,  into two regions.  At  low v e l o c i t i e s the c o l l e c t i o n e f f i c i e n c y decreases with increasing gas v e l o c i t y due to the reduced d i f f u s i o n a l effect and, perhaps, g r a v i t a t i o n a l 70  71  0  10 SUPERFICIAL  Fig. 6.1  20 GAS  VELOCITY  30 cm/sec  Collection E f f i c i e n c y as a Function of Gas Velocity (Bedcdepth = 4.54 cm; c o l l e c t o r diameter = 598.1 ym)  72  10 SUPERFICIAL Fig. 6.2  20 GAS V E L O C I T Y  30 cm/sec  Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 4.54 cm; c o l l e c t o r diameter = 511 ym)  73  0  10 SUPERFICIAL  Fig. 6.3  30  20 GAS  VELOCITY  cm/sec  Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 4.54 cm; c o l l e c t o r diameter =• 363 ym)  Fig. 6.4  Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 2.27 cm; collector diameter = 216 ym)  75  Fig. 6.5  Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 2.27 cm; c o l l e c t o r diameter = 126 ym)  SUPERFICIAL Fig. 6.6  GAS VELOCITY  cm/sec  Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 4.54 cm; c o l l e c t o r diameter = 598 ym)  ON  COLLECTION  LL  EFFICIENCY  %  COLLECTION  o  (TO ON 00  w o fD & fD TJ rt  ro o  hhfD  1 1  n  c tJ m  rt H" O  11 W hh i-h HO HfD  o OJ > o r~  -P• Ui -f>  Q  3  B o  >  n w o  t_> ft)  M fD  o rt  <  m r~ o o  trj  c 0  o o  4* O  i-i rt H. 3 CL 0> O  3 o  ro  HI  ro  en  rt  o 3  i-i cu  ll  co  <  W fD ON I— 1  u> o o B rt  o  °  O  3 21  EFFICIENCY  %  100 h-  20  10  30  40  SUPERFICIAL GAS VELOCITY Fig. 6.10  50  60  70  cm/sec  Collection E f f i c i e n c y as a Function of Gas Velocity (Bed depth = 2.27 cm; c o l l e c t o r diameter = 126 ym) CO o  81 effect for the larger aerosol p a r t i c l e s . v e l o c i t i e s between about 15 and i n e r t i a l effects are weak.  Minimum c o l l e c t i o n occurs at  20 cm/sec where both the d i f f u s i o n a l  As the gas v e l o c i t y increases the  gas  and  collection  e f f i c i e n c y starts to r i s e again because the i n e r t i a l effect becomes dominant.  It may  be noted that, as the aerosol size increases, the v e l o c i t y  minimum c o l l e c t i o n decreases.  of  For example, i n case of 598.0 ym diameter  n i c k e l shot the v e l o c i t y for minimum c o l l e c t i o n i s about 12 cm/sec for 2 ym diameter aerosol p a r t i c l e s and  25 cm/sec for 0.5  ym diameter aerosol  particles. At v e l o c i t i e s greater than about 45 cm/sec the c o l l e c t i o n e f f i c i e n c y was  usually  found to l e v e l off or decline.  This phenomena may  be caused by  bounce-off because re-entrainment i s unlikely for reasons mentioned i n Section  5.8.  6.3  Effect of Flow Direction  The  Figs. 6.6  to 6.10  on Bed  Collection  Efficiency  also show the results for the upflow (dashed lines)  as well as downflow ( s o l i d lines) experiments.  There i s a  substantial  decrease i n c o l l e c t i o n e f f i c i e n c y at the lower v e l o c i t i e s i n the upflow mode especially for the 1.01  ym aerosols.  becomes n e g l i g i b l e at high gas v e l o c i t i e s . p a r t i c l e the smaller the difference  The  difference  in collection  Also, the smaller the aerosol  between upflow and  downflow r e s u l t s .  Since the d i r e c t i o n of flow only influences the gravitational mechanism i t can be concluded that gravity  i s playing a s i g n i f i c a n t role i n  c o l l e c t i o n especially at low gas v e l o c i t i e s and  6.4  The  Effect of Aerosol Diameter on Bed  As seen from Figs. 6.1  to 6.10,  for large aerosols.  Collection  Efficiency  the c o l l e c t i o n e f f i c i e n c y 27 28  decreases with aerosol size.  collection  Many workers  '  usually  29 '  have pointed out  this trend stops at a certain aerosol size after which the  collection  that  82 e f f i c i e n c y starts to increase again due to the enhanced d i f f u s i o n a l e f f e c t . Figure 6.11 shows that no minimum i n the efficiency-aerosol detected i n this work.  size curves was  This may have been due to the lack of experimental 29  results at low gas v e l o c i t i e s and small aerosols.  Chen  has pointed out  that the minimum only occurs at gas v e l o c i t i e s less than about 4 cm/sec. 6.5  The Effect of Collector  Size on Bed Collection  Efficiency  As expected 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 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 i n e r t i a l , d i f f u s i o n a l and g r a v i t a t i o n a l  collec-  tion because the aerosol p a r t i c l e s need to t r a v e l smaller distances to reach the c o l l e c t o r surface.  It i s unlikely that sieving plays a s i g n i f i c a n t role  i n c o l l e c t i o n even f o r the larger.: aerosol p a r t i c l e s (2.02 ym i n diameter) and the smallest c o l l e c t o r p a r t i c l e s 6.6  (126 ym i n diameter).  The Effect of Bed Depth on Collection  Efficiency  Figs. 6.12 to 6.16 summarize the results of varying the bed depth f o r 0.5 ym diameter aerosol p a r t i c l e s and different gas v e l o c i t i e s . by Eq. 3.6, the data are plotted bed  depth (H).  As suggested  as log(100 - % c o l l e c t i o n e f f i c i e n c y ) versus  The results follow straight l i n e s , which pass approximately  through the point of zero c o l l e c t i o n e f f i c i e n c y at zero bed depth.  This i s  i n agreement with Eq. 3.6 whose v a l i d i t y i s therefore confirmed. At large bed depths some deviation from the straight l i n e behaviour occurs and Eq. 3.6 overpredicts the c o l l e c t i o n e f f i c i e n c y .  The deviation  i s accentuated by the log scale and only occurs when the e f f i c i e n c i e s exceed about 90%.  The effect may be due to the presence of a small f r a c t i o n of  undersize aerosol p a r t i c l e s i n the aerosol.  The electron micrographs  (Figs. 4.8 and 4.10) show that several smaller p a r t i c l e s are found together with the larger aerosol.  The c o l l e c t i o n e f f i c i e n c y f o r these smaller sized  0.5 AEROSOL Fig.  6.11  DIAMETER  1.0  2.0  /JLm  Collection E f f i c i e n c y as a Function of Aerosol Diameter at a S u p e r f i c i a l Gas Velcoity of 5.24 cm/sec.  0  5  10 BED  6.12  DEPTH  15  20  cm.  Collection E f f i c i e n c y as a Function of Bed Depth (Collector diameter = 598 urn, aerosol diameter =0.5  ym)  85  5  10 BED  Fig. 6.13  DEPTH  15  20  cm.  C o l l e c t i o n E f f i c i e n c y as a Function of Bed Depth (Collector diameter = 511 ym, aerosol diameter =0.5  ym)  Fig. 6.14  C o l l e c t i o n E f f i c i e n c y as a Function of Bed Depth (Collector diameter = 363 ym, aerosol diameter = 0.5  ym)  Fig. 6.15  Collection E f f i c i e n c y as a Function of Bed Depth (Collector diameter = 216 ym, aerosol diameter = 0.5  ym)  00  88  Fig. 6.16  Collection E f f i c i e n c y 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 i n a reduced, 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 especially at high removal rates. 6.7  Pressure Drop across the Granular Bed Pressure drops across the granular beds were measured for each gas  v e l o c i t y and the detailed results are given i n Appendix A.  From Fig. 6.17  i t can be seen that there i s a good l i n e a r relationship between AP/H and gas 80 velocity.  The results f i t an Ergun —  type equation of the following  + 1.73 —  = ,316 —p c  where the variables have the following  — c  form:  [6.1]  units:  AP/H = dynes/cm cm 2  d  c  = cm  U = cm/sec P  F  = gm/cc  y = gm cm/sec 80 The  c o e f f i c i e n t s 316 and 1.73 l i e within the range observed by others  For the v e l o c i t y range tested, viscous force dominates i n the granular bed as compared to i n e r t i a l e f f e c t s .  The pressure drop was attributable mainly to  viscous energy losses. 6.8 i)  Summary of Experimental Results At low gas v e l o c i t i e s (less than about 10 cm/sec) the c o l l e c t i o n e f f i c iency decreases with increasing  gas v e l o c i t y , probably due to decreasing  d i f f u s i o n a l and gravitational e f f e c t s , ii)  A minimum i s observed i n c o l l e c t i o n e f f i c i e n c y versus gas v e l o c i t y curves when d i f f u s i o n a l and i n e r t i a l effects are both weak,  iii)  The larger the aerosol size the lower the gas v e l o c i t y at which t h i s minimum c o l l e c t i o n occurs.  06  91 iv)  At higher gas v e l o c i t i e s (greater than about 20 cm/sec) c o l l e c t i o n e f f i c i e n c y increases with gas v e l o c i t y because i n e r t i a l  effects  become dominant. v)  The c o l l e c t i o n e f f i c i e n c y increases with increasing aerosol size and decreasing c o l l e c t o r size,  vi)  The c o l l e c t i o n e f f i c i e n c y increases with bed depth as predicted by Eq.  vii)  3.6.  As the c o l l e c t i o n e f f i c i e n c y for downflow i s always greater than upflow at low gas v e l o c i t i e s , i t i s evident that gravitational s e t t l i n g was  viii)  playing a role i n the f i l t r a t i o n ,  For the range of conditions studied, direct interception played role i n the f i l t r a t i o n .  no  CHAPTER 7  STATISTICAL  7.1  ANALYSIS  Introduction From the experimental results i t was  possibly,  and,  a t h e o r e t i c a l model to predict aerosol c o l l e c t i o n i n granular beds.  The model would be based on variables aerosol properties and The  hoped to develop an empirical  o v e r a l l bed  such as bed  depth, gas  velocity,  c o l l e c t o r dimensions. c o l l e c t i o n e f f i c i e n c i e s (EBT), which were determined  experimentally, were f i r s t reduced to single c o l l e c t o r e f f i c i e n c i e s (EB) means of Eq. 3.6.  Since EB i s independent of bed  e f f i c i e n c i e s calculated conditions,  by  depth, the single p a r t i c l e  for d i f f e r e n t bed depths, but otherwise i d e n t i c a l  could be averaged.  As discussed i n Chapter 1, the following  dimensionless groups govern  p a r t i c l e c o l l e c t i o n i n granular beds and were calculated experimental conditions: Interception number (NR);  for each set of  Reynolds number (Re); Stokes number (St); Peclet number (Pe); and Gravity number  These dimensionless groups and  (NG).  single c o l l e c t o r e f f i c i e n c i e s are  tabulated i n Appendix B. 7.2  Evaluation of Various Empirical  Equations  Most workers have concentrated on calculating the individual c o l l e c t i o n e f f i c i e n c i e s due  to i n e r t i a , d i f f u s i o n , gravity and  them to give an o v e r a l l single c o l l e c t o r e f f i c i e n c y . the various dimensionless numbers and 92  interception,  and summed  Others have calculated  combined them i n such a manner as to  93 produce the single p a r t i c l e e f f i c i e n c y .  As pointed out before, neither  method i s e n t i r e l y correct, especially when working i n a region where the magnitude of the effects of several c o l l e c t i o n mechanisms are comparable. The equations developed by other workers were f i t t e d to the present experimental data using a multiple regression programme.  Other equations,  such as polynomials based on the gas v e l o c i t y , as well as aerosol and c o l lector diameters were also tested. The results of a l l regression analyses are summarized i n Appendix C. In general, these equations gave r e l a t i v e l y good f i t s when predicting the c o l l e c t i o n e f f i c i e n c y f o r a single c o l l e c t o r or aerosol size. the o v e r a l l f i t f o r a l l the experimental data was quite poor.  However, Consequently  there was a need to develop a more general equation.  7.3  I d e n t i f i c a t i o n of the Best Empirical Equation The best f i t of the experimental data was obtained with an equation of  the type: d d EB = aC-r-) (d U) + b (d U) d a d a c c 3  / / J  + c  d 2 U  [7.1]  with constants a = 660, b = 0.0148, c = 400,000, and a multiple correlation c o e f f i c i e n t (R) of 0.972.  (The development of t h i s equation i s given i n  Appendix D together with a comparison of the experimental and predicted collection efficiencies.) Equation 7.1 s a t i s f a c t o r i l y predicts the minimum i n the c o l l e c t i o n e f f i c i e n c y versus gas v e l o c i t y curves and the effect of gravity.  Some d i s -  agreement, however, arises at high v e l o c i t i e s , which could be due to bounceoff which i s not taken into  account.  The f i t i s worst f o r the 0.109 ym diameter aerosols which suggests that the d i f f u s i v e effect i s 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 p a r t i c l e counter was used as i t s l i m i t of detection.  (The manufacturer  recommends i t s use only for p a r t i c l e s  greater than 0.3 ym i n diameter.) Figs. 7.1 to 7.6 provide a comparison between some predicted (using Eqs. 3.6 and 7.1) and experimental bed c o l l e c t i o n e f f i c i e n c i e s .  F i g . 7.7  i s a scatter plot of a l l calculated e f f i c i e n c i e s versus experimental e f f i c iencies and the agreement i s 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 c o l l e c -  t i o n e f f i c i e n c i e s predicted by Eq. 7.1 agree with the lead shot results to within ± 1.5%.  Also l i s t e d i n Appendix D are comparisons of the predicted  bed c o l l e c t i o n e f f i c i e n c i e s and the experimental results of other researchers. 