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Deposition of droplets onto solid objects in aerosol flow 2010
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Title | Deposition of droplets onto solid objects in aerosol flow |
Creator |
Petkovic, Bojan |
Publisher | University of British Columbia |
Date Created | 2010-02-25T17:59:47Z |
Date Issued | 2010-02-25T17:59:47Z |
Date | 2010 |
Description | In this work, the effect of velocity on deposition coefficients and capture efficiencies on a circular disk, placed normal to an aerosol flow was investigated. The superficial gas velocity was varied in the range of 0.1 m/s to 1.5 m/s, while the volume median diameter of the droplet size distribution varied between 3.9 and 7.5 microns. The morphology and distribution of deposits on the upstream and downstream surface of the disk were observed and measured. The effect of contact angles (20°, 51°, 94°) on deposition, and dry vs. wet surface effects were also investigated. It was found that in the range of velocity and droplet sizes investigated, deposition on the upstream side was dominated by the inertial impaction mechanism. Capture efficiencies increased with velocity and droplet size, and could be explained by the inertial impaction mechanism from the upward flow, using the potential flow approximation. For the downstream side, capture efficiencies increased with droplet size and showed a minimum with velocity. It is postulated that the governing deposition mechanism for the downstream side is the inertial impaction mechanism with gravity in the flow direction. On the upstream side, it was found that deposits were concentrated closer to the coupon edge, while on the downstream side, the distribution of deposits on the surface was uniform. In the range of investigated contact angles, there was no significant difference observed between the deposition rates. The same can be said for the effect of dry vs. wet coupon surface. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | Eng |
Collection |
Electronic Theses and Dissertations (ETDs) 2008+ |
Date Available | 2010-02-25T17:59:47Z |
DOI | 10.14288/1.0058924 |
Degree |
Master of Applied Science - MASc |
Program |
Chemical and Biological Engineering |
Affiliation |
Applied Science, Faculty of |
Degree Grantor | University of British Columbia |
Graduation Date | 2010-05 |
Campus |
UBCV |
Scholarly Level | Graduate |
URI | http://hdl.handle.net/2429/20891 |
Aggregated Source Repository | DSpace |
Digital Resource Original Record | https://open.library.ubc.ca/collections/24/items/1.0058924/source |
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Deposition of Droplets onto Solid Objects in Aerosol Flow by Bojan Petkovic B.Sc., University of Novi Sad, Serbia, 2004 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Chemical and Biological Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) February 2010 © Bojan Petkovic, 2010 ii Abstract In this work, the effect of velocity on deposition coefficients and capture efficiencies on a circular disk, placed normal to an aerosol flow was investigated. The superficial gas velocity was varied in the range of 0.1 m/s to 1.5 m/s, while the volume median diameter of the droplet size distribution varied between 3.9 and 7.5 microns. The morphology and distribution of deposits on the upstream and downstream surface of the disk were observed and measured. The effect of contact angles (20°, 51°, 94°) on deposition, and dry vs. wet surface effects were also investigated. It was found that in the range of velocity and droplet sizes investigated, deposition on the upstream side was dominated by the inertial impaction mechanism. Capture efficiencies increased with velocity and droplet size, and could be explained by the inertial impaction mechanism from the upward flow, using the potential flow approximation. For the downstream side, capture efficiencies increased with droplet size and showed a minimum with velocity. It is postulated that the governing deposition mechanism for the downstream side is the inertial impaction mechanism with gravity in the flow direction. On the upstream side, it was found that deposits were concentrated closer to the coupon edge, while on the downstream side, the distribution of deposits on the surface was uniform. In the range of investigated contact angles, there was no significant difference observed between the deposition rates. The same can be said for the effect of dry vs. wet coupon surface. iii Table of Contents Abstract…………………………………………………………………………………… ii Table of Contents………………………………………………………….……………...iii List of Tables…………………………………………………………………………….viii List of Figures…………………………………………………………………………….xi Nomenclature…………………………………………………………………………. xviii Acknowledgments………………………………………………………………….… xxvii Chapter 1. Introduction………………………………………………………….……... 1 1.1. Bitumen upgrading and the Fluid Coker………………………………………….. 2 1.2. Fouling in the Scrubber section of the Fluid Coker………………………………. 4 1.3. Project objectives…………………………………………………………………. 5 1.4. Scope of the thesis……………………………………………………….………... 7 Chapter 2. Theory and Literature Review……………………………….……………. 8 2.1. Particle deposition from turbulent flow parallel to solid surfaces………………... 8 2.2. Particle deposition from the flow around bluff bodies and surfaces…………….. 11 2.2.1. Upstream (front) side………………………………………………………..13 2.2.2. Downstream (back) side……………………………………………………. 16 2.3. Distribution of deposits along the coupon radius………………………………... 18 2.4. Contact angle effect………………………………………………………..…….. 19 2.4.1 Wetting and contact angles………………………………………………. 20 2.4.2. Impact of droplets on the solid surface (sticking vs. rebounding)………. 22 2.4.3. Superoleophobicity……………………………………………….……... 25 Chapter 3. Modeling…………………………………………………………….……... 27 3.1. Particle deposition on the upstream and downstream side………………………. 27 3.2. Gas phase flow…………………………………………………………………... 29 3.2.1. Continuity and momentum conservation equations………………………... 29 3.2.2. Potential flow approximation………………………………………………. 30 3.2.3. Potential flow with the viscous sublayer…………………………………… 31 3.3. Inertial impaction mechanism…………………………………………………… 31 3.4. Particle transport due to turbulence……………………..……………………….. 34 iv 3.4.1. Particle transport due to convective diffusion……………………….……... 34 3.4.2. Particle transport due to turbulent diffusion in the inertial regime………….34 3.5. Surface coverage………………………………………………………………… 35 3.5.1. Deposition model……………………………………………………………35 3.5.2. Estimation of deposition rates……………………………………….……... 36 3.6. Deposition coefficients…………………………………………………………... 37 3.7. Droplet size distribution fitting………………………………………………….. 38 3.7. Reaction………………………………………………………………………….. 39 3.8. Drop size estimation in the Hot Unit…………………………………………….. 41 Chapter 4. Experimental Study……………………………………………………….. 46 4.1. Cold Unit apparatus……………………………………………………………… 46 4.1.1. Cold Unit details…………………………………………………….……… 48 4.1.1.1. Cold Unit Setup #1 and Setup #2……………………………….…….. 48 4.1.1.2. Atomizers………………………………………………………..…….. 49 4.1.2.3. Gas distributor………………………………………………………… 50 4.1.2.4. Other settings………………………………………………………….. 51 4.2. Hot Unit apparatus……………………………………………………….……… 53 4.3. Measurement techniques………………………………………………………… 55 4.3.1 Liquid flow and aerosol concentration measurements…………….………... 55 4.3.1.1. Measurements of the liquid flow to the nozzle………………………... 55 4.3.1.2. Measurements of the liquid flow to the aerosol………………………..55 4.3.2. Velocity measurements…………………………………………………….. 59 4.3.3. Shadowgraphy measurements of aerosol drop size distribution…………… 59 4.3.3.1. Shadowgraphy setup…………………………………………………... 59 4.3.3.2. Aerosol sampling……………………………………………………… 62 4.3.3.3. Hardware and software settings……………………………………….. 65 a. Shadowgraphy hardware settings………………………………………... 65 b. RS Image software settings……………………………………….……... 66 4.3.3.4. Sample size……………………………………………………………. 66 4.3.3.5. Image processing and image segmentation settings…………………... 67 4.3.3.6. Calibrations……………………………………………………………. 68 v a. Camera view field calibration……………………………………………. 68 b. Calibration of the Internal focus module…………………………..…….. 69 c. Depth of field calibration………………………………………………… 71 4.3.3.7. Corrections…………………………………………………………….. 73 a. Border correction………………………………………………….……... 73 b. Depth of field correction…………………………………………………. 74 4.3.3.8. Shadowgraphy verification……………………………………………. 74 4.3.3.9. Summary procedure…………………………………………….……... 76 4.3.3.10. Suggestions for improvements………………………………………. 77 4.4.4. Coupon drop size distribution measurements……………………………….77 4.4.4.1. Deposition (sampling)………………………………………………… 78 4.4.4.2. Recording images along the coupon radius…………………….……... 79 4.4.4.3. Image analysis in Image Pro Plus……………………………….…….. 80 4.3.5. Deposition rate measurements……………………………………….……... 82 43.5.1. Load cell measurements………………………………………………...82 4.3.5.2. Analytical balance measurements……………………………………... 84 4.3.6. Contact angle measurements……………………………………………….. 85 4.3.6.1. Measurement procedure………………………………………………..85 4.3.6.2. Accuracy of contact angle measurements……………………………... 86 Chapter 5. Results and Discussions…………………………………………………… 88 5.1. Effect of velocity ………………………………………………………….……..89 5.1.1. Effect of velocity with 50% sugar solution ………………………………... 89 5.1.2. Effect of velocity with triethylene glycol…………………………….……..90 5.1.2.1. Cold Unit nozzle, Setup #1……………………………………………. 90 a. Upstream side……………….……………………………………………. 92 b. Downstream side………………………………………………………… 93 5.1.2.2. Hot Unit nozzle, Setup #2……………………………………….…….. 95 5.2. Effect of droplet size distribution, Cold Unit nozzle, Setup #1…………………. 98 5.2.1. Upstream side…………………………………………………………… 98 5.2.2. Downstream side…………………………………………………………99 vi 5.3. Calculation of capture efficiencies and deposition coefficients for individual drop sizes from experimental results………………….…………….……………………. 100 5.3.1. Effect of drop diameter at different velocities, downstream side…….…… 101 5.3.2. Effect of velocity for different drop diameters, downstream side.………... 104 5.4. Simulations…………………………………………………………………….. 106 5.4.1. Inertial particle transport………………………………………………….. 106 5.4.1.1. Particle trajectories…………………………………………………... 106 5.4.1.2. Discussion of the model validity……………………………………...107 a. Analytical vs. numerical solutions for Stokesian particles, and non- Stokesian vs. Stokesian particles………………………………………….. 107 b. Comparison with the CFD results………………………………….……109 c. Potential flow with patched viscous sublayer…………………………... 110 5.4.1.3. Effect of gravity on inertial particle transport……………………….. 111 a. Capture efficiencies vs. Stokes number…………………………….…... 112 b. Capture efficiencies vs. drop diameter and velocity……………………. 113 5.4.2. Particle transport due to turbulence……………………………………….. 115 5.5. Comparison with experimental data……………………………………….…... 117 5.5.1. Upstream side……………………………………………………………... 117 5.5.2. Downstream side…………………………………………………….……. 118 5.6. Morphology of deposits and their distribution along the disk radius…………... 121 5.7. Contact angle and dry vs. irrigated surface effect……………………….. 125 Chapter 6. Application of the Results to the High Temperature Unit Conditions.. 128 6.1. Estimation of droplet size distribution in the Hot Unit………………………… 128 6.2. Deposition coefficients for high temperature unit conditions……………..……129 6.3. Comparison of results………………………………………………………….. 131 Chapter 7. Conclusions and Recommendations……………………………………. 134 7.1. Conclusions…………………………………………………………………….. 134 7.2. Recommendations……………………………………………………………… 136 7.2.1. Recommendations for further investigations in the Cold Unit……….……136 7.2.2. Recommendations for the industrial case ………………………………… 137 References……………………………………………………………………………... 140 vii Appendix A. Cold Unit Operating Procedure………………………………………. 147 Appendix B. Calibrations…………………………………………………...……….. 150 B.1. Pump calibration……………………………………………………………….. 150 B.2. Rotameter calibration………………………………………………………….. 152 B.2.1. Theoretical background…………………………………………………... 152 B.2.2. Experimental………………………………………………………………153 B.3. Load cell calibration……………………………………………………….…... 157 Appendix C. Equations Development………………………………………………. 158 C.1. Inertial particle transport from potential flow…………………………………. 158 C.1.1. Equations of particle motion……………………………………………… 158 C.1.2. Flow field from potential flow approximation……………………….…... 159 C.1.3. Capture efficiencies for Stokesian particles………………………….……160 C.1.3.1. X-component particle trajectory…………………………………….. 160 a. Conjugate complex roots (St > 1/16)……………………………….…... 161 b. Real roots (St < 1/16)…………………………………………………… 162 C.1.3.2. r-component particle trajectory……………………………………… 163 C.1.3.3. Capture efficiencies…………………………………………………..164 a. No gravity (p = 0)………………………………………………………. 164 b. With gravity (p=1, p=-1)………………………………………………...165 C.1.4. Capture efficiencies for non-Stokesian particles………………….…... 166 C.1.5. Distribution of deposits along the coupon radius……………………... 168 C.2. Drop diameter on a surface ……………………………………………….…... 169 Appendix D. Software Codes………………………………………………………….171 D.1. Image Pro Plus macros………………………………………………………… 171 D.2. MATLAB ® codes……………………………………………………………… 174 D.3. Mathcad code………………………………………………………………….. 191 Appendix E. Tables…………………………………………………………………… 195 viii List of Tables Table 1.1 Bitumen, Synthetic crude, and Conventional crude oil properties [5]…..……...2 Table 2.1 Summary of experimental data and simple theoretical treatments of inertial impaction on the front side of bluff bodies……………………………………………… 15 Table 2.2 Summary of experimental investigations for the downstream (back) side of bluff bodies……………………………………………………………………………… 18 Table 2.3 Degree of wetting explained in terms of solid-liquid and liquid-liquid interaction………………………………………………………………………………...21 Table 2.4 Contact angles of water at 20°C with solids of different surface energies [38]………………………………………………………………………………….…… 21 Table 2.5 Possible outcomes of droplet impact on a solid surface ……………………... 23 Table 3.1 Summary of mechanisms of deposition on the circular disk from an upward flow……………………………………………………………………………………… 29 Table 3.2 Accumulation rate and mass of deposits as a function of time……………….. 41 Table 4.1 Variability in liquid flow rate measurements (g/min), with aqueous sugar solution and tri-ethylene glycol, at different superficial velocities (Setup #1, Fig. 4.3).……………………………………………………………………………………… 58 Table 4.2 Exposures (in microseconds) needed for 50% blurriness of different drop diameters and different velocities…………………………………………….…………. 62 Table 4.3 Comparison of the volume median diameter measured right after the flow is stopped and 5 seconds after the flow is stopped, at 6× magnification and 110 microseconds exposure. Velocity 1 m/s, liquid flow to nozzle 40 ml/min……………… 63 Table 4.4 Comparison of the volume mean diameter measured 5 seconds after the flow is stopped and when the aerosol flows upward.…………………………………………… 64 Table 4.5 Terminal velocities if tri-ethylene glycol in air at room temperature and the time needed to travel 80cm in free fall………………………………………………….. 64 ix Table 4.6 Main shadowgraphy hardware settings………………………………….……. 66 Table 4.7 Main RS Image software settings…………………………………………….. 66 Table 4.8 Effect of sample size on measured volume median diameter (Run 33)……….67 Table 4.9 Internal focus module calibration at different magnifications…………..……. 70 Table 4.10 Main settings for the image segmentation…………………………….…….. 72 Table 4.11 Detection probability for different particle sizes, at 6× magnification (W = 718µm, H = 536µm)……………………………………………………………………...74 Table 4.12 Glass beads in different focus position, captured and analyzed with shadowgraphy…………………………………………………………………………… 76 Table 4.13 Relevant environment settings in the Image Pro Plus for coupon deposit analysis (1−set, 0−not set)………………………………………………………….……. 81 Table 4.14 Variability in contact angle measurements using the sessile drop method……………………………………………………………………………………87 Table 5.1 Properties of 50% aqueous sugar solution and triethylene glycol at 20°C…… 90 Table 5.2 Operating conditions for contact angle tests…………………………….…... 125 Table 5.3 Coupon material and roughness properties at initial dep. rate tests……..…...125 Table B.1 Rotameter #1 calibration data………………………………………………..154 Table B.2 Rotameter #2 calibration data………………………………………………..155 Table B.3 Rotameter #3 calibration data………………………………………………..156 Table C.1 Correction factor for different contact angles………………………………. 170 Table E.1 Summary results for the effect of velocity, triethylene glycol, Cold Unit nozzle, Setup #1…………………………………………………………………….………….. 195 Table E.2 Summary results for the effect of velocity, triethylene glycol, Hot Unit nozzle, Setup #2…………………………………………………………………….…………...196 Table E.3 Summary results for the effect of droplet size distribution, triethylene glycol, Cold Unit nozzle, Setup #1…………………………………………………………….. 198 x Table E.4 Deposition coefficients for the downstream side, m/hr……………………... 199 Table E.5 Weight of deposits (± 0.1mg) at the end of experiment, m(τi), mg…………. 200 Table E.6 Experimental integral deposition rates, exp,idr , mg/hr…………………….…... 200 Table E.7 Correction factors (last column) obtained from several Cold Unit runs……. 201 Table E.8 Estimated volume median diameter after evaporation……………………… 201 Table E.9 Estimation of deposition rates at high temperature conditions from the deposition coefficients in the Cold Unit………………………………………………...201 xi List of Figures Figure 1.1 Schematic representation of the bitumen upgrading process [9]……………… 2 Figure 1.2 Schematic of the Syncrude Fluid Coker……………….……………….……... 3 Figure 1.3 Segment of the packing elements in the Scrubber Section of the Fluid Coker, (a) before start up of the reactor and (b) after reactor shutdown…...……………………...5 Figure 1.4 Side view of the scrubber packing elements, given in Fig. 1.3. The blades are inclined at a 30° angle with the vertical axis [8]….…………………….………………… 5 Figure 1.5 Schematic representation of the side and top view of the 5 cm diameter disk in the 7.5 cm diameter column (aerosol droplets are presented disproportionately large)……………………………………………………………………………………… 6 Figure 2.1 Summary of experimental data on particle deposition from turbulent pipe flow, adapted from Young and Leeming [18]…………………………………………………. 10 Figure 2.2 Experimental and theoretical data on inertial deposition onto front surfaces of disks………………………………………………………………………………………14 Figure 2.3 Schematic representation of the surface tension forces acting on a droplet deposited on the surface…………………………………………………………………. 20 Figure 2.4 Droplet on a surface in the Cassie (metastable) state, showing superhydropho- bic properties, and in the Wenzel (stable) state, wetting the surface……………………. 23 Figure 3.1 Schematic representation of the flow field around a disk, with particle transport mechanisms..…………………………………………………………………...28 Figure 3.2 Schematics of the patched viscous sublayer, linearly increasing from 0=rv at 0=x , to rv r = at 2.0−=x …………………………………………….………………..31 Figure 3.3 Schematic representation of the discrete amounts of deposits on the coupon surface. Layer 1 had more time to react than layer n and release more volatiles…….…. 39 Figure 4.1 Schematic of the Cold Unit Apparatus………………………………………. 47 Figure 4.2 90° and 45° elbows used for removal of large droplets……………….……...48 xii Figure 4.3 Cold Unit Setup #1 and Setup #2, used in the experiments. Setup #1 was used with the Cold Unit nozzle and the nozzle from Spraying Systems Co., while Setup #2 was used for the experiments with the Hot Unit nozzle………………………………………49 Figure 4.4 Cold Unit nozzle details, used in the setup with elbows (Setup #1)………… 49 Figure 4.5 Hot Unit nozzle details, used in the position below the column (Setup #2)………………………………………………………………………………….……. 50 Figure 4.6 1/4QMJ + SUQR220B QuickMist TM nozzle details, used in experiments for shadowgraphy validation………………………………………………………………... 50 Figure 4.7 Drawing and the picture of the gas distributor in the Cold Unit……………...51 Figure 4.8 Fan positioned close to the load cell to remove aerosol droplets causing load cell failures………………………………………………………………………………. 52 Figure 4.9 Rod motion and deposition constraints, installed to reduce oscillations of the coupon and prevent formation of significant amount of deposits on the rod.…………... 52 Figure 4.10 Process flow sheet diagram of the Hot Unit Apparatus [52]...……………... 54 Figure 4.11 Picture of the RK-75211-10 Cole Parmer Console Drive and RK-07002-27 Micropump ® A-mount Suction Shoe Pump Head with its scale………..………………. 55 Figure 4.12 Schematic representation of the tank with the liquid that is pumped to the nozzle (4 liter), and the tank for collecting the washdown (2.5 liter), placed on the balance.…………………………………………………………………………………...56 Figure 4.13 Log of the liquid flow to the aerosol for Run 28 (Cold Unit at 1m/s, Setup #1). Short experiments and the presence of elbows reduce accuracy of droplet flow measurements……………………………………………………………………………. 57 Figure 4.14 Log of the liquid flow to the aerosol for Run 53 (Cold Unit at 1m/s, Setup #2). Straight line from long experiment results in droplet flow measurement accuracy higher than 1%………………………………………………………………………….. 57 Figure 4.15 Schematic representation of the Shadowgraphy system used on the Cold Unit and the path of light rays entering and leaving the droplet…………….………………... 60 xiii Figure 4.16 Pictures of the Shadowgrahy system installed on the Cold Unit and details of the Optem ZOOM XL long distant lenses………………………………………………. 61 Figure 4.17 Schematic of the solution for eliminating glass curvature…………………..61 Figure 4.18 Schematic representation of the shape and intensity of droplet shadows captured at constant aerosol velocity and increased exposure. Sharpness of the images also decreases with a decrease in shadow intensity.……………………….……………. 62 Figure 4.19 Calibration lines of ‘Cool Snap Pro cf camera + OPTEM Zoom 70 XL lens’ and ‘Cool Snap Pro cf camera + OLYMPUS BX41 Microscope’ systems….………….. 69 Figure 4.20 Camera was moved with the help of the moving stage……………………...70 Figure 4.21 Traveled camera distance in X-direction vs. internal focus module position, required to bring the Objective Micrometer back in focus, 6× magnification…………... 71 Figure 4.22 Schematic representation of the depth of field. For larger particles, depth of field is larger…………………………………………………………………………….. 71 Figure 4.23 Glass beads (3.4-16.6 µm) and Polyamid particle (26.2 µm) in the focus, used for depth of field calibration; 6× magnification……………………….…………... 72 Figure 4.24 Depth of field for the shadowgraphy system, using Image Pro Plus settings given in Table 4.10……………………………………………………………………….73 Figure 4.25 Verification of shadowgraphy with glass beads on the microscopic glass slide……………………………………………………………………………………… 75 Figure 4.26 Picture of the Microscope and Camera setup, used for recording images of coupon deposits………………………………………………………………………….. 78 Figure 4.27 Schematic representation of: (a) glass coupon used for deposit size distribution analysis and (b) placement of the coupon in the column …..……………… 79 Figure 4.28 Locations of coupon deposit samples taken from the upstream and downstream side. First image starts as the coupon centre, last image is taken at the coupon edge……………………………………………………………………………... 80 Figure 4.29 Supporting stage made of glass slides ……………………………….……...80 xiv Figure 4.30 Schematic representation of (a) light rays that pass through the spherical cap and (b) one example of deposits on the downstream side, Run 56……………………… 81 Figure 4.31 Identified droplets on the upstream surface, with (a) Convex Hull=0 and (b) Convex Hull=1 option. In the second case, measured diameter is much closer to the real diameter of droplets……………………………………………………………………... 82 Figure 4.32 GSO-50 load cell and DPM-3 data logger from Transducer Techniques………………………………………………………………………………. 83 Figure 4.33 Typical response of the load cell, Run 15…………………………….……. 84 Figure 4.34 Photo of the sessile drop measurement system. Lenses are at 1× magnification, 90 cm away from the drops……………………………………………... 85 Figure 4.35 (a) Coupon on the camera when droplets are deposited from the pipette, and (b) schematics of the coupon on the stage as in Fig. 4.34…………….………………… 86 Figure 4.36 Images of TEG droplets on different surfaces, recorded with Image Pro Plus………………………………………………………………………………………. 87 Figure 5.1 Aerosol concentration vs. velocity for Cold Unit nozzle and Setup #1 experiments, calculated from washdown and shadowgraphy measurements of concentration, for triethylene glycol. 95% confidence intervals are estimated from three repeated experiments……………………………………………………………………. 91 Figure 5.2 Upstream side capture efficiencies, deposition coefficients and volume median diameter vs. velocity. 95% confidence intervals are estimated from three repeated experiments……………….……………………………………………………………... 93 Figure 5.3 Downstream side capture efficiencies, deposition coefficients and volume median diameter vs. velocity. 95% confidence intervals are estimated from three repeated experiments……………………………………………………………………………… 94 Figure 5.4 Aerosol concentration vs. velocity, for Hot Unit nozzle and Setup #2 experiments, calculated from washdown and shadowgraphy measurements of concentration. 95% confidence intervals calculated from two repeated experiments……………………………...………………………………………………. 96 xv Figure 5.5 Capture efficiencies and deposition coefficients vs. velocity for the downstream side………………………………………………………………………….97 Figure 5.6 Capture efficiency and deposition coefficient for the upstream side vs. volume median diameter, at U = 1m/s. 95% confidence interval were estimated from three repeated experiments……………………………………………………………………. 98 Figure 5.7 Capture efficiency and deposition coefficient for the downstream side vs. volume median diameter, at U = 1 m/s. 95% confidence intervals were estimated from three repeated experiments……………………………………………………………… 99 Figure 5.8 Images of triethylene glycol deposits on the (a) upstream and (b) downstream surface of the glass coupon, Run 26………………………………….………………... 100 Figure 5.9 Measured drop size distribution in the aerosol, and on the upstream and downstream side of the glass coupon at 1 m/s, Run 26…………………………….…...101 Figure 5.10 Calculated capture efficiencies vs. drop diameter for the downstream side, at different gas velocities…………………………………………………………………. 102 Figure 5.11 Calculated deposition coefficients vs. drop diameter for the downstream side, at different gas velocities………………………………………………………………. 103 Figure 5.12 Calculated capture efficiencies vs. velocity for the downstream side, at different drop diameters………………………………………………………………... 104 Figure 5.13 Calculated deposition coefficients vs. velocity for the downstream side, at different drop diameters………………………………………………………………... 105 Figure 5.14 Trajectories of (a) 10, (b) 50 and (c) 140 micron droplets (pathlines) in the potential flow field (streamlines), for the upward flow at 1 m/s superficial gas velocity, using Stokes drag force………………………………………………………………… 107 Figure 5.15 Comparison of analytical and numerical solutions for Stokesian particles, with numerical solutions for non-Stokesian particles, for upward, horizontal and downward flow, at 1 m/s superficial gas velocity………………….…………………...109 Figure 5.16 Comparison of numerical solutions for non-Stokesian particles for upward flow, at different velocities, with the CFD results (by Lakghomi [36])……………….. 110 xvi Figure 5.17 Comparison of the capture efficiencies on the upstream side from potential flow with and without viscous sublayer, for non-Stokesian particles, with CFD (Lakghomi [36])………………………………………………………………………... 111 Figure 5.18 Calculated capture efficiencies vs. Stokes number for the horizontal, upward and downward flow, at different superficial gas velocities……………………………. 112 Figure 5.19 Capture efficiencies vs. drop diameter for (a) horizontal, (b) upward, and (c) downward flow, at different superficial gas velocities. Capture efficiencies vs. velocity for downward flow are presented in (d)……………………………….……………….. 114 Figure 5.20 Simulation of deposition by convective diffusion and turbulent inertia from the flow parallel to the coupon surface, based on modeling described in Section 3.4… 116 Figure 5.21 Comparison of the simulation and experimental results for the upstream side at 1 m/s…………………………………………………………………………………. 118 Figure 5.22 Axisymmetric flow pattern about a disk (adapted from Humphries and Vincent [73])…………………………………………………………………………… 119 Figure 5.23 Correlation between the calculated capture efficiencies from the downward flow and experimental data. Simulation over-predicts experimental data by a factor of 2.33……………………………………………………………………………………...119 Figure 5.24 Typical appearance of (a) non-uniform distribution of deposits on the upstream side, and (b) uniform distribution on the downstream side…………………...121 Figure 5.25 Distribution of deposits along the coupon radius on the (a) upstream and (b) downstream side, for Run 56. Solid lines were obtained by averaging measured values from four samples……………………………………………………………………… 123 Figure 5.26 Mass distribution of deposits on the (a) upstream and (b) downstream surface of the coupon, from Runs 46−59………………………………………………………. 124 Figure 5.27 Experimental integral deposition rates, exp,idr , at U=0.7 m/s and U=1.0 m/s, on different surfaces, for the upstream side (a, c) and downstream side (b, d) (Table E.6). 95% confidence intervals are estimated from 3 repeated experiments.………………... 126 xvii Figure 6.1 Calculated capture efficiencies (from exp. results) for the downstream side vs. Stokes number, in the range of droplet sizes (1−20 microns) and velocities (0−1.5 m/s)……………………………………………………………………………………...130 Figure 6.2 Comparison between Hot Unit deposition rates for 5% MEBR, with the predictions from the Cold Unit deposition coefficients, and CFD predictions………… 132 Figure 6.3 Comparison between Hot Unit deposition rates for 10% MEBR, with the predictions from the Cold Unit deposition coefficients, and CFD predictions………… 132 Figure 6.4 Comparison between Hot Unit deposition rates for the effect of velocity, with the predictions from the Cold Unit deposition coefficients……………………………. 133 Figure A.1 Picture of the Cold Unit apparatus………………………………………… 149 Figure B.1 Gear pump calibration curve, with and without differential pressure (200−300 kPa)……………………………………………………………………………………...151 Figure B.2 Schematic representation of the rotameter float…………………………… 152 Figure B.3 Rotameter #2 calibration setup. Rotameter #2 (A) is connected in series with the rotameter with the calibration curve from the manufacturer (B)…………………... 153 Figure B.4 Calibration curve for the second GSO-50 load cell used. The curve is approximately linear and it can be seen that, in this case, true values are about 11% larger than measured.…………………………………………………………………………. 157 Figure C.1 Schematic representation of the flow field in front of the disk and fluid velocity components…………………………………………………………………….158 Figure C.2 Schematic representation of limiting droplet trajectories and the way that capture efficiencies for disk are obtained……………………………………………… 165 Figure C.3 Spherical cap model for droplets deposited on the coupon surface………... 169 xviii omenclature A Upstream or downstream coupon (disk) surface area, 4/ 2πcDA = , m 2 Acolumn Column cross section area, m 2 Adry Dry coupon (disk) surface area, upstream or downstream, m 2 Aan Annular area between the rotameter float and the rotameter tube, m 2 Atube Cross section area of the rotameter tube, m 2 Awet Wet coupon (disk) surface area, upstream or downstream, m 2 Br Blockage ratio, Br=A/Acolumn, dimensionless cb Aerosol concentration in the bulk, kg/m 3 Cc Cunningham slip correction factor, dimensionless Cp Heat capacity, J⋅kg -1 K -1 cwake Aerosol concentration in the wake, kg/m 3 d Characteristic length (total disk surface area divided by the perimeter of a disk, Dc/2), m D Brownian diffusivity, m 2 /s Dc Coupon (disk) diameter, m Dmin Minimum drop diameter, m Dmax Maximum drop diameter, m Dp Particle (droplet) diameter, m Dp,eq Equivalent diameter for a given drop size distribution that has the same specific mass, ms, as that size distribution, m xix ' pD Particle (droplet) diameter on a surface, having diameter Dp in the aerosol, pp DkD ⋅= )( ' θ , m Dp,i Drop diameter of the class i in the aerosol, m Dp,max Drop diameter of the last (maximum) class in the aerosol, m Dp,reference Reference particle (droplet) diameter, m DV,10 10% volume diameter, m DV,50 Volume median diameter, same as VMD, m 50,VD Average volume median diameter, m DV,90 90% volume diameter, m E Capture efficiency, dimensionless Ea Activation energy, J/mol Ei,downstream Capture efficiency of the class i, for the downstream side, m/s Ei,upstream Capture efficiency of the class i, for the upstream side, m/s F Force, , Fa,nozzle Volumetric flow rate of air to the nozzle, at pressure pnozzle, m 3 /s Fa,secondary Volumetric flow rate of secondary air to the gas distributor, at pressure psecondary, m 3 /s Fl Droplet (liquid) flow rate to the aerosol, kg/s g Gravity acceleration, g=9.81, m/s 2 imax Largest diameter class in the distribution, dimensionless h Height of air annulus (in the nozzle), cm Hf Residence time of inertialess particles, dimensionless Hp Residence time of particles with inertia, dimensionless xx k Correction factor for the drop size estimated by correlation, dimensionless k(θ) Drop diameter correction factor, for a drop sitting on a surface, dimensionless kB Boltzmann’s constant, kB =1.386·10 -23 , kg·m 2 ·s -2 ·K -1 kd Particle (droplet) deposition coefficient (velocity), m/s ki,downstream Particle (droplet) deposition coefficient of the class i, for the downstream side, m/s ki,upstream Particle (droplet) deposition coefficient of the class i, for the upstream side, m/s km Mass transfer coefficient, m/s kr First-order reaction constant, s -1 kr,0 Pre-exponential factor for the first order reaction constant, s -1 ks Deposition constant, )/(1, Amrk sds = , s -1 kt Particle (droplet) transport coefficient, m/s kt + Nondimensional particle (droplet) transport coefficient, dimensionless L Plate (surface) length, m m Mass of deposits, kg M Mass of the rotameter float, kg gM & Mass flow rate of a gas (in the nozzle), g/s mi Mass of deposits in the i-th layer, kg mi,0 Mass of the freshly deposited i-th layer, kg mi,f Mass of the i-th layer at the end of reaction (t=∞), kg xxi lM & Mass flow rate of a liquid (in the nozzle), g/s ms Specific mass of a droplet sitting on a surface, kg/m 2 Mw Molar mass of the gas, kg/mol MCR Micro Carbon Residue, dimensionless ,i Number of particles (droplets) in the class i, dimensionless ,’ Statistically corrected number of particles, dimensionless p Gravity orientation parameter {-1, 0, 1}, dimensionless P Pressure, Pa P0 Atmospheric pressure, P0 = 101 325 Pa pi Total detection probability, dimensionless pi,Border Detection probability due to the border correction, dimensionless pi,DOF Detection probability due to the depth of field correction, dimensionless Pnozzle Pressure of the air in the nozzle, Pa Psecondary Pressure of the secondary air in the gas distributor, Pa r Radial coordinate, m R Universal gas constant, R = 8.314 J⋅K-1⋅mol-1 Rc Coupon (disk) radius, m rd Deposition rate, kg/s rd,1 Deposition rate on a dry surface, kg/s rd,2 Deposition rate on a wet surface, kg/s exp ,idr Experimental integral deposition rate for experiment i, kg/s int ,idr Calculated integral deposition rate for experiment i, kg/s xxii Re Reynolds number for a disk, a aUd µ ρ =Re , dimensionless RI Interception parameter, RI = Dp/Dc, dimensionless r Nondimensional radial coordinate, cRrr /= , dimensionless 0r Initial nondimensional radial position at 0t , dimensionless Sc Schmidt number, D Sc a ν = , dimensionless Sh Sherwood number for a disk, D dk Sh m= , dimensionless 50,VD S Standard deviation of the volume median diameter, m 50,VD S Standard deviation of the average volume median diameter, m Sp Particle stopping distance, UtS pp = , m St Stokes number, c p D Ut St = , dimensionless Stcr Critical Stokes number, dimensionless t Time, s T Temperature, K ti Moment of deposition of the i-th layer, s tp Particle relaxation time, a cpp p CD t µ ρ 18 2 = , s tp + Nondimensional particle relaxation time, ( ) a pp v tt ν 2* ⋅= + , dimensionless t Nondimensional time, cRvtt /0⋅= , dimensionless xxiii 't Nondimensional time needed for particle to reach the coupon surface plane ( 0=x ), dimensionless Q Volumetric flow rate of air, m 3 /s U Superficial gas velocity, m/s Unozzle Superficial gas velocity in the column, from the nozzle air, m/s Usecondary Superficial gas velocity in the column, from the secondary air, m/s ur Radial velocity component of a particle (droplet), m/s ux Axial velocity component of a particle (droplet), m/s u Particle (droplet) velocity vector, m/s V Yield of volatiles, dimensionless v0 Axial gas velocity, same as U, m/s Vg Gas velocity (in the nozzle), m/s Vi,aerosol Volume relative frequency of the class i in the aerosol, dimensionless Vi,downstream Volume relative frequency of the class i on the downstream side of the coupon, dimensionless Vi,upstream Volume relative frequency of the class i on the upstream side of the coupon, dimensionless Vl Liquid velocity (in the nozzle), m/s vr Radial gas velocity component, m/s Vt Terminal velocity of a particle (droplet), m/s vx Axial gas velocity component, m/s v * Friction velocity, m/s V * Maximum yield of volatiles, dimensionless xxiv ∞v Average gas free stream velocity, m/s ∝ rv Freestream gas velocity in radial direction, m/s v r Gas velocity vector, m/s rv Nondimensional radial gas velocity, 0/ vvv rr = , dimensionless xv Nondimensional axial gas velocity, 0/ vvv xx = , dimensionless VMD Volume median diameter, same as DV,50, m x Axial coordinate, m x Nondimensional axial coordinate, cRxx /= , dimensionless 0x Initial nondimensional axial position at 0t , dimensionless y Surface coverage, dimensionless z1, z2 Solutions of the characteristic equation, St St z 4 1611 2,1 −±− = , dimensionless Greek symbols γ Surface tension, J/m 2 γL Liquid surface tension, J/m 2 γLV Liquid-vapour surface tension, J/m 2 γS Solid surface tension (surface energy), J/m 2 γSL Solid-liquid surface tension, J/m 2 γSV Solid-vapour surface tension, J/m 2 µa Dynamic viscosity of air, Pa·s xxv µoil Dynamic viscosity of oil, Pa·s νa Kinematic viscosity of air, m 2 /s νl Kinematic viscosity of liquid (in the nozzle), 10 -6 m 2 /s (cSt) θ Equilibrium contact angle, ° θadv Advancing contact angle, ° θrec Receding contact angle, ° ρa Density of air, kg/m 3 ρf Density of fluid flowing through the rotameter, kg/m 3 ρg Density of gas (in the nozzle), g/cm 3 ρp Particle (droplet) density, kg/m 3 σl Liquid surface tension (in the nozzle), 10 -3 J/m 2 (dyn/cm) τi Duration of the experiment i, s List of acronyms ATB Atmospheric Topped Bitumen FBP Final Boiling Point HGO Heavy Gas Oil IBP Initial Boiling Point LGO Light Gas Oil MCR Micro Carbon Residue MEBR Syncrude Canada Ltd. Plant 7 Bitumen product VTB Vacuum Topped Bitumen xxvi TEG Triethylene glycol xxvii Acknowledgments I would like to use this opportunity to thank my supervisors, Dr. Paul Watkinson, Dr. Dusko Posarac and Dr. Fariborz Taghipour, for the supervision of my work on this thesis and all their suggestions and help. Also, I would like to thank Syncrude Canada Ltd., for financing this project and for the opportunity to work on an interesting subject. Finally, I would like to thank my parents for their understanding and support throughout the years. Chapter 1. Introduction 1 Chapter 1. Introduction Total oil sand reserves in Northern Alberta are estimated at around 1.7 trillion barrels of bitumen; this amount is comparable to the total proven world oil reserves of conventional petroleum, where the top seventeen countries hold about 1.24 trillion barrels [1]. One tenth of the bitumen deposits are considered economically recoverable at 2006 oil prices. This portion alone makes Canada’s total oil reserves second-largest in the world, next only to Saudi Arabia’s. As the price of petroleum over the last decade showed a steady rise [2], petroleum production from unconventional oil reserves (oil sands, oil shales, biomass) [3] attracted more attention. Production of synthetic crude oil from bitumen which was extracted from oil sands, became more economically viable, resulting in a great expansion in Northern Canada. Today, 46% of the petroleum in Canada is produced from oil sands, while in 1992 that share was just 17% [4, 5]. Oil sands are a mixture of bitumen, sand, clay and water [6]. Typically, they contain about 84% wt. of solids, 11−12% wt. of crude bitumen and the rest is water. The solids are about 90% quartz, with some amounts of feldspar, muscovite, chert, and clay minerals [5]. Crude bitumen is a complex mixture of organic compounds that contains polymeric asphaltenes and resins of high molecular mass, and high levels of nitrogen, oxygen, sulfur, and metals. It is a highly viscous, black and sticky substance, entirely soluble in carbon disulfide. Its main characteristic is high viscosity in its natural state ( 31 1010 − Pa⋅s) − to the point of pseudoplasticity; it has to be heated or diluted before it will flow [5, 7]. For deep oil-sand deposits, steam injection is used, whereas for shallow deposits, extraction of bitumen begins with the mining process. Mining the oil sands includes removing the overlying overburden, recovering the oil sands and transporting them to a bitumen extraction plant. In the extraction plant, hot water is used to wash out bitumen from the oil sands. The bitumen is then upgraded and refined to produce synthetic crude oil. Chapter 1. Introduction 2 1.1. Bitumen upgrading and the Fluid Coker The purpose of bitumen upgrading is to reduce high boiling fractions, increase the hydrogen to carbon ratio, and remove impurities. Table 1.1 illustrates the property differences between bitumen and crude oils, which suggests a need for bitumen upgrading. Table 1.1 Bitumen, Synthetic crude, and Conventional crude oil properties [5] Bitumen Synthetic crude Conventional crude °API 8 32 41 Sulfur, wt % 4.8 0.08 0.2 Nitrogen, wt % 0.45 0.03 0.04 Viscosity at 40°C, cSt 3000 3.0 2.9 Pour point, °C 18 −4.5 −6 Metals, mg/kg 450 <1 Distillate yield, vol % IBP − C5* 0 4 3 C5 − 195°C 0 18 36 195°C − 345°C 14 47 31 345°C − 560°C 31 18 560°C + 86 0 12 *IBP=Initial Boiling Point, C5=pentane Upgrading consists of two steps: primary and secondary. A schematic diagram of the bitumen upgrading process and its two main steps is given in Fig. 1.1. Figure 1.1 Schematic representation of the bitumen upgrading process [9] D il u e n t R e co v e ry U n it Diluted bitumen Diluent naphta ATB LGO and HGO V a cu u m D is ti ll a ti o n U n it LC - F in e r F lu id C o k e r LGO VTB ATB Coke LGO Overhead products Residue Sour gas Naphta LGO HGO Hydrogen H y d ro T re a te r F ra ct io n a to r Sulfur Synthetic Crude Oil Primary step Secondary step Chapter 1. Introduction 3 The primary step converts high-molecular residues in the bitumen to a distillate. The secondary step includes separating the distillate into desired boiling ranges and adding hydrogen to saturate hydrocarbons and remove impurities. In the primary step, bitumen from the froth treatment step is first sent to the Diluent Recovery Unit (atmospheric distillation column). This unit recovers diluent naptha, and produces Light Gas Oil (LGO) and Atmospheric Topped Bitumen residue (ATB). Produced ATB is sent to the Vacuum Distillation Unit, where LGO and Heavy Gas Oil (HGO) are removed from the top, and the Vacuum Topped Bitumen (VTB) from the bottom is mixed with part of the ATB and sent to the LC-Finer. The LC-Finer is a catalytic reactor where hydrogen is added to increase the hydrogen to carbon ratio and produce cracked LGO. Residue from the LC-Finer is combined with parts of the feed and sent to the Fluid Coker reactor (Fig. 1.2). Figure 1.2 Schematic of the Syncrude Fluid Coker Packing elements Cyclones Steam Pool Sheds HGO wash oil Fluidized bed Stripper section Bitumen “Hot” coke in “Cold“ coke out Product vapour HGO wash oil Recycle Scrubber Chapter 1. Introduction 4 In the Fluid Coker, bitumen is first sprayed into the fluidized bed reactor section. Coking reactions occur on the surface of introduced hot coke particles, at about 510°C to 530°C, where bitumen cracks and forms coke and lighter fractions in the form of vapour. Energy for the reaction is provided by burning in the coke burner part of the produced coke from the reactor, and by re-circulating the hot coke back into the reactor. In the stripping section, bitumen that remains on the surface of the coke particles is stripped off with steam. Product vapour from the coker reactor is then sent to the cyclones that remove unreacted bitumen droplets and particles above about 11 microns [7]. Vapour is then sent to the scrubber section, which consists of the pool, sheds and structured grid (Fig. 1.2). Heavy gas oil at 325°C is sprayed from the top of the structured packing and sheds, in order to cool down the gas and remove (scrub) heavy components from the vapour by condensation. The purpose of the heavy gas oil is to also remove small droplets and coke particles from the product vapour. However, if droplets and particles deposit on the surface of the packing in the Scrubber, they can cause fouling of the Scrubber and plugging of the reactor. 