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Comparison of alternative advanced experimental techniques for measurement of hydrodynamic characteristics… Tebianian, Sina 2015

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COMPARISON OF ALTERNATIVE ADVANCED EXPERIMENTAL TECHNIQUES FOR MEASUREMENT OF HYDRODYNAMIC CHARACTERISTICS OF GAS-FLUIDIZED BEDS by  Sina Tebianian  B.Sc., University of Naples, Federico II, Italy, 2008 M.A.Sc., University of Naples, Federico II, Italy, 2010  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Chemical and Biological Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  May 2015 © Sina Tebianian, 2015 ii  Abstract A novel travelling fluidized bed, designed to facilitate deployment at different research centres, was used to compare advanced measurement techniques for the study of key hydrodynamic properties of gas-fluidized beds. Fast X-ray imaging was employed to visualize the internal flow structures of the bubbling and turbulent fluidization flow regimes. Transition between flow regimes based on X-ray system images were compared with results from pressure fluctuations. Average Shannon entropy reached a maximum plateau at superficial gas velocities close to Uc derived from pressure fluctuations, whereas average kurtosis and skewness leveled off at lower Ug’s. The degree of interference of a 4-mm intrusive probe inserted in the fluidized bed was found to be small by comparing the time-average voidage in a region with and without the probe present.  Voidage data obtained by different measurement techniques in a previous study were extended by new data based on fast X-ray imaging and borescopy. Fair, but imperfect agreement among voidage results from alternate techniques was observed and quantified in terms of deviations from the overall average results of all measurement techniques at each gas velocity.   Radial profiles of time-average particle velocity in FCC (a Geldart A powder) and sand (a Geldart B powder) fluidized beds at different operating conditions, obtained by radioactive particle tracking (RPT – non-invasive, Ecole Polytechnique), positron emission particle tracking (PEPT – non-invasive, University of Birmingham), optical fibre probe (invasive, UBC) and borescopic high-speed particle image velocimetry (invasive, PSRI) were directly compared. For iii  FCC, each of these techniques provided similar trends with respect to profiles of time-average particle velocity, but with significant differences in some cases. For sand, there were significant quantitative differences among the profiles in many cases. The reasons for the discrepancies included lack of matching of tracer particles, probe intrusiveness, unmatched sensitivities to the direction of motion and different analysis procedures.  The RPT, PEPT and borescopy data were further analyzed to obtain solid mass and momentum flux for identical operating conditions. All three techniques provided broadly similar time-average flux profiles. The experimental results obtained in this study provide a unique hydrodynamic benchmark database for validation of CFD codes and other models.  iv  Preface All the work presented in this thesis was completed by the author under the supervision of Professors John R. Grace and Naoko Ellis at the University of British Columbia. The author travelled to different research laboratories to employ the most advanced measurement techniques for the hydrodynamic characterization of a unique gas-fluidized bed. The raw data obtained by each measurement technique were analyzed by the author in order to be directly comparable. Some of the results reported in Chapter 3 were presented by the author and by a fellow PhD candidate, A.H. Ahmadi Motlagh, at the 62nd Canadian Chemical Engineering Conference, held in Vancouver, BC on October 14-17, 2012; and the 11th International Conference on Fluidized Bed Technology, held in Beijing, China on May 14-17, 2014. Some of the results of Chapters 3 and 4 were presented by the author at the Technical Advisory Committee meeting of Particulate Research Inc. held in Chicago, IL on June 24-25, 2014; and at the International Workshop on Fluid-Particle Systems held in Vancouver, BC on June 26-27, 2014, in honour of Dr. John R. Grace. The results presented in Chapters 3, 4 and 5 are summarized in seven manuscripts destined or accepted for publication: [1] K. Dubrawski, S. Tebianian, H. T. Bi, J. Chaouki, N. Ellis, R. Gerspacher, R. Jafari, A. Kantzas, C.J. Lim, G. S. Patience, T. Pugsley, M. Z. Qi, J. X. Zhu, and J. R. Grace, “Traveling column for comparison of invasive and non-invasive fluidization voidage measurement techniques,” Powder Technol., vol. 235, pp. 203–220, 2013. v  [2] S. Tebianian, K. Dubrawski, N. Ellis, R.A. Cocco, R. Hays, S.B.R. Karri, T.W. Leadbeater, D.J. Parker, J. Chaouki, R. Jafari, P. Garcia-Trinanes, J.K. Seville, and J.R. Grace, “Study of solid flux in travelling fluidized bed using alternate measurement techniques,” To be published, 2015. [3] S. Tebianian, K. Dubrawski, N. Ellis, R.A. Cocco, R. Hays, S.B.R. Karri, T.W. Leadbeater, D.J. Parker, J. Chaouki, R. Jafari, P. Garcia-Trinanes, J.K. Seville, and J.R. Grace, “Investigation of particle velocity in FCC gas-fluidized beds based on different measurement techniques,” Chem. Eng. Sci., vol. 127, pp. 310-322, 2015. [4] S. Tebianian, N. Ellis, P. Lettieri, and J.R. Grace, “X-ray imaging for flow characterization and investigation of invasive probes interference in travelling fluidized bed,” To be published, 2015. [5] S. Tebianian, K. Dubrawski, N. Ellis, R.A. Cocco, R. Hays, S.B.R. Karri, T.W. Leadbeater, D.J. Parker, J. Chaouki, R. Jafari, P. Garcia-Trinanes, J.K. Seville, and J.R. Grace, “Comparison of particle velocity measurement techniques in travelling fluidized bed operating in square-nosed slugging regime,” To be published, 2015. [6] S. Tebianian, A.H. Ahmadi