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Development and use of a discrete element model for simulating the bulk strand flow in a rotary drum… Dick, Graeme 2008

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DEVELOPMENT AND USE OF A DISCRETE ELEMENT MODEL FOR SIMULATING THE BULK STRAND FLOW IN A ROTARY DRUM BLENDER  by  Graeme Dick B.Sc., University of British Columbia, 2006  A THESIS SUBMITTTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in  The Faculty of Graduate Studies (Forestry) UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2008 © Graeme Dick, 2008  ABSTRACT  In 2006 resin accounted for approximately 17% of the direct manufacturing costs for oriented strand board (OSB). Because of their increased dependency on pMDI-resins, this percentage is likely greater for oriented strand lumber (OSL) and laminated strand lumber (LSL). The cost of PF- and pMDI-resins is expected to face upward pressure as the cost of their primary constituents, natural gas and crude oil, continue to reach new highs. Therefore, there is strong economic incentive to optimize the use of resin in the production of these three products. This can be accomplished by addressing two key issues: reducing resin wastage and optimizing resin distribution on the strands. Both issues will be overcome by focusing on the blending process, where resin is applied to the strands. This work focused on development and use of a discrete element model (DEM) for simulating strand flow in a rotary drum blender using the EDEM software package. EDEM required the input of three material and three interaction properties. Development of the model involved creating the simulated environment (i.e. physical dimensions) and assigning appropriate material and interaction properties given this environment and the assumptions that were made.  This was accomplished in two steps, completing baseline bench-top  experiments and a literature review to determine appropriate parameters and initial value ranges for these properties, and then fine-tuning these values based on a validation process. Using the validated model, an exploratory study was conducted to determine the effect of four blender design and operating parameters (flight height, number of flights, blender rotational speed, and blender fill level) on bulk strand flow. The results were analyzed with regards to overall trends and by focusing on two perspectives, end users and blender manufacturers.  It was found that there was a strong relationship between these key  parameters and bulk strand flow. These results suggest that operating parameters of a blender, namely rotational speed and tilt angle, should be linked directly to the blender feed rate to ensure an optimal blending environment is maintained. In addition, manufacturers of blenders must take into consideration the range in final operating conditions when designing and positioning flights.  -ii-  TABLE OF CONTENTS Abstract ....................................................................................................................................ii Table of Contents....................................................................................................................iii List of Tables ........................................................................................................................... v List of Figures ........................................................................................................................vii List of Abbreviations ............................................................................................................... x Acknowledgements.................................................................................................................xi Chapter 1: Introduction ....................................................................................................... 1 1.1 Rationale........................................................................................................................ 3 1.2 Objectives and structure of thesis.................................................................................. 7 Chapter 2: Literature Review.............................................................................................. 9 2.1 Rotary drum blending.................................................................................................... 9 2.2 Discrete element method ............................................................................................. 11 2.2.1 Applications for discrete element methods....................................................... 13 2.3 Friction ........................................................................................................................ 15 Chapter 3: Laboratory Determined Coefficient of Static Friction ................................ 18 3.1 Introduction ................................................................................................................. 18 3.2 Materials...................................................................................................................... 19 3.3 Procedure..................................................................................................................... 20 3.4 Results ......................................................................................................................... 24 3.5 Conclusions ................................................................................................................. 27 Chapter 4: Determination of Suitable Material and Interaction Properties for use as Input Parameters in the RDBM ................................................................ 29 4.1 Introduction ................................................................................................................. 29 4.2 Procedure..................................................................................................................... 31 4.2.1 Screening design ............................................................................................... 31 4.2.2 Strand representation in EDEM ........................................................................ 34 4.2.3 Characterization of resination potential ............................................................ 34 4.3 Validation process – selection of appropriate input parameters.................................. 39 4.4 Results ......................................................................................................................... 49 4.4.1 Screening design – material properties ............................................................. 49 4.4.2 Screening design – interaction properties ......................................................... 50 4.4.3 Coefficient of rolling friction............................................................................ 51 4.4.4 Validation - coefficient of static friction........................................................... 52 4.5 Conclusions ................................................................................................................. 60 Chapter 5: Measuring the Effect of Rotary Drum Blender Design and Operating Parameters on the Bulk Strand Flow using a Response Surface Design .... 62 5.1 Introduction ................................................................................................................. 62 5.2 Methodology ............................................................................................................... 62 5.3 Results and discussion................................................................................................. 66 5.3.1 Overall predictive trends................................................................................... 66 5.3.1.1 Skewness ............................................................................................. 67 5.3.1.2 Effect of an atomizer boom on the skewness results........................... 73 -iii-  5.3.1.3 5.3.1.4 5.3.1.5 5.3.1.6  Kurtosis ............................................................................................... 77 Effect of an atomizer boom on the kurtosis results ............................. 80 Average time a strand spent in the resination region .......................... 83 Effect of an atomizer boom on the average time a strand spent in the resination region ........................................................................ 85 5.3.1.7 Discussion ........................................................................................... 85 5.3.2 Research applications........................................................................................ 86 5.3.2.1 Wood strand-based product manufacturers......................................... 87 5.3.2.2 Effect of the atomizer boom for wood strand-based product manufacturers ...................................................................................... 89 5.3.2.3 Blender manufacturers ........................................................................ 91 5.3.2.4 Effect of the atomizer boom for blender manufacturers ..................... 94 5.3.2.5 Discussion ........................................................................................... 97 5.4 Conclusions ................................................................................................................. 98 Chapter 6: Summary and Future Work......................................................................... 100 6.1 Future Work .............................................................................................................. 101 Literature Cited ................................................................................................................. 103 APPENDIX A: APPENDIX B: APPENDIX C: APPENDIX D: APPENDIX E: APPENDIX F: APPENDIX G: APPENDIX H:  Coefficient of Friction SAS Analysis and Results.................................... 108 Mechanical Properties of UHMW and HDPE .......................................... 113 Blender Drawing Provided by Coil Manufacturing.................................. 114 Write-out Every Time Interval Calculation .............................................. 116 VBA Macro for Sorting, Filtering and Analysing EDEM Data ............... 121 Macro for Performing Analysis in Image Pro Plus................................... 130 ANOVA Results for the Mechanical Properties of Aspen Strands .......... 132 ANOVA Results for the Interaction Properties of Aspen Strands and Polyethylene....................................................................................... 134 APPENDIX I: Results from the Student t-test for Shoulder and Toe Angles .................. 136 APPENDIX J: Results from the Exploratory Study Without and With an Atomizer Boom......................................................................................... 137  -iv-  LIST OF TABLES Table 1. Table 2. Table 3. Table 4.  OSB costs for benchmark north-central US mills from 2000 to 2006....................... 5 Pricing data for the constituents of PF- and pMDI-resin from 1999 to 2005............ 6 Strand combinations used for static friction coefficient tests. ................................. 21 Summary of test results for the coefficient of static friction between two wood strands at 22°C and 55% relative humidity ............................................................. 25 Table 5. Summary of test results for the coefficient of static friction between a wood strand and HDPE at 22°C and 55% relative humidity............................................. 26 Table 6. Regression parameters for determining the coefficient of static friction between two wood strands at 22°C and 55% relative humidity............................................. 27 Table 7. Regression parameters for determining the coefficient of static friction between a wood strand and HDPE at 22°C and 55% relative humidity. ............................... 27 Table 8. Required material and interaction properties for the RDBM. ................................. 29 Table 9. Materials used and materials that may come in contact in the RDBM.................... 29 Table 10. (Left) Aspen wood strand material properties and (right) interaction properties simulation design.................................................................................................... 31 Table 11. Factor levels for Quaking Aspen material properties............................................. 32 Table 12. Factor levels for interaction properties................................................................... 32 Table 13. Fixed factor levels for the blender operation and design. ...................................... 33 Table 14. Fixed factor levels for the liner and flights ............................................................ 33 Table 15. Blender rotational speed and fill level combinations for laboratory video recordings. .............................................................................................................. 41 Table 16. Simulation settings. ................................................................................................ 33 Table 17. Frame export settings used in Adobe Premiere Pro CS3. ...................................... 46 Table 18. Factors and response variables for simulations investigating the impact of the material properties.................................................................................................. 50 Table 19. Factors and response variables for simulations investigating the impact of the interaction properties.............................................................................................. 50 Table 20. Rolling and static friction coefficients for the simulations aimed at determining a suitable coefficient of rolling friction. ................................................................. 51 Table 21. Pairs of static friction coefficients used to identify a suitable set of values........... 53 Table 22. Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 4 and the laboratory results................................................. 54 Table 23. Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 5 and the laboratory results................................................. 54 Table 24. Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 6 and the laboratory results................................................. 55 Table 25. Summary of runs 4 to 6 and the laboratory taken shoulder and toe angle results. Italicized values indicate those angles that are significantly different (α = 0.05) from the image results. ........................................................................................... 55 Table 26. Summary of shoulder and toe angles obtained at 15.5 to 25.5 RPM with the coefficients of static friction set at 0.14 and 0.07................................................... 56 Table 27. Summary of material and interaction properties for use with EDEM.................... 61 Table 28. Response surface design matrix. ............................................................................ 64 Table 29. Response surface design factor levels .................................................................... 64 Table 30. Factor levels used in the skewness and average time spent in resination region analyses. ................................................................................................................. 67 -v-  Table 31. List of effects for the skewness showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy................................................................................................................. 68 Table 32. List of effects for the skewness when an atomizer boom is present, showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy. ............................................................. 74 Table 33. List of effects for the kurtosis showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy................................................................................................................. 78 Table 34. List of effects for the kurtosis when an atomizer boom is present, showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy. .................................................... 81 Table B1: Mechanical properties of UHMW ...................................................................... 113 Table B2: Mechanical properties of HDPE ......................................................................... 113 Table G1: ANOVA results for the impact the material properties have on the skewness of the resulting histogram. .................................................................................. 132 Table G2: ANOVA results for the impact the material properties have on the kurtosis of the resulting histogram........................................................................................ 132 Table G3: ANOVA results for the impact the material properties have on the count of the resulting histogram........................................................................................ 132 Table G4: ANOVA results for the impact the material properties have on the processing time of the respective simulation. ....................................................................... 133 Table H1: ANOVA results for the impact the interaction properties have on the skewness of the resulting histogram. .................................................................................. 134 Table H2: ANOVA results for the impact the interaction properties have on the kurtosis of the resulting histogram. .................................................................................. 134 Table H3: ANOVA results for the impact the interaction properties have on the count of the resulting histogram. .................................................................................. 134 Table H4: ANOVA results for the impact the interaction properties have on the processing time of the respective simulation. ..................................................... 135 Table I1: Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 4 and the laboratory results ran at 15.5 RPM. .. 136 Table I2: Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 4 and the laboratory results ran at 25.5 RPM. .. 136 Table J1: Results from exploratory study without an atomizer boom ................................ 137 Table J2: Results from exploratory study with an atomizer boom ..................................... 138  -vi-  LIST OF FIGURES Figure 1. Canadian structural panels production from 1982 to 2005 ...................................... 1 Figure 2. Size of the total North American framing lumber market and the potential market size for engineered wood products............................................................... 4 Figure 3. Flow chart showing the basic constituents that are used in the production of PFand pMDI-resin. The shaded constituents are included in Table 2 ......................... 6 Figure 4. Turner’s spinning disc blender showing a vertical spray pattern ........................... 10 Figure 5. Lignex spinning disc blender showing a diagonal spray pattern............................ 11 Figure 6. Flow chart for operations performed in a typical DEM algorithm......................... 12 Figure 7. Diagram showing the pair of forces that determines the friction torque................ 16 Figure 8. Photograph of sliced aspen veneer strands, (a) primary surface and (b) secondary surface.............................................................................................. 20 Figure 9. Inclined plane jig with the various components indicated ..................................... 21 Figure 10. Two sleds used for the inclined plane test, (left) sled equipped with dowels for .... larger contact pressures and (right) sled equipped with adhesive surface for lower contact pressures. ........................................................................................ 22 Figure 11. Photograph of the testing procedure for the coefficient of static friction of wood strands using the inclined plane technique, showing a parallel – parallel orientation. ............................................................................................................ 23 Figure 12. Schematic of inclined plane jig showing the measurement locations for Equation 5 ............................................................................................................. 24 Figure 13. Static coefficient of friction between two wood strands for increasing contact pressures and different strand sample orientations. .............................................. 25 Figure 14. Static coefficient of friction between a wood strand and HDPE for increasing contact pressures and different strand and HDPE sample orientations. ............... 26 Figure 15. Schematic showing the representation of sticks using a series of six spheres (left) and a schematic showing the placement of a template over top of the six spheres to aid in the visual analysis process (right). ....................................... 34 Figure 16. Blender schematic showing the resination region outlined in blue. ..................... 35 Figure 17. Simulation and photographed examples of increasing skewness caused by increasing rotational speeds from 15.5 RPM to 25.5 RPM .................................. 37 Figure 18. Sample histogram with a respective skewness, kurtosis, and count of -0.3024, -0.2794, and 22 453. ............................................................................................. 38 Figure 19. Schematic showing the placement of the lights and camera/video camera relative to the laboratory blender, with the axis indicated in blue. ....................... 40 Figure 20. Photograph showing the placement of the lights and camera/video camera relative to the laboratory blender. ......................................................................... 40 Figure 21. Example of (left) a screen shot taken of an animated GIF illustrating the simulation results and (right) a screen shot taken of the video footage taken in the laboratory. ................................................................................................... 41 Figure 22. Schematic showing the shoulder, σ, and toe, τ, angles for two points of detachment. The 0o and 90o reference angles are shown in blue. ......................... 42 Figure 23. Illustration showing the identification of the shoulder and toe angle from the laboratory video footage. ...................................................................................... 44 Figure 24. Illustration showing the identification of the shoulder (σ) and toe (τ) angle from the simulation results using the streaming effect. ........................................ 45 Figure 25. Schematic of the x, y, z coordinate system relative to the blender....................... 46 -vii-  Figure 26. Screen shot taken in Image Pro Plus v6 showing the placement of the thick, line profile and the cooresponding grayscale values ............................................ 48 Figure 27. Example of simulation results overlaid on top of grayscale results...................... 49 Figure 28. Skewness as a function of the coefficient of rolling friction ................................ 52 Figure 29. Baseline grayscale results for the laboratory blender running empty................... 57 Figure 30. Grayscale results for the blender running at 15.5 RPM and 1/8th full. ................. 58 Figure 31. Grayscale results for the blender running at 20.5 RPM and 1/8th full. ................. 59 Figure 32. Grayscale results for the blender running at 25.5 RPM and 1/8th full. ................. 59 Figure 33. Schematic of a blender fitted with an atomizer boom, shaded grey ..................... 66 Figure 34. Prediction profiles generated in SAS showing the relationship between the skewness and the (top-left) number of flights, (top-right) flight height, (bottom-left) fill level, and (bottom-right) blender rotational speed..................... 68 Figure 35. Schematic showing the angle of repose, α, for a pile of wood strands on a horizontal surface.................................................................................................. 69 Figure 36. Simulation images showing the charge level per flight and the discharge pattern when a relatively small number of flights are employed. The simulated blender has 4-6 inch flights and is rotating at 23.39 RPM and is 1/8th full ....................... 70 Figure 37. Simulation images showing the charge level per flight and the discharge pattern when a relatively large number of flights are employed. The simulated blender has 16-6 inch flights and is rotating at 23.39 RPM and is 1/8th full ..................... 71 Figure 38. Simulation image showing strands rolling in the corner of the drum, where there are 8-4 inch flights and the blender is rotating at 18.71 RPM and is 1/4 full. ...... 71 Figure 39. (Left) Simulation image showing the dispersion of strands across relatively few flights when the blender is rotating at 18.71 RPM and (right) across many flights when the blender is rotating at 28.07 RPM. In both cases the blender has 16-4 inch flights and is 1/8th full. .................................................................................. 72 Figure 40. Prediction profiles generated in SAS showing the relationship between the skewness and the (top-left) number of flights, (top-right) flight height, (bottom-left) fill level, and (bottom-right) blender rotational speed when an atomizer boom is included in the simulation ........................................................ 75 Figure 41. Simulation images showing the dispersion of strands across the blender diameter when there is (top-left) no atomizer boom and there are 2 inch flights, (top-right) no atomizer boom and there are 6 inch flights, (bottom-left) an atomizer and there are 2 inch flights, and (bottom-right) an atomizer boom and there are 6 inch flights. In all cases there were 16 flights and the blender rotated at 23.39 RPM. ........................................................................................... 76 Figure 42. Simulation image showing strands as they become wedged between the atomizer boom and blender wall when operating at elevated fill levels, indicated by the dashed oval. In this case the blender is ¼ full and is equipped with 8, 4 inch flights and is rotating at 28.07 RPM. ............................................. 77 Figure 43. Prediction profiles generated in SAS showing the impact of the (left) number of flights on the relationship between (right) the kurtosis and the flight height... 79 Figure 44. Prediction profiles generated in SAS showing the impact of the (right) flight height on the relationship between (left) the kurtosis and the number of flights.. 79 Figure 45. Prediction profiles generated in SAS showing the impact of the (left) number of flights on the relationship between (right) the kurtosis and the flight height when an atomizer boom is present........................................................................ 82  -viii-  Figure 46. Prediction profiles generated in SAS showing the impact of the (right) flight height on the relationship between (left) the kurtosis and the number of flights when an atomizer boom is present........................................................................ 82 Figure 47. Prediction profiles generated in SAS showing the relationship between the average time spent in the resination region and the (left) flight height and (right) blender rotational speed............................................................................. 83 Figure 48. Simulation images showing (top-left) the clustering of strands at relatively low speeds with 2-inch flights, (top-right) the dispersion of strands at relatively high speeds with 2-inch flights, (bottom-left) the clustering of strands at relatively low speeds with 6-inch flights, (bottom-right) the dispersion of strands at relatively high speeds with 6-inch flights. .......................................... 84 Figure 49. Contour graphs for the skewness based on the fill level and blender rotational speed using 3, 4, 5, and 6-inch flights. The number of flights has been fixed at 14....................................................................................................................... 88 Figure 50. Contour graphs for the skewness based on the fill level and blender rotational speed using 3, 4, 5, and 6-inch flights when an atomizer boom is present. The number of flights has been fixed at 14.................................................................. 90 Figure 51. Contour graphs based on number of flights and flight height. The rotational speed ranged from 23 to 28 RPM and the fill level was fixed at 25%. ................ 93 Figure 52. Contour graphs for the inclusion of an atomizer boom based on number of flights and flight height. The rotational speed ranged from 23 to 28 RPM and the fill level was fixed at 25%............................................................................... 