1.2. Fouling in the Scrubber section of the Fluid Coker Fouling can be defined as the accumulation of unwanted material on solid surfaces. Fouling in the grid section of the scrubber in the Fluid Coker reactor increases pressure drop along the scrubber and changes the operating conditions of the reactor. The cause of fouling in the scrubber section of the reactor is deposition of fine bitumen droplets, and possibly coke particles, not removed in the cyclones from the product vapour. Under the effect of high temperatures, bitumen droplets deposited on the surface undergo thermal decomposition into volatiles and coke. Formed coke remains on the surface of the packing as a solid material. Build-up of deposits eventually results in plugging of the reactor and its shutdown for maintenance, with a costly disruption of the production. Figure 1.3 shows a comparison between the clean packing in the grid and the packing surface covered with coke. If we could understand the fundamental phenomena that govern deposition on the packing elements of the scrubber, it would be possible to change operating conditions in Chapter 1. Introduction 5 order to minimize the fouling, or change the geometry of the packing and prolong the reactor operation. Figure 1.3 Segment of the packing elements in the Scrubber Section of the Fluid Coker, (a) before start up of the reactor and (b) after reactor shutdown 1.3. Project objectives Fouling in the scrubber section of the Fluid Coker reactor was previously studied theoretically by Subudhi [8]. He simulated the increase in the pressure drop of the scrubber by modeling particle transport to the surface, assuming perfect sticking, and included the effect of the reaction. His model assumed flow parallel to the surface of the packing. Since the orientation of packing elements in the reactor is not fully parallel with the upward flow of the gas (Fig. 1.4), the fluid dynamics around such a geometry is certainly different. Since fluid dynamics plays a key role in particle transport to the surface, there was room for improvements to Subudhi’s approach. Figure 1.4 Side view of the scrubber packing elements, given in Fig. 1.3. The blades are inclined at a 30° angle with the vertical axis [8] (a) (b) 30° Chapter 1. Introduction 6 Because of the complex geometry of the actual packing, it was decided to study deposition onto single elements of simple geometries, placed normal to the flow of aerosol droplets in a gas-vapour mixture. A normal orientation of the disk to the flow, compared to the parallel orientation, yields a different flow field around the disk that is likely more similar to the flow field around the packing elements in the Scrubber. This is especially true for the vortex behind the disk, where flow separation occurs. The idea was to investigate deposition on the 5 cm diameter circular disk (coupon), placed in a 7.5 cm diameter column (Fig. 1.5). The aerosol flow was directed in the upward direction, as is the case in the Fluid Coker reactor. Figure 1.5 Schematic representation of the side and top view of the 5 cm diameter disk in the 7.5 cm diameter column (aerosol droplets are presented disproportionately large) The deposition process was intended to be studied experimentally in two separate experimental units: a room temperature unit (called the Cold Unit) and a high temperature unit (called the Hot Unit). The Cold Unit was intended to be used to investigate the effect of velocity over the range that could not be covered in the Hot Unit (0−1.5 m/s), and the effect of other factors such as droplet size, which was not measured in the Hot Unit. The high temperature unit was used to study deposition of heavy oil hydrocarbons at temperatures of 290−425°C, similar to the conditions in the real Fluid Coker reactor, and the effect of heavy oil composition (Song [52]). Experimental results from both units were used for verification of the computational fluid dynamics (CFD) model predictions, undertaken as part of this overall study (Lakghomi [36]), and that would be later used for simulation of deposition on arbitrary geometries. Upward aerosol flow Chapter 1. Introduction 7 1.4. Scope of the thesis The objective of this thesis was to carry out an experimental investigation of the deposition process at room temperature. For this purpose, the Cold Unit apparatus (Fig. 4.1) was constructed as part of this work. A limited set of experimental factors was selected. To investigate the effect of particle transport on deposition, velocity and droplet size distribution were varied (Sections 5.1−5.3); to quantify the distribution of deposits on the surface, distribution of deposits along the coupon radius was measured (Section 5.6). Lastly, to understand the effect of wettability on sticking and deposition, the effect of contact angles between the liquid and the solid surface was studied (Section 5.7). In particular, the factors to be investigated included: 1. Effect of superficial gas velocity on deposition rate, at a given droplet size distribution, over the range 0−1.5 m/s. 2. Effect of droplet size distribution on deposition rate, at a given velocity, over the range of volume median diameters between 3.9 and 7.5 microns. 3. Morphology of deposits and distribution of deposits along the radius of the disk. 4. Effect of contact angles (20°, 51°, and 94°) between the liquid and the solid surface on deposition rate. In addition to the experimental investigation, the inviscid flow approximation was used to simulate particle transport to the surface and interpret the obtained experimental results (Section 5.4). Furthermore, deposition coefficients from the room temperature unit experiments (Section 5.3) were recalculated to the high temperature conditions, and compared with the independent set of data obtained in the high temperature unit experiments [52] (Chapter 6). The following chapter (Chapter 2) presents the relevant theory of particle deposition from parallel flow and flow around bluff bodies (transport and sticking) used in the modeling section (Chapter 3), and reviews significant work in this area. Chapter 2. Theory and Literature Review 8 Chapter 2. Theory and Literature Review The deposition of small particles and droplets onto solid surfaces from gaseous streams was studied in the literature for two main classes of problems. First is the case when the flow is parallel to solid surfaces (laminar and turbulent flow) and the second is when the flow is normal to solid surfaces. The rationale for this division is that the flow field, and therefore the mechanisms that govern particle deposition, are different in each case. The main aspects of both are reviewed here, since both apply to the object of investigation. 2.1. Particle deposition from turbulent flow parallel to solid surfaces Experimental work on particle deposition was reviewed by Cleaver and Yates [11], who validated their sublayer model for deposition from turbulent flow against the available experimental data. Papavergos and Hadley [10] were first to give a comprehensive review of theoretical developments and available experimental data on deposition from parallel turbulent flow. Epstein [12] presented a review of theory of particle transport, particle attachment and particle re-entrainment. Recently, deposition from parallel flows was also studied by the means of computational fluid dynamics. Tian and Ahmadi [14] compared different turbulent model predictions with the existing body of experimental data, while Zhang and Li [13] simulated deposition on the walls, roof and floor of horizontal ducts, thus distinguishing the effect of gravity. Following Epstein [12], the main deposition phenomena can be summarized as follows. Starting from submicron particles, three mechanisms of deposition dominate as the particle size increases: diffusion, inertia and impaction. In the diffusion regime, particles are sufficiently small that they are carried to the wall through the viscous sublayer by Brownian diffusion. The Brownian diffusivity for a dilute suspension of spheres is given by the Stokes-Einstein equation, pa B D Tk D πµ3 = (2.1) Chapter 2. Theory and Literature Review 9 where kB is the Boltzmann constant, µa is the air dynamic viscosity and Dp is the particle diameter. It can be used in empirical correlations for convective mass transfer of the form ),( ScRefSh = . The calculated Sherwood number yields a mass transfer coefficient, km, equal to the particle transport coefficient, kt, for this case. In the inertia regime, the particles are large enough so that turbulent eddies transfer to them some momentum that is normal to the walls. This momentum is not completely dissipated in the viscous sublayer and particles can reach the surface. A large body of experimental results on deposition in the inertial regime can be summarized by the following empirical correlation, to a good degree of accuracy, wallhorizontalttk ppt ,202.0,105.3 4 <<⋅= ++−+ (2.2) where + tk is the nondimensional deposition coefficient. The key independent variable for the inertia regime is the nondimensional particle relaxation time, + pt , defined as ( ) ( )aa pp v tt ρµ / 2* ⋅=+ . The dimensional particle relaxation time, tp, represents the time needed for a particle to adjust or relax its velocity to a new fluid velocity, a cpp p CD t µ ρ 18 2 = (2.3) where Dp is the particle diameter. It includes fluid viscosity and the Cunningham slip correction factor, Cc, and is therefore affected by changes in temperature and pressure. The deposition coefficient, kt, can be obtained from the nondimensional deposition coefficient, + tk , using the relation */ vkk tt = + . The friction velocity *v , can be calculated from the shear stress or velocity gradient at the wall according to, 2/1 0 * ⋅= =xa a dx dv v ρ µ (2.4) The average velocity gradient, along a surface of length L, may be estimated from the correlations given in the literature (Schlichting [15], Lai and Nazaroff [16]), Chapter 2. Theory and Literature Review 10 ( ) 5/12 0 /2 074.0 −∞∞ = = aa a ax Lvv dx dv ρµ ρ µ (2.5) where ∞v is the average free stream velocity. To account for the effect of gravity, Sehmel [17] extended this theory to predict deposition velocities on the floor and ceiling of horizontal ducts, and obtained, <<⋅ <⋅ = ++− ++− + Ceilingtt Floortt k pp pp t ,501,104 2.0,102 5 3 (2.6a,b) However, these equations fit only a limited set of data (Papavergos and Hadley [10]). As particle size is increased, the inertia regime is followed by the impaction regime, which begins at 20=+pt , where the response of such large particles to turbulent fluctuations becomes limited, and + tk levels off at about 0.12−0.18. At 30≥ + pt , deposition coefficients starts to fall gradually, since such large particles get even more sluggish in their response to turbulent eddies. Figure 2.1 Summary of experimental data on particle deposition from turbulent pipe flow, adapted from Young and Leeming [18] Chapter 2. Theory and Literature Review 11 Gravitational settling becomes important for larger particles with 1≥+pt . The deposition coefficient, kt, from gravitational settling then becomes equal to the particle terminal velocity, Vt. A summary of experimental data on particle deposition from turbulent pipe flow is given in Fig. 2.1 (from Young and Leeming [18]). The above considerations are related to the transport of particles to the surface. If perfect sticking is assumed, the particle transport flux becomes equal to the particle deposition rate and vice versa. Particles can also be re-entrained into the gas stream (Epstein [12]). This phenomenon can happen with solid particles (Vincent and Humphries [19]), but in the case of organic liquid droplets deposited on hydrophilic surfaces, with low contact angles, it is reasonable to assume that re-entrainment does not occur. 2.2. Particle deposition from the flow around bluff bodies and surfaces Mechanisms of deposition on solid surfaces from the flow normal to the surface are encountered in filtration and membrane operations. They also govern the collection of small droplets or particles in wet scrubbers, the deposition of super-cooled water drops on the wings of aircrafts (aircraft icing), and the build-up of deposits in cyclones and other process equipment. An important parameter used to describe deposition on bodies from normal flows is the collection efficiency or capture efficiency. It is defined as the fraction of particles that are approaching the collector in the region defined by the projected area of the collector, that are ultimately deposited on the collector surface, bodythegapproachinareaprojectedtheinparticlesofMass bodytheondepositedareaprojectedthefromparticlesofMass E = (2.7) The deposition coefficient, kd, or deposition velocity, can be obtained by multiplying the capture efficiency, E, with the superficial velocity, U, UEkd ⋅= (2.8) Chapter 2. Theory and Literature Review 12 The deposition rate, rd, is then obtained by multiplying the deposition coefficient, surface area, A, and concentration, cb, Ackr bdd ⋅⋅= (2.9) As described by Hinds [20] and Friedlander [21], the main collection mechanisms that govern deposition from a normal flow are: interception, inertial impaction, diffusion, gravitational settling, electrostatic attraction and thermal forces. However, all these mechanisms rarely occur simultaneously − usually one or two mechanisms dominate the deposition process. Collection by interception occurs when a particle follows a gas streamline that is within one particle radius from the body. A particle will be captured because of its size; the larger the particle, the greater the possibility for interception. This is the only mechanism that is not a result of a particle departing from its original gas streamline. The main parameter that controls interception is the ratio of the particle, Dp, and body diameters, Dc, i.e., cpI DDR /= . Inertial impaction occurs when particles, because of their inertia, are unable to adjust to the change in direction of the flow in the vicinity of the body. Their path starts to deviate from the fluid streamlines, and if the inertia is sufficiently large, particles can reach the surface. The main parameter that controls inertial impaction is the Stokes number, defined as a ratio of particle stopping distance, Sp, and the diameter of the body, c p c p D Ut D S St == (2.10) In the diffusion regime, Brownian motion of small particles causes deviation of particles from the fluid streamlines, and particles can reach the surface. Diffusion depends on the flow characteristics, and therefore the Brownian diffusion coefficient (Eq. (2.1)) should be used in empirical correlations for mass transfer to obtain the deposition coefficient. Gravitational settling can increase the capture efficiency if the flow is in the direction of gravity, or decrease the capture efficiency if it is in the opposite direction. It is important for larger particles only ( 1>+pt ). Chapter 2. Theory and Literature Review 13 Electrostatic deposition can be important, but it requires knowing the charge of the collector and the particles. Thermal forces, which include thermophoresis (migration of particles down a temperature gradient close to the surface) and the thermoelectric effect (heat flux induced thermoelectric voltage in the adjacent coolant stream), can be important, but only when temperature gradients exist. For deposition onto body and surface collectors normal to the flow, we can distinguish between the deposition on the upstream (front) side, and deposition on the downstream (back) side, since each side is characterized by a different flow field. 2.2.1. Upstream (front) side In the literature, it is mainly the inertial impaction mechanism on the upstream (front) surface of single elements that has been studied, both theoretically and experimentally. Early work on the theory of inertial impaction was done by Albrecht [22], Sell [23], Langmuir and Blodgett [24] and Landhal and Herrmann [25]. Their results differed to some degree, depending on the flow approximation, position where the particles were injected, and number of particles, but the results of Langmuir and Blodget were mainly consistent with the results obtained later on. Early experimental measurements by Landhal and Herman [25] and Sell [23], due to the complexity of the phenomena involved, were not successful in separating inertial effects from the diffusion and interception effects. However, results on inertial impaction obtained by Ranz and Wong [26], Wong et al. [27] and May and Clifford [28], could be considered correct. Table 2.1 summarizes the main theoretical and experimental results on inertial impaction. It is worth noting that, according to the theoretical predictions from the literature [30], disks showed the highest capture efficiencies among all simple geometries (ribbon, sphere, cylinder). Also, the ideal flow approximation seemed to be a satisfactory description of the flow in front of the body, in all cases. In the body of experimental data, there are discrepancies among the results, depending on whether particles or droplets are used, and how the flow was oriented. In order to explain experimental capture efficiencies lower than theoretical predictions, Wong et al. [27] suggested that viscous forces should decrease capture efficiencies. Golovin and Putnam [30] suggested the same, but for targets of the order of few centimetres in size (1−2 inches), viscosity effects Chapter 2. Theory and Literature Review 14 should be negligible if Retarget>100. The results of May and Clifford are just slightly below the potential flow predictions for horizontal flow. This is probably because the flow was oriented upward, with gravity acting in the opposite direction to the flow, suggesting that gravity could be responsible (remark of Vincent and Humphries [19]), and not the viscous forces. Experimental results from the literature, along with a theoretical prediction of inertial impaction on disks, are given in Figure 2.2. Calculations and experimental data are given for horizontal flow (except May and Clifford [28], upward flow). It can be seen that the capture efficiencies can be presented as a unique function of the Stokes number. As the Stokes number is increased, particles possess more inertia, and are unable to closely follow the fluid streamlines that go around the body. As a result, particles impact the surface and deposit. Figure 2.2 Experimental and theoretical data on inertial deposition onto front surfaces of disks Table 2.1 Summary of experimental data and simple theoretical treatments of inertial impaction on the front side of bluff bodies Authors Theory Experiments Shape Simulation Shape Materials (solid particles/droplets) Measurements Langmuir and Blodgett [24] Cylinder, Sphere, Ribbon Potential flow, no gravity, non-Stokesian drag force − − − Ranz and Wong [26] Disk, Ribbon Potential flow, no gravity, Stokes drag force Cylinder, Sphere No indications on the flow orientation. Nearly uniform 0.3−1.4 micron droplets of concentrated sulphuric acid (aerosol condensation generator). Collectors: 3-mil platinum wires and 0.9 mm platinum sphere Droplet size not measured, but controlled by changing operating conditions of the aerosol generator. Weight of deposits measured after the experiment. Gregory and Stedman [29] − − Disks, Cylinders, Stripes Horizontal flow. Lycopodium spores, about 28 micron diameter. Velocity: 0.5−9.5 m/s Direct counting of deposited spores under the microscope Wong et al. [27] Cylinders Potential flow, no gravity, Stokes drag force Cylinders No indications on the flow orientation. 0.6−1.4 micron uniform droplets, concentrated sulphuric acid (homogeneous aerosol generator). Collectors: 29−106 micron platinum wires. Velocity: 4−50 m/s, Reynolds number: 13−330 Droplet size not measured, but controlled by changing aerosol generator operating conditions. Weight measured after the experiment. Golovin and Putnam [30], review article Cylinders, Spheres, Ribbon, Airfoils at different angles Potential flow theories, no gravity, Stokes drag force Cylinders Reviewed experimental results for cylinders: Gregory and Stedman (1953), Ranz and Wong (1952), Ranz, Wong and Johnstone (1954), Amelin and Belyakov (1956) - May and Clifford [28] − − Disks, Cylinders, Spheres, Ribbons Upward flow. Uniform dibutyl phthalate droplets 20, 30, 40 microns in diameter (aerosol spinning top generator). Velocity: 2.2−6.2 m/s in the 20×20 cm wind tunnel. Targets: 0.1−2.9 cm (disks: 0.154, 0.480, 0.995, 1.431, 2.875cm). Reynolds: 165−8500. Droplets size measured by magnesium oxide method. No indications on measurements of the weight of deposits. Noll and Pilat [31] Ribbon, Half-body Potential flow, no gravity, non-Stokesian drag force Ribbon, Half-body Flow orientation is not evident. Size distribution of the atmospheric aerosol, with particles larger than 1 micron. Aerosol size distribution measured in the Atmospheric giant particle inertial impactor. Vincent and Humphries [19] − Disks Horizontal flow. Size distribution of dusts. 5 cm diameter disk. 10 times lower efficiencies. Close to the rim there was no dust deposits (bounced off or re-entrained). C h a p ter 2 . T h eo ry a n d L itera tu re R eview15 Chapter 2. Theory and Literature Review 16 Although it does affect capture efficiencies, gravity was often not considered important, and in most cases it was not explicitly stated if the experiments were performed with horizontal, upward or downward flow. From the description of the experimental procedures and the pictures of the experimental setup, it seems that only the experiments of May and Clifford were performed in upward flow, and all others in horizontal flow. In their calculations, Tsai and Liang [32] studied inertial effects along with gravity from the axisymmetric stagnation point flow approximation, but the presented results were for the gravity in the flow direction only. Also, experimental results were available only for small blockage ratio (Br ≈ 0.05, May and Clifford [28]), where the effect of column walls or other neighbour elements, have a negligible effect on the flow field and deposition. Experimental investigation of deposition due to convective diffusion and inertial mechanisms from turbulent flow onto normal surfaces has not been reported in the past, to the best of our knowledge. These deposition mechanisms lead to small amounts of deposits, compared to other mechanisms encountered in normal flow (inertia, gravity or interception). Successful separation of these mechanisms would require working with small droplets (a few microns), flowing over targets in the range of few centimeters. Removal of small droplets was of primary interest in fiber filter technology and was therefore mainly studied for the flow over small fibers (<100 microns), where inertia and interception are the dominating mechanisms. 2.2.2. Downstream (back) side Deposition on the downstream (back) side of bluff bodies did not attract much attention of researchers in the past; probably because in the majority of applications, the upstream side collected significantly more deposits. Also, the imprecisely defined turbulent wake behind the disk did not allow theoretical treatment, and deposition could be investigated only experimentally. Experimental results on the downstream surface were reported by Amelin and Beliyakov [33], who investigated capture efficiencies of the front and back sides of cylinders. As explained by Golovin and Putnam [30], their results showed a linear increase with increased Stokes number (i.e., due to increased velocity). However, the results could not be considered reliable, since their lowest capture efficiencies were of Chapter 2. Theory and Literature Review 17 order 10 -6 , while just due to the interception, capture efficiencies should be at least 10 -4 . Yeomans et al. [34] investigated deposition of DDT solutions on the front and back surfaces of glass discs and leaves in still and moving air. They found that for small particles, deposition on the downstream side exceeded deposition on the upstream side. As the Stokes number was increased (by increasing the drop size), capture efficiencies first increased. At about a Stokes number of 0.06 (calculated from VMD=15 micron, at U=3.6 m/s), the capture efficiencies started decreasing steadily toward zero. At this value, the amount of deposits on the upstream and downstream sides was similar. Goldshmid and Calvert [35], measured deposition of small particles (0.8−2.8 microns) on oscillating drops and observed that for particles below 1 micron in size, capture efficiencies suddenly increased. They tried to explain this by claiming that the deposition takes place in the vortex behind the disk. They employed a simple model based on inertial deposition from the vortex (centrifugal force of particles), which was able to qualitatively explain the results. Vincent and Humphries [19] measured capture efficiencies of dusts onto the front and back surfaces of disks. For the back side, their results showed a decreasing trend with velocity and increasing trend with particle size. The results also showed that the back side capture efficiencies could not be represented solely as a function of the Stokes number. In trying to explain the mechanisms of deposition, they did not consider inertial impaction or gravity, but mentioned turbulent diffusion, Brownian diffusion and electrostatic forces. Again, in none of the works mentioned above was gravity considered important enough to be mentioned how experiments were performed, and whether or not it could have had an effect on deposition. Table 2.2 summarizes the main results on downstream deposition. Chapter 2. Theory and Literature Review 18 Table 2.2 Summary of experimental investigations for the downstream (back) side of bluff bodies Authors Shapes Materials Measurements Amelin and Beliyakov [33] Cylinders n/a n/a Yeomans et al. [34] Glass, wire cloth, filter paper and leaf disks (4.1–15 cm in diameter) Horizontal flow in the 18m long wind tunnel. Droplets of DDT in petroleum (VMD: 8.4 – 33.0 microns) via La Mer-Sinclair homogeneous aerosol generator. Velocities: 3.2 to 25.6 km/h. Weight of DDT deposits at the end of experiment, counting dead mosquitoes, measuring median diameter Goldshmid and Calvert [35] Oscillating drops La Mer-Sinclair homogeneous aerosol generator. Drops of formamide, hexadecane, water and glycerol. Polystyrene particles and sulfur droplets, 0.8–2.8 microns in size. Counting of polystyrene particles and weighing of sulfur deposits Vincent and Humphries [19] Metallic disks Horizontal flow. Graded dusts of brown aloxite, size distribution with median diameter 3.0, 6.5, 13.0 and 17.0 microns. Disks 2.0, 2.8, 5.0 and 10.0 cm diameter. n/a In summary, the inertial deposition onto the upstream side of bluff bodies was investigated mainly with success: theoretically, using the inviscid flow approximation, and experimentally too, although discrepancies between the reported results exist. In all investigations, the flow orientation was not considered important and the effect of gravity was not included into the calculations (except Tsai and Liang [32]). In addition, in the investigations of particle deposition on disks, only the Stokes drag force on particles was used. For the downstream side, there has been no computational treatment of the deposition from the wake (except by Lakghomi [36]), and the mechanisms of deposition were not understood clearly. The experimental results also showed some discrepancies; and to the best of our knowledge, no investigation on the deposition from an upward flow with droplets in the aerosol has been conducted. The following section (Section 2.3) discusses distribution of deposits along the coupon radius. 2.3. Distribution of deposits along the coupon radius In order to predict whether some areas of packing elements in the scrubber section of the Fluid Coker would foul more rapidly and potentially become a bottleneck for the Chapter 2. Theory and Literature Review 19 whole scrubber, and therefore the whole reactor, the mass and size distribution of the deposits on the disk surface had to be determined. Gregory and Stedman [29] reported higher concentrations of Lycopodium spore deposits at the edges of the front side of disks. This is contrary to what they observed for cylinders, in which case there were more deposits in the centre. Noll and Pilat [31] measured local capture efficiencies on the front side of ribbons and found that the pattern is similar to that on disks: more deposits were found close to the ribbon edge. These observations were explained with an inertial deposition model, which predicted more deposits toward the edge of the ribbon. Vincent and Humphries [19] noted that on the front surface of disks, deposits were concentrated close to the centre. However, their capture efficiencies were as much as 10 times below theoretical predictions. Since they worked with solid particles (aloxite dusts), they explained the discrepancies by the probable re-entrainment of dusts particles, and therefore, their results for the distribution of deposits cannot be considered reliable. To summarize, data on the distribution of droplet deposits on the upstream sides of disks are not available in the literature. Also, distribution of deposits on the downstream side of surfaces or body collectors of any shape, to the best of our knowledge, has not been reported. This justifies our intention to determine the distribution of deposits along the radius of the disk. 2.4. Contact angle effect The majority of the prior work on deposition was focused on particle transport to the surface, probably because it was considered more important in the fouling process. Two other factors that can affect the fouling process are droplet sticking and droplet re- entrainment. In our case, it is reasonable to assume that the re-entrainment of liquid droplets deposited on the surface of the disk does not occur; these phenomena are more common for solid particles. The remaining important phenomenon is sticking, and how it can be influenced. To explain sticking, we start by explaining the wetting and contact angles. Chapter 2. Theory and Literature Review 20 2.4.1 Wetting and contact angles Wetting (or wettability) represents the ability of a liquid to maintain contact with a solid surface, which is the result of intermolecular forces of the two phases in contact. The degree of wetting is determined by the equilibrium of adhesive forces between the solid and the liquid, and cohesive forces within the liquid. If the adhesive forces are stronger, the degree of wetting will be higher. Contact angle represents a quantitative measure of wettability, and the relative strength of adhesive and cohesive forces. It is the angle, θ, between the tangent lines of the liquid-vapour and the solid-vapour interfaces, as presented in Fig. 2.3. Figure 2.3 Schematic representation of the surface tension forces acting on a droplet deposited on the surface From a force balance along the three-phase interface, the following relation can be devised (Young’s equation): )cos(θγγγ LVSLSV =− , where SVγ , SLγ , LVγ are the surface tensions on the solid-vapour, solid-liquid and liquid-vapour interface respectively. This equation is often approximated as )cos(θγγγ LSLS =− , where Sγ and Lγ are the surface tensions of the solid and liquid. The surface tension of liquid represents the energy required for a unit increase in area of the liquid-gas interface. Surface tensions of solids have the same meaning. Usually, they are referred to as surface energy. Exact measurements are difficult, and according to Marere and Douillard [37], currently assumed values for surface energies of solids are 10−72 mJ/m2 for low energy solids (e.g. polymers, carbons, and sulfurs), 72−200 mJ/m2 for middle energy surfaces (e.g. clays and clay minerals, silicas, quartz) and 200−2000 mJ/m2 for high energy solids (e.g. metals) [37]. Surface tensions of liquids θ SL γ LV γ SV γ Chapter 2. Theory and Literature Review 21 at 20°C vary from 20−75 mJ/m2; the exception is mercury with surface tension of 425 mJ/m 2 . Table 2.3 summarizes possible combinations of liquid-solids interactions and the relation with contact angles and wettability. Table 2.3 Degree of wetting explained in terms of solid-liquid and liquid-liquid interaction Strength of Contact angle Degree of wetting S/L interactions L/L interactions o 0=θ Perfect wetting Strong Weak Strong Strong oo 900 ≤< θ High wettability Weak Weak oo 18090 << θ Low wettability Weak Strong o 180=θ Perfect non-wetting Weak Strong From Table 2.3, it can be seen that low wettability can be achieved with strong liquid- liquid interactions and weak solid-liquid interactions. Strong L/L interactions are characterized by high surface tension of the liquid, and weak solid-liquid interactions are usually result of low surface energies of solids (the majority of high surface energy solids wet all liquids, i.e. metals, while low surface energy solids give low wetting, i.e. Teflon). The following table shows contact angles of water at 20°C (γ=73 mJ/m2), with different surface energy solids [38]. Table 2.4 Contact angles of water at 20°C with solids of different surface energies [38] Material Surface energy (mJ/m 2 ) Contact angle (°) Clean glass 73 0 Ordinary glass 70 20 Platinum 62 40 Anodized aluminium 50 60 Polymethyl-methacrylate 41 74 Nylon 38 79 Polyethylene 33 96 Polypropylene 26 108 Paraffin 19 110 Teflon 18 112 From this table, we can see that as the surface energy is decreased, contact angles are increased. The role of contact angles in droplet sticking or rebounding is explained in the next section. Chapter 2. Theory and Literature Review 22 2.4.2. Impact of droplets on the solid surface (sticking vs. rebounding) The phenomena governing liquid impacts on solid surfaces are quite complex, and more complicated than those encountered on wetted surfaces. The reason for the additional complexity is the influence of surface texture, i.e. wettability and surface roughness (Yarin [39]). The main types of behaviour when a droplet impacts a dry solid surface (Table 2.5) can be described as follows [39, 40]. a. Deposition. The droplet spreads upon impact and stays deposited on the surface. This mostly occurs with hydrophilic (and oleophilic) surfaces (θ < 90°), but it can also happen with hydrophobic (and oleophobic) surfaces (θ > 90°). For hydrophobic surfaces, it occurs when force that is acting to remove the droplet from the surface is sufficiently small, i.e. droplet deposition velocity is so small that there is no bouncing and the droplet stays on the surface; or, the gravity force on the droplet resting on a slightly inclined hydrophobic surface is not sufficient to cause sliding. b. Splashing (prompt splash or corona splash). An increased impact velocity on a hydrophilic rough surface causes tiny droplets to detach from the edge of the lamella (prompt splash), and if the surface tension of the liquid is reduced, lamella are able to detach from the wall (corona splash). If the impact velocity is high enough, splashing or breakup can also occur on hydrophobic and superhydrophobic surfaces (θ > 150°). c. Rebounding. Rebounding happens most often on hydrophobic surfaces, although according to the simulations of Khatavkar [41], partial rebounding can occur on hydrophilic surfaces also. Rebounding follows retraction of a droplet from the elongated state, where its initial kinetic energy is transformed into the potential energy of surface tension (and partly dissipated inside the droplet via viscous dissipation). If, in retracting, the droplet-surface interactions are strong (hydrophilic surface or hydrophobic surface), and viscous dissipation is present, only partial rebounding can occur. However, if the surface is superhydrophobic, droplet-surface interactions are negligible, and the droplet can fully rebound. This can happen only if viscous dissipation is not significant: e.g. it is unlikely that a drop of honey would rebound from any surface. In addition, advancing and receding contact angles (θadv and θrec) should be similar, in order to avoid contact angle hysteresis as a significant source of energy dissipation. Chapter 2. Theory and Literature Review 23 Table 2.5 Possible outcomes of droplet impact on a solid surface Deposition (drop oscillates a little) Prompt splash Corona splash Partial rebounding Complete rebounding To reduce fouling, we are interested in partial or complete rebounding. From experimental observations, it is known that complete rebounding can occur only on high contact angle surfaces (θ >150°), classified as superhydrophobic surfaces [42, 43, 44]. In nature, examples are the surfaces of the lotus leaf (.elumbo .ucifera), or bird feathers. In addition to having a hydrophobic waxy layer, their surface is enhanced with two levels of roughness on the microscale. The first level consists of 10–20 micron size bumps that do not allow large droplets to penetrate between them. The second level of roughness is made of below micron-size hairs, densely packed all over the surface. Droplets sitting on such surfaces are found in the so-called Cassie state: pockets of air remain below the droplets, and apparent contact angles between the liquid and the surface are usually greater then 150°. Figure 2.4 Droplet on a surface in the Cassie (metastable) state, showing superhydropho- bic properties, and in the Wenzel (stable) state, wetting the surface However, if exposed to increased pressures (e.g. by submerging at certain depths under the water), these surfaces could lose their properties and undergo transition into the Wenzel state, where droplets actually wet the surface. Indeed, recent experiments showed that the surface of the lotus leaf is covered with a hydrophilic (not hydrophobic) waxy layer (θ=74°), and that it loses its superhydrophobic properties if under pressure, or if condensation occurs [45, 46]. In addition, pressure from the droplet impact can cause penetration of water into asperities and wetting of the surface (Wenzel state). Under pressure or by condensation Cassie state Wenzel state Chapter 2. Theory and Literature Review 24 A good review of possible outcomes of drop impact on superhydrophobic surfaces, depending on the impact velocity and Wenzel roughness is given by Rioboo et al. [47]. Their experiments also showed that droplets below 0.1 mm, in the range of impact velocities from 0.1 to 10 m/s, would rebound or stay deposited on the surface. If droplets stayed deposited on the surface, they were in the Cassie state and could be easily removed. Richard and Quere [44] investigated the bouncing of water drops from a superhydrophobic surface with a contact angle of 170°, and noted perfect droplet bouncing with the coefficient of restitution close to 0.9. Bouncing and splashing of droplets on 150° surface was investigated also by Durickovic and Varland [44]. Wang et al. [48] investigated rebounding of water drops from carbon nanotube arrays and observed that for contact angles of 163°, the droplets would bounce off several times, while for contact angles of 140°, they remained pinned to the surface. Bergeron [69], in his popular article on deposition of droplets on the leaves of plants in agricultural applications, explained that sticking or rebounding is governed by inertial, viscous and capillary forces of the drop upon the impact. One way to increase deposition is to reduce the surface tension of the liquid or increase its viscosity; for reducing deposition, the opposite holds. Therefore, in order to promote droplet bouncing, one could: • Increase contact angle, by using low surface energy solids (e.g. Teflon), to achieve partial rebounding. • Increase contact angle, by using superhydrophobic surfaces (θ > 150°), to achieve complete rebounding. In addition, one could promote rebounding by: • Decreasing the viscosity of the liquid, so that the droplet upon impact does not lose energy via viscous dissipation, and has more energy to bounce off. • Increasing the surface tension of the liquid, in order to increase the contact angle and decrease the wettability. Since the superolophobic surfaces with high contact angles look as the most promising for our application, they are discussed in more details in the next section (Section 2.3.4). Chapter 2. Theory and Literature Review 25 2.4.3. Superoleophobicity Recently, a number of authors have reported that they have synthesised surfaces which manifest superhydrophobicity and superoleophobicity at the same time. The first to report super-oil repellent surfaces were Tsujii et al. [49], who coated fractal structures on an oxidized aluminum plate surface with the trifluoromethyl groups of fluorinated monoalkylphosphates. They obtained high contact angles; for rapeseed oil 150°, and for octane 120°. Tuteja et al. [50,51] described designing parameters for such surfaces, and explained that for high contact angles of low surface tension oils, such as decane (23.8 mN/m) and octane (21.6 mN/m), a surface energy of a smooth solid of the order of 5 mN/m was needed. They synthesised a new class of hydrophobic fluoroPOSS molecules (Fluorinated Polyhedral Oligomeric Silsesquioxanes), to cover the roughened surface. Advancing and receding contact angles were 163° and 145° respectively. Wu et al. [52] treated alumina nanowire forests with perfluorocompounds and obtained contact angles higher than 150° for different oils (155.6° for crude oil, 150.4° for silicone oil). High contact angles of oils make them potentially useful for application in causing the rebounding of oil droplets in the scrubber of the coker reactor. However, since all these surfaces are treated with organic compounds (fluoro-groups, silanes) with relatively low melting points, their application at high temperatures above 300°C is questionable. Fractal surfaces of Teflon (melting point 327°C) may provide better performance. Recently, Cao et al. [70] reported superhydrophobic surfaces (water contact angle 159 ± 2°) produced by packing flowerlike hematite particles which are intrinsically hydrophilic. The largest asperities on the surface seemed to be in the order of 1 micron, and such surfaces did not lose their properties after heating in air at 800°C for 10 hours (θ=158 ± 2°). However, they did not report tests with oils. In the case of the scrubber section of the coker reactor, it seems that only complete rebounding could be considered as an option. Partial rebounding would leave some amount of deposits on the surface, which would eventually form a monolayer of coke deposits and the repellent surface properties would diminish. However, superhydrophobic surfaces have also ‘self-cleaning’ properties. Lotus leaves, feathers of birds, etc. have the property of using the water to collect all the dirt (i.e. small particles) Chapter 2. Theory and Literature Review 26 from their surface, while rolling down the surface. In that sense, even partial rebounding of bitumen droplets from superhydrophobic surfaces could be satisfactory. If the wash- oil that is poured from the top doesn’t wet the surface, it would roll off the surface, collecting deposited bitumen droplets. Still, many practical questions remain, • How long could superoleophobic surface be maintained clean, i.e. whether small bitumen droplets would deposit inside the microstructures so that they could not be reached and picked up by the liquid flowing down? How small should asperities on the surface be, to prevent that from happening? • How would superhydrophobic surfaces behave at high temperatures, would they be stable, without sintering? • Would the metastable Cassie state be diminished if the droplet impacting the surface possesses sufficient pressure to penetrate inside the pores? Is the wash-oil sprayed from the top more likely to do so? • Does the condensation of vapours in the scrubber section occur? If so, surfaces would most probably lose the feature of superoleophobicity. To summarize, for complete rebounding, superhydrophobic and superolephobic surfaces, with contact angles higher than 150° are required. To repel oil droplets, in addition to the fractal structure of surface roughness, low surface energy materials are needed. Since such surfaces are not commercially available yet, we decided to test surfaces with contact angles in the range that could be obtained (20−94°) and see if partial rebounding [41] could reduce deposition rates. Goldshmid and Calvert [35], who investigated the collection of polystyrene and sulphur particles from aerosols onto supported liquid drops (water, glycerol, formamide, phenol), showed that with an increased contact angle in the range from 0° to 87°, there is “definite effect of interfacial tension on the collection efficiency”. These results also justify our attempts to investigate the contact angle effect in a similar range. Chapter 3. Modeling 27 Chapter 3. Modeling The main focus of this work was an experimental investigation of the transport and deposition of droplets. Simulation of the deposition phenomena would require knowing the velocity field in front of the disk, and the velocity field in the vortex behind the disk. These types of problems are nowadays usually tackled using Computational Fluid Dynamics (CFD), and this was the objective of a separate thesis work on this project (Lakghomi [36]). However, in order to at least qualitatively explain the obtained results, simple models that describe the flow field around a disk were used. For the upstream side, inviscid flow approximations have been successfully used in the past [24, 26, 27, 31]. Also, in order to estimate deposition rate on a dry surface of different materials, a model for the change of the surface coverage of the disk during deposition was developed. To compare the results of the room temperature studies with the data obtained in the Hot Unit (Song [52]), the effect of reaction of heavy hydrocarbons at elevated temperatures was modeled as well. These models were used in Section 5.4 and Chapter 6, to explain the experimental results. 3.1. Particle deposition on the upstream and downstream side In the work of Subudhi [9], fouling in the scrubber section of the Fluid Coker was modeled as deposition from a turbulent flow parallel to the surface of the packing elements. Although the flow around bluff bodies, such as circular disks, is different from the flow over horizontal surfaces, in the vicinity of the disk surface, flow can be regarded as parallel to the surface. Although this may not be a good approximation of the flow around the small objects usually used in inertial impaction experiments (0.1−1 mm), it should be an acceptable approximation for the 5 cm diameter disks used in this work. This view is supported by the results of the flow field obtained from CFD simulations [36], but also from the simple potential flow field approximation [26, 31]. Experimental observations of the aerosol flow in the vicinity of the coupon surface by the means of shadowgraphy technique (Section 4.3.3), confirm this view. Furthermore, aside from inertial impaction, the concept of ‘eddy impaction’ (from the parallel flow), for deposition from a normal flow over cylinders, was used by Lokare et al. [53]. Therefore, Chapter 3. Modeling 28 the theories of particle transport from parallel flow should also apply to some extent to this case of the normal flow. In the case of normal flow, as stated in Chapter 2, rarely do all mechanisms of deposition occur simultaneously. When the diameter of the body is significantly larger than the diameter of the approaching particle, RI<<1, interception can be neglected [20]. This is the case in our study, where the parameter RI is in the order of 310− (5 cm disk and 1−100 micron droplets). If electrostatic charge on the disks is neglected, and under the assumption that the produced aerosol droplets are free of charge, electrostatic forces can also be neglected. Since we are concerned with isothermal cases (in both the Cold Unit and the Hot Unit), thermal forces are excluded from consideration. Therefore, the main mechanisms of deposition on the surface of a disk from the upward flowing aerosol (schematically shown in Fig. 3.1), can be summarized as in Table 3.1. Close to the surface, flow can be roughly considered parallel on both sides. Relevant mechanisms of deposition are presented in Fig. 3.1 (inertial impaction, gravity, convective diffusion, eddy impaction). Figure 3.1 Schematic representation of the flow field around a disk, with particle transport mechanisms Inertia from parallel flow, by turbulent eddies (“eddy impaction”) + Convective diffusion Flow is approx. parallel with the surface Inertia from parallel flow by turbulent eddies (“eddy impaction”) + Convective diffusion Inertial impaction − gravity Flow is less parallel, but still approximately parallel case Concentration and size distribution probably different (generally lower [72]) than in the aerosol bulk Inertial impaction + gravity Exchange of droplets between the aerosol bulk and the well mixed vortex Chapter 3. Modeling 29 Table 3.1 Summary of mechanisms of deposition on a circular disk from an upward flow Upstream (front) side Downstream (back) side Normal flow Parallel flow From the vortex Parallel flow Inertial impaction Convective diffusion* Inertial impaction Convective diffusion* Gravity in negative direction (decreases deposition) Inertia due to turbulence (“eddy impaction”) Gravity in positive direction (increases deposition) Inertia due to turbulence (“eddy impaction”) * Convective diffusion is categorized under parallel flow. However, the mass transfer coefficient is estimated from mass transfer correlations obtained for flow that is normal to disks [57]. 