20 Comparisons were made with Figueroa's 7000 ym diameter sand.  data based on experiments  with  His other experimental results were not compared  since they were obtained with p l a s t i c bed p a r t i c l e s susceptible to e l e c t r i c a l 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 c o l l e c t o r p a r t i c l e s and D.O.P. aerosol p a r t i c l e s .  Equation 7.1 i s rather poor i n predicting the c o l l e c t i o n  e f f i c i e n c i e s of the 600 ym c o l l e c t o r s , except at the higher v e l o c i t i e s of 30 cm/sec.  The predictions are better for the 110 ym c o l l e c t o r s especially  for the removal of 1.75 ym diameter aerosols.  The poor predictions of  Doganoglu's r e s u l t s could be due to the fact that he used l i q u i d D.O.P. aerosol p a r t i c l e s whereas Eq. 7.1 i s based on dry, s o l i d aerosol p a r t i c l e s . However, this does not explain why i n general the prediction of Eq. 7.1 are higher than the experimental values;  using l i q u i d aerosols should i n fact  improve the c o l l e c t i o n e f f i c i e n c y of the bed.  10  20  30  40  SUPERFICIAL GAS VELOCITY Fig. 7.1  50  60  cm/sec  Comparison of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (Collector diameter = 598.1 ym)  70  Calc. Downflow Experimental A-I.ON  fJLm  • — .804/i.m O - .500/1 m  0  10  20  30 SUPERFICIAL  Fig. 7.2  40 GAS  VELOCITY  50  60  cm/sec  Comparison between Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (Collector diameter = 511.0 ym)  70  100 Calc. Downflow Experimental A-I.OII  Ltm  O—  .804 Li m  O—  .500/Jm  •  50 0  10  20  30 SUPERFICIAL  Fig. 7.3  40 GAS  VELOCITY  50  60  cm/sec  Comparison Between Experimental and Calculated Collection E f f i c i e n c i e s (Collector diameter = 363.9 ym)  -J  70  10  20  30  40  SUPERFICIAL GAS VELOCITY Fig. 7.4  50  cm/sec  Comparison of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (Collector diameter = 216.0 ym)  60  70  30  40  SUPERFICIAL GAS VELOCITY Fig. 7.5  50  60  cm/sec  Comparison of Experimental and Calculated Collection E f f i c i e n c i e s (Upflow and downflow; aerosol diameter = 0.804um; collector diameter = 511.0 ym)  70  SUPERFICIAL GAS VELOCITY Fig. 7.6  cm/sec  Comparison of Experimental and Calculated Collection E f f i c i e n c i e s (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 C o l l e c t i o n E f f i c i e n c i e s (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 i s  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 t h i r d term becomes a gravity number (NG). 1st term:  d  2  p  d  c 3rd term:  2  c  d p g d U _§_ = (_§_) = — TJ 18y U ' U 2  2  V  = NG  The second term i s more d i f f i c u l t to simplify and does not reduce e a s i l y to dimensionless form. EB = 1.018  Thus Eq. 7.1 becomes  St + 0.0148 NR(d  U)~  2 / 3  + 1.25 NG  The e f f i c i e n c y equation therefore consists of three terms.  [7.2] The f i r s t  and t h i r d terms represent the i n e r t i a l and g r a v i t a t i o n a l e f f e c t s , respectively.  The gravity term being p o s i t i v e for downflow and negative for  upflow.  The contribution of the gravity term to EB i s usually very small  and only becomes s i g n i f i c a n t for low gas v e l o c i t i e s and large or dense aerosols.  The contributions of the f i r s t and second terms are highly  dependent on gas v e l o c i t y .  The main contribution to EB i s due to the  second term at low v e l o c i t i e s and the f i r s t ities.  ( i n e r t i a l ) term at high veloc-  I t i s interestingito note that the interception term was  from a l l the equations by the regression analysis.  eliminated  Thus i t can be concluded  that d i r e c t interception was playing a n e g l i g i b l e r o l e i n the aerosol  fil-  t r a t i o n of this work. It i s rather d i f f i c u l t to explain the second term i n Eq. 7.1, which may be due to d i f f u s i o n even though i t cannot be reduced to a Peclet number or a similar dimensionless group.  It i s probably a combination term  r e f l e c t i n g both d i f f u s i o n and i n e r t i a .  103 7.4.1  Modification of the Second Term i n Equation 7.1  An attempt was made to introduce the Peclet number into the second term of Eq. 7.1.  I t i s simple to show that  i (d u)" = (% 2/3  d  c  a  ( ur  1/3  d c  c  2/3  d  Now the Peclet number i s defined as (d U/D ) where the d i f f u s i v i t y c a -2/3 of the aerosol p a r t i c l e i s denoted by D . proportional to d f o r the range 0.1 < d a l/3 . .-2/3 a (j-) ( d U) c a d  /  d  N  c  F i g . 7.8 shows that D  is  < 2.02 jjm. Hence , a,.l/3 .-2/3 (—) ( d U) c d  c  j 4/3 d  a  d  c .-2/3  c d  4  U  a /  3  a  .-2/3  c To render the term completely dimensionless, d  or d . SL  Dividing by d was found to give the best r e s u l t s for predicting  C  EB.  i t could be divided by  C  Thus Eq. 7.1 could be rewritten as EB = a.St + b.NR  4,/3  Pe~  2 / 3  + c.NG  [7.3]  and f i t t e d to the experimental data by regression analysis.  The following  values were found for the constants:  and c = 1.5.  a = 1.0;  b = 150,000;  Equation 7.3 gave equally good predictions of EB as Eq. 7.1, having a multiple c o r r e l a t i o n c o e f f i c i e n t (R) of 0.94.  F i g . 7.9 shows a scatter plot  of the calculated versus experimental c o l l e c t i o n e f f i c i e n c i e s using Eq. 7.3. 4/3 In the present experiments NR >> 1, and the second term i n Eq. 7.3 may be rewritten as: b Pe  /  3  b Pe  /  3  2  or  2  [1 - exp {- N R - b Pe  2  /  3  4/3  }]  exp {- NR  4/3  }  -2/3 The term b Pe b Pe ^ 2  3  represents  the d i f f u s i o n a l effects whereas  exp {- NR ^ } r e f l e c t s the i n t e r a c t i o n between d i f f u s i o n and i n e r t i a . 4  3  105  Fig.  7.9  Scatter Plot of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (using Eqs. 3.6 and 7.3)  106 Although Eq. 7.3 adequately predicts the c o l l e c t i o n e f f i c i e n c i e s obe served i n the present experimental work, i t does not predict a minimum c o l l e c t i o n e f f i c i e n c y with respect to aerosol diameter.  However, as noted  by several workers, this minimum c o l l e c t i o n e f f i c i e n c y i s only observed at low gas v e l o c i t i e s , i . e . , less than 4 cm/sec.  Therefore Eq.7.3's only  l i m i t a t i o n i s i t cannot be used for prediction of EB at gas v e l o c i t i e s below about 5 cm/sec.  For lower gas v e l o c i t i e s aerosol capture i s dominated by  the d i f f u s i o n a l mechanism and equations developed for purely d i f f u s i o n a l , 63,32,81 may be , usedA instead. • *. A deposition 69 A recent paper by Schmidt  discusses the use of an equation of the.,  type: EB = 3.97  St + (8 Pe"  + 2.3 R e  1  1 / 8  Pe~  5 / 8 )  + 1.45 NR + NG  [7.4]  This equation predicts a minimum i n EB with respect to aerosol diameter and i t was therefore f i t 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 R e  1 / 8  Pe"  5 / 8 )  + 1.25 NG  [7.5]  However Eq. 7.5 proved only applicable to aerosols i n the 0.5 to 1.0 ym diameter range; considerably poorer.  the f i t for 0.109 F i g . 7.10  0.5 to 1.0 ym diameter range. that obtained by Eq. 7.1 or 7.5  and 2.02  ym diameter aerosols was  shows a scatter plot for aerosols i n the It i s clear that the f i t i s much poorer than  7.3.  Conclusion An equation (Eq. 7.3) has been developed which predicts the c o l l e c t i o n  of 0.1 to 2.02  ym latex aerosols by beds of spherical c o l l e c t o r s i n the  range of 100 to 600 ym i n 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 s i m p l i c i t y and wide range of  107  Fig.  7.10  Scatter Plot of Experimental and Calculated C o l l e c t i o n E f f i c i e n c i e s (using Eqs. 3.6 and 7.5; aerosol diameters i n the range 0.1 to 5.0 ym)  applicability.  By comparison with other experimental data the equation i s  capable of predicting  c o l l e c t i o n e f f i c i e n c i e s for beds of spherical  tors up to 7000 ym i n diameter.  collec-  Unfortunately the equation i s unable to  determine an aerosol size which gives a minimum c o l l e c t i o n e f f i c i e n c y for a given gas v e l o c i t y .  Thus use of Eq. 7.3 should therefore be limited to gas  v e l o c i t i e s greater than about 5 cm/sec.  CHAPTER 8  CONCLUSIONS  i)  Granular beds of p a r t i c l e s 100 to 600 ym i n diameter were found to be highly e f f i c i e n t aerosol c o l l e c t o r s .  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 n i c k e l shot, having a pressure drop across the bed of 2.5 cm of mercury. ii)  At s u p e r f i c i a l gas v e l o c i t i e s below 10 cm/sec aerosol removal was found to be mainly due to d i f f u s i o n a l deposition, and, to a lesser extent, gravitational s e t t l i n g ,  iii)  At s u p e r f i c i a l v e l o c i t i e s greater than about 20 cm/sec, aerosol removal was mainly due to i n e r t i a l impaction.  iv)  For a l l experimental conditions tested, interception  was found to be  insignificant. v)  Aerosol c o l l e c t i o n was found to be unaffected by bed loading and to take place i n an e l e c t r i c a l l y neutral environment,  vi)  Bounce-off probably occurred at s u p e r f i c i a l gas v e l o c i t i e s greater than about 50 cm/sec causing the theoretical predictions to overestimate c o l l e c t i o n e f f i c i e n c i e s ,  vii)  The present experimental results agreed f a i r l y well with the results of other studies although conclusions on c o l l e c t i o n mechanisms differed.  viii)  An empirical equation (Eq. 7.3) was developed which was able to predict  the single c o l l e c t o r e f f i c i e n c y of a bed p a r t i c l e f o r the 109  110 experimental conditions chosen i n t h i s work, ix) The theoretical expression (eq. 3.4) r e l a t i n g the single  collector  e f f i c i e n c y to the o v e r a l l bed e f f i c i e n c y was confirmed by the results of this study. x) The difference  between the experimental and calculated  (using Eqs.  7.3 and 3.4) bed c o l l e c t i o n e f f i c i e n c i e s 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).  Ill  NOMENCLATURE Symbol  Explanation arid Typical Units  a,b,c  Constants used i n empirical equations  D  Diffusivity  d  &  Diameter of aerosol p a r t i c l e , cm or ym  d  c  Diameter of c o l l e c t o r p a r t i c l e , cm or ym  SL  2 c o e f f i c i e n t of aerosols, cm /sec  D.O.P.  Dioctyl phthlate  E  Single c o l l e c t o r e f f i c i e n c y of an isolated  EB  Single c o l l e c t o r e f f i c i e n c y of a c o l l e c t o r i n a granular bed  EBT  Total c o l l e c t i o n e f f i c i e n c y of a granular bed  ED  Single c o l l e c t o r e f f i c i e n c y due to d i f f u s i o n  EDR  Single c o l l e c t o r e f f i c i e n c y due to d i f f u s i o n and interception  EDIR  Single c o l l e c t o r e f f i c i e n c y due to d i f f u s i o n , i n e r t i a and interception  EG  Single c o l l e c t o r e f f i c i e n c y due to gravity  EI  Single c o l l e c t o r e f f i c i e n c y due to i n e r t i a  EIR  Single c o l l e c t o r e f f i c i e n c y due to i n e r t i a and interception  ER  Single c o l l e c t o r e f f i c i e n c y due to interception  collector  2 g  Gravitational  H  Bed depth, cm  acceleration,  cm/sec  -2/3 ND  Dimensionless d i f f u s i o n parameter (Pe  ND  Dimensionless gravitational parameter(U 7U)  NR  Dimensionless interceptional  P  Penetration, (1 - EBT)  AP  Pressure drop across the granular bed,  Pe  Peclet number (d U/D ) c a Multiple correlation c o e f f i c i e n t  R  )  parameter (d /d )  mm Hg  112 Symbol  Explanation and Typical Units  Re  Reynolds number ( p U  St  Stokes number (d U p„/9 y d ) a F c S u p e r f i c i a l gas v e l o c i t y , cm/sec  U U  g  p  / ) u  2  S e t t l i n g v e l o c i t y of aerosol p a r t i c l e , cm/sec  Greek Symbols a,3,YjO  Constants used i n empirical equations  ctg ,ai ,oi2 ,<X3 ,  Constants used i n empirical equations  ai+ ,015 e  Bed voidage  y  V i s c o s i t y of gas, gm/cm sec  p  Density of aerosol p a r t i c l e , gm/cm  p  Density of dispersion.medium, gm/cm  3  3  113  REFERENCES  1.  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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 i s expressed  as percentage penetration.  The r e l a t i o n s h i p between bed  penetration (P) and bed c o l l e c t i o n e f f i c i e n c y (EBT) i s : P = 1 - EBT or  %P = 100 (1 - EBT)  A l l the results were obtained with the apparatus set up i n the low v e l o c i t y 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 c o l l e c t o r f o r varying s u p e r f i c i a l gas v e l o c i t y .  118 TABLE A . l  P E N E T R A T I O N S FOR N I C K E L SHOT 598.1 UH i DOWNFLOW; BED DEPTH = 4.536 CM )  GAS V E L . CM/SEC  D .109  0.500  AEROSOL 0.600  5.24 8.30 1 1 . 16 16.97 22.37 2 7 . 08 I  8 2 . 50 83.70 8 5 . 10 83.70 86.00 8 4 . 40  6 6 . 90 7 0 . 10 72. 70 72.3 0 75.80 75. 80  6 1 . 30 6 5.60 67.00 69.80 70.40 70.50  rABLE  A.2  PENETRATIONS ( UPFLOW AND  GAS V E L . CM/SEC UP  *  5.24 8.30 11.16 16.97 22.3 7 2 7. 08 16.33* 22.57* 3 5.46* 50.75* 67. 00* APPARATUS  TABLE  A.3  0.500 DOWM  6 6 . 90 7 0 . 10 72,70 72.30 75.80 75.80 71.80 74.50 6 9 . 