95 Figure 53. Simulation images showing the streaming of strands off of the atomizer boom at (a) 18.71 RPM, (b) 23.39 RPM, and (c) 28.07 RPM. The simulated blenders were each equipped with 8-4 inch flights and filled 1/4 full. The angles that the strands stream off of the boom are approximately 14°, 12°, and 7° from vertical respectively. .......................................................................................................... 96 Figure C1: Schematic of blender layout and atomizer spray patter. ................................... 114 Figure D1: Schematic of an example where the write-out time interval is set too large..... 117 Figure D2: Schematic of the extreme case scenario where an object falls from the top of the blender, A, through the resination region, B to C, and collides with the bottom of the blender, D.................................................................................... 118 Figure D3: Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the first interval is located marginally less than one full Δtw from the top of the region. .............................................. 119 Figure D4: Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the last interval is located marginally less than one full Δtw from the bottom of the region......................................... 119 Figure D5: Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the first interval is located marginally below the top of the region................................................................................ 120 Figure D6: Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the last interval is located marginally above the bottom of the region.......................................................................... 120  -ix-  LIST OF ABBREVIATIONS ANOVA – Analysis of variance BBF  – Billion board feet  BSF  – Billion square feet 3/8 inch basis  COV  – Coefficient of variation  DEM  – Discrete element modeling  EWP  – Engineered wood products  GIF  – Graphics interchange format  HDPE  – High density polyethylene  IPP  – Image pro plus  LSL  – Laminated strand lumber  OSB  – Oriented strand board  OSL  – Oriented strand lumber  PE  – Polyethylene  PF  – Phenol formaldehyde  pMDI  – Polymeric diphenyl methane diisocyanate  RPM  – Revolutions per minute  RSM  – Response surface methodology  RDBM  – Rotary drum blending model  SF  – Square feet  UHMW – Ultra high molecular weight polyethylene VBA  – Visual basic for applications  -x-  ACKNOWLEDGEMENTS  I would like to extend my sincere gratitude to those who have helped ensure that this project was a success. To my committee members: Drs. Gregory Smith, Paul McFarlane, and Erik Eberhardt, your guidance throughout this process has certainly been appreciated. To my colleagues: Jo Chau, Emmanuel Sackey, Solace Sam-Brew, Dr. Kate Semple, and Chao Zhang, your assistance and support have made this experience enjoyable. To my family and friends, your ongoing support and devotion have helped me reach this point. And to my wife, Sara, you have kept me grounded throughout this experience by simply listening to my challenges and always being there. A special thank you goes to Weyerhaeuser Canada for their financial support and guidance throughout this project, and to the Natural Sciences and Engineering Research Council of Canada for their financial support.  -xi-  CHAPTER 1  INTRODUCTION  Beginning in the mid-1970s, structural products composed of reconstituted wood strands have increasingly become a major component of Canada’s forest products industry. This transition began with the advent of waferboard and quickly progressed to oriented strand board (OSB), a direct substitute for plywood in the construction market (Figure 1). In 2006, oriented strand board accounted for approximately 63% of all structural panel production in Canada (Louisiana-Pacific Corporation 2008; Spelter et al. 2006). Laminated strand lumber (LSL) and oriented strand lumber (OSL) were subsequently developed to compete with solid sawn lumber in the same market. In today’s North American residential construction market, these wood strand-based products can be found everywhere from the sheathing on exterior walls, to the headers used to span garage door openings, and to the specialty studs used behind kitchen cabinets.  16,000  14,000  Million sf - 3/8" Basis  12,000  10,000  8,000  OSB  6,000  4,000  2,000  Plywood  19 82 19 83 19 84 19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05  0  Year  Figure 1. Canadian structural panels production (million SF - 3/8" basis) from 1982 to 2005 (data from: International Wood Markets Group 2006). -1-  The North American production capacity for OSB is expected to continue increasing into the future. In fact, if all of the OSB projects tabled in 2005 were to go ahead as planned, capacity would balloon from 23.7 million m3 (27.5 BSF) in 2005 to 31.9 million m3 (37 BSF) by 2010 (International Wood Markets Group 2006). However, because of recent slowdowns in the US housing market, largely driven by the sub-prime mortgage crisis, and an accompanying over-supply of OSB, these previous projections have been stifled. According to a report by Dixon (2008), North American OSB capacity had already reached 26.2 million m3 by the end of 2007; however, any additional capacity that was planned to come on stream by 2010 had been postponed indefinitely. The increased production of OSB is also being experienced beyond North American borders. While most of the additional capacity that was expected to come on stream in the near future is located in North America, Europe’s OSB industry has also been expanding, albeit at a considerably lower volume (International Wood Markets Group 2006).  This is largely  because of the relatively slow adoption of OSB into European building codes (World Forest Institute 2007). This progress has been further hindered by the effect of North American OSB producers dumping excess supply in Europe, discouraging the development of new domestic facilities (Higgs 2008). The total European capacity reached 3.9 million m3 by the end of 2007. By 2009 an additional 1.4 million m3 is expected to come on stream. As mentioned, there are three products that fall beneath the umbrella of wood strand-based products: OSB, LSL, and most recently OSL. During the manufacture of these products a mat consisting of a large number of strands is consolidated under heat and pressure to form a single entity, or billet. In order for the consolidation to be effective, resin must be employed to hold the final product together. The application of resin onto the strands is perhaps the least studied and understood aspect of the manufacturing process; however, it has one of the most significant effects on the strength and durability of the final product and in 2006 accounted for nearly 17% of the direct manufacturing costs (Spelter et al. 2006). The application of resin onto the strands begins when the strands are fed from dry strand bins and deposited in the blender. Blenders are between 8 and 11 feet in diameter and extend 20 to 35 feet in length. As the drum rotates at typically between 8 and 22 RPM the strands tumble along its length and become resinated (Smith 2005). -2-  The strands are resinated using either a series of spinning disc atomizers mounted along the drum’s axis of rotation for liquid resin, or using a conveyor metering system for powdered resin.  Spinning disc atomizers are the predominant system employed in blenders  commissioned since the early-1990s. The objective of blending is to achieve a uniform resin distribution on both sides of all strands. The ability of the process to effectively resinate the strands is dependent on the overall blender design, such as the drum diameter, atomizer locations, and flight design; as well as on the operational environment, such as the rotational speed, fill level, and tilt angle of the blender (Coil 2007b; Coil 2008; Maloney and Huffaker 1984; Smith 2005; Smith 2006). 1.1  Rationale  The respective market share of structural products composed of reconstituted wood strands is forecast to continue increasing. This is particularly true for OSB where its share of the structural panel demand in North America has increased from approximately 35% in 1995 to 63% in 2008. OSB market share is forecast to further increase to approximately 72% by 2012 (Louisiana-Pacific Corporation 2008). In addition to OSB’s market share growth however, there is great potential for LSL and OSL to increase their share of the framing lumber market. LSL and OSL are both members of the family of products referred to as engineered wood products (EWP). Currently, EWP only capture approximately 30% of the potential 12 BBF North American framing lumber market, with the sub-sector of wood strand-based products only accounting for 5% (Figure 2) (Louisiana-Pacific Corporation 2008).  -3-  Total North America Framing Lumber (~24 BBF)  Current & Potential EWP Market (~12 BBF)  Lumber 70%  Applications suitable for EWP substitution 50%  LVL & I-Joists 25%  Potential Market Growth for EWP  OSL & LSL 5%  Figure 2. Size of the total North American framing lumber market and the potential market size for engineered wood products (adapted from: Louisiana-Pacific Corporation 2008). Although the five year period between 2001 and 2006 saw the growth of the wood strandbased product sector outpace the growth of the overall construction market (by 11% compared to 2% (Louisiana-Pacific Corporation 2008), continued growth will be largely dependant on the relative manufacturing costs. As an example, in 2004 the average total manufacturing cost for structural lumber, OSL, and LSL was similar. Lumber was 188 US$/m3, while OSL and LSL were approximately 180 US$/m3 (International Wood Markets Group 2006; Spelter et al. 2006). These figures assume that OSL and LSL have a similar cost structure as OSB. In reality the cost of OSL and LSL will be marginally greater than OSB because of the type of resin employed, product density, and wood utilization. Subsequently, the costs are likely nearer, or even past those of structural lumber. In recent years the total manufacturing cost of wood strand-based products has faced increased pressure. In 2006 the average cost reached 201 US$/m3 of OSB (Table 1) (Spelter et al. 2006). Much of this increase was caused by escalating wood costs, affecting solid lumber and EWP alike. In addition to wood costs however, wood strand-based products have experienced escalating resin costs, increasing by 61% between 2000 and 2006 (Table 1) (Spelter et al. 2006). Increasing resin costs have created a need to optimize and subsequently reduce the amount of resin employed in the manufacture of these products in order to remain -4-  cost competitive in the structural panel and framing markets. Optimization is only possible however if there exists a thorough understanding of the process in which resin is applied to the strands in a rotary drum blender. Table 1. OSB costs for benchmark north-central US mills from 2000 to 2006 (data from: Spelter et al. 2006). Cost (US$/m3) 2000 2001 2002 2003 2004 2005 2006 Direct costs Wood 56 54 53 60 67 85 82 Labor 20 20 20 21 21 22 22 Resin 18 19 19 26 27 32 29 Wax 6 6 6 7 7 8 7 Energy 11 13 12 15 17 19 19 Supplies 14 14 14 15 15 15 15 Total direct 125 125 124 144 154 181 175 Fixed costs General 6 6 6 6 6 6 6 Depreciation 23 21 20 21 20 20 20 Total fixed 29 27 26 27 26 26 26 Total costs 154 153 150 171 180 207 201 There are only a few studies on the operation of a rotary drum blender in the literature with these dating from the mid-1980s (Beattie 1984; Coil and Kasper 1984; Lin 1984). More recently, Smith (2005) examined the modes of tumbling in a full-sized rotary drum blender. All of these studies were focused on OSB. To date there have not been any published studies on the blending of OSL and LSL. The blending of these products differs from OSB in several important aspects. First, OSL and LSL strands exceed 6 inches in length, while OSB strands rarely exceed 5 inches. Second, LSL operations only employ polymeric diphenyl methane diisocyanate (pMDI) resin, compared with OSB operations that typically use a combination of phenol formaldehyde (PF) and pMDI resins. During blending approximately 3.5% resin based on the oven dry weight of furnish is added. The precise amount depends on the operation, resin type, and product grade (Spelter et al. 2006). As indicated, resin costs are a major materials cost in the production of wood strandbased products. Because PF- and pMDI-resins are derived from crude-oil and natural gas (Table 2 and Figure 3), it is very likely that resin costs will remain high or even increase over the next five years. Significant resin savings may be possible through blending optimization. -5-  Due to the large volume of resin used in the manufacture of strand technology products, even small decreases in resin consumption will lead to significant savings. Table 2. Pricing data for the constituents of PF- and pMDI-resin from 1999 to 2005 (data from: Winchester 2005). Methanol Urea Phenol Crude Oil Natural Gas US$/USG US$/ton US$/lb US$/Barrel US$/MMBTU 1999 0.26 – 0.40 100 – 140 0.25 – 0.36 17 3.75 2001 0.35 – 0.80 140 – 290 0.30 – 0.40 24 5.24 2003 0.75 – 1.00 160 – 230 0.40 – 0.45 26 5.81 2005 0.90 – 0.95 270 - 300 0.50 – 0.70 60+ 9.80  Natural Gas  Crude Oil  Methanol  Phenol  Methanol  Formaldehyde  Benzene  Formaldehyde  Phenol  PF  pMDI  Figure 3. Flow chart showing the basic constituents that are used in the production of PFand pMDI-resin. The shaded constituents are included in Table 2 (adapted from: Winchester 2005). The design and operation of rotary drum blenders has remained virtually unchanged since the mid-1980s when the long-retention time, Mainland Manufacturing blenders emerged as the blender of choice amongst the wood strand-based product industry. Although Mainland Manufacturing has subsequently been bought out by Coil Manufacturing, very little has been changed with regards to the operation and design of the blenders. In general, as the capacity demands have increased over the years with new, sophisticated operations, the blender dimensions have been scaled up. In the 1950s and 60s, rotary drum blenders were 4 to 5 feet in diameter and 20 feet long (Coil 2002; Watkins 1981). More recently, blenders can be up to 11 feet in diameter and 45 feet long (Coil 2007b; Coil and Kasper 1984; Smith 2005). While this process of scaling the blenders has been widely accepted throughout the industry, as previously mentioned resin costs have placed increased pressure on the end users of rotary -6-  drum blenders to optimize the process. The primary challenge hindering progress is the lack of research into the inner dynamics of the blending process and the inability to quantify and model the bulk strand flow. In the past, blender design and operating parameters have been selected based on visual inspection and past experience. Although these empirical approaches have resulted in a blender design that fits with the spectrum of end-users’ needs and a reasonable understanding of the impact design and operating parameters have on the strand flow, a quantitative, systematic approach is necessary to further enhance the process. 1.2  Objectives and structure of thesis  This study seeks to understand the blending process by developing and evaluating a quantitative discrete element model (DEM) of the blending process. Chapter 2: Literature review on discrete element modeling and friction. A review of static, kinetic, and rolling friction will facilitate the selection of initial coefficients as input parameters in the DEM. Additionally, this review will help to understand how these coefficients should change to achieve better correlation between the simulated and laboratory results. Chapter 3: Determination of static friction coefficients between Aspen wood strands and between an Aspen wood strand and high density polyethylene. The flights and the inside liner of the blender are constructed of either high density polyethylene or ultra high molecular weight polyethylene. For the purpose of this project, and because the specifications of these two materials do not differ considerably, it will be assumed that the liner and flights are both constructed of high density polyethylene. The friction values will be used as a starting point within the EDEM software package and may be adjusted accordingly during a subsequent study. Chapter 4: Calibration of the rotary drum blending model (RDBM) with experiments conducted in the 6 foot laboratory blender. This process will be completed by adjusting various material and interaction properties in the model. Chapter 5: Completion of an exploratory study aimed at determining the impact several blender design and operating parameters have on the bulk strand flow within a -7-  simulated 6 foot blender. This study will provide a profound understanding of the impact changes made to the blending environment will have on the strand flow through a blender. Chapter 6: Evaluation of potential future work. As the software and computing technology advances many of the limitations that were present during this project will become less significant. The most logical progression will be the scaling of the simulated blender up to a full size industrial blender. This will enable research to be completed that focuses on the impact blender tilt angle has on the residence time of strands.  -8-  CHAPTER 2  LITERATURE REVIEW  2.1  Rotary drum blending  Rotary drum blending has been the method used for coating wood strands with resin and wax for the manufacture of oriented strand board since this product’s industrial emergence in the late-1970s (Moeltner 1980). In fact, this blending technique was also employed for OSB’s predecessor, waferboard, since its emergence in 1955 (Gunn 1972). Although the resin was applied exclusively in a powdered form until the mid- to late-1970s, the fundamental process was similar to today’s blenders that tend to employ liquid resins. During the blending process strands enter from one end of the blender and are then lifted by a series of flights, which extend from the inside of the drum’s circumference. The strands eventually fall from the flights and migrate along the length of the blender. This process repeats until the strands are discharged from the opposite end of the blender. The rate of migration along the blender length is a function of the blender tilt angle. As reported by Smith (Smith 2005), the strands move forward the most while they are in freefall. As the strands move along blender length they are coated with wax and resin. The manner in which powdered and liquid resin adhere to and coat the strands is considerably different. While powdered resin adheres to the strands via the wax droplets that are applied at the onset of the blending process, liquid resin adheres directly to the strands in droplet form (Coil 2002). The transition towards liquid resin was largely driven by the relative cost advantage of liquid resin, the health concerns caused by the dust from powdered resin, and the relatively high wax content required to improve the affinity of the powdered resin to the wood surface (Chiu and Scott 1981; Maloney and Huffaker 1984). Early rotary drum blenders were 4 to 5 feet in diameter and 20 to 25 feet long (Coil 2002; Watkins 1981). By the early 1980s it was widely accepted that blender diameters of 8 feet and greater were required to ensure adequate resin coverage on the strands and/or wafers and to meet capacity requirements (Beattie 1981). -9-  At around this same time liquid resin  increased in popularity and a system was developed and adopted across the industry for metering liquid resin into the blenders and distributing it onto the strands. This system involved using a series of spinning disc atomizers (Beattie 1984; Coil and Kasper 1984; Lin 1984). After several variations in the positioning of these atomizers within the blenders (Figures 4 and 5), a design was eventually accepted whereby the atomizers were mounted along a stationary shaft running down the length of the blender.  The atomizers were  positioned to disperse resin in a horizontal plane. Except for the plane of the spray pattern and the stationary shaft or boom, this design was similar to Turner’s design (Figure 4). Spinning disc  Rotating shaft  Resin spray region  Figure 4. Turner’s spinning disc blender showing a vertical spray pattern (adapted from: Beattie 1984).  -10-  Resin spray region  Spinning disc  Resin feed  Figure 5. Lignex spinning disc blender showing a diagonal spray pattern (adapted from: Beattie 1984). Modern blenders are provided nearly exclusively by Coil Manufacturing Limited of Surrey, British Columbia. Their blenders range in size from 8 feet in diameter and 20 feet long up to 11 feet in diameter and 45 feet long; however, the 11 foot diameter blenders are most common in newer operations requiring relatively high capacity (Coil 2007b; Smith 2005). These blenders operate with strand volumes ranging from 25% to 50% of the blender volume and with a tilt angle of approximately 3°. Blenders revolve at between 8 and 22 RPM depending on the blender diameter, number of flights, flight height, and resin type (Coil 2008). As a general rule, liquid resins require higher speeds than powdered resins and as the diameter increases the speed decreases (Coil 2008). 2.2  Discrete element method  Discrete element methods (DEM), or distinct element methods as they are also known (Cundall 1989), are a family of numerical techniques suitable for modeling the movement and interaction of rigid or deformable bodies, particles, or arbitrary shapes that have been subjected to external stresses or forces (Bicanic 2004). As reported by Mustoe and Miyata (2001), most of these methods are based on cylindrical- or spherical-shaped particles because of the inherent ease in detecting contacts between particles. In recent years there has been an increased number of DEMs based on noncircular-shaped bodies, such as polygonal bodies, for specific applications. The vast majority of the commercially available software packages -11-  however, still rely on cylindrical- or spherical-shaped particles for 2D and 3D modeling respectively. These particles may be clustered and/or overlapped rigidly or elastically to form different shaped bodies (Collop et al. 2004; Mustoe 2001). DEMs are based on Newton’s Second Law of Motion (Bertrand et al. 2005; Serway 2000):  mi ai = Ftotal ,i  [1]  d 2 xi = Ftotal ,i or, mi dt 2  [2]  where:  mi is the mass of particle i, ai is the acceleration of particle i, xi is the position of particle i, and Fi is the total force acting on particle i. This equation is used to calculate the total force that acts on a particle due to a collision and is subsequently integrated to find the respective particle’s new velocity and distance of travel (Bertrand et al. 2005). During a simulation, the location of all particles is tracked at a specified time interval. When a collision between particles is detected Newton’s Second Law of Motion is applied to determine each particle’s resulting position and velocity. Figure 6 shows the steps of a typical DEM algorithm. Calculate force increment caused by each contact between particles  Calculate velocity and position increments caused by forces  Find which particles have come into contact t = t + ∆t Figure 6. Flow chart for operations performed in a typical DEM algorithm (Schafer et al. 2001). -12-  Although the basis of the DEM approach is relatively straight forward, the computational requirements quickly become overwhelming when more than a few particles are present. Because DEMs are routinely used for simulating a large number of particles, the effectiveness of the method is largely dependent on the ability of the model algorithms to detect particle contacts quickly and efficiently (Bicanic 2004). There are several DEMs that have been developed for describing how the particles behave when they come into contact with each other. A typical DEM has the following features (Cundall 1989; Bertrand et al. 2005; Mustoe 2001): 1. They allow finite displacements and rotations of discrete bodies, including complete detachment, and 2. They recognize new contacts automatically as the calculation progresses. Two of the more commonly applied models include the linear spring-dashpot model and the Hertz Mindlin model. As Bertrand (2005) described, the principal difference between these two models is that the linear spring-dashpot model considers any particle contact to lead to inelastic deformation, while models based on Hertz theory considers this contact to lead to elastic deformation. There is no consensus on what model is best; however, DEM solutions (2008) report that the linear spring model is simpler because it requires less computational overhead. For EDEM, the selected software package for this research project, the Hertz Mindlin model is the default model because of its accurate and efficient force calculation (DEM Solutions 2008).  This model was also used for the duration of this project.  Ultimately, the choice of model will depend on the environment being simulated and the ability to validate the results. For additional information concerning the choice of models, Bertrand (2005) provides a reasonable explanation of several of the more commonly employed models. Additionally, Cundall and Strack (1979) and DEM Solutions (2008) provide information on the model algorithms. 2.2.1 Applications for discrete element methods The DEM was first pioneered by Cundall (1971) for problems involving rock mechanics. Since the early-1970s this method has branched out and adapted for use in a wide range of engineering applications. Mining has perhaps benefited most from DEMs where they have -13-  been shown to be particularly effective at analyzing granular material flow, power draw, and liner wear in semi-autogenous grinding mills (Cleary 1998; Cleary 2006; Djordjevic et al. 2004; McIvor 1983; Mishra and Rajamani 1992; Powell 1991). In addition to mining, other industries that have benefited include: pharmaceutical, chemical, agricultural, advanced materials, and food (Bertrand et al. 2005). An area that has gained recent attention is the modeling of granular material mixing. This topic covers a variety of industries, but its significance is seen most prominently in the pharmaceutical manufacturing arena. As Bertrand (2005) reported, even slight changes to ingredient properties or process operating conditions can have significant implications on the quality of a drug and/or resulting health effects. Consequently, pharmaceutical companies are reluctant to make process changes based on DEM results alone and still rely heavily on process monitoring to ensure quality (Bertrand et al. 2005). Despite the widespread use of DEMs in various engineering applications, it has never been used specifically for modeling the rotary drum blending of wood strand-based particles; however, its successful use in semi-autogenous grinding (SAG) and other rotating drum type processes suggests that it is possible (Kaneko et al. 2000; Moakher et al. 2000; Stewart et al. 2001). In this process wood strands are deposited inside a rotating drum at the front end. The strands are then lifted by a series of flights and cascade and tumble along the drum length. The dynamics of the process are similar to those encountered in a SAG mill; however, the process objectives more closely resemble those of pill coating in the pharmaceutical industry (Thibault 2008). In a rotary drum blender as the strands migrate along the drum length resin is applied in either liquid or powdered form. The objective is to maximize the resin deposition on the strands and the distribution of resin amongst the strands, while minimizing strand breakage. In a SAG mill the aim is to breakdown and grind the rocks. As mentioned, the objectives of resination are therefore more closely related to those of pill coating. In pill coating the pills tumble in a drum while a coating is sprayed onto them. Although the primary objective is to coat the pills, the pills must also remain intact in order to avoid contamination (Thibault 2008). Because DEMs, and in particular the EDEM software package, have been used for  -14-  modeling both processes it is believed that this is a suitable method for modeling the rotary drum blending process as well. For this project a DEM will be used for simulating the trajectory and distribution of strands as the blender revolves. The primary challenges associated with its use are the relatively high slenderness ratio and thinness of the wood strands and the large quantity of strands in the process. Simplifications and assumptions will be required to assemble a model that can simulate the process with reasonable accuracy and within a reasonable time span. 2.3  Friction  Friction forces are a critical phenomenon when performing discrete element modeling. For objects that slide relative to each other the key friction properties are static and kinetic friction (Serway 2000). The only difference between the equations used for determining these two forms of friction is the relevant coefficient of friction, µ. This equation is known as Amontons Law (Equation 3). F f = FN μ i  [3]  where:  µi is either static kinetic friction, and FN is the normal force. If the shape of an object permits rolling to occur, such as a sphere, then the resistance to rolling manifests as a torque that opposes the direction of rolling, Tf (Equation 4). Rolling friction is caused by the deformation of either the rolling sphere/cylinder or the plane (Figure 7). T f = FN μ R  [4]  where:  FN is the normal force, and µR is the rolling coefficient.  -15-  Lower rolling friction  Higher rolling friction  Fg  Fg  FN  FN  Figure 7. Diagram showing the pair of forces that determines the friction torque, where FN is the reaction force acting on the object by the plane and Fg is the normal component of the object’s weight. The coefficient of rolling friction is the arm of the pair of forces (Domenech et al. 1987). According to Amontons Law, knowledge of the coefficient of friction is vital when examining the interaction between objects.  Because this coefficient depends on the  interaction between surfaces of different objects, it is most accurately considered to be a system property rather than a material property. This is particularly relevant for this research as true coefficients of frictions were not known. Instead coefficients were chosen based on the resemblance of the model system to the actual observed systems. For modeling the rotary drum blending process for wood strands there are broadly three systems of objects that must be considered: strands and flights, strands and drum liner, and the interaction between strands themselves. In light of the limited published information pertaining to the static coefficient of friction values for the aforementioned systems, a series of tests aimed at determining the respective values for the particular materials used in the laboratory was conducted. Because it was anticipated that during the modeling stage the drum liner and flights would be grouped as one material type, the strand and drum liner interaction was dropped and instead replaced with the strand and flight interaction properties. Classic theoretical research related to static and kinetic friction has shown that frictional coefficients are independent of surface area and contact pressure. However, more recently Bejo et al (2000) found that “these generalizations are not necessarily true if at least one of the [objects] in the system is wood or a wood-based composite.” As a result, the initial study -16-  of this project focused predominately on determining the relationship between the range of contact pressures that may be encountered during blending and the friction coefficient.  -17-  CHAPTER 3  LABORATORY DETERMINED COEFFICIENT OF STATIC FRICTION  3.1  Introduction  Friction coefficients are perhaps the most important material interaction property to consider when developing a rotary drum blending model based on the discrete element method because of the significant impact they have on particle dynamics (DEM Solutions 2008). As described in section 2.3, assigning the respective friction coefficients is complicated by the fact that the friction coefficients within systems involving at least one wood substrate are dependent on the contact pressure. The selected software package for this research, EDEM, assumes constant coefficients regardless of the contact pressure, as is widely accepted for most systems of materials. In addition, most of the published friction coefficient values for systems involving wood are based on clear wood blocks, rather than strands. Wood strands tend to be less smooth and relatively flexible, generally resulting in higher coefficients. As a result, a series of experiments were conducted in the laboratory to determine the impact of contact pressure and wood grain orientation on the coefficient of friction for wood on wood and wood on polyethylene (PE) systems of materials. Collectively, these experiments will investigate all of the material interactions that will occur during the simulations: strand – strand, strand – flight, and strand – blender liner. It was hypothesized that the coefficient of friction would increase with decreasing contact pressure and that the coefficient of friction would increase from parallel – parallel to parallel – perpendicular and to perpendicular – perpendicular grain orientation.  These results will  be used as a starting point for the initial development of the RDBM. Subsequently, blending experiments and simulations will be compared to adjust these values until there is close correspondence in the strand dynamics.  Objectives: 1. To determine the relationship between contact pressure and coefficient of friction for wood – wood and wood – PE systems of materials,  -18-  2. To determine the relationship between grain orientation and coefficient of friction for wood – wood and wood – PE systems of materials, and 3. To determine the ratio between the coefficients of friction for wood – wood and wood – PE systems of materials. 3.2  Materials  A total of 40 sliced veneer, aspen wood strands were randomly selected from a 10.1 kg bag of strands. The strands had been previously cut to approximately 12 inches long by 1½ inches wide and 0.030 inches thick.  Aspen strands were used in this case because it  represents the predominant species used in the manufacturing of wood strand-based products in Canada (Industry Canada 2007). There were two requirements for the selected strands. First, the strands had to have an area that was at least 9 inches by 1¼ inches void of any splits, and second the strands could not exhibit excessive warp. Either of these flaws could impact the experiment. The selected strands were divided into two sets of twenty, one to be used as the ‘primary surface’ and one to be used as the ‘secondary surface’. The primary surface strands were trimmed to 9 inches by 1¼ inches using a guillotine paper cutter, removing any splits or defects. The edges of the strands were then lightly sanded using 220 grit sandpaper to remove any burrs that might otherwise affect the test results. The secondary surface strands were prepared in a similar manner; however, they were trimmed to 8 inches by 1 inch so that they would easily lay flat atop the primary strands without their edges contacting. If the edges were to come in contact the concern was that any remaining burrs may mechanically interlock, resulting in a confounded reading of the static friction coefficient. These relatively large strands were used for this experiment because it provided adequate room for weights to be added to the surfaces, as described in Section 3.3. Ultimately the surface area does not impact the friction coefficient so this was assumed to be a reasonable simplification for the test procedure (Serway 2000). The strands in each set were labeled 1 through 20 with the appropriate suffix added: ‘a’ for the primary surface strands and ‘b’ for the secondary surface strands (Figure 8). Each set of strands was then lightly clamped with a protective wood block on either face. Clamping helped to prevent the strands from warping before testing. -19-  1-inch  a  b  Figure 8. Photograph of sliced aspen veneer strands, (a) primary surface and (b) secondary surface. In addition to the wood samples, two HDPE specimens were also prepared. The samples were removed from an extra 5 inches T-flight for the 6 foot by 3-foot Coil laboratory blender. The flight was trimmed into two specimens measuring 9½ inches by 4⅛ inches and 8½ inches by 1¼ inches.  The edges of the samples were also sanded using 220 grit  sandpaper to remove any burrs and then washed in warm water and left to air dry. 3.3  Procedure  The experimental procedure is based on the inclined plane technique (American Standards for Testing and Materials 2002a; American Standards for Testing and Materials 2002b; Bejo et al. 2000). This method was selected because of its relative simplicity and the shape of the test specimens. A photograph of the testing apparatus is shown in Figure 9.  -20-  4  2  3 2  1 7 6  5  7 Figure 9. Inclined plane jig with the various components indicated ((1) scissor lift, (2) measuring guides, (3) platform with stop block, (4) raised primary surface platform, (5) bullseye level, (6) base, and (7) leveling glides). The coefficient of static friction for the system involving two wood strands was determined using five combinations of primary and secondary surface strands. These combinations were generated using a random number generator in Microsoft Excel (Table 3). Table 3. Strand combinations used for static friction coefficient tests. Pair Primary surface Secondary surface strand strand 1 9 18 2 5 17 3 14 18 4 19 9 5 8 11 Because of the orthotropic nature of wood, each combination was tested for all three combinations of grain orientation. In addition, seven contact pressures were used to study the impact contact pressure has on the coefficient of static friction. The included orientations and target contact pressures are listed below: 1. Strand orientations (secondary on primary): parallel - parallel, perpendicular – perpendicular, and perpendicular - parallel. 2. Target contact pressures: 23 Pa, 47 Pa, 94 Pa, 188 Pa, 375 Pa, 750 Pa, and 1500 Pa.  -21-  For each orientation the primary surface strand was attached to the raised primary platform using double-sided tape. The platform was then placed on the inclined plane in contact with the stop block. The secondary surface strand was attached to one of two sled designs (Figure 10) also using double-sided tape.  For the first two strand orientations the sled equipped with dowel  extensions was used for contact pressures greater than, and including, 188 Pa. Weights were hung from the extensions to adjust the contact pressure (Figure 11). For contact pressures less than 188 Pa, the sled equipped with an adhesive surface was used. This was necessary as the first sled produced a contact pressure that was greater than 94 Pa without the addition of any weights. Small weights were attached to the adhesive surface of the second sled to adjust the contact pressure.  For the third strand orientation the second sled was used  exclusively. Because the contact surface area was significantly less for the third orientation, the weights had to be reduced accordingly to achieve the appropriate contact pressure. For each pair of strands the same surfaces were in contact for the three orientations tested.  1-inch  Figure 10. Two sleds used for the inclined plane test, (left) sled equipped with dowels for larger contact pressures and (right) sled equipped with adhesive surface for lower contact pressures.  -22-  Figure 11. Photograph of the testing procedure for the coefficient of static friction of wood strands using the inclined plane technique, showing a parallel – parallel orientation. For the coefficient of static friction tests involving wood strands and HDPE the same test format was followed, including three orientations and seven contact pressures. Instead of using a variety of HDPE samples however, only two were used. The larger HDPE sample was used for the first two orientations and the smaller sample was used for the third orientation. In all three cases the HDPE was the primary surface and the wood strand was the secondary surface. The HDPE sample was placed directly on the inclining plane in contact with the stop block for the first two orientations. For the third orientation the HDPE was attached to the raised platform, which was then placed on the inclined plane. The raised platform added stability to the HDPE sample, preventing it from shifting during the tests. The same secondary surface strands from the first set of tests were used for this second set of tests. The secondary surface was prepared identically as before using the two sleds. After the strands were mounted to the respective surfaces the testing apparatus was leveled using the adjustable glides. The appropriate weight was then added to the sled. The angle of inclination was slowly increased until the secondary surface began to slip along the primary surface. The heights from the base of the apparatus to two predetermined points along the inclined plane as well as the distance between those two points along the inclined plane, the -23-  hypotenuse, were recorded when the sled began to slip. These measurement points remained constant across all of the tests.  The coefficient of static friction was then determined  according to Equation 5. This procedure was repeated for each contact pressure, strand orientation, and system of materials. The complete set of results were then analyzed using SAS version 9.1 to develop a model that predicted the coefficient of static friction based on the material combination, orientation, and contact pressure. ⎛  μ = tan ⎜ arcsin ⎝  h2 − h1 ⎞ ⎟ l ⎠  [5]  hypotenuse, l  α height 1, h1  height 2, h2  Figure 12. Schematic of inclined plane jig showing measurement locations for Equation 5. 3.4  Results  The test results aimed at determining the coefficients of static friction for strand to strand and strand to flight interactions clearly showed a decreasing coefficient of static friction value for increasing contact pressures (Table 4, Figure 13, Table 5, and Figure 14). This is particularly apparent when increasing from 23 Pa to 94 Pa. The coefficient of static friction appears to be constant for pressures greater than and including 94 Pa. These results are consistent with -24-  those obtained by Bejo et al. (2000). Bejo found that as the contact pressure decreased below approximately 5 kPa the coefficient of static friction increased substantially. Above 5 kPa the static friction coefficient began to stabilize. It was also found that the grain orientation had a considerable impact Table 4. Summary of test results for the coefficient of static friction between two wood strands at 22°C and 55% relative humidity1. Primary strand orientation Parallel  Secondary strand orientation Parallel  Approximate contact pressure (Pa) 23  Mean 0.63 COV % 24 Perpendicular Perpendicular Mean 0.88 COV % 13 Parallel Perpendicular Mean 0.89 COV % 28 1 Average ambient strand moisture content was 9.2%.  47  94  188  375  750  1500  0.55 21 0.81 12 0.60 11  0.53 19 0.77 19 0.50 20  0.49 17 0.66 12 0.51 15  0.41 26 0.64 12 0.41 10  0.44 20 0.63 18 0.36 12  0.41 25 0.70 6 0.35 11  1 0.9 0.8  Perpendicular - Perpendicular PERP/PERP  0.7  Static COF  0.6 0.5  Parallel - PAR/PAR Parallel 0.4 PAR/PERP Parallel - Perpendicular  0.3 0.2 0.1 0 0  100  200  300  400  500  600  700  800  900  1000 1100 1200 1300 1400 1500 1600  Contact Pressure (Pa)  Figure 13. Static coefficient of friction between two wood strands for increasing contact pressures and different strand sample orientations.  -25-  Table 5. Summary of test results for the coefficient of static friction between a wood strand and HDPE at 22°C and 55% relative humidity2. Primary strand orientation Parallel  Secondary strand orientation Parallel  Approximate contact pressure (Pa) 23  Mean 0.31 COV % 16 Perpendicular Perpendicular Mean 0.38 COV % 18 Parallel Perpendicular Mean 0.39 COV % 20 2 Average ambient strand moisture content was 9.2%.  47  94  188  375  750  1500  0.30 23 0.31 10 0.40 20  0.26 12 0.29 9 0.32 12  0.22 12 0.29 6 0.29 20  0.24 8 0.29 1 0.26 27  0.25 6 0.28 8 0.26 12  0.24 16 0.28 5 0.27 17  0.45  0.40  0.35  Perpendicular - Perpendicular PERP/PER  0.30 Static COF  P  Parallel PAR/PERP - Parallel 0.25  PAR/PAR Parallel - Perpendicular 0.20  0.15  0.10  0.05  0.00 0  100  200  300  400  500  600  700  800  900  1000 1100 1200 1300 1400 1500 1600  Contact Pressure (Pa)  Figure 14. Static coefficient of friction between a wood strand and HDPE for increasing contact pressures and different strand and HDPE sample orientations. The test results were analyzed using multiple regression analysis in SAS version 9.1. A logarithm transformation was necessary to normalize the data so that a model could be fit that accurately predicted the static friction coefficient (Equation 6), while meeting the assumptions of multiple linear regression analysis at a α = 0.05 (Kleinbaum 1988).  -26-  μ s = 10 b + b Log 0  1  10 ( x ) + b2 ( x )  [6]  where:  µs is the predicted static friction coefficient, x is the contact pressure in pascals, and bi is the predicted parameters for i = 0 to 2. The appropriate coefficients for the respective systems of materials and orientation are shown in Tables 6 and 7. In general, these results show an approximate 2:1 ratio between the static coefficient of friction for wood to wood and wood to HDPE. The complete SAS analysis is included in Appendix A. It is important to note that this relationship has only been verified for the range of data presented above and at the ambient temperature and relative humidity encountered during the test, i.e. approximately 21oC and 50% respectively. Table 6. Regression parameters for determining the coefficient of static friction between two wood strands at 22°C and 55% relative humidity. Primary strand orientation Parallel Perpendicular Parallel  Secondary strand orientation Parallel Perpendicular Perpendicular  b0  b1 -2  4.242 x 10 1.112 x 10-1 2.454 x 10-1  b2 -1  -1.748 x 10 -1.290 x 10-1 -2.634 x 10-1  8.835 x 10-5 8.835 x 10-5 8.835 x 10-5  Table 7. Regression parameters for determining the coefficient of static friction between a wood strand and HDPE at 22°C and 55% relative humidity. HDPE orientation Parallel Perpendicular Parallel  3.5  Strand orientation Parallel Perpendicular Perpendicular  b0 -3.530 x 10-1 -2.842 x 10-1 -1.500 x 10-1  b1 -1.222 x 10-1 -1.216 x 10-1 -1.179 x 10-1  b2 8.835 x 10-5 8.835 x 10-5 8.835 x 10-5  Conclusions  The coefficient of static friction tests confirmed previous work by Bejo et al. (2000) where it was found that, contrary to classical theoretical research pertaining to friction, the coefficient of static friction is in fact dependent on the contact pressure between surfaces when at least one surface is wood.  In general, the contact pressure and coefficient of friction were  inversely related, as the contact pressure decreased the friction coefficient increased and vice-versa. It was also found that the coefficient of friction was highest when the wood grains were aligned perpendicular - perpendicular and least when they were aligned parallel parallel to the sloped plane. Finally, the relationship between the coefficient of friction between two aspen strands versus that between an aspen strand and HDPE was found to be approximately 2:1. -27-  These findings suggest that knowledge of the contact pressures encountered during the blending operation is necessary to fully describe the slipping of strands in the RDBM. Because the currently available discrete element modeling software packages are unable to accommodate for a variable coefficient of static friction, a value must be selected that results in the most accurate resemblance between the RDBM simulations and the actual observed dynamics. As an initial starting point for the model validation process, the average of the two extreme strand orientations will be used together with the average of the higher, more rapidly changing friction coefficients (contact pressure ≤188 pa) and the lower, more stable friction coefficients (contact pressure >188 pa).  -28-  CHAPTER 4  DETERMINATION OF SUITABLE MATERIAL AND INTERACTION PROPERTIES FOR USE AS INPUT PARAMETERS IN THE RDBM  4.1  Introduction  The RDBM required the input of three mechanical properties for each material used in a simulation and three interaction properties for each pair of materials that may come in contact during a simulation (Tables 8 and 9). While all of these properties must be included for a simulation to be initiated, not all of them have a significant effect on the bulk strand dynamics. Instead, some of these properties are only significant outside of the tested ranges and/or are used for measuring incidents of little consequence to this study, such as compressive forces acting on the particles. Because this research is focused predominantly on measuring the bulk strand flow within a rotary drum blender, it is only necessary to select representative values for those factors that are vital to the accurate representation of said strand flow. Table 8. Required material and interaction properties for the RDBM. Material properties Interaction properties Modulus of rigidity (G) Coefficient of restitution Poisson’s ratio (ν) Coefficient of rolling friction Density (ρ) Coefficient of static friction Table 9. Materials used and materials that may come in contact in the RDBM. Materials Interactions Aspen wood strands Strand - Strand Polyethylene1 Strand - Polyethylene 1  Polyethylene (PE) has been used here to describe both the high density polyethylene flights (HDPE) and the ultra high molecular weight polyethylene drum liner (UHMW). This will be discussed further in section 4.2.1.  Focusing on the behavior of the overall system introduces several inherent challenges. First, published values for these properties are typically based on measurements taken of individual pieces of clear wood samples. These values may or may not be accurate for characterizing the behavior of large collections of strands. They do however provide a useful foundation for beginning such research. Second, these properties must also incorporate other events that are occurring in an actual rotary drum blender but are not able to be incorporated into the model -29-  because of constraints, such as the representation of strands using a series of spheres or the lack of any air flow dynamics in the model. In addition to potentially affecting the strand dynamics, preliminary simulations and literature (DEM Solutions 2008) have also shown that the material properties have a significant impact on the processing time for a simulation.  The processing time increases  with increasing shear modulus of rigidity and decreases with increasing density and Poisson’s ratio. If it can be found that any of the above listed material properties do not significantly impact the bulk material dynamics then values may be chosen that minimize the time required for processing a simulation. The relationship between the density, ρ; modulus of rigidity, G; Poisson’s ratio, ν; particle radius, R; and processing time as represented by the idealized time step, TR is (DEM Solutions 2008): TR =  πR ⎛ρ⎞ ⎜ ⎟. 0.1631ν + 0.8766 ⎝ G ⎠  [7]  In this case where strands are being modeled, the particle radius refers to the individual particles, or spheres, that are joined to form a strand. As a result, the particle radius is ½ inch as will be discussed further in Section 4.2.2. This study was therefore divided into two distinct phases. The first phase consisted of two 2level, full factorial experimental designs aimed at determining which material properties and interaction properties were in fact significant to the overall strand dynamics. The second phase consisted of a systematic series of simulations aimed at determining suitable values for those properties that were deemed significant during phase 1.  Published values and  experimental results from section 3.4 were employed as initial values from which these values were improved upon. In order to assess the effectiveness of the tested values at accurately simulating the bulk strand flow, a series of experiments were simultaneously conducted and video recorded in a 6 foot laboratory blender for validation purposes. It was hypothesized in this leg of the project that there is a particular set of input parameters that produces simulated bulk strand flow that is reasonably similar to reality. Although there are several materials involved in this process (HDPE, UHMW, and Aspen wood strands), this study focused exclusively on the material properties of Aspen wood -30-  strands for several reasons. First, because of the large quantity of strands used in the simulation, it was assumed through consultation with the software providers that changes made to the material properties of the strands has a significantly larger impact than changes made to the material properties of either the blender liner or flights. And second, the software package assumes the materials to be isotropic. Wood strands are highly anisotropic and therefore there is not a single value for each of the mechanical properties available in the public literature (USDA, Forest Products Laboratory 1999). Instead, these values were selected based on exploratory simulations using published ranges.  Objectives: 1. To determine which material and interaction properties are significant to the bulk strand flow, and 2. To assign suitable values to those properties deemed to be significant. 4.2  Procedure  4.2.1 Screening design The significance of the six factors listed in Table 8 was determined using a full factorial, 2k design for each the material and the interaction properties (Montgomery 2005; Pyzdek 2003). Two individual 2k designs were followed to minimize the required number of runs and to facilitate clarity in the results (Table 10). This required that it be assumed there would not be any significant interactions between the two groups. In total, 16 simulation runs were required. Table 10. (Left) Aspen wood strand material properties and (right) interaction properties simulation design. Simulation Factors Simulation Factors Coefficient Coefficient Coefficient Run Modulus Run Poisson’s of of rolling of static Density of rigidity ratio restitution friction friction 1 -1 -1 -1 1 -1 -1 -1 2 -1 -1 1 2 -1 -1 1 3 -1 1 -1 3 -1 1 -1 4 1 -1 -1 4 1 -1 -1 5 1 1 -1 5 1 1 -1 6 1 -1 1 6 1 -1 1 7 -1 1 1 7 -1 1 1 8 1 1 1 8 1 1 1 -31-  The aspen strand material property levels were selected based on published ranges (USDA, Forest Products Laboratory 1999), recommendations made by representatives from DEM Solutions, laboratory results, and preliminary modeling results (Tables 11 and 12). For the blender liner and flights, which are constructed of UHMW and HDPE respectively, the material properties were provided by Coil Manufacturing and are listed in Appendix B. To facilitate the model setup, the averages of these values were used for both components and this set of values will be referred to as simply polyethylene (PE) for the duration of this report (Table 13). Because the material properties differ by less than 20% and they are not the focus of this study it was felt that this was a reasonable simplification to the model. As a means of further streamlining this portion of the study, the linear interaction factors, which include wood to wood and wood to PE material contacts, were tested using the same value for both material contacts. This was largely done to allow for a clearer understanding of the results. Table 11. Factor levels for Quaking Aspen material properties. Material properties (Quaking Aspen) Low level Modulus of rigidity (G) 1 x 108 Pa Poisson’s ratio (ν) 0.038 Density (ρ) 123.3 kg/m3 (7.7 pcf) Table 12. Factor levels for interaction properties. Interaction properties Low level Coefficient of restitution 0.01 (wood-wood & wood-PE) Coefficient of rolling friction 0.01 (wood-wood & wood-PE) Coefficient of static friction 0.24 (wood-wood & wood-PE)  High level 1 x 109 Pa 0.453 379.6 kg/m3 (23.7 pcf) High level 0.10 1.00 0.64  All operating and blender design factors, aside from the six specified, were fixed for the duration of this project. This included the blender rotation speed, the number of and the shape of the flights, the blender diameter, and the flight and liner material properties. These fixed values were selected based on industry standards and limitations of the laboratory blender (Table 14).  -32-  Table 13. Fixed factor levels for the liner and flights. Material properties Value (liner and flights) Modulus of rigidity (G) 3.39 x 108 Pa Poisson’s ratio (ν) 0.42 Density (ρ) 935 kg/m3 Table 14. Fixed factor levels for the blender operation and design. Fixed blending factors Value Blender diameter 6.04 ft (1.840 m) Blender length 1 ft (304.8 mm) Drum rotation speed 25.5 rpm Number of flights 8 Flight height 4 in. (101.6 mm) Flight shape L-shaped Fill level 1/8th In addition, the strands were represented using ‘sticks’ of the following dimensions: length = 6 inches, width = 1 inch, and thickness = 1 inch (Figure 15). Simplification of the strand dimensions was necessary because of computing and software limitations. If the actual strand dimensions were used then the maximum sized sphere possible would be 0.030 inches, or equivalent to the strand thickness.  Consequently, more than 6500 spheres would be  required to represent each 6 inch long by 1 inch wide strand. Because the software is limited to approximately 100 000 to 200 000 spheres, using 0.030 inch spheres would significantly reduce that amount of strands that could be simulated. The key assumption is that the motion of actual wood strands in a blender does not differ significantly from the sticks. The simulator settings have been included below in Table 15. For each simulation the first 2 revolutions (approximately 6 seconds) were discarded. Visual interpretation of the bulk strand flow revealed that the strands behaved erratically during this time, and this period was not representative of the actual blending dynamics. Table 15. Simulation settings. Fixed simulator settings Time step Write-out every frequency Simulation time  -33-  Value 40% of TR 0.01 sec 24 sec (8 revs)  Further, the sticks were generated inside the drum throughout the first revolution. Gradually creating the sticks during a complete revolution facilitated the dispersion of sticks around the drum and resembled the feeding of strands into an industrial blender. 