3.2. Gas phase flow To describe the motion of particles, the first step is to describe the flow field around the disk. 3.2.1. Continuity and momentum conservation equations The flow of the gas phase is described by mass, momentum and energy conservation equations. Since experiments are performed at isothermal conditions, the energy equation can be omitted [54]. Therefore, Continuity: 0=⋅∇+ v t r ρ ∂ ∂ρ (3.1) Momentum: FvPvv t v rrrr r +∇+−∇=∇⋅+ 2)( µ ∂ ∂ ρ (3.2) For a flow which is symmetric around the x-axis (axisymmetric flow) in cylindrical coordinates, the θ -direction can be neglected. The steady-state equations are then, 0)( 1 =+ x v rv rr x r ∂ ∂ ∂ ∂ (3.3) x: x xxx x x r g x v r v r rrx p x v v r v v ρµρ + ∂ ∂ + ∂ ∂ ∂ ∂ ⋅+ ∂ ∂ −= ∂ ∂ + ∂ ∂ ])( 1 [)( 2 2 (3.4) r: r rrr x r r g x v r v r rrr p x v v r v v ρµρ + ∂ ∂ + ∂ ∂ ∂ ∂ ⋅+ ∂ ∂ −= ∂ ∂ + ∂ ∂ ])( 1 [)( 2 2 (3.5) Chapter 3. Modeling 30 These are second-order nonlinear partial differential equations. They are, at present, usually solved using CFD, which also employs turbulence models to describe the flows at high Reynolds numbers. For the case of an ideal fluid (inviscid fluid, flow is characterized by irrotational motion), the equations of the flow field around the disk can be simplified to yield the equations of potential flow. This approach had been found useful in prior work (Table 2.1, Chapter 2), and was used in this study. 3.2.2. Potential flow approximation Potential flow results when viscous forces are neglected, and is characterized by an irrotational velocity field. This approximation is valid in many cases of external flow, except very close to a solid boundary, where the action of viscosity is important, and in the wake region of a solid obstacle where instabilities and turbulence can occur [55]. In general, this approximation should be valid for high Reynolds numbers, when the ratio of inertial to viscous forces is sufficiently large (Re > 100, [30]). In deriving the velocity field equations, the flow of the gas is considered incompressible and the effect of gravity on the flow field is also neglected. After solving Eqs. (3.3)−(3.5), the velocity field components, are given by [26, 31], xv x 2−= (3.6.a) rv r = (3.6.b) where new non-dimensional variables are used: dimensionless axial and radial positions, cR x x = and cR r r = , and dimensionless axial and radial velocities, 0v v v xx = and 0v v v rr = . Equations (3.6a,b) are derived neglecting the effects of column walls around the disk, and are valid for the region in front of the disk only. Salmanzadeh et al. [56] showed that capture efficiencies on the front face of a rectangular obstruction in a duct flow increased by 10−15% with the increase in the blockage ratio (Br=A/Acolumn) from 0.1 to 0.5. Therefore, it may be expected that this flow field, which does not consider the presence of column walls, somewhat underestimates deposition on the disk inside the column (Br=0.45). Chapter 3. Modeling 31 3.2.3. Potential flow with a viscous sublayer The flow field close to the coupon surface plays an important role in determining if the particle will reach the surface, especially for particles with smaller inertia. Higher radial velocities will sweep particles away from the surface, while lower radial velocities, occurring in the viscous sublayer, should allow more particles to reach the surface. To investigate the validity of the inviscid flow approximation, an attempt is made to calculate deposition with a viscous sublayer, added to the free-stream inviscid flow. A 5 mm thick viscous sublayer that has a velocity linearly increasing from 0=rv at the coupon surface, to rv r = at 5 mm from the coupon, was added. From the linear velocity gradient close to the wall, and the free-stream velocity, the thickness of the boundary layer was estimated to be: 6.5 mm at 0.2 m/s, 3.8 mm at 0.4 m/s, 1.8 mm at 1 m/s and 1.2 mm at 1.6 m/s. The value of 5 mm, somewhat above most of the above estimated values, was chosen to see if it would yield a noticable effect. Although this is a simplified model, it should indicate the sensitivity of the results to the excluded boundary layer. <<−⋅ − −< = 02.0, 2.0 2.0, xx r xr v r (3.7a,b) Figure 3.2 Schematics of the patched viscous sublayer, linearly increasing from 0=rv at 0=x , to rv r = at 2.0−=x 3.3. Inertial impaction mechanism Calculation of the trajectory of droplets in the flow field requires that particle motion be described. Although the model for inertial deposition on a circular disk from potential flow was presented by Ranz and Wong [26], it was concerned with horizontal flows, and hence the effect of gravity was not included. Also, in order to obtain linear 0.2Rc Rc x r Chapter 3. Modeling 32 equations that could be solved analytically, they used the Stokes drag force on the particles. Since we are concerned with the upward flow of an aerosol, the model should include the effect of gravity. To represent the drag force on larger particles more faithfully, it was also desirable to include a non-Stokesian drag force in the calculations. The results of simulations for the upward flow captured some interesting characteristics of inertial impaction. Also, it turned out that with gravity in the downward direction, the same model was capable of explaining the trends of deposition on the downstream side (Chapter 5). The detailed inertial particle deposition model with its solution procedure (analytical and numerical) is described in Appendix C. Here, only the most important steps are presented. The equation of particle motion in vector notation, in the presence of gravity, under the assumption of Stokes drag force on the particle is given by [26], gmuvD dt umd p +−= )(3 )( πµ (3.8) where u is particle velocity, v is fluid velocity, and mg is the gravity force. If the vector notation is removed, and the gravity force is retained, for each component we can write, x: pmguvD dt mud xxp x +−= )(3 )( πµ (3.9a) r: )(3 )( rrp r uvD dt mud −= πµ (3.9b) where parameter { }1,0,1−∈p denotes the orientation of the gravity field. After introducing dimensionless variables, the following equations are obtained, x: 02 0 2 2 =−−+ v gt pv td xd td xd St p x (3.10a) r: 02 2 2 =−+ rv td rd td rd St . (3.10b) Chapter 3. Modeling 33 Here, tp is the particle relaxation time, a pp p D t µ ρ 18 2 = , and St is the Stokes number c p R vt St 2 0= . If the equations of the flow field derived from the potential flow approximation are used (Eqs. (3.7a,b)), and the solution procedure described in detail in Appendix C is followed, the following expression for the capture efficiencies can be obtained, 2 ' 1 ' 2 12 21 − − = tztz ezez zz E (3.11) where z1 and z2 are solutions of the characteristic equation St St z 4 1611 2,1 −±− = (Eq. (C.13)), and 't is the time needed for particle to reach the coupon surface (Eq. (C.32)). When gravity is involved, 't must be calculated numerically, by solving Eq. (C.37). Also, if the non-Stokesian drag force is used, Eqs. (3.10a,b) are nonlinear, and must be solved numerically. It should be mentioned that Eqs.(3.9a,b) are not strictly valid for horizontal flow, since the problem is not axisymmetric anymore due to the presence of gravity. However, in the case of fine droplets with small terminal velocities, gravity can be neglected and the approximation expressed by Eqs. (3.9a,b) should be satisfactory. Distribution of deposits along the coupon radius predicted by this model can be deduced from the following equation (also derived in Appendix C), 0 ' 21 1 0 ' 12 2 00 21)( rconste zz z re zz z rrr tztz ⋅= − + − = (3.12) where 0r is the initial radial position of the particle where it is injected. The equation states that the final position of the particle on the disk is linear function of its initial radial position. This indicates that deposits should be uniformly distributed along the coupon radius. Chapter 3. Modeling 34 3.4. Particle transport due to turbulence Since deposition from the normal flow also occurs from the flow parallel to the surface (Table 2.1, Fig. 3.1), a description of the latter deposition phenomena was attempted with the models described below. 3.4.1. Particle transport due to convective diffusion As already stated in Chapter 2, in the diffusion regime, submicron and micron- size droplets are carried to the surface by Brownian diffusion through the boundary layer. The transport coefficients can then be obtained from the relevant empirical correlations or theoretically developed equations for forced convection mass transfer [12]. Empirical correlations for forced convection mass transfer from circular disks are given by Beg [57], who investigated sublimation of naphthalene from 5 cm disks into air. Mass transfer from the front side of a disk can be described by the following equation, 3/154.0 )()(67.0 ScReSh = (3.13) and from the back side with, 3/154.03/160.0 )()(67.0)()(532.0 ScReScReSh −= (3.14) for Reynolds numbers in the range 34900270 << Re , and a Schmidt number of 1.75. If we use values for the Brownian diffusivity of droplets in the Schmidt (Sc=νa/D) and Sherwood (Sh=kt/D) numbers, we can estimate deposition coefficients (kt) for different droplet sizes at different Reynolds numbers. 3.4.2. Particle transport due to turbulent diffusion in the inertial regime In addition to convective diffusion, when the flow is turbulent, particles can be deposited by inertia. If we can assume a parallel flow to the surface (Fig. 3.1), and if the particles are sufficiently large ( 2.0>+pt ), turbulent eddies give them some transverse free-flight velocity, which enables particles to travel through the viscous sublayer (Fig. 3.1). This assumption holds true more for the upstream side than for the downstream side, because of the nicely defined flow field in front of the coupon, and imprecisely defined turbulent wake behind the coupon (Fig. 3.1). Correlations for deposition from turbulent Chapter 3. Modeling 35 flow in the inertia regime, given in Chapter 2 (Eqs. (2.2), (2.6a,b)), were used for this purpose. 3.5. Surface coverage In order to investigate the effect of the contact angle on deposition, surfaces of disks had to be kept dry somehow, so that deposition does not take place on the liquid layer. One possibility was to use Vycor ® porous glass disks (pore diameter 0.4 microns), that would absorb the liquid film from the surface by capillary forces. To keep the surface dry, the rate of absorption should be faster than the deposition rate. Calculations of the rate of absorption, using the Washburn equation, showed that this process would not be sufficiently fast; larger capillaries in the material, or a less viscous liquid were needed. The other possibility was to perform short experiments (10−120 sec.), where deposition would still take place on a dry surface. In order to estimate deposition rates on a dry and irrigated surface from experimental data, this approach required a proper model. This is for the reason that low amounts of deposits were expected from such short experiments (1−3 mg), and a scatter in the experimental data was anticipated. 3.5.1. Deposition model The deposition rate on a disk surface, partly covered with liquid, can be written as, yryrr ddd ⋅+−⋅= 2,1. )1( (3.15) where rd,1 is the deposition rate on a dry surface and rd,2 is the deposition rate on a wet surface. Surface coverage y, is defined as the ratio of the surface area covered with liquid and the total surface area, A A y wet= . If we assume that deposition on the wet surface does not increase surface coverage (a small droplet will be ‘eaten’ by a liquid deposit without spreading too much), the decrease in a dry surface area can be written as a first-order process, drys dry Ak dt dA ⋅−= (3.16) Chapter 3. Modeling 36 The deposition constant, ks, is equal to Am r s d ⋅ 1, , where ms is specific mass (kg/m 2 ) of a droplet sitting on a surface, ( )2 2 3 )( 3 2 4 ' 6 θρ π ρ π kD D D m pp p p p s ⋅⋅= ⋅ = (3.17) Here, Dp is the diameter of a droplet in the aerosol, pp DkD ⋅= )( ' θ is the diameter of a droplet on the surface, and )(θk is the correction factor derived in Appendix C. Using the definition of the surface coverage, and replacing dryA with wetAA − , Eq. (3.16) becomes, )1( yk dt dy s −⋅= (3.18) After integration of Eq. (3.18) we get, t mA r s d ety ⋅ ⋅ − −= 1, 1)( (3.19) Equation (3.15) then finally becomes, ( ) 2,2,1, 1, )( d t mA r ddd rerrtr s d +⋅−= ⋅ ⋅ − (3.20) For a size distribution of droplets, specific mass ms to be used in Eq. (3.20) is calculated according to: ( ) ( )∑ = ⋅⋅= n i downstreamiipps VDkm 1 ,, 2 )( 3 2 θρ (3.21) where Dp,i is the maximum diameter of the class i of the distribution in the aerosol, having relative volume frequency on the downstream side of the coupon, Vi,downstream. 3.5.2. Estimation of deposition rates Deposition rates from individual experiments are calculated from the mass of deposits at the end of each experiment i, Chapter 3. Modeling 37 i i id mm r τ τ )0()(exp , − = (3.22) where τi is duration of the experiment i, m(0) and m(τi) denote the masses of the deposits at the beginning and end of the experiment, and exp,idr is the deposition rate calculated from experimental data. This deposition rate represents the integral of all deposition rates during the experiment and is given by, i d id i dttr r τ τ ∫ = 0exp, )( (3.23) Integral deposition rate at the end of experiment predicted by the model, int,idr , is obtained by integrating Eq. (3.20) from 0 to τi. This gives, 2, 1, 2,int , 1, 11 d mA r d d i s id re r rmA r i s d + −⋅ −⋅ ⋅ = ⋅ − τ τ (3.24) To estimate rd,1 and rd,2 from experimental data, sum of squares of relative errors between deposition rates from experiments (Eq. (3.22)) and from the model predictions (Eq. (3.24)) was minimized. The objective function also included weights to account for the variability in measurements. The parameter estimation problem can be finally stated as, 4434421 weights iid iid n i id idid rr r r r rr Minimize dd )max( exp, exp , 1 2 exp , int , exp , , 2,1, τ τ ⋅ ⋅ ⋅ − ∑ = (3.25) 3.6. Deposition coefficients Deposition coefficients and capture efficiencies calculated from Eqs. (2.7) and (2.8) are valid only for monosize aerosols, or for the particular aerosol drop size distribution used in the experiment (as was the case in this study). Since drop size distributions on the disk surface and in the aerosol were measured, it was possible to calculate the deposition coefficients for each droplet size. Knowing the deposition coefficients for each droplet size and velocity gives more generality to the obtained Chapter 3. Modeling 38 results, since deposition rates for any size distribution at a given velocity can then be easily calculated. For the upstream side, we can write, aerosolib upstreamid upstreami VcA Vr k , , , ⋅⋅ ⋅ = (3.26) U k UVcA Vr E upstreami aerosolib upstreamid upstreami , , , , 1 = ⋅⋅ ⋅ = (3.27) where ki,upstream is the deposition coefficient of the droplet class i for the upstream side, Vi,upstream is the volume relative frequency of the droplet class i on the upstream side of the coupon, and Vi,aerosol is the volume relative frequency of the droplet class i in the aerosol. In Eq. (3.27), Ei,upstream is capture efficiency of the droplet class i for the upstream side, and U is the gas velocity. The same equations (only with index ‘downstream’) are valid for the downstream side too. 3.7. Droplet size distribution fitting To fit the size distribution of droplets in the aerosol produced by atomization, usually a two-parameter log-normal probability density function is employed [77]. This ‘skewed’ distribution is widely encountered in nature [78]. In our case, generated size distribution of droplets (presumably log-normal) was affected by deposition of droplets from the outer part of the spray cone on the column walls around the nozzle, and by removal of large droplets in the elbows (see Section 4.1.1.1). Therefore, it is possible that the size distribution of droplets that remain in the aerosol is a modified log-normal distribution, which can not be fitted satisfactorily by adjusting the two parameters only. To allow for a proper fitting, a standard log-normal probability density function was extended with two additional parameters (a1 and a3): ( ) −− − − = 2 4 2 32 24 1 2 )ln( exp )(2 ),( a aax axa a xf x π a (3.28) where x represents the independent variable, and a is the vector of four parameters (a1, a2, a3, a4) to be determined by fitting. In the fitting procedure, a sum of squares of Chapter 3. Modeling 39 differences between the model predictions and experimental measurements (2-norm) was minimized (function f2lognormalpdf.m in Appendix D), ( )∑ = − max 1 2 ,, ),( i i aerosoliipx VDfMinimize a a (3.29) It proved that in our case, more meaningful fitting of the experimental data was obtained by setting the first parameter a1=1. Therefore, only parameters a2, a3, a4 were reported in the tables presented in Appendix E. 3.8. Reaction In order to compare results of the room temperature studies with the data obtained in the Hot Unit (Song [52]), the effect of reaction of heavy hydrocarbons at elevated temperatures had to be considered and required modeling. In the high temperature unit experiments, deposits of heavy oil droplets were exposed to temperatures from 295°C to 425°C. At these temperatures, heavy oil undergoes thermal decomposition into volatile fractions and coke, VolatilesCokeOilHeavy H + → >∆ 0 Volatiles evaporate from the coupon surface and can reduce the observed deposition rate (or accumulation rate). Droplets deposited at the beginning of the experiment have more time to react than droplets deposited later on. Therefore, the rate of reaction during the experiment is changing. Deposits on the coupon can be represented as a series of thin layers, as in Fig. 3.3, with the first layer being deposited at the start of experiment, and the last layer n being deposited at the end. Figure 3.3 Schematic representation of the discrete amounts of deposits on the coupon surface. Layer 1 had more time to react than layer n and release more volatiles … … layer 1 layer i layer n coupon Chapter 3. Modeling 40 Assuming a first-order decomposition reaction of heavy oils (Yue et al. [58]), the weight loss from the i-th layer (Fig. 3.3) can be written as, )( , fiir i mmk dt dm −⋅−= (3.30) where kr is the first-order reaction constant, and fim , is the mass of the layer i at the end of reaction (t=∞). After integration and differentiation of Eq. (3.30) we get, ( ) )(,0, ir ttkfiiri emmk dt dm −⋅−⋅−⋅−= (3.31) where mi,0 is the mass of the freshly deposited layer, and ti is the moment of deposition of the layer i. The accumulation (fouling) rate is then the sum of the deposition rate rd, and the weight loss rates from all n layers (assuming no restriction due to overlying layers), ∑ = += n i i d dt dm r dt dm 1 (3.32) Substituting Eq. (3.31) into Eq. (3.32), along with MCRmm ifi ⋅= 0,, , results in, ( ) ∑ = −⋅−⋅⋅−⋅−= n i ttk ird inremMCRkr dt dm 1 )( 0,1 (3.33) In the previous equation MCR stands for Micro Carbon Residue, which is a measure of potential coke yield from a given feedstock, obtained by heating the sample under prescribed conditions of time and temperature (Yue et al. [58]). The right hand side of Eq. (3.31) is equivalent to ( ) ∑ = ⋅−⋅⋅−⋅− n i tk ird iremMCRkr 1 0,1 . The sum can be replaced by the integral, and since )( 10, iidi ttrm −⋅= + , it is also dtrdm di ⋅=0, . This yields, ( ) ⋅−⋅−⋅= ∫ ⋅− dteMCRkrdt dm t tk rd r 0 11 (3.34) After integration, the accumulation rate is finally given by, Chapter 3. Modeling 41 ( )( )tkd reMCRMCRr dt dm ⋅−⋅−+⋅= 1 (3.35) and the weight of deposits as a function of time is, ( ) −⋅ − +⋅⋅= − tk r d re k MCR tMCRrtm 1 1 )( (3.36) In the paper of Yue et al. [58], the yield of volatiles from the decomposition of Athabasca pitch is described as )1()( * VMCRkVVk dt dV −−⋅=−⋅= . This form is essentially equivalent to Eq. (3.30), with the constant k being equal to kr. For the first-order reaction constant, )/exp(0, RTEkk arr −⋅= , the pre-exponential factor and activation energy values (adopted from Yue et al. [58]) are 1130, min102334.1 −⋅=rk and molkJEa /5.197= . Table 3.2 shows limiting cases for the effect of reaction over time. Table 3.2 Accumulation rate and mass of deposits as a function of time t t = 0 t = ∞ Accumulation rate [ ]tkd reMCRMCRr −⋅−+⋅ )1( rd rd⋅MCR Mass of deposits −⋅ − +⋅⋅ − )1( )1( tk r d re k MCR tMCRr 0 rd⋅MCR⋅t To compare the results from room temperature and high temperature units, size distribution of droplets in the Hot Unit experiments had to be known. The following section (Section 3.9) describes how this size distribution was estimated. 3.9. Drop size estimation in the Hot Unit In order to obtain high temperatures (up to 425°C) in the Hot Unit, heating elements were required to be placed around and along the whole chamber length (Fig. 4.2). With the heating elements in place, setting up a shadowgraphy system, that would look inside the chamber interior, and measure the droplet size distribution, presented a difficulty. It was also estimated that, due to the high temperature difference between the chamber interior and the environment, condensation of vapours from the chamber would Chapter 3. Modeling 42 occur on the inner side of glass slides (Fig. 4.17), and block the camera view field. This essentially eliminates the possibility of proper measurements of the droplet size distribution. The shadowgraphy system was therefore used only on the Cold Unit. In the Hot Unit experiments, size distribution was estimated with the aid of an empirical correlation (Eq. (3.37)), and shadowgraphy measurements performed in the Cold Unit (using the Hot Unit nozzle). Firstly, the droplet size distribution at a few common gas and liquid flow rates to the nozzle (of the Hot Unit experiments), using the Hot Unit nozzle and air and water as fluids, was measured with the shadowgraphy technique in the Cold Unit. Then, the empirical correlation for twin fluid atomizers [59] was used to calculate the volume median diameter (Eq. (3.37)) of the size distribution, for the same operating conditions. By comparing the measured and calculated volume median diameters in the Cold Unit, a correction factor was obtained. This factor indicates how many times the true (measured) volume median diameter is larger or smaller than the diameter predicted by the correlation (due to the reasons discussed below). The correction factor was then used to correct volume median diameters predicted by the correlation at high temperature conditions, and estimate the ‘true’ value, which would most probably be measured with shadowgraphy. The volume median diameter, VMD, can be calculated from the following empirical equation (Wigg [59]), 13.02.01.0 5.0 1.05.0 1.0 6.0 )(1 5.21200 −− −⋅⋅⋅⋅ +⋅⋅= ⋅ ⋅+⋅⋅= lggl g l ll l g l VVh M M M4 M M M 4VMD ρσν & & & & & & (3.37) valid for a wide range of parameters. Lower limit of the volume median diameter data correlated with this equation is about 10 microns [59]. Symbols in the Eq. (3.37) are explained in the Nomenclature, along with the appropriate units that should be used. Approximations used to estimate missing parameters in this equation are as follows, Chapter 3. Modeling 43 • The surface tension of 5% and 10% MEBR in Voltesso is assumed to be 49 mN/m, as for pure Voltesso [71]. Voltesso is a mixture of volatile oil, while MEBR stands for a mixture of heavy hydrocarbon materials. The critical temperature of Voltesso (IBP=218°C, FBP=420°C) is estimated to be about 500°C, from comparison of boiling points and critical temperatures of n-paraffins given in [60]. Surface tension dependence on temperature can be approximated from the following linear equation, 0,0 0 0, )( )( )0( )( l c l l TT TT T σ σ σ +−⋅ − − = (3.38) According to Eq. (3.37), the volume median diameter is not very sensitive to surface tension (VMD ~ σl 0.2), and therefore these assumptions are acceptable. • The temperature of the liquid in the nozzle, which affects liquid and gas properties, is calculated from the heat balance equation, assuming ideal mixing of nitrogen and oil in the nozzle, oilpoil4p4 oiloilpoil44p4 CMCM TCMTCM T , . , , . , . 22 22 2 + + = & (3.39) The temperature of oil in the nozzle was taken to be 100°C, at which )/(1.2, kgKkJC oilp = and )/(05.12, kgKkJC 4p = [52]. The resulting nozzle temperatures varied between 170°C and 215°C for all runs. • There is no evaporation of the liquid in the nozzle itself, and thus no increase in the gas flow rate. This seems a valid assumption, since the maximal estimated temperature in the nozzle (215°C) is just below the Voltesso’s initial boiling point (218°C). • The velocities of gas, Vg, and liquid, Vl, are calculated from their flow rates through the nozzle orifice, at the nozzle temperature and pressure. Although it is not stated clearly how these velocities should be calculated, the same method was used for obtaining the correction factor from the Cold Unit experiments and in subsequent drop size estimation in the Hot Unit. Therefore, the choice for calculating the correction factor should have no effect on the estimated volume median diameter. Chapter 3. Modeling 44 • The viscosities of oils at a given temperature are obtained by extrapolating available experimental data for 5% and 10% MEBR (Hot Unit Progress Report, Feb 27 th , 2009) in the temperature range 30−150°C using the equation, ⋅ +− ⋅− ⋅= 9.26 06.69 3 0126.0 101000 Te oilµ (3.40) where T is in (°C) and µoil is in (cP). The extrapolated curve followed the same trend as that of the experimental data, and Eq. (3.40) is believed to be a good approximation. Estimated viscosities were in the range 1.3−1.8 cP. • The percentage of oil as droplets after evaporation is taken from the Hot Unit data obtained from HYSYS predictions [52]. The drop size distribution was estimated according to the following procedure, 1. The Hot Unit nozzle was placed in the Cold Unit and size distribution for nine Hot Unit run settings, with the air and water as fluids, was measured with shadowgraphy method (run numbers: S-5, S-17, S-18, S-19, S-20, S-21, S-27, S-34, S-36) [52]. 2. The empirical correlation (Eq. (3.37)) was used to estimate volume median diameter for these experiments, using the physical properties of air and water. 3. The measured volume median diameter was about 4−5 times lower than the volume median diameter predicted by the correlation, leading to correction factors of 0.25 (at liquid flow rate 10 ml/min) and 0.17 (at the liquid flow rate 20 ml/min). The measured droplet sizes are lower than predicted by the correlation, most likely due to the impaction of large droplets from the spray cone, on the column walls close to the nozzle. The smaller correction factor at the higher liquid flow rate (0.17 vs. 0.25) is probably due to the fact that, although larger droplets were generated, all droplets above some ‘critical drop diameter’ impacted column walls. Therefore, the aerosol was left only with fine droplets, which resulted in larger discrepancy between predicted and measured values and the smaller correction factor. The other reason could be the ambiguous use of the characteristic dimension ‘h’ in the correlation, since it is not clearly stated how this value should be chosen [59]. Chapter 3. Modeling 45 4. To estimate droplet diameters in the Hot Unit, estimated volume median diameters at Hot Unit conditions (at a different temperature, with different oil and gas properties, e.g. Eq. (3.40)) were multiplied by the correction factor 0.25 when the oil flow rate was 10 ml/min, and by 0.17 when the flow rate was 20 ml/min. 5. The final volume median diameter of the size distribution after evaporation was calculated from the fraction of oil that remained in the liquid phase, from the HYSYS predictions [52]. 6. A log-normal size distribution, with the volume median diameter as calculated in point 5, was generated and used in further calculations. Chapter 4. Experimental Study 46 Chapter 4. Experimental Study 4.1. Cold Unit apparatus In order to experimentally investigate the deposition of droplets from an aerosol at room temperature, the Cold Unit apparatus, with its measurement and data acquisition systems, was designed and built (by the author). The Unit consisted of a 180 cm high glass column, 7.5 cm inside diameter, in which the 5 cm diameter circular coupon was placed 55 cm below the top of the column (Fig. 4.1). The coupon was attached to a 1.6 mm diameter st.steel rod connected to a load cell, which was positioned 10 cm above the column. The aerosol was generated in a two-fluid nozzle, using air and a 50% wt. aqueous sugar solution or tri-ethylene glycol. Before entering the vertical column, the aerosol passed through two short sections (45 cm and 30 cm) connected with 90º and 45º elbows, in order to remove large droplets (>100 microns). Since the atomizer was placed in the 7.5 cm diameter column, droplets from the outer part of the spray cone deposited on the column walls, creating a liquid film. This liquid was continuously drained and collected below the column as a washdown stream. The concentration of droplets in the aerosol was then determined as the difference between the flow rate of liquid to the nozzle and the washdown flow rate (Section 4.3.1), divided by the volumetric flow of the air. The aerosol droplet size distribution was measured with a shadowgraphy system, installed in the middle section of the column. For this purpose, the flow of aerosol had to be momentarily stopped (Section 4.3.3). The exit from the column was placed about 45 cm above the coupon, which was high enough behind the coupon, not to disturb the flow. The droplet size distribution was changed by changing the flow rate of liquid to the nozzle, at a constant air flow rate. The volume median diameter of the distribution varied between 3.9 and 7.5 microns. The velocity in the column was changed by adding secondary air to the column. This was done at constant air and liquid flow rates to the nozzle, in order to keep the size distribution constant. The range of superficial velocities covered was from 0.05 to 1.5 m/s. The complete Cold Unit operating procedure is given in Appendix A. Chapter 4. Experimental Study 47 Figure 4.1 Schematic of the Cold Unit apparatus washdown reservoirs rod support and protection coupon load cell washdown to ventilation ball valve LED lights balance feedstock reservoir nozzle pump air to nozzle air supply (500−600 kPa) Rotameters #1, #2 and #3 fan to PC to PC CCD camera PI-1 PI-2 PI-3 TI-1 secondary air 90° elbow 45° elbow gas distributor to PC Chapter 4. Experimental Study 48 4.1.1. Cold Unit details 4.1.1.1. Cold Unit Setup #1 and Setup #2 Initially, the Cold Unit nozzle was positioned below the column. At velocities about 0.8 m/s and higher, large droplets from the aerosol (100 microns and larger) were depositing on the coupon upstream surface, controlling the deposition rate. Although the gas velocity profile close to the coupon was well developed (according to CFD simulations [36]), droplets reaching the coupon did not have uniform velocities. The main reason for large droplets having higher velocities is that the air exiting the nozzle orifice at about 100 m/s transferred momentum to the droplets. This momentum dissipated faster for smaller droplets, because of their smaller particle relaxation time, but the large droplets retained their momentum longer, eventually reaching the coupon surface. Velocities of these large droplets were significantly higher than the aerosol bulk velocity. To remove large droplets, one 45 cm long PVC column section with a 90° elbow was added to the bottom of the column. Although it was successful in droplet removal, it was not suitable for continuous draining of the washdown liquid and proper measurement of the aerosol concentration. The 90° elbow was replaced with a 45° elbow (Fig. 4.2), but draining issues persisted. Secondary air from the gas distributor exerted drag force on the liquid film, preventing it from flowing down, which eventually resulted in air from the nozzle bubbling through liquid. Figure 4.2 90° and 45° elbows used for removal of large droplets Finally, a solution was obtained by installing one column section with the 90° elbow, followed by a second section with a 45° elbow, as shown in Figs. 4.1 and 4.3 (Setup #1). Draining of the liquid from the column was stable, since the air from the gas distributor helped the flow of the liquid film from the column walls. 90° elbow 45° elbow Chapter 4. Experimental Study 49 For the experiments with the Hot Unit nozzle, the nozzle was installed at the bottom of the column (Setup #2, Fig. 4.3). It worked sufficiently well in terms of draining, although the upstream side of the coupon was still collecting large droplets for the reasons mentioned above. Upstream results from these experiments were disregarded, and only results from the downstream deposition were used (Section 5.1.2.2). Figure 4.3 Cold Unit Setup #1 and Setup #2, used in the experiments. Setup #1 was used with the Cold Unit nozzle and the nozzle from Spraying Systems Co., while Setup #2 was used for the experiments with the Hot Unit nozzle 4.1.1.2. Atomizers Two atomizers (nozzles) were used in the experiments: the Cold Unit nozzle and the Hot Unit nozzle. A third atomizer (Quick Mist, from Spraying Systems Co.) was used for shadowgraphy validation only. The details of all three nozzles are given in Figs. 4.4−4.6. Figure 4.4 Cold Unit nozzle, used in the setup with elbows (Setup #1) Setup #1 Setup #2 0.317 mm (1/8 inch) OD tube 2.0 mm hole 11.0 mm 2.8 mm Chapter 4. Experimental Study 50 N2 passage 5 holes oil line (18inch) Mix zone Figure 4.5 Hot Unit nozzle, used in the position below the column (Setup #2) Figure 4.6 1/4QMJ + SUQR220B QuickMistTM nozzle, used in experiments for shadowgraphy validation 4.1.2.3. Gas distributor In order to evenly introduce secondary air in the column, a gas distributor made of 9.52 mm (3/8 inch) OD stainless steel tube, was placed around the nozzle. Fifteen 2.3 mm holes, evenly spaced, were drilled along the perimeter of the distributor (Fig. 4.7). 5 holes, 0.6 mm dia. N2 passage, 5.0 mm ID Oil line, 3.2mm OD 1.5 mm Mixing zone Chapter 4. Experimental Study 51 Figure 4.7 Drawing and the picture of the gas distributor in the Cold Unit At first, the gas distributor was positioned at the bottom of the column, while the nozzle was installed as in Setup #1. This was done in order to change the concentration of the aerosol in a controlled manner: by diluting the aerosol with the known flow rate of pure air that would mix with the aerosol. This arrangement did not work well since the turbulence created by introduced secondary air caused significant deposition of droplets on the column walls. The distributor was then placed close to the nozzle, and the concentration of droplets in the aerosol was measured at each operating condition. 4.1.2.4. Other settings The exit pipe from the column was placed 15−20 cm away from the ventilation suction. This was done to eliminate significant fluctuations of the load cell readings (max. ±300 mg), caused by variations in the ventilation pressure. If the pressure drop downstream of the column was significant, and the column operated at pressures higher than atmospheric, variations in the ventilation pressure would not cause significant fluctuation in the load cell readings. Close to the load cell, a small computer fan (50 W) was installed in order to blow away droplets passing through the clearance between the rod and the cap (Fig. 4.8). It was determined that, at velocities higher than 1 m/s, these aerosol droplets were depositing in the load cell, causing permanent load cell failures. gas inlet 2.3 mm holes 9.52 mm OD tube Chapter 4. Experimental Study 52 Figure 4.8 Fan positioned close to the load cell to remove aerosol droplets causing load cell failures Oscillations of the rod at higher velocities (>1 m/s) were reduced with a support that constrained the motion of the coupon. The rod was also protected from deposition by a 2.5 cm diameter plastic pipe, placed around it (Fig. 4.9). The plastic pipe ended about 15 cm before the coupon, to avoid disturbing the flow field of the wake behind the coupon (Fig. 4.1). Figure 4.9 Motion constraint and deposition protection, installed to reduce oscillations of the coupon and prevent formation of deposits on the rod Proper measurements of the difference between the liquid to the nozzle and the washdown flowrate required that the feedstock and washdown reservoirs were disconnected from the reservoirs on the balance. Therefore, they were attached only when the concentration measurements were finished (usually after 1 hour). The complete Cold Unit operating procedure is given in Appendix A. 5 mm hole aerosol fan 3 mm hole Chapter 4. Experimental Study 53 4.2. Hot Unit apparatus To investigate deposition at high temperatures with the mixtures of heavy hydrocarbons, the Hot Unit experimental apparatus was used (Fig. 4.10). The experiments were performed by Dr. J. Song [52]. In the Hot Unit apparatus, the coupon was placed in the middle of the upper section of the 1 m high and 7.5 cm diameter spray chamber, heated with external heaters. A mixture of MEBR and Voltesso was pumped from the heated oil tank to the nozzle, positioned below the chamber, and sprayed with a flow of nitrogen. Temperature in the unit was varied from 295°C to 425°C; 5% and 10% wt. concentrations of MEBR in Voltesso were used. The velocity was varied from 0.25 to 0.92 m/s. Deposition rates were measured via a load cell placed in a chamber above the unit, protected from overheating by a flow of cold nitrogen into the chamber. The remaining aerosol was sent to the Condenser where it was cooled down. Part of the oil was captured in the Oil Trap. The remaining fine droplets in the aerosol were partially removed in the Demister, stuffed with steel wool. The aerosol was then treated in a Scrubber with a solution of sodium hydroxide, to remove sulphur components. The remaining aerosol was combusted in the afterburner. Chapter 4. Experimental Study 54 ScrubberDemister pump Condenser 2 pump aOH solution 2 to ozzle Secondary 2 Oil feeding 2 to oil tank P1TC1 P2TC2 P3T2 P4T1 Oil receiver T3 T4 P5 T7 Cold water in Cold water out T8 T9 TC5 TC4 TC3 Spray chamber Oil trap Oil tank Afterburner To ventilation T6 T10 T5 PC1 Load cell Heater Figure 4.10 Process flow sheet diagram of the Hot Unit Apparatus [52] Chapter 4. Experimental Study 55 4.3. Measurement techniques The following variables in the Cold Unit experiments were measured: liquid flow to the nozzle, washdown liquid flow, velocity of the aerosol, droplet size distribution in the aerosol, droplet size distribution of deposits on the coupon, deposition rate, and contact angles of droplets on the coupon. All measurement techniques employed in measuring these variables are described in the sections that follow. 4.3.1 Liquid flow and aerosol concentration measurements 4.3.1.1. Measurements of the liquid flow to the nozzle For pumping liquid to the nozzle, a gear pump was used (Fig. 4.11), since it provided flow without pulsations, while being able to deliver liquid at differential pressures up to 700 kPa (100 psi). The scale on the console drive was labelled and the pump was calibrated with and without differential pressure. The desired flow rate was then obtained by setting the position on the console drive. Details of the pump calibration are given in Appendix B. Figure 4.11 Picture of the RK-75211-10 Cole Parmer Console Drive and RK-07002-27 Micropump® A-mount Suction Shoe Pump Head with its scale 4.3.1.2. Measurements of the liquid flow to the aerosol The concentration of droplets in the aerosol bulk, cb, can be calculated as, column l b AU F c ⋅ = (4.1) Chapter 4. Experimental Study 56 where Fl represents the droplet flow rate of the aerosol (g/s), U is the superficial velocity of the gas in the column (m/s) and Acolumn is the column cross-sectional area (m 2). If the aerosol droplet concentration is known, the deposition coefficient, kd, can be calculated from the measured deposition rate rd, Ac r k b d d ⋅ = (4.2) Therefore, it was necessary to measure the flow of liquid to the aerosol, Fl. Since the aerosol was generated in the relatively small diameter column (7.5 cm), as mentioned before, droplets close to the edge of the spray cone impacted the column walls, creating a film of liquid. The liquid film formed a washdown stream drained below the column and collected in a separate tank (Fig. 4.12). The droplet flow rate of the aerosol was measured as a difference between the flow of liquid to the nozzle and the washdown liquid. The mass flow rate of the liquid to the aerosol, Fl, was estimated from the slope of the weight loss curve, and recalculated as the liquid volume flow. Figs. 4.13 and 4.14 show logs of droplet flow for two different Cold Unit arrangements (Setup #1 and #2, Fig. 4.3). Figure 4.12 Schematic representation of the tank with the liquid that is pumped to the nozzle (4 liter), and the tank for collecting the washdown (2.5 liter), placed on the balance Washdown from the column To the pump To the RS-232 port on PC Chapter 4. Experimental Study 57 Figure 4.13 Log of the liquid flow to the aerosol for Run 28 (Cold Unit at 1 m/s, Setup #1, Figure 4.3). Short experiments and the presence of elbows reduce accuracy of droplet flow measurements. Figure 4.14 Log of the liquid flow to the aerosol for Run 53 (Cold Unit at 1 m/s, Setup #2, Figure 4.3). Straight line from long experiment results in droplet flow measurement accuracy higher than 1%. Chapter 4. Experimental Study 58 As can be noted from the figures, the slopes of the curves are significantly higher (from 2−8 times) during the first several minutes, depending on the experimental conditions. This is due to the transient period needed to establish a steady flow of washdown liquid. This effect is more pronounced in experiments performed with the Cold Unit arrangement with elbows, since it takes more time for the liquid film to form in the two PVC elbow sections. The variability of liquid flow measurements was determined in separate experiments, and the results are given in Table 4.1. The tests lasted from 15 to 20 minutes, with 2−3 minute pauses in between. The liquid flow was estimated by a linear interpolation of all the data, excluding the 2−5 minute transient period at the beginning. Table 4.1 Variability in liquid flow rate measurements (g/min), with aqueous sugar solution and tri-ethylene glycol, at different superficial velocities (Setup #1, Fig. 4.3) 50% aqueous sugar solution Tri-ethylene glycol Velocity Test # 0.43 m/s (Run 4) 0.87 m/s (Run 7) 1.37 m/s (Run 11) 0.44 m/s (Run 14) 0.87 m/s (Run 17) 1.42 m/s (Run 19) 1 2.08 4.75 7.19 1.57 3.12 3.65 2 1.99 4.43 6.56 1.63 2.58 3.88 3 1.86 4.18 6.66 2.83 4.64 4 2.03 4.09 6.92 3.65 4.74 St. dev. 4.7% 3.9% 4.1% 2.6% 15.1% 12.9% The accuracy of the droplet flow measurements for the Setup #1 could have been improved by performing longer experiments, for more than 30 minutes. However, safe recovery from the column, of the coupon its adhering liquid deposits, without danger of losing any, set a limit of about 200−300 mg of deposits on the upstream side. At velocities higher than about 0.8 m/s, this limit is reached in about 10−15 minutes. This was the main constraint for keeping the experiment durations below 15 minutes. For the Setup #2, the variability is estimated to be not more than 1%, except at very low gas velocities (<0.1 m/s) when the flow of liquid to the aerosol was quite low (0.1−0.5 g/min) and the error somewhat larger (1−2%). Chapter 4. Experimental Study 59 4.3.2. Velocity measurements The velocity in the column, U, was calculated from the flow of air to the nozzle, Fa,nozzle (m 3/s), and the flow of secondary air, Fa,secondary (m 3/s), measured by means of rotameters, atm ondary column ondarya atm nozzle column nozzlea ondarynozzle P P A F P P A F UUU secsec,, sec ⋅+⋅=+= (4.3) where Pnozzle is the pressure in the nozzle and Psecondary is the pressure in the gas distributor. The velocity from the nozzle varied from 0.1−0.6 m/s, with a pressure in the range of 100−500 kPa, depending on the nozzle type. The velocity of the secondary air varied in the range 0−1 m/s, with a pressure from 100−200 kPa, depending on the gas distributor type. Details on the rotameter calibrations are given in Appendix B. 4.3.3. Shadowgraphy measurements of aerosol drop size distribution To measure size distribution of droplets in the aerosol, a shadowgraphy technique was selected. Shadowgraphy is an imaging technique that is used to visualize particles (e.g., solid particles, gas bubbles, liquid droplets) based on imaging with pulsed backlight illumination. For transparent particles, shadowgraphy utilizes difference in the index of refraction between the dispersed phase and the surrounding medium [61]. The direction of light rays that leave a dispersed phase is different than the direction of the same rays that enter, which makes the object non-transparent (Fig. 4.15). 