70 66.50 66.60 HIGH V E L O C I T Y  4,536  BED 9,071  5.24 8.30 1 1 . 16 16.97 22,37 27.08  6 6 . 90 70.10 72,70 72.30 75.80 75.80  44. 60 46 . 30 50.80 54.40 56.90 6 0 , 50  GAS V E L . CM/SEC 5.24 2 7 . 08  49.30 52.30 56,70 60.70 60.70 61 . 3 3  1.011  2. 0 2 0  39.60 42.60 46.03 5 1 . 20 5 3 . 20 52.50  11 . 8 8 14.09 15.50 13.50 7.88 1 .95  AEROSOL DIAMETER 0.804 UP DOWM  UM  53,20 5 4 . 50 57.50 6 2 . 40 6 3 . 60 60.10 6 0 . 90 64.40 54.90 52.50  49 . 3 3 5 2 . 30 56.70 60.70 6 0 . 70 61 . 8 0 58.90 59.00 54 . 1 0 48 . 10 48 . 6 0 CONFIGURATION  P E N E T R A T I O N S FOR N I C K E L SHOT 598. 1 UM ( DOWNFLOW; VARYING BED D E P T H ; AEROSOL DIAMETER = 0.5 UM }  GAS V E L . CM/SEC  TABLE A.4  UM  FOR N ICKEL SH3T 5 9 8 . 1 UM DIAM5 T E R . DOWNFLOW; 3ED DEPTH = 4 . 5 3 6 CM )  71.00 74.20 75.30 76.60 79.90 78.20 76.40 77.60 7 3 . 60 72.00 IN  DIAMETER 0 . 804  DIAMETER.  DEPTH CM 13.607  18. 142  3 0.20 32.20 36.50 4 0 . 60 45.30 47.50  20.50 2 3 . 00 26.50 3 1 . 00 35.00 37.53  P E N E T R A T I O N S FOR N I C K E L SHOT 598. 1 UM i DOWNFLOW; BED DEPTH = 2.2 6 8 CM >  0.109  AEROSOL 0.500  92.30 90,40  85.70 78.40  D I A M E T E R UM 0.600 0.804 83.00 76.70  77.70 71.70  UP 43.83 5 2 . 00 53.50 56.80 5 7 . 80 55 . 2 0  -  -  --  1 .011 DOWN 36.90 42.60 46.00 51 . 2 0 53.2 0 52 . 5 0 50.89 5 2 . 70 47.77 3 7.20 34.12  DIAMETER.  DIAMETER,  119 TABLE  A.5  GAS V E L . CM/SEC 5.24 8.3 0 11.16 16.97 22.37 27.08 'ABLE  A.6  P E N E T R A T I O N S FOR N I C K E L I DOWNFLOW; BED DEPTH =  0 . 109  0 . 500  AEROSOL 0.600  75.7 78.50 80.50 83.00 8 3. 60 83.60  60.00 6 5 . 30 69.00 71.30 75. 00 73 . 10  4 5 . 40 52.70 5 7 . 30 61.60 66.60 6 7 . 20  PENETRATIONS ( UP FLOW AND  GAS V E L . CM/SEC UP  *  5.24 8.30 11.16 16.97 22.37 2 7 . 08 1 6 . 3 3* 22. 57* 35.46* 50.75* 67.00* APPARATUS  TA8LE  A.7  GAS V EL . CM/SEC 5.24 8.30 1 1 . 16 16.97 22.37 2 7 . 08 TABLE  A.8  GAS V E L . CM/SEC 5.24 2 7 . 08  SHOT 5 1 1 . 0 UM 4 . 5 3 6 CM )  36.80 41 . 0 0 45.40 50.30 55 .2 0 55.50  0. 500 DOWN  6 0 . 00 65.30 6 9 . 00 71.30 75.00 73. 1 0 72.30 75.90 6 8 . 40 67.20 6 5 . 00 HIGH V E L O C I T Y  -  AEROSOL D I A M E T E R 0. 804 DOWM UP  1.011 2 9 . 50 37.50 4 0 . 00 4 4 . 10 45.00 4 3 . 50  .  2.020 6. 802 8.614 10.909 8. 3 8 7 1.526 0.096  2.268  BED DEPTH CM 4 . 5 36 9.071  75.20 78.20 8 2 . 20 82.70 85.20 8 7. 40  6 0 . 00 65.30 6 9 . 00 71 . 3 0 75.00 73.1 0  3 7 . 20 43.00 46.50 51.20 55.70 5 9.1 0  13.607  UP  AEROSOL DIAMETER UM 0.109 0.600 0.804 73.50 55.60  33 . 80 38.70 42 . 5 0 4 8 . 70 48.90 46.00  —  UM  1.011 DOWM 29.50 3 7 . 50 40 . 0 0 44.10 45 . 0 0 43 . 5 0 45.45 39 . 6 9 35.24 30.03 27.46  DIAMETER.  18.142  25.00 30.00 32 . 6 0 3 7 . 50 44.00 45.00  P E N E T R A T I O N S FOR N I C K E L SHOT 5 1 1 . 0 { DOWNFLOW; BED DEPTH = 2 . 2 6 8 CM )  82.80 6 6 . 80  UM  3 9 . 80 36.80 44.90 41 . 0 0 48.90 45.43 50.30 53.30 56.20 55.20 5 9 . 50 55.50 54.00 5 1 . 30 57.40 53.50 5 6 . 00 53.6 0 54.00 45.00 49 .63 45.00 CONFIGURATION  P E N E T R A T I O N S FOR N I C K E L SHOT 5 1 1 . 0 ( DOWN FLOW; V A R Y I N G BED D E P T H ; AEROSOL DIAMETER = 0 .5 U*l )  90.20 87.00  UM  FOR N I C K E L SHOT 5 1 1 . 0 UM D I A M E T E R . DOWNFLOW; BED DEPTH = 4 . 5 3 6 CM )  62.20 66.80 6 9 . 00 75.00 75.70 7 6 . 20 73.80 76.00 73.00 70.20 IN  DIAMETER 0.804  DIAMETER.  18.30 24.30 27.30 3 1 . 50 3 7 . 00 38.70 UM  DIAMETER.  120 TABLE  A.9  P E N E T R A T I O N S FOR N I C K E L S.H3T 3 6 3 . 9 ( DOWNFLOW; BED DEPTH = 4 . 5 3 6 CM )  UM  DIAMETER 0.804  UM  GAS V E L . CM/SEC  0 . 109  0 . 5 00  AEROSOL 0 . 6 00  5.24 8.3 0 11.16 1 6 . 97 22.37 27.08  40.50 4 8 . 20 51.20 57.60 62.2 0 65.40  29.10 33. 30 36.90 38*10 43.00 46.70  21.90 26.70 3 1 . 10 37.30 3 9 . 90 4 4 . 30  TABLE  A.10  *  TABLE  A.11  GAS V E L . CM/SEC 5.24 8.3 0 1 1 . 16 16.97 22.3 7 27.08 TABLE  A.12  GAS V E L . CM/SEC 5.24 27.08  1.011  2.020  1 2 . 50 19.90 2 2 . 90 26.80 26.40 23.30  0. 561 0.736 1. 1 2 9 0.055 0.0016 0.0003  P E N E T R A T I O N S FOR N I C K E L SHOT 3 6 3 . 9 UM D I A M E T E R . < UPFLOW AND DOWNFLOW; BED DEPTH = 4 . 5 3 6 CM )  GAS V E L . CM/SEC  5.24 8.3 0 11.16 16.97 22. 37 27.08 1 6 . 3 3* 22.57* 35.46* 50. 75* 67.00* APPARATUS  14.80 19.23 2 4 . 70 29.00 31 . 0 0 30.80  DIAMETER.  AEROSOL 0 .500 UP DOWN 29.10 33.30 36.90 38.10 43.00 4 6 . 70 40.00 4 1 . 60 44,60 37.80 4 0 . 70 HIGH V E L O C I T Y  32.30 3 6.00 40.30 43.40 45.60 49.30 42.50 5 0 . 00 46.70  IN  -  D I A M E T E R UM 0. 804 UP DOWN  1 4 . 80 19.20 24.70 2 9 . 00 31 . 0 0 30.80 28.10 31.10 2 9 . 20 25.10 20.03 CONFIGURATION 2 1 . 10 22.10 2 5 . 60 29.40 33.20 3 3 , 90 31,00 33.90 32.00 24.60  P E N E T R A T I O N S FOR N I C K E L SHOT 3 6 3 . 9 UM i DOWN FLOW ; V A R Y I N G BED D E P T H ; AEROSOL DIAMETER = 0 . 5 UM >  2,268  BED 4 . 5 36  54.4 0 58,00 6 1 . 00 63.7 0 66.00 66.40  2 9 . 10 33.30 3 6 . 90 38.10 43.00 46.70  DEPTH CM 9.071 10.00 12.40 14.00 16.50 20.00 24. 40  80.80 66.60  35.80 54.00  46.00 62.80  1 2 . 50 19 . 9 0 22 . 9 0 26.80 26.40 23.30 2 7 . 30 26.04 1 9 . 63 13.62 12.60  DIAMETER.  13 . 6 0 7  18.142  4.20 5 .00 6.00 8. 20 11 . 4 0 14.90  3 . 40 3.90 4.90 6.40 9 .30 12.00  P E N E T R A T I O N S FOR N I C K E L SHOT 3 6 3 . 9 UM ( D0WNFL3W; BED DEPTH = 2 . 2 6 8 CM ) AEROSOL D I A M E T E R UM 0.109 0.600 0.804  1. O i l DOWN  DIAMETER.  121 TABLE  A.13  GAS V E L . CM/SEC  P E N E T R A T I O N S FOR N I C K E L SHOT 2 1 5 , 1 i DOWNFLOW; BED DEPTH = 2. 2 6 8 CM )  0.109  0. 5 00  5.24 8.30 11.16 1 6 . 97 22.37 27.0 8 # BED DEPTH  31.60 14.30 3 5.00 16.50 20.90 37.10 4 2 . 10 24.30 48.30 27.60 28.40 48.50 = 0. 567 CM  TABLE  PENETRATIONS ( UPFLOW AND  A.14  GAS V E L . CM/SEC  *  TABLE  A.15  GAS V E L . CM/S EC 5.24 8.30 11.16 16.97 22.37 27.08 TABLE  A.16  GAS V E L . CM/SEC 5.24 2 7 . 08  6 .00 7. 80 11.40 13.20 16.60 19.02  AEROSOL DOWN  14.90 1 5 . 70 1 7.90 2 4 . 70 28.90 28.30 25.00 29.50 2 8 . 00 21.50 IN  14.30 16.50 20.90 2 4 . 30 27.60 28.40 2 4 . 30 27.20 2 5 . 90 20.50 18.30 HIGH V E L O C I T Y  D I A M E T E R UM 0. 80'* 1.011 5 .45 7.46 9.60 11.53 12.00 12.50  DIAMETER UM 0.804 DOWN UP  4,50 6.90 8 . 10 10 .20 9 . 20 5.80  2 . 0 2 0# 1.891 3 .13 8 1. 218 0.261 0. 080 0. 180  0.567  BED 1.134  5 8. 70 64.00 68.00 7 0 . 80 73.80 7 4 . 80  38.3 0 41.00 45.40 49.20 53.00 56.00  5 .45 7.45 9.60 11 . 5 0 12.00 12.50 9.70 12.80 10.33 5.40 4.80 CONFIGURATION  4.50 6 . 80 8 . 10 10.20 9 . 20 5.80 10.51 13.01 2.98 0 . 20 0.01  -  UM  DIAMETER,  SHOT 2 1 6 . 1 UM 1 . 1 3 4 CM )  DIAMETER.  DEPTH CM 2. 268  4. 536  14.30 1 6 . 50 20.90 2 4 . 30 27.60 31 . 3 0  7.40 9.40 11 . 8 0 16.80 20.50 22 . 0 0  P E N E T R A T I O N S FOR N I C K E L I DOWNFLOW; BED DEPTH = AEROSOL DIAMETER UM 0.109 0.600 0,304 46.20 25.00  1.011 DOWN  7.00 8.70 10.50 12.50 12.20 16.20 1 2 . 00 13.70 12-30 6. 50  P E N E T R A T I O N S FOR N I C K E L SHOT 2 1 6 . 1 ( DOWNFLOW; VARYING BED D E P T H ; AEROSOL DIAMETER = 0 . 5 UM  68.20 56.40  DIAMETER,  FOR N I C K E L SHOT 2 1 6 . 1 JM D I A M E T E R . DOWNFLOW; BED DEPTH = 2 . 2 6 8 CM )  0. 500 UP  5. 24 8.30 11.16 16.97 22.37 2 7 . 08 16.33* 22.57* 3 5. 4 6 * 50.75* 67.00* APPARATUS  AEROSOL 0. 6 0 0  UM  35.70 21.50  122  TABLE  A . 1 7  PENETRATIONS DOWNFLOW;  i GAS  0 .109  0.500  '5.24 8.3 0 11.16 16.97  126.0UM DIAMETER. CM } UM  DIAMETER  0.600  0.804  1.011  2. 0 2 0 # 1.2030  3 .50  0.827  0.353 6  0. 2 5 2 7  0. 1 0 1 5  4.90  1.612  0.5110  0.4000  0.1721  1. 1 7 0 0  5. 7 0  2. 5 7 6  0.6350  0.5415  0.3370  1.4722  3.588  1.7390  1. 5 6 0 3  13.70  5.004  2.4230  2.1699  0. 0 9 8 2 0.0196  1.4454  22. 3 7 27.08  15.00  6. 8 7 6  2.6850  2. 3 6 5 5  0. 0 0 2 4  1.1041  9.90  BED DEPTH  TABLE  A.18  =  0.283  UPFLOaI  AND  FOR N I C K E L  S H O T 1 2 6 . 1 UM DIAMETER. DEPTH = 2 .268 CM )  DOWNFLOW; B E D  GAS V E L .  DIAMETER  AEROSOL 0. 500  CM/SEC UP 5.24  1.3170  CM  PENETRATIONS {  1.352  UM  0. 8 0 4  0.600  DOWN  DOrfN  0.827  0.353 6  1.  Oil  DOWN  DOWN  2. 1 5 1 0  0.2527  0. 1 0 1 5 0 . 1 7 21 0.3370  UP  2.400  1.612  0.5110  1.9910  0.4000  11.16  2.873  2. 5 7 6  0. 6 3 5 0  1. 4 1 7 0  0.5416  16.97  3.588  1.7390  1.3890  1.5603  0. 0 9 8 2  22.3 7  3.717 5. 3 9 6  5. 0 0 4  2.4230  1.5510  2.1699  0.0196  27.08  5 . 3 52  6.876  2.6850  1. 6 1 5 0  2. 3 6 5 5  0.0024  8.30  —  16.3 3*  -  22.57*  -  35.46* 50.75*  -  67.00* *  SHOT  = 2.268  AEROSOL  VEL .  CM/SEC  *  FOR N I C K E L BED DEPTH  APPARATUS  TABLE  A.19  IN HIGH  --VELOCITY  PENETRATIONS (  0.1034  2.8280  0.4260  0.0348  1.3690  0.0765 0.0100  0.0016 0.0005  0.0032  0.0002  0.3940 0. 2 4 1 0 CONFIGURATION  FOR N I C K E L  DOWNFLOW; V A R Y I N G AEROSOL  DIAMETER  BED  GAS V E L .  DEPTH  =  29 .00  8.30  3 4 . 60  12.30  1 .612  38. 10  15.30 17.00  2. 5 7 6 3.588  1. 1 3 4  2.268  9.00  0.827  22. 3 7  43. 7 0  19.20  5.004  27.08  47.00  25.60  6.876  A.20  PENETRATIONS {  GAS V E L .  D0WNFL3W; AEROSOL  FOR N I C K E L BED DEPTH  DIAMETER  0.109  0.6 0 0  5.24  38.60  17. 80  27.08  2 0.90  5. 5 0  CM/SEQ  DIAMETER.  CM  5.24  TABLE  1 2 6 . 1 UM  DEPTH;  0.5  0. 5 6 7  41.00  SHOT  BED  CM/SEC  11.16 16.97  -  0.4244  2.5000  SHOT  =  UM 0.804  15.50 5. 8 0  1 2 6 . 1 UM  1 . 1 3 4 CM  )  DIAMETER.  123 TABLE  A.21  P E N E T R A T I O N S FOR L E A D SHOT 1800 UM D I A M E T E R . i DOWNFLOW; AEROSOL DIAMETER = 0 . 5 UM )  GAS V E L . CM/SEC  4.536  BED DEPTH CM 9. 071 13.607  5.24 1 1 . 16 16.97 2 2 . 37 2 7 . 08  95.80 9 0 . 20 89.50 96.50 92.40  92.90 92.80 87.50 87.70 85.60  83.90 86.05 86.2 0 86.50 88.30  18.142 78.60 80.50 85.6 0 85.00 8^.40  124 TABLE  A.22  GAS V E L . CM/SEC 5.24 8.30 11.16 16.97 22.37 2 7 . C8 16.33 22.57 3 5 . 46 50.75 67.00  TABLE  A.23  GAS V E L . CM/SEC 5.24 8.30 11*16 16.97 22.37 27.08 16.33 2 2 . 57 35.46 50.75 67.00  TABLE  A.24  GAS V E L . CM/SEC 5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00  P R E S S U R E DROP IMM.HG) 5 9 8 . 1 UM D I A M E T E R -  4.53 6 1.4 2.5 3.0 5.0 6.4 7.3 5.0 6.5 10.0 14.0 18.7  BED DEPTH CM 9.071 13.607 3.5 4.5 5.5 9.0 13.0 16.0  4.4 5.0 8.0 13.0 16.5 21.0  -  -  -  —  P R E S S U R E DROP (MM.HGJ 5 1 1 . 0 UM D I A M E T E R .  4.536 2.5 3.0 4. 1 6.5 7.0 8.0 5.0 7.0 11.7 16.0 21.3  BED 9.071 3.5 4.0 6. 0 9.5 13.5 15.0  5*5 5.5 9.5 14.0 18.0 22.5  -  -  -  --  4.3 5.1 7.0 10.3 13.4 16.4 11.0 14.3 26.3 35.0 43.0  BED 9.071 7.0 8.0 13.0 19.5 27.0 31.0  -  —  -  -  ACROSS  D E P T H CM 13.607  -  P R E S S U R E DROP IMM.HG) 3 6 3 . 9 UM D I A M E T E R .  4.53 6  ACROSS  ACROSS  DEPTH CM 13.60 7 10.0 13.0 18*5 28.0 38.0 47.0  --  BEDS  18.141 5.5 7.0 10.0 15.5 21.5 29.0  -BEDS  18.141 6.5 8.0 12.5 17.5 25.0 31.0  -  --  BEDS  18.141 13.0 18.0 27.5 40.0 54*0 68.0  -  OF N I C K E L  SHOT  DP/H MM.HG/CM 0.312 0.416 0.602 0.974 1.311 1.58 4 1.102 1. 4 3 3 2.205 3.086 4.120  OF N I C K E L  SHOT  DP/H MM.HG/CM 0.392 0.429 0.683 1.014 1.432 1.695 1. 102 1.543 2. 5 7 9 3.527 4.960  OF N I C K E L  SHOT  DP/H MM.HG/CM 0.741 0.982 1. 49 7 2.209 2.969 3.496 2.425 3.153 5.79 8 7.716 9.480  125  ABLE  A-25  GAS V E L . CM/SEC 5.24 8.30 11.16 16.97 22.40 27.08 16.33 22.57 35.46 50.75 67.00  TABLE  A.26  GAS V E L . CM/SEC 5.24 8.30 11.16 16.<57 22.37 2 7 . C8  TABLE  A.27  GAS V E L . CM/SEC 5.24 1 1 . 16 1 6 . 97 22.37 27. C 8  P R E S S U R E DROP (MM. HGJ 2 1 6 . 1 UM D I A M E T E R .  1.134 3.5 5.0 7.0 11.5 14.0 16.5  -  —  ACROSS BEDS  BED DEPTH CM 2.268 4.536 7.0 9.5 12.5 19.4 26.0 32.0 20.5 28.0 44.0 59.0 76.0  12.0 16.0 24.0 34.0 45.0 56.0  -  —  P R E S S U R E DROP (MM.HGJ 1 2 6 . 0 UM D I A M E T E R .  ACROSS  0.567  BED DEPTH CM 1. 134 2. 26 8  5.0 7.0 8.5 12.0 15.4 18.0  8.0 12.0 16.0 22. 0 28,5 34.0  17.0 24.0 33.0 46.0 61.5 73.0  P R E S S U R E DROP 1MM.HG) 1 8 0 0 UM D I A M E T E R .  4.536 0.13 0.26 0.44 0.66 0.88  ACROSS  BED DEPTH CM 9.071 13.607 0.26 0.49 0.83 1.23 1.75  0.35 0.76 1.20 1.81 2.51  OF N I C K E L  DP/H MM.HG/CM  6.804 19. 0 26.5 37. 0 55.0 73.0 91. 0  3.870 4.005 5.413 8.568 10.563 13.59 5 9.039 12.346 19.400 26.014 33.510  --  —  BEDS  OF  NICKEL  SHOT  DP/H MM.HG/CM  4.536  7.489 10.545 14.219 19.950 2 6 . 135 31.820  3 0.0 47.5 60.0 86.0 114.0 143.0  BEDS  SHOT  OF L E A D  18.141 0.44 0.96 1.54 2.32 3.14  SHOT  DP /H MM.HG/CM 0.026 8 0.0551 0.0905 0.1322 0.1860  126  APPENDIX B CALCULATIONS OF EB AND DIMENSIONLESS GROUPS For each set of experimental conditions the value of EB was from the experimentally measured value of EBT using Eq. 3.6.  calculated  The values of  EB are l i s t e d with the corresponding dimensionless groups, v i z . , 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 n i c k e l shot. Bed depth (H) = 4.536 cm Voidage (e) = 0.415 S u p e r f i c i a l gas v e l o c i t y = 5.24 cm/sec Experimental bed c o l l e c t i o n e f f i c i e n c y  (EBT) = 0.331  From Eq. 3.6 i t follows: EB - - l n ( l - 0.0331) -3 2.5184 x 10  0.05981 1.5  0.415 , 1 0.415 4.536 ;  TABLE B.1  DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORSESPONDING TO TESTS ON BEDS OF NICKEL SHOT 598.1 UM DIAMETER. ( DOWNFLOW ) ST  NG  SE  0. 109 0. 109 0.109 0. 109 0. 109 0. 109  5.24 8.30 11.16 16.97 22.37 27.08  2. 176 3. 447 4. 635 7. 048 9. 291 11. 248  0.674659E- 05 0.106864E- 04 0.143687E- 04 0.218492E- 04 0.288018E- 04 0.348660E- 04  0.182244E- 03 0.182244E- 03 0. 182244E-03 0. 182244E- 03 0. 182244E-03 0. 182244E- 03  0.522870E 0.828209E 0. 