4.2.2 Strand representation in EDEM The wood strands were represented using a series of six, 1 inch diameter spheres. The spheres were rigidly connected at their points of contact (Figure 15). Within EDEM, the six spheres are treated as an individual body with measures, such as its location, being related to its center of mass. In most cases a 6 inch by 1 inch by 1 inch stick template was placed over each of the sphere groupings. This helped to distinguish between the sticks. It is important to recognize that the template is not the interaction surface of the particles; it is merely applied during post-processing to aid in identifying the individual strands. As a result, the sticks can overlap at their edges when the maximum diameter of a sphere protrudes into the valley between adjacent spheres. The stick template is best thought of as a virtual surface.  Figure 15. Schematic showing the representation of sticks using a series of six spheres (left) and a schematic showing the placement of a template over top of the six spheres to aid in the visual analysis process (right). 4.2.3 Characterization of resination potential A subgroup of 150 strands of the 1 027 in the blender were tracked as they passed through the resination region (Figure 16). The resination region is based on an atomizer spray pattern provided by Coil Manufacturing Ltd (Appendix C) and includes an 11-inch tall region located at the center of the drum. The width of the resination region is 1840 mm and it covers the entire drum length. While in this region within an industrial blender equipped with atomizers, strands have the best opportunity to make contact with resin directly leaving the atomizers. Ideally, all of the strands in the system would have been tracked; however,  -34-  because of computing, software, and time constraints, tracking all 1 027 strands was not practical.  Resination region z  y  x  Figure 16. Blender schematic showing the resination region outlined in blue. Three parameters were recorded for each strand while in the resination region: simulation time, x-location (across the diameter of the blender), and vertical velocity. The vertical velocity was used solely for determining which strands were being lifted by the flights and which strands were in free-fall. These parameters were recorded at a set time-interval of every 0.01 seconds. This interval ensured that at least 91% of the time a strand was within the region it was recorded. The complete details of this analysis are given in Appendix D. These data were then used for computing a set of response variables. Three response variables were selected for characterizing the strand flow through the resination region: skewness, kurtosis, and count. All three of these measures were applied to the x-location data. In this analysis the skewness (Equation 8 and Figure 17) and kurtosis (Equation 9) characterize the distribution of the strands across the diameter of the drum as they descend. Skewness is an indicator of the central tendency of the strand distribution and kurtosis is an indicator of the uniformity of the strand distribution. Ideally, the strands should be dispersed evenly, or uniformly across the diameter in order to maximize the opportunity for an even resin distribution (Figure 17). A uniform distribution is described by a skewness of 0.0 and a kurtosis of -1.2 (Snedecor and Cochran 1980). -35-  ⎛ xi − x ⎞ n ⎜ ⎟ skewness = ∑ (n − 1)(n − 2) ⎜⎝ s ⎟⎠  3  4 2 ⎧⎪ ⎛ xi − x ⎞ ⎫⎪ n(n + 1) 3(n − 1) ⎜ ⎟ kurtosis = ⎨ − ∑⎜ ⎟ ⎬ ⎪⎩ (n − 1)(n − 2 )(n − 3) ⎝ s ⎠ ⎪⎭ (n − 2 )(n − 3)  where:  n is the sample size, xi is the value of the ith sample, x is the average x value, and s is the sample standard deviation.  -36-  [8]  [9]  15.5 RPM  Skewness = -0.3983  20.5 RPM  Skewness = -0.3024  25.5 RPM  Skewness = -0.0451 Figure 17. Simulation and photographed examples of increasing skewness caused by increasing rotational speeds from 15.5 RPM to 25.5 RPM. Note that the skewness results are based on entire simulation, not the individual still image. The illustrated blenders have 8-4" flights and are 1/8th full.  -37-  The count is an indicator of the average total time the strands, or sticks, spent in the resination region.  When any of the 150 strands were within the resination region a  timestamp was recorded every 0.01 seconds for each strand. These timestamps were then accumulated to determine the total time that the overall subset of strands was within the resination region. The count is significant because it measures the opportunity the wood strands have to come into contact with the resin, and therefore should be maximized. In addition to determining the total time spent in the resination region, a histogram of the count data was also generated to visually interpret the x-position results. The histogram consisted of 32 intervals, or bins, where each bin was 57.5 mm wide (Figure 18). Cumulatively, the bins form the width of the resination region, 1840 mm. In order to postprocess the data files produced by the RDBM, a macro was written in VBA to parse out the needed data and compute the required statistics. A listing of the VBA code for the macro, called “Histogram_And_Commulative_Graph,” is given in Appendix E.  1,800 1,600 1,400  Count  1,200 1,000 800 600 400 200 0 1  3  5  7  9  11  13  15  17  19  21  23  25  27  29  31  Bin  Figure 18. Sample histogram with a respective skewness, kurtosis, and count of -0.3024, 0.2794, and 22 453.  -38-  4.3  Validation process – selection of appropriate input parameters  Validation of the discrete element model was completed using three techniques. These techniques were performed in the order listed below. The first technique acted as a screening test because of its relative speed and simplicity in performing.  The second and third  techniques were only performed if the previous test was successful. The first technique is a visual comparison between a one minute video recording of the lab blender and an animation created from the simulation results. Validation by means of a visual comparison has been the most common approach taken for discrete element modeling because of its inherent simplicity (Rajamani et al. 2000; Yang et al. 2006). While these previous papers used still images for comparison, a video recording was used in this study because it resulted in a better understanding of the bulk strand dynamics; in particular strand surging, a common phenomenon in rotary drum blending. It is important to recognize that one of the shortcomings of this approach is that it is a purely qualitative measure and is therefore subjective. In order to observe and record the strand dynamics in a rotary drum blender, a custom built, 6 foot diameter by 3 foot deep Coil laboratory-scale blender was used. This blender is unique in that it is outfitted with a tempered glass front that enables the motion of the strands inside the blender to be easily observed, photographed, or videotaped. The bulk dynamics of the strands was recorded using a Sony Handycam, model DCRDVD108, mounted on a tripod in line with the axis of rotation of the drum and 156 inches back from the front of the glass blender face. The blender was illuminated with two pairs of tripod mounted, 500 watt halogen lights positioned to minimize dark regions inside the blender drum and to avoid reflections (Figures 19 and 20). Black tarpaulins were draped behind and around the video camera to reduce any reflections on the tempered glass front. Five minutes of strand tumbling was recorded for 16 different combinations of fill level and drum speed (Table 16). This video footage was transferred from the video camera to the computer using Picture Motion Browser Disc Importer Version 1.1.01.01170.  Once  downloaded, a 1 minute interval beginning at the 3 minute mark was extracted and saved to be used for the validation process. This time interval was selected because visually it appeared that steady state had been reached in the blender. -39-  6′ Laboratory Blender Halogen lights  z  156"  51  67"  Still camera / video camera  51"  72"  x  y  67" Halogen lights  Figure 19. Schematic showing the placement of the lights and camera/video camera relative to the laboratory blender, with the axis indicated in blue.  Figure 20. Photograph showing the placement of the lights and camera/video camera relative to the laboratory blender.  -40-  Table 16. Blender rotational speed and fill level combinations for laboratory video recordings. Fill level (%) Drum speed (RPM) 1/64th 15.5 20.5 25.5 30.5 1/32nd 15.5 20.5 25.5 30.5 15.5 20.5 25.5 30.5 1/16th 1/8th 15.5 20.5 25.5 30.5 The simulated strand flow footage from the RDBM was converted into GIF animations. The GIF was created by first exporting still images every 0.1 seconds from EDEM under the Analyst tab. A detailed description on how to perform this task is presented in the EDEM 1.3 User Guide (DEM Solutions 2008). The still images were then strung together as frames using the Animation Wizard in Jasc Animation Shop 3 and saved as a GIF. The RDBM GIF and the video footage of the blender drum were put side by side in a Microsoft PowerPoint slide and their strand flows compared by visual inspection (Figure 21). At this stage of the validation, the objective was to determine whether or not the strand flows appear to be similar based on the strands’ approximate point of detachment from the drum and their ultimate point of collision. In addition, the patterns of strand detachment should have been similar. Subsequent validation stages compared the simulated and laboratory results more thoroughly using quantitative techniques.  Figure 21. Example of (left) a screen shot taken of an animated GIF illustrating the simulation results and (right) a screen shot taken of the video footage taken in the laboratory. The second technique, and less often employed, compares the shoulder and toe angles from a series of still images taken of the laboratory blender with the graphical simulated results. As Cleary (2003) stated, “the shoulder and toe locations are the primary quantitative information available from [an experiment] for comparison with the DEM results.” The principle -41-  advantage of this approach over the visual comparison is the fact that this is a quantitative measure, and as a result, reduces the degree of subjectivity and bias. The definition of the shoulder and toe angle and the measurement approach is described in detail by Cleary (2003), and therefore, is only briefly summarized here. The shoulder angle is the maximum vertical height reached by the bulk of the strands after detaching from the drum liner. Conversely, the toe angle is the impact point of the bulk of the strands that move through the shoulder and land on the drum (Figure 22). The term ‘bulk’ is used here to differentiate between the mass flow of the majority of strands and the sporadic flow of individual, rogue strands. Because this research is focused on the overall bulk strand dynamics, the movement of individual strands is of little interest. 90o  1.0  drum liner  0.8  Shoulder  0.6  y-position (m)  0.4  σA τA  0.2  σB  0o  τB  0.0  -0.2 -0.4 -0.6 -0.8  direction of rotation  Toe  -1.0  (a)  -1.0  -0.8  -0.6  -0.4  -0.2  0.0  0.2  0.4  0.6  0.8  1.0  x-position (m)  Figure 22. Schematic showing the shoulder, σ, and toe, τ, angles for two points of detachment. The 0o and 90o reference angles are shown in blue. The strand volume and drum rotational speed have a significant effect on the ability to accurately determine the shoulder and toe angles through visual inspection. For instance, with volumes less than 1/8th full and with speeds greater than 25.5 RPM it is very difficult to locate the shoulder and toe angles and to identify them both on the same image. As a result, -42-  for this analysis only three speeds were chosen: 15.5 RPM, 20.5 RPM, and 25.5 RPM. All of the experiments were conducted at a 1/8th fill level. The still images were taken using a tripod mounted, Nikon Coolpix S3 digital camera. The lighting and camera to blender configuration was the same as for the previous analysis (Figure 19). With the blender running at steady state, forty to fifty pictures were taken in the standard camera mode over approximately two minutes. As described by Cleary (2003), by leaving the shutter open for a prolonged period a streaking effect is obtained, making it easier to identify the relevant angles (Figure 23). However, because this particular camera model does not allow for the shutter speed to be set directly, leaving the camera in the default standard mode, instead of using a high speed or sports mode, it was possible to achieve the desired outcome. In this case the shutter speed, as recorded in the image file, varied between 1/10th and 1/11th of a second. The shoulder and toe location were then determined for each image. The first 30 images that clearly showed both the shoulder and toe location were selected for analysis. As one can imagine from viewing the still image of the blender in Figure 23, determining the precise location of these locations is not without some error. Because of this, 30 images were included in the analysis to reduce the significance of any erroneous measurements. In measuring the shoulder and toe locations, the angles were measured to the nearest degree.  -43-  Shoulder  τ σ  Toe Figure 23. Illustration showing the identification of the shoulder and toe angle from the laboratory video footage. A similar approach was taken with the graphical simulation to facilitate the location of the shoulder and toe angles.  Instead of representing the strands using the stick template,  EDEM’s streaming effect was used (DEM Solutions 2008). The streaming effect draws a straight line between the respective strand’s last positions. For this analysis the software was set to connect the last two positions (Figure 24). As with the visual validation, still images were exported every 0.1 seconds from EDEM. The first two blender revolutions were not included because steady state had not been reached. 35 random images were then selected and the shoulder and toe angles determined. Again, the first 30 images that clearly showed the shoulder and toe location in the same picture were selected for analysis.  -44-  τ σ  Figure 24. Illustration showing the identification of the shoulder (σ) and toe (τ) angle from the simulation results using the streaming effect. Once the shoulder and toe angles were compiled from the pictures and simulation results they were compared using a student t-test to determine if the mean shoulder and toe values were similar. The third technique relied on grayscale, or light intensity measures to determine the presence of wood strands in the laboratory drum. This is a relatively new technique and has only been found once in the literature as a model validation tool (Nakamura et al. 2007). This method is based on the premise that the back of the blender drum is black, or low intensity and grayscale values, and that the strands are relatively light, or higher intensity and grayscale values. As a result, as the strands travel through the line of sight in front of the drum back they are recorded as relatively high intensity regions. This approach removes nearly all subjectivity, which is its primary advantage over the previous two methods. However, there are several inherent challenges associated with its use.  First, although it is simple to  determine the presence of at least one strand in any y-z plane (Figure 25) it is unable to determine the degree of strand saturation. For instance, it is unable to decipher between a -45-  single strand blocking the sight of the blender back or multiple strands blocking the sight of the blender back. In addition, this technique is unable to account for parallax, and because the drum is 3 feet deep this can be significant at the outer edges of the drum.  z  x  y  Figure 25. Schematic of the x, y, z coordinate system relative to the blender. The laboratory images used for this analysis were extracted from the one minute video clip used for the visual validation. The video was converted from an MPG format to an AVI format using Cyberlink PowerDirector v6 (Anonymous 2007). The AVI version was then imported into Adobe Premiere Pro CS3 and exported as individual still images (Adobe Systems Incorporated 2007). This step was completed with the Export Frame Settings shown in Table 17. Table 17. Frame export settings used in Adobe Premiere Pro CS3. General: File Type TIFF Video: Frame Size 640 x 480 Frame Rate 29.97 Pixel Aspect Ratio 1.0 Keyframe and Rendering: Deinterlace video footage ‘select’ Note: with the exception of the above listed settings, all other parameters were left at their respective default settings. -46-  Using Image Pro Plus v6 (IPP), the still images were converted into 8-bit grayscale images. With 8-bit grayscale, 0 corresponds to black and 255 corresponds white. The intensity, or grayscale value, was determined for each column of pixels across the width of the resination region. This is done using the Line Profile command in IPP, selecting Thick Horz under the report options, and then positioning the boundaries of the resination region (Figure 26). This was performed for every third image of the 1 800 that were extracted. The average grayscale value and associated variance was determined for each column of pixels. A macro was written in VBA to perform this operation and is listed in Appendix F.  -47-  Resination region  Figure 26. Screen shot taken in Image Pro Plus v6 showing the placement of the thick, line profile and the cooresponding grayscale values. The indicated grayscale values are an average of each column of pixels across the width of the resination region. The histogram data from the RDBM simulations were then overlaid on top of the light intensity data to determine the degree of similarity (Figure 27). To facilitate the direct comparison of the RDBM histograms with the light intensity data, the light intensity data was grouped and averaged according to the same 51 mm bin size as the histograms. A critical assumption in this analysis is that the light intensity values are directly related to the count values from the simulation results.  -48-  nd  20.5 RPM - 1/32 Full 550  190  500  180  450  170  Count (Simulation)  150  350  140  300  130 250 120 200  110  150  Grayscale (Imaging)  160  400  100  100  90  50  80  0  70  -50  60 1  3  5  7  9  11  13  15  17  19  21  23  25  27  29  31  Bin Imaging  Simulation  Figure 27. Example of simulation results overlaid on top of grayscale results. The bin id’s are shown on the x-axis. 4.4  Results  4.4.1 Screening design – material properties After completing the full factorial simulation design the respective factor levels and response variables were compiled (Table 18) to be analyzed in SAS version 9.1 using an analysis of variance (ANOVA).  In addition to the three response variables previously mentioned:  skewness, kurtosis, and count; the required processing time was also included.  The  processing time was included because one of the objectives of this initial study was to determine a suitable combination of material properties that would minimize the required processing time without compromising the quality of the simulation results. Therefore, the results for the processing time will only be used for determining, if appropriate, where assumptions could be made to reduce the time required to run subsequent simulations.  -49-  Table 18. Factors and response variables for simulations investigating the impact of the material properties. Run 1 2 3 4 5 6 7 8  Shear modulus (psi) 1 x 108 1 x 108 1 x 108 1 x 109 1 x 109 1 x 109 1 x 108 1 x 109  Factors Poisson’s ratio 0.038 0.038 0.453 0.038 0.453 0.038 0.453 0.453  Response variables Density (kg/m3) 62.208 380.000 62.208 62.208 62.208 380.000 380.000 380.000  Skewness  Kurtosis  Count  -0.0744 -0.1921 -0.1704 -0.0544 -0.2613 -0.2429 -0.1068 -0.1537  -1.0043 -1.1023 -1.0837 -1.0776 -1.1146 -1.0365 -1.0940 -1.0274  14267 15027 15063 14305 15352 15160 14902 14772  Proc. Time (hrs) 11.10 4.73 11.70 34.30 37.00 14.20 5.03 15.10  The ANOVA results showed that none of the material properties: shear modulus, Poisson’s ratio, or density; had a significant impact on the skewness, kurtosis, or count at a 95% confidence level (α = 0.05) (Appendix G). This is demonstrated by the p-values consistently being greater than 0.05. As expected from Equation 7, the processing time was significantly affected by the material properties, specifically by the shear modulus and density. 4.4.2 Screening design – interaction properties The results from the simulations investigating the impact of the interaction properties were also analyzed using an ANOVA in SAS version 9.1 (Table 19). Table 19. Factors and response variables for simulations investigating the impact of the interaction properties. Run 1 2 3 4 5 6 7 8  Coef. of restitution 0.01 0.01 0.01 0.10 0.10 0.10 0.01 0.10  Factors Coef. of rolling friction 0.01 0.01 1.00 0.01 1.00 0.01 1.00 1.00  Response variables Coef. of static friction 0.24 0.64 0.24 0.24 0.24 0.64 0.64 0.64  Skewness  Kurtosis  Count  -0.5587 -0.2302 0.3976 -0.4195 0.4187 -0.1145 1.2969 1.2521  -0.8274 -1.0118 -0.8940 -0.9959 -0.7253 -0.9241 0.9665 0.8854  16863 15260 13569 15671 13429 14487 12855 12749  Proc. Time (hrs) 5.24 4.79 5.18 5.18 5.25 4.72 4.4 4.35  The ANOVA results (Appendix H) showed that the coefficient of rolling friction and the coefficient of static friction had a significant effect on the skewness of the data at a 95% confidence level, while only the coefficient of rolling friction had a significant effect on the count. None of the factors significantly impacted the kurtosis. Based on these results, it was necessary to complete additional simulations and research to determine appropriate coefficients of rolling and static friction. -50-  4.4.3 Coefficient of rolling friction An appropriate coefficient of rolling friction value for this project was determined by completing a series of simulations at both the upper and lower static friction coefficient values measured in the laboratory for seven different values of rolling friction (Table 20 and Figure 28). This provided insight into the affect of rolling friction on the bulk dynamics of the strands. Common sense suggested that because strands do not roll, but instead slide along the liner, flights, or adjacent strands in an actual rotary drum blender, the coefficient of rolling friction should be set as high as possible to prevent the strands from rolling. However, the impact of the rolling friction on the strand dynamics was not completely known and therefore these simulations were necessary. For these studies the coefficient of static friction was set independently for wood to wood and wood to PE (Table 20). Table 20. Rolling and static friction coefficients for the simulations aimed at determining a suitable coefficient of rolling friction. Run 1 2 3 4 5 6 7 8 9 10 11 12 13 14  Static friction Wood to Wood Wood to PE 0.66 0.3 0.66 0.3 0.66 0.3 0.66 0.3 0.66 0.3 0.66 0.3 0.66 0.3 0.54 0.26 0.54 0.26 0.54 0.26 0.54 0.26 0.54 0.26 0.54 0.26 0.54 0.26  -51-  Rolling friction 0.010 0.175 0.340 0.505 0.670 0.835 1.000 0.010 0.175 0.340 0.505 0.670 0.835 1.000  x-position skewness -0.22873 1.18975 1.49009 1.06571 0.71122 0.51079 0.59923 0.03421 1.22647 1.31727 0.83199 0.57810 0.53392 0.51188  1.6 1.4 1.2  µwood/wood = 0.66 µwood/PE = 0.30  1  Skewness  0.8  µwood/wood = 0.54 µwood/PE = 0.26  0.6 0.4 0.2 0 0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1  -0.2 -0.4 CRF  Figure 28. Skewness as a function of the coefficient of rolling friction (CRF). In both cases the simulation results showed that the rate of change of skewness with rolling friction is smallest above 0.7. It would therefore be ideal to operate in this range. However, in order for the simulation to remain stable the rolling friction coefficient should not be more than 0.7 (Cook 2008). Thus for the purposes of this research a value of 0.67 was used to ensure model stability. A disadvantage of this approach is that it removes some of the control we have over the bulk dynamics of the strands, only leaving the coefficient of static friction for controlling the simulated strand flow. 4.4.4 Validation - coefficient of static friction Once a suitable coefficient of rolling friction was determined, attention was focused on the coefficient of static friction. As previously indicated, the static friction coefficients used in the model may not be necessarily the same as those values found in the laboratory experiments. This is largely because of assumptions that were made in the model. For instance, the bulk flow of strands in an actual blender is much more complicated than individual specimen tests. There are many factors that impact specimen interactions, such as air flow or the presence of fine particles acting as lubricant on the material surfaces. As a -52-  result, a series of simulations were carried out in a systematic manner to narrow in on a pair of static friction coefficients that best produces realistic strand flow.  The validation  techniques outlined in the Methodology section were used to understand whether or not the simulation results were improving with each successive simulation. Six static friction levels were required to narrow in on a suitable combination of values (Table 21). Runs 1 and 2 used the upper and lower laboratory determined values. Neither of these runs agreed using visual validation. The strands were lifted too high up on the drum wall before detaching and impacted the drum at too small an angle on their decent. Table 21. Pairs of static friction coefficients used to identify a suitable set of values. Run Static coefficient of friction Wood to wood Wood to HDPE 1 0.66 0.30 2 0.54 0.26 3 0.02 0.01 4 0.14 0.07 5 0.10 0.05 6 0.12 0.06 Runs 3 to 6 used values that were considerably less than the laboratory determined coefficients, however were necessary to correct for the disparity between runs 1 and 2 and the video footage taken in the laboratory. Throughout these runs a ratio of approximately 2:1 was maintained between the wood to wood and the wood to PE coefficient values. This ratio was found to be reasonably accurate from the laboratory results in Section 3.4. Run 3 was an extreme case.  This simulation tested the lowest levels possible while  maintaining a 2:1 ratio. The visual results of this run showed that the point of detachment and collision were both too low on the drum, indicating that the optimal static friction coefficients were between the levels used in runs 2 and 3. The visual results of run 4 were promising. The point of detachment and collision both appeared to be similar to the laboratory video footage; as a result, validation using the shoulder and toe angle measurements was also completed (Table 22). The results of the student t-test suggested that there was not a significant difference between the shoulder angle  -53-  in the simulated and laboratory results assuming a 95% confidence level. The toe angles were however significantly different, with the simulated toe angle being lower. Table 22. Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 4 and the laboratory results. Shoulder angle Toe angle Simulation Laboratory Simulation Laboratory Mean 55.8 53.9 247.7 256.2 Variance 38.90 20.53 44.42 29.98 Observations 30 30 30 30 Hypothesized mean dif. 0 0 Degrees of freedom 53 56 t-statistic 1.397 -5.419 P(T≤ t) two-tail 0.168 1.313 E-6 t-critical two-tail 2.006 2.003 Runs 5 and 6 were completed to determine if the results of run 4 could be improved upon. Again, visually both of these runs were promising, warranting validation by means of the shoulder and toe angles (Tables 23 and 24). With run 5 the toe angle was closer to the laboratory results; however, the simulation shoulder was again lower. In run 6, the shoulder and toe angles were both significantly lower than the laboratory results. Table 23. Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 5 and the laboratory results. Shoulder angle Toe angle Simulation Laboratory Simulation Laboratory Mean 45.2 53.9 255.6 256.2 Variance 20.39 20.53 34.79 29.98 Observations 30 30 30 30 Hypothesized mean dif. 0 0 Degrees of freedom 58 58 t-statistic -7.392 -.408 P(T≤ t) two-tail 6.438 E-10 0.685 t-critical two-tail 2.002 2.002  -54-  Table 24. Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 6 and the laboratory results. Shoulder angle Toe angle Simulation Laboratory Simulation Laboratory Mean 47.7 53.9 251.4 256.2 Variance 44.98 20.53 53.90 29.98 Observations 30 30 30 30 Hypothesized mean dif. 0 0 Degrees of freedom 51 54 t-statistic -4.173 -2.911 P(T≤ t) two-tail ≤0.001 0.005 t-critical two-tail 2.008 2.005 A summary of the shoulder and toe angle results from runs 4 to 6 and the results from the images taken of the laboratory blender is shown in Table 25. The italicized values indicate those angles that are significantly different from the laboratory results at the 95% confidence level (α = 0.05). These results show a decline in the shoulder angle with a decreasing coefficient of static friction.  