4.3.3.1. Shadowgraphy setup The shadowgraphy system that was used in this work is schematically presented in Fig. 4.1. The LED lights were placed opposite to the camera, with its axis aligned with the camera axis. This way, the light rays that pass through the column and a 20 cm long lens could reach the camera chip. A synchronization signal for the lights is sent from the camera, and the camera shutter was controlled from the software on the computer. Chapter 4. Experimental Study 60 Figure 4.15 Schematic representation of the Shadowgraphy system used on the Cold Unit and the path of light rays entering and leaving the droplet This shadowgraphy system was designed and assembled (by the author); it was made partly from components existing in the lab (Fig. 4.16). • Lights were 19-LED Constellation Lights, with collimated light beams, from IDT Inc. (San Jose, CA, 6024 Silver Creek Valley Rd.). The power of the lights was 130 W, with an illuminance of 60,000 lux at 1 foot distance. • Camera was 36-bit Cool Snap cf Color Camera, 1392×1040 with 4.65 micron pixels, from Photometric (Tucson, AZ, 3440 E. Britannia Dr.). • Lenses were OPTEM Zoom 70 XL long distant lenses with maximum 14× magnification, from QIOPTIQ (La Verne, CA, 1318 Palomares Ave.). They were mounted on the camera via a C-mounts. • Software used to control the camera and take images was RS Image 1.9.2 from Photometrics, while image analysis was performed in Image Pro Plus 5.0.1. Similar systems are also commercially available from La Vision ($35,000) and Dantec Dynamics ($60,000). Power Focal plane CCD Lens LED lights Sync to the lights (BNC cable) PC with the frame grabber RS Image software, Image Pro Plus software To the frame grabber (MDR cable) Chapter 4. Experimental Study 61 Figure 4.16 Pictures of the Shadowgrahy system installed on the Cold Unit and details of the Optem ZOOM XL long distant lenses In order to maximize the intensity of light and use the shortest possible exposure, the camera and lights were placed right next to the column. The camera was mounted on an Edmund Optics XYZ moving stage (60 mm travel in X and Y, 40 mm in Z direction, Fig. 4.3). With the additional 2× magnification mounted on the basic lens, the focal plane was 35 mm away from the lens tip, or 25 mm inside the column (at one third of the column diameter). Since the curvature of the glass column did not allow taking undistorted images of droplets, an acrylic column section was used instead, with two 2.5 cm (1 inch) circular openings, opposite each other, cut into the column. Acrylic tube pieces with rubber gaskets on the outer side were inserted in the openings and glued to the column. Flat microscopic glass slides were then put on top of the gaskets and attached to the column with tape. This setup prevented aerosol leaking and also allowed easy removal of the glass slides for cleaning (Fig. 4.17). Figure 4.17 Schematic of the solution for eliminating glass curvature 2× magn. lens module Internal focus module, 0−66 scale 1−7× magn. lens module Iris, 0−27 scale acrylic tube gasket glass slide column wall Chapter 4. Experimental Study 62 4.3.3.2 Aerosol Sampling Aerosol measurements frequently require that an aerosol sample be conveyed to a measurement device by withdrawing a sample from its environment and transporting it to the device [20, 62]. Ideally, sampling at the inlet of the sampler would be isokinetic, with no deposition or settling in the sample transport system. In the present case, the shadowgraphy system was pointed directly into the environment, and therefore no sampling systems were required. Because the aerosol was moving (Fig. 4.18), in order to get sharp shadow images of droplets, short exposures were needed. Figure 4.18 Schematic representation of the shape and intensity of droplet shadows captured at constant aerosol velocity and increased exposure. Sharpness of the images also decreases with a decrease in shadow intensity. If we define blurriness, B, as a ratio of the droplet path, L, (traveled at velocity U during exposure time ∆t) and its diameter, Dp, pp D tU D L B ∆⋅ == (4.4) exposures that will yield a given blurriness can be easily calculated (Table 4.2). Table 4.2 Exposures (in microseconds) needed for 50% blurriness of different drop diameters and different velocities 1 5 10 20 30 50 100 0.1 5 25 50 100 150 250 500 0.5 1 5 10 20 30 50 100 1.0 0.5 2.5 5 10 15 25 50 1.5 0.33 1.67 3.33 6.67 10.00 16.67 33.33 We can see that even at 50% blurriness and 1 m/s, the required exposures are on the order of few microseconds. The lowest possible exposure at the maximum light intensity that produced images bright enough to be analyzed was about 100 microseconds. This was L = U⋅∆t Dp(µm) U(m/s) Chapter 4. Experimental Study 63 too long to capture acceptably sharp images of droplets, and the droplets had to be slowed down somehow. The solution was to stop the flow and capture the images shortly after the flow was stopped. Firstly, the supply of air to the nozzle and gas distributor was shut off, by closing the ball valve shown in Fig. 4.1. Aerosol droplets continued moving upward under their inertia, then stopped, and started falling down slowly under the effect of gravity. To wait for the droplets to slow down, image recording was started 5 seconds after the flow was stopped. In about 14 seconds, 130 images were recorded in a frame sequence. The same procedure was repeated 10 times. Two consecutive frame sequences of 130 images were joined together to form a sequence of 260 images. This is what is referred to as one sample throughout this text. To investigate the effect of the waiting period (5 seconds) on the sampling procedure, size distributions from images taken right after the flow is stopped, and 5 seconds after the flow is stopped were compared. From Table 4.3, this difference is within the sampling error (standard deviation 0.5 microns, Table 4.8). Corrected values for the number of droplets, volume of droplets, volume median diameter and maximum diameter are based on the border and depth of field corrections described in Section 4.3.3.7. The corrected values for the number of droplets are about 10 9667 78115 < times the uncorrected values, primarily because of the depth of field correction. Table 4.3 Comparison of the volume median diameter measured right after the flow is stopped and 5 seconds after the flow is stopped, at 6× magnification and 110 microseconds exposure. Velocity 1 m/s, liquid flow to nozzle 40 ml/min. Immediately after the flow is stopped 5 sec. after the flow is stopped measured corrected measured corrected No. of droplets 9667 78115 10365 72170 DV,50 (µm) 8.3 5.5 7.9 5.5 Dmax (µm) 29 29 25 25 To investigate the effect of stopping the flow on the sampling process, the new Cold Unit nozzle (Quick Mist, Fig. 4.5) was placed below the column and set to produce large droplets (air velocity 0.15 m/s, liquid flow 90 ml/min). Because of the low velocity Chapter 4. Experimental Study 64 and large droplet sizes in the aerosol, a 2× magnification and a 60 microseconds exposure could be used. The comparison is presented in Table 4.4. Table 4.4 Comparison of the volume mean diameter measured 5 seconds after the flow is stopped and when the aerosol flows upward. In the flow 5 sec. after the flow is stopped measured corrected measured corrected No. of droplets 27959 330352 28508 297269 Volume of droplets (mm3) 0.033 0.142 0.028 0.116 DV,50 (µm) 33.8 13.6 29.2 12.7 Dmax (µm) 92 92 80 80 Again, the volume median diameter in the aerosol flow is somewhat larger than when the flow is stopped (both measured and corrected values). The observed difference could be within the experimental error (standard deviation is about 0.5 micron, Table 4.8), but it is possible that the difference exists. To explain this, we consider a disappearing of larger aerosol droplets from the camera view field by gravitational settling. Table 4.5 shows the terminal velocities of tri-ethylene glycol droplets in air at room temperature as calculated using a non-Stokesian drag force. Also it shows the time needed for the droplets to fall down and vanish from the 80 cm high column segment above the shadowgraphy section. Table 4.5 Terminal velocities of tri-ethylene glycol in air at room temperature and the time needed to travel 80 cm in free fall Dp (µm) 1 10 20 30 40 50 60 70 80 90 100 Vt (cm/s) 0.00 0.34 1.35 3.04 5.40 8.44 12.15 16.54 21.60 27.34 33.75 Time (s) 23705.1 237.1 59.3 26.3 14.8 9.5 6.6 4.8 3.7 2.9 2.4 Based on Table 4.5, it seems that only droplets below 40 microns would be fully recorded during the first 19 (=5+14) seconds after the flow is stopped. However, since at 6× magnification, the volume of 5 samples is quite small (about 1 mm3 for 10 µm droplet), and the diameter of the largest recorded droplet is not higher than 35 microns (Table E.1), the settling of droplets does not affect the droplet size distribution measured at 6× magnification. The data from Table 4.3 support this conclusion to a certain degree. Therefore, the sampling procedure described above (flow stopped, images taken after 5 seconds) was accepted and used further on. Chapter 4. Experimental Study 65 4.3.3.3. Hardware and Software settings The parameters in the shadowgraphy hardware and software were determined and set as described in the following sections (Sections a and b). a. Shadowgraphy hardware settings Iris on the long distant lenses was completely open (scale 27) to maximize the light intensity and enable using the shortest possible exposure. Internal focus module scale was set at the middle of the scale, at 33. The recorded droplet size distribution did not change with the change in the position in the internal focus. Magnification. To select the optimal magnification of the lens considering all the constraints of the shadowgraphy hardware, software and process parameters, the following procedure was followed. From the experimental results (chapter 5) it is known that droplets below 1−2 microns do not contribute significantly to the deposition rates. Also, when the diameter of the droplet is close to the wavelength of visible light (400−700 nm), light diffraction occurs and the images of droplets obtained with shadowgraphy become blurry. The manufacturers of commercially available shadowgraphy systems also claim that the lower limit for proper measurements of particle size is about 2 microns [63]. Therefore, it was not possible (and also not too important in our case) to measure droplets smaller than 1-2 microns accurately. From Fig. 4.21, at 6× magnification, a 2 micron particle is represented by a square made of 4×4 pixels. Although it is desirable to have more pixels representing the smallest particle, increased magnification decreases the XY view field, and also reduces the depth of focus. Reduced depth of focus results in a decreased depth of field, with fewer particles being recorded, which further increases the number of images required for analysis and the number of samples needed to be taken above practical limit. In addition, magnifications larger than 6× magnification require a higher light intensity or longer exposures than currently used. However, maximum possible light intensity was already used (LED lights at full power, iris open to maximum), and longer exposures than currently used (110 µs), resulted in blurry and low-contrast droplet shadows (see section Chapter 4. Experimental Study 66 b), which caused improper droplet identification. Considering all the constraints, 6× magnification (at 110 µs exposure) represented the upper limit. Magnification below 6× would increase the number of droplets recorded, but droplets larger than 2−3 microns would be improperly identified. Therefore, 6× magnification was considered to be the optimal choice. Table 4.6 summarizes the main shadowgraphy hardware settings, discussed in this section. Table 4.6 Main shadowgraphy hardware settings Iris 27 (maximum) Internal focus 33 Magnification 6× (2×3)* * 3× zoom, plus 2× magnification lens b. RS Image software settings Shadowgraphy images were recorded using RS Image 1.9.2 software. To enable acquisition of images clear enough for droplet identification, the exposure had to be set to not less than 60 microseconds. Since the concentration of the aerosol varied from 4−10 mg/m3, with volume median diameter from 3.9−7.5 microns, light transmittance of the aerosol also varied. Denser aerosols with smaller particles required longer exposures to obtain proper images. Therefore, the exposure was set to the value that was appropriate for the most dense aerosol, that is to 110 microseconds. The main RS Image software settings are given in Table 4.7. Table 4.7 Main RS Image software settings Exposure Type Normal Exposure Mode Times Manual Exposure 110 µs 4.3.3.4. Sample size To obtain a meaningful size distribution of droplets in the aerosol, a sufficient number of droplets had to be recorded. In the initial stages of experimentation, when the image analysis procedure was not automated (Appendix D), a sample contained 260 images. Later on, the number was increased to 5 samples, each consisting of 260 images. Chapter 4. Experimental Study 67 Table 4.8 shows the effect of sample size on the volume median diameter, and its standard deviation. Table 4.8 Effect of sample size on measured volume median diameter (Run 33) Sample 50,VD (µm) Joined samples 50,V D (µm) 50,VD S (µm) 50,VD (µm) 50,VDS (µm) 1 11.0 1 11.02 2 12.4 1 to 2 11.77 0.98 11.72 0.70 3 10.7 1 to 3 11.43 0.90 11.39 0.52 4 10.0 1 to 4 10.97 1.02 11.03 0.51 5 10.4 1 to 5 10.85 0.92 10.91 0.41 6 8.5 1 to 6 10.49 1.29 10.51 0.52 7 12.5 1 to 7 10.72 1.38 10.79 0.52 8 11.3 1 to 8 10.79 1.29 10.85 0.46 9 12.0 1 to 9 10.92 1.27 10.98 0.42 10 10.4 1 to 10 10.87 1.22 10.92 0.38 From the results in Table 4.3, it was decided that a sufficient number of samples would be 5, after which the volume median diameter showed little change. 4.3.3.5. Image processing and image segmentation settings Image segmentation refers to the process of partitioning a digital image into multiple segments (sets of pixels). Image segmentation is typically used to locate objects and boundaries (lines, curves, etc.) in images. In this case, the objects were shadow images of droplets in the aerosol. To identify object boundaries, commercial shadowgraphy systems (such as La Vision’s ParticleMaster Shadow software [63]) use a thresholding segmentation algorithm, applied to grey-scale images. In this work, the Image Pro Plus software was used, and color images of the aerosol were recorded. Therefore, image segmentation was performed using a segmentation technique implemented in the Image Pro Plus, i.e. based on the histogram ranges for the red, green and blue component of images. For this step, valid histogram ranges had to be specified, as described below. Before segmentation, the images were pre-processed to even out background color variations and remove the noise in the images. Images were filtered with a Bright Flatten filter, with a 15 pixel strength. It was applied in two passes, and proved to be sufficient in removing background noise. This eliminated the need for background Chapter 4. Experimental Study 68 subtraction. Image segmentation was based on the histogram ranges of the red, green and blue components of the images. Investigation of the identification process led to the following choices for the red, green and blue ranges: Red: 0−255, Green: 0−200, Blue: 0−255. Shadowgraphy verification, described in Section 4.3.3.8, confirms the validity of this choice. Important image analysis options also included a Convex Hull feature for the shadowgraphy of the aerosol droplets. The results reported include the surface area, as well as the minimum, mean and maximum droplet diameter. The size distribution of the aerosol was based on the minimum droplet diameter. 4.3.3.6. Calibrations Calibrations of the shadowgraphy system used in this work included: (a) calibration of the camera view field, (b) calibration of the internal focus module and (c) depth of field calibration. a. Camera view field calibration In order to properly size particles observed with shadowgraphy and under the microscope (Section 4.3.4), the camera view field had to be calibrated (Figure 4.19). The view field was calibrated using an Objective Micrometer MA285 glass slide, with a 1 mm scale and 0.01 mm divisions. The slide was attached to the side opening of the column (Fig. 4.18), and observed under different magnifications. The same micrometer slide was used to calibrate images from the OLYMPUS BX41 microscope. Chapter 4. Experimental Study 69 Figure 4.19 Calibration lines of ‘Cool Snap Pro cf camera + OPTEM Zoom 70 XL lens’ and ‘Cool Snap Pro cf camera + OLYMPUS BX41 Microscope’ systems b. Calibration of the Internal focus module The depth of the view field for a given drop diameter (section c) was determined with the help of the OPTEM Zoom internal focus module (Figs. 4.16, 4.20). The scale on this module (0−66) was calibrated in the following manner. First, the Objective Micrometer was attached to the side opening of the column and the camera was focused on the slide. The camera was then moved in the X-direction and the internal focus was adjusted in order to bring the focus back on the Micrometer slide (Fig. 4.20). The micrometer on the X-axis of the XYZ stage was then used to measure the displacement of the camera. This procedure was repeated at several points and for each data point, the camera displacement and internal focus position were recorded. This was performed at every magnification. Chapter 4. Experimental Study 70 Figure 4.20 Camera on the moving stage for the Internal focus module calibration Figure 4.21 shows the estimation of the slope from 12 measured points at 6× magnification (6 points from moving the stage in the positive X-direction and 6 points from going backwards in the negative X-direction). The slopes at all other magnifications (1−4×, 8−12×) were estimated from 3 points, by moving the camera in one direction only. The results are given in Table 4.9. Table 4.9 Internal focus module calibration at different magnifications Magnification (×) 2 4 6 8 10 12 14 Microns per 1 scale 37 36.4 35.1 33.9 34.5 34.2 34.9 The results show that the change in focus is independent of the magnification; one scale division shifts focus by about 0.35 mm. Internal focus module Camera on the XYZ moving stage with caliper X Y Z Micrometer 0 66 Chapter 4. Experimental Study 71 Figure 4.21 Traveled camera distance in X-direction vs. internal focus module position, required to bring the Objective Micrometer back in focus, 6× magnification c. Depth of Field Calibration The depth of field, as presented in Fig. 4.22, represents the length of the view field in the X-direction (Fig. 4.20), where particles are seen by the camera. It is a function of the particle diameter; for smaller particles, the depth of field will be smaller, for larger particles, the depth of field is larger. Figure 4.22 Schematic representation of the depth of field. For larger particles, depth of field is larger To calibrate the depth of field, fine solid particles were deposited on a microscopic glass slide using a paintbrush, and the excess deposits were removed by blowing air on the slide. Spherical glass beads from Potter Industries Inc. (Spheriglass 6000A, mDV µ0.750, = ) were used for particles in the range 3−16 microns, while 20 Focal plane Depth of field Chapter 4. Experimental Study 72 micron Polyamid seeding particles (Dantec Dynamics Ltd.) provided particles larger than 20 microns. The slide was then fixed on the column openings (as in Fig. 4.20). The camera focus was then changed in 0.035 mm steps, using the internal focus on the lenses. For the smallest particle (3 micron), this step was 50% smaller (0.0175 mm). Images were then analyzed in Image Pro Plus with settings given in Table 4.10. From the X- positions of the particle when it entered the view field and was identified, and from its position when it was lost from the view field, the depth of the field was calculated. This procedure is somewhat different from the depth of field determination implemented in the commercial shadowgraphy software [63], where a criteria based on the color gradient at the edge of the object is used. There, the particle is removed from counting if the gradient on its edge is below a certain value, meaning that the image is too blurry, and that the particle is too far from the focus. Table 4.10 Main settings for the image segmentation Option Setting Histogram range Red (0−255), Green (0−200), Blue (0−255) Convex Hull Yes Analysis based on Dmin All images were recorded at 6× magnification. An enhancement filter was applied to all images (Flatten, Bright, 15 pixel strength, 2 passes) in order to even out the background variations. Figure 4.23 shows in-focus images of glass beads and Polyamid particles, used for the depth of field calibration. 3.4 µm 5.0 µm 6.8 µm 8.9 µm 11.2 µm 16.4 µm 26.2 µm Figure 4.23 Glass beads (3.4−16.6 µm) and Polyamid particle (26.2 µm) in the focus, used for depth of field calibration; 6× magnification The measured depth of field for different drop diameters is shown in Fig. 4.24. The data points were fitted with a linear function that goes through the origin, since it is known that the depth of field is a linear function of particle diameter [63, 64]. Chapter 4. Experimental Study 73 Figure 4.24 Depth of field for the shadowgraphy system, determined using Image Pro Plus settings given in Table 4.10 It is believed that the glass beads are faithful representation of tri-ethylene glycol spherical droplets in the aerosol since the refractive index of tri-ethylene glycol is 1.46 − very close to the refractive index of glass (1.46−Pyrex glass, 1.52−Crown glass). 4.3.3.7. Corrections Since different particle sizes have different depths of field, and a different probability of being captured in the XY view field, it is necessary to introduce corrections in the measured particle size distribution. a. Border correction Larger particles have a lower probability of being inside the XY view field than smaller particles (Fig. 4.22). Hence, the following border correction must be applied [63], HW DHDW p ipip Borderi ⋅ −− = ))(( ,, , (4.5) Chapter 4. Experimental Study 74 where Borderip , is the probability of a particle being detected inside the window, W is the window width, H is the window height and Dp,i is the particle diameter (in the class i). This correction assumes that particles on the border of the image are not counted. Table 4.11 Detection probability for different particle sizes, at 6× magnification (W=718 µm, H=536 µm) Dp.i (µm) 1 5 10 20 30 50 100 pi,border 0.997 0.984 0.968 0.936 0.905 0.844 0.7 b. Depth of field correction The depth of field correction increases the relative weighting of smaller particles. The detection probability, DOFip , , can be written in the following form [63], referencep ip DOFi D D p , , , = (4.6) where referencepD , is the reference diameter, usually set to the largest diameter measured, in order to keep probabilities smaller than 1. The value of the reference diameter is not relevant, as long as the depth of field is linearly dependent on the particle diameter. Including the border correction, the total probability of detection is calculated as, DOFiBorderii ppp ,, ⋅= (4.7) The statistically corrected number of particles '3 is then given by, i i i i 3 p 3 ⋅= ∑ = max 1 1 ' (4.8) 4.3.3.8. Shadowgraphy verification The shadowgraphy technique used in this study employed an image segmentation algorithm based on the histogram range values of the red, green and blue color components. According to the depth of field criteria employed, a droplet is counted as ‘in focus’ al long as it is seen in the view field. Since this method is somewhat different from the ones employed in the commercial systems, the shadowgraphy technique had to be Chapter 4. Experimental Study 75 verified with a known size distribution of particles, that would behave like a real aerosol. For this purpose, the following procedure was devised and followed. Glass beads with DV,50=7.0 µm from Potter Industries Inc. were deposited on the glass slide and attached to the column (Fig. 4.25). The camera was traversed in the Y- direction using the moving stage and 120 images were taken in each image series sample. During 12 seconds, the camera was moved 16 mm at a velocity about 1.33 mm/s. Then, the camera was moved from the focus for one scale (0.035 mm) and a new series of images was taken. This procedure was repeated in both the negative and positive X- directions until the glass beads became too far from the focal plane to be identified by the software. Series of images obtained in this manner emulated a real aerosol, by having the droplets of known size in and out of focus. Figure 4.25 Verification of shadowgraphy with glass beads on the microscopic glass slide The data from this experiment are given in Table 4.12. It can be seen that, at focus position 26, the volume median diameter is 7.1 micron and very close to the one specified by the manufacturer. This agreement verified that in-focus images are identified properly. Also, the corrected volume median diameter is 7.3 microns, which is very close to the 7.1 micron measured in the focus. Therefore, it was concluded that the applied border and depth of field corrections are valid, and could be used in the measurement process. Moving through the focus, image series 18, 19,…, 26, …36 Glass beads, DV,50 = 7 µm Collecting 120 images in one image series X Y Chapter 4. Experimental Study 76 Table 4.12 Glass beads in different focus position, captured and analyzed with shadowgraphy Focus position Number of image series Number of glass beads DV,50 (µm) Number of glass beads, corrected DV,50 (µm), corrected 26 1 17467 7.1 17467 25−27 3 45966 7.4 223854 5.8 24−28 5 60139 8.4 318911 6.4 23−29 7 67095 9.1 352819 6.8 22−30 9 71104 9.6 372716 7 21−31 11 73674 9.9 385656 7.2 20−32 13 74850 10 391464 7.3 19−33 15 75683 10.1 395894 7.3 18−34 17 76190 10.1 399054 7.3 18−36 19 76491 10.1 401082 7.3 4.3.3.9. Summary procedure The procedure used for measuring droplet size distribution in the aerosol, using shadowgraphy technique, can be summarized as follows. Before each run, shadowgraphy was used to record images at the operating conditions for that run. The atomizer was put into operation, and 10−15 seconds after the atomizer startup (but before the experiment was performed), the supply of air and liquid to the nozzle was cut off. After 5 seconds, image acquisition was started. After taking images of two samples at velocities 0−0.6 m/s, and one sample at velocities 0.8−1.4 m/s, the glass slides were removed and cleaned. Deposition on the glass slides was quite intense at higher velocities and if this procedure was not followed, low contrast images were obtained, which introduced errors in the sampling process. After five samples of 260 images were recorded, the images were analyzed in Image Pro Plus (Appendix D), and the results of individual droplet sizes are further processed using the MATLAB script shadow.m (Appendix D), to give a size distribution and characteristic diameters. Chapter 4. Experimental Study 77 4.3.3.10. Suggestions for improvements For future work, the performance of the shadowgraphy system could be improved by implementing the following changes: • Adopt an improved segmentation algorithm that segments droplets based on the color gradient on their edge, such as the one implemented in LaVision’s ParticleMaster Shadow software [63]. This would allow the droplets far away from the focus, which are identified as somewhat smaller objects, to be eliminated from counting. • Using a stronger light source, such as PalFlash 501 (The COOKE Corporation), would provide enough light for low exposures, down to few microseconds, which would in turn enable freezing small aerosol droplets at velocities up to 1.5 m/s. This way, the droplet size distribution and the concentration of droplets at any point in the aerosol (e.g., in front of the coupon, in the vortex behind the coupon) could be measured. • Long distance lenses of better quality (with higher resolving power), such as the lenses used on the OLYMPUS microscope, would improve accuracy by increasing the sharpness of the droplet images. • Using an 8-bit camera that would produce grey-scale images would be beneficial, since it would improve the white balance issues. 4.3.4. Coupon drop size distribution measurements In order to determine deposition coefficients and capture efficiencies for each droplet size, the drop size distribution on each coupon had to be measured. Hence, the following technique was developed and used. For these measurements, the coupon deposits had to be observed under a microscope, and therefore, a transparent coupon was used. Based on the results of the interfacial tension effect, droplet rebounding should occur only at very high contact angles (θ > 150º). This means that at low contact angles, perfect sticking can be assumed, and the size distributions of droplets on the glass (θ=20º) and stainless steel (θ=50º) Chapter 4. Experimental Study 78 coupon should be the same. Therefore, a glass coupon can be used to determine size distribution of deposits on a stainless steel coupon. Figure 4.26 Picture of the Microscope and Camera setup, used for recording images of coupon deposits For each Cold Unit experiment, a short deposition experiment with the 5 cm (2 inch) glass coupon, under identical operating conditions was performed. A Cool Snap Pro cf camera was attached to the OLYMPUS microscope via a C-mount, and deposit images were taken by means of the RS Image software (Fig. 4.26). Although droplets on the surface were not full spheres but spherical caps, the shadowgraphy effect applied to a certain degree (Fig. 4.30) and enabled identification of the droplets. The procedure consisted of: deposition on the glass coupon in the column (sampling), taking images of deposits under the microscope, analysis of images in Image Pro Plus software and drop size distribution analysis using the Matlab scripts shadow.m and coupon.m (Appendix D). 4.3.4.1. Deposition (sampling) Firstly, a 4 mm long joint made of 3.175 mm (1/8 inch) diameter acrylic rod was cut and a hole was drilled in it. The hole was threaded with a 1.58 mm (1/16 inch) thread, to enable attachment of the rod. Then, the joint was glued to the glass coupon (Fig. 4.27). The experiment was started and after 15−20 seconds of atomization when the flow seemed stable, the coupon was inserted in the column by hand, 15 cm below the Camera C-mount Coupon RS Image software Chapter 4. Experimental Study 79 exit, and held by hand normal to the aerosol flow during deposition. It is estimated that this distance was enough not to affect the vortex behind the coupon. Figure 4.27 Schematic representation of: (a) glass coupon used for deposit size distribution analysis and (b) placement of the coupon in the column Since these sampling experiments had to be quite short in order to avoid coalescence of droplets on the surface (10−15 seconds), variability in the sampling process could be considerable. The main sources of sampling errors could be during the period of placing the coupon in the column (approximately 1 second) and during the period of taking the coupon out from the column (also around 1 second). 4.3.4.2. Recording images along the coupon radius Images of droplet deposits were taken starting from the coupon centre and moving the coupon on the microscope stage toward the coupon edge (Fig. 4.28). In about 12 seconds, 120 consecutive images of deposits were taken and saved into a file as a frame sequence. The microscope stage was moved, by turning the wheel on the stage micrometer, at a speed that the coupon traveled for 2.5 cm, in about 12 seconds. The time was counted, and the last image in the sequence was taken when the camera view field was at the coupon edge. If the timing was not right, sampling was repeated. Four samples along the coupon radius were taken. When there were deposits on both the upstream and downstream surfaces, sampling was done for each case, since placing the coupon on the stage removed part of deposits from the surface touching the stage. Threaded rod Acrylic piece with threaded hole Sumo Glue Glass coupon 15 cm (a) (b) Chapter 4. Experimental Study 80 Figure 4.28 Locations of coupon deposit samples taken from the upstream and downstream side. First image starts at the coupon centre, last image is taken at the coupon edge. Droplet deposits on the upstream side were observed under 4× magnification, while droplets on the downstream side were observed with 10× magnification. For taking images of the upstream side, the coupon was placed on the additional stage made of glass slides, to allow placing the coupon in the horizontal plane (Fig. 4.29). Figure 4.29 Supporting stage made of glass slides 4.3.4.3. Image Analysis in Image Pro Plus As can be seen schematically from Fig. 4.30, light rays that pass through the central part of deposited droplets do not deviate significantly from their original path. However, light rays close to the coupon edge, where curvature of the gas-liquid interface is more pronounced, bend more and produce shadow-like images. 1… 120 Coupon Stage Chapter 4. Experimental Study 81 Figure 4.30 Schematic representation of (a) light rays that pass through the spherical cap and (b) one example of deposits on the downstream side, Run 56 From 120 images of deposits, only 30 images were analyzed (every fourth). This means that each image covers 1.6 mm along the coupon radius at 4× magnification, and 0.64 mm at 10× magnification, while only 0.83 mm (=25.4/30 mm) contains a new information. This means that at 4× magnification, the number of different droplets that were analyzed is about two times smaller than the reported number. The images were first enhanced by applying the ‘Flatten’ filter, with a 15 pixel strength, in two passes, to equalize background variations. Object identification was based on the histogram range values R(0−255), G(0−200), B(0−255), as used in the shadowgraphy measurements. Some settings for the upstream deposit image analysis are given in Table 4.13. Table 4.13 Relevant environment settings in the Image Pro Plus for coupon deposit analysis (1−set, 0−not set) Convex Hull Fill Holes Clean Border Upstream 1 1 1 Downstream 0 1 1 The difference in the settings is in the Convex Hull property. It is used in the case of upstream deposits where droplets are quite large, and where in about 10−20% cases, the droplet borders were not sufficiently dark for proper droplet identification (Fig. 4.31). On Microscope Objective 100 µm (a) (b) Chapter 4. Experimental Study 82 the downstream side, there was no need for using this option since the droplets were smaller and sufficiently dark. Figure 4.31 Identified droplets on the upstream surface, with (a) Convex Hull=0 and (b) Convex Hull=1 option. In the second case, measured diameter is much closer to the real diameter of droplets. Size distribution analysis in MATLAB was performed using the scripts shadow.m and coupon.m (Appendix D). The reported results were based on the mean droplet diameter. This is logical since the mean drop diameter is most representative of the mean droplet diameters on the surface, which combined with the mean contact angle gives the best estimate of the drop diameter in the aerosol. To account for the spreading of spherical droplets on the surface, correction factor derived in Appendix C was used. 4.3.5. Deposition rate measurements In order to monitor potential changes in deposition rates over time (deposition on a dry coupon, thin, and thick layer of deposits), the weight of deposit on the coupon was monitored during the whole experiment, using the load cell. In addition, the weight of the deposit was measured at the end of experiments using an analytical balance. 4.3.5.1. Load cell measurements The load cell, GSO-50, with a DPM-3 data logger from Transducer Techniques, with 1 mg precision was used for the experiments. The load cell was mounted above the column, on a 20×20 cm square wood panel, and covered with plastic protection. The system for connecting the load cell with the rod attached to the coupon is shown in Fig. (a) (b) Chapter 4. Experimental Study 83 4.32. This was needed in order to avoid a stiff connection of the rod with the load cell that, would lead to incorrect measurements. Although the load cell was calibrated by the manufacturer, it was also calibrated in the laboratory, when installed on the Cold Unit. The details are given in Appendix B. Figure 4.32 GSO-50 load cell and DPM-3 data logger from Transducer Techniques The load cell was operated in the following manner. When the coupon is attached to the load cell, a certain amount of time is needed for the load cell to respond to the step change and reach equilibrium. For the new load cell, this time is about 10 minutes; but as the load cell is used more its response becomes slower, up to 45−60 minutes (Fig. 4.33). After the air is introduced and the drag force on the coupon reduces its weight, at high velocities and with a used load cell, some time is required for the response to settle down (2−3 minutes). After that, the liquid is introduced and the deposition starts. The deposition rate curve shows that the deposition rate is generally constant during the whole experiment. This enables deposition rates to be estimated from the mass of deposits at the end of the experiment. 6.35 mm thread Load cell Wire loop St.steel rod O-ring loop Chapter 4. Experimental Study 84 Figure 4.33 Typical response of the load cell, Run 15 From the deposition curve (Fig. 4.33), it can be also noted that the deposition rates are slightly higher at the beginning than later on; this is most certainly due to the continuing effect of the initial load cell response on the attached coupon. At velocities larger than 1 m/s, fluctuation and noise are greater, such that at 1.3 m/s, estimation of deposition rates from the graph is quite unreliable. 4.3.5.2. Analytical balance measurements The mass of deposits was measured at the end of each experiment on the analytical balance (AND GR-200) with 0.1 mg precision. Once the aqueous sugar solution was replaced by tri-ethylene glycol, there was no evaporation and loss of weight of the deposits after the experiment. Therefore, the analytical balance measurements are considered more accurate than the load cell measurements, and were used to calculate the deposition rates. Also, the amounts of deposits on the rod, upstream and downstream sides could be measured separately on the analytical balance, results that were not possible to obtain from the load cell readings alone. Chapter 4. Experimental Study 85 4.3.6. Contact angle measurements Contact angles between the liquid and the solid surface were measured using the sessile drop method [65, 66]. The drops were dispensed on the coupon surface and observed from the side with a camera (Fig. 4.34). The shadowgraphy system was adapted for this purpose by putting the adjustable stage between the camera and the light source on which the coupon was placed. The stage was adjusted using fine screws to position the coupon in the horizontal plane. The droplet images were recorded using the Image Pro Plus software and the contact angles were then determined by image analysis using the FTA 32 software. Figure 4.34 Photo of the sessile drop measurement system. Lenses are at 1× magnification, 90 cm away from the drops 4.3.6.1. Measurement procedure The surface of the coupon was first cleaned with water and dried. The coupon was placed on the camera mounted on the moving stage (Fig. 4.35a) with a micropipette fixed above. The camera was then lifted toward the micropipette, and when the coupon touched the drop pending from the pipette tip, it was slowly pulled back down. This was important in order to eliminate variability due to the way that drop is applied to the surface [65]. The droplet volume was 2 microliters, which should be enough for proper contact angle measurements [67]. The next drop was deposited in the same manner, 3−4 mm adjacent to the previous one by moving the camera in the Y-direction. This created a series of drops that lie in a line. The coupon was then placed on the stage (Fig. 4.35b) so Chapter 4. Experimental Study 86 that the droplets were positioned in the focal plane of the camera. Bounded with strips, the coupon was moved in the Y-direction and images of the droplets were recorded. Figure 4.35 (a) Coupon on the camera when droplets are deposited from the pipette, and (b) schematics of the coupon on the stage as in Fig. 4.34 Although the pendant drop method is generally more accurate [65], it requires that needles used for dispensing the liquid be made of the materials in question (st.steel, graphite, Teflon etc.) which was not suitable for this work. Contact angles were measured 1−2 minutes after the droplets were deposited on the coupon, when it is assumed that equilibrium was reached (there is only a small difference between the values in the second and third column of the Table 4.14). 4.3.6.2. Accuracy of contact angle measurements Sessile drop measurements of contact angles assume a spherical shape of the droplet, and a circular contact line with the surface [65]. In reality, irregularities in surface roughness and impurities cause a noncircular wetting line, which results in variability in the measured contact angles. Repeated measurements are the only way to estimate the true value [68]. The variability in contact angle measurements of tri-ethylene glycol droplets on the stainless steel coupon surface is presented in Table 4.14. In this particular case, results obtained from 4−7 repeated measurements yield a relative error (standard deviation of the arithmetic average) of about 1.4−1.6%. The estimated true value of the contact angle is θavg=48.9 ± 1.6° (95.5% confidence interval). (a) Stage Plastic stripes to constraint the coupon motion Droplets in focal plane Coupon Camera view window (b) Chapter 4. Experimental Study 87 Table 4.14 Variability in contact angle measurements using the sessile drop method Drop # Contact angle (°) Contact angle after 1 hour (°) Average contact angle, from the drop #1 Standard deviation starting from the drop #1 (°) Standard deviation of the average contact angle (°) Relative error (%) 1 47.0 47.6 47.0 2 49.4 48.3 48.2 1.7 1.2 2.4 3 45.9 45.0 47.4 1.8 1.0 2.3 4 47.6 46.6 47.5 1.5 0.7 1.5 5 49.5 49.0 47.9 1.6 0.7 1.4 6 51.3 50.3 48.5 2.0 0.8 1.6 7 51.6 50.4 48.9 2.2 0.8 1.6 Images of tri-ethylene glycol (TEG) droplets on different surfaces are shown in Fig. 4.36. The exposure that was used to record images of droplets in Image Pro Plus was 100 milliseconds at 1× magnification, a value that should be kept constant to obtain consistent results. Glass, 20° St.steel (2B finish), 51° Teflon, 94° Figure 4.36 Images of TEG droplets on different surfaces, recorded with Image Pro Plus Chapter 5. Results and Discussions 88 Chapter 5. Results and Discussions In order to investigate the effect of velocity and droplet size on the deposition rate, four sets of experiments were performed. The first and second sets of experiments investigated the effect of velocity at an (almost) constant droplet size distribution. Aqueous sugar solution of concentration 50% (Section 5.1.1), and triethylene glycol (Section 5.1.2), with Setup #1 (Fig. 4.3) were used. The second set of experiments was performed using triethylene glycol, to eliminate issues encountered with the sugar solution, as described below. The third set of experiments was performed using the Hot Unit nozzle (Fig. 4.5) in the Cold Unit (Setup #2, Fig. 4.3) and investigated the effect of velocity on downstream deposition only (Section 5.1.2.2). This was done in order to provide more accurate results, from which downstream deposition coefficients for each drop size at a given velocity could be calculated (Section 5.3). The fourth set of experiments investigated the effect of droplet size distribution, at constant aerosol velocity (U=1 m/s), using triethylene glycol (Section 5.2). The Cold Unit nozzle and Setup #1 were used. These experiments were performed in order to gain insights about the behaviour of the system when the drop size distribution is varied. In the next step, models developed in Chapter 3 were used to simulate deposition and compare the results of simulations with the experimental data (Sections 5.4, 5.5). The morphology and distribution of deposits on the coupon surface were also studied and the results are presented in Section 5.6. Finally, to investigate the effect of contact angle on deposition rates, short experiments on dry and partly wet disk surfaces (glass, stainless steel and Teflon), using triethylene glycol were performed. The results are presented in Section 5.7. Recall that deposition rates, deposition coefficients and capture efficiencies were introduced in Section 2.2 (Eqs. (2.7)−(2.9)). The deposition rate can represent the rate of fouling at a given aerosol concentration. The deposition coefficients are independent of the aerosol concentration, and can be viewed as a direct measure of the deposition rates. Capture efficiencies represent the measure of the aerosol removal by deposition: higher Chapter 5. Results and Discussions 89 capture efficiencies mean a lower concentration of droplets in the aerosol leaving the unit and higher product purity. Therefore, to minimize fouling, one should operate at the minimum deposition coefficients, but to maximize droplet removal (and product purity), one should operate at the highest capture efficiencies. The effects of the investigated factors on capture efficiencies and deposition coefficients are presented in the following sections. 5.1. Effect of velocity The velocity of the aerosol was varied by adding secondary air, using a gas distributor placed around the nozzle. In order to keep the drop size distribution constant, the flow of air to the nozzle was kept constant. However, the addition of secondary air changed the size distribution to a certain degree, and the effect of velocity should be considered bearing in mind the change in the volume median diameter. Total deposition coefficients were calculated by dividing mass deposition rates by the droplet concentration and the surface area of the coupon, while capture efficiencies were obtained by dividing the deposition coefficients by the velocity (as already mentioned in Section 2.2, Eqs. (2.7), (2.8)). 5.1.1. Effect of velocity with 50% sugar solution In the first set of experiments, a 50% wt. aqueous sugar solution was used. This solution was chosen because of its stickiness and moderate viscosity (0.015 Pa⋅s at 20°C), which is not too high to make atomization difficult. It was easy to handle and did not require treatment of the aerosol leaving the Cold Unit. The experiments were performed using the Cold Unit nozzle (Fig. 4.4) and Setup #1 (Fig. 4.3). The experimental results showed low reproducibility (standard deviation was 54%) that was attributed to the evaporation of water from the deposits on the coupon surface. Evaporation took place during the experiments (humidity in the column was not controlled and varied between 5−30%), and after the experiments, during measurements on the analytical balance. In order to reduce the variability in measuring the deposition rates, saturation of the air in the column was attempted in several ways. The ‘air to the nozzle’ stream (Fig. 4.1) was humidified using the following designs: spray column, bubble column, bubble Chapter 5. Results and Discussions 90 column with packing, and bubble column with packing and heated water. Saturated air in the column was not obtained in any of these cases. It can be shown from calculations that even if the air before the nozzle is saturated, after it expands from 300−400 kPa (nozzle pressure) to 101.3 kPa (atmospheric pressure in the column), the relative humidity in the column cannot be higher than about 30%. Therefore, in the subsequent work, the aqueous sugar solution was replaced by triethylene glycol, due to its low vapour pressure (0.02 Pa at 20°C), and ease of handling. A comparison of the relevant physical properties of a 50% aqueous sugar solution and triethylene glycol is given in Table 5.1. Table 5.1 Properties of 50% aqueous sugar solution and triethylene glycol at 20°C Property 50% wt. aq. sugar solution Triethylene glycol Density (kg/m 3 ) 1230 1127 Dynamic viscosity (Pa⋅s) 0.015 0.049 Surface tension (mN/m) 78 45 Vapour pressure (Pa) 2200 0.02 5.1.2. Effect of velocity with triethylene glycol Experiments with triethylene glycol were performed in the same manner as with the 50% aqueous sugar solution. The air and liquid flows to the nozzle were kept constant, and the velocity was changed by adding secondary air, via the gas distributor placed around the nozzle. Two sets of experiments were performed: one using the Cold Unit nozzle and Setup #1, and the other using the Hot Unit nozzle and Setup #2. 