Motlagh, S. Vashisth, R.A. Cocco, N. Ellis, R. Hays, S.B.R. Karri, and J.R. Grace, “Extending the comparison of voidage measurement and modeling techniques in fluidized beds,” in Proc. 11th Int. Conf. on Fluidized Bed Technology, e.d. J.Li., F.Wei, X.J. Bao, and W. Wang, Chemical Industry Press, Beijing, China, pp. 137–142, 2014. [7] S. Vashisth, A. H. Ahmadi  Motlagh, S. Tebianian, M. Salcudean, J.R. Grace, “Comparison of numerical approaches to model FCC particles in gas-solid bubbling fluidized bed”  vi  Chemical Engineering Science, 2015, in press, http://dx.doi.org/10.1016/j.ces.2015.05.001 The first paper, written mostly by Kristian Dubrawski, was completed by the author of this thesis, with the results further analyzed and the manuscript concluded by adding paragraphs regarding pressure fluctuations measurements and overall comparison. The other manuscripts were written mostly by the author and revised by the supervisors and other co-authors. In all of these cases, the experiments were performed by the author, with assistance from the local host’s expert in the specific techniques. Also the author was in charge of data processing and analysis, with consultation as required from personnel at visited centres. The last two manuscripts resulted from a direct collaboration with CFD modellers, where some of the experimental data presented in this study were compared with the predictions of different CFD codes. The entire database of experimental data obtained in this study is available online for interested readers.                                                 Contact jgrace@chbe.ubc.ca or nellis@chbe.ubc.ca for access. vii  Table of Contents  Abstract .................................................................................................................................... ii Preface ...................................................................................................................................... iv Table of Contents ....................................................................................................................vii List of Tables ............................................................................................................................ xi List of Figures......................................................................................................................... xiv List of Symbols ....................................................................................................................... xxi List of Acronyms ................................................................................................................ xxviii Acknowledgements ................................................................................................................ xxx Dedication ............................................................................................................................ xxxii Chapter 1: Introduction ............................................................................................................ 1 1.1 Importance of hydrodynamics of gas-fluidized beds.....................................................2 1.1.1 Voidage distribution, solids velocity and flux ...........................................................2 1.1.2 Pressure fluctuations ................................................................................................3 1.2 Computational Fluid Dynamics (CFD) model validation ..............................................4 1.3 Hydrodynamic measurements in gas-fluidized beds .....................................................5 1.4 Research objectives .....................................................................................................9 1.5 Conclusion................................................................................................................. 11 Chapter 2: Experimental equipment and measurement methods......................................... 12 2.1 Travelling fluidized bed equipment ............................................................................ 12 2.2 Solid (particulate) materials ....................................................................................... 16 2.3 Experimental operating conditions ............................................................................. 17 viii  2.4 Measurement techniques ............................................................................................ 18 2.4.1 Voidage measurements .......................................................................................... 18 2.4.2 Particle velocity measurements .............................................................................. 19 2.4.2.1 Optical fibre probes ........................................................................................ 19 2.4.2.2 Borescopic high-speed Particle Image Velocimetry (PIV) .............................. 24 2.4.2.3 Radioactive particle tracking (RPT)................................................................ 29 2.4.2.4 Positron emission particle tracking (PEPT)..................................................... 36 2.4.3 Solid flux measurements ........................................................................................ 43 2.4.3.1 Borescopy methodology for determining solid flux ........................................ 43 2.4.3.2 PEPT and RPT methodology for determining solid flux ................................. 47 2.4.4 Dynamic pressure measurement ............................................................................. 50 2.4.5 Fast X-ray imaging ................................................................................................ 51 Chapter 3: Flow regime characterization, voidage distribution and interference of invasive probes with flow structures .................................................................................................... 