At the same time, the toe angle steadily increased with  decreasing friction values. Table 25. Summary of runs 4 to 6 and the laboratory taken shoulder and toe angle results. Italicized values indicate those angles that are significantly different (α = 0.05) from the image results. Shoulder Toe Lab images 53.9 256.2 Coefficient of static friction1: Run 4 (0.14/0.07) 55.8 247.7 Run 5 (0.10/0.05) 255.6 45.2 Run 6 (0.12/0.06) 47.7 251.4 1  The values are shown as the wood to wood and the wood to PE coefficient of static friction respectively.  Of these three runs, it was determined that run 4 resulted in simulation results that most closely resembled the laboratory results. This decision was based on the close resemblance of the shoulder angles obtained in run 4 and the laboratory images. Although the toe angle was significantly different from the laboratory results, it was ultimately decided that an accurate shoulder angle was more important than an accurate toe angle. If the shoulder angle was incorrect it would more negatively impact subsequent simulations that included an atomizer boom in the middle of the blender, the which the strands would ultimately interact. The results of runs 4 to 6 were expected based on previous work by Smith and Davis (Davis 1919; Smith and Gutiu 2002). As the coefficient of friction increases so does the angle of -55-  detachment from the drum wall. In the simplest case, with a flight of zero height, this angle is predicted by (Smith and Gutiu 2002):  ⎛ 1 α = arcsin⎜ ⎜ 1+ μ 2 s ⎝  2 2 ⎞ ⎟ − arcsin 4π rn ⎟ g 1 + μ s2 ⎠  [10]  where:  α is the detachment angle relative to the vertical axis, µs is the static friction coefficient, r is the radius of the drum, and n is the rotational speed. To further verify these results, run 4 was re-run at 15.5 RPM and 25.5 RPM. Using a higher and lower speed was expected to show a clear movement in the shoulder and toe angles. The results of these additional simulations showed that the shoulder and toe angles had a clear dependency on the rotational speed. A summary of the results for run 4 at the various speeds is shown below (Table 26). The detailed t-test results for 15.5 and 25.5 RPM are shown in Appendix I. Table 26. Summary of shoulder and toe angles obtained at 15.5 to 25.5 RPM with the coefficients of static friction set at 0.14 and 0.07. Italicized values indicate those angles that are significantly different (α = 0.05) from the image results. Shoulder angle Toe Angle RPM Simulation Laboratory Simulation Laboratory 15.5 40.4 38.9 258.0 259.0 20.5 55.8 53.9 256.2 247.7 25.5 63.1 227.4 67.0 217.9 Although both the simulated shoulder and toe angle were significantly different from the laboratory results at 25.5 RPM, the values were close enough to be satisfied with using 0.14 and 0.07 as the coefficient of static friction for wood to wood and wood to PE respectively. As a final confirmation, the third validation technique relying on light intensity was also completed for 0.14 and 0.07 static friction values. This validation was completed for a blender fill level of 1/8th at speeds of 15.5 RPM, 20.5 RPM, and 25.5 RPM.  Before  completing this analysis a baseline test was completed to determine the light intensity of the blender without the presence of strands.  -56-  For the baseline test the light intensity was measured across the resination region with the blender empty (Figure 29). The adjusted average grayscale value was then calculated and subtracted from subsequent analyses. Because of the occurrence of parallax the region of interest was narrowed to avoid inclusion of the drum liner for this validation technique. The drum liner is nearly white and would have caused the results to be false near the left- and right-hand extents of the resination region. The thatched regions, or first and last 4 bins, in the following graphs were not included in the analysis. The average grayscale value for the region between the two cut-off points was found to be 66.2.  250  Cut-off  Cut-off  200  Gray-scale  150  100  50  Average = 66.2  0 1  3  5  7  9  11  13  15  17  19  21  23  25  27  29  31  Bin  Figure 29. Baseline grayscale results for the laboratory blender running empty. The cut-off points are indicated by the solid, vertical red lines. The drum liner is contained in the thatched region. Note that the width of each bin is 57.5 mm. The light intensity analyses showed close correspondence with the simulation results (Figures 30 to 32). In particular, the initial points of inclination (middle to left side of graphs) and the peaks appear to be reasonably aligned. This is especially true at 20.5 RPM and 25.5 RPM. At 15.5 RPM the laboratory data are skewed slightly further to the right, or negatively skewed. This disparity is difficult to interpret however. Because the peak of the -57-  laboratory data are contained within the cut-off region it is likely impacted by the lightness of the drum liner and therefore the precise location of the peak is not known. Although the graphs of the simulation results appear to resemble the laboratory images for the entire region between the cut-off points, the region to the right of the graphs’ peak is less capable of accounting for changes in strand volume. This is because at a 1/8th fill level the drum tends to become saturated with strands fluttering beneath the cascading stream of strands. This blocks the view of the drum back, inhibiting the Image Pro Plus software from observing differences in the grayscale level. The simulation and laboratory results contained here are for a blender running counter-clockwise; and therefore, the this region is to the right of the peak in these graphs.  206.0  4000  3500  186.0  3000  2500 146.0 2000 126.0 1500 106.0 1000 Laboratory results 86.0  Simulation results  500  0  66.0 1  3  5  7  9  11  13  15  17  19  21  23  25  27  29  Bin  Figure 30. Grayscale results for the blender running at 15.5 RPM and 1/8th full.  -58-  31  Gray-scale (Laboratory)  Count (Simulation)  166.0  186.0  1800  1600 166.0  146.0  Count (Simulation)  1200  1000 126.0 800  106.0  600  Gray-scale (Laboratory)  1400  Laboratory results 400  Simulation results  86.0  200  0  66.0 1  3  5  7  9  11  13  15  17  19  21  23  25  27  29  31  Bin  Figure 31. Grayscale results for the blender running at 20.5 RPM and 1/8th full. 1000  166.0 156.0  800  146.0  700  136.0  600  126.0  Simulation results  500  116.0  400  106.0  300  96.0  200  86.0  100  76.0  0  Gray-scale (Laboratory)  Count (Simulation)  Laboratory results 900  66.0 1  3  5  7  9  11  13  15  17  19  21  23  25  27  29  31  Bin  Figure 32. Grayscale results for the blender running at 25.5 RPM and 1/8th full. Based on the validation results the coefficients of static friction were similarly determined to be 0.14 and 0.07 for wood to wood and wood to PE respectively. Using this combination of -59-  coefficients produced simulation results that closely mimicked those obtained in the laboratory blender. The final coefficient of static friction values for use in EDEM are considerably lower than the 0.66 and 0.30 values obtained through the bench-top laboratory experiments. Much of this difference is likely a result of the choice in strand representation. Because the sticks are composed of a series of spheres the contact surfaces between sticks have ridges that the adjacent surfaces must slide over. This results in mechanical interlocking between the sticks. Reducing the friction coefficient acts as a lubricant for the surfaces, allowing them to more easily slide along each other or separate if necessary. A second explanation for this disparity is the lack of fine particles in the model. In an actual rotary drum blender, including the one used for validating this model, fine particles are generated within the process. These fine particles coat the surfaces of the strands, flights, and drum liner and ultimately behave similar to very small ball bearings and effectively reduce the friction between surfaces. 4.5  Conclusions  The selection of suitable material and interaction parameters has been shown to be critical to the successful implementation of a discrete element model for two principal reasons. First, the accuracy of the simulation results is largely determined by the input parameters. The adage “garbage in, garbage out” has been shown to be particularly relevant here (Hirsch et al. 2002). The findings of this study show that many of the parameters listed in Table 8 have no significant impact on the bulk dynamics of wood strands in the RDBM. The only parameters that did have a significant impact were the coefficients of rolling friction and static friction. Second, the combination of parameters may significantly impact the processing time required for an individual run. During this project, processing times for a 24 second simulation ranged from as low as 4.7 hours to as high as 34.3 hours. Accuracy of the simulation results being equal, shorter processing times are preferred. Shorter processing times are achieved by using relatively high material densities or low shear moduli.  -60-  Based on the findings of these simulations and analyses the complete set of material and interaction properties for this particular project is shown below in Table 27. By using these input parameters the RDBM accurately, and processor efficiently, predicts the bulk dynamics of wood strands in a 6 foot rotary drum blender. Table 27. Summary of material and interaction properties for use with EDEM. Material Properties Shear modulus 1x108 psi Poisson’s ratio 0.453 Density 380 kg/m3 Interaction Properties Coefficient of rolling friction 0.67 Coefficient of static friction: Wood on wood 0.14 Wood on HDPE 0.07 Coefficient of restitution 0.01  -61-  CHAPTER 5  MEASURING THE EFFECT OF ROTARY DRUM BLENDER DESIGN AND OPERATING PARAMETERS ON THE BULK STRAND FLOW USING A RESPONSE SURFACE DESIGN  5.1  Introduction  Until this point the research project was largely focused on calibrating the RDBM with laboratory results. This was necessary before exploratory studies could be completed using the model. This next portion of the research therefore relies on these calibration results for conducting an exploratory study aimed at understanding the design and operation of rotary drum blenders. This work utilizes the quantification techniques used in Chapter 4, together with a response surface design, to determine the relationship between four operating and blender design parameters and the distribution of strands across the blender diameter as well as the average time a strand spends in the resination region. The four factors of interest are specific to the Coil Manufacturing, long-retention blenders, and include: the flight height, number of flights, blender fill level, and blender rotational speed.  This is not an exhaustive list of factors;  however, they are the few parameters that do not require fundamental or significant changes to the current blending process. It is hypothesized that there are ideal combinations of blender design and operating parameters that results in the optimal blending environment.  Objective: 1. To understand the impact of blender design and operating parameters on the strand distribution across the drum diameter and the average time a strand spends in the resination region. 5.2  Methodology  A response surface design was selected for determining the impact several of the rotary drum blender design and operating parameters have on the distribution of strands across the drum diameter, as described by the skewness and kurtosis, as well as the average time a strand spends in the resination region.  Response surface methodology (RSM) was followed -62-  because it provides an efficient means of determining the relationship between several factors and response variables. For this reason, RSM has been used extensively for product and process optimization (Myers and Montgomery 2002). A modified four factor, Box-Behnken response surface design was followed for these simulations (Tables 28 and 29). How this design differs from a traditional Box-Behnken design is that the number of flights and fill level increase geometrically. Consequently, the median value, or factor level, is not equal to the mean value, as is the case with traditional Box-Behnken designs (SAS Institute Inc.). The design scheme was altered in response to limitations with the design of the laboratory blender. In particular, additional flights could only be positioned at set locations. The laboratory blender was pre-drilled for 16 flights; therefore, in order to maintain a symmetric flight placement along the blender circumference, the number of flights was increased from 4 to 8 to 16. Although it was ultimately decided that the laboratory blender was not required for further validation of the RDBM, at the onset of this analysis it was desired to maintain that option.  -63-  Table 28. Response surface design matrix. Run Number of Flight flights height 1 -1 -1 2 -1 1 3 1 -1 4 1 1 5 -0.33 0 6 -0.33 0 7 -0.33 0 8 -0.33 0 9 -1 0 10 -1 0 11 1 0 12 1 0 13 -0.33 -1 14 -0.33 -1 15 -0.33 1 16 -0.33 1 17 -1 0 18 -1 0 19 1 0 20 1 0 21 -0.33 -1 22 -0.33 -1 23 -0.33 1 24 -0.33 1 25 -0.33 0 26 -0.33 0 27 -0.33 0  Fill level -0.33 -0.33 -0.33 -0.33 -1 -1 1 1 -0.33 -0.33 -0.33 -0.33 -1 1 -1 1 -1 1 -1 1 -0.33 -0.33 -0.33 -0.33 -0.33 -0.33 -0.33  Table 29. Response surface design factor levels. Low level Factor Units (-1) Number of flights 4 Flight height inches 2 1 % 6.25 Fill level Rotational speed rpm 18.71 1  Rotational speed 0 0 0 0 -1 1 -1 1 -1 1 -1 1 0 0 0 0 0 0 0 0 -1 1 -1 1 0 0 0  Mid level (0 or -0.33) 8 4 12.50 23.39  High level (1) 16 6 25.00 28.07  Fill level is represented as the fraction of blender volume occupied by strands if the blender drum was stopped during operation and the strands settled on the base of the drum.  The factor levels were selected based on discussions with Coil Manufacturing (Coil 2007b; Coil 2008) and by balancing computational and physical limitations, as previously mentioned. For instance, the fill level of an industrial blender is typically 25% to 50%. This level is based on the fraction of the blender volume occupied by strands when the blender is not rotating and the strands are resting on the bottom of the blender drum under self-weight. -64-  Because of computing limitations, which include both the speed in which the software can solve a simulation and the speed in which the computer can run the software, the maximum fill level simulated was 25%. The results show distinct trends however, which may be useful for extrapolating towards the higher fill levels. In addition, the simulated blender diameter was limited to 1.84 meters (6.04 feet). This corresponds to the laboratory blender and minimizes the computational requirements. Industrial blenders are as large as 11 feet in diameter; however, it is anticipated that results from the 6 foot blender will provide valuable insight into the strand dynamics. Further, it is assumed that many of the effects caused by the design and operational parameters will be relevant regardless of the blender diameter. As will be outlined in the Future Work section, it is recommended that future experiments be conducted that investigate the validity of scaling the model results for an industrial blender. The selected blender rotational speeds were 60, 75, and 90% of the calculated critical speed (Smith and Gutiu 2002). It is important to note that instead of reporting the total number of 0.1 second time steps that the 150 tracked strands spent in the resination region, as was the case with the sensitivity study (Chapter 4), the average time an individual strand spent in the resination region was reported in this study. The reason for this slight change in the reporting format is because of the varying blender fill levels investigated in this study. Reporting the average time helps avoid misinterpretation of the results and relates directly to the overall objective, which is to maximize the time spent in the resination region. Throughout this study, a tracked sample size of 150 strands was maintained. For all of the simulations, the number of recorded revolutions was maintained at 10; however, the first 2 revolutions were discarded to allow the model to reach steady state. Consequently, 8 complete revolutions were included in the analysis for each simulation. The response surface design was completed twice, once without an atomizer boom and once with a single atomizer boom (Figure 33). The location of the boom was selected based on drawings provided by Coil Manufacturing (Coil 2007b). As an initial investigation of the dynamics and the role design and operational parameters have on it, most of the attention was focused on the scenario without an atomizer boom. This would allow for an optimal boom location to be selected based on the strand flow, while still providing some insight into the impact the boom will have on the resulting strand flow. -65-  Downward rotating side  Upward rotating side  CCW Rotation Atomizer boom  Figure 33. Schematic of a blender fitted with an atomizer boom, shaded grey. The upward and downward rotating sides of the blender are also indicated. All of the simulations were run using EDEM version 1.3.1 and post processed and sorted in Microsoft Excel using the VBA script listed in Appendix E. The results were subsequently analyzed using SAS version 9.1’s response surface design tools. Quadratic models were fit in SAS using the ANOVA selection method at a 95% confidence level (α = 0.05). For the skewness and kurtosis it was necessary to include several of the insignificant effects to maintain the model hierarchy. These effects are indicated in the Results and Discussion section. 5.3  Results and discussion  5.3.1 Overall predictive trends The results of the study using a 6 foot RDBM (Appendix J) show that all three response variables were significantly affected by at least two of the four factors, either as a main effect or as an interaction effect. The skewness was impacted most, being affected by all four factors. Kurtosis was affected by the number of flights and flight height, while the average time spent in the resination region was affected by the flight height and rotational speed. The relationships between the response variables and the significant factors are presented in the following sections. -66-  These relationships are shown in the prediction profile graphs that were generated in SAS (Figures 34, 40, 43, and 44 to 47). The factors are shown on the x-axes and the response variables on the y-axes. These relationships are unique to the factor levels employed and may change accordingly if the factor levels were to change. For the graphs included in this study, factor levels representative of industry norms were used for the skewness and average time spent in resination region analyses (Table 30) (Coil 2008; Smith 2005). Table 30. Factor levels used in the skewness and average time spent in resination region analyses. Factor Factor level Number of flights 14 Flight height (inches) 4 Fill level (fraction) 0.25 Rotational speed (rpm) 24.0 The factor levels used for the kurtosis analyses are described in Section 5.3.1.3. The factor levels are indicated by a vertical line and accompanying x-axis label on the respective graphs. In order to facilitate comparison of the simulation means, 95% confidence intervals are included on each of the following graphs. 5.3.1.1 Skewness All four factors had a significant effect on the skewness (Table 31 and Figure 34). The skewness increased with an increasing rotational speed and number of flights and a decreasing fill level. The skewness increased with an increasing flight height from 2 to 4 inches and then began to decrease. The model for predicting the skewness is shown in Equation 11.  This model yields an F-value of 27.1357 (p-value < 0.0001), which is  significant at a 95% confidence level (α = 0.05).  -67-  Table 31. List of effects for the skewness showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy. Factor Number of flights Flight height Fill level Rotational speed Number of flights x Flight height Flight height x Fill level Rotational speed2 Flight height2 x Rotational speed  Factor Number of flights Flight height Fill level Rotational speed Number of flights x Flight height Flight height2 Flight height x Fill level Flight height x Rotational speed Rotational speed2 Flight height2 x Rotational speed  p-value 0.0093 0.0092 0.0232 0.0032 0.0121 0.0051 0.0237 0.0410  p-value 0.0093 0.0092 0.0232 0.0032 0.0121 0.1106 0.0051 0.0516 0.0237 0.0410  Sk = 5.3128 + 0.2006 X 1 −1.6325 X 2 + 6.4648 X 3 − 0.7499 X 4 − 0.0282 X 1 X 2 + 0.2652 X 22 − 2.4520 X 2 X 3 + 0.1409 X 2 X 4 + 0.01145 X 42 − 0.0144 X 22 X 4  [11]  where:  Sk is the predicted skewness, X1 is the number of flights, X2 is the flight height in inches, X3 is the blender fill level as a fraction of the total blender volume, and X4 is the blender rotational speed in rpm’s.  fr  Figure 34. Prediction profiles generated in SAS showing the relationship between the skewness and the (top-left) number of flights, (top-right) flight height, (bottom-left) fill level, and (bottom-right) blender rotational speed. The vertical lines and x-axes labels indicate the factor levels used for the creation of these specific graphs. -68-  Skewness was shown to increase with an increasing number of flights and decrease with an increasing blender fill level. Recall that a positive skewness implies that the majority of the strands passed through the resination region on the downward rotating side of the drum, while a negative skewness implies that the majority of the strands passed through the resination region on the upward rotating side of the drum as they descended (Figure 33). Ideally the strands would be symmetrically distributed, which would be identified by a skewness of 0. The impact of flight height and fill level is best described by considering the angle of repose. Although this measure is most applicable for granular material, it is also relevant for wood strands. The angle of repose refers to the internal angle formed between a horizontal surface and a pile of granular material (Figure 35). This angle is largely influenced by the coefficient of static friction and determines the height and width of the resulting pile for a given volume of material (Smith 2006).  furnish furnish  α  Figure 35. Schematic showing the angle of repose, α, for a pile of wood strands on a horizontal surface. With fewer flights the loading per flight was relatively high, causing the strands to pile higher atop of each flight. This is easily seen for the flight identified by the arrow in Figure 36a. In this case, where there are only 4 flights, the amount of strands that the flight is able to carry is determined by the angle of repose.  As the flight moves along the drum  circumference the angle of the flight relative to the horizontal axis increases. This causes some of the strands to detach and slough off of the flight because the angle of repose has been exceeded, as shown in Figure 36b. This is particularly relevant for the strands furthest away from the flight where the angle is greatest and the strands are less supported. Once the flight reaches the location shown in Figure 36e the strands begin to slough off of the flight in a continuous flow. With only 4 flights the strands slough off of the flight while the flight passed through the entire right half of the blender.  -69-  (a)  (b)  (c)  (d)  (h)  (g)  (f)  (e)  Figure 36. Simulation images showing the charge level per flight and the discharge pattern when a relatively small number of flights are employed. The simulated blender has 4-6 inch flights and is rotating at 23.39 RPM and is 1/8th full. The arrow indicates the position of a specific flight as the drum rotates. As the number of flights increased the loading of strands per flight diminished, reducing the height of the strand pile atop of each flight. This is seen in Figure 37a. As a result, the distance between the strands nearest to the flight and the strands furthest from the flight has decreased. In this case, the flights need to travel further along the drum circumference before the angle of repose is overcome. This is illustrated in the following example where the strands do not begin detaching until the flight reaches the location shown in Figure 37d. Consequently, the strand piles sloughed off of their respective flight within a narrow timeframe. With 16 flights, most of the strands detached as the flight passed through the upper-right drum quadrant. A smaller loading per flight would be the preferred scenario for an industrial operation as it results in better control over the moment of detachment from the flight and the strand trajectory.  -70-  (a)  (b)  (c)  (d)  (h)  (g)  (f)  (e)  Figure 37. Simulation images showing the charge level per flight and the discharge pattern when a relatively large number of flights are employed. The simulated blender has 16-6 inch flights and is rotating at 23.39 RPM and is 1/8th full. The arrow indicates the position of a specific flight as the drum rotates. As anticipated, increasing the fill level caused the skewness to decrease. As more strands were loaded into the blender the flights tended to become overloaded, causing the strands to slough off the flights relatively early. This placed downward pressure on the skewness. Similar to the effect of the number of the flights, increasing the rotational speed also caused the skewness to increase. At less than approximately 21 RPM however, the speed appeared to have only a minimal impact on the skewness. One explanation for this is that as the speed decreased the strands became less dispersed across the drum diameter. This consolidation of strands continued until the strands were packed in the lower-right drum quadrant, rolling amongst themselves (Figure 38). 21 RPM could be the speed at which point there is only minimal free fall of strands and the majority of strands are rolling in this region.  Figure 38. Simulation image showing strands rolling in the corner of the drum, where there are 8-4 inch flights and the blender is rotating at 18.71 RPM and is 1/4 full. -71-  A positive relationship between the skewness and rotational speed was expected based on previous work (Davis 1919; Smith and Gutiu 2002). As the rotational speed, n, increased so to did the centrifugal force, FC (Equation 12). This caused the strands to stay in contact with the flights or drum wall longer as the centrifugal force caused detachment to occur at a higher angle.  FC =  Fgω 2  [12]  rg ω = 2π r n where:  [13] ω is the angular velocity, r is the distance from the center of the drum, g is gravitational acceleration, and n is the rotational speed in rpm.  This effect is magnified by the fact that as the flow of strands moves further across the drum the falling strands are dispersed amongst a larger number of flights. This reduces the likelihood of strands piling in the lower-right drum quadrant waiting to be collected by a passing flight. Figure 39 shows an example of flight utilization. At 18.71 RPM the strands are dispersed across only 9 flights, compared to 14 at 28.07 RPM.  Figure 39. (Left) Simulation image showing the dispersion of strands across relatively few flights when the blender is rotating at 18.71 RPM and (right) across many flights when the blender is rotating at 28.07 RPM. In both cases the blender has 16-4 inch flights and is 1/8th full. The piling of strands in the blender and the movement of the passing flights through the pile is a possible contributor to strand attrition caused by the grinding of strands. It may also result in poorly aligned strands on the flights as the strands become interlocked. Poor alignment creates challenges for predicting when the strands will detach from their respective  -72-  flight. Generally, the results show that poorly aligned strands detach prematurely, placing downward pressure on the skewness. Flight height had an interesting effect on the skewness. Between 2 and 4 inches a positive relationship was anticipated. This is because as the flight height increased each flight was capable of carrying a larger number of strands, resulting in an increased overall system capacity. As seen prior, with a fixed volume of strands, the capacity had a direct impact on the skewness. Beyond 4 inches however, the relationship between the flight height and skewness became negative. This was not foreseen but can be explained by examining the forces acting on the strands. As the flight height increased the edge of the flights were closer to the center of rotation of the blender, resulting in a lower centrifugal force acting on those strands located nearer the edge of the flights. This caused the strands to begin detaching and descending sooner than with shorter flights that were further from the center of rotation. This same trend may not have been seen with flights between 2 and 4 inches because the shorter flights were incapable of lifting an adequate amount of strands. As a result, the quantity of strands that prematurely fell from the shorter flights had less impact on the overall strand flow statistics. Based on these findings, it appears that flights that are between 4 and 5 inches in height strike a good balance between capacity and control over the strand detachment point for this particular 1.840 meter (6.04 feet) diameter blender. It is important to recognize however that the difference in the predicted skewness for flights that are 4 inches and larger in height in not significant. 