1 11359E 0.169334E 0.223217E 0.270216E  05 05 06 06 06 06  0.719975E- 05 0.454538E- 05 0.338053E- 05 0.222314E- 05 0. 168649E-05 0.139316E- 05  0.119953E- 02 0. 110949E-02 0. 100605E- 02 0.110949E- 02 0.940452E- 03 0. 105755E- 02  0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500  5.24 8.30 11.16 16.97 22. 37 27.08 16.33 22.57 35.46 50.75 67.00  2. 176 3. 447 4. 635 7.048 9. 291 11. 248 6. 783 9. 374 14.728 21. 079 27.828  0.141962E- 03 0.22 486 3E-03 0.302346E- 03 0. 45975 1E-03 0.606047E- 03 0.733650E- 03 0. 442412E-03 0.611466E- 03 0.96 0681E-03 0. 137492E-02 0. 181516E-02  0,835981E- 03 0.835981E- 03 0.835981E- 03 0.835981E- 03 0.835981E- 03 Q..835981E-03 0.835981E- 03 0. 835981E-03 0.835981E- 03 0.835981E- 03 0.835981E- 03  0.4 892 55E 0.774966E 0.104200E 0. 158448E 0.208867E 0.252844E 0.152472E 0.210735E 0.331088E 0.473849E 0.6 255 75E  06 06 07 07 07 07 07 07 07 07 07  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  0.251840E- 02 0.232389E- 02 0.206494E- 02 0. 193148E- 02 0. 171063E-02 0. 161401E- 02 0.206572E- 02 0. 183554E-02 0.225082E- 02 0.254388E- 02 0. 253451E-02  0.600 0.600 0.600 0.600 0.600 0.600  5.24 8.30 11.16 16.97 22.37 27.08  2. 176 3.447 4. 635 7. 048 9. 291 11. 248  0.204425E- 03 0.323803E- 0 3 0. 43 5379E-03 0. 66 204 1E-03 0. 872707E-03 0. 105646E-02  0. 100318E- 02 0. 100318E-02 0. 100318E-02 0. 100318E-02 0. 100318E- 02 0. 100318E-02  0.613062E 0.971071E 0.130568E 0.198543E 0.261721E 0.316826E  06 06 07 07 07 07  0.218156E- 03 0.1377 27E-03 0.102432E- 03 0.673622E- 04 0.511013E- 04 0.422133E- 04  0. 305158E-02 0. 262884E- 02 0. 249717E- 02 0.224188E- 02 0.218851E- 02 0.217966E- 02  NE  PE  EB  VEL. CM/SEC  a .  UM  TABLE B. 1  ( CONTINUED ) ST  Nfi  PE  VEL. CM/SEC  .RE  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  2. 176 3. 447 4. 635 7. 048 9. 291 11.248 6.783 9. 374 14.728 21. 079 27. 828  0. 367066E-03 0.581421E- 03 0.7 8176 5 E-03 0.118876E- 02 0.156703E- 02 0. 189697E- 02 0. 114393E-02 0. 158104E- 02 0.248400E- 02 0.355507E- 02 0.469340E- 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 0.134426E- 02  0.869726E 0.137762E 0. 185232E 0.281665E 0.371293E 0.449469E 0.271043E 0.374613E 0.588559E 0.842340E 0.1112 05E  06 07 07 07 07 07 07 07 07 07 08  0.391721E- 03 0.247303E- 03 0. 183926E- 03 0.12 0956E- 03 0. 917576E-04 0.757982E- 04 0. 125696E- 03 0.909444E- 04 0.578854E- 04 0.404456E- 04 0.306361E- 04  0.441002E- 02 0.404167E- 02 0.353799E- 02 0.311292E- 02 0.311292E- 02 0.300093E- 02 0.330062E- 02 0.329004E- 02 0.383068E- 02 0. 456367E-02 0.449919E- 02  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  2. 176 3. 447 4.635 7. 048 9.291 11. 248 6. 783' 9. 3 74 14. 728 21. 079 27.828  0.580409E- 03 0.919349E- 03 0.123614E- 02 0.187968E- 02 0.247781E- 02 0.29 9952E- 02 0. 18 0879E-02 0. 249997E-02 0. 392773E-02 0.562133E- 02 0. 742126E-02  0./169035E- 02 0.169035E- 02 0. 169035E-02 0. 169035E-02 0.169035E- 02 0, 169035E-02 0, 169035E-02 0. 169035E-02 0.169035E- 02 0,169035E- 02 0. 169Q35E- 02  0.113349E 0.179541E 0.241408E 0.3.67087E 0.483896E 0.585781E 0.353242E 0.488223E 0.767053E 0.109780E 0.144931E  07 07 07 07 07 07 07 07 07 08 08  0.619394E- 03 0.391039E- 03 0.290826E- 03 0.191256E- 03 0.145088E- 03 0.119853E- 03 0.198752E- 03 0.143802E- 03 0.915291E- 04 0.639531E- 04 0.484421E- 04  0.621651E- 02 0.532083E- 02 0.484203E- 02 0.417422E- 02 0.393528E- 02 0.367137E- 02 0.421209E- 02 0.399416E- 02 0.460568E- 02 0.616603E- 02 0. 6704 92E-02  2.020 2.020 2.020 2.020 2.020 2.020  5.24 8. 30 11,16 16.97 22.37 27.08  2. 176 3. 447 4. 635 7. 048 9.291 11. 248  0. 226629E-02 0. 358974E-02 0.482668E- 02 0.733950E- 02 0.967498E- 02 0.117120E- 01  0. 337736 E-02 0.337736E- 02 0. 337736E-02 0.337736E- 02 0. 337736E- 02 0. 337736E-02  0.243670E 0.385966E 0.518962E 0.789138E 0.104025E 0.125927E  07 07 07 07 08 08  0.241845E- 02 0.152683E- 02 0.113554E- 02 0.746769E- 03 0.566503E- 03 0.467971E- 03  0. 132835E-01 0.122197E- 01 0. 116250E-01 0..124864E- 01 0. 158433E-01 0,245512E- 01  da  UM  NG  EB  TABLE B.2  d OM  DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 598.1 UM DIAMETER. { UPFLOW )  VEL. CM/SEC  RE  0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500  5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35. 46 50.75 67. 00  2. 176 3.447 4.635 7.048 9. 291 11.248 6.783 9. 374 14.728 21.079 27.828  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. 835981E-03 0.489255E 06 0.835981E-03 0.774966E 06 0.835981E-03 0. 1 042 00E 07 0.835981E-03 0.158448E 07 0.8359 81E-03 0.208867E 07 0.835981E-03 0.252844E 07 0.835981E-03 0.152472E 07 0.835981E-03 0.210735E 07 0. 835981E-03 0.331088E 07 0.835981E-03 0.473849E 07 0. 835981E-03 0.625575E 07  0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804 0.804  5.24 2. 176 8. 30 3. 447 11.16 4. 635 16.97 7.048 22.37 9. 291 27.08 11.248 16.33 6.783 22. 57 9.374 35.46 14.728 50.75 21.079 67.00 27.828  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. 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  0.869726E 0.137762E 0.185232E 0.281665E 0.371293E 0.449469E 0.271043E 0.374613E 0.588559E 0.842340E 0.111205E  1.011 1.011 1.011 1.011 1.011 1.011  5.24 8.30 11.16 16.97 22.37 27.08  0.580409E-03 0.919349E-03 0. 123614E-02 0. 187968E-02 0.247781E-02 0.299952E-02  0.169035E-02 0. 169035E-02 0. 169035E-02 0. 169035E-02 0. 169035E-02 0. 169035E-02  0. 1 133 49E 07 0.179541E 07 Q.241408E 07 0.3 67087E 07 0.483896E 07 0.585781E 07  a  2. 176 3.447 4.635 7.048 9.291 11.248  ST  NR  PE  NG  06 07 07 07 07 07 07 07 07 07 08  EB  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  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  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  0.393528S-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  0.619394E-03 0.391039E-03 0.290826E-03 0.191256E-03 0.145088E-03 0.119853E-03  0.514760E-02 0.407755E-02 0. 390022E-02 0.352700E-02 0.341818E-02 0.337517E-02  TABLE B.3  Ul!  VEL, CM/SEC  0.109 0. 109 0. 109 0.109 0. 109 0. 109  5.24 8.30 11.16 16.97 22.37 27.08  0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500  5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00  0.600 0.600 0.600 0.600 0.600 0.600  5.24 8. 30 11.16 16.97 22.3 7 27.08  DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 511.0 UM DIAMETER. { DOWNFLOW ) RE  ST  NR  NG  PE  EB  0.772358E- 05 0. 122339E-04 0, 164495E- 04 0.250132E- 04 0.329726E- 04 0.399150E- 04  0.213307E- 03 0.213307E- 03 0. 213307E-03 0. 213307E-03 0.213307E- 03 0.213307E- 03  0.446725E 0.707599E 0.9 51423E 0.144674E 0.190711E 0.2 30865E  05 05 05 06 06 06  0.704185E- 05 0.444570E- 05 0.330639E- 05 0.217438E- 05 0.164950E- 05 0. 136260E-05  0.148311E- 02 0. 128962E- 02 0. 1 15559E-02 0. 992655E-03 0.954282E- 03 0. 954282E- 03  1. 859 0.162520E- 03 2. 945 0.257426E- 03 3. 960 0.346130E- 03 6. 022 0.526328E- 03 7. 938 . 0.693810E-03 9. 610 0. 83 989 2E-03 5. 795 0.506478E- 03 8.009 0.700013E- 03 12. 583 0.109980E- 02 18.009 0.157402E- 02 23.776 0.207802E- 02  0. 9784 74 E-03 0. 978474E-03 0. 978474E-03 0. 978474 E-03 0.9784 74 E-03 0.978474E- 03 0, 978474E-03 0.97 84 74 E-03 0. 978474E-03 0. 97 84 74 E-03 0.978474E- 03  0.4 180 06E 0.662109E 0.890258E 0.1353 73E 0. 178450E 0.216023E 0. 130268E 0.1 80046E 0.282872E 0.404844E 0.534474E  06 06 06 07 07 07 07 07 07 07 07  0.148175E- 03 0.935464E- 04 0.695731E- 04 0.457534E- 04 0.347088E- 04 0.286719E- 04 0.475466E- 04 0.344012E- 04 0.218961E- 04 0.152992E- 04 0.115886E- 04  0,260589E- 02 0.221898E- 02 0.200242E- 02 0. 177579E- 02 0. 151652E- 02 0. 149617E-02 0. 172793E- 02 0. 146905E- 02 0.202334E- 02 0.211763E- 02 0.229496E- 02  0.234028E- 03 0.370694E- 03 0. 4984 27E-03 0. 757912E-03 0.999086E- 03 0. 120944E-02  0. 117417E-02 0. 117417E- 02 0. 117417E-02 0. 117417E- 02 0. 117417E-02 0. 117417E-02  0..5 237 83E 06 0.829656E 06 0. 1 11554E 07 0. 169630E 07 0.2 236 07E 07 0.270688E 07  0.213372E- 03 0. 134707E- 03 0. 100185E- 03 0.658849E- 04 0.499807E- 04 0.412876E- 04  0.420684E- 02 0.341250E- 02 0.296668E- 02 0.258118E- 02 0.216541E- 02 0.211763E- 02  1. 8 59 2. 945 3. 960 6. 022 7. 938 9. 610  1. 859 2. 945 3. 960 6. 022 7. 938 9. 610  TABLE B.3 a UM  ( CONTINUED }  VEL. CM/SEC  BE  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  1, 859 2.945 3.960 6.022 7. 938 9.610 5.795 8.009 12.583 18.009 2 3.776  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  0.157339E- 02 0. 157339E-02 0. 157339 E-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  0.743070E 0.1 17700E 0.158257E 0.240647E 0.317223E 0.384014E 0.231571E 0.3200 59E 0.502848E 0.719672E 0.9501 08E  06 07 07 07 07 07 07 07 07 07 07  0.383130E- 03 0.2418 80E-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  0.532568E-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  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  1.859 2.945 3.960 6. 022 7.938 9.610 5.795 8.009 12.583 18.009 23.776  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. 197847E-02 0. 197847E-02 0. 197847E-02 0. 197847E-02 0.197847E- 02 0. 197847E-02 0.1S7847E- 02 0.197847E- 02 0, 197847E- 02 0. 197 847 E-02 0.197847E- 02  0.968423E 0.153395E 0.206252E 0.313629E 0.413428E 0.500475E 0.301801E 0.417124E 0.655349E 0.937929E 0.123825E  06 07 07 07 07 07 07 07 07 07 08  0.605810E- 03 0.382463E- 03 0.284448E- 03 0.187062E- 03 0.141906E- 03 0.117225E- 03 0.194393E- 03 0.140649E- 03 0.895218E- 04 0.625506E- 04 0.473798E- 04  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  2.020 2.020 2.020 2.020 2.020 2.020  5.24 8.30 11.16 16.97 22.37 27.08  1 .859 2.945 3.960 6.022 7.938 9.610  0. 265258E-02 0.420161E-02 0.56 4939E-0 2 0.85 9052E-02 0. 113241E-01 0.137084E-01  0.395303E- 02 0.395303E- 02 0.395303E- 02 0.395303E- 02 0.395303E- 02 0.395303E- 02  0.208185E 0.329759E 0.443387E 0.674218E 0.888760E 0.1075 89E  07 07 07 07 07 08  0.241845E- 02 0.1526 83E-02 0.1 13554E- 02 0.746769E- 03 0.566503E- 03 0.467971E- 03  0. 143198E-01 0. 130617E-01 0.118033E-01 0. 132039E-01 0.222820E-01 0. 370180E-01  d  ST  NB  PE  NG  EB  TABLE B.4  VEL. UM  DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 511.0 tJM DIAMETER. ( UPFLOW ) RE  CM/SEC  ST  NR  NG  PE  EB  |0.500 0.500 0.500 0.500 G.500 0.500 0.500 0.500 0.500 0.500 0.500  5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00  1. 859 2.945 3.960 6. 022 7. 938 9.610 5.795 8. 009 12.583 18.009 23.776  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. 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  0.4180 06E 06 0.662109E 06 0.890258E 06 0.135373E 07 0. 178450E 07 0.2 16023E 07 0. 1 30268E07 0. 1800 46E 07 0.282872E 07 0.404844E 07 0.534474E 07  0.148175E- 03 0.935464E- 04 0.695731E- 04 0.457534E- 04 0.347088E- 04 0.286719E- 04 0.475466E- 04 0.344012E- 04 0.218961E- 04 0.152992E- 04 0. 115886E-04  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  0.804 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  1.859 2.945 3.960 6. 022 7.938 9.610 5.795 8.009 12.583 18.009 23.776  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. 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  0.7430 70E 0.1 177 00E 0.158257E 0.240647E 0.317223E 0.384014E 0.231571E 0.320059E 0.502848E 0.719672E 0.950108E  06 07 07 07 07 07 07 07 07 07 07  0.383130E- 03 0.2418 80E-03 0. 179893E-03 0."^^^18303 E-03 0.897453E- 04 0.741359E- 04 0.122939E- 03 0.889500E- 04 0.566159E- Q4 0.395586E- 04 0.299642E- 04  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  1.011 1.011 1.011 1.011 1.011 1.011  5.24 8.30 11.16 16.97 22.37 27.08  1. 859 2.945 3.960 6.022 7.938 9.610  0.664459E-03 0. 105248E-02 0.141515E-02 0.215188E-02 0. 283663E-02 0.343388E-02  0.197847E-02 0.197847E-02 0.197847E-02 0. 197847E-02 0. 197847E-02 0. 1S7847E-02  0.968423E 0.1533 95E 0.206252E 0.313629E 0.413428E 0.500475E  06 07 07 07 07 07  0.605810E- 03 0.382463E- 03 0.284448E- 03 0.187062E- 03 0.141906E- 03 0.117225E- 03  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 ) ST  NG  RE  0.109 0. 109 0. 109 0.109 0. 109 0. 109  5.24 8.30 11.16 16.97 22.37 27.08  1. 324 2. 097 2. 820 4. 288 5. 653 6. 843  0. 108457E-04 0.171793E- 04 0.230989E- 04 0.35124 4E-04 0.46 3012E-04 0.56 049 9E-04  0.299533E- 03 0. 299533E-03 0. 299533E-03 0.299533E- 03 0.2995 33 E-03 0. 299533E-03  0.318128E 0.503905E 0.677539E 0.103027E 0.135811E 0.1644 07E  05 05 05 06 06 06  0.704185E- 05 0.444570E- 05 0.330639E- 05 0.217438E- 05 0.164950E- 05 0.136260E- 05  0.342913E- 02 0.276878E- 02 0.2539 71E-02 0.20 9 286E-02 0. 1801 37E- 02 0.161104E- 02  0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500  5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00  1. 324 2. 097 2. 820 4. 288 5.653 6. 843 4. 127 5. 704 8.961 12.825 16. 931  0.228215E- 03 0.361486E- 03 0.486046E- 03 0.739087E- 03 .0.974270E-03 0.1179 40E-02 0.711213E- 03 0.98 2981E-03 0.154437E- 02 0.221029E- 02 0.291802E- 02  0.137400E- 02 0.137400E- 02 0. 137400E-02 0. 137400E-02 0. 137400E-02 0.137400E- 02 0.137400E- 02 0.137400E- 02 0.137400E- 02 0. 137400E-02 0. 137400E-02  0.297676E 0.471510E 0.633982E 0.964039E 0.127080E 0.153837E 0.927681E 0. 128217E 0.201443E 0.288303E 0.3806 16E  06 06 06 06 07 07 06 07 07 07 07  0. 148175E-03 0.935464E- 04 0.695731E- 04 0.457534E- 04 0.347O88E- 04 0. 286719E-04 0.475466E- 04 0.344012E- 04 0. 218961E-04 0.152992E- 04 0.115886E- 04  0. 455698E-02 0. 408838E- 02 0. 375427E- 02 0.350035E- 02 0.313599E- 02 0. 289057E-02 0.347625E- 02 0.332746E- 02 0.306328E- 02 0.369087E- 02 0.341044E- 02  0.6 00 0.600 0.600 0.600 0.600 0.600  5.24 8.30 11.16 16.97 22.3 7 27.08  1.324 2. 