61 3.1 Fluidization flow regime ............................................................................................ 61 3.1.1 Pressure fluctuations for flow regime determination ............................................... 61 3.1.2 X-ray imaging for flow regime determination ........................................................ 63 3.2 Degree of interference of invasive probes with local hydrodynamics ......................... 71 3.3 Voidage distribution .................................................................................................. 73 3.4 Overall comment and conclusions .............................................................................. 84 Chapter 4: Results and discussion: particle velocity ............................................................. 85 4.1 Particle velocity: FCC ................................................................................................ 85 4.1.1 Radial profiles of time-average particle velocity .................................................... 85 ix  4.1.2 Probability distribution function of solid velocity ................................................. 104 4.1.3 Discussion ........................................................................................................... 107 4.2 Particle velocity: Sand ............................................................................................. 114 4.2.1 Radial profile of time-average particle velocity for sand ...................................... 114 4.2.2 Instantaneous solid velocity and probability distribution function ........................ 121 4.2.3 Discussion specific to sand results ....................................................................... 125 4.3 Overall comment and conclusions ............................................................................ 126 Chapter 5: Results and discussion: solid flux ....................................................................... 128 5.1 Solids flux: FCC ...................................................................................................... 129 5.1.1 Radial profiles of time-average mass and momentum flux ................................... 129 5.1.2 Discussion ........................................................................................................... 144 5.2 Solids flux: Sand ...................................................................................................... 146 5.2.1 Radial profiles of time-average mass and momentum flux ................................... 146 5.2.2 Discussion ........................................................................................................... 160 5.3 Overall comment and conclusions ............................................................................ 161 Chapter 6: Conclusions and recommendations ................................................................... 163 6.1 Conclusions ............................................................................................................. 163 6.2 Recommendations for future work ........................................................................... 166 References.............................................................................................................................. 169 Appendices ............................................................................................................................ 178 Appendix A − Voidage radial profile data obtained by different techniques ......................... 178 Appendix B − Volume-based analysis of PEPT and RPT .................................................... 194 Appendix C − Examples of analysis of variance for solid velocity ....................................... 205 x  Appendix D − Square-nosed slugging ................................................................................. 207 Appendix E − Brief study of the effect of the distributor geometry ...................................... 213  xi  List of Tables Table 2.1 – Experimental particle properties.............................................................................. 16 Table 2.2 – Experimental operating conditions .......................................................................... 17 Table 2.3 – Optical probe properties .......................................................................................... 22 Table 2.4 – Borescopic high-speed PIV system properties ......................................................... 26 Table 2.5  – Origin and RPT detector locations .......................................................................... 32 Table 2.6 –RPT tracer particle physical properties ..................................................................... 33 Table 2.7 – Properties of radioactive tracer particles in the PEPT experiments ........................... 43 Table 3.1 – Average percent deviations from overall average voidage (%). ............................... 83 Table 5.1 – Cross-sectional time-average upward and downward mass flux for sand ............... 150 Table 5.2 – Cross-sectional time-average upward and downward momentum flux for sand ..... 158 Table A.1 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.40 m/s, z = 0.24 m ....................................................................................................... 178 Table A.2 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.40 m/s, z = 0.40 m ....................................................................................................... 179 Table A.3 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.40 m/s, z = 0.56 m ....................................................................................................... 180 Table A.4 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.50 m/s, z = 0.24 m ....................................................................................................... 