5.1.2.1. Cold Unit nozzle, Setup #1 Since deposition coefficients and capture efficiencies are calculated from measured aerosol concentrations (and deposition rates), the accuracy of the aerosol concentration measurements with the Cold Unit Setup #1 (Fig. 4.3) is discussed first. The aerosol concentrations calculated from washdown and shadowgraphy measurements are presented in Fig. 5.1. It can be noted that the trends of the data obtained from these two measurement techniques are similar, but the concentration from shadowgraphy measurements is lower (by a factor of 1.5−2) than the concentration obtained from washdown measurements. This is most probably because a portion of the large droplets, which significantly contribute to the droplet mass concentration in the Chapter 5. Results and Discussions 91 aerosol, deposits in the elbows and is not measured by shadowgraphy (correct measurement). These droplets may stay deposited on the column walls and do not form part of the washdown stream, which causes an increase in the measured concentrations (incorrect measurement). The difference is more pronounced at higher velocities, where the removal of larger droplets is more pronounced. Therefore, for the Cold Unit Setup #1 (Cold Unit nozzle, 90° and 45° elbows), the better measurement method is shadowgraphy. The concentrations measured by shadowgraphy were therefore considered more reliable, and, consequently, were used in the calculation of deposition coefficients and capture efficiencies. For the Hot Unit nozzle and Setup #2, the washdown and shadowgraphy measurements of concentration match more closely (Fig. 5.4, pg. 95). Figure 5.1 Aerosol concentration vs. velocity for Cold Unit nozzle and Setup #1 experiments, calculated from washdown and shadowgraphy measurements of concentration, for triethylene glycol. 95% confidence intervals are estimated from three repeated experiments One would expect that as more secondary air was added, the aerosol would be diluted and the concentration would show a systematic reduction. However, since the secondary air was introduced from the gas distributor that was placed around the nozzle, Chapter 5. Results and Discussions 92 injected air increased the drag force on the droplets from the spray in the axial direction, thereby reducing impaction on the column walls. As the velocity was increased, less washdown was formed, resulting in an increased flow of droplets to the aerosol. Interestingly, the droplet flow to the aerosol increased linearly with the velocity, and as a result the aerosol concentration did not change significantly over the entire range of velocities. a. Upstream side The effect of velocity on the upstream deposition rates was investigated in the range of U=0.44−1.44 m/s. At velocities below about U=0.55 m/s, there were no deposits on the upstream side. Above U=0.55 m/s, deposition rates increased almost linearly from 0 to 1390 mg/hr, as given in Table E.1. The effect of velocity on capture efficiencies and deposition coefficients for the upstream side is presented in Fig. 5.2. The capture efficiencies show a steady increase with velocity, starting from E=0 at about U=0.55 m/s, to E=0.03 at U=1.25 m/s. At velocities above U=1.25 m/s, the capture efficiencies decrease, although this difference could be within the experimental error. If the decrease in capture efficiencies exists, the only explanation could be the removal of large droplets (due to higher superficial velocities) in the elbows. If the size distribution of droplets wasn’t reduced in this manner, there would be no other reason for the capture efficiencies to decrease. The deposition coefficients, obtained by multiplying capture efficiencies with velocity, show a similar increasing trend. The volume median diameter slightly decreased with velocity from 6.5 microns to about 6.0 microns, as a result of inertial deposition of larger droplets in the elbows. The observed increase in capture efficiencies with velocity is expected: according to the mechanism of inertial impaction, capture efficiencies increase with the Stokes number, which is a linear function of velocity ( cp DUtSt /= ). However, a proper quantitative comparison is limited to monosize droplets, where Stokes numbers can be calculated. This was done in Section 5.5, where the measured size distribution of droplets in the aerosol and on the coupon were used to calculate the capture efficiencies and deposition coefficients for each drop size. Chapter 5. Results and Discussions 93 Figure 5.2 Upstream side capture efficiencies, deposition coefficients and volume median diameter vs. velocity. 95% confidence intervals are estimated from three repeated experiments b. Downstream side Deposition rates on the downstream side were significantly lower than deposition rates on the upstream side; they varied from 80.9 mg/hr at U=0.64 m/s to about 152 mg/hr at U=1.26 m/s (Table E.1). The effect of velocity on capture efficiencies and deposition coefficients for the downstream side is presented in Fig. 5.3. The capture efficiencies decrease with velocity in the range U=0.44−0.64 m/s. After U=0.64 m/s, although the variability in the data is significant, the capture efficiencies show little change and remain almost constant (E≈0.0035). As a result of almost constant capture efficiencies, the deposition coefficients show a steady increase with velocity. The trend of the data presented in Fig. 5.3 could be explained satisfactorily with the inertial impaction mechanism and gravity in the flow direction, as will be shown in Sections 5.4 and 5.5. Chapter 5. Results and Discussions 94 Figure 5.3 Downstream side capture efficiencies, deposition coefficients and volume median diameter vs. velocity. 95% confidence intervals are estimated from three repeated experiments In summary, 1. Increasing the velocity increased the capture efficiencies on the upstream side of the coupon, in accordance with the theory of inertial impaction. A quantitative comparison with theoretical predictions is possible only for each drop size, and is presented in Section 5.5.1. 2. For the downstream side, an initial decrease with velocity was followed by a region of constant capture efficiencies. The deposition coefficients showed a minimum between U=0.4 m/s and U=0.7 m/s. The downstream capture efficiencies were up to 10 times lower than the capture efficiencies for the upstream side. Chapter 5. Results and Discussions 95 5.1.2.2. Hot Unit nozzle, Setup #2 From the experiments performed in the Hot Unit [52], there were little or no deposits on the upstream side (even at U=0.92 m/s), which suggested that the Hot Unit nozzle produced very fine droplets, carried with the aerosol. The drop size distribution from this nozzle is similar to the distribution that is estimated to be in the scrubber section of the Fluid Coker (<11 microns, [8]). Therefore, the Hot Unit nozzle was used in the next set of experiments. Recall that Setup #2 (Fig. 4.2) had the nozzle spraying upward in a straight cylindrical section. This arrangement caused uncontrolled deposition of large droplets entrained in the aerosol from the bottom of the column on the upstream side, at velocities U >0.7 m/s. This is the reason why elbows were installed initially. Therefore, although the results on upstream deposition are presented in Table E.2, they could not be considered reliable, and are not discussed below. As already mentioned (Section 5.1.2.1), the validity of the aerosol concentration measurements is an important factor in calculating the deposition coefficients and capture efficiencies. While shadowgraphy measurements are considered to be more accurate than washdown measurements, Figure 5.1 shows that the shadowgrahy measurements are less precise (have greater scatter) than the washdown measurements. For the Hot Unit nozzle and Setup #2, the results from the two measurement methods match closely for two reasons: (1) the size of the shadowgraphy sample is increased 5 times while the variability is reduced, and (2) washdown issues (deposition of droplets in elbows) do not persist with Setup #2 anymore, hence, accuracy is improved. Since the washdown measurements showed less scatter (Fig. 5.4), they were used in the calculation of downstream deposition coefficients and capture efficiencies (Section 5.3). Chapter 5. Results and Discussions 96 Figure 5.4 Aerosol concentration vs. velocity, for Hot Unit nozzle and Setup #2 experiments, calculated from washdown and shadowgraphy measurements of concentration. 95% confidence intervals calculated from two repeated experiments In these experiments, the deposition rates on the downstream side varied between 30.5 mg/hr at U=0.5 m/s, and 123.9 mg/hr at U=1.5 m/s (Table E.2). The volume median diameter was almost constant over the whole range of velocities (4.9−5.4 microns), with the exception of the first point, when the flow of air to the nozzle was quite low and the nozzle produced large droplets. Capture efficiencies and deposition coefficients vs. velocity are presented in Fig. 5.5. The capture efficiencies showed an exponential-like decrease from about 1.5% at U= 0.05 m/s to about 0.1% at U = 0.7 m/s. In the range from 0.7 m/s to about 1 m/s, the capture efficiencies remained constant, and at U>1m/s they showed a slight increase. One might expect that as the velocity is decreased below 0.05 m/s, the capture efficiencies would approach one. This would be the case for the coupon side facing a fresh stream of slow aerosol that flows in the downward direction (gravitational settling would be approached). For upward flow, the capture efficiencies would probably still increase as the velocity is reduced below 0.05 m/s, but only up to the point when the flow becomes too slow to transport droplets in the upward direction. Deposition coefficients showed a Chapter 5. Results and Discussions 97 minimum at about 0.6 m/s, indicating that the minimum deposition (fouling) rate could be expected at that velocity. It can be noted that the observed trends are in accordance with the trends obtained in Section 5.1.2.1.b, when the Cold Unit nozzle and Setup #1 were used. These results can also be explained by the inertial impaction mechanism along with gravity in the flow direction (Sections 5.4, 5.5). Figure 5.5 Downstream side capture efficiencies, deposition coefficients and volume median diameter vs. velocity In summary, 1. The downstream side capture efficiencies showed an exponential-like decrease to a minimum value of 0.0009 (<0.1%) at U=1.0 m/s. The deposition coefficients showed a minimum (kd=2.35 m/hr) at about U=0.6 m/s. 2. In addition, the observed trends were in accordance with the results obtained for the downstream side using the Cold Unit nozzle and Setup #1 (Fig. 5.3). Chapter 5. Results and Discussions 98 5.2. Effect of droplet size distribution, Cold Unit nozzle, Setup #1 To investigate the effect of the droplet size distribution (quantified by its volume median diameter) on deposition, the liquid flow to the nozzle was varied from 7.2 ml/min to 95 ml/min, while the air flow rate to the nozzle was kept constant. As the liquid flow was increased, the volume median diameter increased from 3.9 to about 7.5 microns. Qualitatively speaking, this change is in accordance with the empirical correlation for twin-fluid atomizers (Eq. (3.37)). The resulting velocity in the column from the air flow rate to the nozzle was Unozzle = 0.43 m/s, and the total velocity was kept at Utotal = 1 m/s. 5.2.1. Upstream side Deposition rates on the upstream side varied from 12.3 mg/hr for the smallest size distribution of droplets (VMD=3.9 microns), to about 1380 mg/hr for the largest size distribution. As the liquid flow rate was increased, the concentration increased almost linearly from 1.1 g/m 3 to 5.54 g/m 3 (Table E.3). The capture efficiencies and deposition coefficients for the upstream side are presented in Fig. 5.6. Figure 5.6 Capture efficiency and deposition coefficient for the upstream side vs. volume median diameter, at U = 1 m/s. 95% confidence interval were estimated from three repeated experiments Chapter 5. Results and Discussions 99 From Figure 5.6, it can be seen that increasing the volume median diameter caused a major increase in capture efficiencies (and deposition coefficients). Increasing the median diameter from 5 to 7 microns resulted in an increase in capture efficiencies of more than an order of magnitude. These results are logical, because as the volume median diameter is increased, the concentration of large droplets in the aerosol is increased. This means that there were more droplets with a larger Stokes numbers present in the aerosol, which according to the theory of inertial impaction, increased the total capture efficiency. 5.2.2. Downstream side As the volume median diameter was increased, the deposition rates on the downstream side increased from 10.5 mg/hr to 137 mg/hr (Table E.3). The capture efficiencies and deposition coefficients for the downstream side are given in Fig. 5.7. Figure 5.7 Capture efficiency and deposition coefficient for the downstream side vs. volume median diameter, at U = 1 m/s. 95% confidence intervals were estimated from three repeated experiments From Fig. 5.7, it can be noted that capture efficiencies show a slight but definite increase with the volume median diameter. The increase in capture efficiencies with drop diameter can be explained by the increased Stokes number, which according to the theory of Chapter 5. Results and Discussions 100 inertial impaction and gravity in the flow direction, increases capture efficiencies (Sections 5.4 and 5.5). The solid lines in Fig. 5.6 and Fig. 5.7 represent the best-fit polynomial curves, which can be used for calculating the change in capture efficiencies, depending on the volume median diameter of the size distribution. 5.3. Calculation of capture efficiencies and deposition coefficients for individual drop sizes from experimental results From their experiments of deposition on the front and back surfaces of disks, Vincent and Humphries [19] concluded that although difficult to interpret, meaningful experiments could be carried out using polydisperse dusts. Polydispersity almost always characterizes natural or ‘real’ systems, and there are many phenomena that are not revealed when working with monodisperse systems. For this reason, in this section, the effects of the size distributions of the droplets in the aerosol and on the coupon were investigated. Therefore, to obtain more general results and draw meaningful conclusions that could be explained quantitatively from a theoretical point of view, the calculation of deposition coefficients and capture efficiencies for each drop size at a given velocity was carried out. This was done by the use of Eq. (3.26) and Eq. (3.27). Since measurements of deposition rates and aerosol concentration are believed to be sufficiently accurate, proper determination of the size distributions on the coupon and in the aerosol proved to be important for the validity of results. Images of the deposits on the upstream and downstream glass coupon surfaces for Run 26 are given in Fig. 5.8. Figure 5.8 Images of triethylene glycol deposits on the (a) upstream and (b) downstream surface of the glass coupon, Run 26 (a) (b) 100 µm 100 µm Chapter 5. Results and Discussions 101 The size distributions of droplets in the bulk aerosol, and on the upstream and downstream surfaces of the coupon, for Run 26, are given in Fig. 5.9. Figure 5.9 Measured drop size distributions in the aerosol, and on the upstream and downstream sides of the glass coupon at 1 m/s, Run 26 From Fig. 5.9, it can be noted that only the size distribution of deposits on the downstream side significantly overlaps with the size distribution in the aerosol (up to Dp=25 µm). Therefore, reliable estimation of deposition coefficients should be possible in the region from 1−25 microns. On the upstream side, only droplets larger than about 28 microns deposit (by inertial impaction) and notably contribute to the mass of deposits. Hence, it was expected that the correct estimation of deposition coefficients would be difficult, since it includes calculations that require extrapolation of the aerosol size distribution curve. 5.3.1. Effect of drop diameter at different velocities, downstream side The effect of drop diameter at different velocities was determined from experiments performed with the Hot Unit nozzle and Setup #2 (Section 5.1.2.2), using Eqs. (3.26) and (3.27). The results are presented in Figs. 5.10 and 5.11, and are given in Chapter 5. Results and Discussions 102 Table E.3. The fitted size distributions of droplets in the aerosol and coupon deposits were used in the calculations, and for that reason, the ‘experimental’ curves obtained appeared smooth. Over the whole range of velocities, the capture efficiencies and deposition coefficients show a definite increase with the drop diameter. The deposition coefficients at 1.5 m/s approach the deposition coefficients for gravitational settling (Fig. 5.11). Figure 5.10 Calculated capture efficiencies vs. drop diameter for the downstream side, at different gas velocities Chapter 5. Results and Discussions 103 Figure 5.11 Calculated deposition coefficients vs. drop diameter for the downstream side, at different gas velocities The results are shown for the range of drop sizes from 2−20 microns, since they are obtained by dividing the parts of distribution that are more accurate (significant overlap, Fig 5.9). Above Dp=20−25 microns, the deposition coefficients and capture efficiencies still increase, but eventually must reach maximum and fall down to zero at higher Stokes numbers (at the highest velocity, U=1.5 m/s, the deposition coefficients reached a maximum at 17 microns and then start decreasing at St=0.03). This is because it is expected that droplets with high inertia would follow their original pathlines, and would not be entrained in the vortex behind the coupon (Fig. 3.1). From the results of the downstream deposit analysis (Table E.2), it can be seen that larger droplets were not entrained in the vortex behind the coupon (Dmax for all runs is in the range from 27−40 microns, from at least 20,000 sampled droplets). If they were entrained, they would be deposited due to high inertia. At the same time, it is known that large droplets (>30 microns) are present in the aerosol, since some of them deposit on the upstream side. Therefore we may presume that large droplets with high inertia either deposit on the upstream side, or bypass the coupon, without being entrained in the vortex. Chapter 5. Results and Discussions 104 5.3.2. Effect of velocity for different drop diameters, downstream side The capture efficiencies and deposition coefficients calculated in the previous section can be plotted versus velocity. The effect of velocity for different drop diameters is presented in Figs. 5.12 and 5.13. The results are given in Table E.4. The capture efficiencies for all drop sizes show an exponential-like decrease with velocity, followed by a region of almost constant values. This is more pronounced for larger droplets. The results show good qualitative agreement with the results obtained using the size distribution of droplets (Fig. 5.5). The deposition coefficients for the smaller droplets (3, 5 micron) are almost constant over the range of velocities investigated, while for the larger droplets (10−25 microns), the deposition coefficients first decrease, then remain constant, and somewhere between 0.6 m/s and 1 m/s start to increase again. These trends are also in agreement with the results obtained in experiments with size distribution, using the Cold Unit nozzle and Setup #1 (Fig. 5.3). Figure 5.12 Calculated capture efficiencies vs. velocity for the downstream side, at different drop diameters Chapter 5. Results and Discussions 105 Figure 5.13 Calculated deposition coefficients vs. velocity for the downstream side, at different drop diameters From Figs. 5.10−5.13, it can be definitively concluded that on the downstream side, deposition coefficients and capture efficiencies, in the range from 2−20 microns, increase with droplet size. The same trend was observed in experiments with drop size distribution (Fig. 5.7). Also, it can be concluded that for larger droplets (>10 microns), the deposition coefficients show a minimum value, somewhere between velocities of 0.5 m/s and 1 m/s. For smaller droplets, in the velocity range of 0.5−1 m/s, deposition coefficients are mainly constant, and at U>1 m/s, they start to increase. As the drop diameter is increased, the increase in deposition coefficients occurs sooner, at lower velocities. All these phenomena can be explained by the mechanisms of inertial impaction and gravity in the flow direction, as is shown in the next two sections (Sections 5.4 and 5.5). Deposition coefficients for each drop size and velocity, obtained in this section, can be further used in the calculation of deposition coefficients for any drop size distribution at a given velocity. Knowing the aerosol concentration, deposition rates can be then easily calculated (Eq. (2.9)). Chapter 5. Results and Discussions 106 5.4. Simulations In order to explain the experimental results of deposition on the upstream and downstream sides of the disk (coupon), the results of the simulations of inertial deposition, with and without gravity, are presented here. The results of calculating deposition due to turbulent particle transport are also presented. 5.4.1. Inertial particle transport To simulate inertial deposition of droplets on the upstream side, the equations of particle motion in a potential flow field (Chapter 3) were solved analytically and numerically (Appendices C and D). The analytical solutions of droplet trajectories and capture efficiencies were obtained for Stokesian particles (Appendix C), while non- Stokesian particles required numerical calculations (Appendix D). In the following sections, the two solution methods, the validity of the potential flow approximation, and the effect of gravity on the inertial particle transport are discussed. To get a visual sense of the deposition phenomena, trajectories of particles before the coupon are presented first. 5.4.1.1. Particle trajectories The droplet pathlines are shown in Fig. 5.14, for single droplets of different sizes, placed in the flow at a distance 5.0/ −== cRxx , upstream of the disk. Initial velocity of injected droplets was equal to the superficial gas velocity, corrected for the droplet terminal velocity. From Fig. 5.14a we can see that smaller droplets closely follow the fluid streamlines and do not reach the coupon surface via the inertial deposition mechanism (Dp<42 microns). Intermediate size droplets (Fig. 5.14b) deposit on the surface (42<Dp<135 microns), while very large droplets (Fig. 5.14c), which are heavy enough, fall down before they reach the coupon surface (Dp>135 microns). Start and end point diameters for inertial deposition (42 and 135 microns) are obtained from the simulations, using properties of tri-ethylene glycol droplets in air at room temperature. These values can be read from Fig. 5.19b, for the superficial velocity U = 1 m/s. Chapter 5. Results and Discussions 107 -0.5 -0.4 -0.3 -0.2 -0.1 0 0 0.2 0.4 0.6 0.8 1 streamlines pathlines -0.5 -0.4 -0.3 -0.2 -0.1 0 0 0.2 0.4 0.6 0.8 1 streamlines pathlines -0.5 -0.4 -0.3 -0.2 -0.1 0 0 0.2 0.4 0.6 0.8 1 streamlines pathlines Figure 5.14 Trajectories of (a) 10, (b) 50 and (c) 140 micron droplets (pathlines) in the potential flow field (streamlines), for an upward flow at 1 m/s superficial gas velocity, using the Stokes drag force 5.4.1.2. Discussion of the model validity To confirm the validity of the numerical procedure, analytical and numerical solutions for Stokesian particles were compared (section a). To compare the effect of different drag force, numerical solutions for Stokesian and non-Stokesian particles are presented as well. Since the potential flow is an approximation of the actual flow field, the results of potential flow simulations were compared with the CFD results [36], where a more faithful flow field was used (section b). To investigate the effect of the absence of a viscous sublayer in the potential flow model, deposition from a flow that includes a viscous sublayer was simulated too (section c). a. Analytical vs. numerical solutions for Stokesian particles, and non-Stokesian vs. Stokesian particles Analytical and numerical solutions for Stokesian particles, as well as the numerical solution for non-Stokesian particles are presented in Fig. 5.15. From Fig. 5.15, it can be noted that, r/Rc r/Rc r/Rc x/ R c x/ R c x/ R c (a) (b) (c) Chapter 5. Results and Discussions 108 1. The results of the numerical procedure for Stokesian particles (open “data” points) match analytical solutions for Stokesian particles (smooth curves). Hence, the numerical procedure is valid and can be used further for non-Stokesian particles. 2. For an upward flow, a higher drag force in the radial direction prevents droplets from reaching the coupon surface (non-Stokesian drag force−solid “data” points versus Stokes drag force−“open” data points) and shifts the onset of deposition toward larger droplets (from 42 to 45 microns). Also, the higher drag force is able to transport “heavier” droplets upward, so the end of deposition on the upstream surface is again shifted toward larger droplets (from 135 to 161 microns). According to the simulations, deposition due to inertia is confined to a range of Stokes numbers (drop diameters), at a given velocity. Below a certain minimum diameter (Stokes number), inertial effects are too small for deposition to occur. For droplets larger than some maximum diameter, upward flow is too slow to support droplets and transport them toward the coupon surface. 3. For horizontal and downward flows, at a given Stokes number (drop diameter), capture efficiencies calculated using the non-Stokesian drag force are from 1 to 5% lower than the capture efficiencies calculated using the Stokes drag force. Therefore, the Stokes drag force can be used as a relatively good approximation. For upward flow, non- Stokesian drag force should be used. The shapes of the obtained curves for all three flow orientations are further discussed in Section 5.4.1.3. Chapter 5. Results and Discussions 109 Figure 5.15 Comparison of analytical and numerical solutions for Stokesian particles, with numerical solutions for non-Stokesian particles, for upward, horizontal and downward flow, at 1 m/s superficial gas velocity b. Comparison with the CFD results Capture efficiencies calculated for potential flow and non-Stokesian drag force are compared with the CFD results of Lakghomi [36], at three velocities: 1, 2 and 5 m/s (Fig. 5.16). This was done in order to see how good an approximation potential flow is in terms of deposition. Chapter 5. Results and Discussions 110 Fig. 5.16 Comparison of numerical solutions for non-Stokesian particles for upward flow, at different velocities, with the CFD results (by Lakghomi [36]) From Fig. 5.16, when comparing potential flow (open points) with CFD (solid points) capture efficiencies, there is a surprisingly good agreement between the two results, particularly for St>0.15. Although the flow field is not the same as the one predicted by CFD, in terms of deposition, it gives a good match. The potential flow predictions are lower than the CFD results at lower Stokes numbers (below 0.13), probably since there is no viscous sublayer, or because deposition by turbulence is not included. These assumptions are investigated in the sections that follow (Sections 5.4.1.2.c and 5.4.2). c. Potential flow with patched viscous sublayer To investigate the effect of the presence of a viscous sublayer on the capture efficiency, a 5 mm thick viscous sublayer, defined by equations in Section 3.2.3, was added to the free-stream inviscid flow. The results of the simulations are presented in Fig. 5.17. Chapter 5. Results and Discussions 111 Figure 5.17 Comparison of the capture efficiencies on the upstream side from potential flow with and without a viscous sublayer, with CFD, for non-Stokesian particles (Lakghomi [36]) From Fig. 5.17, we can see that there is higher predicted capture efficiency (2−3%) with the included viscous sublayer than without it. This is the expected result since the intensity of radial velocity close to the disk surface, which moves droplets along the surface, is reduced (while the axial gas velocity component remained unchanged). Yet, there is still no deposition at low Stokes numbers. Therefore, an attempt was made to include convective diffusion and inertial impaction from turbulent parallel flow, as described in Section 3.4. The results are presented in Section 5.4.2, after all considerations of inertial deposition are completed. 5.4.1.3. Effect of gravity on inertial particle transport As mentioned before, although the capture efficiencies from potential flow around a disk were known in the literature and were solved analytically, the effect of gravity was not considered (except Tsai and Liang [32]). Deposition due to inertial impaction from upward flow, as is the case in the Scrubber, has not been reported elsewhere to the best of Chapter 5. Results and Discussions 112 our knowledge. Therefore, the effect of gravity, i.e. flow orientation, on the inertial deposition on the upstream surface of a disk is presented here. a. Capture efficiencies vs. Stokes number The calculated capture efficiencies on the upstream side of a disk (side facing the flow), for all three cases of flow orientation (horizontal, upward and downward) are presented in Fig. 5.18. Figure 5.18 Calculated capture efficiencies vs. Stokes number for the horizontal, upward and downward flow, at different superficial gas velocities For a horizontal flow (no gravity), the capture efficiency curves at all velocities overlap (thick line in the middle). This line separates efficiency curves for upward and downward flow. At higher velocities (above 2−3 m/s), curves for upward and downward flow approach the curve for horizontal flow. However, as already mentioned in Section 3.3, used particle motion equations (and thus their solutions) are not strictly valid for the horizontal (flow) orientation of our coupon-in-column system, since the problem is not axisymmetric anymore. Gravity will cause settling of larger droplets (e.g. at St=2.2 and Dp=180 µm, terminal velocity is 1 m/s and the droplet will settle before it reaches the Chapter 5. Results and Discussions 113 coupon surface). It is expected that the capture efficiency curve for the disk inside the pipe will reach its maximum and start to fall down. For an upward flow (gravity in direction opposite to the flow), at velocities below 0.735 m/s, there is no deposition on the upstream side. As the velocity is increased above this value, deposition starts taking place on the upstream side. As the velocity is increased further, the minimum drop diameter that deposits on the upstream side decreases, since smaller droplets have sufficient inertia to penetrate the gas layer in the vicinity of the coupon and reach the surface. Also, the maximum droplet diameter that is depositing is increased, since higher gas velocities are able to support and transport upward particles with larger terminal velocities. When the velocity becomes high enough and gravity forces become negligible compared to the inertial forces, the efficiency curve overlaps with the curve for horizontal flow. For a downward flow (gravity in the flow direction) as the velocity is decreased, the capture efficiency curve is shifted toward unity, and when the gas velocity becomes zero (there is no gas flow), we have pure gravitational settling. There is no fluid to sweep particles away from the surface and capture efficiencies for all particles become equal to unity. As the velocity is increased, particles are swept away from the coupon surface and capture efficiencies first decrease. As the velocity approaches 2−3 m/s, gravitational forces become negligible compared to inertial forces and the capture efficiencies become equal to the capture efficiencies for the horizontal flow. b. Capture efficiencies vs. drop diameter and velocity The results of simulations (section a) can be presented as capture efficiencies vs. drop diameter and velocity (Figs. 5.19a-d). Deposition coefficients can be obtained by multiplying capture efficiencies by the gas velocity. For a horizontal flow (Fig. 5.19a), it can be noted that the minimum droplet diameter that is deposited by inertia decreases as the velocity is increased, and there is no minimum velocity at which deposition on the upstream side occurs. Above 3 m/s, the capture efficiency curve would change only a little, in order to stay in agreement with the Fig. 5.18. Chapter 5. Results and Discussions 114 For an upward flow (Fig. 5.19b), at each velocity there exist a minimum and maximum drop diameter that deposits via the inertial impaction mechanism. There is no deposition on the upstream side below 0.735 m/s. At velocities higher than 3 m/s, the capture efficiency curve would change little, approaching the curve for horizontal flow (Fig. 5.18). At constant capture efficiencies, deposition coefficients would however increase linearly with velocity, according to Eq. (2.8). Figure 5.19 Capture efficiencies vs. drop diameter for (a) horizontal, (b) upward, and (c) downward flow, at different superficial gas velocities. Capture efficiencies vs. velocity for downward flow are presented in (d). For a downward flow, the capture efficiencies increase with the drop diameter as given in Fig. 5.19c. As the velocity is increased, they first decrease and then increase toward capture efficiencies for horizontal flow. The results are somewhat different from what was observed in first two cases: capture efficiencies first decrease with velocity, and then increase. This is better seen in Fig. 5.19d. (a) (b) (c) (d) Chapter 5. Results and Discussions 115 From the calculated capture efficiencies for downward flow vs. velocity, there is a velocity for each drop size at which capture efficiency is minimal. Approaching U=0 m/s, capture efficiencies become very high, asymptotically approaching unity (not exactly shown in Fig. 5.19). This is in accordance with Fig. 5.18, and the explanation presented. As the velocity is increased, the capture efficiencies are reduced because the radial velocity removes particles from the surface and reduces deposition. When the inertial forces become significant, the capture efficiencies increase again, showing a similar dependence as for horizontal flow. As expected, at a given velocity, inertial effects first come into play for larger particles and therefore, a sharp increase for 20 micron droplet is seen at about 2 m/s, while for the 15 micron droplet, it happens at about 4 m/s. Interestingly, the same trend was observed for capture efficiencies calculated from experimental data for the downstream side (Figs. 5.10, 5.12). This can be explained by the fact that the gravity in the simulation was oriented in the same direction as it is in the vortex (downward), and that flow field in a vortex could be somewhat similar to the potential flow field (see Fig. 5.22). Therefore, this simulation can help explain the mechanisms that govern deposition of droplets from the vortex. A quantitative comparison of the simulations and experimental data is given in Section 5.5 (Fig. 5.23). 5.4.2. Particle transport due to turbulence To estimate deposition from parallel flow at low Stokes numbers, models described in Section 3.4 were used. Figure 5.20 represents calculated capture efficiencies from an assumed parallel flow to the disk surface, as described in Section 3.4. According to this model, in the range of Stokes numbers from 0.0001 to about 0.01, calculated capture efficiencies decrease, since the main mechanism of deposition is convective diffusion. The transport coefficient in this case is proportional to the Brownian diffusivity of the particles, which decreases as the Stokes number (droplet size) is increased. In this range, deposition from inertial effects is negligible, since the particles are too small (their relaxation time is small) so that the momentum transferred to them by turbulent eddies is dissipated in the viscous sublayer. At a Stokes number of about 0.008, or particle diameter of 11 microns, the equivalent non-dimensional particle relaxation time at U=1 m/s is about 0.23. In this region, inertia starts to dominate the deposition (see Fig. 2.1) Chapter 5. Results and Discussions 116 and we can observe an increase in deposition with an increase in the Stokes number (droplet size). Curves presented in Fig. 5.20 are summation curves of calculated convective diffusion and turbulent inertia over the whole range of Stokes numbers. Compared with the CFD results presented in Fig. 5.17, in the range of Stokes numbers 0.001−0.1, the capture efficiencies calculated here are significantly lower (~10 -5 vs. ~10 - 2 ). This could be due to the different flow field and different turbulence models used. Validity of the CFD predictions in this range of Stokes numbers was not verified experimentally; however, there are indications from this work that CFD over-predicts deposition in this range of Stokes numbers (experimental capture efficiencies at St<0.05 are estimated to be less than 10 -3 (0.1%)) and that the true capture efficiencies are between the two model predictions. Figure 5.20 Simulation of deposition by convective diffusion and turbulent inertia from a flow parallel to the coupon surface, based on the modeling described in Section 3.4 In summary, for Stokes numbers larger than 0.1, the inertial deposition model using the potential flow approximation and a non-Stokesian drag force, proved to be very close to the CFD model (Lakghomi [36]). Gravity had an important effect on capture efficiency, and therefore, the flow orientation in the Scrubber could affect fouling. For upward and downward flows, capture efficiencies could be represented as a function of Chapter 5. Results and Discussions 117 the Stokes number and velocity; for a horizontal flow, capture efficiencies are only a function of the Stokes number. The results predicted by the turbulent deposition model (convective diffusion and turbulent inertia) are lower than the CFD model prediction [36] in the range of St<0.1, most probably due to the different turbulence models and the flow field used in simulations. Measured capture efficiencies seem to be between the two model predictions. 5.5. Comparison with experimental data In this section, experimental results for the upstream and downstream side (Sections 5.1 and 5.3) are compared with the results of simulations from the previous section (Section 5.4). 5.5.1. Upstream side Simulation results for the upstream side presented in this section (Fig. 5.21) were obtained for an upward flow at the velocity U=1 m/s (Fig. 5.16). The experimental results (Fig. 5.21) were also obtained at superficial velocity U=1 m/s, and calculated from Eq. (3.27) by dividing the size distribution of the droplets on the coupon by that in the aerosol (Fig. 5.9). From Fig. 5.9, it is possible to observe that the distribution of deposits on the upstream side is bimodal: in the range of Dp=1−27 µm, there is a small amount of deposit due to turbulent diffusion (in 1 of 5 cases it is not even recorded), while for Dp>27 microns, deposition is significant, as a result of inertial impaction. The measured critical diameter at which inertial impaction starts (Dp=27 µm) corresponds to the critical Stokes number Stcr=0.05, while calculations suggested a value of 43 microns (Stcr=0.125). This discrepancy can be explained with the fact that the real flow field is yet different (stronger) from the potential flow. This is since the potential flow approximation did not consider the presence of column walls, and it is known from the results of Salmanzadeh et. al. [56], that the increase in blockage ratio increases deposition. Droplets that deposit on the upstream side are very rare in the aerosols used (VMD=3.9−7.5 microns), since from 5 aerosol samples (about 15,000−20,000 droplets recorded), no droplet was larger than 25−30 microns (Table E.1), although they must be present in the aerosol, since they deposited on the coupon. Therefore, their concentration Chapter 5. Results and Discussions 118 is estimated by extrapolation of the size distribution obtained from fitting the data in the range 1−30 microns, and used in calculation of capture efficiencies (Eq. (3.27)). From Fig. 5.21, we can see that the experimental results overestimate the simulation results by a factor of 4−5. This suggests that the concentration of large droplets in the aerosol that deposit on the upstream side (Dp>27 µm) is underestimated by shadowgraphy (4−5 times), most probably because its concentration is estimated from the extrapolated size distribution curve. The shape of the capture efficiency curve obtained, however, is similar to the efficiency curve predicted by the simulation, meaning that the trends of the size distributions in the aerosol and on the coupon are correct, while the main discrepancy is due to underestimating the concentration of larger droplets in the aerosol. Figure 5.21 Comparison of the simulation and fitted experimental results for the upstream side at 1 m/s 5.5.2. Downstream side Flow on the downstream side of the disk is represented by a vortex with turbulent fluctuations of velocity. Although certainly different from the real flow field, potential flow was tested in describing the flow in the vortex, due to some resemblance of the potential flow pattern to the actual flow pattern in the wake (Fig. 5.22). Also, the results 43 µm 27 µm Chapter 5. Results and Discussions 119 of simulations with gravity in the flow direction (Fig. 5.19d), indicated that this approach may be useful in explaining the experimental results (Fig. 5.12). Figure 5.22 Axisymmetric flow pattern about a disk (adapted from Humphries and Vincent [73]) The results for the downstream side were obtained from the downward flow simulation (p=1), using the same potential flow field equations as for upward flow (Eqs. (3.6a,b)) at velocity U=1 m/s. For the downstream side, the size distribution of droplets in the aerosol and size distribution on the coupon overlap significantly (Fig. 5.9). It is believed that in this case, the experimental results are correct, and that the model is somewhat oversimplified. However, the model does seem capable of predicting the main trends and gives quantitative confirmation of the experimental results within a factor of 2.3 (Fig. 5.23). Figure 5.23 Correlation between calculated capture efficiencies from the downward flow and experimental data. Simulation over-predicts experimental data by a factor of 2.33 Region of pathlines similar to the potential flow pathlines Bubble boundary Turbulent mixing layer Chapter 5. Results and Discussions 120 From Fig. 5.23, we can see that the simulation over-predicts the experimental data by a factor of 2.3. One reason for discrepancy is certainly because the real flow field in the wake is different from the potential flow field used in the simulations. The other reason is because the size distribution and concentration of droplets in the vortex is different from the size distribution and concentration in the aerosol (used in the simulations). The latter claim can be supported with the experimental data of Humphries and Vincent [72], who investigated transport and detention of airborne dusts in the near wake of a disk. Their experimental results showed that the dimensionless mean residence time of particles in the vortex (Hp) decreases with Stokes number, and is always lower than the residence time of inertialess particles (Hp<Hf=7.44). Based on theoretical considerations, they suggested that the concentration of particles in the wake, cwake, is related to the concentration in the bulk, cb, according to, )/( fpbwake HHcc = . This implies that the concentration of particles in the wake is always lower than the concentration in the bulk (up to 1.6 times), particularly for larger particles. This explains to a certain degree why the simulation over-predicted the experimental results. Similar experimental findings, on the dispersion of large particles in the near wake of disks, were also reported by Sato et al. [74]. Apart from over-predicting the results by a constant factor (2.3), a good correlation between the simulation and experimental values exists (R 2 =0.89), indicating that the model is capable of explaining the observed trends in the experimental data. From these considerations, we can postulate that inertial impaction and gravity in the flow direction, are governing mechanisms on the downstream side. To summarize, deposition on the upstream side of a disk was simulated by the inertial impaction mechanism, using the potential flow approximation and gravity in the direction opposite to the flow. The model was able to describe deposition qualitatively. The main discrepancy was due to the underestimation of the concentration of large droplets in the aerosol (Dp>30 microns), obtained by extrapolation of the log-normal distribution curve. For the downstream side, the same potential flow approximation with the inertial impaction mechanism and gravity in the flow direction proved capable of describing the deposition, but the simulation over-predicted experimental results by a factor of 2.3, mainly due to the actually lower concentration of droplets in the vortex than in the bulk stream. Chapter 5. Results and Discussions 121 5.6. Morphology of deposits and their distribution along the disk radius From the images of deposits taken after each experiment, it can be noted that deposits on the upstream side were not uniformly distributed; more droplets were deposited toward the edge and less in the centre of the coupon (Fig. 5.24a). Also, because of the relatively large amounts of deposit that were collected (200−300 mg), droplets merged and formed grain-like shapes on the surface. Again, this was more pronounced close to the coupon edge. On the downstream side, deposits appeared to be uniformly distributed along the radius (Fig. 5.24b). Figure 5.24 Typical appearance of (a) non-uniform distribution of deposits on the upstream side, and (b) uniform distribution on the downstream side It is interesting to note that although the morphology of the surface was changing during the experiment from a flat coupon surface to a surface covered with a few mm size grains of liquid, the deposition rates remained constant (straight line in Fig. 4.33). This indicates that the changed morphology of the coupon surface did not change the flow field appreciably such that the deposition rates would be affected. The distribution of deposits along the disk radius was determined by measuring the droplet number, size, and mass fraction of the deposits along the radius of a glass coupon, using the methodology and the setup described in Section 4.4.4. To collect the deposits for the measurement process, deposition on the coupon lasted from 10 to 60 seconds, depending on the experimental conditions. In any case, to avoid merging of (a) (b) Chapter 5. Results and