097 2. 820 4. 288 5. 653 6. 843  0.328630E- 03 0.520540E- 03 0.699907E- 03 0.. 106428E-02 0. 140295E-02 0.169834E- 02  0.164880E- 02 0. 164880E-02 0. 164880 E-02 0. 164880E-02 0. 164880E- 02 0.164880E- 02  0.373003E 0.590825E 0.794411E 0.1207 99E 0.159238E 0.1 92766E  06 06 06 07 07 07  0.213372E- 03 0.134707E- 03 0. 100185E- 03 0.658849E- 04 0.499807E- 04 0.412876E- 04  0.576163E- 02 0.500978E- 02 0. 443105E-02 0. 37 4139E-02 0. 3477 20E-02 0.308888E- 02  NR  PE  EB  VEL. CM/SEC  UM  134  CN CN CN CN CN CN CN CN o o o 0 o 0 o o 1 I I 1 II W w w w Pa ft] N p- oo cn t n cn CO T — (\J CN CO CO o r- CN s t CN CO CN CN Q> 00 o IT) VOcn p». i n r- O at U"i at vO O Cn at vo r- oop- s t O CN CN oo vo at s t oo s t VO CN *p- vo i n at at- sx. s t st st tO VO o o o o o o o o o o o  CN CN CM CN CN CN CN CN CN CN CN 0 o o o o o o 0 oO O 1 I I I 1 I Ww M W W W W W W W W i n i n c i o 5 at p* CN 00 st CN o cn CN VO VO i n at ro t n ro i n CTv at CN i n CN vo i n i n vo CO CN cn en i n CN CN o p~ St 00 vo t n CO T - m o o in cn i n oo p-.. vo tO. at U0 m at ID AO r -> P»  oo m oo oo .3. ro st s t st s t O © © © © 0 o o o© o I I 1 i w I I w pa W W W ww oo W w en o cn vO CN o o oo cn o cr> CT\ 00 o i n co st ro co CO 00 m t n cn i n T-.IT> vo t - 00 cn 00 CN en vo i n cn 00 St i t 00 CN 00 vo cn cn «— CO tn no CN oo CN  00 00 00 00 00oo oo oo at st s t  Q O O O O O O O O O O oo r-  o  «*r>fsr"r>-p-r<r'r*<r* o o o o o o o o o o o  vO P** p s P** P*^ t** P*** P** P** P^ p s  CN CN CN O O 0 I I 1 tO w w p~  1  0> St  SB M 6H ES  O U  tn #  >  y  6M  a  r  r  a  o  1  1  w o tn cn CO *—  pa tn p> o tn CO  st st  •  o o o  o CM CN CN OO 00 o*) 0 o0 o O O I I 1 I 1 I w ww w w w tn oo =t cn oo <"* at CO i n vo o r» co vo tn p- m cn 00 VO st m r * at vo r~VO vo CN f" T" P* tn «t O O O O O O P*"  p s p s p** p s  P**  o o o o o o  00 00 CN CN CN CN CN CN CN CN CN  oo CN CN CN CN CN CN CN CN CN o o O o O o o o O o o  rCN CN CN O O o O O O i  1  w o at cn o CN CN  1  1  w w o o at at cn cn o o CN CN CN CN  1  w o at cn o CN CN  1  W o at cn o CN CN  1  1  1  w O at cn o CN CN  w o at cn o CN CN  w o at cn o CN CN  )  ow ar cn o CN CN  o w vo at VO cn  1  1  1  1  1  i 1  1  1  W w W w w cn •at w cn 00 r~ 00 o cn p» CN cn p~ cn 00 r - p- CO p~ o 00 r- oo CN 00 CN o 00 at cn o cn 00 cn o oo ro at CN at cn * • * « • • » « o O O o o o o O w m in o  1  1 1  1  w at w oo m at r - P- o at VO 00 r - 00 cn 00 o r ~ VO cn • * • O o O  ar r- O oo oo 00 at <N cn CN co tn at CN o VO CN oo oo o CO CN vo CO *~ r*. cn co cn  at r~ o oo 00 oo p- at T— in r* CN cn CN CO i n at CN O VO CN 00 oo o 00 CN vo 00 p-» cn 00 cn  cNCNarinvoatmoocNvo  CN CN at i n VO at tn 00 CN vo  ™  r-  w w w ww w vo CN o oo tn vo i n oo uo oo r - p CN oo p ~ r~ cn co at tn o CN vo at oo t— co oo vo «*" CN 00 ^t' vb p » o o o o o o CN CN CN o o o i i 1 1 w w r-~ w rpcn cn cn o o o in in in in m in m m tn  I  I  I  1 www wO w f* w O at vo p» in CO O o oo v cn at O 00 vo O at CN O oo o cn CN P- cn cn CN tn cn 00 in r»- r— • T—• • * « • • o O o o o o 1  I  |  1  at p- o co oo oo' * CN cn CN CO 00 O CO CN VO: CO r-  CN CN at tn vp  at o vo P- P~ co oo r~- vo m O. CN 00 v- cn oo o oo i n at P~ O  atovop~p»cooop-voino CN 00 T~' cn 00 o oo i n at r~ O  at O VO r> P- co CN 00 •"*• cn oo O  i n oo  tn oo  m CO  VO CN p> vo CN m o P* CN oo tn vo r~ ?~ CN CN  vo CN p» VO CN i n o r~ CN CN CN oo tn vo  V vo T~  CN r~CN CN  o o o O O O CN CN CN CN CN CN 00 CO: CO CO CO 00 CO 00 CO CO CO- • o - o O- O O' O^ O" o - o^ o O • O-O-O O ' O - O • t • • t • * • » * • • • • t * # • • • » • • • CN CN CN CN CN <N o o o o o o o o o o O• at. at st at at •at at at at 'at at O O O O O O ' O O o o o  W '  1  1  O o o o O O O O o o O  1  w o at cn o CN CN  T  00  1  1  H H w P- cn i n vo CN h oo r * ar VO VO O St cn co p- CO CN "' "  o o o o o o O o o O O  1  w o at cn o CN CN  'T—  •  •  o o o o o o o o o o  U tn n vo  o o O o  CN CN CN o o o 1 I 1 w w rw rpcn cn cn o o o i n tn tn i n i n tn m tn i n  o O o o o o o o o o 1 t ! 1 I t 1 w 1 1 1 w w iWn 00/* w VO 00 P- CN w w w at VP CO CN CO CO r» o ^ i n cn VO CN O O o vo vo r — cn cn 00 T— oo tn i n at OO aT' cn «— at o at to cn 00 (N cn i n O CO i h cn p"* i n T— en T< N oo CN oo m p» in • • • • • » • • • • • o o O o oo o o o oO  W  t  1  CN CN CN CN CN CN CN CN CM CN CN O o o o o O O O o o Oi 1 1 1 1 1 1 1 1 1 1 w w at w at w at w at w at w at w at w at w at w at at CN CN CN CN CN CN CN CN CN CN CN CO 00 00 00 CO CO CO 00 00 00 CO P- r - p* r- p- r-> rp- p* PP- p- p* r» r» p» p» P* rCN CN CN CN CN CN CN CN CN CN CN  O'  m a  1  1  O O O O o o  CN CN CN CN CN CN CN CN CN CN CN o o o o o o Q O o o O  Q  o 0 o o 0 oo o 0 o 1 I t 1 II 1 I ww w w w ww ww ww o oo CO CN VO tn oo cn co VO 00 CN cn st r~ vo o cn CO 5 * st vo o CN oo vo CN i n p» st © cn P- at o tn tn oo i n CN st P* r~ cn st cn CN Po 00 t" CO vo at vo oo co co ar 0  o o  o o o o o o o o o o w w w ww w w w w w co cn i n vo tn CN oo tn o cn 00 P-* at T " o <N at cn oo cn CN 00 oo at at cn o vo cn p» cn vo 00 at VO at P" vO p- r~ CM cn tn cn vo vo oo COO J CN CN VO r~ T 00 CN CN at vo CO O o o o o O O O o o o  Kl W W W W w w . w w w w at o o oo tn cn o tn tn CN oo V0 CO O P " ovo T - CN cn o o rr* r*> oo cn st cn cn o i n vo cn oo CN «~ tn O") at r*» CO CN so CN 00 r - P- CM p* vo CN i n r - p» tn 00 r - T- CN CN r - cN oo tn vo o o o o o o o O o o O  oo  o p o o o o o o o o o  r- r" r »  TABLE B. 6  DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY COBRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 363.9 Ufl DIAMETER. { UP FLOW ) ST  NR  PE  NG  EB  VEL. CM/SEC  SE  0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500  5.24 8.30 11.16 16.97 22.37 27.08 16.33 22. 57 35.46 50.75 67.00  1. 324 2.097 2. 820 4. 288 5.653 6.843 4.127 5.704 8.961 12.825 16.931  0.228215E- 03 0.361486E- 03 0.486046E- 03 0.739087E- 03 0.974270E- 03 0. 117940E-02 0.711213E- 03 0.982981E- 03 0. 154437E-02 0.221029E- 02 0.291802E- 02  0. 137400E- 02 0. 137400E- 02 0. 137400E-02 0.1374 00E-02 0. 137400E- 02 0.137400E- 02 0. 137400E-02 0.1374 00E-02 0.137400E- 02 0.137400E- 02 0.137400E- 02  0.297676E 0.4715 10E 0.633982E 0.964039E 0.127080E 0.153837E 0.927681E 0. 128217E 0.201443E 0.2 883 03E 0.380616E  06 06 06 06 07 07 06 07 07 07 07  0. 148175E-03 0. 935464E-04 0.695731E- 04 0.457534E- 04 0.347088E- 04 0.286719E- 04 0.475466E- 04 0.344012E- 04 0.218961E- 04 0. 152992E- 04 0.115886E- 04  0.428742E- 02 0. 387597E-02 0.344791E- 02 0.316675E- 02 0.297915E- 02 0. 268317E-02 0.324625E- 02 0. 262968E- 02 0.288872E- 02 0.283228E- 02 0.315802E- 02  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 35.4 6 50.75 67.00  1.324 2.097 2.820 4.288 5.653 6.843 4. 127 5.704 8.961 12. 825 16.931  0.590088E- 03 0.934682E- 03 0.125675E- 02 0.191103E- 02 0.251914E- 02 0.304954E- 02 0.183896E- 02 0.254166E- 02 0.399323E- 02 0.571507E- 02 0.754"5G2E- 02  0. 220940E-02 0.220940E- 02 0. 220940E-02 0. 220940E-02 0.220940E- 02 0. 220940E-02 0.220940E- 02 0.220940E- 02 0.220940E- 02 0.220940E- 02 0. 220940E- 02  0.529164E 0.838180E 0.112700E 0.171373E 0.225905E 0.273469E 0.164910E 0.227925E 0.358095E 0.512502E 0.6 766 03E  06 06 07 07 07 07 07 07 07 07 07  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  0.590281E- 02 0. 572714E-02 0.516939E- 02 0.464431E- 02 0.418315E- 02 0. 410400E-02 0.444327E- 02 0. 410400E- 02 0,432282E- 02 0.532056E- 02 0.541424E- 02  UM  TABLE B.7  d  a  DM  VEL. CM/SEC  DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 216.0 UM DIAMETER. { DOWNFLOW ) RE  ST  NR  PE  NG  EB  0.109 5.24 0. 109 8.30 0. 109 11.16 0. 109 16.97 0. 109 22. 37 0. 109 27.08  0.786 1.246 1. 675 2.547 3.357 4. 064  0.182635E- 04 0.289289E- 04 0.388972E- 04 0.591474E- 04 0.779686E- 04 0. 94384 9E-04  0. 504396E- 03 0.504396E-03 0. 504396E- 03 0.504396E- 03 0. 504396E- 03 0. 504396E-03  0.188918E 0.299241E 0.402353E 0.611822E 0.806509E 0.976319E  05 05 05 05 05 05  0.704185E- 05 0.444570E- 0 5 0.330639E- 05 0.217438E- 05 0.164950E- 05 0.136260E- 05  0.5190 85E-02 0.473038E- 02 0.446783E- 02 0.389815E- 02 0.327911E- 02 0.326049E- 02  0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500  5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00  0.786 1. 246 1,675 2. 547 3.357 4, 064 2.451 3. 387 5.321 7. 616 10.055  0.384301E- 03 0.608722E- 03 0.818474E- 03 0.124458E- 02 0.164062E- 02 0.198605E- 02 0.119764E- 02 0.165528E- 02 0.260063E- 02 0.372200E- 02 0.491378E- 02  0.231374E- 02 0. 231374E- 02 0.231374E- 02 0.2313 74E-02 0.231374E- 02 0.231374E- 02 0. 2313 74 E-02 0.231374E- 02 0. 231374E- 02 0.231374E- 02 0.231374E- 02  0.176773E 0.280003E 0.376487E 0.572489E 0.754660E 0.913553E 0.550898E 0.761407E 0. 119626E 0.171207E 0.2260 27E  06 06 06 06 06 06 06 06 07 07 07  0.148175E- 03 0.935464E- 04 0.695731E- 04 0.457534E- 04 0.347088E- 04 0.286719E- 04 0.475466E- 04 0.344012E- 04 0.218961E- 04 0.152992E- 04 0.115886E- 04  0.900468E- 02 0.806578E- 02 0.704028E- 02 0.633001E- 02 0.566594E- 02 0.52 30 74E-02 0.637446E- 02 0.586646E- 02 0.608713E- 02 0.714069E- 02 0.765222E- 02  0.600 0.600 0.600 0.600 0.600 0.600  5.24 8.30 11.16 16.97 22.37 27.08  0.786 1. 246 1.675 2.547 3.357 4.064  0.553394E- 03 0.876560E- 03 0.117860E- 02 0.179219E- 02 0.236248E- 02 0.28599 1E-02  0.277649E- 02 0. 277649E- 02 0. 277649E-02 0.277649E- 02 0.277649E- 02 0.277649E- 02  0.221506E 0.350858E 0.471756E 0.717357E 0.945626E 0.114473E  06 06 06 06 06 07  0.213372E- 03 0.134707 E-03 0.100185E- 03 0.658849E- 04 0.499807E- 04 0.412876E- 04  0. 126769E- 01 0. 1149 47E- 01 0.978480E- 02 0. 912422E- 02 0. 809154E- 02 0.747833E- 02  TABLE B.7  { CONTINUED )  VEL. CM/SEC  RE  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  0.786 1.246 1.675 2.547 3.357 4.064 2.451 3.387 5.321 7,616 10.055  0.993674E-03 0.157395E-02 0.211630E-02 0.3218G6E-02 0.424208E-02 0.513525E-02 0.309670E-02 0.428000E-02 0.672437E-02 0.962385E-02 0.127054E-01  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  0.314241E 0.497749E 0.669262E 0.101769E 0.134152E 0.162398E 0.9 793 06E 0.135352E 0.212653E 0.304346E 0.401797E  06 06 06 07 07 07 06 07 07 07 07  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  0.131101E-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  011 011 011 011 011 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  0.786 1.246 1.675 2.547 3.357 4.064 2.451 3.387 5.321 7.616 10.055  0.157121E-02 0.248875E-02 0. 334632E-02 0.508844E-02 0.670762E-02 0.811992E-02 0.489654E-02 0.676760E-02 0.106327E-01 0. 152173E-01 0.200899E-01  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  0.409542E 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  0.605810E-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. 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  2.020 2.020 2.020 2.020 2.020 2.020  5.24 8.30 11.16 16.97 22.37 27.08  0.786 1.246 1.675 2.547 3.357 4.064  0.627241E-02 0.993531E-02 0.133588E-01 0.203135E-01 0.267775E-01 0.324154E-01  0. 934752E-02 0.934752E-02 0. 934752E-02 0. 934752E-02 0. 934752E-02 0. 934752E-02  0.880407E 0.139454E 0.187507E 0.285124E 0.375853E 0.454989E  0.241845E-02 0.152683E-02 0.113554E-02 0.746769E-03 0.566503E-03 0.467971E-03  0.715000E-01 0.624000E-01 0.794600E-01 0. 107230E 00 0. 128550E 00 0. 113930E 00  Uti  ST  NS  PE  NG  06 07 07 07 07 07  EB  138  S3  O  CN  co  I  C N CN  O O 0 I  1  CM fM CN CN C N o 0 o O O O  CN I  1  I  I  I  I  C N CN O O I I  1— «—•*- CN 0 o o o  i i  1  fN O I  f N CN C N C N r O O O O O I I I I I  O  st =t r~  i  rO I  pa PaPa.pa pa capa Pa ca ca w ca pa pa ppaa capa pa pa aa pa no r*» a- 5t en 00 cn o oo o CN ON r-  to  ca  CO  ca  o o  vo o o vo no r**00 no oo CN •p** i n oo in no roo oo co r- vo  £3* a t  CN CD  ^  CN CN i n  vo no in o tn ON a t CN Ch ON oo  CN C N no r» VO O 00 st O m «~ r» ON CO CN cn no C N f N i n vo vo m f**. f^. in in m vo vo o o o o o o o o o o o  oo o m ON f N cn o r- vo ON T~* V Q ff)r-  no a r a t 0 o 0  no no no n o a o o' 0  T™"- T—  C h CN vo CN a t O i n a t co o ON o rco cn r~ r~ f*» a t  o o o o o o o o o o o  Si H Q  z o ex. to w szs  u  U  H  CM  w  M  ft  <W  pa oo rr~ VO  o  iH CJ • M as ca H  o w u  S3  OS 55 -•  H  CO  —  Pu O  o  •  H  <N  CN  CN  CN  1  1  Pa ar  1  1  1  pa w acat  at  o o CN  CN  O  O  at  at ar  ar  1  pa  i  ?— r -  CO  CM  CN  CN  T~ CN  CN  W OS  U .tOPa p a\ > 3?3 U _3  cds  no  CN a t CN r-- a r  00 00 oo o *— no VO oo ar  ar ar  CN  O  r- rv© vo vo p» r» p» vo p~ o o o o o o o o o o o pa pa cn  »— at  ar  CN at T-  p» r»  pa pa  VO CN Ch VO VO  pa  pa pa ca  ca pa ca no VD rVO i n ON o i n i n a t ON no no no VO no r rr - a t CN ON i n CN a t O no VO p- no «— o O r~ON T— CN no  CN C h  CN  00  VO  CN  o  o  CN  CN  CN  CN  CN  CN  1  |  1  1  1  1  pa apa pa pa r at ar  ar  r-  CN CN  CN CN  CN  O O O o o  in o in o VO  oo i n no CN o o o o  O  r"  ON  CN  o o  V  VO  00 vo en at  o a  O  no m no no rr> no no no CN  at  o  o  r - r» r - o r - P* r~ p» p» oo 00 oo no no no no no no ro no no no  00  o o o  CN CN 1  o  r- r~  o o o  o  O o O O O at  no CN  O  } 1 1 1 1 1 1 pa c1a pa aca c a c a c a c a c a p a t 00 CN 00 no o i n pa !