5.3.1.2 Effect of an atomizer boom on the skewness results  The significant main effects that were determined according to the ANOVA selection method, using a 95% confidence level, was reduced from all four factors to only two factors when the atomizer boom was included. These factors were the fill level and the blender rotational speed. All four factors were ultimately included however in order to maintain the skewness model hierarchy. The inclusion of an atomizer boom in the simulations had a slight impact on the overall relationship between two of the main effects and the skewness (Table 32). While in general -73-  these relationships did not drastically change over the tested ranges (Figures 34 and 40), they are worth evaluating in order to better understand the bulk strand dynamics and the impact the atomizer boom placement has on it. The model for predicting the skewness is shown in Equation 14.  This model yields an F-value of 18.3728 (p-value < 0.0001), which is  significant at a 95% confidence level (α = 0.05). Table 32. List of effects for the skewness when an atomizer boom is present, showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy. Factor Fill level Rotational speed Number of flights x Rotational speed Flight height x Fill level Flight height x Rotational speed Fill level2 Rotational speed2 Number of flights2 x Rotational speed  Factor Number of flights Flight height Fill level Rotational speed Number of flights2 Number of flights x Rotational speed Flight height x Fill level Flight height x Rotational speed Fill level2 Rotational speed2 Number of flights2 x Rotational speed  p-value 0.0126 0.0023 0.0127 0.0463 0.0046 0.0070 0.0443 0.0419  p-value 0.1720 0.1517 0.0126 0.0023 0.6020 0.0127 0.0463 0.0046 0.0070 0.0443 0.0419  Sk =19.1295 − 1.4394 X 1 −1.1450 X 2 − 22.0559 X 3 − 1.2556 X 4 + 0.0536 X 12 + 0.0664 X 1 X 4 −1.6584 X 2 X 3 + 0.0764 X 2 X 4 + 76.4595 X 32 + 0.0149 X 42 −0.0024 X 1 X 2 X 4 where: Sk is the predicted skewness, X1 is the number of flights, X2 is the flight height in inches, X3 is the blender fill level as a fraction of the total blender volume, and X4 is the blender rotational speed in rpm’s.  -74-  [14]  fr  Figure 40. Prediction profiles generated in SAS showing the relationship between the skewness and the (top-left) number of flights, (top-right) flight height, (bottom-left) fill level, and (bottom-right) blender rotational speed when an atomizer boom is included in the simulation. The vertical lines and x-axes labels indicate the factor levels used for the creation of these specific graphs. The main effect and skewness relationships that changed involve the flight height and blender fill level. In both cases it was in the upper portion of the tested ranges where a deviation in the results was observed. When the atomizer boom was not included in the simulations the skewness was not significantly affected by flights greater than 4 inches. With the atomizer boom in place however skewness increased with flight height across the entire tested range. Recall that an increasing skewness is an indicator of more strands being concentrated on the downward rotating half of the drum. A possible explanation for this discrepancy is that the strands that detached prematurely from the longer flights tended to contact the top of the atomizer boom. These strands then traveled over the boom and descended on the downward rotating half of the drum, instead of the upward rotating half or near the drum center. This had a positive impact on the skewness.  Conversely, when the  flights were relatively short and the strands were not carried as far up the blender wall before detaching, many of the strands collided with the side of the atomizer boom during their decent. These strands were unable to travel as far across the blender drum, resulting in a lower, or more negative, strand distribution (Figure 41). -75-  2-inch flights  6-inch flights  No atomizer boom  Atomizer boom  Figure 41. Simulation images showing the dispersion of strands across the blender diameter when there is (top-left) no atomizer boom and there are 2 inch flights, (top-right) no atomizer boom and there are 6 inch flights, (bottom-left) an atomizer and there are 2 inch flights, and (bottom-right) an atomizer boom and there are 6 inch flights. In all cases there were 16 flights and the blender rotated at 23.39 RPM. The skewness decreased consistently with an increasing fill level when the atomizer boom was not present. This was a result of the fixed blender capacity and the inability of the blender to lift, carry, and disperse the increasing amount of strands across the blender diameter. With the atomizer boom in place this same trend was not observed across the tested range. In fact at a 20% fill level the relationship between the predicted skewness and fill level became positive. This change in behavior is a result of strands becoming wedged between the atomizer boom and the blender wall. When the fill level reaches a particular point, in this case around 20%, there is a chance that collections of strands will become wedged in this region (Figure 42). The collection of strands is then carried over the atomizer boom and deposited on the opposite side of the drum, positively affecting the skewness. Because these strands are forced together between the boom and blender wall, there is also a greater chance that they will become interlocked and move as a clump through the drum, -76-  causing the phenomenon to repeat itself. This strand behavior may be a contributing factor to surging in blenders. Wedge region  Figure 42. Simulation image showing strands as they become wedged between the atomizer boom and blender wall when operating at elevated fill levels, indicated by the dashed oval. In this case the blender is ¼ full and is equipped with 8, 4 inch flights and is rotating at 28.07 RPM. Surging occurs when a large number of strands become mechanically interlocked and a portion of these strands are lifted by the flights. Those strands that are not supported by the flights, but instead are being lifted because they are mechanical interlocked with those strands that are supported, eventually break free and descend as a clump of strands. This clump of strands overwhelms the flights that they fall upon and the process continues. Once this process begins it will typically perpetuate until there is a disruption, for example when the affected strands are discharged from the blender. Unfortunately, the resin distribution amongst those strands will be generally poor. 5.3.1.3 Kurtosis  In addition to skewness, kurtosis was also used to describe the distribution of strands across the drum diameter. While skewness is an indicator of how symmetric the strand distribution is between the upward rotating and downward rotating half of the blender, kurtosis is an indicator of the uniformity of the strand distribution across the blender diameter. If the strands were normally distributed the kurtosis would be 0. For these simulations however, a uniform distribution is sought and is obtained for a kurtosis value of –1.2.  -77-  Using an ANOVA to determine the significant effects it was found that none of the main effects were significant; however, three of the interactions were (Table 33). The most notable interaction was between the number of flights and the flight height.  This  combination is present in all three of the significant interactions shown in Table 33. The model for predicting the kurtosis is shown in Equation 15 and yields an F-value of 17.8156 (p-value < 0.0001), which is significant at a 95% confidence level (α = 0.05). Table 33. List of effects for the kurtosis showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy. Factor Number of flights x Flight height Number of flights2 x Flight height Number of flights x Flight height2  p-value 0.0056 0.0243 0.0442  Factor Number of flights Flight height Number of flights2 Number of flights x Flight height Flight height2 Number of flights2 x Flight height Number of flights x Flight height2  K = 47.8071 − 6.3111X 1 − 15.8225 X 2 + 0.1999 X 12 + 1.6924 X 1 X 2 + 1.1599 X 22 − 0.04115 X 12 X 2 − 0.0770 X 1 X 22  p-value 0.7843 0.5681 0.1128 0.0056 0.1041 0.0243 0.0442  [15]  where: K is the predicted kurtosis, X1 is the number of flights, and X2 is the flight height in inches. In order to facilitate the interpretation of these results the graphs shown in Figures 43 and 44 were generated in SAS. These graphs present four combinations of the number of flights and the flight height. Figure 43 shows kurtosis with the flight height fixed at 4 inches and the number of flights at 4 and 16, while Figure 44 shows kurtosis with the number of flights fixed at 14 and the flight height at 2 and 6 inches. As shown in the graphs, the combination of effects had a considerable impact on the kurtosis trends. Note that the y-axis scale is not the same for the top and bottom sets of graphs in both figures; however, the graphs showing the relationship between the kurtosis and number of flights (left) in Figure 43 are in fact the same except for the 95% confidence interval, which is unique to the chosen factor level. This is also true for the graphs showing the relationship between the kurtosis and the flight height (right) in Figure 44.  -78-  Figure 43. Prediction profiles generated in SAS showing the impact of the (left) number of flights on the relationship between (right) the kurtosis and the flight height. The vertical lines and x-axes labels indicate the factor levels used for the creation of these specific graphs.  Figure 44. Prediction profiles generated in SAS showing the impact of the (right) flight height on the relationship between (left) the kurtosis and the number of flights. The vertical lines and x-axes labels indicate the factor levels used for the creation of these specific graphs. -79-  As the number of flights increased from 4 to 16 the significance of flight height quickly diminished. With only 4 flights, the kurtosis decreased quickly with increasing flight height. With 16 flights however, kurtosis increased slowly with increasing flight height, but overall the trend was insignificant. Building upon the skewness discussion and interpretation, these results were likely caused by the combination of the blender fill level and the capacity of the blender to lift and disperse strands. With only a few relatively short flights, the blender capacity was low. As a result, the majority of the strands remained in the lower-right quadrant of the drum and the quantity of strands that were lifted out of this quadrant and dispersed was insignificant. With only 4 flights, increasing the length of the flight had a large impact on the capacity and the resulting kurtosis. As one might expect, increasing the number of flights diminished the impact of increasing flight height due to the strands being spread across more flights. Focusing now on the scenario where the number of flights was fixed at 14, as the flight height increased from 2 to 6 inches the impact of the number of flights on the kurtosis changed considerably.  With 2 inch flights, increasing the number of flights caused the  kurtosis to decrease. This was true up until 13 flights, after which the kurtosis stabilized at around –1.4. With 6 inch flights the kurtosis increased when there were 4 to 10 flights and then decreased when there were 13 to 16 flights; however, the difference was only minimally significant across this latter range. This was consistent with the previous scenario and the skewness findings. With 2 inch flights, increasing the amount of flights had a significant impact on the capacity of the blender to lift and disperse strands. With 6 inch flights the relationship between kurtosis and the number of flights became considerably less significant as the demand for additional capacity decreased. 5.3.1.4 Effect of an atomizer boom on the kurtosis results  The presence of an atomizer boom in the simulations did not impact those effects that were found to be significant according to the ANOVA selection method. It did however impact the significance of the number of flights – flight height interaction on the kurtosis (Table 34, Figures 45 and 46). With 16 flights the relationship between the flight height and kurtosis went from marginally positive to significantly negative (Figure 45). One explanation for this occurrence is that the atomizer boom helps disperse strands more evenly on either side of the drum. This is because as the strands fall on top of the boom they slide off on both sides. -80-  However, in order for this to occur, the detachment point of the strands must be higher than the boom so that they may fall on top of it. This is why the kurtosis became highly positive with shorter flights. As discussed previously, with shorter flights the strands collide with the side of the boom and then fall in a near perfect vertical direction to the bottom of the drum. This caused a spike in the frequency of strands falling within a narrow region on the upward rotating side of the atomizer boom. The relationship between the number of flights and kurtosis remained relatively unchanged with the inclusion of the atomizer boom when the flight height was set at 2 and 6 inches. The model for predicting the kurtosis is shown in Equation 16 and yields an F-value of 11.0681 (p-value < 0.0001), which is significant at a 95% confidence level (α = 0.05). Table 34. List of effects for the kurtosis when an atomizer boom is present, showing (left) the significant effects and (right) the significant effects as well as those that were included to maintain the model hierarchy. Factor Number of flights x Flight height Flight height2 Number of flights2 x Flight height Number of flights x Flight height2  Factor Number of flights Flight height Number of flights2 Number of flights x Flight height Flight height2 Number of flights2 x Flight height Number of flights x Flight height2  p-value 0.0106 0.0279 0.0070 0.0438  K = 42.3048 − 5.3881X 1 −13.3962 X 2 + 0.1921X 12 + 1.3854 X 1 X 2 + 0.9161X 22 − 0.0413 X 12 X 2 − 0.0503 X 1 X 22  where: K is the predicted kurtosis, X1 is the number of flights, and X2 is the flight height in inches.  -81-  p-value 0.6595 0.6766 0.0880 0.0106 0.0279 0.0070 0.0438  [16]  Figure 45. Prediction profiles generated in SAS showing the impact of the (left) number of flights on the relationship between (right) the kurtosis and the flight height when an atomizer boom is present.  Figure 46. Prediction profiles generated in SAS showing the impact of the (right) flight height on the relationship between (left) the kurtosis and the number of flights when an atomizer boom is present. -82-  5.3.1.5 Average time a strand spent in the resination region  The average time a strand spent in the resination region for a fixed number of revolutions was shown to be strongly related to the flight height and the blender rotational speed (Figure 47). The average time decreased with both increasing flight height and rotational speed. The model for predicting the average time a strand spends in the resination region is shown in Equation 17 and yields an F-value of 33.8102 (p-value < 0.0001), which is significant at a 95% confidence level (α = 0.05). t = 3.5407 − 0.1124 X 2 − 0.0794 X 4  [17]  where:  Average time in resination region (sec)  Average time in resination region (sec)  t is the predicted average time in seconds, X2 is the flight height in inches, and X4 is the blender rotational speed in rpm’s.  Figure 47. Prediction profiles generated in SAS showing the relationship between the average time spent in the resination region and the (left) flight height and (right) blender rotational speed. The vertical lines and x-axes labels indicate the factor levels used for the creation of these specific graphs. As demonstrated in Figure 48, the negative relationship between the flight height and the average time spent in the resination region as well as the rotational speed and the average time was caused by similar phenomena. With relatively small flights and/or low rotational speeds the strands tended to cluster and roll amongst themselves in the lower-right drum quadrant. These strands fell slowly through the resination region as they moved within the cluster. In addition, because they were clustered within a small area the strands did not have to travel far before making a complete revolution.  The strands therefore passed more  frequently through the resination area. As the flight height and/or rotational speed increased the rolling motion decreased as a greater fraction of the strands were lifted by the flights and -83-  dispersed across the blender. These strands passed relatively quickly through the resination region on their descent and made fewer revolutions. Low speed  High speed  2-inch flights  6-inch flights  Figure 48. Simulation images showing (top-left) the clustering of strands at relatively low speeds with 2-inch flights, (top-right) the dispersion of strands at relatively high speeds with 2-inch flights, (bottom-left) the clustering of strands at relatively low speeds with 6-inch flights, (bottom-right) the dispersion of strands at relatively high speeds with 6-inch flights. Note that strands cluster more with shorter flights and/or slower blender rotational speeds. The blender rotational speeds were 18.71 RPM and 28.07 RPM respectively. Although the overall objective of an operation is to devise a set of operating and design parameters that results in the strands spending the maximum time possible in the resination region, there are other criteria that must first be met. For instance, the strands should be well dispersed across the blender diameter. Scenarios where there is clustering and rolling of strands (Figure 48) is not desirable because only the strands on the surface of the cluster would become resinated. As reported by Smith (2006), PF-resin does not spread well after its initial contact with the wood substrate. Therefore, blending operations cannot rely on the smearing and transfer of resin between strands for resination purposes, as is the case with particleboard blending (Maloney 1993).  PMDI-resin is able to transfer; however, this -84-  scenario is still not desirable as it is not an efficient use of resin and the blender (Smith 2006). 5.3.1.6 Effect of an atomizer boom on the average time a strand spent in the resination region  The inclusion of an atomizer boom in the simulations had an effect on the selection of significant factors, ultimately reducing the number of factors that impacted the predicted average total time a strand spends in the resination region from two to one. The model for predicting the average time a strand spends in the resination region is shown in Equation 18 and yields an F-value of 33.4386  (p-value < 0.0001), which is significant at a 95%  confidence level (α = 0.05). t = 3.0912 − 0.0772 X 4  [18]  where: t is the predicted average time in seconds, and X4 is the blender rotational speed in rpm’s. With the atomizer boom present only the blender rotational speed was significant. It is not surprising that the flight height was no longer significant.  As was shown before, the  principal difference between the flow pattern of the strands when the blender is equipped with long flights versus short flights is which side of the atomizer boom the majority of strands fall on. With longer flights the strands are more likely to fall on top of the atomizer boom and slide off on either or both sides of the blender. With shorter flights the strands tend to collide with the side of the boom and fall almost entirely on the upward rotating side of the blender. In either case the strands fall near vertically to the bottom of the drum after collision with the boom. This near vertical drop of the strands through the resination region for both scenarios resulted in a relatively short period of time spent in that region. This is compared to the case where there is no atomizer boom and the associated longer parabolic trajectory of a strand that detaches from the drum and does not collide with a boom. 5.3.1.7 Discussion  The results showing the general relationship between the factors and response variables confirmed many of the previous speculations regarding the operation of rotary drum blenders. In particular, the results show that the skewness increased with an increasing -85-  number of flights, flight height, and blender rotational speed within the tested ranges. The impact of flight height on the skewness diminished as the flight height increased, likely due to early detachment that is a result of the strands being closer to the axis of rotation of the drum. Increasing the blender fill level had the opposite effect on the skewness, causing it to decrease. These interactions are largely related to the overall capacity of the blender to lift, carry, and finally disperse a fraction of the total strands across the blender diameter. The capacity is broadly determined by two factors, the size of the individual flight and the number of flights that the strands are spread across. In addition to confirming some previous thoughts regarding blending dynamics, the results also presented several interesting findings.  Most notable was the significance of the  interaction between the flight height and the number of flights on the kurtosis. This suggests that during the manufacturing of blenders it is vital that care and attention be focused on the selection and placement of flights. Once the blender is in operation it is very difficult to change either of these parameters. Further, it was shown that the average time a strand spent in the resination region was negatively related to the flight height and the rotational speed. Upon visual inspection of the results it was determined that, although strands spent more time in the resination region with smaller flights and/or at lower speeds, the additional time spent in the region was not beneficial because a considerably smaller percentage of the strands were actually exposed to the atomized resin. The impact of the atomizer boom on the strand dynamics was largely dependent on whether or not the strands were carried high enough by the flights to cascade over top of the atomizer boom. In either case the strands tended to stream off of the respective side(s) of the boom. In several extreme cases where the blender was filled ¼ full the strands became wedged between the atomizer boom and the drum wall, resulting in a surging effect. 5.3.2 Research applications  These results were further analyzed based on two perspectives: the wood strand-based product manufacturers (end-users), and the blender manufacturers. This work focused on the opportunities both groups have for optimizing their blenders given the available resources, such as the ability for an operation to make changes within a short timeframe. The goal is to -86-  gain unique insight into the impact each of the aforementioned segments may have on the bulk strand dynamics by making changes to the blender design and/or operating parameters. 5.3.2.1 Wood strand-based product manufacturers  For existing operations it may not be possible or practical to change the number of flights or flight height. While the flight height can be changed by purchasing new flights and installing them during an extended downtime, the number of flights is determined by the drilled hole pattern in the blender drum and would require considerable time to change. Generally however, neither alteration is desirable. In addition, the blender fill level is largely determined by the demand from the proceeding process and the feed rate from the dry strand bins. While there is a target fill level, this level can fluctuate during disturbances in the manufacturing process. This leaves the blender rotational speed as the only factor that can be changed accordingly while the process is running. Figure 49 shows the contour graph for the skewness based on the fill level and simulated blender rotational speed for four common flight heights: 3, 4, 5, and 6 inch with no boom present. The number of flights was fixed at 14, or approximately every 16 inches along the circumference, which is typical for an industrial blender (Coil 2007b; Coil 2008).  In  addition to the skewness, the predicted average time a strand spends in the resination was also included in the graphs. The aim is to select operating parameters that result in a skewness of 0 while maximizing the average time spent in the resination region. All of the contour graphs are for a 6 foot simulated blender. Although this diameter is smaller than that of typical industrial blenders, as outlined in Section 5.2 it is anticipated that the results of this study can be scaled for use on an industrial blender.  -87-  (sec)  (sec)  (sec)  (sec)  Figure 49. Contour graphs for the skewness based on the fill level and blender rotational speed using 3, 4, 5, and 6-inch flights. The number of flights has been fixed at 14. The graphs suggest that as the fill level decreases the rotational speed must also decrease to maintain a skewness of 0. This relationship becomes more apparent as the flight height increases. For example, with 3 inch flights, a drop in the fill level from 25% to 7% only requires a slight reduction in speed from 25.5 RPM to 24 RPM. However, with 6 inch flights, a drop in the fill level from merely 25% to 19% requires a reduction in speed from 25 -88-  RPM to 18.9 RPM. Throughout the wood strand-based product industry, the growing trend has been to use higher flights in conjunction with larger diameter blenders to increase capacity. Consequently, if it is assumed that this relationship between the blender fill level and rotational speed remains true as the drum diameter increases, operations run the risk of operating their blenders sub-optimally with only slight fluctuations in the blender feed rate. Therefore, it is imperative that operations link the blender rotational speed with the blender feed rate. This way the process could adapt accordingly to changes in the strand flow and the resulting blender fill level.  Alternatively, shorter flights could be employed if blender  capacity is not a concern. This would reduce the impact strand flow fluctuations have on the blending environment. 5.3.2.2 Effect of the atomizer boom for wood strand-based product manufacturers  The contour graphs indicate a sizeable shift in the required rotational speed given a specific fill level when an atomizer boom is present (Figure 50). In addition to this, the relationship between the blender fill level and the blender rotational speed was no longer strictly positive, instead all four of the flight heights included exhibit a negative relationship above a particular fill level.  -89-  (sec)  (sec)  (sec)  (sec)  Figure 50. Contour graphs for the skewness based on the fill level and blender rotational speed using 3, 4, 5, and 6-inch flights when an atomizer boom is present. The number of flights has been fixed at 14. Until the point of inflection where the required rotational speed begins to decrease for an increasing fill level, the required rotational speed to achieve and maintain a skewness of 0 is considerably higher when the atomizer boom is present. As an example, with 14-4 inch flights, and operating at 18% full, the required rotational speed when an atomizer boom is present is 27 RPM, versus less that 22 RPM when the atomizer boom is not present. The -90-  reason for this necessary increase in rotational speed is because the boom impedes on the trajectory of strands.  When the atomizer boom is not present the strands can travel  unobstructed through the center of the blender after detaching from the flights. When the atomizer boom is included however, many of those strands collide with the side of the boom. As a result, the blender must rotate faster to increase the centrifugal force acting on the strands so that they detach at a later point and fall on top of the atomizer boom, or at least so that the strands are dispersed more evenly on either side of the boom. Interestingly, above a certain fill level the required rotational speed begins to decrease. This was not observed when the atomizer boom was not present. This change in behavior is due to the phenomenon first discussed when investigating the impact of the atomizer boom on the skewness, where it was found that strands became wedged between the atomizer boom and blender wall at elevated fill levels. As the cluster of strands travels over top of the atomizer boom they eventually descend on the downward rotating side of the blender, increasing the skewness. The easiest way to avoid this from occurring is to reduce the blender rotational speed. Unfortunately, this results in considerably fewer strands being lifted and dispersed by the flights, instead the strands cluster in the lower-right drum quadrant (Figure 38). As shown in the contour graphs presented in Figure 50, an alternative solution is to use higher flights. Higher flights reduce the dependency of the fill level on the required rotational speed. 