Discussions 122 droplets and errors in the measurement process, the surface coverage should not exceed 10%. Typical distributions of deposits on the upstream and downstream side for Run 56 are shown in Fig. 5.25. Similar trends were obtained in all other experiments. For the upstream side (Fig. 5.25a), it can be noted that the volume median diameter of deposit of droplets did not vary along the coupon radius. The maximum diameter was about 20−30% larger at the coupon edge, due to the merging of droplets at the coupon edge, where the surface coverage was about 15%. The number of droplets, their mass distribution and surface coverage increased from the coupon centre toward the edge. In Fig. 5.25, the mass fraction of total deposits increased from about 1.8% close to the coupon centre, to about 6% at the coupon edge, which is more than a three-fold increase. For the downstream side (Fig. 5.25b), the volume median diameter on the downstream side was constant along the coupon radius, as was the maximum drop diameter. The number of fine deposited droplets was usually higher close to the coupon centre, possibly due to the turbulence caused by the piece used for rod attachment. Mass distribution of deposits and surface coverage was constant along the radius, with surface coverage being somewhat higher close to the coupon centre, where many fine droplets were deposited. Data on the mass distribution of deposits along the coupon radius, from all experiments with the Hot Unit nozzle and Setup #2 (Section 5.1.2.2), are given in Figs. 5.26a,b. The data were correlated with parabolic and linear functions respectively, and show that for the upstream side, more deposits were formed close to the coupon edge, and on the downstream side, the mass of deposits just slightly decreased along the coupon radius. Chapter 5. Results and Discussions 123 Figure 5.25 Distribution of deposits along the coupon radius on the (a) upstream and (b) downstream side, for Run 56. Solid lines were obtained by averaging measured values from four samples. (a) Upstream side (b) Downstream side Chapter 5. Results and Discussions 124 Figure 5.26 Mass distribution of deposits along the radius of the (a) upstream and (b) downstream surface of the coupon, in 30 classes, from Runs 46−59 Regarding the Scrubber, pictures of deposits on the surface of the packing elements (Fig. 1.3b) suggest that the coke is found everywhere across the packing elements, on both the downstream and upstream sides. The packing elements in the Scrubber are triangular sections with 3.3 cm long sides (equivalent disk diameter is 3.7 cm) [9]. If we assume a normal orientation of flow over these elements, and use the operating conditions and physical properties of vapour and droplets in the reactor (vapour viscosity 0.023 mPas, droplet density ~900 kg/m 3 , velocity 1.35 m/s, maximum droplet diameter 11 microns [8, 9]), the calculated Stokes number is St≈0.01. This value is 5 times smaller than the critical Stokes number at which inertial impaction would occur (Stcr=0.05, Fig. 5.21). At the given conditions, the critical diameter of the obstacle positioned normal to the flow, for which Stcr=0.05, would be around 7 mm. Therefore, inertial deposition probably takes place on the parts of the packing elements smaller than 7 mm. This includes parts of the triangular sections close to its vertices, but also the 2−3 mm thick metal sheets that support the packing elements. The deposits formed on these parts could cause early blockage of the reactor. However, the actual situation in the Scrubber, where the wash oil is poured from the top and over the packing, could prevent this from happening. Reliable predictions should be based on a more realistic fluid flow field, and consider the interaction with the wash oil. Based on the results for the downstream side, the back side of the packing should foul uniformly. Again, proper consideration should include the effect of the wash oil sprayed from the top, and the actual geometry of the packing. (a) (b) Chapter 5. Results and Discussions 125 5.7. Contact angle and dry vs. wet surface effect To investigate the effect of contact angles on deposition, coupons made of different materials were used, while the liquid was kept the same (triethylene glycol). Short deposition experiments were performed in order to compare deposition rates between surfaces when part of the surface of the coupon is still dry. Longer duration runs allowed comparison with a wet surface. To cover the widest range that we could attain with triethylene glycol, a glass, stainless steel and Teflon coupons were used (measured contact angles were 21°, 51° and 94° respectively). Short runs were performed to keep the coupon surface dry before it becomes covered with the layer of liquid. Deposition rates from short runs (e.g. 30 seconds) vs. longer ones (e.g. 300 seconds) should show a difference between dry and liquid-covered coupon surface (if any). The operating conditions and the surface properties are provided in Tables 5.2 and 5.3 respectively. Table 5.2 Operating conditions for contact angle tests Parameter Setting Air to the nozzle 0.45 m/s (setting 75, PG 426 kPa) Secondary air 0.57 m/s (setting 2.0, PG 34.6 kPa) Liquid flow 95 ml/min (setting 9) Nozzle 1/4QMJ+SUQ, Spraying Systems Co. Table 5.3 Coupon material and roughness properties at initial dep. rate tests Glass St.steel Teflon Contact angle 21° 51° 94° Surface roughness Polished glass 2B finish Treated with sand paper The weight of deposits after each experiment was measured on the analytical balance with 0.1 mg precision, and the results are given in Table E.5. It is estimated, however, that due to the sampling error, the deviation in the measurements is higher than 0.1 mg, especially for the short runs. Calculated integral deposition rates, exp,idr (Eq. (3.22)), are given in Table E.6, and plotted versus experiment duration in Figs. 5.27a−d. Chapter 5. Results and Discussions 126 It was expected that the lower contact angles would give higher deposition rates, but from the short duration tests in Figs. 5.27a−d, this could not be clearly concluded. No significant difference between the surfaces, for the upstream or downstream side, at U=0.7 m/s or U=1.0 m/s, could be observed. If any difference existed, it was within the experimental error. The exception is the Teflon coupon (at U=1 m/s, Fig. 5.27c,d), which was expected to yield lower, but showed higher deposition rates. We hypothesise that due to the higher surface roughness of the Teflon disk (after cutting, it was treated with sand paper), turbulence intensity increased and caused an increase in deposition rates. This difference is more pronounced at 1 m/s than at 0.7 m/s, since the tests at 1 m/s were performed first, and it is likely that by cleaning the Teflon coupon, surface roughness was diminished by friction. As a result, in Fig. 5.27b, there is no significant difference between the Teflon and other materials, as in Fig. 5.27d. 0 .7 m /s 1 .0 m /s Figure 5.27 Experimental integral deposition rates, exp,idr , at U=0.7 m/s and U=1.0 m/s, on different surfaces, for the upstream side (a, c) and downstream side (b, d) (Table E.6). 95% confidence intervals are estimated from 3 repeated experiments (a) (b) (c) (d) upstream downstream Chapter 5. Results and Discussions 127 Also, no significant difference between the deposition rates on a dry (short experiments) and already wet surface (longer experiments) could be observed (if any, it seems to be within the experimental error). The exception is the rough Teflon coupon (Fig. 5.27d), which showed higher deposition rates in the initial stages of deposition, on the presumably rough surface. However, after the first layer of deposits was formed, effect of surface roughness would no longer affect the deposition. To summarize, even if the partial rebounding of droplets from different surface materials may have occurred and reduced deposition rates, the difference between surfaces with contact angles 20−94° and between the rough and smooth surface became insignificant after the initial layer of deposits was formed (1−2 minutes). For the glass and st.steel coupons, differences between deposition rates on a dry and wet surface were not significant, while for the Teflon coupon, the deposition rate on a roughened dry Teflon surface seemed to be higher than on the already wetted surface (downstream side). Regarding the industrial case, it seems unlikely that changing the surface of the packing, with contact angle in the range 20−94°, could reduce the fouling rates. Although the effect of roughness requires a more detailed study, it seems that it does have effect on the deposition (especially on the downstream side), since it promotes turbulence and increases deposition. However, even an ideally smooth surface would be unable to prevent the formation of the first layer of deposits. After a layer of deposits has been formed, properties of the surface material (contact angle and surface roughness) become irrelevant for further deposition. Experimental investigation of superoleophobic materials, with contact angles higher than 150°, could show if the formation of the first layer of deposits could be prevented and the deposition reduced, if not eliminated. Chapter 6. Application of the Results to the High Temperature Unit Conditions 128 Chapter 6. Application of the Results to the High Temperature Unit Conditions Since experiments in the Cold Unit and the Hot Unit were performed for the same geometry (5 cm circular disk in a 7.5 cm circular column), deposition coefficients from the Cold Unit experiments were used to calculate deposition rates at high temperature conditions. This was done in order to support the validity of estimated deposition coefficients from the Cold Unit experiments, and perform an independent check of the results obtained in the Hot Unit. Given that the droplet size distribution in the Hot Unit could not be easily measured, it was estimated from an empirical correlation and the experimental procedure described in Section 3.9. The concentration of droplets in the aerosol in the Hot Unit experiments was estimated from HYSYS simulations of the vapour-liquid equilibrium, as given by Lakghomi [36] and by Song [52]. Predictions were based on the Peng-Robinson equation of state; experimental TBP (True Boiling Point) curves for the hydrocarbon blending components Voltesso and MEBR were supplied to the HYSYS simulator. 6.1. Estimation of droplet size distribution in the Hot Unit Measured and estimated volume median diameters from the procedure described in Section 3.9, are presented in Table E.7 in Appendix E. The correlation used (Eq. (3.37)) predicted about a 4 times larger volume median diameter than was measured in all experiments the where liquid flow rate was 10 ml/min, and about 6 times larger in experiments where the liquid flow rate was 20 ml/min. This discrepancy is most likely due to the impaction of large droplets from the spray cone on the column walls close to the nozzle, and due to the ambiguous use of the dimension ‘h’ in the correlation (as already discussed in Section 3.9). Therefore, it was concluded that the correlation would always predict about a 4 or 6 times larger volume median diameter, depending on the liquid flow. A corrected diameter is then estimated by multiplying the estimated volume median diameter from the correlation with the correction factor 0.25 or 0.17 (last column of the Table E.7). Chapter 6. Application of the Results to the High Temperature Unit Conditions 129 Volume median diameters in the Hot Unit, for experiments that investigated the effect of temperature and velocity, are shown in the last column of Table E.8 in Appendix E. These values are estimated at the temperature conditions in the nozzle. Depending on the temperatures in the chamber, a significant portion of droplets from the spray (from 94% to 98%) evaporated, reducing the droplet size. From the amount of evaporated liquid, a corrected volume median diameter is calculated and is shown in the last column. Volume median diameters of droplets approaching the coupon are between 2.5 and 4.8 microns. From these values, log-normal size distributions were generated and used in further calculations. 6.2. Deposition coefficients for high temperature unit conditions Deposition coefficients from the Cold Unit experiments are valid for tri-ethylene glycol droplets in air. In the high temperature unit experiments, the gas phase was a mixture of nitrogen and Voltesso vapours. The liquid phase feed was a mixture of heavy components of a volatile oil (Voltesso), and a heavy hydrocarbon stream (MEBR). The temperature varied between 295°C and 425°C and affected the physical properties of the gas and liquid, which were calculated using HYSYS. This required recalculation of deposition coefficients from the Cold Unit to different operating conditions. In all Hot Unit experiments, the majority of deposits were formed on the downstream side of the coupon (Song [52]); therefore, only deposition coefficients for the downstream side were used in predicting deposition rates. From the comparison of experimental results and simulations of inertial impaction with gravity in the flow direction (Section 5.5.2), we can conclude that deposition on the downstream side, in the range of droplet sizes (1−20 microns) and velocities (0−1.5 m/s), is governed by the Stokes number and velocity. Figure 6.1 shows a plot of capture efficiencies (obtained by calculation from experimental results, Section 5.3) versus Stokes number. The dependence of capture efficiencies on Stokes number is almost linear over the wide range of Stokes numbers, at all velocities. At a given Stokes number, as the velocity is raised, the capture efficiencies decline. Chapter 6. Application of the Results to the High Temperature Unit Conditions 130 Figure 6.1 Capture efficiencies calculated from experimental results for the downstream side vs. Stokes number, in the range of droplet sizes (1−20 microns) and velocities (0−1.5 m/s) Therefore, the change in the capture efficiencies at a given velocity can be predicted by the change in the Stokes number, due to the different gas viscosity and droplet density, TEG oil air UnitColdUnitHot StSt ρ ρ µ µ ⋅⋅= 2 (6.1) Over a wide range of Stokes numbers, capture efficiencies are close to a linear function of the Stokes number, CE=k⋅St. The relative change in the capture efficiencies due to the change to the hot temperature unit conditions (different droplet density and gas viscosity) can be easily deduced from the relative change of the Stokes number according to, TEG oil air UnitCold UnitHot UnitCold UnitHot Stk Stk E E ρ ρ µ µ ⋅= ⋅ ⋅ = 2 (6.2) The linear dependence does not strictly hold over the whole interval of Stokes numbers presented in Fig. 6.1, particularly at low Stokes numbers. However, since the relative Chapter 6. Application of the Results to the High Temperature Unit Conditions 131 change in the Stokes numbers is not greater than 2 times, this dependence can be approximated with the linear function in this interval, and equation (6.2) will still hold. 6.3. Comparison of results Predicted deposition rates in the Hot Unit are calculated from the Cold Unit deposition coefficients and presented in Figs. 6.2−6.4, along with the experimental Hot Unit deposition rates. Figure 6.2. represents the effect of temperature on deposition rates for 5% MEBR, and the effect of reaction. Deposition rates predicted from the Cold Unit experiments are higher than the deposition rates measured in the Hot Unit, except at 295°C, where the predicted deposition rates are lower. It is possible that the concentration of droplets at this temperature is underestimated by HYSYS. The reaction effect becomes important at temperatures above 370°C, and it can be noted that the two last points in the figure match well. Generally, we can say that a good match between the two sets of data can be observed. Also, predictions from the Cold Unit are close to the deposition rates predicted by CFD [36]. For the 10% MEBR (Fig. 6.3), deposition rates predicted from the Cold Unit deposition coefficients are up to 20% higher than deposition rates measured in the Hot Unit. Again, the reaction effect becomes important at temperatures above 370°C and good agreement between the trends of the two sets of data can be observed. The decrease in deposition rate with increasing temperature is attributed to a decrease in the concentration of aerosol droplets (Table E.9, Appendix E). Comparison of the results for the effect of velocity is shown in Fig. 6.4. Predictions from the Cold Unit are within few percent of the Hot Unit data, with exception of the data point at 0.25 m/s, where Hot Unit deposition rates are underestimated by about 30%, and one data point at 0.92 m/s, which most probably contains error. Still, good agreement between the two sets of experimental results can be observed. Chapter 6. Application of the Results to the High Temperature Unit Conditions 132 Figure 6.2 Comparison between Hot Unit deposition rates for 5% MEBR, with the predictions from the Cold Unit deposition coefficients, and CFD predictions Figure 6.3 Comparison between Hot Unit deposition rates for 10% MEBR, with the predictions from the Cold Unit deposition coefficients, and CFD predictions Chapter 6. Application of the Results to the High Temperature Unit Conditions 133 Figure 6.4. Comparison between Hot Unit deposition rates for the effect of velocity, with the predictions from the Cold Unit deposition coefficients In summary, a good agreement between the Hot Unit experimental data [52], CFD results [36], and deposition rates predicted from the Cold Unit deposition coefficients was obtained. Given the fact that the deposition coefficients at the high temperature conditions were calculated from the change in the Stokes number (Eqs. (6.1), (6.2)), and that the main parameter governing the deposition due to inertial impaction is the Stokes number, the obtained results support the hypothesis, that the main mechanisms of deposition from the vortex on the downstream side, are inertial impaction and gravity. Chapter 7. Conclusions and Recommendations 134 Chapter 7. Conclusions and Recommendations 7.1. Conclusions The objective of this work was to experimentally investigate the deposition of droplets from aerosol flow onto solid surfaces, namely a circular disk (coupon). The investigated factors included: (a) the effect of gas velocity, (b) the effect of droplet size, and (c) the effect of contact angle on deposition rates on the upstream (front) and downstream (back) side of a disk. In addition, morphology and distribution of deposits on the disk surface were studied as well. For the purpose of this work, the Cold Unit apparatus, with complete measurement and data acquisition system was successfully designed and assembled. Experiments in the Unit were carried out for an upward flowing aerosol, for a 5 cm diameter circular disk, placed in the 7.5 cm diameter column. To measure the droplet size distribution in the aerosol, a shadowgraphy technique, with a modified image analysis procedure which was different from commercial systems, was developed and used with success. A technique for measuring size and mass distribution of deposits along the coupon radius was developed as well. Furthermore, a software code for complete analysis of the individual drop size data was developed and implemented in the MATLAB ® environment. To explain the experimental results, particle transport from a potential flow, in the presence of gravity, was modeled and simulated. To account for the effect of reaction at high temperature conditions [52], the effect of decomposition of heavy oil deposits was also included in the model. The three main parameters that were used to describe deposition were: (a) deposition rates, which represent the rate of fouling at a given aerosol concentration, (b) deposition coefficients, which are independent of concentration and represent a direct measure of deposition rates and (c) capture efficiencies, which denote the extent of aerosol removal by deposition. Experiments performed with a size distribution of triethylene glycol droplets in air, showed that the main mechanism of deposition on the upstream side of the disk was inertial impaction. At superficial gas velocity of 1 m/s, Chapter 7. Conclusions and Recommendations 135 deposition on the upstream surface started at critical Stokes number Stcr=0.05, and droplet diameter Dp=27 microns. Simulations of the inertial impaction from the upward flow, obtained using the potential flow approximation, showed good qualitative agreement with the experimental results. According to the simulations, capture efficiencies are a function of the Stokes number and velocity, and increase as the velocity and Stokes numbers increase. It can be said that to reduce deposition due to inertial impaction, the Stokes number should be decreased, which means that velocity and droplet size should be reduced, or the diameter of the obstacle increased. Deposition by convective diffusion and inertia (‘eddy impaction’) from parallel flow seemed to be negligible compared to the deposition from inertial impaction. However, a more detailed study of these phenomena should be undertaken. Experimental results for the downstream side, showed that for a given droplet size distribution, deposition coefficients showed a minimum with velocity. An increase in the volume median diameter of the size distribution, from 4 to 7 microns, resulted in an increase in deposition coefficients, by a factor of three. Calculated capture efficiencies and deposition coefficients, using size distributions in the aerosol and on the coupon (in the range U=0−1.5 m/s and Dp=3−20 microns), also showed an increasing trend with the drop diameter. At higher velocities and larger droplets, it is estimated that capture efficiencies and deposition coefficients will reach a maximum and start to decrease, since the droplets would be unable to follow the curvature behind the coupon and be entrained in the vortex. Simulations performed using potential flow approximation with gravity in the flow direction, showed a good correlation with the experimental results for the downstream side. Therefore, inertial impaction and gravity were postulated to be the governing mechanisms of deposition on the downstream side. To reduce deposition on the downstream side, droplet size should be reduced, and an optimum velocity, for a given droplet size distribution, should be calculated from the deposition coefficients for each drop size. Investigation of the distribution of deposits along the radius of a glass coupon showed that, for the upstream side, deposits were more concentrated close to the edge of the coupon. On the downstream side, where the flow field is characterized by the vortex, Chapter 7. Conclusions and Recommendations 136 deposits were uniformly distributed along the radius. These results suggest that the downstream side of the packing would foul uniformly, while for the upstream side it is possible that the outer parts of packing elements would foul more rapidly than the inner parts. Therefore, inertial impaction on the upstream side should be avoided, if possible, by operating at lower superficial gas velocity and with smaller droplet sizes. The effect of contact angle on deposition was investigated in the range of 20−95°, using glass, stainless steel and Teflon coupons. The results showed that there was no significant difference in deposition rates between the surfaces. If a difference existed, it was within the experimental error. The same can be said for the effect of dry vs. wet coupon surfaces: no significant differences between deposition rates could be observed; again, if there were any, they were within the experimental error. Although the effect of surface roughness requires a more detailed study, experiments with a roughened Teflon coupon suggested that surface roughness could have an impact on the deposition, by promoting turbulence and increasing deposition of fine droplets. Lastly, results obtained from ambient temperature experiments (Cold Unit) were compared with an independent set of experimental data, obtained at high temperature conditions (Hot Unit, Song [52]). Using physical properties of the gas and liquid phase at high temperature conditions, and assuming that deposition in the wake is governed by inertial impaction and gravity in the flow direction, deposition coefficients from the ambient conditions were recalculated to the high temperature unit conditions. Good agreement between the two sets of experimental data was observed, indicating that the hypothesis of inertial impaction and gravity in the flow direction is correct. 7.2. Recommendations 7.2.1. Recommendations for further investigations in the Cold Unit For the future work, investigation of deposition in the room temperature unit could be extended at velocities above 1.5 m/s. This should give information on the effect of velocity over a wider range, and confirm or disprove the assumption that on the downstream side, at high Stokes numbers, capture efficiencies and deposition coefficients reach their maximum and start decreasing. Chapter 7. Conclusions and Recommendations 137 Regarding the droplet size effect, it would be interesting to investigate experimentally deposition on the upstream side, due to turbulent diffusion solely. To properly measure small amounts of deposit from turbulent diffusion, experiments should be performed at such conditions, where inertial impaction would not occur. Using fine monodisperse aerosols, or polydisperse aerosols without any large droplets that would impact on the upstream surface, along with the larger coupons that would lead to a smaller Stokes numbers, could be a helpful strategy. The effect of contact angle (and surface roughness) is important in the initial stages of deposition only, until the surface of the coupon becomes fully covered with the first layer of deposits (1−2 minutes). Hence, from a practical point of view, it is unlikely that increasing the contact angle in the range 20−94° could significantly reduce fouling rates in the Scrubber. The only possibility for deposit prevention via surface effects seems to be a complete repelling of bitumen droplets, or collection of bitumen droplets already deposited on the surface, with the washoil sprayed from the top (surface with the self-cleaning property). Such behaviour might be possible to achieve using superoleophobic surfaces, which exhibit contact angles higher than 150°. Experimental investigation would be the only way to prove or disprove this assumption. To find application in the Scrubber of a Fluid Coker reactor, these surfaces should maintain an oil repellent behaviour at elevated temperatures, and over a long period of time. 7.2.2. Recommendations for the industrial case To minimize fouling in the Scrubber, one should operate under conditions of minimum deposition coefficients, but to maximize heavy component droplet removal, one should operate at highest capture efficiencies. These are two opposing requirements and entail that the optimum operating conditions are determined by minimizing a cost function, which includes the cost of fouling in the scrubber and the benefits having a heavy-component free product which enters the downstream equipment. The present work was, however, limited to understanding of the effects of phenomena that govern the deposition process. Knowledge from this investigation, along with the needed economic parameters, can be used in determining the optimal operating conditions. Chapter 7. Conclusions and Recommendations 138 Unfortunately, it seems unlikely that the velocity and droplet size in the reactor could be changed purposely in order to reduce fouling. Still, understanding of the velocity and droplet size effects could be useful in predicting the change in the rate of fouling in the Scrubber, if the rate of production (reactor throughput) is changed. For example, if the production rate increases, superficial gas velocity in the Scrubber will increase (from the current U=1.35 m/s), resulting in increased deposition coefficients and deposition rates on the packing elements. Since the gaseous product stream is treated in the cyclones before it enters the Scrubber, increase in the productivity would improve removal of droplets in the cyclones by means of inertial deposition. As a result, a decrease in the droplet size would be followed by a decrease in the deposition (fouling) rate. It is possible that the two opposite effects would cancel out and that the fouling rate would remain unchanged. Nevertheless, proper calculations should include a model for deposition of droplets in the cyclones [8], to account for the simultaneous changes in velocity and droplet size. In the case where the packing in the Scrubber section needs to be redesigned, knowledge of the velocity and droplet size effect can assist in understanding the effect of local velocities. For example, from the experimental results on the upstream and downstream side, we know that high velocity regions, which lead to high Stokes numbers and deposition by inertial impaction, should be avoided. Proper predictions of the deposition rates should, however, include a more realistic fluid mechanics model, specific to the geometry of the packing. To discuss a possible fouling scenario in the Scrubber, consider an arrangement of surface elements (e.g. disks), one above the other, such as the arrangement of packing elements in the Scrubber. Capture efficiencies of disks are independent of concentration, and for a given droplet size, they are constant along the Scrubber height. Since the change in the aerosol concentration due to deposition on the packing elements is a first- order process, an exponential-like decrease in the aerosol concentration, from the bottom of the scrubber to the top, is expected. Furthermore, since capture efficiencies of larger droplets are higher than capture efficiencies of smaller droplets, it is expected that the size distribution of droplets in the aerosol will decrease along the Scrubber height. These two factors combined indicate that the fouling rate in the lower section of the Scrubber would be considerably higher than in the upper parts. Therefore, it is possible that fouling Chapter 7. Conclusions and Recommendations 139 in the lower section of the Scrubber could lead to early blockage of the grid. To avoid this situation, one could consider using larger packing elements at the bottom (lower Stokes number, and lower capture efficiencies), and allow more void space between the packing elements to distribute the fouling (deposition) rate more uniformly along the whole height of the Scrubber. Industrial data which indicates where the deposition starts would be useful. From the above discussion, it seems unlikely that by changing some of the investigated parameters (gas velocity, droplet size, contact angle, degree of surface wetting), fouling rates could be wittingly reduced or eliminated. However, fouling could be reduced by using a new packing with a different geometry, but at the same time, this may lead to a lower collection efficiency and more heavy droplets in the product stream. Even if the redesigned packing would yield a somewhat lower fouling rate, the fouling problem would still persist. Thus, attention may be shifted toward wet scrubbers without internal elements, such as spray towers [75] or venturi scrubbers [76]. These scrubbers are used to remove particles by inertial impaction (spray tower) and additional deposition mechanisms (venturi scrubber). In the case of the spray tower, which is more similar to the existing design of the Scrubber, optimum drop diameter for the washoil could be determined. If the collection efficiency using the optimal drop diameter, and given scrubber height are not sufficient to remove heavy oil droplets from the product vapour, additional separation system, installed after the scrubber, could be considered. Fibrous filters made of the stainless steel fibers, used for air cleaning [20], could be employed for this purpose. Two such filters may be installed in parallel, and operate in turn, in order to allow continuous operation and maintenance. Downward orientation of the flow, with gravity aiding the deposition, would be the best of all three possibilities (upward, horizontal, downward). References 140 References 1. Wikipedia, “Oil reserves”, http://en.wikipedia.org/wiki/Oil_reserves, Date of access: 09/15/2009. 2. Wikipedia, “Petroleum prices”, http://en.wikipedia.org/wiki/Price_of_petroleum, Date of access: 09/11/2009. 3. Wikipedia, “Unconventional oil”, http://en.wikipedia.org/wiki/Unconventional_oil, Date of access: 09/11/2009. 4. Wikipedia, “Petroleum production in Canada”, http://en.wikipedia.org/wiki/Petroleum _production _in_Canada, Date of access: 09/11/2009. 5. Mink, F. J., and Houlihan, R. N., “Tar sands”, Ullmann's Encyclopedia of Industrial Chemistry, John Wiley & Sons Inc., 2009. 6. Wikipedia, “Oil sands”, http://en.wikipedia.org/wiki/Oil_sands, Date of access: 09/15/2009. 7. Wikipedia, “Bitumen”, http://en.wikipedia.org/wiki/Bitumen, Date of access: 09/17/2009. 8. Jankovic, J., “Simulation of the Scrubber section of a Fluid Coker”, M.A.Sc. Thesis, University of British Columbia, 2005. 9. Subudhi, N., “Simulation of pressure drop and coke deposition in the grid of a scrubber”, M.A.Sc. Thesis, University of British Columbia, 2006. 10. Papavergos, P. G., and Hadley A.B., “Particle deposition behaviour from turbulent flows”, Chemical Engineering Research and Design 62, 275−295, 1984. 11. Cleaver, J. W., and Yates, B., “A sublayer model for the deposition of particles from a turbulent flow”, Chemical Engineering Science 30, 983−992, 1975. 12. Epstein, N., “Elements of particle deposition onto nonporous solid surfaces parallel to suspension flows”, Experimental Thermal and Fluid Science 14, 323−334, 1997. 13. Zhang, J., and Li, A., “CFD simulation of particle deposition in a horizontal turbulent duct flow”, Chemical Engineering Research and Design 86, 95−106, 2007. References 141 14. Tian, L., and Ahmadi, G., “Particle deposition in turbulent duct flows-comparisons of different model predictions”, Aerosol Science 38, 377−397, 2007. 15. Schlichting, H., “Boundary layer theory”, McGraw-Hill, 7th Edition, 1979. 16. Lai, A. C. K., and Nazaroff, W. W., “Modeling indoor particle deposition from turbulent flow onto smooth surfaces”, Journal Of Aerosol Science 31, No. 4, 463−476, 2000. 17. Sehmel, G. A., “Particle eddy diffusivities and deposition for isothermal flow and smooth surfaces”, Journal Of Aerosol Science 4, 125−138, 1973. 18. Young, J., and Leeming, A., “A theory of particle deposition in turbulent pipe flow”, Journal of Fluid Mechanics 340, 129−159, 1997. 19. Vincent, J. H., and Humphries, W., “The collection of airborne dusts by bluff bodies”, Chemical Engineering Science 33, 1147−1155, 1978. 20. Hinds, W., “Aerosol technology: properties, behavior, and measurement of airborne particles“, 2 nd Edition, Wiley-Interscience, 1999. 21. Friedlander, S., “Smoke, dust, and haze: fundamentals of aerosol dynamics“, 2 nd Edition, Oxford University Press, 2000. 22. Albrecht, F., “Theoretische Untersuchungen über die Ablagerung von Staub aus strömender Luft und ihre Anwendung auf die Theorie der Staubfilter”, Physikalische Zeitschrift 32, 48−56, 1931. 23. Sell, W., Forsch Gebiete Ingenieur 2, Supplement No. 347, August 1931. 24. Langmuir, J., and Blodgett K. B., "A mathematical investigations of water droplet trajectories," AAF Technical Report 5418, 1946. 25. Landhal, H. D., and Herrmann, R. G., “Sampling of liquid aerosols by wires, cylinders, and slides, and the efficiency of impaction of the droplets”, Journal of Colloid Science 4, 103−136, 1949. 26. Ranz, W. E., and Wong, J. B., “Impaction of dust and smoke particles on surface and body collectors”, Industrial and Engineering Chemistry 44, 1371−1381, 1952. References 142 27. Wong, J. B., Ranz, W. E., and Johnstone, H. F., “Inertial impaction of aerosol particles on cylinders”, Journal of Applied Physics 26, No. 2, 244−249, 1955. 28. May, K. R., and Clifford, R., “The impaction of aerosol particles on cylinders, spheres, ribbons and discs”, Annals of Occupational Hygiene 10, 83−95, 1966. 29. Gregory, P. H., and Stedman, O. J., “Deposition of air-borne Lycopodium spores on plane surfaces”, Annals of Applied Biology 40, 651−674, 1953. 30. Golovin, M. N., and Putnam, A. A., “Inertial impaction on single elements”, Industrial and Engineering Chemistry Fundamentals 1, No. 4, 264−273, 1962. 31. Noll, K. E., and Pilat, M. J., “Inertial impaction of particles upon rectangular bodies”, Journal of Colloid and Interface Science 33, No. 2, 197−207, 1970. 32. Tsai, R., and Liang, L. J., “Inertial effect on aerosol particle deposition from an axisymmetric stagnation point flow approximation”, International Communication Heat Mass Transfer 29, No. 4, 489−496, 2002. 33. Amelin, A. G., and Beliyakov, M. I., Doklady Akademii Nauk S.S.S.R. 108, No. 1, 31−39, 1956. 34. Yeomans, A. H., Rogers, E. E., and Ball, W. H., “Deposition of aerosol particles”, Journal Of Economic Entomology 42, No. 4, 591−596, 1949. 35. Goldshmid, Y., and Calvert, S., “Small particle collection by supported liquid drops”, A. I. Ch. E. Journal 9, No. 3, 352−358, 1963. 36. Lakghomi, B., “CFD simulation of aerosol flow and hydrocarbon fouling on a circular disk”, M.A.Sc. Thesis, University of British Columbia, 2009. 37. Medout-Marere V., and Douillard, J.-M., “Studies of divided solids by immersion calorimetry”, Encyclopedia of Surface and Colloid Science, Marcel Dekker Inc., New York, 2002. 38. “Cleanliness measurements using contact angles”, FTA Application Notes, 2000, http://www.firsttenangstroms.com/papers/papers.html, Date of Acces: 03/05/2009. 39. Yarin, A. L., “Drop impact dynamics: splashing, spreading, receding, bouncing…”, Annual Review of Fluid Mechanics 38, 159−192, 2006. References 143 40. Durickovic, B., and Varland K., “Between bouncing and splashing: water drops on a solid surface”, Term Paper, 2006, http://pub.bojan.info/bounce.pdf, Date Of Access: 03/05/2009. 41. Khatavkar, V. V., Anderson, P. D., and Meijer, H. E. H., “Impact of micro-drops on a solid surface”, Eindhoven University of Technology, http://www.mate.tue.nl/mate/pdfs/ 4851.pdf, Date Of Acces: 12/01/2009. 42. Rioboo, R., Tropea, C., Marengo, M., “Outcomes from a drop impact on solid surfaces”, Atomization and Sprays 11, 155−165, 2001. 43. Callies, M., and Quere, D., “On water repellency”, Soft Matter 1, 55−61, 2005. 44. Richard, D., and Quere, D., “Bouncing water drops”, Europhysics Letters 50, No. 6, 769–775, 2000. 45. Cheng, Y.-T., and Rodak, D. E., “Is the lotus leaf superhydrophobic?”, Applied Physics Letters 86, 144101, 2005. 46. Cheng, Y.-T., Rodak, D. E., Angelopoulos, A., and Gacek, T., “Microscopic observations of condensation of water on lotus leaves”, Applied Physics Letters 87, 194112, 2005. 47. Rioboo, R., Voue, M., Vaillant, A., and De Coninck, J., “Drop impact on porous superhydrophobic polymer surfaces”, Langmuir 24, 14074−14077, 2008. 48. Wang, Z., Lopez, C., and Koratkar, N., “Impact dynamics and rebound of water droplets on superhydrophobic carbon nanotube arrays”, Applied Physics Letters 91, 023105, 2007. 49. Tsujii, K., Yamamoto, T., Onda, T., and Shibuichi, S., “Super oil-repellent surfaces”, Angewandte Chemie International Edition 36, No. 9, 1011−1012, 1997. 50. Tuteja, A., Choi, W., Ma, M., Mabry, J. M., Mazzella, S. A., Rutledge, G. C., McKinley, G. H., Cohen, R. E., “Designing superoleophobic surfaces”, Science 318, 1618−1622, 2007. 51. Tuteja, A., Choi, W., McKinley, G. H., Cohen R. E., and Rubner, M. F., “Design parameters for superhydrophobicity and superolephobicity”, MRS Bulletin 33, 752−758, 2008. References 144 52. Wu, W., Wang, X., Wang, D., Chen, M., Zhou, F., Liu, W., and Xue, Q., “Alumina nanowire forests via unconventional anodization and super-repellency plus low adhesion to diverse liquids”, Chemical Communications 9, 1043−1045, 2009. 52. Song, J., “Role of aerosols in coupon fouling-Hot Unit”, Final Syncrude Canada Ltd. Report, University Of British Columbia, 2009. 53. Lokare, S. S., “A mechanistic investigation of ash deposition in pulverized-coal and biomass combustion”, Ph.D. Dissertation, Brigham Young University, 2008. 54. Bird, R. B., Stewart, W. E., Lightfoot, E. N., “Transport phenomena”, 2 nd Edition, Wiley, 2007. 55. Wilkes, J. O., “Fluid mechanics for chemical engineers”, Prentice Hall PTR, 1 st Edition, 1998. 56. Salmanzadeh, M., Rahnama, M., and Ahmadi, G., “Particle transport and deposition in a duct flow with a rectangular obstruction”, Particulate Science and Technology, 25, 401−412, 2007. 57. Beg, S. A., “Forced convective mass transfer from circular disks”, Wairme- und Stoffubertragung 1, 45−51, Springer-Verlag, 1973. 58. Yue, C., Watkinson, A. P., Lucas, J. P., Chung, K. H., “Incipient coke formation during heating of heavy hydrocarbons”, Fuel 83, 1651–1658, 2004. 59. Wigg, L. D., “Drop-size prediction for twin-fluid atomisers”, Journal of the Institute of Fuel 11, 46–52, 1964. 60. Gupta, V. S., “Boiling point and critical temperature of n-paraffins”, Journal of Chemical Physics 24, 164−165, 1956. 61. Settles, G. S., “Schlieren and shadowgraph techniques: visualizing phenomena in transparent media”, Springer-Verlag Berlin Heidelberg New York, 2001. 62. Baron, P. A., and Willeke, K., “Aerosol measurement: principles, techniques and applications”, John Wiley & Sons Inc., 2001. 63. La Vision, “ParticleMaster Shadow manual”, LaVision GmbH, Gottingen, 2008. 64. Lee, S.-Y., Kim, Y. D., “Sizing of spray particles using image processing technique”, KSME International Journal 18, No. 6, 879−894, 2004. References 145 65. Woodward, R. P., “Contact angle measurements using the drop shape method”, First Ten Angstroms, http://www.firsttenangstroms.com/pdfdocs/CAPaper.pdf, Date Of Access: 12/03/2009. 66. “Sessile drop interfacial tension measurements”, FTA Application Notes, http://www.firsttenangstroms.com/pdfdocs/SessileDropIFT.pdf, Date Of Access: 12/03/2009. 67. “Influence of drop’s volume on contact angle”, http://www.firsttenangstroms.com/ /pdfdocs/DropVolumeAndCA.pdf, Date Of Access: 12/03/2009. 68. “Cleanliness measurements using contact angles”, http://www.firsttenangstroms.com/ /pdfdocs/Cleanliness.pdf, Date Of Access: 12/03/2009. 69. Bergeron, V., and Quere, M., “Water droplets make an impact”, Physics World 14, No. 5, 27−31, 2001. 70. Cao., A., Cao, L., and Gao, D., “Fabrication of nanoaging superhydrophobic surfaces by packing flowerlike hematite particles”, Applied Physics Letters 91, 034102, 2007. 71. “Voltesso product data sheet”, http://www.imperialoil.com/Canada-English/Files/ Products_Lubes/IOCAENWPOESVoltesso.pdf, Date Of Access: 08/12/2009. 72. Humphries, W., and Vincent, J., H., “The transport of airborne dusts in the near wakes of bluff bodies”, Chemical Engineering Science 33, 1141−1146, 1978. 73. Carmody, T., “Establishment of the wake behind a disk”, Journal of Basic Engineering, Transactions of ASME, 869−882, Dec. 1964. 74. Sato, S., Vincent, J. H., Pui, D. Y. H., “Dispersion of large particles in the near wake of a disc in a turbulent free stream”, Journal of Aerosol Science 27, No. 4, 559−573, 1996. 75. Wikipedia, “Spray tower”, http://en.wikipedia.org/wiki/Spray_tower, Date Of Access: 12/02/2009. 76. Wikipedia, “Venturi scrubber”, http://en.wikipedia.org/wiki/Venturi_scrubber, Date Of Access: 12/02/2009. References 146 77. Schick R. J., “Spray technology reference guide: understanding drop size”, Spraying Systems Co., http://service.spray.com/web/register/view_lit.asp?code=B459B, Date of Access: 12/02/2009. 78. Limpert, E., Werner, S. A., Abbt, M., “Log-normal distributions across the sciences: keys and clues”, Bioscience 51, No. 5, 341−352, 2001. Appendix A. Cold Unit Operating Procedure 147 Appendix A. Cold Unit Operating Procedure A.1. Pre-experimental procedure 1. Turn the lights, fan, camera, and the balance on. Turn the computers on. 2. Place the 2.5 liter waste reservoir below the column, to collect the washdown waste stream from washing the column. 3. Wash the column from the top; clean the top flange and 30−40 cm of the column interior from the top. 4. Clean the nozzle by atomizing water (if previously worked with sugar solution) and switch to triethylene glycol for about 10−15 seconds. 5. Replace the reservoir that collected washdown waste with an empty one. 6. Fill the 4 liter reservoir on the balance with triethylene glycol. 7. Prepare softwares and file names for data logging; PC #1: 1) RSImage for shadowgraphy 2) RS232 Data Logger for balance data PC #2: 1) Transducer Technique software for Load Cell data 2) Hyper Terminal for temperature data logging. A.2. Experimental procedure 1. Measure droplet size distribution with shadowgraphy - clean glass slides from deposits - turn the pump on - open the ball valve and introduce air - wait about 10 sec for the flow to stabilize and close the ball valve quickly - wait 5 sec and start acquiring images (130 images during 14 seconds, using 60 microseconds exposure at 6x magnification) - repeat this procedure 10 times to collect sufficient number of samples. 2. Place the coupon in the column and attach it to the Load Cell. 3. Make sure that the rod is not touching the constraint and the PVC cap on the top. 4. Start logging Load Cell and Temperature data. Do not open any other Load Cell log file while logging data since data in old files will be overwritten! Appendix A. Cold Unit Operating Procedure 148 5. Wait about 15 min. for stable readings from the Load Cell and record the weight in the notebook. 6. Turn the pump on and introduce air. 7. Start logging balance data. 8. If the run will take longer than 30 min, connect the washdown reservoir on the balance with the large washdown reservoirs and make sure that all the valves are open. 9. Keep experiment running. Do not allow collecting more than 300−400mg of deposits on the coupon, since it will be difficult to remove it from the column without loosing some deposits. 10. Take images of the coupon surface when change in the slope is noticed (increase or decrease). 11. At the end of experiment, stop the air and turn the pump off. 12. Wait about 15 min for stable readings and record the total weight in the notebook. 13. Stop the Load Cell and Temperature data logging. 14. Carefully remove the coupon from the column so that droplets from the coupon surface aren’t lost. 15. Measure the weight of 7 nuts and wire (known mass) in the current load cell position, to allow load cell calibration check. 16. Take images of the upstream and downstream side of the coupon. 17. Measure coupon weight on the analytical balance: - weight of the stand - weight of the stand with the coupon and all deposits (all) - clean the rod and measure (all – rod deposits) - clean the upstream side and measure (all – rod – upstream deposits) - clean the downstream side and measure (all – rod – upstream – downstream deposits) - weight of the clean coupon A.3. Post-experimental procedure 1. Empty the waste tank and pour the liquid from the reservoirs that collected triethylene glycol, back in the 4 liter reservoir. 