-» m VO o VO CN vo o oo o r-  S O S H W Q PQ —  cn  no  ON ar  i  w to ft  pa  ar at  00  no no no CN CN CN f N C N CN C N C N o O o O o O O• O Oi O O |  W  S5 SB  O o o o CN CN  r - p* ro o o o  VO  pa ca pa pa Pa pa 00 00 p- vo r- p> i n C h o CN o CN i n 00 a r vo CN o VO no o T— ON i n VO T— r- CN ON i n p» r » r - CN  o O O O o o  CN  CO  VO  VD  o O O o  O  1  O•  wu  VO  o  at  CO a. H o o O M CM CO O  cq  o  W w w ca cn r- C h o o 00 00 VO o a t a t VO o VO CN a T 00 r> r- m CN no i n r -  pa KJ at  ca a 25 S3  00  at  o 0  O o O O O o  M  2:  at at  o  ON m no CN h- a t <~ i n r~ a t no CN ^o at o o O o o o o o o  WD VO O O o  H  CO  Ch  O o  u  o  ar  o 0  oO O0 oo o i i i1 I t I 1 I 1 I I 1 I 1 I 1 I ca paca ca Paca pa ca ca caPa caca caca caca ca ca ca o cn VO CN cn o o no no no m a t rc™a acfaoo CN CN VO no co cn o m ON ON o i n oo a r r- vo no no CO ~ VO in no vo T— vo cn ON 00 i n T- in vo T- CO oo no a r o r> « - at r~ i n no T— ch oo r- no o> tn vo m cn oo tn i n r- r> voiant a ot oo ON 00 tN in CO a t r*> T— cn r~ f N oo v p cn cn a r CO at n o v»  S3 W  to  ar at  o o  T  03 03 O  Q  ar at  CN no CN r — r- C h C N no a t  <o  CN  CN  CN  CN  CN  CN  1  1  1  1  1  1  O O O O O O o O O O O  pa pa pa pa pa pa oooo oooo in in in in in in in in pa pa  1  Pa pa pa  G  oo  in m m o o o o o o o o o o o CN  CN  CN  CN  o  o o o  CN CN  CN  CN  o  o o o o  CN  CN  CN  o  o  p- (-» p- p» !> p* P« p» r- r- rno no no no no no no no no no no  no CN CN f N CN CN C N CN C N CN O o o O O O o o O O o 1 1 | 1 1 1 • 11 t 1 1 1 1 1 c ca VO pa oo ca icna oa oca pa ican =Pat cat ip a na o cn no o o CN o oo CO i n CO CN i n VO o a r no o VO no r C h T" a t no r> no 00 C N CN ON i n r~ CN CN T— o CN r» v O C N ON f N no a r m no a t Ch  o o o o o o o o o o o  o o o o o o o o o o o  iOvoinr-i^afr-iNi-voin co=rr*-arinioincocNT— m r*» CN vo m n o o a r n o o o v o o  vovomr^r~-arT-r ~'—voin ooarr^srmvomoofMT-vn fN vo in no o ar no no vo o  O r -  ,  rMnoarrNinoinr-o  r - C N O O a t C N O O m O O  at o vo r» r» oo no t-vvo in o rsi no 1— cn no o no in = r r>« o  ato^or^r^conor^vomo CN no r~ cn no o no i n ar r> o  moo»~vocNr»vocNmof^T-r-fMcN»-(Nnoinvo  m co  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 i n i n m m tn m i n i n  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  vOCNf-VQCNtnoO r - C N C N ' ~ f N n 0 t n v 0  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  TABLE B.9  UM  VEL. CM/SEC  0. 109 5.24 0. 109 8.30 0.109 11.16 0. 109 16.97 0. 109 22.37 0. 109 27.08  DIMENSION LESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TESTS ON BEDS OF NICKEL SHOT 126.1 UM DIAMETER. ( DOHNFLOW ) RE 0.458 0.726 0,976 1.485 1.957 2.369  ST  NR  PE  NG  EB  0.31323 4E-04 0.496153E- 04 0.667117E- 04 0. 101442E-03 0.133722E- 03 0.161878E- 03  0.865079E- 03 0. 865079E- 03 0.865079E- 03 0. 865079E-03 0.865079E- 03 0.865079E- 03  0.110151E 0.174477E 0.234597E 0.356731E 0.470246E 0.569256E  05 05 05 05 05 05  0.704185E- 05 0.444570E- 05 0.330639E- 05 0.217438E- 05 0.164950E- 05 0.136260E- 05  0.880751E- 02 0.792353E- 02 0.752621E- 02 0.607580E- 02 0.522232E- 02 0.498415E- 02  0.500 0.500 0.500 0.500 0.500 0.500  5.24 8.30 11.16 16.97 22.37 27.08  0. 458 0.659107E- 03 0.726 0.104401E- 02 0.976 0.140375E- 02 1.485 0.213455E- 02 1.957 0.281379E- 02 2. 369 0.340623E- 02  0. 396825 E-02 0. 396825E-02 0.396825E- 02 0.396825E- 02 0.396825E- 02 0.396825E- 02  0.1030 70E 0.163260E 0.219516E 0.3 337 97E 0.4400 14E 0.532660E  06 06 06 06 06 06  0.148175E- 03 0.935464E- 04 0.695731E- 04 0.457534E- 04 0.347088E- 04 0.286719E- 04  0. 127530E-01 0. 110029E-01 0.987256E- 02 0. 914087E-02 0.841301E- 02 0. 737581E-02  0.600 0.600 0.600 0.600 O.600 0.600 0.600 0.600 0.600 0.6 00 0.600  5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00  0.458 0.726 0.976 1.485 1.957 2. 369 1.429 1, 975 3. 103 4.441 5. 862  0.949115E- 03 0. 150337E-02 0.202140E- 02 0.307375E- 02 0.405185E- 02 0.490497E- 02 0.29 5783E- 02 0.408807E- 02 0.642283E- 02 0.919228E- 02 0.121356E- 01  0.476190E- 02 0.476190E- 02 0.476190E- 02 0. 476190E-02 0. 476190E-02 0. 476190E-02 0.476190E- 02 0. 476190E-02 0. 476190E-02 0.476190E- 02 0. 4761 90E-02  0.129152E 0.204573E 0.275064E 0.418265E 0.551360E 0.667449E 0.402491E 0.556290E 0.873994E 0.125085E 0.165137E  06 06 06 06 06 06 06 06 06 07 07  0.213372E- 03 0.134707E- 03 0.100185E- 03 0.658849E- 04 0.499807E- 04 0.412876E- 04 0.684671E- 04 0.495377E- 04 0.315304E- 04 0.220309E- 04 0.166876E- 04  0. 148300E-01 0. 138627E- 01 0. 132919E-01 0.106451E- 01 0. 977369E-02 0.950394E- 02 0.969150E- 02 0.936762E- 02 0.112736E- 01 0.145458E- 01 0.158372E- 01  TABLE B.9 d  a  UM  VEL. CM/SEC  { CONTINUED ) 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  5.24 8.30 11. 16 16.97 22.37 27.08 16.33 22. 57 35. 46 50.75 67.00  0.458 0.726 0.976 1.485 1.957 2.369 1.429 1.975 3. 103 4.441 5.862  0.170423E-02 0.269945E-02 0.362962E-02 0.551923E-02 0.727550E-02 0.880735E-02 6.531108E-02 0.734055E-02 0.115328E-01 0.165057E-01 0.217907E-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. 1832 23E 0.290219E 0.3 902 22E 0.5933 76E 0.782193E 0.946884E 0.570998E 0.789187E 0.123990E 0.177453E 0.2342 73E  06 06 06 06 06 06 06 06 07 07 07  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. 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  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  0.458 0.726 0.976 1.485 1.957 2.369 1.429 1.975 3. 103 4.441 5.862  0.269475E-02 0.426840E-02 0.573920E-02 0.872708E-02 0. 115041E-01 0.139263E-01 0.839795E-02 0.116070E-01 0. 182358E-01 0.260990E-01 0.344558E-01  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  0.238789E 0.3782 35E 0.508566E 0.773331E 0.101941E 0.1234 05E 0.744166E 0.102853E 0. 161593E 0.231270E 0.3 05322E  06 06 06 06 07 07 06 07 07 07 07  0.605810E- 03 0.382463E- 03 0.284448E- 03 0.187062E- 03 0.141906E- 03 0.117225E- 03 0. 194393E-03 0.140649E- 03 0.895218E- 04 0.625506E- 04 0.473798E- 04  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  2.020 2.020 2.020 2.020 2.020 2.020  5.24 8.30 11.16 16.97 22.37 27.08  0.458  0. 107577E-01  0.976 1.485 1.957 2.369  0.229114E-01 0.348393E-01 0.459255E-01 0.555950E-01  0, 160317E-01 0. 160317E-01 0. 160317E-01 0.160317E-01 0. 160317E-01 0. 160317E-01  0.513333E 0.813104E 0.1 09328E 0. 166246E 0.219146E 0.265288E  06 06 07 07 07. 07  0.241845E- 02 0. 1526 83E-02 0.113554E- 02 0.746769E- 03 0.566503E- 03 0.467971E- 03  0.929000E-01 0.935000E-01 0.886000E-01 0.890500E-01 0.910000E-01 0.947000E-01  0.726  0.170398E-01  TABLE B.10  da  UB  VEL. CM/SEC  DIMENSIONLESS GROUPS AND SINGLE COLLECTOR EFFICIENCY CORRESPONDING TO TEST ON BEDS OF NICKEL SHOT 126.1 UM DIAMETER. { UPFLOB ) RE  ST  NR  PE  NG  EB  •  0.500 0.50 0 0.500 0.500 0.500 0.500  5.24 8.30 11. 16 16.97 22.37 27.08  0. 458 0.726 0.976 1. 485 1. 957 2.369  0.659107E- 03 0.104401E- 02 0. 140375E-02 0.213455E- 02 0.281379E- 02 0.340623E- 02  0. 396825E-02 0.396825E- 02 0.396825E- 02 0.396825E- 02 0.396825E- 02 0.3S6825E- 02  0.10 3070E 0.163260E 0.219516E 0.3337 97E 0.4400 14E 0.532660E  06 06 06 06 06 06  0.148175E- 03 0.935464E- 04 0.695731E- 04 0.457534E- 04 0.347088E- 04 0.286719E- 04  0.113065E- 01 0.979875E- 02 0.932615E- 02 0.864948E- 02 0.767020E- 02 0. 769171E-02  0.804 0.804 0.804 0.804 0.804 0.804  5.24 8.30 11.16 16.97 22.37 27.08  0.458 0.726 0.976 1. 485 1.957 2. 369  0. 170423E-02 0.269945E- 02 0.362962E- 02 0.551923E- 02 0.727550E- 02 0.880735E- 02  0.638095E- 02 0,638095E- 02 0. 638095E-02 0.638095E- 02 0.638095E- 02 0. 63 8095 E-02  0.183223E 0.290219E 0.390222E 0.5 933 76E 0.7 82193E 0.946884E  06 06 06 06 06 06  0.383130E- 03 0.2418 80E-03 0.179893E- 03 0.1 18303E- 03 0.897453E- 04 0.741359E- 04  0. 100865E-01 0.102896E- 01 0. 111831E-01 0. 112355E-01 0. 1094 57E-01 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 c o l l e c t o r e f f i c i e n c y (EB).  Several other types of equations were also  t r i e d i n 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  where E  = a  + ctiCE)  0  [C.l]  = EI + ER + ED + EG  EI = 2 St  1.13  ER = 1.5 NR ED = 8 P e  _ 1  (Paretsky  9  +2.3  Pe" ^ 5  EG = NG  8  Re ' 1  31  )  (Friedlander 8  f\~\  )  (Johnstone and  Roberts ) 63  (Ranz ) 67  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 c o l l e c t i o n takes place. evident this was not the case with the results of this work. 59 tions such as that of Landahl and Hermann  It was Other equa-  (Eq. 2.5) gave excessively low  c o l l e c t i o n e f f i c i e n c i e s again bearing no r e l a t i o n to this data.  143 -2/3 For the value of ED equations of the type ED = g Pe would have been s a t i s f a c t o r y .  (Eq.  2.15)  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 l i m i t of Re had to be less than  7.38  which was not the case i n this work. The interception term ER was chosen from Eq. 2.7 as most of the experiments were conducted i n the creeping flow region.  Again equations of  Langmuir and Natanson suffered due to the l i m i t i n g value of Re. The other equations tested were:EB = ct0 + a  x  St + a  2  EB = a  0  + a-i NR + a  EB = a  0  + ai NG + a  NR St + a  NR S t  3  2  St  2  (Davies ) 16 8 31 (Davies , Meisen , Paretsky  [C.2]  16  ) [C.3]  23 2  St  (Doganoglu  )  [C.4]  23 EB = a  + ai NG + a Re St — 2/3 —— EB = tag + OLI Sc Re + a 0  2  2  NR  Re  2  2  2  —  (Doganoglu  ) 61 (Friedlander )  [C.5] [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 l i s t e d f o r con-  ditions r e l a t i n g to constant aerosol or c o l l e c t o r size, i . e . , for each aerosol the variables are gas v e l o c i t y and c o l l e c t o r diameter and for each c o l l e c t o r the variables are gas v e l o c i t y and aerosol diameter. value of the a's were calculated for a l l the data.  Also, the  To compare the degree of  f i t of each equation the square of the multiple c o r r e l a t i o n c o e f f i c i e n t was calculated.  This i s defined as:n  R2  =  -  Z (Yk - Y ) k=3_ n _ E (Yk - Y ) k=l  2  2  (R)  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 value of R  i s to unity the better the model.  The actual  measures the proportion of t o t a l v a r i a t i o n about the mean  accounted for by the regression.  For example i f R  2  = 0.9 then the model  explains 90% of the t o t a l v a r i a t i o n within the data. TABLE C . l . RESULTS OF FITTING EQUATION C . l TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION d  c  ym  a  0  >< 10  3  ai  R  2  0.704 0.102 0.391 0.308 9.396  1.590 1.870 2.012 3.411 1.484  0.855 0.874 0.935 0.870 0.684  2.467 2.364 2.470 3.990 4.667 10.270  1.985 0.509 0.289 1.157 0.623 0.967  0.498 0.397 0.353 0.748 0.755 0.711  A l l results 1.630  1.890  0.692  598.1 511.0 363.9 216.0 126.0 d  a  ym  0.109 0.500 0.600 0.804 1.011 2.020  TABLE C.2.  dc  ao x  ym  io  a  3  2.46 2.66 3.30 7.10 12.60  598.1 511.1 363.9 216.1 126.1  da  RESULTS OF FITTING EQUATION C.2 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION  2  x 10  - 2  5.126 3.430 4.150 4.510 1.247  -  3  a  x 10"  R  4  1.5576  -  2  0.867 0.893 0.956 0.9101 0.744  ym 2.705 2.749 4.180 8.060 10.800 0.507  0.109 0.500 0.600 0.804 1.011 2.02 A l l results  TABLE C.3.  d  ym  598.1 511.0 363.9 216.0 126.1  da  -  --  1.700  -  0.513  -  -  -  7.055 -  1.005 1.616  0.489 0.425 0.365 0.889 0.801 0.716  3.330 2.654 1.117  1..724  RESULTS OF FITTING EQUATION C .3 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION  ag  x  10  4  aj  a  2  R'  -2.76 2.36 6.68 -78.'62 -103.70  2.35 0.11 0.86 4.41 4.66  1.03 0.17 0.21 2.87 0.57  0.852 0.870 0.922 0.903 0.887  -2.61 -2.83 -=11.24 12.90 -19.60 6.92  3.31 2.69 3.03 1.60 1.05 1.67  1.41 0.22 0.11 0.09 1.16 0.63  0.800 0.780 0.808 0.618 0.701 0.828  1.817  0.66  0.854  ym  0.109 0.500 0.600 0.804 1.011 2.020 All results  -0.08  TABLE C.4.  •d  ym  598.1 511.0 363.9 216.0 126.1  RESULTS OF FITTING EQUATION C.4 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION  do x 10  ctj  d  0-2  R'  1.11 0.89 1.26 -0.90 3.06  3.76 2.97 3.76 21.60 34.60  1.48 0.19 0.22 3.66 1.48  0.947 0.895 0.884 0.941 0.960  0.109 0.500 0.600 0.804 1.011 2.020  0.62 1.31 1.13 2.70 2.15 6.47  12.44 7.85 9.61 8.73 17.80 19.15  2.35 0.69 0.65 0.39 1.44 0.89  0.774 0.960 0.922 0.899 0.785 0.848  All results  0.99  15.80  1.24  0.764  d  ym  TABLE C.5.  d  ym  598.1 511.0 363.9 216.0 126.1 d  a  a  RESULTS OF FITTING EQUATION C.5 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION  0  x 10  3  ai  a  x 2  10  - 1  R  2  1.204 0.968 1.512 0.342 3.970  5.51 5.56 7.97 34.20 43.40  1.42 2.19 3.35 9.09 6.26  0.960 0.941 0.943 0.884 0.931  1.590 1.810 1.730 3.130 4.390 10.560  1.93 8.12 9.72 9.08 20.77 17.17  4.46 0.25 0.25 0.24 1.52 1.38  0.511 0.878 0.796 0.874 0.837 0.682  4.250  13.45  0.74  0.204  ym  0.109 0.500 0.600 0.804 1.011 2.020 All results  147  RESULTS OF FITTING EQUATION C. 6 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION  TABLE C. 6.  d  ym  c  598.1 511.0 363.9 216.0 126.1 d  a  0  x 10  1.31 0.93 1.13 -4.17 4.99  a  3  x 2  10  - 2  R  2  -  4.85 0.51 4.81 7.37 2.74  0.904 0.848 0.910 0.953 0.882  9.92  ym  a  0.109 0.500 0.600 0.804 1.011 2.020  3.78 1.98 1.92 3.58 2.83 6.13  -  7.47 2.89 2.52 1.17 3.33 1.79  0.764 0.573 0.533 0.402 0.605 0.792  All results  0.80  20.53  2.32  0.837  In general i t was possible to obtain r e l a t i v e l y good predictions f o r equations f i t t e d to the results r e l a t i n g to one c o l l e c t o r 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 i n the range of 0.5 to 0.7.  In many cases the value of the intercept  ctg was comparable to the  single c o l l e c t o r e f f i c i e n c y and therefore dominated the equations.  