5.3.2.3 Blender manufacturers  Unlike the end users of rotary drum blenders, blender manufacturers have nearly complete flexibility on the blender design. Given a specific set of operating parameters, they can prescribe a specific flight design and drill the holes for a particular number flights that would result in the optimal strand distribution. As a result, blender manufacturers should be most interested in knowing the relationship between flight height and the required number of flights and its impact on the strand distribution. This interaction was shown previously to have a significant impact on the strand distribution. Blenders are designed and sourced based on the required maximum throughput (Coil 2008). The combination of the required throughput and the design and operating parameters will ultimately determine the blender fill level. Once the blender design and operating parameters -91-  have been established for this maximum fill level, it was shown that the strand distribution can be controlled by reducing the rotational speed accordingly as the fill level fluctuates below this maximum point. During the initial sourcing stage however, it is necessary to first establish the maximum fill level and rotational speed so that the flight height and placement can be determined accordingly. The graphs shown in Figure 51 were generated assuming the maximum fill level was 25%. They illustrate the impact various rotational speeds and combinations of flight height and number of flights have on the predicted skewness and kurtosis of the strand distribution and the predicted average time a strand spends in the resination region.  While blender  manufacturers should strive to achieve a kurtosis of -1.2 and to maximize the average time a strand spends in the resination region, balancing the distribution of strands on either side of the blender is perhaps the most important characteristic to accomplish as an initial step. A balanced distribution is identified by a skewness of 0. Figure 51 suggests that the required number of flights and flight height are largely dependent upon each other as well as the rotational speed. Generally, as the number of flights increases the flight height that maintains a skewness of 0 decreases. Further, the required number of flights and/or flight height also decreases with increasing rotational speeds. From previous work it has been shown that flights between 4 and 5 inches in height appear to strike the optimal balance between capacity and control over strand placement. Based on this target flight height, the required number of flights ranges from approximately 15 at 23 RPM to 4 at 28 RPM. When the kurtosis is included in this analysis however, it is shown that there must be at least 11 flights present to achieve a kurtosis of -1.2. This creates an upper bound for the rotational speed of between 25 and 26 RPM. Note that the average total time that a strand spends in the resination region has not been included in these graphs to improve legibility. In all cases, the average total time increases from right to left on the graphs.  -92-  fr  fr  fr  fr  fr  fr  Figure 51. Contour graphs based on number of flights and flight height. The rotational speed ranged from 23 to 28 RPM and the fill level was fixed at 25%.  -93-  5.3.2.4 Effect of the atomizer boom for blender manufacturers  The atomizer boom had a significant effect on the resulting contour graphs. Given the specified boom location it is virtually impossible to achieve a kurtosis of -1.2, or at least a relatively even strand distribution, without using either 4 or 16, 6 inch flights. This is consistent with the findings of the Overall Predictive Trends. However, with 4 flights the strands are not well positioned to come into contact with the resin discharging from the atomizers (Figure 38). The general relationship between the number of flights and the flight height that maintained a skewness of 0 remained similar with and without the atomizer boom. However, the required flight height that corresponds to a particular number of flights increased across all of the tested rotational speeds when the fill level was fixed at 25%. For example, at 26 RPM and with 11 flights, the required flight height increased from approximately 3.8 inches to 4.6 inches when the boom was included. This increase was necessary because the strands needed to be lifted higher, or to a larger angle, before detaching from the flights. This caused more of the strands to fall on top of the atomizer boom and disperse into the downward rotating half of the blender.  -94-  fr  fr  fr  fr  fr  fr  Figure 52. Contour graphs for the inclusion of an atomizer boom based on number of flights and flight height. The rotational speed ranged from 23 to 28 RPM and the fill level was fixed at 25%. -95-  In addition to an increased required flight height, the results also show opportunity for optimizing the configuration of the atomizer mounts.  The alignment of the mounts  ultimately determines the alignment of the atomizers, whether they be vertical or at an angle. Most existing operations have their atomizer mounts oriented vertically. While the option is now available for a staggered mount design (Appendix C), it is still relatively uncommon for atomizer mounts to be positioned at an angle. The simulation images show however that the angle in which the strands stream off of the atomizer boom, or in front of the atomizer itself, is largely dependent on the rotational speed (Figure 53). In fact, this angle ranged from 14° at 18.71 RPM to 7° at 28.07 RPM. This suggests that the angle of the atomizer mount should be adaptable to changes in the rotational speed of the blender. If the strands collide with the atomizer, or come within close proximity, individual strands will collect a disproportionate amount of resin, starving other strands of resin.  14°  18.71 RPM  (a)  7°  12°  (b)  23.39 RPM  (c)  28.07 RPM  Figure 53. Simulation images showing the streaming of strands off of the atomizer boom at (a) 18.71 RPM, (b) 23.39 RPM, and (c) 28.07 RPM. The simulated blenders were each equipped with 8-4 inch flights and filled 1/4 full. The angles that the strands stream off of the boom are approximately 14°, 12°, and 7° from vertical respectively. -96-  5.3.2.5 Discussion  The analyses focused on the end users of rotary drum blenders and the blender manufacturers presented several considerable implications and opportunities. First, these findings reveal whether or not an operation is even capable of achieving the desirable strand distribution. For instance, with 14-4 inch flights and operating with fill levels much less than 14%, it is unlikely that a skewness of 0 can ever be achieved, and the minimum fill level whereby this target can still be reached only increases with increasing flight heights. Fortunately, most operations tend to run their blenders between 25% and 50% full anyways, so this may only be an issue during severe disruptions in the process. Second, these findings suggest that operations should link the blender rotational speed with the factors that impact the blender fill level, such as the feed rate and blender tilt angle. As the fill level increases the rotational speed should also increase to maintain the optimal blending dynamics. Because of the extent of automation that is present in most operations, linking these processes would not be an insurmountable challenge. The challenge is knowing the relationship between the factors; however, based on the results with 5 and 6 inch flights, this challenge is certainly worth overcoming because of the significant impact changes to the fill level have on the skewness when the rotational speed remains unchanged. Third, this modeling approach could be used for determining when blender maintenance is required. During normal operation the inside of a blender drum becomes coated with strands, effectively reducing the inside drum diameter and changing the flight profile. By modeling the strand dynamics with different drum diameters and flight shapes, it would be possible to develop a threshold for an acceptable amount of strand build up before it will begin significantly affecting the strand dynamics. Fourth, as was seen in the Overall Predictive Trends, the interaction between the flight height and the number of flights had a significant impact on the strand dynamics. This is where considerable implications lie for the blender manufacturers. The optimal combination of flight height and number of flights is dependant on the maximum fill level and rotational speed. The results show that if the blender is sourced and designed using these expected maximum values, then the rotational speed alone can be used for counteracting any downward fluctuations in the fill level during operation. -97-  Finally, the inclusion of an atomizer boom proved to have a significant impact on the strand dynamics. Diligence must be practiced when selecting the position for the atomizer boom(s) and selecting a maximum fill level. As was demonstrated, when the fill level exceeds a particular point there is an increased risk that the strands will begin traveling as clusters over top of the atomizer boom, resulting in surging. Also, the angle that the strands stream off of the boom, or immediately in front of the atomizers, should be taken into consideration when the orientation of the atomizer mounts is decided. The results suggest that this angle should be adjustable to cope with changes to the blending conditions. 5.4  Conclusions  Response surface methodology proved to be an effective method for reviewing the impact multiple blender design and operating parameters have on the wood strand dynamics, as described by the skewness and kurtosis of the strand distribution and the average time a strand spent in the resination region. This technique was used for evaluating the results on three levels: an overview of the general relationship between the factors and response variables, the implications this research has for end users of rotary drum blenders, and finally the implications this research has for blender manufacturers. The findings of this research are summarized below: General •  All four blender design and operating parameters significantly affected the skewness, o With increasing the number of flights or blender rotational speed the skewness  increased, o With increasing the fill level the skewness decreased, and o With increasing the flight height between 2 and 3 inches the skewness  increased, otherwise the skewness stabilized for flights 4 inches or more in height. •  Only the interaction between flight height and the number of flights had a significant effect on the kurtosis,  •  Increasing the flight height and blender rotational speed both caused the average time a strand spent in the resination region to decrease, and  -98-  •  The inclusion of an atomizer boom had a significant effect on the bulk strand dynamics, particularly at elevated fill levels.  Specific •  The blender rotational speed and tilt angle should be linked to the blender feed rate to autocorrect for disruptions in the process,  •  Considerable attention should be made during the initial sourcing and design of a blender to find the optimal combination of flight height and number of flights for a specific maximum rotational speed and fill level, and  •  An adjustable atomizer mount angle would create a significant benefit when/if changes in the blending conditions occur. This angle should be linked to the blender rotational speed.  -99-  CHAPTER 6  SUMMARY AND FUTURE WORK.  This research project was divided into three distinct phases.  The first phase laid the  groundwork before work could begin using the RDBM. Perhaps the most critical input parameter for a model that simulates the rotary drum blending process is the static friction coefficients. Because of the challenges associated with systems of material surfaces where at least one wood surface is present (as discussed in Section 2.3), specific static coefficient of friction values are not readily available in the published literature. As a result, a series of laboratory experiments were conducted. The objectives were to first determine the impact of contact pressure and grain alignment on the coefficient. And second, to determine the relationship between the static coefficients of friction for systems involving two wood strand surfaces versus systems involving a single wood strand surface and a HDPE surface. The findings of this work suggested that the contact pressure has a significant effect on the coefficient of static friction. It also found that the two systems were related by a ratio of approximately 2:1 respectively. Although the absolute coefficient of friction values were ultimately adjusted for the final RDBM, this 2:1 ratio remained in effect. During the second phase of the project it was determined which of the six material and interaction input parameters were significant to the bulk strand dynamics in the RDBM. Together with software literature (DEM Solutions 2008), it was shown that the optimal combination of input parameters will not only result in representative strand flow dynamics, but will also minimize the overall required processing time for a simulation. A series of simulations were conducted in a systematic manner to find the combination of those significant parameters where the simulated results closely resembled those obtained using a 6 foot laboratory blender. It was also during this phase that three quantification techniques were decided upon for measuring the strand flow. Skewness and kurtosis were used for quantifying the strand distribution across the drum diameter, and the average time a strand spent in the resination region was used for quantifying the opportunity a strand had to become resinated.  -100-  After the RDBM had been calibrated for this particular model setup (including the strand size and shape and blender diameter) and the effectiveness of the quantification techniques had been tested, an exploratory study was designed to investigate the significance of several blender design and operating parameters on the bulk strand flow. These parameters included: the flight height, number of flights, blender rotational speed, and blender fill level on the bulk strand flow. In general the impact of these properties on the bulk strand flow, as described by the skewness and kurtosis of the strand distribution across the drum diameter, could be explained by focusing on their influence on the blending system capacity, or the ability of the blending system to lift, carry, and disperse strands across the blender. As the capacity increased the strands detached from the drum circumference later and traveled further across the diameter on their decent. As the capacity decreased, or the strand volume increased, the strand loading per flight increased resulting in a relatively early detachment point for a large quantity of strands. Increasing the flight height, number of flights, and/or rotational speed all resulted in an increased blender capacity. 6.1  Future Work  The exploratory component of this research was relatively limited, only focusing on two blender design and two operational parameters. A more thorough investigation of a broader range of parameters would be a significant contribution to both industry and academia. The range of possible factors to consider has increased substantially since the beginning of this project. This is because of advancements in both the software and computing capabilities. The most obvious and probably worthwhile factors to consider are the flight shape and blender diameter. This research only focused on flights that were 90o to the drum wall. In reality, flights are typically purchased bull-nosed or become bull-nosed while in service due to the buildup of strands along the surfaces. The effect of flight shape is likely significant to the strand flow. The angle of the leading face of the flight would effectively cause the strands to detach earlier. Examining the effect of the drum diameter would also be worthwhile. This research only focused on a 6 foot diameter blender. This was partially due to software and computing limitations, but mostly because it coincided with the size of the laboratory blender. Simulating a 6 foot blender therefore allowed for validation experiments to be carried out as -101-  required. Industrial blenders range in size from 8 to 11 feet however. As a result, focusing on larger diameter blenders would certainly be worthwhile from an industrial perspective. Fortunately, software and computing capabilities will now permit simulating larger diameter blenders in a timely manner. Because of these software and computing advancements it is also now possible to extend the length of the simulated blender.  This research relied on a 1 foot section of blender.  Extending the length to even 6 feet would enable one to examine the effect of blender tilt angle on the residence time. Residence time, or the time that a strand spends in the blender, ultimately affects the opportunity strands have to become resinated. If the residence time must be increased the blender tilt may be either decreased or the drum lengthened. In addition to scaling the model towards a full sized, industrial blender, it would also be worthwhile to examine the impact the atomizer boom location has on the strand flow. For the study presented in Chapter 5 the atomizer boom was placed in a position typical of today’s industrial blenders. This location may not be the optimal solution however. Ultimately, future research should focus first on determining the validity of scaling the 6 foot by 1 foot RDBM to an industrial blender. Additional research can then be pursued to investigate the effect of flight shape and atomizer boom location on the strand flow.  -102-  LITERATURE CITED  Adobe Systems Incorporated. 2007. Adobe® premiere® pro CS3 user guide for windows® and mac OS. California, USA. American Standards for Testing and Materials. 2002a. Standard guide for measuring and reporting friction coefficients. ASTM G 115-04. 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Status and trends: Profile of structural panels in the United States and Canada. USDA, FPL-RP-636. Stewart, R. L., J. Bridgwater, Y. C. Zhou, and A. B. Yu. 2001. Simulated and measured flow of granules in a bladed mixer—a detailed comparison. Chemical Engineering Science 56, (19) (10): 5457-71. Thibault, Scott. 2008. Telephone discussion related to EDEM renewal and similar applications where EDEM has been successful. May 18. USDA, Forest Products Laboratory. 1999. Wood handbook: Wood as an engineering material. Watkins, W. L. 1981. Some early headaches of the first waferboard plant in Canada. Paper presented at 1980 Canadian Waferboard Symposium Proceedings - Special Publication SP505E. Winchester, Guy. 2005. Cost of goods sold: An analysis of marketplace mechanics affecting resin costs and supply. APA/Engineered Wood Journal. [cited June 11 2008]. Available from http://www.apawood.org/level_b.cfm?content=pub_ewj_arch_f05_resin. World Forest Institute. Wood products trade: Europe. 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Minerals Engineering 19, (10) (8): 984-94.  -107-  APPENDIX A COEFFICIENT OF FRICTION - SAS ANALYSIS AND RESULTS The GLM Procedure Class Level Information Class Levels Orientation 3 Material_Combination 2  Values 1 2 3 1 2  Number of Observations Read Number of Observations Used  210 210  The GLM Procedure Dependent Variable: y3 Source Model Error Corrected Total  DF 10 199 209  Sum of Squares 6.17918736 0.91518322 7.09437058  Source Model Error Corrected Total R-Square 0.870999  Coeff Var -16.88059  Source Orientation Material_Combination x3 x x3*Orientat*Material  DF 2 1 1 1 5  DF 2 1 1 1 5  F Value 134.36  Pr > F <.0001  Root MSE 0.067815 Type I SS 0.53410516 4.31967482 0.78723955 0.08728987 0.45087795  Source Orientation Material_Combination x3 x x3*Orientat*Material Source Orientation Material_Combination x3 x x3*Orientat*Material  Mean Square 0.61791874 0.00459891  -108-  Mean Square 0.26705258 4.31967482 0.78723955 0.08728987 0.09017559  F Value 58.07 939.28 171.18 18.98 19.61  Pr > F <.0001 <.0001 <.0001 <.0001 <.0001  Type III SS 0.09711957 0.52906674 0.45125425 0.08342778 0.45087795  Source Orientation Material_Combination x3 x x3*Orientat*Material  y3 Mean -0.401735  Mean Square 0.04855979 0.52906674 0.45125425 0.08342778 0.09017559  Pr > F <.0001 <.0001 <.0001 <.0001 <.0001  F Value 10.56 115.04 98.12 18.14 19.61  Parameter Intercept Orientation Orientation Orientation Material_Combination Material_Combination x3 x x3*Orientat*Material x3*Orientat*Material  1 2 3 1 2  1 1 1 2  Estimate -.1499945172 -.1342523657 -.2029989310 0.0000000000 0.3954160209 0.0000000000 -.1792096345 0.0000883487 0.0501600042 0.0576087429  Parameter Intercept Orientation Orientation Orientation Material_Combination Material_Combination x3 x x3*Orientat*Material x3*Orientat*Material  B B B B B B B B B  Standard Error 0.04380096 0.04501753 0.04501753 . 0.03686604 . 0.02150605 0.00002074 0.02505086 0.01987184  t Value -3.42 -2.98 -4.51 . 10.73 . -8.33 4.26 2.00 2.90  Pr > |t| 0.0007 0.0032 <.0001 . <.0001 . <.0001 <.0001 0.0466 0.0042  1 2 3 1 2  1 1 1 2  The GLM Procedure Parameter x3*Orientat*Material x3*Orientat*Material x3*Orientat*Material x3*Orientat*Material  2 2 3 3  1 2 1 2  Estimate 0.0043934394 0.0569813680 -.0841658662 0.0000000000  Parameter x3*Orientat*Material x3*Orientat*Material x3*Orientat*Material x3*Orientat*Material  2 2 3 3  1 2 1 2  B B B B  Standard Error 0.02505086 0.01987184 0.01678230 .  t Value 0.18 2.87 -5.02 .  Pr > |t| 0.8610 0.0046 <.0001 .  NOTE: The X'X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter 'B' are not uniquely estimable.  -109-  Plot of resid8*yhat8.  Legend: A = 1 obs, B = 2 obs, etc.  resid8 ‚ ‚ 0.20 ˆ ‚ A ‚ A ‚ ‚ 0.15 ˆ A AA ‚ A ‚ A ‚ A A A A ‚ A A 0.10 ˆ A AA A ‚ B A A A A ‚ A A ‚ A A A A A A A A ‚ A B A 0.05 ˆ D B A BC A A A ‚ A AA A AA A A A A ‚ A CAA A A CAA A ‚ A AA B A A A ABA A ‚ A D A A B A 0.00 ˆ A AAA C A ‚ D A A A B A A ‚ A AAA BAA AA B B ‚ A A A BA AA A ‚ C AB A AAB A A A -0.05 ˆ ABB AA A B A A A A ‚ A A A A AA A A ‚ A AA A A A A ‚ B A A A A A A ‚ A A A -0.10 ˆ A A A A ‚ A A A A ‚ A ‚ B A ‚ A -0.15 ˆ A A ‚ Šƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒˆƒƒ -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 yhat8  -110-  N Mean Std Deviation Skewness Uncorrected SS Coeff Variation  The UNIVARIATE Procedure Variable: resid8 Moments 210 Sum Weights 0 Sum Observations 0.06617301 Variance 0.22525581 Kurtosis 0.91518322 Corrected SS . Std Error Mean  Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation Median -0.00250 Variance Mode -0.02963 Range Interquartile Range  210 0 0.00437887 -0.1163466 0.91518322 0.00456637  0.06617 0.00438 0.34095 0.09199  Tests for Location: Mu0=0 Test -Statistic-----p Value-----Student's t t 0 Pr > |t| 1.0000 Sign M -3 Pr >= |M| 0.7302 Signed Rank S -275.5 Pr >= |S| 0.7555  Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling  Tests for Normality --Statistic--W 0.993373 D 0.042515 W-Sq 0.057665 A-Sq 0.337946  -----p Value-----Pr < W 0.4714 Pr > D >0.1500 Pr > W-Sq >0.2500 Pr > A-Sq >0.2500  Quantiles (Definition 5) Quantile Estimate 100% Max 0.18973526 99% 0.15372204 95% 0.11689399 90% 0.08794163 75% Q3 0.04498097 50% Median -0.00249597 25% Q1 -0.04701096 10% -0.08154204 5% -0.10513642 1% -0.13710322 0% Min -0.15121120 Extreme Observations ------Lowest------  ------Highest-----  Value  Obs  Value  Obs  -0.151211 -0.148265 -0.137103 -0.133042 -0.129082  105 49 178 210 4  0.147689 0.149581 0.153722 0.180071 0.189735  18 185 19 118 91  -111-  The UNIVARIATE Procedure Variable: resid8 Stem 18 16 14 12 10 8 6 4 2 0 -0 -2 -4 -6 -8 -10 -12 -14  Leaf 00  3804 142 1338477 036782458 00078012235 000455566788991111456 002247788890011223469999 113689111233466777899 997665443300009733210 98866542110007444431000 76655211000088765443322100 9876542886642200 3293321 42652210 73990 18 ----+----+----+----+----+Multiply Stem.Leaf by 10**-2  # 2 4 3 7 9 11 21 24 21 21 23 26 16 7 8 5 2  Boxplot 0 | | | | | | +-----+ | | | + | *-----* | | +-----+ | | | | |  Normal Probability Plot 0.19+ ** | + | ****++ | ***++ | ****+ | ***+ | *** | ***** | **** | **** | +*** | +**** | ***** | **** | +** | **** | **** -0.15+**++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2  -112-  APPENDIX B MECHANICAL PROPERTIES OF UHMW AND HDPE  Poisson's ratio (Coil 2007a): UHMW - 0.46 HDPE - 0.38. Table B1: Mechanical properties of UHMW(Coil 2007a). UHMW Product Properties: Mechanical1 Tensile Strength @ Yield Elongation @ break Flexural modulus Tensile impact strength Tensile impact @ -40°C ESCR, F50 (a) Brittleness temperature Hardness shore D Thermal Vicat softening temperature Heat deflection temp., 66psi  Typical Values English Units SI Units  ASTM (1) D638 D638 D790 D1822 D1822 D1693 D746 D2240  3 600 psi 700% 155 000 psi 120 ft-lb/in2 110 ft-lb/in2 > 800 hr < -76°C 68  25Mpa 700% 1070 Mpa 25 J/cm2 25 J/cm2 > 800 hr <-105°F 68  D1525 D746  123°C < 69°C  254°F <157°F  1  23 degrees C, 50% relative humidity unless noted **Product properties represent average laboratory values and are intended as a guide line. Final testing is the responsibility of the end user.  Table B2: Mechanical properties of HDPE(Coil 2007a). HDPE Product Properties:  ASTM (1)  Mechanical1 Density Tensile Strength @ Yield Elongation @ break Flexural modulus Hardness shore D  D792 D638 D638 D790 D2240  1  Typical Values English Units SI Units  2 900 - 3 400 psi 300 - 450 % 100 000 - 150 000 psi 64 - 66  0.930 - 0.940 g/cm 20 - 23 Mpa 300 - 450 % 689 - 1 033 Mpa 64 - 66  23 degrees C, 50% relative humidity unless noted **Product properties represent average laboratory values and are intended as a guide line. Final testing is the responsibility of the end user.  -113-  3  APPENDIX C  Resinating region being considered  BLENDER DRAWINGS PROVIDED BY COIL MANUFACTURING  Figure C1: Schematic of blender layout and atomizer spray patter (Coil 2007b).  -114-  For the purposes of this project only the horizontal spray pattern will be considered. The diagonal spray pattern is a relatively recent option and is not currently present in many existing industrial operations. In addition, the EDEM software package is unable to restrict particle tracking to a diagonal region. As a result, computing and software constraints would quickly be reached if the diagonal spray pattern was considered.  -115-  APPENDIX D WRITE-OUT EVERY TIME INTERVAL CALCULATION  In discrete element modeling the frequency that the particle position and velocity are calculated is referred to as the time-step, Δt. Because these values are extremely small, for example in the neighborhood of 4x10-5 seconds, data is typically recorded for future analysis using a considerably larger interval. This interval is referred to as the “write-out every” interval, Δtw, in the software package. The write-out every interval refers to how frequently the simulator records data for analysis purposes. This is not related to the time-step used in the simulator in any way except for that it must be equal to or larger than the time-step used in the simulator. The write-out every interval begins when the simulation starts; however, only the write-out every intervals that occur within the resination region are considered. The selected interval may directly affect the simulation time; therefore, it is important to select a reasonable value. When selecting the write-out every time interval one must be aware of the process and the desired information. For instance, in this particular problem, where the objective is to record the x-position, velocity, and ID of the particles as they pass through the resinating region, the write-out every time interval must be small enough to capture this information while the particles are in the resinating region. Figure D1 shows an example of a situation where a particle passes through the resinating region but the write-out every interval is set too large, resulting in the exported data suggesting that the particle did not spend any time in the resinating region.  -116-  Path of object Measurement at t = 0 Blender drum  Measurement at t  Measurement at t + Δtw  Resinating region  Figure D1: Schematic of an example where the write-out time interval is set too large. An appropriate write-out every time interval was determined for this problem based on kinematic equations for motion in a straight line under constant acceleration (Equation D2) (Serway 2000, 1551). Assuming an object is dropped from the highest point in the blender, A, and allowed to fall through the diameter of the blender until is collides with the bottom of the drum, D, under constant acceleration, an extreme scenario, is shown in Figure D2.  x f − xi = v xi t + t=  1 axt 2 2  2 (x f − xi − x xi t ) a where: x is the position in meters, t is the time in seconds, vxi is the initial velocity, and a is the acceleration, assumed to be 9.81m/s2.  -117-  [D1] [D2]  Path of object  Blender drum  A  B  C Resinating region  D  Figure D2: Schematic of the extreme case scenario where an object falls from the top of the blender, A, through the resination region, B to C, and collides with the bottom of the blender, D. In this case, the total time spent in the resinating region is 0.066 seconds. Therefore, the write-out every time interval must be less than 0.066 seconds. However, because the time spent in the region will be estimated based partly on the write-out every time interval (Equation D3), its impact on the accuracy of the estimated time must also be considered. As a result the range in accuracy was tested for a proposed write-out every time interval of 0.01 seconds. tˆRR = xt Δt w  [D3]  where: tˆRR is the estimated time spent in the resinating region, xt is the number of write-out every time intervals that occurs in the resinating region, and Δt w is the write-out every time interval. One of two scenarios will result in the largest underestimation of the actual time spent in the resination region. First, when a write-out time interval is less, for example 1%, than a full Δtw inside the top of the region (Figure D3). And second, when a write-out time interval is less than a full Δtw inside the bottom of the region (Figure D4). In this analysis both scenarios result in the discrete element modeling software recording 6 write-out every intervals while -118-  the particle is in the resinating region. The estimated time spent in the resinating region is therefore 0.06 seconds, or 91% of the actual time. Path of particle Blender 0.775 m Resinating region  0.99 Δtw A: 0.814 m  B: 0.854 m  C: 0.896 m  D: 0.938 m  E: 0.981 m  F: 1.026 m 1.054 m  Figure D3: Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the first interval is located marginally less than one full Δtw from the top of the region. Path of particle Blender 0.775 m Resinating region  A: 0.799 m  B: 0.839 m  C: 0.880 m  D: 0.923 m  E: 0.966 m  F: 1.010 m 1.054 m  0.99 Δtw  Figure D4: Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the last interval is located marginally less than one full Δtw from the bottom of the region. Similarly, one of two scenarios will result in the largest overestimation of the actual time spent in the resination region. First, when a write-out every time interval is marginally below the top of the region (Figure D5). And second, when a write-out every time interval is marginally above the bottom of the region (Figure D6). In this analysis both scenarios result in the discrete element modeling software recording 7 write-out every intervals while the particle is in the resinating region. The estimated time in the resinating region is therefore 0.07 seconds, or 106% of the actual time. -119-  Path of particle  0.775 m  Blender  0.01 Δtw  A: 0.775 m  B: 0.815 m Resinating region  C: 0.855 m  D: 0.896 m  E: 0.939 m  F: 0.982 m  G: 1.027 m  1.054 m  Figure D5: Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the first interval is located marginally below the top of the region. Path of particle Blender 0.775 m Resinating region  A: 0.799 m C: 0.880 m  B: 0.839 m D: 0.922 m  E: 0.965 m  F: 1.009 m 1.054 m  G; 1.054 m  0.01 Δtw  Figure D6: Location of the write-out every time intervals within the resinating region, relative to the top of the blender, when the last interval is located marginally above the bottom of the region. It can therefore be concluded that under these idealized assumptions, the estimated time a particle spends inside the resinating region will be between 91% and 106% of the actual time. A write-out time interval, Δtw, 0.01 produces reasonably accurate results for the purposes of this project. In reality, the particles will be replaced by strands, most of which will fall through the resinating region along a parabolic path resulting in a larger fraction of their time in the region accounted for.  -120-  APPENDIX E VBA MACRO FOR SORTING, FILTERING, AND ANALYSING EDEM DATA Option Explicit Public Sub Histogram_And_Commulative_Graph() Application.ScreenUpdating = False Dim tmpSng As Single Dim aRow_SD As Long Dim aRow_RD As Long Dim aColumn_RD As Integer Dim aColumn_SD As Integer Dim aRow_CD As Long Dim aColumn_TD As Integer Dim aRow_TD As Integer Dim NumOfTrackedParticles As Integer Dim NumOfTrackedParticlesB As Integer Dim LowerTimeRange As Single Dim UpperTimeRange As Single Dim LowerRow_SD As Long Dim UpperRow_SD As Long Dim LowerTimeConst As Single Dim UpperTimeConst As Single Dim LengthofSimulationRecorded As Single Dim BinSizeCummDist As Single Dim NumBinsCummDist As Single Dim DrumDiameter As Single Dim DrumRadius As Single Dim BinSizeHist As Single DrumDiameter = 1632 '(mm) MUST BE SET!!!! DrumRadius = DrumDiameter / 2 BinSizeHist = 102 '(mm) MUST BE SET!!!! 'Set bin size for cummulative distribution graph BinSizeCummDist = 0.5 'MUST BE SET!!!! 'Set time constraints for analysis 'Should be based on specific number of runs under steady-state LowerTimeConst = 4.71 'MUST BE SET!!!! UpperTimeConst = 23.53 'MUST BE SET!!!! 'Set number of tracked particles NumOfTrackedParticles = 150 'MUST BE SET!!!! NumOfTrackedParticlesB = NumOfTrackedParticles + 1 tmpSng = Timer 'rename raw data worksheet ActiveSheet.Name = "raw_data"  -121-  'add new worksheet "sorted_data" Worksheets.Add(After:=Worksheets("raw_data")).Name = "sorted_data" 'Find Particle ID's aRow_SD = 1 For aRow_RD = 1 To xlLastRow("raw_data") / 2 'divided by two to avoid overloading 'Excel with data causing it to crash If Worksheets("raw_data").Cells(aRow_RD, 1).Value = "TIME:" Then 'Transfers x-positions For aColumn_RD = 2 To xlLastCol("raw_data") If Worksheets("raw_data").Cells(aRow_RD + 1, aColumn_RD).Value <> "no data" Then If Worksheets("raw_data").Cells(aRow_RD + 1, aColumn_RD).Value <> "" Then Worksheets("sorted_data").Cells(aRow_SD, 1).Value = Worksheets("raw_data") _ .Cells(aRow_RD + 1, aColumn_RD).Value aRow_SD = aRow_SD + 1 End If End If Next aColumn_RD aColumn_RD = 2 End If Next aRow_RD 'remove duplicate particle ID's and sort data Dim x As Long For x = xlLastRow("sorted_data") To 1 Step -1 If Application.WorksheetFunction.CountIf(Range("A1:A" & x), Range("A" & x).Text) > 1 Then Range("A" & x).EntireRow.Delete End If Next x Range("A1:A30000").Select Selection.Sort Key1:=Range("A1"), Order1:=xlAscending, Header:=xlGuess, _ OrderCustom:=1, MatchCase:=False, Orientation:=xlTopToBottom, _ DataOption1:=xlSortNormal 'transpose data Worksheets("sorted_data").Range("$A$1:$A$250").Copy Worksheets("sorted_data").Cells(2, 2).PasteSpecial Paste:=xlPasteAll, Operation:=xlNone, SkipBlanks:= _ False, Transpose:=True Worksheets("sorted_data").Range("$A$1:$A$250").Clear 'Transfer times Worksheets("sorted_data").Cells(2, 1) = "TIME" Worksheets("sorted_data").Cells(1, 1) = "First Ent.:" aRow_SD = 3 For aRow_RD = 1 To xlLastRow("raw_data") If Worksheets("raw_data").Cells(aRow_RD, 1).Value = "TIME:" Then Worksheets("sorted_data").Cells(aRow_SD, 1).Value = Worksheets("raw_data").Cells(aRow_RD, 2).Value LowerTimeRange = Worksheets("sorted_data").Cells(3, 1) 'Transfer x-positions For aColumn_RD = 2 To xlLastCol("raw_data") For aColumn_SD = 2 To NumOfTrackedParticlesB  -122-  If Worksheets("raw_data").Cells(aRow_RD + 1, aColumn_RD).Value = Worksheets("sorted_data") _ .Cells(2, aColumn_SD).Value Then 'Lookup if particle velocity is negative (moving downward) and includes it in the analysis if it is If Worksheets("raw_data").Cells(aRow_RD + 3, aColumn_RD).Value <= 0 Then Worksheets("sorted_data").Cells(aRow_SD, aColumn_SD).Value = Worksheets("raw_data") _ .Cells(aRow_RD + 2, aColumn_RD).Value End If End If Next aColumn_SD Next aColumn_RD aColumn_RD = 2 aColumn_SD = 2 aRow_SD = aRow_SD + 1 End If Next aRow_RD 'Look-up first time when strands enter resination region for cummulative distribution graph aColumn_SD = 2 Do While Worksheets("sorted_data").Cells(2, aColumn_SD) <> "" aRow_SD = 3 Do While Cells(aRow_SD, aColumn_SD) = "" aRow_SD = aRow_SD + 1 Loop Worksheets("sorted_data").Cells(1, aColumn_SD) = Worksheets("sorted_data").Cells(aRow_SD, 1) aColumn_SD = aColumn_SD + 1 Loop 'String columns of data together 'add new worksheet "tmp_data" Worksheets.Add(After:=Worksheets("sorted_data")).Name = "tmp_data" 'Lookup rows that correspond to time constraints LowerRow_SD = 3 'If LowerTimeConst = 0 Then LowerRow_SD = 3 Else Do While Worksheets("sorted_data").Cells(LowerRow_SD, 1) < LowerTimeConst LowerRow_SD = LowerRow_SD + 1 Loop 'End If UpperRow_SD = 3 Do While Worksheets("sorted_data").Cells(UpperRow_SD, 1) < UpperTimeConst UpperRow_SD = UpperRow_SD + 1 Loop If UpperTimeConst <> Worksheets("sorted_data").Cells(xlLastRow("sorted_data"), 1) _ Then UpperRow_SD = UpperRow_SD - 1 'transfer data to tmp_data Worksheets("sorted_data").Range("$B$" & LowerRow_SD & ":$IV$" & UpperRow_SD).Copy _ Destination:=Worksheets("tmp_data").Cells(1, 1) 'remove empty cells and shift left Worksheets("tmp_data").Range(Cells(1, 1), Cells(xlLastRow("tmp_data"), NumOfTrackedParticlesB)) _ .SpecialCells(xlCellTypeBlanks).Delete Shift:=xlToLeft 'remove empty cells and shift up Worksheets("tmp_data").Range(Cells(1, 1), Cells(xlLastRow("tmp_data"), NumOfTrackedParticlesB)) _ .SpecialCells(xlCellTypeBlanks).Delete Shift:=xlUp  -123-  'add new worksheet "compiled_data" Worksheets.Add(After:=Worksheets("tmp_data")).Name = "compiled_data" 'Transfer x-positions aRow_CD = 1 For aColumn_TD = 1 To xlLastCol("tmp_data") For aRow_TD = 1 To xlLastRow("tmp_data") If Worksheets("tmp_data").Cells(aRow_TD, aColumn_TD).Value <> "" Then Worksheets("compiled_data").Cells(aRow_CD, 1).Value = Worksheets("tmp_data") _ .Cells(aRow_TD, aColumn_TD).Value aRow_CD = aRow_CD + 1 End If Next aRow_TD Next aColumn_TD 'Worksheets("tmp_data").Delete ' Make a histogram from the selected values. ' The top value is used as the histogram's title. Dim selected_range As Range Dim title As String Dim r As Integer Dim score_cell As Range Dim num_scores As Integer Dim count_range As Range Dim new_chart As Chart Dim Data_Range As Range Set Data_Range = Worksheets("compiled_data").Range(Cells(1, 1), Cells(65536, 1)) Worksheets.Add(After:=Worksheets("compiled_data")).Name = "Histogram" Worksheets("Histogram").Cells(2, 2) = "HISTOGRAM" Worksheets("Histogram").Range("B2:B2").Select With Selection .HorizontalAlignment = xlLeft .Font.Bold = True End With ' See how many bins we will have. Dim num_bins As Integer num_bins = DrumDiameter / BinSizeHist ' Make the bin separators. Worksheets("Histogram").Cells(3, 2) = "Bins" For r = 1 To num_bins - 1 Worksheets("Histogram").Cells(r + 3, 2) = -DrumRadius + r * BinSizeHist - 0.1 Next r r = num_bins '+ 1 Worksheets("Histogram").Cells(r + 3, 2) = -DrumRadius + r * BinSizeHist ' Make the counts. Worksheets("Histogram").Cells(3, 3) = "Counts"  -124-  Set count_range = Worksheets("Histogram").Range("C4:C" & num_bins + 3) count_range.FormulaArray = "=Frequency(sorted_data!B$" & LowerRow_SD & ":$IV$" & _ UpperRow_SD & ", B4:B" & num_bins + 3 & ")" ' Make the range labels. Worksheets("Histogram").Cells(3, 4) = "Ranges" For r = 1 To num_bins - 1 Worksheets("Histogram").Cells(r + 3, 4) = "'" & _ -DrumRadius + BinSizeHist * (r - 1) & " to " & _ -DrumRadius + BinSizeHist * (r - 1) + BinSizeHist - 0.1 Worksheets("Histogram").Cells(r + 3, 4).HorizontalAlignment = _ xlRight Next r r = num_bins '+ 1 Worksheets("Histogram").Cells(r + 3, 4) = "'" & _ -DrumRadius + BinSizeHist * (r - 1) & " to " & DrumRadius Worksheets("Histogram").Cells(r + 3, 4).HorizontalAlignment = xlRight ' Make the chart. Set new_chart = Charts.Add() With new_chart .ChartType = xlColumnClustered .SetSourceData Source:=Worksheets("Histogram").Range("C4:C" & _ num_bins + 3), _ PlotBy:=xlColumns .Location Where:=xlLocationAsObject, _ Name:=Worksheets("Histogram").Name End With ' Format chart With ActiveChart .HasTitle = True .ChartTitle.Characters.Text = ActiveWorkbook.Name .Axes(xlCategory, xlPrimary).HasTitle = True .Axes(xlCategory, _ xlPrimary).AxisTitle.Characters.Text = "Scores" .Axes(xlValue, xlPrimary).HasTitle = True .Axes(xlValue, xlPrimary).AxisTitle.Characters.Text _ = "Count" ' Display score ranges on the X axis. .SeriesCollection(1).XValues = "='" & _ Worksheets("Histogram").Name & "'!R4C4:R" & _ num_bins + 3 & "C4" End With With ActiveChart.Axes(xlCategory) .HasMajorGridlines = False .HasMinorGridlines = False End With With ActiveChart.Axes(xlValue) .HasMajorGridlines = False .HasMinorGridlines = False End With ActiveChart.HasLegend = False With ActiveChart.PlotArea.Border .ColorIndex = 16 .Weight = xlThin .LineStyle = xlContinuous End With  -125-  With ActiveChart.PlotArea.Interior .ColorIndex = 2 .PatternColorIndex = 1 .Pattern = xlSolid End With With ActiveSheet.ChartObjects(1) .Width = 500 .Height = 300 .Left = 400 .Top = 100 End With With ActiveChart.Axes(xlCategory).TickLabels .Alignment = xlCenter .Offset = 100 .ReadingOrder = xlContext .Orientation = 45 End With ActiveChart.SeriesCollection(1).Select With ActiveChart.ChartGroups(1) .Overlap = 0 .GapWidth = 0 .HasSeriesLines = False .VaryByCategories = False End With ' Place Skewness and Kurtosis titles Worksheets("Histogram").Cells(3, 7) = "Statistics" Range("G3:H3", "B3:D3").Select With Selection .HorizontalAlignment = xlCenter .Font.Bold = True End With Range("G3:H3").Merge Worksheets("Histogram").Cells(4, 7) = "Average" Worksheets("Histogram").Cells(5, 7) = "Std Dev" Worksheets("Histogram").Cells(6, 7) = "Skewness" Worksheets("Histogram").Cells(7, 7) = "Kurtosis" Worksheets("Histogram").Cells(8, 7) = "Count" ' Calculate Skewness and Kurtosis Worksheets("Histogram").Cells(4, 8) = Application.Average(Data_Range) Worksheets("Histogram").Cells(5, 8) = Application.StDev(Data_Range) Worksheets("Histogram").Cells(6, 8) = Application.Skew(Data_Range) Worksheets("Histogram").Cells(7, 8) = Application.Kurt(Data_Range) Worksheets("Histogram").Cells(8, 8) = Application.Count(Data_Range) 'Cummulative frequency chart Worksheets("Histogram").Cells(36, 2) = "CUMMULATIVE FREQUENCY GRAPH" Worksheets("Histogram").Range("B36:B36").Select With Selection .HorizontalAlignment = xlLeft .Font.Bold = True End With ' See how many bins we will have. LengthofSimulationRecorded = Worksheets("sorted_data").Cells(xlLastRow("sorted_data"), 1) _  -126-  - Worksheets("sorted_data").Cells(3, 1) NumBinsCummDist = LengthofSimulationRecorded / BinSizeCummDist ' Make the bin separators. Worksheets("Histogram").Cells(37, 2) = "Bins" For r = 1 To (NumBinsCummDist - 1) Worksheets("Histogram").Cells(r + 37, 2) = r * BinSizeCummDist + LowerTimeRange - 0.01 Next r r = NumBinsCummDist Worksheets("Histogram").Cells(r + 37, 2) = r * BinSizeCummDist + LowerTimeRange ' Make the counts. Worksheets("Histogram").Cells(37, 3) = "Counts" Set count_range = Worksheets("Histogram").Range("C38:C" & NumBinsCummDist + 37) count_range.FormulaArray = "=Frequency(sorted_data!B1:IV1, B38:B" & _ NumBinsCummDist + 37 & ")" ' Make the range labels. Worksheets("Histogram").Cells(37, 6) = "Ranges" For r = 1 To NumBinsCummDist - 1 Worksheets("Histogram").Cells(r + 37, 6) = "'" & _ BinSizeCummDist * (r - 1) + LowerTimeRange & " to " & _ BinSizeCummDist * (r - 1) + BinSizeCummDist + LowerTimeRange - 0.01 Worksheets("Histogram").Cells(r + 37, 6).HorizontalAlignment = _ xlRight Next r r = NumBinsCummDist Worksheets("Histogram").Cells(r + 37, 6) = "'" & _ BinSizeCummDist * (r - 1) + LowerTimeRange & " to 20" Worksheets("Histogram").Cells(r + 37, 6).HorizontalAlignment = xlRight ' Calculate cummulative values. Worksheets("Histogram").Cells(37, 4) = "Cumm." r=1 Worksheets("Histogram").Cells(r + 37, 4) = Worksheets("Histogram").Cells(r + 37, 3) Worksheets("Histogram").Cells(r + 37, 4).HorizontalAlignment = _ xlRight For r = 2 To NumBinsCummDist Worksheets("Histogram").Cells(r + 37, 4) = Worksheets("Histogram").Cells(r + 37, 3) + _ Worksheets("Histogram").Cells(r + 37 - 1, 4) Worksheets("Histogram").Cells(r + 37, 5).HorizontalAlignment = _ xlRight Next r ' Calculate cummulative percentages. Worksheets("Histogram").Cells(37, 5) = "Cumm.Per." For r = 1 To NumBinsCummDist Worksheets("Histogram").Cells(r + 37, 5) = Worksheets("Histogram").Cells(r + 37, 4) / _ (NumOfTrackedParticlesB - 1) Worksheets("Histogram").Cells(r + 37, 5).HorizontalAlignment = _ xlRight Worksheets("Histogram").Cells(r + 37, 5).NumberFormat = "0.0%" Next r Range("B37:F37").Select With Selection  -127-  .HorizontalAlignment = xlCenter .Font.Bold = True End With ' Make the chart. Set new_chart = Charts.Add With new_chart .ChartType = xlLine .SetSourceData Source:=Worksheets("Histogram").Range("E38:E" & _ NumBinsCummDist + 37), PlotBy:=xlColumns .Location Where:=xlLocationAsObject, _ Name:=Worksheets("Histogram").Name End With ' Format chart With ActiveChart .HasTitle = True .ChartTitle.Characters.Text = ActiveWorkbook.Name & " - Cummulative Distribution" .Axes(xlCategory, xlPrimary).HasTitle = True .Axes(xlCategory, _ xlPrimary).AxisTitle.Characters.Text = "Time (seconds)" .Axes(xlValue, xlPrimary).HasTitle = True .Axes(xlValue, xlPrimary).AxisTitle.Characters.Text _ = "Commulative Percent" ' Display time ranges on the X axis. .SeriesCollection(1).XValues = "='" & _ Worksheets("Histogram").Name & "'!R38C6:R" & NumBinsCummDist + 37 & "C6" End With With ActiveChart.Axes(xlCategory) .HasMajorGridlines = False .HasMinorGridlines = False End With With ActiveChart.Axes(xlValue) .HasMajorGridlines = False .HasMinorGridlines = False End With ActiveChart.HasLegend = False With ActiveChart.PlotArea.Border .ColorIndex = 16 .Weight = xlThin .LineStyle = xlContinuous End With With ActiveChart.PlotArea.Interior .ColorIndex = 2 .PatternColorIndex = 1 .Pattern = xlSolid End With With ActiveSheet.ChartObjects(2) .Width = 500 .Height = 300 .Left = 400 .Top = 450 End With With ActiveChart.Axes(xlCategory).TickLabels .Alignment = xlCenter .Offset = 100 .ReadingOrder = xlContext .Orientation = 45  -128-  End With Application.ScreenUpdating = True MsgBox "Total processing time:" & Round((Timer - tmpSng) / 60, 5) & " minutes" End Sub 'Find the last populated row in a specified worksheet Function xlLastRow(Optional WorksheetName As String) As Long With Worksheets(WorksheetName) On Error Resume Next xlLastRow = .Cells.Find("*", .Cells(1), xlFormulas, _ xlWhole, xlByRows, xlPrevious).Row If Err <> 0 Then xlLastRow = 0 End With End Function 'Find the first populated row in a specified worksheet Function xlFirstRow(Optional WorksheetName As String) As Long With Worksheets(WorksheetName) On Error Resume Next xlFirstRow = .Cells.Find("*", .Cells(.Cells.Count), xlFormulas, _ xlWhole, xlByRows, xlNext).Row If Err <> 0 Then xlFirstRow = 0 End With End Function 'Find the last populated column in a specified worksheet Function xlLastCol(Optional WorksheetName As String) As Long With Worksheets(WorksheetName) On Error Resume Next xlLastCol = .Cells.Find("*", .Cells(1), xlFormulas, _ xlWhole, xlByColumns, xlPrevious).Column If Err <> 0 Then xlLastCol = 0 End With End Function  -129-  APPENDIX F MACRO FOR PERFORMING THE GRAYSCALE ANALYSIS IN IMAGE PRO PLUS  Option Explicit Sub setLineProfile() ret = IpProfCreate() ret = IpProfLineMove(133, 205, 503, 268) ret = IpProfSetAttr(LINETYPE, THICKHORZ) ret = IpProfLineMove(133, 205, 503, 268)  ' opens line analysis operation ' sets the line analysis operation to "Thick Horizontal" ' positions the horizontal lines  End Sub Sub analyzeImagesUsingLineProfile() Dim id As Integer For id = 0 To 1800 Step 3 ' cycles through images labelled 0 to 1800, skipping to every 3rd Dim FileName As String ' set file location and name FileName = "C:\Documents And Settings\gdick\My Documents\My Videos\January 31 2008 Lab Blender\Baseline\BW Images\Baseline (" ret = IpWsLoad(FileName & id &").tif","tif") Call setLineProfile() ret = IpProfSave("", S_DDE+S_DATA+S_HEADER+S_LEGEND+S_X_AXIS+S_COORDS) ret = IpProfSelect(0) ret = IpProfDestroy() ret = IpDocClose() ret = IpAnShow(0) ' run Excel macro Dim exl As Object Set exl = Get_Excel_Object exl.Application.Run "ImageDataCompTMP.xls!AddWorksheet" Next id exl.Application.Run "ImageDataCompTMP.xls!deleteWorksheet" End Sub ' This function tries to find a running ' instance of Excel. If it can't find one ' it starts one: Function Get_Excel_Object() As Object Dim exl As Object ' GetObject will fail if Excel is not running. On Error GoTo start_excel Set exl = GetObject(,"Excel.Application") On Error GoTo 0 GoTo excel_running  -130-  start_excel: ' Start Excel via CreateObject. If this ' fails, we exit the macro. On Error GoTo error_excel Set exl = CreateObject("Excel.Application") exl.Visible = True exl.Workbooks.Add excel_running: Set Get_Excel_Object = exl Exit Function error_excel: MsgBox "Can't find Excel" End Function  -131-  APPENDIX G ANOVA RESULTS FOR THE MECHANICAL PROPERTIES OF ASPEN STRANDS  Table G1: ANOVA results for the impact the material properties have on the skewness of the resulting histogram. Source Shear Modulus Poissons Ratio Density Shear Modulus x Poissons Ratio Shear Modulus x Density Poissons Ratio x Density  DF 1 1 1 1 1 1  SS 0.003553 0.002061 0.002278 0.001431 0.00009 0.028489  MS 0.003553 0.002061 0.002278 0.001431 0.00009 0.028489  F 2.156907 1.250968 1.382878 0.868728 0.054499 17.29343  Pr > F 0.380567 0.464437 0.448632 0.522379 0.853996 0.150235  Model Error Total  6 1 7  0.037902 0.006317 3.834568 0.001647 0.001647 0.039549  0.37218  Table G2: ANOVA results for the impact the material properties have on the kurtosis of the resulting histogram. Source Shear Modulus Poissons Ratio Density Shear Modulus x Poissons Ratio Shear Modulus x Density Poissons Ratio x Density  DF 1 1 1 1 1 1  SS 0.000099 0.001225 0.00005 0.000233 0.006997 0.002238  MS 0.000099 0.001225 0.00005 0.000233 0.006997 0.002238  F 0.459528 5.663485 0.231139 1.078402 32.34766 10.34488  Pr > F 0.620747 0.253247 0.714702 0.48799 0.110801 0.191901  Model Error Total  6 1 7  0.010843 0.001807 8.354182 0.258832 0.000216 0.000216 0.011059  Table G3: ANOVA results for the impact the material properties have on the count of the resulting histogram. Source Shear Modulus Poissons Ratio Density Shear Modulus x Poissons Ratio Shear Modulus x Density Poissons Ratio x Density  DF 1 1 1 1 1 1  SS MS F Pr > F 13612.5 13612.5 0.412194 0.636651 221112.5 221112.5 6.695408 0.234776 95484.5 95484.5 2.891323 0.338442 18 18 0.000545 0.98514 13122 13122 0.397341 0.641941 693842 693842 21.00992 0.136746  Model Error Total  6 1 7  1037192 33024.5 1070216  -132-  172865.3 5.234455 0.322657 33024.5  Table G4: ANOVA results for the impact the material properties have on the processing time of the respective simulation. Source Shear Modulus Poissons Ratio Density Shear Modulus x Poissons Ratio Shear Modulus x Density Poissons Ratio x Density  DF 1 1 1 1 1 1  SS MS F Pr > F 578.6802 578.6802 2057.53 0.014033 2.53125 2.53125 9 0.204833 378.6752 378.6752 1346.401 0.017345 0.91125 0.91125 3.24 0.322829 104.8352 104.8352 372.7474 0.032945 0.55125 0.55125 1.96 0.394863  Model Error Total  6 1 7  1066.184 177.6974 631.8129 0.030444 0.28125 0.28125 1066.466  -133-  APPENDIX H ANOVA RESULTS FOR THE INTERACTION PROPERTIES OF ASPEN STRANDS AND POLYETHYLENE  Table H1: ANOVA results for the impact the interaction properties have on the skewness of the resulting histogram. Source CORestitution CRFriction CSFriction CORestitution x CRFriction CORestitution x CSFriction CRFriction x CSFriction  DF 1 1 1 1 1 1  SS 0.006682 2.74742 0.699944 0.009709 0.000999 0.151027  MS 0.006682 2.74742 0.699944 0.009709 0.000999 0.151027  F 29.6063 12172.26 3101.054 43.01392 4.425826 669.1154  Pr > F 0.115709 0.00577 0.011431 0.096326 0.282484 0.024599  Model Error Total  6 1 7  3.615781 0.60263 2669.912 0.014813 0.000226 0.000226 3.616007  Table H2: ANOVA results for the impact the interaction properties have on the kurtosis of the resulting histogram. Source CORestitution CRFriction CSFriction CORestitution x CRFriction CORestitution x CSFriction CRFriction x CSFriction  DF 1 1 1 1 1 1  SS 5.51E-06 1.991802 1.410029 0.003542 5.01E-06 1.605559  MS 5.51E-06 1.991802 1.410029 0.003542 5.01E-06 1.605559  F 0.000172 62.2212 44.04739 0.110656 0.000156 50.15548  Pr > F 0.991647 0.080279 0.095206 0.795559 0.992039 0.089302  Model Error Total  6 1 7  5.010942 0.835157 26.08918 0.148756 0.032012 0.032012 5.042954  Table H3: ANOVA results for the impact the interaction properties have on the count of the resulting histogram. Source CORestitution CRFriction CSFriction CORestitution x CRFriction CORestitution x CSFriction CRFriction x CSFriction  DF 1 1 1 1 1 1  SS 611065.1 11710380 2185095 369370.1 25651.13 242556.1  F 32.98041 632.0327 117.934 19.93565 1.384443 13.09124  Pr > F 0.109754 0.025309 0.058457 0.140267 0.448454 0.171665  Model Error Total  6 1 7  15144118 2524020 136.2264 18528.13 18528.13 15162646  0.06549  -134-  MS 611065.1 11710380 2185095 369370.1 25651.13 242556.1  Table H4: ANOVA results for the impact the interaction properties have on the processing time of the respective simulation. Source CORestitution CRFriction CSFriction CORestitution x CRFriction CORestitution x CSFriction CRFriction x CSFriction  DF 1 1 1 1 1 1  SS 0.001513 0.070312 0.838512 0.002813 0.002112 0.074112  Model Error Total  6 1 7  0.989375 0.164896 0.001513 0.001513 0.990888  -135-  MS F Pr > F 0.001513 1 0.5 0.070312 46.4876 0.09271 0.838512 554.3884 0.027022 0.002813 1.859504 0.40282 0.002112 1.396694 0.447071 0.074112 49 0.090334 109.022  0.07318  APPENDIX I RESULTS FROM STUDENT T-TEST FOR SHOULDER AND TOE ANGLES  Table I1: Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 4 and the laboratory results ran at 15.5 RPM. Shoulder angle Toe angle Simulation Laboratory Simulation Laboratory Mean 40.37 38.93 257.97 258.97 Variance 52.79 37.79 11.90 22.93 Observations 30 30 30 30 Hypothesized mean dif. 0 0 Degrees of freedom 56 53 t-statistic 0.825 -0.928 P(T≤ t) two-tail 0.413 0.358 t-critical two-tail 2.003 2.006 Table I2: Student t-test for two sample means assuming unequal variance for the shoulder and toe angles in Run 4 and the laboratory results ran at 25.5 RPM. Shoulder angle Toe angle Simulation Laboratory Simulation Laboratory Mean 67.03 63.13 217.93 227.43 Variance 42.24 19.64 67.65 39.77 Observations 30 30 30 30 Hypothesized mean dif. 0 0 Degrees of freedom 51 54 t-statistic 2.716 -5.020 P(T≤ t) two-tail 0.009 5.960 E -6 t-critical two-tail 2.008 2.005  -136-  APPENDIX J RESULTS FROM THE EXPLORATORY STUDY WITHOUT AND WITH AN ATOMIZER BOOM  Table J1: Results from exploratory study without an atomizer boom. Run  # of Flights Flight height Fill level  RPM  Skewness Kurtosis  Count  1  4  2  1/8  23.39  -2.796074 10.57709  14261  2  4  6  1/8  23.39  0.181865 -1.003007  16046  3  16  2  1/8  23.39  -0.411452 -0.432711  19656  4  16  6  1/8  23.39  1.055151 0.157969  13356  5  8  4  1/16  18.71  -0.343624 -0.724349  24282  6  8  4  1/16  28.07  7  8  4  1/4  18.71  8  8  4  1/4  28.07  9  4  4  1/8  10  4  4  11  16  12  1.1601  0.175024  11068  -0.773404 0.022419  26218  -1.073637  14726  18.71  -0.710635 0.990473  25525  1/8  28.07  0.171931 -1.090594  13541  4  1/8  18.71  0.067189 -0.990335  21693  16  4  1/8  28.07  1.166465  11497  13  8  2  1/16  23.39  -1.665463 3.232918  26819  14  8  2  1/4  23.39  -1.093679 2.099582  22917  15  8  6  1/16  23.39  1.336239 0.894518  12610  16  8  6  1/4  23.39  -0.020098 -1.059842  17494  17  4  4  1/16  23.39  -0.046351 -0.824065  16558  18  4  4  1/4  23.39  -1.064182 1.452961  21355  19  16  4  1/16  23.39  0.742821 -0.565052  13758  20  16  4  1/4  23.39  -0.178404 -1.142662  18609  21  8  2  1/8  18.71  -1.213237 2.456989  29897  22  8  2  1/8  28.07  -1.123317 0.773495  19346  23  8  6  1/8  18.71  0.149338 -0.887824  21209  24  8  6  1/8  28.07  1.192715 0.594237  11720  25  8  4  1/8  23.39  -0.107397 -0.533136  17952  26  8  4  1/8  23.39  -0.301508 -0.484515  18770  27  8  4  1/8  23.39  -0.156009 -0.852739  18410  -137-  0.16858  0.8005  Table J2: Results from exploratory study with an atomizer boom. Run  # of Flights Flight height Fill level  RPM  Skewness Kurtosis  Count  1  4  2  1/8  23.39  -2.753631 10.27182  17414  2  4  6  1/8  23.39  -0.544805 -0.912654  15773  3  16  2  1/8  23.39  -1.456965  22188  4  16  6  1/8  23.39  0.500032 -1.177029  14287  5  8  4  1/16  18.71  -0.493197 0.475805  25009  6  8  4  1/16  28.07  1.127426 0.109028  11052  7  8  4  1/4  18.71  -1.617404 2.214585  26383  8  8  4  1/4  28.07  -0.098553 -1.577502  14992  9  4  4  1/8  18.71  -0.691708 1.882807  25275  10  4  4  1/8  28.07  -0.915169 -0.227513  15823  11  16  4  1/8  18.71  -1.232934 2.204677  24619  12  16  4  1/8  28.07  0.683892 -1.002647  12391  13  8  2  1/16  23.39  -1.541192 3.088706  25728  14  8  2  1/4  23.39  -1.520084 3.775611  23605  15  8  6  1/16  23.39  16  8  6  1/4  17  4  4  18  4  19  -0.37011  13005  23.39  -0.435279 -1.347452  18236  1/16  23.39  -0.86338  0.100537  17349  4  1/4  23.39  -1.50092  1.824392  21616  16  4  1/16  23.39  0.427871 -1.184065  14658  20  16  4  1/4  23.39  -0.600083 -1.133607  19818  21  8  2  1/8  18.71  -1.229002 3.385995  28478  22  8  2  1/8  28.07  -1.830354 3.381662  20421  23  8  6  1/8  18.71  -1.536919 2.754155  22487  24  8  6  1/8  28.07  0.721061 -0.920876  12542  25  8  4  1/8  23.39  -0.987434 0.148008  19596  26  8  4  1/8  23.39  -0.973097  18870  27  8  4  1/8  23.39  -0.877569 -0.298419  -138-  0.96552  2.43358  0.04603  19043  

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