2. Copy data files to the office computer. Appendix A. Cold Unit Operating Procedure 149 Figure A.1 Picture of the Cold Unit apparatus Appendix B. Calibrations 150 Appendix B. Calibrations All measurement techniques (except the contact angle measurement technique) had to be calibrated. These included, a) Pump calibration for measurement of liquid flow to the nozzle and aerosol concentration (Section 4.3.1) b) Rotameter calibration for the gas velocity measurements (Section 4.3.2) c) Calibration of the shadowgraphy system for drop size distribution measurements, in the aerosol and on the coupon (Sections 4.3.3 and 4.3.4), and d) Load cell calibration for deposition rate measurements (Section 4.3.5) All calibrations are presented here, with the exception of the shadowgraphy system calibrations, which, for the continuity of presentation, were retained in the main text (Section 4.3.3.6). B.1. Pump calibration For measuring flow of liquid to the aerosol (Section 4.3.1.1), the gear pump had to be calibrated. Full scale on the console drive was divided into 30 equidistant sections, further divided into 4 smaller sections each (Fig. 4.11). The pump was calibrated without and with differential pressure (200−300 kPa) between the inlet and the outlet. Liquid was pumped from the reservoir placed on the balance, and the data from the balance were logged into a file. Mass flow rate of the liquid was estimated from the slope of the weight loss curve, and recalculated to the liquid volume flow. There was no significant difference (lower than 1 ml/min) between the liquid flow rates measured with and without differential pressure (Fig. B.1). Although the manufacturer specified increase in the liquid flow over the entire range, above pump setting 9 (close to one third of the full scale), there was no additional increase in the liquid flow. This is most likely due to imperfect sealing of gears, or their imperfect placement in the pump casing. Therefore, each time after the gears are Appendix B. Calibrations 151 replaced, the calibration should be checked. In the range 0−9, liquid flow proved to be linearly dependent on the pump setting. Figure B.1 Gear pump calibration curve, with and without differential pressure (200−300 kPa) The details of the equipment used are as follows. The pump head was RK-07002- 27 Micropump ® A-mount Suction Shoe Pump Head from Cole Parmer, with graphite gears and PTFE seals. It was mounted on the RK-75211-10 Cole Parmer Console Drive. For measuring liquid flow rate to the aerosol, an Ohaus Ranger balance, with 6 kg capacity and 0.1 g precision was used. The balance was connected to the serial port on the computer equipped with RS-232 Data Logging software. Communication setting in the software were set to: Baud rate: 300 bps, Data bits: 7, Parity: None, Stop bits: 1 and Flow control: None. Data from the balance were read each 0.5 seconds. Appendix B. Calibrations 152 B.2. Rotameter calibration All three rotameters on the Cold Unit Apparatus (Fig. 4.1) had to be calibrated. Rotameter #1 was Brooks model No. 8408-2193, 0−300 l/min, Rotameter #2 was Brooks type 9-1110, 0−300 l/min, and Rotameter #3 was from Cole Parmer, 0−100 l/min. B.2.1. Theoretical background Rotameter is a flow-measuring device that depends on the change of an annular area Aan between the float and the tube, which is a function of the vertical location of the float, to yield essentially fixed pressure drop at all flow rates (Fig. B.2) Figure B.2 Schematic representation of the rotameter float After solving equations for conservation of mass, energy and upward momentum for the flow around the rotameter float [55], the flow rate can be expressed as, tubef an A Mg AQ ρ 2 = (B.1) where M is the mass of the float, Atube is the tube area, and ρf is the density of the fluid flowing through the rotameter. After replacing RT PM w f =ρ , at each position of the float, at the constant temperature T, product PQ is a constant. The flow of air at pressure P, can be then calculated from the calibration data (Q0 vs. P0) as, P k P P QPQ p 1 )( 00 == (B.2) where kp is the rotameter constant, 00 PQk p = . The flow of air in the column at P0 = 101.3 kPa can be then calculated from the flow of air through the rotameter as, Mg Annular area Aan Tube area Atube Appendix B. Calibrations 153 0 , 0 P P QQ pcolumn = (B.3) B.2.2. Experimental Rotameter #1 was calibrated by connecting it in series with the mass flow meter K-2908-23 from Cole Parmer, capacity 0−50 l/min. The inlet of the mass flow meter was connected to the outlet of the rotameter and readings at 15 points were recorded (Table B.1). Data were fitted with a second order polynomial. Limited flow range allowed calibration of only one part of the total scale (0−70), but the curve was extrapolated with confidence to the range (70−100). Rotameter #2 was calibrated by connecting it in series with the high flow capacity rotameter, with the calibration curve from the manufacturer (Brooks rotameter type 1110- 13B-A, tube size: R13M-25-1 BR-2-18G10, float: 13-RS-510, max. capacity approximately 3000 l/min). Schematic of the measurement setup is given in Fig. B.3, and the data points are given in Table B.2. Rotameter #3 was calibrated using the above mentioned mass flow meter (K- 2908-23). Calibration was performed for 12 points over the scale 0−50. Pressure did not increase appreciably above the atmospheric pressure, and no corrections were included. Values for the range 50−80 were obtained by extrapolation (Table B.3). Figure B.3 Rotameter #2 calibration setup. Rotameter #2 (A) is connected in series with the rotameter with the calibration curve from the manufacturer (B). PG-1 PG-2 PG-3 A B Appendix B. Calibrations 154 Table B.1 Rotameter #1 calibration data Setting PG, (psi) Flow of air at P0=14.7 psi (l/min) k = Q⋅√(P0+PG), (m 3⋅s-1⋅psi0.5) 0 0 3.37 0.00022 5 0 7.17 0.00046 10 0 10.91 0.00070 15 0.5 14.84 0.00093 20 1 18.67 0.00115 25 1 22.71 0.00140 30 1.5 26.76 0.00163 35 2 30.76 0.00184 40 2.5 34.6 0.00204 45 3 39.01 0.00227 50 3.2 43 0.00249 55 3.8 47.04 0.00268 60 4.2 51.29 0.00289 65 5 55.45 0.00306 70 5.5 60.29 0.00329 75 64.34 0.00346 80 68.74 0.00365 85 73.18 0.00383 90 77.66 0.00401 95 82.18 0.00418 100 86.74 0.00435 Appendix B. Calibrations 155 Table B.2 Rotameter #2 calibration data Rot A setting PG-1 (psi) Rot B setting PG-2 (psi) PG-3 (psi) kB (m/hr) Q (m 3 /s) at PG-3 (psi) Q (m 3 /s) at PG-1 (psi) kA=Q⋅√ (P0+PG), (m 3⋅s-1⋅psi0.5) 3.4 8.5 10.8 0.4 0 0.0175 0.0046 0.002891 0.013924 3.3 8.2 10.4 0.3 0 0.0169 0.0044 0.002835 0.013565 3.2 8 9.9 0.25 0 0.0162 0.0042 0.002741 0.013061 3.1 7.9 9.4 0.2 0 0.0155 0.0041 0.002635 0.012527 3 7.7 9.2 0.15 0 0.0153 0.0040 0.002611 0.012357 2.9 7.5 8.7 0.05 0 0.0146 0.0038 0.002514 0.011847 2.8 7 8.2 0 0 0.0139 0.0036 0.00245 0.011412 2.7 6.9 7.7 0 0 0.0132 0.0034 0.002338 0.010868 2.6 6.6 7.3 0 0 0.0126 0.0033 0.002272 0.010486 2.5 6.3 7 0 0 0.0122 0.0032 0.002229 0.010215 2.4 6 6.6 0 0 0.0117 0.0030 0.00216 0.009826 2.3 5.8 6.3 0 0 0.0112 0.0029 0.002104 0.009525 2.2 5.6 5.9 0 0 0.0107 0.0028 0.002021 0.009106 2.1 5.2 5.5 0 0 0.0102 0.0026 0.001957 0.008728 2 5 5.2 0 0 0.0097 0.0025 0.001897 0.008419 1.9 4.9 4.8 0 0 0.0092 0.0024 0.0018 0.00797 1.8 4.8 4.4 0 0 0.0087 0.0023 0.001703 0.007519 1.7 4.7 4.2 0 0 0.0084 0.0022 0.001658 0.007303 1.6 4.4 3.9 0 0 0.0080 0.0021 0.001603 0.007004 1.5 4.2 3.6 0 0 0.0076 0.0020 0.001537 0.006684 1.4 4.1 3.2 0 0 0.0070 0.0018 0.001436 0.006225 1.3 4 2.9 0 0 0.0066 0.0017 0.001361 0.005884 1.2 3.9 2.6 0 0 0.0062 0.0016 0.001285 0.005542 1.1 3.8 2.4 0 0 0.0060 0.0016 0.001237 0.005319 1 3.6 2.1 0 0 0.0056 0.0015 0.001166 0.004988 0.9 3.5 1.9 0 0 0.0053 0.0014 0.001116 0.004761 0.8 3.5 1.6 0 0 0.0049 0.0013 0.001032 0.004402 0.7 3.2 1.4 0 0 0.0046 0.0012 0.000992 0.004197 Appendix B. Calibrations 156 Table B.3 Rotameter #3 calibration data Setting Flow of air at P0=14.7 psi (l/min) k=Q⋅√(P0+PG), (m 3⋅s-1⋅psi0.5) 4 5.2 0.000332 6 7 0.000447 8 9 0.000575 10 11.1 0.000709 15 16.9 0.001080 20 22.6 0.001444 25 28.1 0.001796 30 34.1 0.002179 35 39.7 0.002537 40 46 0.002939 45 52.1 0.003329 50 58.3 0.003725 60 71.2 0.004401 70 84.4 0.005197 80 98.2 0.006013 90 112.3 0.006849 100 126.9 0.007705 Appendix B. Calibrations 157 B.3. Load cell calibration Although the load cell was calibrated from the manufacturer, it was also calibrated in the laboratory, when installed on the Cold Unit. For this purpose, a wire with ten nuts, whose weight was determined on the analytical balance (0.1 mg precision), were used. Nuts were successively added to the load cell, and the total weight from the display was recorded, 2 minutes after each new nut was added. ‘True’ vs. measured values of the weight of nuts were plotted on the graph, and the calibration curve was determined by linear interpolation. Figure B.4 shows calibration curve for the second load cell. In addition, because of great sensitivity of the load cell to its position in the horizontal plane, after each run, a weight of known mass that is similar to the weight of the coupon and the rod (a wire and 7 nuts, ~25 g) was measured on the load cell, to correct the calibration curve for that position of the load cell. Calibration curve was determined for the each new load cell used. Figure B.4 Calibration curve for the second GSO-50 load cell used. The curve is approximately linear and it can be seen that, in this case, true values are about 11% larger than measured. Appendix C. Equation Development 158 Appendix C. Equations Development The following sections contain development of the equations that were deployed in this work. Derivations of the deposition model (Section 3.5.1), and the reaction model (Section 3.7), due to their brevity, were retained in the main text. C.1. Inertial particle transport from potential flow C.1.1. Equations of particle motion Let us consider an axisymmetric flow around a disk, as presented in Fig. C.1, Figure C.1 Schematic representation of the flow field in front of the disk and fluid velocity components The equation of particle motion in vector notation, in the presence of gravity field and under the assumption of Stokes drag force on the particle is given by, gmuvD dt umd p +−= )(3 )( πµ (C.1) where u is the particle velocity, v is the fluid velocity, and gm is the gravity force. If the vector notation is removed, for each component we can write, x: pmguvD dt mud xxp x +−= )(3 )( πµ (C.2a) r: )(3 )( rrp r uvD dt mud −= πµ (C.2b) where parameter { }1,0,1−∈p denotes a direction of the gravity field. The X-component can be further written as, r x vr vx v u Appendix C. Equation Development 159 033 2 2 =−−+ pmgvD dt dx D dt xd m xpp πµπµ (C.3) or, { { 0 1818 2 2 22 =−−+ pg D v dt dx dt xdD pp t p x t p µ ρ µ ρ (C.4) Now we can introduce dimensionless coordinates cc R r r R x x == , , dimensionless time cR v tt 0⋅= , and dimensionless velocities 0v v v xx = , 0v v v rr = . After differentiation of the first two relations, we get xdRxd c 22 ⋅= and 2 2 0 2 td v R dt c ⋅ = , which when used in the X-component particle motion equation give, x: 02 0 2 2 =−−+ v gt pv td xd td xd St p x (C.5) where c p R vt St 2 0= is the Stokes number. Similarly, for the r-component we get, r: 02 2 2 =−+ rv td rd td rd St . (C.6) C.1.2. Flow field from potential flow approximation The velocity components of the flow field around the coupon, from the potential flow approximation are given by [26, 31], x: 0 2 1 ,2 <<−−= xxv x (C.7a) r: 11, <<−= rrv r (C.7b) Appendix C. Equation Development 160 These equations were obtained from the axisymmetric potential flow approximation around a disk. After integration of Eqs. (C.7a,b), axial and radial coordinates of the streamlines are, texx 20 −⋅= (C.8a) terr 20 −⋅= (C.8b) where 00 , rx are initial positions at 0t . C.1.3. Capture efficiencies for Stokesian particles If we substitute equations of the flow field into the Eqs. (C.5), (C.6), we get, x: 022 0 2 2 =−++ v gt px td xd td xd St p (C.9a) r: 02 2 2 =−+ r td rd td rd St (C.9b) These are two linear, second-order, ordinary differential equations, which can be solved separately. First equation is non-homogeneous and the second one is homogeneous equation. C.1.3.1. X-component particle trajectory For the first equation, solution can be found as a sum of homogeneous and particular solution, PH xxx += (C.10) Homogeneous solution can be found in the form, tztz H eCeCx 21 21 += (C.11) where parameters z1 and z2 are obtained as a solution of the characteristic equation, 022 2 =++⋅ zzSt (C.12) Appendix C. Equation Development 161 St St z 4 1611 2,1 −±− = (C.13) a. Conjugate complex roots (St > 1/16) If we write iz βα +=1 and iz βα −=2 , where St4 1 −=α and St St 4 161− =β , homogeneous part of the solution is, titi tittit titi H eAeA eeCeeC eCeCx ββ βαβα βαβα − − −+ += += += 10 21 )( 2 )( 1 (C.14) Components tie β and tie β− provide a basis for the two-dimensional "solution space" of the second order differential equation, meaning that the linear combinations of these solutions will also be solutions. From the Euler’s formula, we can get 2 )cos( ϕϕ ϕ ii ee −+ = and i ee ii 2 )sin( ϕϕ ϕ −− = , meaning that homogeneous solution can be also written in the form, )sin()cos( 21 teCteCx tt H ββ αα += (C.15) Particular solution is equal to some constant, wx P = , which after differentiation and use in the characteristic equation leads to, 0 2002 v gt pwSt p=++⋅ (C.16) 00 2 1 2 1 v gt px v gt pw p p p =⇒= (C.17) The solution is finally, 0 21 2 1 )sin()cos( v gt pteCteCxxx ptt PH ++=+= ββ αα (C.18) Appendix C. Equation Development 162 Constants C1 and C2 can be determined from the initial conditions at 0=t . From 0)0( xx = we get, 0 01 2 1 v gt pxC p−= (C.19) and from ( ) 00 2 2 = td xd (velocity of the particle is equal to the fluid velocity), we have, 0 02 v gt px td xd p=+ (C.20a) βα 21 0 02 CC v gt px td xd p +=+−= (C.20b) β α ) 2 1 )(2( 0 0 2 v gt px C p−+− = (C.20c) After rearranging, the solution is finally, 00 0 2 1 )sin( 2 )cos( 2 1 )( v gt ptt v gt pxetx ppt + + − −= β β α βα (C.21) b. Real roots (St < 1/16) The solution is a sum of homogeneous and particular solution, 0 21 2 1 21 v gt peCeCx ptztz ++= (C.22) From the initial conditions at 0=t , 0)0( xx = we have, 0 210 2 1 v gt pCCx p++= (C.23a) 0 102 2 1 v gt pCxC p−−= (C.23b) Appendix C. Equation Development 163 and from ( ) 00 2 2 = td xd , tztzp eCzeCz v gt px td xd 21 2211 0 0 0 2 +=+−= (C.24a) − − + = 0 0 12 2 1 2 12 v gt px zz z C p (C.24b) The constant C2 can be then calculated as, − − + = 0 0 21 1 2 2 12 v gt px zz z C p (C.25) The solution is finally, 021 1 12 2 0 0 2 122 2 1 )( 21 v gt pe zz z e zz z v gt pxtx ptztzp + − + + − + −= (C.26) C.1.3.2. r-component particle trajectory For the r-component, there is only a homogeneous solution, tztz H eCeCr 21 21 += (C.27) Initial condition 0)0( rr = at 0=t gives, tztz eCeCr 21 210 += (C.28a) 210 CCr += (C.28b) 102 CrC −= (C.28c) And from the second initial condition, 0)0( = td rd , tztz ezCezC 21 22110 += (C.29a) 2211 zCzC −= (C.29b) Appendix C. Equation Development 164 − = 12 2 01 zz z rC (C.29c) The constant C2 is then, − = 21 1 02 zz z rC (C.29d) The solution is finally, tztz e zz z re zz z rtr 21 21 1 0 12 2 0)( − + − = (C.30) C.1.3.3. Capture efficiencies a. *o gravity (p = 0) In the case of no gravity (p = 0), capture efficiencies can be determined analytically. The X-component solution simplifies to, + −= )sin( 2 )cos()( 0 ttextx t β β α βα (C.31) If we set 0)( =tx , we will have )sin( 2 )cos( tt β β α β + = . The time needed for particle to reach the surface plane at 0=x is given by, − ⋅ = 18 4 tan 1 ' St St at β β (C.32) At the time 't , the r component will be, ' 21 1 0 ' 12 2 0 21)'( tztz e zz z re zz z rtr − + − = (C.33) We are interested in particles for which at time 't , r ≤ 1, which means they have reached the coupon surface, Appendix C. Equation Development 165 ' 21 1 0 ' 12 2 0 211 tztz e zz z re zz z r − + − = (C.34) ' 1 ' 2 12 0 21 tztz ezez zz r − − = (C.35) All particles, with 0r lower than the value defined by Eq. (C.35), will reach the coupon surface. Fraction of particles approaching, which finally impacts the coupon surface (capture efficiency) is then, 2 ' 1 ' 2 12 2 0 21 − − == tztz ezez zz rE (C.36) This equation is equivalent to the equation reported by Ranz and Wong [26]. Figure C.2. explains the calculation of capture efficiencies in 3-D, from the results obtained using the 2-D axysimmetric model. Figure C.2 Schematic representation of limiting droplet trajectories and the way that capture efficiencies for disk are obtained b. With gravity (p = 1, p = -1) When gravity is present, time needed for particles to reach the coupon surface plane at 0=x must be determined numerically, by solving the nonlinear equation for t , 0 2 1 )sin( 2 )cos( 2 1 )( 00 0 =+ + − −= v gt ptt v gt pxetx ppt β β α βα (C.37) Once the time t is determined, capture efficiency can be calculated from the Eq. (C.36). NO Deposition NO Deposition Limiting trajectory Deposition … … C.E. is 1/3 in 2-D… but (1/3) 2 in 3-D Appendix C. Equation Development 166 C.1.4. Capture efficiencies for non-Stokesian particles Non-Stokesian drag force is better representation of the real drag force, especially for larger particles. In this case, differential equations are nonlinear, and particle trajectories must be obtained by numerical integration of the system of two, second order, nonlinear ordinary differential equations (C.38a,b), x: 0 12 0 2 2 =−−+ v gt p k v td xd td xd k St p D x D (C.38a) r: 0 2 2 2 =−+ r D v td rd td rd k St (C.38b) where for the coefficient kD, we use 3/2 3/2 )( 6 1 1Re 6 1 1 24 Re − +=+== a apD D uvDC k µ ρ . Detailed equations are then, x: 0 )( 6 1 1 1 )( 6 1 1 2 0 3/22 2 3/2 = −+ −−+ −+ v gt p v td xdD v td xd td xd v td xdD St p x a ap x x a ap µ ρ µ ρ (C.39a) r: 0 )( 6 1 1 2 2 2 3/2 =−+ −+ r r a ap v td rd td rd v td rdD St µ ρ (C.39.b) After incorporating equations of the flow field (Eqs. (C.8a,b)), we get, x: 0 )2( 6 1 1 1 2 )2( 6 1 1 2 0 3/22 2 3/2 = ++ −++ ++ v gt p x td xdD x td xd td xd x td xdD St p a ap a ap µ ρ µ ρ (C.40a) r: 0 )( 6 1 1 2 2 2 3/2 =−+ −+ r td rd td rd r td rdD St a ap µ ρ (C.40b) This system can be transformed into the system of 4 ODE’s, Appendix C. Equation Development 167 ( ) ( )23,3 2 2 2 3 2 2 0 01 , 0 01 ,1 2 0 2 1 0 0 2 2 1 2 2 1 2 2 xx St k td xd td xd x td xd xr v gt p St xx St k v gt p k xx St k td xd td xd x td xd xx rD pxDp x xD +−== = = +−−= +−−== = = (C.41) where, 3/2 , )2( 6 1 1 ++= x td xdD k a ap xD µ ρ , and 3/2 , )( 6 1 1 −+= r td rdD k a ap rD µ ρ . Initial conditions are, 0 1 2 3 02 0, 01 00 = = +−= = x rx v gt p k xx xx p xD (C.42) To calculate capture efficiencies for this case, trajectories of 100 particles, positioned at a distance 5.0−=x , and 1,...,02.0,01.0,0=r were calculated. A particle was counted as deposited if at the time when it reached 0=x , its radial position was 1≤r , meaning that it did not go around the disk. Number of deposited particles was then divided by the total number of particles (one hundred) and squared to yield the capture efficiency (see Fig. C.2). This procedure in the form of pseudocode is given below, while its implementation in the Mathcad Professional 2001 software is given in Appendix D. Appendix C. Equation Development 168 ----------------------------------------------------------------------------------------- %Integrates system of differential equations from time t=0 to t=tmax, from the position %(x0,r0), for particle diameter Dp and fluid velocity V0. Orientation of gravity is %determined by parameter p. function xr(tmax,Dp,V0,x0,r0,p) Integrate ODE system with the given initial condition, from t=0 to t=tmax (function ‘Rkadapt’ in Mathcad, Runge-Kutta method of 4th order) Return x,r coordinates of the last point at t=tmax end ----------------------------------------------------------------------------------------- %Solves nonlinear equation and returns time at which x = 0 function time(t0,Dp,V0,x0,r0,p) Solve nonlinear equation xr(t,Dp,V0,x0,r0,p)1 = 0 for t, with the initial guess t=t0 (Solve block in Mathcad, Levenberg-Marquardt method). Return obtained time, t end ----------------------------------------------------------------------------------------- %Calculates capture efficiency by simulating particle trajectories of 100 particles %injected at equidistant points, starting from (x,r) = (-1,0) to (x,r) = (-1,1). function efficiency (Dp,V0,x0,r0,p) Guess the time needed for particle to reach the coupon surface (t0 = 1) Calculate the time needed for particle to reach x = 0 (call function 'time') and assign the result to tmax for i = 1 to 100 Integrate ODE system (call function 'xr', with obtained tmax) Assign the obtained result to xfinal and rfinal if (rfinal<1) and (xfinal>0.0001) Increase number of particles that reached the coupon surface n = n + 1 end Calculate the efficiency: Efficiency = (n/100)^2 end end ----------------------------------------------------------------------------------------- C.1.5. Distribution of deposits along the coupon radius If we use time needed for particle to reach the coupon surface from Eq. (C.32) and substitute it into Eq. (C.30), we get, ' 21 1 0 ' 12 2 0 21)'( tztz e zz z re zz z rtr − + − = (C.43) This value is constant for a given droplet size and velocity. It can be restated as, Appendix C. Equation Development 169 0 ' 21 1 0 ' 12 2 00 21)( rconste zz z re zz z rrr tztz ⋅= − + − = (C.44) This equation states that the final position of the particle on the disk is linear function of its initial radial position where the particle is injected. This leads to the conclusion that, according to this model, deposits should be uniformly distributed along the coupon radius. C.2. Drop diameter on a surface In each case when the contact angle of droplet sitting on a solid surface is less than 180º (which means always), the measured droplet diameter is larger than the diameter of the same droplet before deposition. If the spherical cap is assumed, and the contact angle of droplets on the surface is known, real droplet diameter can be calculated. Geometry of the drop on a surface is schematically shown in Fig. C.3. Figure C.3 Spherical cap model for droplets deposited on the coupon surface Volume of the spherical cap, V, is given by, ( ) hhaV ⋅+⋅⋅= 223 6 π , (C.45) and from the figure we can see that, ( )θ−⋅−=−= 90sinrrxrh , (C.46) which is equivalent to, ))cos(1()cos( θθ −⋅=⋅−= rrrh . (C.47) Also it can be noted that, r h D’p=2a θ α a x Dp<D’p in the aerosol on the surface deposition Appendix C. Equation Development 170 ( ) ( )θθ sin90cos ⋅=−⋅= rra . (C.48) This gives, ( ) )sin( cos1 2 ' θ θ− ⋅= p D h (C.49) which by the use of half-angle identities, can be presented as, ⋅= 2 tan 2 ' θpD h . After incorporating this into the equation for the volume we get, + ⋅⋅= 33' 2 tan 2 tan3 48 θθπpD V (C.50) If we equate this expression with the expression for the volume of the spherical droplet 6 3πpD V = , we arrive to the following expression for the droplet diameter, 44444 344444 21 )( 3 3 ' 2 tan 2 tan3 2 1 θ θθ k pp DD + ⋅= . (C.51) This equation was used in the Matlab codes shadow.m and coupon.m (Appendix D). Some correction factors k(θ), for several contact angles θ, are given in Table C.1. In this work, droplets of tri-ethylene glycol on the glass or acrylic plate with contact angles 20° and 43° were observed. Table C.1 Correction factor for different contact angles Angle, θ (º) 20 40 60 90 k(θ) 0.406 0.522 0.622 0.794 Appendix D. Software codes 171 Appendix D. Software codes D.1. Image Pro Plus macros Macros written in the Image Pro Plus software were used for automatization of the image analysis process. If the image analysis process was not programmed, analysis of shadowgrahy images would be a tedious and practically impossible task. Macro procedure ‘coupon’ analyzes images of coupon deposits; it opens sequences of 120 images recorded along the coupon radius and extracts every fourth image. It flattens images, loads Image Pro Plus environment settings and histogram ranges for the image segmentation and performs analysis. It measures object area, maximum, minimum and median diameter, and writes results into files. Macro procedure ‘shadowgraphy’ analyzes shadowgraphy images of droplets in the aerosol; opens sequences of 130 images and performs analysis. It measures and reports the same variables as the macro procedure ‘coupon’. The structure of the input and output files are described inside the code and should be strictly followed. Parameters regarding the number of runs to be processed automatically, and the number of samples that are supplied, should be changed in the code, accordingly. coupon ‘Analyzes images of coupon deposits. Opens image sequence of 120 images along the coupon ‘radius and takes every fourth image from it. Flattens image, loads environment settings ‘and histogram ranges and performs analysis. Measures Area, Dmax, Dmin, and Dmean and ‘writes results into files. Sub coupon() 'Input: For each run provide 4 image sequences with 120 images each, for upstream and ‘downstream side both. Files should be named as 1-u-1.tif, 1-u-2.tif, ... 1-d-1.tif, ..., ‘1-d-4.tif where the first letter is the run number, second denotes upstream or ‘downstream side, and the third letter represents the sample number (1-4). 'Output: 1)30 files for each image (window) along the coupon radius (e.g. 1-u-1-1.txt, ‘... 1-u-1-30.txt), 2) 1 file for each sample-image sequence (e.g. 1-u-1.txt), 3) 1 file ‘for all 4 samples on the upstream and downstream surface (e.g. 1-u.txt, 1-d.txt) 'Parameters: 'r1' and 'r2' are first and last run number, and 'samples' is the number of ‘samples 'Declaration of variables and definition of constants' Const N = 120 'adjust to the number of images in the frame sequence' Dim i, j, k, m, r1, r2, samples As Integer Dim side As String Appendix D. Software codes 172 'first and the last run number' r1 = 1 r2 = 10 ‘number of samples of image sequences on the coupon side’ samples = 4 For i = r1 To r2 For m = 1 To 2 If m = 1 Then side = "u" Else side = "d" End If For j = 1 To samples For k = 1 To N 'Opening the sequence' ret = IpSeqOpen("C:\My Documents\WORK\images\" + Right$(Str(i), Len(Str(i))-1) + "-" + side + "-" + Right$(Str(j), Len(Str(j))-1) + ".tif", "tif", (k-1)*4, 1) 'Image processing' ret = IpFltFlatten(0, 15) ret = IpFltFlatten(0, 15) 'Loading environment settings and histogram ranges' If side = "u" Then ret = IpBlbLoadSetting("C:\My Documents\WORK\coupon- settings\environmentsettings-convexhull.env") Else ret = IpBlbLoadSetting("C:\My Documents\WORK\coupon- settings\environmentsettings.env") End If ret = IpSegLoad("C:\My Documents\WORK\coupon- settings\colorsettingsR(255)G(200)B(255).rge") 'Counting' ret = IpBlbCount() ret = IpBlbUpdate(0) 'Writting data to a file' ret = IpBlbSaveData("C:\My Documents\WORK\coupon-results\" + Right$(Str(i), Len(Str(i))-1) + "-" + side + "-" + Right$(Str(j), Len(Str(j))-1) + "-" + Right$(Str(k), Len(Str(k))-1) + ".txt", S_DATA) ret = IpBlbSaveData("C:\My Documents\WORK\coupon-results\" + Right$(Str(i), Len(Str(i))-1) + "-" + side + "-" + Right$(Str(j), Len(Str(j))-1) + ".txt" , S_APPEND) ret = IpBlbSaveData("C:\My Documents\WORK\coupon-results\" + Right$(Str(i), Len(Str(i))-1) + "-" + side + ".txt" , S_APPEND) 'Close the image from the sequence' ret = IpDocClose() Next k Next j Next m Next i End Sub shadowgraphy ‘Analyzes shadowgraphy images of droplets in the aerosol or on the coupon. Opens image ‘sequence of 130 images, flattens images, loads environment settings and histogram ranges ‘and performs analysis. Measures Area, Dmax, Dmin, and Dmean and writes results into ‘files. Sub shadowgraphy() Appendix D. Software codes 173 'Input: For each run provide 10 samples (image sequences) with 130 images each. Files ‘should be named as 1-1.tif, 1-2.tif...1-10.tif where the first is the run number and ‘the second is the sample number 'Output: 1) 5 files with results of 2 adjacent samples joined into one new sample (e.g. ‘ 1-1.txt,...,1-5.txt) and 2) 1 file of all samples joined together (e.g. 1.txt) 'Parameters: change 'r1' and 'r2' for first and last run number, and 'samples' to the ‘number of samples 'Declaration of variables and constant definition' Const N = 130 'adjust to the current number of pictures in the frame sequence - 1' Dim i, j, k, s, r1, r2, samples As Integer 'first and last run number' r1 = 1 r2 = 10 ‘number of samples (of image sequences) in the aerosol’ samples = 10 For i = r1 To r2 Step 1 For j = 1 To samples 'Choosing folder name for the each sample' If (j=1) Or (j=2) Then s=1 ElseIf (j=3) Or (j=4) Then s=2 ElseIf (j=5) Or (j=6) Then s=3 ElseIf (j=7) Or (j=8) Then s=4 ElseIf (j=9) Or (j=10) Then s=5 End If For k = 0 To N-1 'Opening the sequence' ret = IpSeqOpen("C:\My Documents\WORK\images\" + Right$(Str(i), Len(Str(i))-1) + "-" + Right$(Str(j), Len(Str(j))-1) + ".tif", "tif", k, 1) 'Image processing' ret = IpFltFlatten(0, 15) ret = IpFltFlatten(0, 15) 'Loading environment settings and histogram ranges' ret = IpBlbLoadSetting("C:\My Documents\WORK\shadow- settings\environmentsettings.env") ret = IpSegLoad("C:\My Documents\WORK\shadow- settings\colorsettingsR(255)G(200)B(255).rge") 'Counting' ret = IpBlbCount() ret = IpBlbUpdate(0) 'Writting data to a file' ret = IpBlbSaveData("C:\My Documents\WORK\shadow-results\" + Right$(Str(i), Len(Str(i))-1) + "-" +Right$(Str(s), Len(Str(s))-1) + ".txt", S_APPEND) ret = IpBlbSaveData("C:\My Documents\WORK\shadow-results\" + Right$(Str(i), Len(Str(i))-1) + ".txt" , S_APPEND) 'Close image from the image sequence' ret = IpDocClose() Next k Next j Next i End Sub Appendix D. Software codes 174 D.2. MATLAB ® codes To analyze results on the size of individual droplets reported by Image Pro Plus, script files in the MALAB ® software were programmed. Script file ‘shadow.m’ generates size distribution from the data reported by Image Pro Plus. Firstly, it recalculates drop size from pixels into microns and computes size distribution based on the specified number of classes or class width. Then, it applies border and depth of field correction and deals with the outliers. It performs curve fitting with the log-normal distribution function (‘fdist.m’). Finally, it reports the main results on the screen and plots results for relative and cumulative frequencies of the distribution curve. All results are then written into files. This script is used for analysis of drop size distribution in the aerosol and on the coupon (it covers fitting modal and bimodal size distribution for the upstream side). Script file ‘coupon.m’ processes data on the individual droplet sizes of coupon deposits and generates size distribution. It calculates minimum, maximum and median diameter,number of droplets, mass fraction and surface coverage along the coupon radius, for both upstream and downstream side. It displays results on the screen and writes results into files. Script file ‘eff.m’ is used to calculate deposition coefficients of individual drop sizes at given velocity (Section 5.3). All other scripts (functions) used, ‘eff.m’ ‘f2normlognormalcdf.m’, ‘f2normlognormalpdf.m’, ‘fcdf.m’, ‘fdist.m’, ‘fdmean.m’, ‘flognormalcdf.m’, ‘flognormalpdf.m’ and ‘fpdf.m’, are called from these three main scripts. coupon.m %Calculates: Dmin, Dmax, Dv50, Number of droplets, Mass fraction and Surface coverage %along the coupon radius, for both upstream and downstream side. Displays results on the %screen and plots the figures, then writes results into files. %%INPUT SECTION %Input the run number only (e.g. 1). Program automatically goes through all downstream %and upstream files (e.g. 1-u-1-1.txt, 1-u-1-2.txt....1-d-1-1.txt etc.) %Files must be provided by Image Pro Plus and placed in the directory defined by datapath %File naming e.g.: 1-d-2-3.txt (1-run number, d-downstream side (‘d’ or ‘u’), 2-sample %number (1-4), window number (1-30). clear all; sample = input ('1.Sample number: ','s'); magnification = input('2.Magnifications used [upstream, downstream]: '); Appendix D. Software codes 175 choice = input('3.Size distribution of: (1)Dmax, (2)Dmin, (3)Dmean: '); nwchoice = input('3.Define: (1)Number of Classes, (2)Class Width: '); if nwchoice == 1 nclasses = input('3a.Number of classes: '); nw0 = [nclasses; 0]; %set zero where not defined else cwidth = input('3b.Class width(um): '); nw0 = [0; cwidth]; %set zero where not defined end outlier = input ('4.Remove outliers larger than (default is 100 um):'); if isempty(outlier) outlier = 100; end diam = 2*0.0254; %coupon diameter N = 30; %number of images in the sample sequence datapath = 'C:\Documents\WORK\coupon-results\'; %calculate no. of microns per pixel (from the calibration data) teta = 20; %TEG on glass, 20 deg contact angle k1 = (3*tan((teta/2)*(2*pi/360)) + tan((teta/2)*(2*pi/360))^3)^(1/3)/2;%correction due to the contact angle k2 = 1/(0.2173*magnification - 0.0030); %microns per pixel k12 = k1*k2; W = k2 * 1392; H = k2 * 1040; %% HERE START LOADING ALL FILES OBTAINED WITH IMAGE PRO PLUS samplename = sample; column = 1; %i walks through upstream and downstream for i = ['u','d'] %j walks through 4 samples and samples 5 containing all samples joined together for j = ['1', '2', '3', '4', '5'] %k walks through all N images (windows) k = 1; samplename = strcat(sample, '-', i,'-', j, '-', num2str(k), '.txt'); while (exist(samplename, 'file')==2) data = load(strcat(datapath, samplename)); %pick appropriate column for diameter if i == 'u' x = k12(1)*data(:, choice + 1); else x = k12(2)*data(:, choice + 1); end %% CALCULATION OF THE DISTRIBUTION AND POSTPROCESSING OF THE RESULTS %calculate the distribution and remove outliers [dcmax, dcmed, nw, d, vol] = fdist(x, nw0); Dv50 = fdmean(0.5, dcmax, fcdf(vol/sum(vol))); for t = 1:max(size(x)) if x(t)> outlier x(t) = 1; end end [dcmax, dcmed, nw, d, vol] = fdist(x, nw0); vpdf = vol/sum(vol); if i=='u' surfacecoverage = sum((x/k1).^2*pi/4)/(W(1)*H(1)); else surfacecoverage = sum((x/k1).^2*pi/4)/(W(2)*H(2)); end %% CALCULATING CHARACTERISTIC DIAMETERS Dmin = min(x); Dmax = max(x); Dv50 = fdmean(0.5, dcmax, vcdf); %write data into matrix Appendix D. Software codes 176 results(k, (column-1)*6+1 : (column)*6) = [Dmin, Dv50, Dmax, sum(d), sum(vol)*10^-9, surfacecoverage]; %increase image number and update sample name k = k + 1; samplename = strcat(sample, '-', i,'-', j, '-', num2str(k), '.txt'); end column = column + 1; end end window = (1:N)'; results = [window , results]; %average values of all 4 samples %upstream results(:,26) = (results(:,2) + results(:,8) + results(:,14) + results(:,20))/4; results(:,27) = (results(:,3) + results(:,9) + results(:,15) + results(:,21))/4; results(:,28) = (results(:,4) + results(:,10) + results(:,16) + results(:,22))/4; results(:,29) = (results(:,5) + results(:,11) + results(:,17) + results(:,23))/4; results(:,30) = (results(:,6) + results(:,12) + results(:,18) + results(:,24))/4; results(:,31) = (results(:,7) + results(:,13) + results(:,19) + results(:,25))/4; t = size(results); if t(1,2)>31 %downstream results(:,56) = (results(:,32) + results(:,38) + results(:,44) + results(:,50))/4; results(:,57) = (results(:,33) + results(:,39) + results(:,45) + results(:,51))/4; results(:,58) = (results(:,34) + results(:,40) + results(:,46) + results(:,52))/4; results(:,59) = (results(:,35) + results(:,41) + results(:,47) + results(:,53))/4; results(:,60) = (results(:,36) + results(:,42) + results(:,48) + results(:,54))/4; results(:,61) = (results(:,37) + results(:,43) + results(:,49) + results(:,55))/4; end %results are in the form: %[window#, Dmin-upstreamsample1, Dv50-upstreamsample1, Dmax-upstreamsample1, n- upstreamsample1, %vol-upstreamsample1, surfacecoverage-upstreamsample1, and continues for ... %...us2, us3, us4, uALL, ds1, ds2, ds3, ds4, dALL] %% WRITTING RESULTS INTO FILES A = {'Window#', 'Dmin-u1', 'Dv50-u1', 'Dmax-u1', 'N%-u1', 'V%-u1', 'Area%-u1',... 'Dmin-u2', 'Dv50-u2', 'Dmax-u2', 'N%-u2', 'V%-u2', 'Area%-u2',... 'Dmin-u3', 'Dv50-u3', 'Dmax-u3', 'N%-u3', 'V%-u3', 'Area%-u3',... 'Dmin-u4', 'Dv50-u4', 'Dmax-u4', 'N%-u4', 'V%-u4', 'Area%-u4',... 'Dmin-uALL', 'Dv50-uALL', 'Dmax-uALL', 'N%-uALL', 'V%-uALL', 'Area%-uALL',... 'Dmin-d1', 'Dv50-d1', 'Dmax-d1', 'N%-d1', 'V%-d1', 'Area%-d1',... 'Dmin-d2', 'Dv50-d2', 'Dmax-d2', 'N%-d2', 'V%-d2', 'Area%-d2',... 'Dmin-d3', 'Dv50-d3', 'Dmax-d3', 'N%-d3', 'V%-d3', 'Area%-d3',... 'Dmin-d4', 'Dv50-d4', 'Dmax-d4', 'N%-d4', 'V%-d4', 'Area%-d4',... 'Dmin-dALL', 'Dv50-dALL', 'Dmax-dALL', 'N%-dALL', 'V%-dALL', 'Area%-dALL'}; xlswrite(strcat(datapath, sample, '-distribution','.xls'), A); xlswrite(strcat(datapath, sample, '-distribution','.xls'), results, 'Sheet1', 'A2'); %% PLOT RESULTS %UPSTREAM SIDE h1 = figure(1); %Dmin subplot(2,3,1) plot(1000*(diam/2)*(window/max(window)), results(:,2) , 'ro', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,8) , 'bs', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,14) , 'gd', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,20) , 'm^', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,26) , 'kx-', 'LineWidth', 1.5 , 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); title('Dmin, upstream'); xlabel('Distance (mm)'); ylabel('Dmin (microns)'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); Appendix D. Software codes 177 %Dv50 subplot(2,3,2) plot(1000*(diam/2)*(window/max(window)), results(:,3) , 'ro', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,9) , 'bs', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,15) , 'gd', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,21) , 'm^', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,27) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); title('Dv50, upstream'); xlabel('Distance (mm)'); ylabel('Dv50 (microns)'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %Dmax subplot(2,3,3) plot(1000*(diam/2)*(window/max(window)), results(:,4) , 'ro', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,10) , 'bs', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,16) , 'gd', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,22) , 'm^', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,28) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); title('Dmax, upstream'); xlabel('Distance (mm)'); ylabel('Dmax (microns)'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %Number of Droplets subplot(2,3,4) plot(1000*(diam/2)*(window/max(window)), results(:,5) , 'ro', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,11) , 'bs', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,17) , 'gd', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,23) , 'm^', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,29) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); title('Number of droplets, upstream'); xlabel('Distance (mm)'); ylabel('Number of droplets'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %Mass Distribution subplot(2,3,5) plot(1000*(diam/2)*(window/max(window)), results(:,6)/sum(results(:,6)) , 'ro', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,12)/sum(results(:,12)) , 'bs', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,18)/sum(results(:,18)) , 'gd', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,24)/sum(results(:,24)) , 'm^', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,30)/sum(results(:,30)) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); title('Mass fraction, upstream'); xlabel('Distance (mm)'); ylabel('Mass fraction'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %Surface Coverage subplot(2,3,6) plot(1000*(diam/2)*(window/max(window)), results(:,7) , 'ro', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,13) , 'bs', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,19) , 'gd', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,25) , 'm^', 'MarkerSize', 5); Appendix D. Software codes 178 plot(1000*(diam/2)*(window/max(window)), results(:,31) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); title('Surface coverage, upstream'); xlabel('Distance (mm)'); ylabel('Surface coverage'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %position it right left = 10; bottom = 10; width = 1000; height = 750; set(h1, 'Position', [left, bottom, width, height]); %write figure(1) in the file saveas(h1, strcat(datapath, sample, '-upstream', '.bmp')); %========================================================================= %DOWNSTREAM SIDE t = size(results); if t(1,2)>31 h2 = figure(2); %Dmin subplot(2,3,1) plot(1000*(diam/2)*(window/max(window)), results(:,32) , 'ro', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,38) , 'bs', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,44) , 'gd', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,50) , 'm^', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,56) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); title('Dmin, downstream'); xlabel('Distance (mm)'); ylabel('Dmin (microns)'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %Dv50 subplot(2,3,2) plot(1000*(diam/2)*(window/max(window)), results(:,33) , 'ro', 'MarkerFaceColor', 'r', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,39) , 'bs', 'MarkerFaceColor', 'b', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,45) , 'gd', 'MarkerFaceColor', 'g', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,51) , 'm^', 'MarkerFaceColor', 'y', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,57) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); title('Dv50, downstream'); xlabel('Distance (mm)'); ylabel('Dv50 (microns)'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %Dmax subplot(2,3,3) plot(1000*(diam/2)*(window/max(window)), results(:,34) , 'ro', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,40) , 'bs', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,46) , 'gd', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,52) , 'm^', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,58) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); Appendix D. Software codes 179 title('Dmax, downstream'); xlabel('Distance (mm)'); ylabel('Dmax (microns)'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %Number of droplets subplot(2,3,4) plot(1000*(diam/2)*(window/max(window)), results(:,35) , 'ro', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,41) , 'bs', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,47) , 'gd', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,53) , 'm^', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,59) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); title('Number of droplets, downstream'); xlabel('Distance (mm)'); ylabel('Number of droplets'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %Mass Distribution subplot(2,3,5) plot(1000*(diam/2)*(window/max(window)), results(:,36)/sum(results(:,36)) , 'ro', 'MarkerFaceColor', 'r', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,42)/sum(results(:,42)) , 'bs', 'MarkerFaceColor', 'b', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,48)/sum(results(:,48)) , 'gd', 'MarkerFaceColor', 'g', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,54)/sum(results(:,54)) , 'm^', 'MarkerFaceColor', 'y', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,60)/sum(results(:,60)) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties xlim([0, 25.4]); title('Mass fraction, downstream'); xlabel('Distance (mm)'); ylabel('Mass fraction'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %Surface coverage subplot(2,3,6) plot(1000*(diam/2)*(window/max(window)), results(:,37) , 'ro', 'MarkerSize', 5); hold on; plot(1000*(diam/2)*(window/max(window)), results(:,43) , 'bs', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,49) , 'gd', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,55) , 'm^', 'MarkerSize', 5); plot(1000*(diam/2)*(window/max(window)), results(:,61) , 'kx-', 'LineWidth', 1.5, 'MarkerSize', 5); hold off; %setting the axis properties title('Surface coverage, downstream'); xlabel('Distance (mm)'); ylabel('Surface coverage'); %legend ('sample 1', 'sample 2', 'sample 3', 'sample4'); %position it right left = 10; bottom = 10; width = 1000; height = 750; set(h2, 'Position', [left, bottom, width, height]); %write figure(2) in the file saveas(h2, strcat(datapath, sample, '-downstream' ,'.bmp')); end eff.m %Calculates k-values and capture efficiencies for each droplet size, based on the size %distribution results in the aerosol and on the coupon %% INPUT SECTION Appendix D. Software codes 180 %Input: run number, velocity(m/s), droplet flow(g/min), and upstream and downstream %deposition rates(mg/hr). Supply aerosol and coupon distribution data in %the directory specified by datapath. %Output: k-values and capture efficiencies for each droplet size, written %in files and plotted clear all; %Input parameters and change to SI units sample = input('Run number:', 's'); U = input('Velocity(m/s):'); F = input('Droplet flow(g/min):'); F = F * 0.001/60; %kg/s ru = input('Upstream dep.rate(mg/hr):'); ru = ru*10^(-6)/3600; %kg/s rd = input('Downstream dep.rate(mg/hr):'); rd = rd*10^(-6)/3600; %kg/s A = 0.0254^2*pi; %coupon area C = F/(U*((3*0.0254)^2*pi/4)); %kg/m3 %% READ DISTRIBUTION DATA AND CALCULATE K-values and EFFICIENCIES FOR EACH DROPLET SIZE %aerosol data datapath = 'C:\Documents\WORK\shadow-results\'; dataa = xlsread(strcat(datapath, sample, '-distribution.xls')); dmaxa = dataa(:,1); vpdfcorra = dataa(:,6); vpdfcorrfita = dataa(:,8); clear dataa; %coupon data datapath = 'C:\Documents\WORK\coupon-results\'; %upstream distribution try u = xlsread(strcat(datapath, sample, '-u-distribution.xls')); dmaxu = u(:,1); vpdfcorru = u(:,6); vpdfcorrfitu = u(:,8); clear u; catch disp('Warning: file for upstream distribution not found!'); dmaxu = (1:60)'; vpdfcorru = zeros(60,1); vpdfcorrfitu = zeros(60,1); end n = min(max(size(vpdfcorrfitu)),max(size(vpdfcorrfita))); vpdfcorru = vpdfcorru(1:n); vpdfcorrfitu = vpdfcorrfitu(1:n); vpdfcorrfita = vpdfcorrfita(1:n); vpdfcorra = vpdfcorra(1:n); dmaxu = dmaxu(1:n); Eu = ru/(U*A*C)*(vpdfcorrfitu./vpdfcorrfita); ku = Eu*U; %downstream distribution d = xlsread(strcat(datapath, sample, '-d-distribution.xls')); dmaxd = d(:,1); vpdfcorrd = d(:,6); vpdfcorrfitd = d(:,8); n = min(max(size(vpdfcorrfitd)),max(size(vpdfcorrfita))); vpdfcorrd = vpdfcorrfitd(1:n); vpdfcorra = vpdfcorra(1:n); vpdfcorrfitd = vpdfcorrfitd(1:n); vpdfcorrfita = vpdfcorrfita(1:n); dmaxd = dmaxd(1:n); Ed = rd/(U*A*C)*(vpdfcorrd./vpdfcorrfita); kd = Ed*U; %% DISPLAY RESULTS disp('Concentration(g/m3):'); disp (C*1000); disp('Upstream k-value(m/hr):'); disp (ru/(A*C)*3600); disp('Downstream k-value(m/hr):'); disp (rd/(A*C)*3600); disp('Upstream capture efficiency:'); disp (ru/(U*A*C)); disp('Downstream capture efficiency:'); disp (rd/(U*A*C)); %% PLOT THE RESULTS Appendix D. Software codes 181 h1 = figure(1); plot(dmaxu, ku*3600, 'r-', dmaxd, kd*3600, 'b--' ); %title and labels title('Deposition coefficients'); xlabel('Drop diameter (micron)'); ylabel('k-values (m/hr)'); left = 20; bottom = 300; width = 560; height = 420; set(h1, 'Position', [left, bottom, width, height]); legend('k-upstream', 'k-downstream', 'Location', 'NorthWest');legend('boxoff'); ylim ([0 max(max(ku*3600,kd*3600))]); h2 = figure(2); plot(dmaxu, Eu, 'r-', dmaxd, Ed, 'b--' ); %title and labels title('Capture efficiencies'); xlabel('Drop diameter (micron)'); ylabel('Capture efficiency'); left = 600; bottom = 300; width = 560; height = 420; set(h2, 'Position', [left, bottom, width, height]); legend('CE-upstream', 'CE-downstream', 'Location', 'NorthWest','boxoff');legend('boxoff'); ylim ([0 max(max(Eu,Ed))]); %% SAVE THE RESULTS filepath = 'C:\Documents\WORK\'; %write deposition coefficients and figure(1) into file saveas(h1, strcat(filepath, sample, '-k', '.bmp')); xlswrite(strcat(filepath, sample, '.xls'), {'dmax','k-u(m/hr)','k-d (m/hr)'}); xlswrite(strcat(filepath, sample, '.xls'), [dmaxu, ku*3600, kd*3600],'Sheet1', 'A2'); %write capture efficiencies and figure(2) into file saveas(h2, strcat(filepath, sample, '-ce', '.bmp')); xlswrite(strcat(filepath, sample, '.xls'), {'CE-u','CE-d'}, 'Sheet1', 'D1'); xlswrite(strcat(filepath, sample, '.xls'), [Eu, Ed],'Sheet1', 'D2'); %write data into files B = {'Input:',' '; 'Run',sample; 'Velocity(m/s)',U; 'Droplet flow(g/min)',F*60*1000; 'Upstream dep.rate(mg/hr)',ru*3600*10^6; 'Downstream dep.rate(mg/hr)',rd*3600*10^6; 'Output:',' '; 'Concentration(g/m3)', C*1000; 'k-upstream(m/hr)', ru/(A*C)*3600; 'k-downstream(m/hr)', rd/(A*C)*3600; 'CE-upstream', ru/(U*A*C); 'CE-downstream', rd/(U*A*C)}; xlswrite(strcat(filepath, sample, '.xls'), B , 'Sheet1', 'G1'); f2normlognormalcdf.m %Calculates 2-norm (sum of squares) of differences between data and curve for cumulative %log-normal distribution with 4 parameters %Input: Initial guess vector a, vector of diameters xdata and vector of frequencies %(relative or cumulative), ydata %Output: sum of squares function f = f2normlognormalcdf(a, xdata, ydata) a(1) = 1; f = norm(((1/2)*erf((1/2)*sqrt(2)/a(4)*log(xdata-a(2))-(1/2)*(a(3)/a(4))*sqrt(2))*a(1)) - ydata); end f2normlognormalpdf.m %Calculates 2-norm (sum of squares) of differences between data and log-normal %distribution curve with 4 parameters Appendix D. Software codes 182 %Input: Initial guess vector a, vector of diameters xdata and vector of frequencies %(relative or cumulative), ydata %Output: sum of squares function f = f2normlognormalpdf(a, xdata, ydata) a(1) = 1; %reduce number of parameters from 4 to 3 by setting this coefficient to 1 f = norm(((a(1)*(1./((xdata-a(2))*a(4)*sqrt(2*pi))).