This  was obviously u n r e a l i s t i c and the regression analysis was repeated by forcing the equations through the o r i g i n .  Furthermore,  the t o t a l single  c o l l e c t o r e f f i c i e n c y , which by d e f i n i t i o n i s made up of the individual e f f i c i e n c i e s , should equal zero when a l l these individual e f f i c i e n c i e s are zero.  Thus setting ag = 0 should probably r e s u l t i n a more precise model.  TABLE C.7.  d  c  RESULTS OF FITTING EQUATION C.l TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO)  ym  598.1 511.0 363.9 216.0 126.1 d  a  A l l results  TABLE C.8.  c  ym  598.1 511.0 363.9 216.0 126.1 d  a  R^  1.65 1.79 1.89 3.14 1.64  0.829 0.843 0.872 0.814 0.640  17 75 2 64 37 97  0.706 0.490 0.090 0.187 0.661 0.865  1.97  0.689  ym  0.109 0.500 0.600 0.804 1.011 2.020  d  cti  RESULTS OF FITTING EQUATION C.3 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO)  cti 2.12 1.28 1.18 2.19 2.90  0t  2  R^  0.96 1.51 1.71 2.90 0.84  0.874 0.817 0.832 0.803 0.817  ym  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.  d  um  RESULTS OF FITTING EQUATION C.4 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO)  ai  a  R  4.67 4.11 5.74 24.00 37.10  1.52 1.80 1.95 3.13 1.49  0.899 0.846 0.865 0.884 0.960  0.109 0.500 0.600 0.804 1.011 2.020  48.00 39.70 37.90 22.50 13.90 2.90  4.10 2.26 1.82 1.39 1.42 2.17  0.476 0.518 0.533 0.757 0.846 0.846  A l l results  14.00  2.16  0.765  c  598.1 511.0 363.9 216.0 126.1 d  a  c  2  um  TABLE C. 10.  d  2  RESULTS OF FITTING EQUATION C.5 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO)  ym  598.1 511.0 363.9 216.0 126.1  R? 7.2 9.7 11.4 40.3 49.5  0.11 0.15 0.22 0.58 0.50  0.109 0.500 0.600 0.804 1.011 2.020  67.33 46.30 45.00 27.22 18.80 6.46  4.04 0.14 0.37 0.10 0.10 0.26  0.006 0.096 0.075 0.025 0.144 0.576  A l l results  23.20  0.31  0.434  d  a  0.781 0.723  6.689 0.740 0.865  ym  150 TABLE C . l l . RESULTS OF FITTING EQUATION C.6 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO)  d  ym  cti  598.1 511.0 363.9 216.0 126.1  3.19 2.66 3.95 3.06 7.09  5.35 5.30 4.80 6.60 2.88  0.869 0.843 0.891 0.914 0.878  3.06 20.40 32.20 38.70 36.30 42.20  32.30 2.38 1.85 1.80 2.17 5.62  0.865 0.895 0.870 0.857 0.899 0.783  5.96  3.78  0.750  d  c  a  x 2  10  - 2  R  2  ym  a  0.109 0.500 0.600 0.804 1.011 2.020 A l l results  Once again equations could be f i t t e d reasonably well to the data r e l a t i n g to one aerosol or c o l l e c t o r size but the f i t to a l l the data was s t i l l poor. tions  Generally there was l i t t l e improvement i n forcing the equa-  (C.l to C.6) through the o r i g i n except they are more r e a l i s t i c .  Equations of t h i s type are good for predicting EB f o r a given c o l l e c t o r diameter but have limited a b i l i t y for predicting EB over large c o l l e c t o r and aerosol size ranges. 23 Comparisons of the c o e f f i c i e n t s from the equations of Doganoglu  with  those from equivalent equations developed i n t h i s work are shown i n Tables C.12 and C.13.  151 TABLE C.12.  d  c  ym  110 600 All  COMPARISON OF THE COEFFICIENTS OF EQUATION C.4 WITH THOSE FROM DOGANOGLU'S WORK This work  ai  ct2  37.10 4.67 14.00  TABLE C.13.  1.49 1.52 2.16  110 600 All  a  6.89 0.97 8.60  2.89 0.83 2.69  COMPARISON OF THE COEFFICIENTS OF EQUATION C.5 WITH THOSE FROM DOGANOGLU'S WORK This work  d ym c  Doganoglu " oil z  ai 4.95 7.20 23.2  Doganoglu ot2  04  a  0.50 0.11 0.31  9.27 1.42 9.8  2.53 0.06 0.15  2  The c o e f f i c i e n t s agree i n magnitude i f not i n actual value and demonstrate equations of this form can adequately predict EB f o r a given c o l l e c t o r diameter. C.3  Parameter Equations Equations were formulated based on single dimensionless groups and  were f i t t e d by regression analysis to the experimental data.  The equations  were of the type:EB = a + ax Re + a 0  and  2  St + a ND + ak NR + a NG  EB = a + cti Re St + a 0  3  2  5  ND + a NR + ah NG 3  [C.7] [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  a\  a.2  «3  «i+  1.11 14.10 1.92 -0.89 3.06  -  1.48 2.09 2.32 3.66 1.48  -  -  3.76  -  21.60 34.60  0.946 0.869 0.916 0.943 0.966  1.07 0.27 2.70 2.15 0.69 -1.95  -  0.66 0.49 0.39 1.42 0.63 1.02  0.52 27.06  2.34 0.96 1.67 0.85  2.56 7.44 8.73 17.7 6.44  0.964 0.941 0.903 0.785 0.824 0.899  A l l r e s u l t s -6.08  -  1.30  9.39  2.62  10.31  0.810  cL ym  ag x 10  598.1 511.0 363.9 216.0 126.1 d  a  3  a  5  R  2  ym  0.109 0.500 0.600 0.804 1.011 2.011  TABLE C.15.  d  £  ym  598.1 511.0 363.9 216.0 126.0 d  a  RESULTS OF FITTING EQUATION C.8 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION  ctQ x 10^  oq  1.20 0.97 1.51 0.34 _  0.14 0.22 0.33 0.91 _  a  2  _  a  R  3  _  5.51 5.55 7.97 34.20 _  0.958 0.941 0.943 0.884  5.35 5.53 7.44 -  0.960 0.935 0.903 0.794 0.819 0.810  7.43  ym 0.38 -0.39 2.30 0.08 -1.76 -2.06  0.020 0.015 0.020 0.117 0.098 0.053  9.82  1.53 1.95 0.54 2.22 2.47 2.61  All r e s u l t s -8.77  0.091  9.55  4.91  0.109 0.500 0.600 0.804 1.011 2.020  ±  -  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 o r i g i n , 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 i n an equation similar to equation (6 ..4). TABLE C.16.  d  c  ym  RESULTS OF FITTING EQUATION C.7 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO)  oti  598.1 511.0 363.9 216.0 126.1 d  a  a  2  1.26 2.08 2.22 3.14 1.49  a  015  3  2.60 4.15 5;70  -  0.755  -  3.45 24.5 36.4  5.56  R  2  0.927 0.789 0.821 0.891 0.968  ym  _  0.109 03500 0.600 0.804 1.011 2.020  1.31 1.17 1.08 1.22 2.09  A l l results -  2.34  4.57 25.06 37.25 47.50 50.40 104.00  _ -  -  15.3  0.762 0.905 0.893 0.908 0.916 0.846 0.740  154 TABLE C.17.  ym  ai x 10  598.0 511.0 363.9 216.0 126.1  6.70 11.32 15.90 46.5 33.0  1.35 1.49 2.50 2.25 2.56  1.78 2.40 3.81 4.91 15.90  4.57 11.57 42.66 -  d  d  c  a  a  2  a  2  R  3 3.62 4.53 6.23 30.60 35.00  1.76 1.31 1.51 1.71 1.43  2  0.865 0.757 0.723 0.750 0.904  ym  0.109 0.500 0.600 0.804 1.011 2.020 All results  C.4  RESULTS OF FITTING EQUATION C.8 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION (INTERCEPT SET TO ZERO)  4.89  —  _ -  1.71 2.10 2.43 3.08  5.39 -  0.762 0.949 0.792 0.828 0.828 0.757  3.90  5.8  0.689  -  Polynomial Equations It was attempted to develop an equation which avoided the problem of  combining the dimensionless numhens which was equivalent to combining the c o l l e c t i o n e f f i c i e n c i e s of the individual capture mechanism.  The variables  were therefore reduced to t h e i r simplest form, namely the s u p e r f i c i a l gas velocity  (U), c o l l e c t o r diameter (d ) and aerosol diameter (d ). c a  Several combinations of these variables were t r i e d , the best results being obtained by a term of the form: C = (/) u c  n  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 t h i s type were discontinued.  Also the equation bore l i t t l e  r e l a t i o n to the data as i t could not predict a minimum value f o r the c o l l e c t i o n e f f i c i e n c y with increasing gas v e l o c i t y . TABLE C.18.  n  0.05 0.20 0.30 0.50  a  x 0  10  4.47 5.21 4.79 47.90  4  RESULTS OF FITTING EQUATION C.9 TO ALL THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION  ai 0.89 -  a  x 2  10~  25.72 7.11 0.17  2  a  3  x 10"  4.79 -  3  R  at*  -  2  0.712 0.803 0.756 0.717  156  APPENDIX D  DEVELOPMENT OF THE  D.1  BEST EMPIRICAL EQUATION  Introduction T h i s s e c t i o n shows the steps  taken to o b t a i n the b e s t  e m p i r i c a l equation  which c o u l d p r e d i c t 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 b a s i c v a r i a b l e s (d , d , and  U).  The  e q u a t i o n s were t e s t e d by  fitting  them to the  experi-  mental d a t a u s i n g r e g r e s s i o n a n a l y s i s . Having e s t a b l i s h e d the best  e m p i r i c a l equation,  were c o n v e r t e d i n t o the o v e r a l l bed calculated values values.  f o r EBT  A l s o the best  mental r e s u l t s of other  D.2  e f f i c i e n c y EBT  where NR  0  e m p i r i c a l e q u a t i o n was  used to p r e d i c t the  2  NR  U + a  3  NR  -2/3  = d /d a c  T h i s e q u a t i o n i s based  on:  p r o p o r t i o n a l to U -2/3  D i f f u s i o n being Gravity being  measured experi-  p r o p o r t i o n a l to U  p r o p o r t i o n a l to U ^  I n t e r c e p t i o n being  independent of  EB  selected. U  U.  +  NR  U  -1  EB  These  workers.  + a-]. NR + a  I n e r t i a being  3.4.  were then compared w i t h the e x p e r i m e n t a l l y  e q u a t i o n of the f o l l o w i n g form was EB = a  and  u s i n g Eq.  Development of the Best E q u a t i o n f o r P r e d i c t i n g An  i t s predictions for  [D.l]  157 TABLE D . l .  d  c  a  jM  a  *  10  3  -1.70 -2.78 -4.30 -1.97 -1.52  598.1 511.0 363.9 216.0 126.1 d  0  RESULTS OF FITTING EQUATION D.l TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION  a  2  x  4.53 4.87 5.16 10.41 5.48  10  2  a  x lO"  3  R  2  0.803 0.672 0.656 0.740 0.810  _  -  -  -  0.37  2  —  um  0.109 0.500 0.600 0.804 1.011 2.020  -0.294 -0.017 0.336 0.192 -0.590 -1.610  0.88 6.69  A l l results  -5.30  5.58  3.49 11.02 1.02 0.78 0.73  -  0.884 0.949 0.922 0.912 0.846 0.689  -  -  0.706  _  -  -  -  3.95 3.95 5.23 6.53  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 u n r e a l i s t i c .  Therefore t r i a l s were made forcing the equation through the o r i g i n , i . e . , using EB = ct! NR + ct NR U + ct NR 2  3  u" ^ + a 2  3  k  NR U  _ 1  [D.2]  T r i a l s were carried out just with data f o r constant aerosol size as the f i t appeared better than f o r constant c o l l e c t o r size,(see Table  D.2).  158 -TABLE D.2.  d  a  ym  0.109 0.500 0.600 0.804 1.011 2.020 All-results  RESULTS OF FITTING EQUATION D.2 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION a  1  x 2  10  a  2  x 10"  3  0.593 6.54  4.20 4.11 5.47 7.11 -  3.730 1.006 1.062 0.788 -  -  4.92  0.912  a x lO"  2  R  2  k  1.19 -  (d ).  0.880 0.953 0.908 0.897 0.922 0.689 0.757  It was not-leed that £or aerosols up'to _. 0 um there was a tendency of 0:3 to decrease with increasing aerosol diameter  2  f o r the value  From a plot of  3.  on log paper i t was found that ct  versus d -2/3 (d )  .  a  Therefore the equation was modified to  EB = 0 4 NR + a  2  NR U + a  TABLE D.3.  d  a  ym  0.109 0.500 0.600 0.804 1.011 2.011  a  2  -  NR (d U ) " ^ 2  3  Si  3  NR u"  +  [D.3]  1  RESULTS OF FITTING EQUATION D.3 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION a  2  x 10  a  2  4.77 4.79 6.09 7.82 29.20  This change forced the value of a aerosol diameters at ^ 0.0156.  3  x 10 1.79 1.35 1.66 1.45 1.56 1.57  3  R  2  -  2  0.876 0.951 0.908 0.897 0.826 0.828  to be nearly constant for a l l  I t was also noticed that there was an  approximate l i n e a r relationship between a aerosol.  i s roughly proportional to  3  cL  2  and d  with the exception of 2 ym  Therefore the i n e r t i a term was modified from NR U to NR (d U). a The equation needed a g r a v i t a t i o n a l term to explain the effects of  159 upflow and downflow.  Thus d /U and d /U were t r i e d i n the last term. a a  The  2  c  best results were obtained with a value of d /U f o r the g r a v i t a t i o n a l term. 2  cl  The modified equation was now of the form EB = cti NR + ct NR (d U) + a3 NR (d U ) ~  + on* d  2 / 3  2  3.  et  TABLE D.4.  d  a  ym a i  [D.4]  RESULTS OF FITTING EQUATION D.4 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION  a  0.109 0.500 0.600 0.804 1.011 2.020  After eliminating  /U  cl  2  x 10"  2  a  x  3  10  ai+ x  2  -  _  1.79 1.48 1.58 1.17 1.21 1.57  9.49 8.11 7.79 8.40 14.45  10  5  ' R  2  0.876 0.929 0.910 0.914 0.850 0.850  6.7 7.4 4.9 6.3 —  several experimental results (e.g., those at high  v e l o c i t i e s , i . e . , 67 cm/sec, which are probably affected by bounce-off and the inaccurate results of the c o l l e c t i o n of 2.02 ym diameter aerosols on 210 and 126 ym diameter c o l l e c t o r s ) , the equation was then f i t t e d to the remaining r e s u l t s .  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 i n the c o l l e c t i o n . TABLE D.5.  RESULTS OF FITTING EQUATION D.4 TO ALL THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION ( 0 4 SET TO ZERO) a  A l l results  2  x  1CT  2  a  3  x  10  2  a x k  10  -  5  R  2  12.41  0.916  32.59  0.784  A l l results less results f o r gas v e l o c i t y of 67 cm/sec  7.58  1.359  5.84  0.93  A l l results less r e s u l t s f o r gas v e l o c i t y of 67 cm/sec and 2.02 ym aerosols on 216 and 120 ym c o l l e c t o r s  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 _?/-} EB = 660 - j ^ (d U) + 0.0148 (d U) ' + 400,000 d a d a c c  d  1  [D.5]  U  where the multiple c o r r e l a t i o n c o e f f i c i e n t (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 i n Tables D.6 to D.25. Aerosol removal i s given i n a l l of the tables as percent penetration where the relationship between penetration (P) and bed c o l l e c t i o n e f f i c i e n c y (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 i n Tables D.26 to D.29. D.5  Regression T r i a l s 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  The results of the regression analysis are given i n Table D.30.  [D.6]  TABLE D.6  GAS VEL. CM/SEC 5. 24 8.30 11. 16 16.97 22.37 27,08 16.33 22.57 34.46 50.75 67.00 TABLE D.7  GAS 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  COMPARRISQN BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 598.1 UM DIAMETER. | AEROSOL DIAMETER = 0.5 UM; BED DEPTH = 4.536 CM ) DOWNFLOW EXP. , CALC, 66.90 70.10 72.70 72.30 75. 80 75.00 71.80 74.50 .. 69.50 66.50 66.60  58,40 66.30 70. 10 73.80 75.00 75.30 73.60 75.00 74.60 72. 10 68.50  UPFLOW EXP. , CALC. 71.00 74.20 75.30 76.60 79.90 78.20 76.40 77.60 73.60 72.00  -  62, 10 68.90 72.20 75.20 76.10 76.16 75.00 76.10 75.3 0 72.50 68.80  C0MPAR8IS0N BETWEEN PREDICTED AND EXPERIMENTAL PENET RATIONS FOR NICKEL SHOT 598. 1 UM DIAMETER. { AEROSOL DIAMETER = 0.804 UM; BED DEPTH = 4. 536 CM ) DOWNFLOW EXP. CALC. 49.30 52.30 56.70 60.70 60.70 61.80 58. 80 59.00 54. 10 48. 10 48.60 '  49.40 57.10 60.40 62.30 61.70 60.30 62.30 61.70 56.90 49.80 42.60  UPFLOW EXP. , CALC. 53.20 54.50 57.50 62. 40 63.60 60, 10 60.90 64. 40 54.90 52.90 —  •  57.90 63.10 65.10 65.50 64.10 62.20 65.60 64.00 58.20 50.60 43.10  162  TABLE D.8  GAS VEL. CM/SEC 5.24 . 8.30 1 1.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00 TABLE D.9  GAS VEL., CM/SEC 5.24 8.30 11.16 16.97 22.37 27.08  COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 598.1 DM DIAMETER. ( AEROSOL DIAMETER = 1.011 UM; BED DEPTH = 4.536 CM ) DOWN FLOW EXP. CALC. 36. 90 42. 60 46.00 51. 00 53.00 52.50 50. 80 52.70 47.80 37.20 34. 10  43.60 50.90 53.50 54.00 52.00 49.50 54. 10 51.80 44.40 35.40 27.30  UPFLOW EXP. CALC. 43.80 52.00 53.50 56.80 57.80 55.20  -—  56.0 0 59.60 60.20 58.30 55.10 51.90  --  —  COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 598.1 UM DIAMETER. ( ADDITIONAL DOWNFLOW COMPARRISONS; BED DEPTH =4.536 CM ) 0. 109 EXP. , CALC. 82. 50 83.70 85. 10 83.70 86.00 84.40  74.50 80.40 83.60 87. 10 89.00 90.20  AEROSOL DIAMETER UM 0.600 EXP. CALC. 61.30 6 5.60 6 7.00 69.80 70.40 70.50  55.30 63.30 66.90 70.20 70,90 70.60  2.020 EXP. CALC. 1 1.90 14. 10 15.50 13.50 7.90 1.95 .  19.40 23, 10 22.70 18.30 13. 80 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, CM/SEC 5. 24 8.30 1 1. 16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00  DOWNFLOW EXP. ., CALC. 60. 00 65.30 69.00 71. 30 75. 00 73.10 72.30 75. 90 68.40 67.20 65.00  48.20 57. 10 61.70 66. 10 67.50 67.80 65.80 67.60 67.10 63.90 59.60  UPFLOW EXP. CALC. , 62.20 66.80 69.00 75.00 75.70 76.20 73.80 76.00 73. 00 72. 10 —  51.70 59.80 67,60 67.60 68.70 68.80 67.30 68.70 67.80 64.30 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., CM/SEC 5. 24 8.30 11. 16 16.97 22.37 27.08 16. 33 22.57 35.46 50.75 67.00  DOWNFLOW EXP. ... CALC. 36. 80 41.00 45.40 50.30 55.20 55.50 51.30 53.50 53.60 45.00 49.60  38.60 46.90 50.50 52. 60 51.80 50. 10 52. 60 51.80 46.30 38.60 31.10  UPFLOW EXP. , CALC. 39.80 44. 90 48.90 53.30 56.20 59.50 54.00 57.50 56.00 54.00 45.00  46.50 52.70 55.10 55.70 54.10 52.00 55.80 54.00 47.60 39.30 31.60  164  TABLE D. 12  GAS 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  COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 511.0 UM DIAMETER. ( AEROSOL DIAMETER = 1.011 UM; BED DEPTH = 4.536 CM ) DOWNFLOW EXP. . CALC. 29.50 37.50 40.00 44. 10 45. 10 43.50 45.40 39.70 35.20 30.00 27.50  32.80 40.30 43.00 43.30 41.00 38.30 43.50 40.90 33.00 24. 10 17.00  UPFLOW EXP. , CALC. 33.80 38.70 42.50 48.70 48.90 46.00  --  44.10 48.40 49.30 47.40 44.6 0 40.50  -  —  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., CM/SEC 5.24 8.30 1 1.16 16.97 22.37 27.08  0. 109 EXP. CALC. 75.70 78.50 80.50 83.00 83.60 83.60  66.85 74.30 78.20 82.90 85.30 86.80  AEROSOL DIAMETER UM 0. 600 EXP. , CALC. 45.40 52.70 57.30 61.60 66.60 67. 20  44.90 53.70 58.00 61.80 62.50 62.20  2.020 EXP. CALC. 6.80 8.60 1 0.90 8.40 1.50 0.096  11.70 14.30 13.70 10.10 6. 80 4.70  TABLE D. 14  GAS VEL. CM/SEC 5.24 8.30 11, 16 16.97 2 2.37 27.08 1 6.33 22.57 35.46 50.75 67,00 TABLE D.15  GAS 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  COHPARBISON BETHEES PREDICTED AMD EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 363.9 UM DIAMETER. { AEROSOL DIAMETER = 0.5 OM; BED DEPTH .= 4. 536 CM ) DOHNFLOH EXP. CALC. , 29. 10 33. 30 36.90 38,10 43.00 46.60 40.00 41.60 44. 60 37.80 40.80  24.20 33.60 38.90 44.50 46.40 46.60 44. 10 46.40 45.60 41.40 36. 10  UPFLOS EXP. CALC. 32.30 36.00 40.30 43.40 45.60 49.30 42.50 50.00 46.70  -  26.70 35.70 40,80 45.90 47.50 47.60 45.50 47.50 46.30 41.80 36.30  COHPARBISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 363.9 UM DIAMETER. ( AEROSOL DIAMETER = 0.804 UM; BED DEPTH = 4.536 CM ) DOWNFLOW EXP. 14.80 19.20 24.70 29.00 31.00 30.80 28. 10 31.10 29.20 25. 10 20.00  16.20 23.20 26.70 28.70 27.70 26.00 28.60 27.60 22. 10 15.40 10.00  UPFLOW EXP. CALC. 21.00 22.10 25.60 29.40 33.20 33.90 31.00 33.90 32.00 2 4.60 —  21.10 27.40 30.10 31 .00 29.40 27.30 31.10 29.30 22.90 15.80 10.20  166  TABLE D. 16  GAS 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  COUPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 363.9 UM DIAMETER. ( AEROSOL DIAMETER = 1.011 UM; BED DEPTH = 4. 536 CM ) DOWNFLOW EXP. CALC. 12.50 19.90 22.90 26.80 26.40 23.30 27.30 26.00 19.60 13.60 12. 60  12. 10 17.50 19.70 19.70 17.60 15.30 19.80 17.50 11. 40 6.14 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. CM/SEC 5.24 8. 30 11. 16 16.97 22. 37 27.08  0. 109 EXP. CALC. 40. 50 48.20 51. 20 57.60 62.20 65.40  45.20 55.70 61.70 69. 10 73.20 75.70  AEROSOL DIAH ETER UM 0.600 EXP. CALC. 21.90 26.70 31.10 37.30 39.90 44.30  21 .20 29.90 34.60 39.00 * 39.90 39.40  2.020 EXP. . CALC. 0.56 0.74 1.13 0.06 0.02 0.003  2.03 2.67 2.34 1.20 0.54 0.2 5  167  TABLE D.18  GAS ?EL. CM/SEC 5.24 8.30 11.16 16.97 22.37 27.08 16.33 22.57 35.46 50.75 67.00 TABLE D,19  GAS YEL. CM/SEC 5. 24 8.30 11. 16 16.97 22.37 27.08 16.33 22. 57 35.46 50.75 67.00  COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 216.1 UM DIAMETER. ( AEROSOL DIAMETER = 0.5 UM; BED DEPTH = 2.268 CM ) DOWNFLOW EXP. CALC. 14. 30 16.50 20. 90 24.50 27.60 28.40 24.30 27.20 25.90 20.50 18.30  13.70 21.70 26.50 32.00 33.70 34. 10 31.60 33.90 33.00 28.70 23.60  UPFLOW EXP. , CALC. 14.90 15.70 17. 90 24.70 2 8.90 28.30 25.00 29.50 28.00 21. 50 —  14.96 22.70 27.70 32.80 34.50 34.80 32.50 34.60 33.40 29.00 23.70  COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 216.1 UM DIAMETER. ( AEROSOL DIAMETER = 0.804 UM; BED DEPTH = 2.268 CM ) DOWN FLOW EXP. CALC., 5.50 7.50 9.60 " 11.50 12.70 12.50 9.70 12. 80 10. 30 5.40 4. 80  8.16 13.20 15.90 17.40 16.40 14.90 17.40 16.40 11.70 7. 10 3.90  UPFLOW EXP. , CALC. 7.00 8.70 10.50 12.50 12.20 16.20 12.00 13.70 12.30 6. 50 —  10.10 15.20 17.60 18.60 17.30 15.60 18.70 17.30 12 .30 7.20 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., CM/SEC 5.24 8.30 11. 16 16.97 22.37 27.08 16.33 2 2.37 35.46 50.75 67.00  DOWNFLOW EXP. , CALC. 4.50 6. 80 8.10 10.20 9.20 5. 80 10.50 13.01 2. 98 0.20 0.008  5.60 9.10 10.60 10. 40 8.76 7. 16 10.50 8.70 4.70 1.90 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. CM/SEC 5.24 8.30 11. 16 16.97 22.37 27.08  0. 109 EXP. CALC. 31.60 35. 00 37. 10 42. 10 48.30 48.50  32.50 43.60 51. 40 59.40 59.20 64.20  AEROSOL DIAMETER UM 0.600 EXP. , CALC. 6.00 7.80 11.40 13.20 16.60 19.02  11.60 18.50 22.70 26,70 27.40 26.90  2. 020 EXP. CALC. 0.00 0.00 0.00 0.00 0.0 0 0.00  0..64 0.79 0.61 0.22 0.07 0.02  TABLE D.22  GAS 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 TABLE D.23  GAS 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  COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOB NICKEL SHOT 126.0 UM DIAMETER. ( AEROSOL DIAMETER = 0.5 UM; BED DEPTH = 2.268 CM ) DOWNFLOW EXP.  UPFLOW EXP. CALC.  0.35 0.51 0.64 1.74 2.42 2.69 2.50 2.83 1.37 0.39 0.24  1.35 2.40 2.87 3.72 5.39 5.35  0. 19 0.74 1.32 2.10 2. 27 2. 14 2.05 2.27 1.65 0.81 0.32  • -•  0.36 1 .26 2.23 3.72 4.3 0 4.4 0  -  —  COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 126.0 UM DIAMETER. { AEROSOL DIAMETER = 0.804 UM; BED DEPTH = 2.268 CM ) DOWN FLOW EXP. CALC. 0. 250 0.400 0.540 1. 560 2.170 2.360 0.420 0.430 0.076 0.010 0.003  0.072 0.280 0.470 0.610 0.510 0.380 0.610 0.510 0. 190 0.042 0.007  UPFLOW EXP. . CALC. 2.150 1.990 1.420 1.390 1.550 1.615  -  —  •  0. 105 0.360 0. 570 0.680 0.560 0.410  —  170  TABLE D. 24  GAS 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 TABLE D. 25  GAS VEL. CM/SEC 5.24 8.30 1 1. 16 16.97 22.37 27.08  COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 126.0 UM DIAMETER, { AEROSOL DIAMETER = 1.011 UM; BED DEPTH = 2.268 CM ) DOWNFLOW EXP. CALC. 0. 100 0. 170 0.337 0.098 0.019 0.002 0. 103 0.035 0.0016 0.0005 0.00023  0.027 0. 100 0. 148 0. 136 0.081 0.044 0. 142 0.079 0.0125 0.0009 0.00005  COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR NICKEL SHOT 126.0 UM DIAMETER. ( ADDITIONAL DOWNFLOW COMPARRISONS; BED DEPTH = 2.268 CM ) 0. 109 EXP. , CALC. 3. 50 4.90 5.70 9. 90 13.70 15.00  3.68 8.70 13.30 21.40 27.20 31.30  AEROSOL DIAMETER UM 0. 500 EXP. ' CALC. 0.35 0.51 0.64 1.74 2.40 2.69  0.19 0.73 1.30 2.10 2.27 2.14  2.020 EXP. CALC. 0.0 0.0 0.0 0.0 0.0 0.0  0.027 0. 100 0.150 0. 130 0.081 0.040  171  TABLE D.26  GAS VEL. CM/SEC 5. 24 11.16 16.97 22.37 27.08  TABLE D.27  GAS VEL. ,. CM/SEC 3. 10 4. 11 5. 14 6. 17 7.20 8.20 9.30 10.30 11.30 12.30 13.40 14.40 15.40 16.50 17.50 18.50  COMPARRISON BETWEEN PREDICTED AND EXPERIMENTAL PENETRATIONS FOR LEAD SHOT 1800 UM DIAMETER. ( DOWNFLOW; AEROSOL DIAMETER =0.5 UM; BED DEPTH = 4.536 CM ) EXP., 93.76 94.36 95.00 96.29 96.07  CALC. 93.47 95.89 96.53 96.75 96.80  COMPARRISON BETWEEN PREDICTED PENETRATIONS AND THE RESULTS OF A.FIGUEROA. ( COLLECTOR DIAMETER = 7000 UM; BED DEPTH = 2 CM ) 0. 500 EXP. / CALC. 80.3 81.9 84.0 83.8 87.1 87.2 85. 9 90.0 87.2 89.0 90. 1 87.5 88.7 88.4 89.8 90.2  78.5 81.8 84.0 85.5 86.7 87.6 88.3 88.8 89.3 89.7 90.0 90. 3 90.5 90.7 90.8 90.9  AEROSOL DIAMETER UM 1 .099 EXP. , CALC. 81.2 82.4 84.6 86. 4 84.6 88.6 85.0 88.8 86.4 89.7 88.5 86.0 87.2 86. 1 87.8 88.6  67.1 71.6 74.6 76.5 77.8 78.8 79.4 80.0 80.2 80.3 80.4 80.4 80.3 80.2 80.0 79.8  2. 020 EXP. CALC. 64. 4 66.9 68. 9 73.9 70. 1 76. 0 68.8 74.0 69.7 71.3 67. 6 67.8 64. 9 57.7 56.7 51.6  47.9 53.8 57.4 59.5 60.8 61.5 61.7 61.6 61.3 60.9 60.3 59.6 58.8 58.0 57. 1 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., CM/SEC 2.86 3.83 6.04 12.37 19.51 31.46 43.80 TABLE D.29  GAS VEL. CM/SEC 0.98 2.02 2.69 3.83 3.83 4.92 6.04 8.70 10.53 12.37 13.20 19.50  EXP.  1. 35  AEROSOL DIAMETER UM CALC. 0.935E-2  0. 124E-2 0.720E-3  0.779E-2  0.100E-3 0.600E-4 0.285E-2 0.81 IE-2  0.536E-2 0.593E-2 0.765E-2 0.975E-2  -  -  EXP.  1 .75  0.515E-2 0.417E-2 0.297E-2 0.332E-2 0.240E-2 0.632E-2 0.151E-1  CALC., 0.120E- 1 0.101E- 1 0.814E- 2 0.762E- 2 0.893E-2 0.121E- 1 0.158E- 1  COMPARRISON BETWEEN PREDICTED SINGLE COLLECTOR EFFICIENCY AND THE RESULTS OF Y.DOGANOGLU. ( COLLECTOR DIAMETER = 10 8.5 CM; LIQUID D.O.P. AEROSOL )  EXP.  AEROSOL DIAMETER UM 1. 35 1 .75 CALC. EXP. CALC  0.328E- 1 0.355E- 1 0.343E- 1 0.371E- 1 0.369E- 1 0.253E- 1 0.259E- 1 0.302E- 1 0.278E- 1 0.367E- 1 0.572E- 1 0.838E- 1  0.784E- 1 0.489E- 1 0.413E- 1 0.342E- 1 0.342E- 1 0.306E- 1 0.285E- 1 0.26 5E- 1 0.264E- 1 0.268E- 1 0.271E- 1 0.320E- 1  0.4 89E- 1 0.577E- 1 0.501E- 1 0.354E- 1 0.38 5E- 1 0.412E- 1  0.906E- 1 0.568E- 1 0.483E- 1 0.408E- 1 0.408E- 1 0.374E- 1  0.415E- 1 0.441E- 1 0.442E- 1 0.737E- 1 0. 92 7E-1  0.349E- 1 0.360E- 1 0.374E- 1 0.382E- 1 0.562E- 1  -  -  173 RESULTS OF FITTING EQUATION D.,6 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION  TABLE D.30.  d iim c  a  2  x 10  a  x 10  3  - 1  R  2  1.43  0.26 0.27 0.43 2.68 3.39  0.91 0.87 0.84 0.93 0.89  1.46 1.36 1.38 1.29 1.31  24.40 2.23 2.24 1.51 0.85  0.92 0.88 0.86 0.89 0.86  1.29 1.52 1.64 2.87 1.36  1.76 1.11 0.71  18.90 1.46 1.18 1.11 1.19  598.7 511.0 363.9 216.0 126.1  - 5  -  d urn a 0.109 0.500 0.600 0.804 1.011 2.020 All results  The value of a  -  -  3  1.76  - .  1.48  1.15  . .  -  0.89  i n a l l cases i s too large and therefore Eq. D.6 does  not f i t the upflow data.  Thus the value f o r 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 (ct SET AT 1.25) 3  d  a  ai  ym  0.109 0.500 0.600 0.804 1.011 2.020  a  x  2  10  R  5  2  20.79 1.58 1.14 1.12 1.20 1.55  1.57 1.48 1.55 1.45 1.42 1.89  0.82 0.86 0.88 0.89 0.94 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 f i n a l form of the equation was derived. EB = 1.0 St + 150,000 NR  4j/3  P e " ^ + 1.25 NG  [D.7]  3  69 D.6  Regression T r i a l s with the Equation of Schmidt The term for interception (NR) was ignored as interception plays no  r o l e i n the present work. EB - a i St + a  The equation used was of the form:  (8 Pe" +2.3 Pe" '' R e ^ ) + a 1  2  Again the value of a  3  5  8  8  3  NG  [D.8]  was fixed at 1.25 and the regression t r i a l s  carried out only f o r constant aerosol sizes.  TABLE D.32.  d  a  RESULTS OF FITTING EQUATION D.8 TO THE EXPERIMENTAL DATA BY MULTIPLE REGRESSION a  um  0.109 0.500 0.600 0.804 1.011 2.020  R  2  2  15.48 1.04 1.07 0.94 1.24 1.41  0.95 5.98 8.73 11.03 11.40 28.40  0.81 0.82 0.83 0.86 0.84 0.50  1.19  8.06  0.82  A l l r e s u l t s less the r e s u l t s of 2.02 ym aerosol  further optimization the f i n a l form of the equation was derived EB = 0.8 St + 8.0 (8 Pe" + 2.3 P e ~ 1  5 / 8  Re~  1/8  ) + 1.25 NG  [D.  

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