*exp(-((log(xdata-a(2))- a(3)).^2)/(2*a(4)^2)))) - ydata); end fcdf.m %Calculates cumulative frequencies from relative frequencies. %Input: vector of relative frequencies, x %Output: vector of cumulative frequencies, y function y = fcdf(x) n = max(size(x)); for i = 1:n y(i) = sum(x(1:i)); end y; end fdist.m %Calculates size distribution from the vector of drop diameters x. %Input: nw is a vector that defines whether the size distribution will be calculated in a %number of points or with defined class width. %Output: xcmax is vector of the maximum class diameter, xcmed is vector of median %diameter of the class, nx is the new nw vector, d is the count distribution, and vol is %the volume distribution vector. function [xcmax, xcmed, nw, d, vol] = fdist(x,nw) n = max(size(x)); %determine max and min element and correct them a little to avoid problems in counting [xmax,row] = max(x); x(row) = 0.99999*xmax; [xmin,row] = min(x); x(row) = 1.00001*xmin; %volume of droplets v = x.^3.*pi/6; %class width is defined, calculate number of classes if nw(1) == 0 nw(1) = ceil(xmax/nw(2)); %number of classes xmin = 0; xmax = nw(1) * nw(2); xclass = linspace(xmin, xmax, nw(1) + 1); else %number of classes is defined xclass = linspace(xmin, xmax, nw(1) + 1); nw(2) = (xmax-xmin) / nw(1); end %set numbers of droplets and volume in each class to zero d = zeros(nw(1),1); vol = zeros(nw(1),1); try for i = 1:n j = ceil((x(i)-xmin)/nw(2)); %class number d(j) = d(j)+1; %increase number of droplets in the class for 1 vol(j) = vol(j)+v(i); %add droplet volume to the class total volume end catch Appendix D. Software codes 183 %just to skip potential problems due to droplets that could fall out of range end %maximum and medium class diameter xcmax = xclass(2 : nw(1) + 1)'; xcmed = xcmax - nw(2)/2; end fdmean.m %Calculates mean diameter by linear interpolation between two adjacent points %a is desired mean diameter (e.g. for Dv50, a=0.5), x is vector of droplet size classes %and V is vector of volume relative frequencies function y = fdmean(a,x,V) n = max(size(x)); V = V/max(V); for i = 1:n if V(i) > a if i==1 result = V(i); else result = x(i-1)+(a-V(i-1))*(x(i)-x(i-1))/(V(i)-V(i-1)); end break; end end y = result; end flognormalcdf.m %Four-parameter cumulative log normal distribution function f = flognormalcdf(a, xcmax) f = (1/2)*erf((1/2)*sqrt(2)/a(4)*log(xcmax-a(2))-(1/2)*(a(3)/a(4))*sqrt(2))*a(1); end flognormalpdf.m %Four-parameter log normal distribution function f = flognormalpdf(a, xcmax) f = (a(1)*(1./((xcmax-a(2))*a(4)*sqrt(2*pi))).*exp(-((log(xcmax-a(2))- a(3)).^2)/(2*a(4)^2))); end fpdf.m %Calculates relative frequencies from cumulative frequencies (probability density %function), from the cumulative frequencies (cumulative density function). %Input: vector of cumulative frequencies, x %Output: vector of relative frequencies, y function y = fpdf(x) n = max(size(x)); for i = 1:n if i == 1 y(i) = x(i); else y(i) = x(i) - x(i-1); end end y; end Appendix D. Software codes 184 shadow.m %Analyzes individual drop size data, reported from Image Pro Plus. Calculates drop size %from pixels into microns, and computes size distribution based on the specified number %of classes or class width. Applies border and depth of field correction and deals with %outliers. It is used for analysis of drop size distribution in the aerosol and on the %coupon (one or two separated distributions). It also performs curve fitting using %function ‘fdist.m’. Finally, it reports results on the screen and plots results for %relative and cumulative frequencies. All the results and graphs are written into files. %% INPUT SECTION %Input file name(run number or sample number) e.g. 1, 1-u, or 1-d %Files should be placed in the folder defined by variable datapath clear all; sample = input ('1.Sample number: ','s'); ac = input ('2.Size distribution (1)In the Aerosol (2)On the Coupon: '); if ac == 2 minpoint = input ('2a.Minimum point that separates two dristributions (enter for none):'); else minpoint = []; end magnification = input('3.Magnification used: '); choice = input('4.Size distribution of: (1)Dmax, (2)Dmin, (3)Dmean: '); nwchoice = input('5.Define: (1)Number of Classes, (2)Class Width: '); if nwchoice == 1 nclasses = input('5a.Number of classes: '); nw0 = [nclasses; 0]; else cwidth = input('5b.Class width(um): '); nw0 = [0; cwidth]; end fitting = input ('6.Fit volume distribution: (1)Cumulative, (2)Relative: '); outlier = input ('7.Remove outliers X times larger than Dv50, or >Dmax (default is 10x and Dmax = 150):'); if isempty(outlier) outlier = 10; end %% LOADING DATA AND INITIAL PROCESSING %load data obtained by Image Pro Plus if ac == 1 datapath = 'C:\Documents\WORK\shadow-results\'; else datapath = 'C:\Documents\WORK\coupon-results\'; end data = load(strcat(datapath, sample, '.txt')); %calculate no. of microns per pixel (from the calibration data) teta = 20; %TEG on glass, 20deg contact angle if ac == 1 k1 = 1; k2 = 1/(0.3257*magnification - 0.0004); elseif ac ==2 k1 = (3*tan((teta/2)*(2*pi/360)) + tan((teta/2)*(2*pi/360))^3)^(1/3)/2; k2 = 1/(0.2173*magnification - 0.0030); end %width and height of the view field k = k1 * k2; W = k2 * 1392; H = k2 * 1040; %pick appropriate column for diameter x = k*data(:, choice + 1); %% CALCULATING THE DISTRIBUTION AND POSTPROCESSING OF THE RESULTS %calculate the distribution and remove outliers [dcmax, dcmed, nw, d, vol] = fdist(x, nw0); Dv50 = fdmean(0.5, dcmax, fcdf(vol/sum(vol))); Appendix D. Software codes 185 for i = 1:max(size(x)) if or(x(i)> outlier*Dv50, x(i)>150) x(i) = 1; end end [dcmax, dcmed, nw, d, vol] = fdist(x, nw0); nclasses = nw(1); deltad = nw(2); %aerosol distribution and non-separated coupon distribution nclasses1 = nclasses; dcmax1 = dcmax; dcmed1 = dcmed; d1 = d; vol1 = vol; %separated distributions on the coupon (if it exists on the upstream side) if not(isempty(minpoint) %first distribution from turbulent diffusion nclasses1 = minpoint; dcmax1 = dcmax(1:minpoint); dcmed1 = dcmed(1:minpoint); d1 = d(1:minpoint); vol1 = vol(1:minpoint); %second distribution from inertial impaction nclasses2 = nclasses - minpoint; dcmax2 = dcmax(minpoint + 1 : nclasses); dcmed2 = dcmed(minpoint + 1 : nclasses); d2 = d(minpoint + 1 : nclasses); vol2 = vol(minpoint + 1 : nclasses); end %%DEPTH OF FIELD AND BORDER CORRECTION if ac == 1 %(aerosol) %border and DOF corrections p1 = ((W-dcmax1).*(H-dcmax1)/(W*H)) .* (dcmax1/dcmax1(nclasses1)); %depth of field in microns for the largest droplet, calibrated at 2x3magnification DOF = 40.5*dcmax1(nclasses1); elseif ac == 2 %(coupon) %only border correction DOF = 0; if not(isempty(minpoint)) p1 = ((W-dcmax1).*(H-dcmax1)/(W*H)); p2 = ((W-dcmax2).*(H-dcmax2)/(W*H)); else p1 = ((W-dcmax1).*(H-dcmax1)/(W*H)); end end %aerosol and non-separated coupon distribution: corrected number of droplets and volume d1corr = round((1./p1).*d1); vol1corr = (dcmed1.^3*pi/6).*d1corr; vpdf1 = vol1/sum(vol1); vcdf1 = fcdf(vpdf1)'; vpdf1corr = vol1corr/sum(vol1corr); vcdf1corr = fcdf(vpdf1corr)'; %volume and concentration V = W*H*DOF; %um3 C = 1127*sum(vol1corr)/(1300*V); %for 1300 images, kg/m3 C = C*1000; %g/m3 %separated distributions on the coupon: corrected number of droplets and volume if not(isempty(minpoint)) %first distribution d1corr = round((1./p1).*d1); vol1corr = (dcmed1.^3*pi/6).*d1corr; vpdf1 = vol1/sum(vol); vcdf1 = fcdf(vpdf1)'; %second distribution d2corr = round((1./p2).*d2); Appendix D. Software codes 186 vol2corr = (dcmed2.^3*pi/6).*d2corr; vpdf2 = vol2/sum(vol); vcdf2 = fcdf(vpdf2)'; %first and second distribution vpdf1corr = vol1corr/(sum(vol1corr)+sum(vol2corr)); vcdf1corr = fcdf(vpdf1corr)'; vpdf2corr = vol2corr/(sum(vol1corr)+sum(vol2corr)); vcdf2corr = fcdf(vpdf2corr)'; end %%CHARACTERISTIC DIAMETERS %aerosol, non-separated distribution and first of two separated distributions Dmin1 = min(x); Dmax1 = max(dcmax1); Damd1 = sum(d1.*dcmax1)/(sum(d1)); Damd1corr = sum(d1corr.*dcmax1)/(sum(d1corr)); Dv101 = fdmean(0.1, dcmax1, vcdf1); Dv101corr = fdmean(0.1, dcmax1, vcdf1corr); Dv501 = fdmean(0.5, dcmax1, vcdf1); Dv501corr = fdmean(0.5, dcmax1, vcdf1corr); Dv901 = fdmean(0.9, dcmax1, vcdf1); Dv901corr = fdmean(0.9, dcmax1, vcdf1corr); RSF1 = (Dv901-Dv101)/Dv501; RSF1corr = (Dv901corr-Dv101corr)/Dv501corr; %second separated distribution if not(isempty(minpoint)) Dmin2 = min(dcmax2); Dmax2 = max(d2); Damd2 = sum(d2.*dcmax2)/(sum(d2)); Damd2corr = sum(d2corr.*dcmax2)/(sum(d2corr)); Dv102 = fdmean(0.1, dcmax2, vcdf2); Dv102corr = fdmean(0.1, dcmax2, vcdf2corr); Dv502 = fdmean(0.5, dcmax2, vcdf2); Dv502corr = fdmean(0.5, dcmax2, vcdf2corr); Dv902 = fdmean(0.9, dcmax2, vcdf2); Dv902corr = fdmean(0.9, dcmax2, vcdf2corr); RSF2 = (Dv902-Dv102)/Dv502; RSF2corr = (Dv902corr-Dv102corr)/Dv502corr; end %FITTING AND DISTRIBUTION CURVE BASED ON FITTING a0 = [1, 0.1, 2.2, 0.6]; %initial guess %select fitting relative or cumulative frequencies switch fitting case 1 %cumulative frequencies %aerosol, non-separated distribution and first of two separated distributions %[a1, fval1] = lsqcurvefit(@flognormalcdf, a0, dcmax1, vcdf1corr); f = @(a)f2normlognormalcdf(a, dcmax1, vcdf1corr); [a1, fval1] = fminunc(f, a0); vcdf1corrfit = flognormalcdf(a1, dcmax1); vpdf1corrfit = fpdf(vcdf1corrfit)'; SSE1corr = sum((vcdf1corr - vcdf1corrfit).^2); RMSE1corr = (SSE1corr/(max(size(dcmax1))))^0.5; %second separated distribution if (ac == 2)&&(not(isempty(minpoint))) %[a2, fval2] = lsqcurvefit(@flognormalcdf, a0, dcmax2, vcdf2corr); f = @(a)f2normlognormalcdf(a, dcmax2, vcdf2corr); a0(2) = a0(2) + minpoint; %better initial guess for the shift along x-axis [a2, fval2] = fminunc(f, a0); vcdf2corrfit = flognormalcdf(a2, dcmax2); vpdf2corrfit = fpdf(vcdf2corrfit)'; SSE2corr = sum((vcdf2corr - vcdf2corrfit).^2); RMSE2corr = (SSE2corr/(max(size(dcmax2))))^0.5; end case 2 %relative frequencies %aerosol, non-separated distribution and first of two separated distributions %[a1, fval1] = lsqcurvefit(@flognormalpdf, a0, dcmax1, vpdf1corr); f = @(a)f2normlognormalpdf(a, dcmax1, vpdf1corr); [a1, fval1] = fminunc(f, a0); vpdf1corrfit = flognormalpdf(a1, dcmax1); vcdf1corrfit = fcdf(vpdf1corrfit)'; SSE1corr = sum((vpdf1corr - vpdf1corrfit).^2); RMSE1corr = (SSE1corr/(max(size(dcmax1))))^0.5; %non-corrected distribution (only for the aerosol and first coupon distribution) f = @(a)f2normlognormalpdf(a, dcmax1, vpdf1); [a11, fval11] = fminunc(f, a0); vpdf1fit = flognormalpdf(a11, dcmax1); vcdf1fit = fcdf(vpdf1fit)'; Appendix D. Software codes 187 SSE1 = sum((vpdf1 - vpdf1fit).^2); RMSE1 = (SSE1/(max(size(dcmax1))))^0.5; %second separated distribution if (ac == 2)&&(not(isempty(minpoint))) %[a2, fval2] = lsqcurvefit(@flognormalpdf, a0, dcmax2, vpdf2corr); f = @(a)f2normlognormalpdf(a, dcmax2, vpdf2corr); a0(2) = a0(2) + minpoint; %better initial guess for the shift along x-axis [a2, fval2] = fminunc(f, a0); vpdf2corrfit = flognormalpdf(a2, dcmax2); vcdf2corrfit = fcdf(vpdf2corrfit)'; SSE2corr = sum((vpdf2corr - vpdf2corrfit).^2); RMSE2corr = (SSE2corr/(max(size(dcmax2))))^0.5; end end %% DISPLAY RESULTS disp('------------------------------------------------------------------------------'); disp(' R E S U L T S:'); disp('------------------------------------------------------------------------------'); disp('Distribution:'); disp(sprintf('%15s','#1', ' #1corrected', ' #2', ' #2corrected')); if (ac == 2) && not(isempty(minpoint)) disp('Number of droplets:'); disp(sprintf('%15.0f', sum(d1), sum(d2), sum(d1corr), sum(d2corr))); disp('Volume of droplets(um3):'); disp(sprintf('%15.0f', sum(vol1), sum(vol2), sum(vol1corr), sum(vol2corr))); disp('Class width(um):'); disp(sprintf('%15.2f', deltad, deltad, deltad, deltad)); disp('Arithmetic mean diameter, Damd(um):'); disp(sprintf('%15.2f', Damd1, Damd2, Damd1corr, Damd2corr)); disp('Minimum diameter, Dmin(um):'); disp(sprintf('%15.2f', Dmin1, Dmin2, Dmin1, Dmin2)); disp('10 percent volume diameter, Dv10(um):'); disp(sprintf('%15.2f', Dv101, Dv102, Dv101corr, Dv102corr)); disp('50 percent volume diameter (VMD), Dv50(um):'); disp(sprintf('%15.2f', Dv501, Dv502, Dv501corr, Dv502corr)); disp('90 percent volume diameter, Dv90(um):'); disp(sprintf('%15.2f', Dv901, Dv902, Dv901corr, Dv902corr)); disp('Maximum diameter, Dmax(um):'); disp(sprintf('%15.2f', Dmax1, Dmax2, Dmax1, Dmax2)); disp('Relative Span Factor, RSF = (Dv90-Dv10)/Dv50:'); disp(sprintf('%15.2f', RSF1, RSF2, RSF1corr, RSF2corr)); else disp('Number of droplets:'); disp(sprintf('%15.0f', sum(d1), sum(d1corr))); disp('Volume of droplets(um3):'); disp(sprintf('%15.0f', sum(vol1), sum(vol1corr))); disp('Class width(um):'); disp(sprintf('%15.2f', deltad, deltad)); disp('Arithmetic mean diameter, Damd(um):'); disp(sprintf('%15.2f', Damd1, Damd1corr)); disp('Minimum diameter, Dmin(um):'); disp(sprintf('%15.2f', Dmin1, Dmin1)); disp('10 percent volume diameter, Dv10(um):'); disp(sprintf('%15.2f', Dv101, Dv101corr)); disp('50 percent volume diameter (VMD), Dv50(um):'); disp(sprintf('%15.2f', Dv501, Dv501corr)); disp('90 percent volume diameter, Dv90(um):'); disp(sprintf('%15.2f', Dv901, Dv901corr)); disp('Maximum diameter, Dmax(um):'); disp(sprintf('%15.2f', Dmax1, Dmax1)); disp('Relative Span Factor, RSF = (Dv90-Dv10)/Dv50:'); disp(sprintf('%15.2f', RSF1, RSF1corr)); end disp('------------------------------------------------------------------------------'); disp(' F I T T I N G R E S U L T S:'); disp('------------------------------------------------------------------------------'); if (ac == 2) && not(isempty(minpoint)) disp('Parameters a(1), a(2), a(3), a(4): '); disp('Distribution 1: '); Appendix D. Software codes 188 disp(sprintf('%15.5f', a1(1), a1(2), a1(3), a1(4))); disp('Distribution 2: '); disp(sprintf('%15.5f', a2(1), a2(2), a2(3), a2(4))); disp('Sum of Squares of Errors, SSE: '); disp(sprintf('%15.5f', SSE1corr, SSE2corr)); disp('Root Mean Square Error, RMSE: '); disp(sprintf('%15.5f', RMSE1corr, RMSE2corr)); else disp('Parameters a(1), a(2), a(3), a(4)'); disp('Corrected distribution: '); disp(num2str(a1(1),'%15.5f')); disp(num2str(a1(2),'%15.5f')); disp(num2str(a1(3),'%15.5f')); disp(num2str(a1(4),'%15.5f')); disp('Noncorrected distribution: '); disp(num2str(a11(1),'%15.5f')); disp(num2str(a11(2),'%15.5f')); disp(num2str(a11(3),'%15.5f')); disp(num2str(a11(4),'%15.5f')); disp('Sum of Squares of Errors, SSE: '); disp(sprintf('%15.5f', SSE1corr)); disp('Root Mean Square Error, RMSE: '); disp(sprintf('%15.5f', RMSE1corr)); end disp('Sample volume(mm3): '); disp(sprintf('%15.3f', V*10^(-9))); disp('Concentration(g/m3): '); disp(sprintf('%15.2f', C)); %% WRITTING RESULTS INTO FILES % separated distributions on the coupon if (ac == 2) && not(isempty(minpoint)) A= {'Magnification', magnification, magnification, magnification, magnification; '(1)Dmax,(2)Dmin,(3)Dmean', choice, choice, choice, choice; 'Fitting (1)cum, (2)rel', fitting, fitting, fitting, fitting; 'Outlier (times>Dv50)', outlier, outlier, outlier, outlier; 'Distribution ', '#1', '#1corrected', '#2', '#2corrected'; 'Ntot', sum(d1), sum(d2), sum(d1corr), sum(d2corr); 'Vtot(um3)',sprintf('%15.0f',sum(vol1)), sprintf('%15.0f', sum(vol2)), sprintf('%15.0f', sum(vol1corr)), sprintf('%15.0f', sum(vol2corr)); 'deltad(um)',sprintf('%15.2f',deltad), sprintf('%15.2f', deltad), sprintf('%15.2f',deltad), sprintf('%15.2f', deltad); 'Damd(um)',sprintf('%15.2f',Damd1), sprintf('%15.2f', Damd2), sprintf('%15.2f', Damd1corr), sprintf('%15.2f', Damd2corr); 'Dmin(um)',sprintf('%15.2f',Dmin1), sprintf('%15.2f',Dmin2), sprintf('%15.2f', Dmin1), sprintf('%15.2f', Dmin2); 'Dv10(um)',sprintf('%15.2f',Dv101), sprintf('%15.2f',Dv102), sprintf('%15.2f', Dv101corr), sprintf('%15.2f', Dv102corr); 'Dv50(um)',sprintf('%15.2f',Dv501), sprintf('%15.2f',Dv502), sprintf('%15.2f', Dv501corr), sprintf('%15.2f', Dv502corr); 'Dv90(um)',sprintf('%15.2f',Dv901), sprintf('%15.2f',Dv902), sprintf('%15.2f',Dv901corr), sprintf('%15.2f',Dv902corr); 'Dmax(um)',sprintf('%15.2f',Dmax1), sprintf('%15.2f',Dmax2), sprintf('%15.2f',Dmax1), sprintf('%15.2f',Dmax2); 'RSF', sprintf('%15.2f',RSF1), sprintf('%15.2f', RSF2), sprintf('%15.2f',RSF1corr), sprintf('%15.2f',RSF2corr); 'F I T T I N G ','','','',''; 'a(1),a(2),a(3),a(4)',sprintf('%15.5f', a1(1)), sprintf('%15.5f', a1(2)), sprintf('%15.5f', a1(3)), sprintf('%15.5f',a1(4)); 'SSE',sprintf('%15.5f', SSE1corr), sprintf('%15.5f', SSE2corr), sprintf('%15.5f', SSE1corr), sprintf('%15.5f', SSE2corr); 'RMSE',sprintf('%15.5f', RMSE1corr), sprintf('%15.5f',RMSE2corr), sprintf('%15.5f', RMSE1corr), sprintf('%15.5f',RMSE2corr) 'Sample vol(mm3)',sprintf('%15.5f', V*10^(-9)), sprintf('%15.5f',V*10^(-9)); 'Conc.(g/m3)',sprintf('%15.5f', C), sprintf('%15.5f',C)}; % write distribution data into xls files xlswrite(strcat(datapath, sample,'.xls'),A); B0 = {'dcmax', 'd', 'vpdf', 'vcdf', 'dcorr', 'vpdfcorr', 'vcdfcorr', 'vpdfcorrfit', 'vcdfcorrfit'}; B = {[dcmax1;dcmax2], [d1;d2], [vpdf1;vpdf2], [vcdf1;vcdf2], [d1corr;d2corr], [vpdf1corr;vpdf2corr], [vcdf1corr;vcdf2corr],[vpdf1corrfit;vpdf2corrfit],[vcdf1corrfit;vcdf2corrfit]}; xlswrite(strcat(datapath, sample, '-distribution','.xls'), B0); Appendix D. Software codes 189 xlswrite(strcat(datapath, sample, '-distribution','.xls'), B, 'Sheet1', 'A2'); else %aerosol and nonseparated coupon distribution A= {'Magnification', magnification, magnification; '(1)Dmax, (2)Dmin, (3)Dmean', choice, choice; 'Fitting (1)cum, (2)rel', fitting, fitting; 'Outlier (times>Dv50)', outlier, outlier; 'Distribution ', '#1', '#1corrected'; 'Ntot', sum(d1), sum(d1corr); 'Vtot(um3)',sprintf('%15.0f',sum(vol1)), sprintf('%15.0f', sum(vol1corr)); 'deltad(um)',sprintf('%15.2f',deltad), sprintf('%15.2f',deltad); 'Damd(um)',sprintf('%15.2f',Damd1), sprintf('%15.2f', Damd1corr); 'Dmin(um)',sprintf('%15.2f',Dmin1), sprintf('%15.2f', Dmin1); 'Dv10(um)',sprintf('%15.2f',Dv101), sprintf('%15.2f', Dv101corr); 'Dv50(um)',sprintf('%15.2f',Dv501), sprintf('%15.2f', Dv501corr); 'Dv90(um)',sprintf('%15.2f',Dv901), sprintf('%15.2f', Dv901corr); 'Dmax(um)',sprintf('%15.2f',Dmax1) sprintf('%15.2f', Dmax1); 'RSF', sprintf('%15.2f',RSF1), sprintf('%15.2f',RSF1corr); 'F I T T I N G','',''; 'noncorrected','',''; 'a(1), a(2)',sprintf('%15.5f', a11(1)), sprintf('%15.5f', a11(2)); 'a(3), a(4)',sprintf('%15.5f', a11(3)), sprintf('%15.5f', a11(4)); 'SSE',sprintf('%15.5f', SSE11corr), ''; 'RMSE',sprintf('%15.5f', RMSE11corr), ''; 'corrected','',''; 'a(1), a(2)',sprintf('%15.5f', a1(1)), sprintf('%15.5f', a1(2)); 'a(3), a(4)',sprintf('%15.5f', a1(3)), sprintf('%15.5f', a1(4)); 'SSE','', sprintf('%15.5f', SSE1corr); 'RMSE','', sprintf('%15.5f', RMSE1corr); 'Sample vol(mm3)',sprintf('%15.5f', V*10^(-9)), sprintf('%15.5f',V*10^(-9)); 'Conc.(g/m3)',sprintf('%15.5f', C), sprintf('%15.5f',C)}; % distribution data into xls files xlswrite(strcat(datapath, sample,'.xls'),A); B0 = {'dcmax', 'd', 'vpdf', 'vcdf', 'dcorr', 'vpdfcorr', 'vcdfcorr', 'vpdfcorrfit', 'vcdfcorrfit'}; B = [dcmax1, d1, vpdf1, vcdf1, d1corr, vpdf1corr, vcdf1corr, vpdf1corrfit, vcdf1corrfit]; xlswrite(strcat(datapath, sample, '-distribution','.xls'), B0); xlswrite(strcat(datapath, sample, '-distribution','.xls'), B, 'Sheet1', 'A2'); end %% PLOTTING THE DATA % FIGURE 1 %volume pdf distribution h1 = figure(1); plot (dcmax, vol/sum(vol), 'rs', 'MarkerSize', 5); hold on; plot (dcmax1, vpdf1corr, 'bo', 'MarkerFaceColor', 'b', 'MarkerSize', 5); plot (dcmax1, vpdf1corrfit, 'k-', 'LineWidth', 1); plot (dcmax1, vpdf1fit, 'k-', 'LineWidth', 1); if not(isempty(minpoint)) plot (dcmax2, vpdf2corr, 'bo', 'MarkerFaceColor', 'b', 'MarkerSize', 5); plot (dcmax2, vpdf2corrfit, 'k--', 'LineWidth', 1); hold off; end ylim ([0, max(max(vpdf1corr), max(vpdf1corrfit))*1.2]); %title and labels title('Volume distribution'); xlabel('Droplet diameter (micron)'); ylabel('Volume %'); %position it left left = 20; bottom = 300; width = 560; height = 420; set(h1, 'Position', [left, bottom, width, height]); %FIGURE 2 %volume cdf distribution h2 = figure(2); plot (dcmax, fcdf(vol/sum(vol))', 'rs', 'MarkerSize', 5); hold on; plot (dcmax1, vcdf1corr, 'bo', 'MarkerFaceColor', 'b', 'MarkerSize', 5); plot (dcmax1, vcdf1corrfit, 'k-', 'LineWidth', 1); Appendix D. Software codes 190 plot (dcmax1, vcdf1fit, 'k-', 'LineWidth', 1); if not(isempty(minpoint)) plot (dcmax2, vcdf2corr + max(vcdf1corr), 'bo', 'MarkerFaceColor', 'b', 'MarkerSize', 5); plot (dcmax2, vcdf2corrfit + max(vcdf1corrfit), 'k--', 'LineWidth', 1); hold off; end ylim ([0 1]); %title and labels title('Cumulative volume distribution'); xlabel('Droplet diameter (micron)'); ylabel('Volume %'); %position it right left = 600; bottom = 300; width = 560; height = 420; set(h2, 'Position', [left, bottom, width, height]); %% WRITTING FIGURES INTO FILES %write figure(1) in the file saveas(h1, strcat(datapath, sample, '-vpdf', '.bmp')); %write figure(2) in the file saveas(h2, strcat(datapath, sample, '-vcdf' ,'.bmp')); Appendix D. Software codes 191 D.3. Mathcad code To calculate capture efficiencies for non-Stokesian drag force, system of nonlinear differential equations was solved in the program written in the Mathcad Professional 2001 software. The ODE’s system was solved using function ‘Rkadapt’, which implements the Runge-Kutta method of the 4 th order, while nonlinear equations were solved in the ‘Solve block’, using Levenberg-Marquardt algorithm. gravity in negative direction (upward flow)p 1−:= nondimensional y distance (y=r, radial component)y0 0.1:= nondimensional x distancex0 0.5−:= initial velocityV0 1:= particle diameterDp 50 10 6− ⋅:= Parameter definition (must be defined before the function definition). In SI units: Particle motion equations y t y0,( ) y0 e t ⋅:=x t x0,( ) x0 e 2− t⋅ ⋅:= Flow field from potential flow Stokes number functionSt Dp V0,( ) ρ Dp 2 ⋅ 18 µ⋅ V0 2 Rc⋅ ⋅:= coupon radius, mRc 0.0254:= air density, kg/m3ρ a 1.203:= air viscosity, Pasµ 1.81510 5− ⋅:= TEG density, kg/m3ρ 1127:= Parameters Initial velocity calculation (different from fluid velocity due to the gravity effect): Given Appendix D. Software codes 192 x1 2− x0⋅ p 1 1 6 Dp ρ a⋅ µ x1 2 x0⋅+⋅ 2 3 ⋅+ ρ Dp( ) 2 ⋅ 18 µ⋅ 9.81 V0 ⋅ ⋅+ init x0 x1, Dp, V0, p,( ) Find x1( ):= init x0 2− x0⋅ p ρ Dp( ) 2 ⋅ 18 µ⋅ 9.81 V0 ⋅ ⋅+, Dp, V0, p, 0.921= Initial conditions and system of diff.equations definition: X x0 init x0 2− x0⋅ p ρ Dp( ) 2 ⋅ 18 µ⋅ 9.81 V0 ⋅ ⋅+, Dp, V0, p, y0 0 Dp V0 p := D t X,( ) X 1 1 1 6 Dp ρ a⋅ µ X 1 2 X 0 ⋅+⋅ 2 3 ⋅+ 2 St X 4 X 5 ,( )⋅ X 1 − 2 X 0 ⋅−( )⋅ 1 2 St X 4 X 5 ,( )⋅ X 6 ⋅ ρ X 4( ) 2 ⋅ 18 µ⋅ 9.81 X 5 ⋅ ⋅+ X 3 1 1 6 Dp ρ a⋅ µ X 3 X 2 −⋅ 2 3 ⋅+ 2 St X 4 X 5 ,( )⋅ X 3 − X 2 +( )⋅ 0 0 0 := Appendix D. Software codes 193 Function xyp returns (x,y) position of a particle of size Dp, at time t, starting from the initial position (x0,y0), with initial velocity V0, and gravity orientation p. xyp t Dp, V0, x0, y0, p,( ) n 100← X x0 init x0 2− x0⋅ p ρ Dp( ) 2 ⋅ 18 µ⋅ 9.81 V0 ⋅ ⋅+, Dp, V0, p, y0 0 Dp V0 p ← res rkfixed X 0, t, n, D,( ) Rkadapt X 0, t, n, D,( )on error← xp res n 1, ← yp res n 3, ← xp yp := Function timexyp returns the time needed for particle to reach the coupon surface (x=0). TOL 10 3− := Given xyp t Dp, V0, x0, y0, p,( )0 0 t 0> timexyp t Dp, V0, x0, y0, p,( ) Find t( ):= Function E calculates capture efficiency for particle size Dp, starting with initial velocity V0, from position (x0,y0), with gravity orientation p. . Appendix D. Software codes 194 E D p V0, x0, y 0, p,( ) n 0← N 100← tmax 0← tmax timexyp 1 D p, V0, x0, y 0, p,( )←on error x 1−← x xyp tmax D p, V0, x0, y0, p,( )0←on error y 0← y xyp tmax D p, V0, x0, y0, p,( )1←on error n n 1+← y 1<( ) x 0.001−>( )∧if break otherwise y0 1 N 2 N , 1..∈for n N 2 := Function Ecurve calculates capture efficiencies for particles starting with initial velocityV0, from position (x0,y0), with gravity orientation p. Ecurve V0 x0, y0, p,( ) M "Stokes" "Capture efficiency"( )← Dp D 10 6− ⋅← M stack M St Dp V0,( ) E Dp V0, x0, y0, p,( )( ), ← D 1 21, 201..∈for submatrix M 1, rows M( ) 1−, 0, cols M( ) 1−,( ) := M1 Ecurve V0 x0, y0, 1,( ):= M2 Ecurve V0 x0, y0, 0,( ):= M3 Ecurve V0 x0, y0, 1−,( ):= St1 M1 0〈 〉:= Eff1 M1 1 〈 〉 := St2 M2 0 〈 〉 := Eff2 M2 1 〈 〉 := St3 M3 0 〈 〉 := Eff3 M3 1 〈 〉 := 0.01 0.1 1 10 0 0.2 0.4 0.6 0.8 1 1 0 Eff1 Eff2 Eff3 100.01 St1 St2, St3, 195 Appendix E. Tables Table E.1 Summary results for the effect of velocity, triethylene glycol, Cold Unit nozzle, Setup #1 Run 14 43 37 38 17 39 40 41 21 19 20 Run time (min) 45.5 60.0 27.3 23.0 20.0 10.0 10.0 10.0 10.0 15.0 15.0 Air and liquid settings Rotameter 1 90/39 90/38 90/37 90/37 90/39 90/37 90/37 90/37 90/39 91/40.1 91/40 Rotameter 2 0/0 0/0 0.5/2 1.0/3 1.5/4.8 2.0/5 2.4/9 2.7/11 3.13/11. 3 3.13/11. 4 3.14/11. 4 Rotameter 3 0/0 30/1 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 Pump setting 8 8 8 8 8 8 8 8 8 8 8 Velocity Air to nozzle (m/s) 0.438 0.430 0.430 0.430 0.438 0.430 0.430 0.430 0.438 0.446 0.446 Secondary air (m/s) 0 0.12 0.211 0.320 0.433 0.552 0.713 0.832 0.972 0.973 0.977 Total air (m/s) 0.44 0.55 0.64 0.75 0.87 0.98 1.14 1.26 1.41 1.42 1.42 Liquid Liquid flow rate (g/min) 68.2 70 70 70 68.1 70 70 70 68.1 68.1 68.1 Liquid flow rate to aerosol (g/min) 1.02 1.46 1.60 2.03 2.44 3.19 3.35 3.79 3.52 3.72 3.44 Aerosol concentration from washdown (g/m3) 8.49 9.73 9.10 9.88 10.20 11.88 10.71 10.98 9.11 9.58 8.85 Aerosol concentration from shadowgraphy (g/m3) 6.00 6.31 6.34 5.16 7.33 5.1 4.64 4.95 5.07 2.94 4.37 Aerosol shadowgraphy Number of 260 image samples 1 5 5 5 1 5 5 5 1 1 1 Uncorrected Number of droplets 2011 10993 10377 9066 2148 9222 8961 9548 1775 1199 1493 Dmin (µm) 0.99 0.51 0.91 0.94 0.97 0.94 0.72 0.85 0.9 1.14 0.99 DV,10 (µm) 3.92 3.88 4.08 3.9 4.65 3.83 3.62 3.62 3.76 3.63 3.91 DV,50 (µm) 10.84 10.25 11.35 10.9 12.67 10.22 8.83 9.19 9.47 9.42 10.46 DV,50 st.dev. (µm) − 0.71 0.723 0.742 − 0.624 0.326 0.468 − − − DV,90 (µm) 27.48 21.55 25.05 23.46 24.58 22.02 19.92 20.47 18.57 16.52 17.38 Dmax (µm) 30 33 32 32 29 28 29 32 21 23 23 Log-normal distribution parameters a2, a3, a4 1.10009, 2.34139, 0.83173 1.09535, 2.2716, 0.80057 0.99316, 2.40646, 0.81847 0.80759, 2.3736, 0.79407 -0.5288, 2.6324, 0.66471 1.0953, 2.27252, 0.81418 1.0994, 2.09936, 0.7545 1.09528, 2.13731, 0.78397 1.08816, 1.6958, 0.68193 -3.6326, 2.59415, 0.41959 1.07643, 1.84745, 0.78458 SSE 0.01108 0.00247 0.00365 0.00445 0.00979 0.00378 0.00526 0.00312 0.00723 0.0153 0.00617 RMSE 0.01922 0.00866 0.01069 0.01179 0.01837 0.01162 0.01347 0.00988 0.01856 0.02579 0.01638 Corrected Number of droplets 16473 101010 92030 82055 17021 72739 73365 86829 10182 8207 9724 DV,10 (µm) 3.12 3.09 3.14 3.05 3.22 3.04 3.02 3 3.12 2.78 3.03 DV,50 (µm) 6.59 6.27 6.74 6.52 7.53 6.22 5.84 5.8 6.12 6.03 7.15 DV,50 st.dev. (µm) − 0.17 0.19 0.12 − 0.18 0.09 0.15 − − − DV,90 (µm) 17.78 16.08 18.08 16.71 19.5 15.95 13.74 14.15 14.56 13.52 14.09 Log-normal distribution parameters a2, a3, a4 1.08402, 1.74506, 0.71937 1.08446, 1.72098, 0.70602 1.08273, 1.78901, 0.74361 1.07873, 1.74996, 0.74785 1.08192, 1.92377, 0.79304 1.08191, 1.70306, 0.71071 1.08535, 1.62847, 0.65976 1.08329, 1.62282, 0.67139 1.08816, 1.6958, 0.68193 1.07369, 1.69518, 0.74402 1.07643, 1.84745, 0.78458 SSE 0.00683 0.00439 0.00439 0.00473 0.00627 0.00379 0.00526 0.00567 0.00723 0.00569 0.00617 RMSE 0.01509 0.01153 0.01172 0.01216 0.0147 0.01164 0.01347 0.01331 0.01856 0.01573 0.01638 Weight of deposits Upstream (mg) 0.1 1.0 62.0 143.6 187.6 148.9 174.8 231.2 168.0 279.0 231.1 Downstream (mg) 77.7 88.0 36.8 41.5 40.0 21.0 22.7 25.4 22.0 33.0 34.5 Deposition rates Upstream deposition rate from A.B.∗ (mg/hr) 0.13 1.0 136.3 374.3 562.8 893.4 1045.3 1387.2 1008 1116 924.4 Downstream deposition rate from A.B. (mg/hr) 103 88.0 80.9 108.2 120 126 135.7 152.4 132 132 138 k upstream (m/hr) 0.01 0.05 7.39 18.69 27.2 37.1 48.18 62.33 54.6 57.5 51.6 k downstream (m/hr) 6.01 4.46 4.39 5.40 5.81 5.23 6.26 6.85 7.15 6.80 7.70 E upstream 0 0 0.0032 0.0069 0.0087 0.0105 0.0117 0.0137 0.0108 0.0113 0.0101 E downstream 0.00381 0.00225 0.00190 0.00200 0.00185 0.00148 0.00152 0.00151 0.00141 0.00133 0.00150 k upstream (m/hr) 0.01 0.08 10.61 35.79 37.89 86.42 111.2 138.3 98.1 187.3 104.4 k downstream (m/hr) 8.50 6.88 6.30 10.34 8.08 12.18 14.45 15.19 12.85 22.16 15.59 E upstream 0 0 0.0046 0.0133 0.0121 0.0244 0.0270 0.0304 0.0193 0.0367 0.0204 E downstream 0.00539 0.00347 0.00273 0.00383 0.00258 0.00345 0.00351 0.00334 0.00253 0.00434 0.00304 196 Table E.2 Summary results for the effect of velocity, triethylene glycol, Hot Unit nozzle, Setup #2 Run 55 54 48 46 47 50 49 52 51 56 53 57 58 59 Run time (min) 120 130 120 120 120 120 120 150 123 120 120 40 40 40 Air and liquid settings Rotameter 1 11/5 21/15 .5 34/41 44/67 44/67 44/67 44/67 44/67 44/67 44/67 44/67 43/67 44/67 44/67 Rotameter 2 0/0 0/0 0/0 0/0 0/0 0/0 0.9/3. 5 1.32/ 5.5 1.7/7 1.98/ 9 2.28/ 10.5 2.72/ 15 2.92/ 17.5 3.25/ 22 Rotameter 3 0/0 0/0 0/0 0/0 25/0 47/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 Pump setting 6 6 6 6 6 6 6 6 6 6 6 6 6 6 Velocity Air to nozzle (m/s) 0.05 0.10 0.20 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.30 Secondary air (m/s) 0.00 0.00 0.00 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.90 1.00 1.10 Total air (m/s) 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.20 1.30 1.40 Liquid Liquid flow rate (g/min) 19 19 19 19 19 19 19 19 19 19 19 19 19 19 Liquid flow rate to aerosol (g/min) 0.131 0.281 0.451 0.484 0.679 0.834 1.188 1.452 1.661 1.80 1.98 2.586 3.043 3.504 Aerosol conc. from washdown (g/m3) 9.57 10.27 8.24 5.99 6.2 6.1 7.24 7.58 7.59 7.155 7.24 7.876 8.55 8.54 Aerosol conc. from shadowgraphy (g/m3) 9.68 10.16 5.75 4.95 6.94 6.96 8 6.93 8.27 6.23 7.99 6.36 7.72 7.62 Aerosol shadowgraphy Number of 260 image samples 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Uncorrected Number of droplets 14256 2317 2 1960 9 1803 1 1634 6 1584 4 1876 8 1757 0 1823 5 1502 6 1751 3 1405 7 1679 6 1585 3 Dmin (µm) 0.9 0.73 0.73 0.76 0.81 0.73 0.91 0.92 0.81 0.91 0.72 0.73 0.94 0.81 DV,10 (µm) 4.39 3.35 3.18 3.22 3.29 3.3 3.28 3.21 3.38 3.25 3.37 3.4 3.36 3.45 DV,50 (µm) 12.06 7.79 6.7 6.67 7.21 7.15 7.1 6.6 7.78 7.33 7.73 8.09 7.4 8.21 DV,50 st.dev. (µm) 0.58 0.47 0.17 0.145 0.199 0.368 0.291 0.218 0.508 0.273 0.237 0.304 0.406 0.439 DV,90 (µm) 24.37 20.66 16.9 14.94 15.31 17.09 16.32 15.55 18.14 16.35 16.8 17.48 16.46 18.37 Dmax (µm) 34 31 27 22 22 23 24 23 37 27 24 25 26 27 Log-normal distribution parameters a2, a3, a4 0.7259 9, 2.4818 7, 0.7820 4 1.088 09, 1.955 84, 0.783 88 1.087 44, 1.803 08, 0.721 67 1.092 97, 1.797 16, 0.691 94 1.093 19, 1.893 61, 0.718 55 1.091 2, 1.874 31, 0.742 61 1.090 49, 1.863 7, 0.739 08 1.090 52, 1.780 03, 0.706 26 1.090 51, 1.935 18, 0.769 78 1.088 68, 1.888 23, 0.737 15 1.092 81, 1.951 84, \0.76 237 1.092 58, 2.006 23, 0.764 67 1.095 21, 1.906 33, 0.731 74 1.094 65, 2.009 22, 0.772 46 SSE 0.0023 2 0.003 58 0.004 11 0.003 7 0.002 94 0.006 11 0.005 18 0.006 98 0.005 92 0.003 57 0.005 48 0.002 41 0.004 26 0.004 0 RMSE 0.0082 7 0.010 74 0.012 33 0.012 96 0.011 56 0.016 3 0.014 69 0.017 43 0.012 65 0.011 5 0.015 11 0.009 83 0.012 81 0.012 17 Corrected Number of droplets 129454 2101 95 1605 59 1165 08 1073 71 1049 35 1320 10 1173 71 1944 19 1206 43 1214 48 1032 21 1238 80 1215 01 DV,10 (µm) 3.23 2.76 2.59 2.7 2.72 2.89 2.8 2.75 2.98 2.65 2.97 2.78 2.92 3 DV,50 (µm) 7.16 5.18 4.87 4.92 5.2 5.03 4.97 4.78 5.11 5.09 5.22 5.41 5.19 5.4 DV,50 st.dev. (µm) 0.17 0.105 0.07 0.064 0.11 0.12 0.06 0.091 0.135 0.064 0.051 0.143 0.096 0.136 DV,90 (µm) 19.22 13.1 11.49 10.76 11.73 12.46 12.03 11.45 13.33 11.48 13.24 12.94 12.26 13.41 Log-normal distribution parameters a2, a3, a4 1.0863 1, 1.8593, 0.7534 1 1.082 55, 1.469 89, 0.606 27 1.079 9, 1.407 05, 0.587 16 1.084 36, 1.427 8, 0.576 65 1.081 47, 1.490 38, 0.617 05 1.088 57, 1.436 54, 0.563 89 1.086 3, 1.435 11, 0.572 69 1.087 27, 1.388 1, 0.546 3 1.089 81, 1.458 37, 0.568 03 1.079 04, 1.457 06, 0.621 95 1.087 55, 1.484 15, 0.592 44 1.080 56, 1.532 19, 0.645 38 1.088 37, 1.479 86, 0.584 25 1.087 02, 1.525 3, 0.613 63 SSE 0.0031 5 0.006 08 0.005 96 0.006 51 0.005 35 0.011 04 0.008 77 0.011 22 0.010 06 0.006 58 0.010 24 0.005 15 0.007 25 0.008 12 RMSE 0.0096 2 0.014 0.014 85 0.017 21 0.015 6 0.021 91 0.019 12 0.022 08 0.016 49 0.015 61 0.020 66 0.014 35 0.016 7 0.017 34 197 Run 55 54 48 46 47 50 49 52 51 56 53 57 58 59 Coupon deposits Upstream, corrected Number of 30 image samples 0 0 0 0 0 0 0 4 4 4 4 0 0 0 Number of droplets − − − − − − − 8790 2453 2829 7052 5 − − − Dmin (µm) − − − − − − − 1 1.78 1 0.94 − − − Dmin,inertial (µm) − − − − − − − − − − DV,10 (µm) − − − − − − − 48.57 44.02 41.2 41.37 − − − DV,50 (µm) − − − − − − − 71.9 72.59 68.8 84.28 − − − DV,90 (µm) − − − − − − − 106.1 9 108.6 2 119.9 4 132.5 2 − − − Dmax (µm) − − − − − − − 144 138 131 150 − − − Log-normal distribution parameters a2, a3, a4 − − − − − − − 3.325 17, 4.232 76, 0.299 77 - 14.10 942, 4.471 61, 0.310 5 2.990 27, 4.211 14, 0.413 03 - 85.36 634, 5.157 49, 0.233 18 − − − SSE − − − − − − − 0.004 25 0.006 44 0.002 92 0.002 27 − − − RMSE − − − − − − − 0.005 43 0.006 83 0.004 72 0.003 89 − − − Downstream, corrected Number of 30 image samples 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Number of droplets 7861 0 6081 4 3500 5 4341 3 3921 9 3900 9 2828 2 1454 92 1329 886 3404 8 1324 43 2350 8 5473 4 1957 6 Dmin (µm) 0.56 0.37 0.56 0.56 0.67 0.42 0.56 0.53 0.56 0.67 0.42 0.67 0.67 0.53 DV,10 (µm) 5.74 5.12 4.54 3.15 3.45 3.47 3.84 3.07 3.3 4.01 4.01 5.11 4.04 4.98 DV,50 (µm) 14.55 12.74 11.04 8.42 9.18 8.1 9.1 7.93 8.22 9.67 9.95 11.12 9.67 9.66 DV,90 (µm) 28.7 25.49 20.74 15.94 18.28 15.31 16.66 16.41 18.82 18.76 19.49 18.97 19.33 17.11 Dmax (µm) 46 37 32 34 30 28 29 31 37 33 35 32 38 33 Log-normal distribution parameters a2, a3, a4 - 4.762 39, 2.993 04, 0.463 37 - 2.717 66, 2.780 91, 0.508 27 - 6.657 09, 2.904 8, 0.348 3 - 6.133 36, 2.696 29, 0.338 06 - 4.189 25, 2.619 81, 0.411 5 - 2.335 43, 2.388 34, 0.427 18 - 6.233 66, 2.754 55, 0.317 42 - 1.762 16, 2.320 35, 0.506 21 - 3.195 7, 2.455 93, 0.408 17 - 4.684 68, 2.693 31, 0.377 41 - 3.832 99, 2.656 28, 0.423 26 - 12.95 815, 3.193 8, 0.219 54 - 5.841 46, 2.765 34, 0.337 04 - 4.331 5, 2.671 83, 0.302 65 SSE 0.001 21 0.000 74 0.000 99 0.001 42 0.002 12 0.001 01 0.001 5 0.000 42 0.002 28 0.000 67 0.000 35 0.001 14 0.001 11 0.000 64 RMSE 0.005 12 0.004 48 0.005 57 0.006 46 0.008 41 0.006 0.007 18 0.003 66 0.007 85 0.004 52 0.003 18 0.005 96 0.005 41 0.004 41 Weight of deposits Upstream (mg) 0 0 0 0 0 0 1.2 14.0 28.2 59.3 308.5 484.5 2493 * 5103 Downstream (mg) 102.4 158.2 100.8 66.5 66.6 61.1 69.0 95.0 87.6 90.5 120.7 47.9- 2.5 70.5- 5.7 88.2- 5.6 Deposition rates Upstream deposition rate from A.B. (mg/hr) 0 0 0 0 0 0 0.6 5.6 13.8 29.65 123.4 726.7 5 3740 7650 Downstream deposition rate from A.B. (mg/hr) 51.2 72.9 50.04 33.25 33.3 30.55 34.5 38 42.73 45.25 48.28 68.11 97.2 123.9 Deposition coefficients from washdown concentration k upstream (m/hr) 0 0 0 0 0 0 0.04 0.36 0.90 2.04 8.41 45.53 215.8 441.9 k downstream (m/hr) 2.64 3.50 2.99 2.78 2.65 2.47 2.35 2.47 2.78 3.12 3.29 4.27 5.61 7.16 Capture efficiencies from washdown concentration E upstream 0 0 0 0 0 0 0.000 0189 0.000 145 0.000 311 0.000 63 0.002 34 0.010 5 0.046 1 0.081 8 E downstream 0.014 6 0.009 73 0.004 15 0.002 57 0.001 84 0.001 37 0.001 09 0.000 981 0.000 965 0.000 962 0.000 914 0.000 988 0.001 19 0.001 33 * calculated from the load cell data 198 Table E.3 Summary results for the effect of droplet size distribution, triethylene glycol, Cold Unit nozzle, Setup #1 Run 23 24 25 31 26 33 28 29 30 Run time (min) 123 76.4 60 20 15 10 13 11 10 Air and liquid settings Rotameter 1 96/33 95/33 91.5/37 91/37 90/38 88/39 89.5/40 88.7/39.8 89/40 Rotameter 2 2.02/6.5 2.02/6.5 2.03/6.4 1.98/7.2 2.02/6.2 1.98/7.1 2/6.2 2.01/6.2 2.02/6.2 Rotameter 3 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 0/0 Pump setting 5.5 6 7 7.33 8 9 10 12 14 Velocity Air to nozzle (m/s) 0.433 0.431 0.419 0.434 0.434 0.430 0.440 0.436 0.438 Secondary air (m/s) 0.577 0.573 0.579 0.577 0.573 0.576 0.568 0.571 0.573 Total air (m/s) 1.01 1.00 1.00 1.01 1.01 1.01 1.01 1.01 1.01 Liquid Liquid flow rate (g/min) 7.2 20.3 46.4 54.1 72 94 92 95 95 Liquid flow rate to aerosol (g/min) 0.60 2.34 4.08 3.14 7.61 4.65 2.81 2.87 3.14 Aerosol concentration from washdown (g/m3) 2.18 8.52 14.94 11.36 27.61 16.91 10.18 10.41 11.36 Aerosol concentration from shadowgraphy (g/m3) 1.09 2.93 5.76 5.15 4.8 5.59 5.66 6.13 5.54 Aerosol shadowgraphy Number of 260 image samples 1 1 3 1 1 10 1 1 1 Uncorrected Number of droplets 685 1438 6568 1882 1810 18521 1732 1815 1733 Dmin (µm) 0.99 0.91 0.94 0.97 0.87 0.79 0.99 0.99 1.05 DV,10 (µm) 2.81 3.2 3.7 3.83 3.79 4.04 4.32 4.29 4.13 DV,50 (µm) 4.76 6.32 9.18 9.6 10.37 10.87 12.04 10.93 10.95 DV,50 st.dev. (µm) - - - - - - - DV,90 (µm) 8.64 17.04 19.43 24.23 34.31 24.2 22.27 23.54 21.97 Dmax (µm) 10 19 28 26 35 42 25 26 28 Log-normal distribution parameters a2, a3, a4 1.0948, 1.44027, 0.52844 1.09277, 1.75241, 0.68363 1.09006, 2.15188, 0.76024 1.0978, 2.22714, 0.7864 1.0941, 2.27518, 0.85806 1.10066, 2.33014, 0.82339 -0.47964, 2.56818, 0.65273 0.89148, 2.42341, 0.76659 0.3632, 2.44412, 0.71741 SSE 0.00846 0.01346 0.00409 0.00814 0.03168 0.00259 0.00931 0.00786 0.00654 RMSE 0.02908 0.02662 0.01209 0.01769 0.03009 0.00785 0.0193 0.01738 0.01528 Corrected Number of droplets 2093 8001 52113 13820 18045 213365 11796 12456 13003 DV,10 (µm) 2.45 2.71 2.96 2.97 2.97 3.12 3.18 3.27 3.19 DV,50 (µm) 3.93 4.87 5.96 6.25 6.05 6.5 7.14 7.11 6.86 DV,50 st.dev. (µm) − − n/a − − n/a − − − DV,90 (µm) 7.31 11.36 13.77 15.37 14.72 17.41 17.61 17.5 17.2 Log-normal distribution parameters a2, a3, a4 1.08832, 1.2311, 0.45211 1.08723, 1.40511, 0.54452 1.08264, 1.66709, 0.68653 1.08097, 1.71144, 0.70952 1.0804, 1.66653, 0.70145 1.10066, 2.33014, 0.82339 1.08339, 1.87036, 0.7667 1.09103, 1.83889, 0.72186 1.08652, 1.80964, 0.73229 SSE 0.00757 0.00958 0.00291 0.0028 0.00781 0.00259 0.00627 0.0048 0.00527 RMSE 0.02751 0.02245 0.01019 0.01039 0.01494 0.00785 0.01584 0.01359 0.01372 Coupon deposits Weight of deposits Upstream (mg) 25.2 67 273.8 154.6 159.6 207.7 277.5 231.2 230.5 Downstream (mg) 21.5 40.6 73.1 31.5 24.9 22.9 24.4 22.0 20.0 Deposition rates Upstream deposition rate from A.B. (mg/hr) 12.29 52.60 273.8 463.8 638.4 1246 1281 1261 1383 Downstream deposition rate from A.B. (mg/hr) 10.5 31.9 73.1 94.5 100 137 113 120 120 Deposition coefficients from washdown concentration k upstream (m/hr) 2.8 3.1 9.0 20.1 11.4 36.4 62.1 59.8 60.0 k downstream (m/hr) 2.37 1.85 2.41 4.10 1.78 4.01 5.46 5.69 5.21 Capture efficiencies from washdown concentration E upstream 0.0008 0.0008 0.0025 0.0055 0.0031 0.0101 0.0171 0.0165 0.0165 E downstream 0.00065 0.00051 0.00067 0.00113 0.00049 0.00111 0.00150 0.00157 0.00143 199 Table E.4 Deposition coefficients for the downstream side, m/hr Run 55 54 48 46 47 50 49 52 51 56 53 57 58 59 Dp (µm) U (m/s) 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.2 1.3 1.5 2 1.09 1.08 1.17 1.35 3.50 2.35 2.65 2.06 3.67 4.00 1.63 2.68 1.57 4.71 1.62 3 1.94 0.48 0.43 0.43 0.89 0.78 0.77 0.55 0.87 1.00 0.65 0.77 0.63 1.28 0.84 4 3.04 0.51 0.51 0.49 0.88 0.81 0.83 0.59 0.85 0.98 0.76 0.81 0.75 1.34 1.27 5 4.37 0.65 0.75 0.74 1.17 1.07 1.14 0.85 1.12 1.29 1.10 1.10 1.13 1.88 2.21 6 5.95 0.86 1.16 1.19 1.68 1.49 1.64 1.30 1.57 1.79 1.64 1.60 1.79 2.81 3.74 7 7.78 1.13 1.76 1.89 2.41 2.07 2.32 1.96 2.22 2.48 2.40 2.31 2.79 4.17 5.95 8 9.84 1.47 2.61 2.92 3.38 2.80 3.19 2.87 3.10 3.37 3.40 3.26 4.18 6.03 8.83 9 12.15 1.86 3.77 4.38 4.60 3.68 4.25 4.05 4.24 4.43 4.63 4.48 6.02 8.43 12.29 10 14.70 2.31 5.29 6.33 6.06 4.72 5.48 5.50 5.66 5.68 6.10 5.99 8.30 11.38 16.16 11 17.50 2.80 7.24 8.85 7.75 5.88 6.89 7.20 7.42 7.08 7.79 7.80 10.97 14.86 20.19 12 20.53 3.34 9.65 12.00 9.63 7.16 8.44 9.14 9.52 8.62 9.65 9.90 13.94 18.84 24.16 13 23.81 3.91 12.61 15.81 11.67 8.54 10.12 11.26 12.02 10.27 11.67 12.30 17.08 23.22 27.84 14 27.34 4.50 16.15 20.31 13.81 10.00 11.90 13.50 14.93 12.01 13.78 14.99 20.23 27.93 31.05 15 31.10 5.12 20.33 25.49 16.02 11.50 13.76 15.80 18.28 13.81 15.96 17.93 23.25 32.85 33.66 16 35.11 5.74 25.20 31.33 18.22 13.04 15.68 18.11 22.09 15.64 18.15 21.12 25.97 37.87 35.60 17 39.36 6.37 30.81 37.78 20.39 14.58 17.64 20.36 26.40 17.48 20.32 24.52 28.28 42.89 36.85 18 43.86 7.00 37.20 44.77 22.47 16.11 19.61 22.49 31.22 19.30 22.42 28.11 30.08 47.79 37.42 19 48.60 7.61 44.41 52.24 24.42 17.60 21.58 24.46 36.57 21.09 24.43 31.85 31.32 52.49 37.37 20 53.58 8.22 52.47 60.10 26.22 19.05 23.52 26.23 42.48 22.82 26.32 35.71 31.97 56.90 36.77 21 58.80 8.80 61.42 68.24 27.83 20.44 25.43 27.78 48.95 24.49 28.07 39.67 32.06 60.95 35.71 22 64.27 9.37 71.28 76.59 29.25 21.76 27.29 29.08 56.00 26.07 29.65 43.68 31.62 64.60 34.29 23 69.98 9.90 82.08 85.03 29.08 30.13 63.65 27.56 31.06 47.74 30.72 67.80 32.58 24 75.93 10.41 93.83 93.47 36.28 30.92 28.95 32.30 51.79 29.43 70.53 30.68 25 82.13 10.89 106.56 101.83 38.58 30.23 33.35 27.84 72.78 28.65 26 88.57 11.34 120.27 110.00 31.41 34.22 74.55 26.56 27 95.25 11.75 134.99 117.93 32.48 34.92 24.46 28 102.18 12.13 150.72 33.43 29 109.34 12.48 167.46 34.28 30 194.39 12.79 185.21 35.02 31 13.07 203.99 35.65 32 13.31 62.18 36.18 33 13.53 66.13 36.61 34 13.71 36.95 35 37.20 36 37.37 37 37.46 200 Table E.5 Weight of deposits (± 0.1mg) at the end of experiment, m(τi), mg 0.7 m/s 1.0 m/s Downstream Upstream Downstream Upstream Time,τi (sec) Glass St.steel Teflon Glass St.steel Teflon Glass St.steel Teflon Glass St.steel Teflon 30 0.8 0.4 0.7 1.3 1.3 1.5 0.7 0.6 1.2 2.1 2.2 2.7 60 1.8 1.4 2.1 2.1 2.3 2.8 1.2 1.3 1.8 3.6 3.6 4.1 90 2.2 2.4 2.6 3.9 2.9 4 1.4 1.4 2.8 6.4 6.2 8.8 120 2.9 2.5 2.9 5.1 5.4 5.8 2.2 2 3.4 8.3 8.9 9.5 180 4.2 4.5 4.2 7.9 7.6 8.2 3.2 2.9 4.1 12.4 11.5 13.1 300 5.6 7 7.5 14.4 13.1 12.2 4.6 6 6.5 18.9 18.8 20.1 Table E.6 Experimental integral deposition rates, exp,idr , mg/hr 0.7 m/s 1.0 m/s Downstream Upstream Downstream Upstream Time,τi (sec) Glass St.steel Teflon Glass St.steel Teflon Glass St.steel Teflon Glass St.steel Teflon 30 96 48 84 156 156 180 84 72 144 252 264 324 60 108 84 126 126 138 168 72 78 108 216 216 246 90 88 96 104 156 116 160 56 56 112 256 248 352 120 87 75 87 153 162 174 66 60 102 249 267 285 180 84 90 84 158 152 164 64 58 82 248 230 262 300 67 84 90 172.8 157 146.4 55 72 78 227 226 241 Table E.7 Correction factors (last column) obtained from several Cold Unit runs Equivalent Hot Unit Run* Cold Unit test Nozzle air velocity (m/s) Sec. air velocity (m/s) Total velocity (m/s) Liquid flow to the nozzle (ml/min) DV,50 (µm) DV,50,corr (µm) St. dev. of DV,50,corr (µm) Estimated DV,50 from the correlation, DV,50,est (µm) Correction factor, estV corrV D D k ,50, ,50, = S-5 T-1 0.162 0.090 0.25 10.9 7.37 5.52 0.26 23.8 0.232 S-17 T-2 0.151 0.099 0.25 10.9 9.02 6.28 0.10 25.3 0.248 S-18 T-3 0.162 0.099 0.26 10.9 7.97 5.87 0.04 23.8 0.247 S-19 T-4 0.162 0.000 0.16 10.9 8.09 5.97 0.07 23.8 0.251 S-20 T-5 0.151 0.050 0.20 10.9 8.36 6.07 0.07 25.3 0.240 S-21 T-6 0.139 0.270 0.41 10.9 9.61 6.52 0.25 26.7 0.244 S-27 T-7 0.151 0.107 0.26 21.5 10.58 6.88 0.15 37.6 0.183 S-34 T-8 0.112 0.847 0.96 21.5 11.31 7.81 0.23 49.8 0.157 S-36 T-9 0.151 0.406 0.56 10.9 7.94 5.97 0.10 25.3 0.236 *Hot Unit run with the same air velocity and liquid flow as used in the Cold unit test 201 Table E.8 Estimated volume median diameter after evaporation Run DV,50,est (µm) Correction factor, k k⋅DV,50,est (µm) Final k⋅DV,50,est, after evaporation (µm) 5% MEBR CO*CE*TRATIO* (effect of temperature) S-5 44.8 0.23 10.4 3.30 S-17 47.5 0.25 11.8 3.31 S-18 52.2 0.25 12.9 3.47 S-7 37.9 0.25 9.5 2.46 S-11 40.2 0.25 10.1 2.34 10% MEBR CO*CE*TRATIO* (effect of temperature) S-14 48.3 0.25 12.1 4.84 S-15 46.5 0.25 11.6 4.08 S-16 44.9 0.25 11.2 3.58 S-13 44.9 0.25 11.2 3.31 S-12 40.5 0.25 10.1 2.61 Effect of velocity S-34 75.4 0.16 11.8 4.55 S-35 85.5 0.16 13.7 5.27 S-36 46.9 0.24 11.1 4.25 S-37 35.6 0.26 9.3 3.33 Table E.9 Estimation of deposition rates at high temperature conditions from the deposition coefficients in the Cold Unit Run T (oC) Hot Unit dep.rate (mg/hr) Oil density (g/cm3) Gas viscosity (Pa⋅s) Aerosol conc. (g/m3) StHot Unit StCold Unit Relative change in C.E. due to St number Relative change in C.E. due to decrease in DV,50 Total relative change in C.E., k-values or dep. rates k-value for DV,50=5.0 µm in the Cold Unit, at a given velocity Dep. rate from the Cold Unit (mg/hr) Dep. rate at the Hot Unit conditions (mg/hr) 5% MEBR effect of temperature S-5 296 16.15 0.88 2.8E-05 4.47 0.51 0.51 0.9 0.461 2.83 25.64 11.83 S-17 340 4.66 0.88 3E-05 3.14 0.49 0.49 0.9 0.439 2.85 18.12 7.96 S-18 370 2.31 0.88 3E-05 3.14 0.47 0.47 0.9 0.426 2.82 17.94 7.64 S-7 390 3.53 0.88 3.1E-05 2.00 0.46 0.46 0.85 0.395 2.77 11.22 4.43 S-11 425 1.18 0.88 3.2E-05 1.46 0.45 0.45 0.85 0.382 2.77 8.21 3.14 10% MEBR effect of temperature S-14 296 23.08 0.89 2.8E-05 9.55 0.52 0.52 1 0.517 2.86 55.27 28.59 S-15 340 13.85 0.89 3E-05 6.54 0.49 0.49 0.95 0.468 2.86 37.91 17.73 S-16 370 7.73 0.89 3E-05 4.45 0.48 0.48 0.9 0.430 2.81 25.39 10.91 S-13 390 4.89 0.89 3.1E-05 3.47 0.47 0.47 0.9 0.421 2.80 19.69 8.30 S-12 425 2.58 0.89 3.2E-05 2.08 0.45 0.45 0.85 0.385 2.77 11.69 4.50 Effect of velocity S-19 344 7.02 0.88 3E-05 5.44 0.49 0.49 0.9 0.437 3.26 35.94 15.72 S-20 333 4.15 0.88 2.9E-05 4.63 0.49 0.49 0.9 0.443 2.97 27.90 12.35 S-17 340 4.66 0.88 3E-05 3.14 0.49 0.49 0.9 0.439 2.85 18.12 7.96 S-21 315 1.50 0.88 2.9E-05 2.31 0.50 0.50 0.9 0.451 2.64 12.34 5.57
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