181 Table A.5 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.50 m/s, z = 0.40 m ....................................................................................................... 182 xii  Table A.6 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.50 m/s, z = 0.56 m ....................................................................................................... 183 Table A.7 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.60 m/s, z = 0.24 m ....................................................................................................... 184 Table A.8 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.60 m/s, z = 0.40 m ....................................................................................................... 185 Table A.9– Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.60 m/s, z = 0.56 m ....................................................................................................... 186 Table A.10 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.30 m/s, z = 0.24 m .................................................................................................. 187 Table A.11 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.30 m/s, z = 0.40 m .................................................................................................. 188 Table A.12– Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.30 m/s, z = 0.56 m ....................................................................................................... 189 Table A.13 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.40 m/s, z = 0.24 m .................................................................................................. 190 Table A.14 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.40 m/s, z = 0.40 m .................................................................................................. 191 Table A.15 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.40 m/s, z = 0.56 m .................................................................................................. 191 Table A.16– Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.50 m/s, z = 0.24 m ....................................................................................................... 192 xiii  Table A.17 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.50 m/s, z = 0.40 m .................................................................................................. 193 Table A.18 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.50 m/s, z = 0.56 m .................................................................................................. 193 Table C.1 – ANOVA results with true null hypothesis, FCC, Ug = 0.50 m/s, z = 0.56 m, r/R=0.6 .......................................................................................................................................... 205 Table C.2 – ANOVA results with false null hypothesis, FCC, Ug = 0.30 m/s, z = 0.40 m, r/R=0 .......................................................................................................................................... 206  xiv  List of Figures Figure 2.1 − Traveling fluidized bed (TFB) column: a) assembled; b) exploded modular view .. 14 Figure 2.2 − Schematic of fluidizing gas delivery system .......................................................... 15 Figure 2.3 – Cumulative particle size distribution. ..................................................................... 17 Figure 2.4 – Optical fibre probe system configuration and schematic. ....................................... 19 Figure 2.5 – Sensitivity to measurement angle of optical probe. ................................................ 24 Figure 2.6 – Borescopic high-speed PIV system configuration for TFB experiments. ................ 25 Figure 2.7 – Velocity vectors obtained by PIVlab in a region of interest for: (a) FCC; (b) sand. 29 Figure 2.8 – Plan view showing NaI detectors deployed around TFB column (adapted from Dubrawski et al., 2013)........................................................................................................ 32 Figure 2.9 – PEPT system configuration for TFB experiments. ................................................. 39 Figure 2.10 – Example of Otsu method failure applied to a snapshot corresponding to an extremely dilute flow. .......................................................................................................... 44 Figure 2.11 – Borescopic threshold as a function of average image grayscale intensity .............. 45 Figure 2.12 –Binarization of images obtained by borescope based on average intensity threshold for: (a) FCC; and (b) sand particles. ..................................................................................... 46 Figure 2.13 – X-ray system configuration and optical probe insertion schematic. Source to Intensifier Distance (SID): 0.78 m, Object to Intensifier Distance (OID): 0.10 m. ................ 53 Figure 2.14 – Pincushion distortion correction: (a) original image; (b) corrected image. The red grid is intended to check the alignment of the points. ........................................................... 57 Figure 3.1 – Standard deviation of differential pressure fluctuations for measurements between z = 0.56 and z = 0.72 m for: (a) FCC; and (b) sand. ................................................................ 62 xv  Figure 3.2 – Pressure fluctuation data and FFT analysis for sand and FCC at Ug = 0.50 m/s between z = 0.40 and z = 0.56 m .......................................................................................... 63 Figure 3.3 – Examples of gray-scale intensity PDF and relative flow structures for sand fluidized in: (a) bubbling and; (b) slugging flow regimes. .................................................................. 65 Figure 3.4 – Examples of gray-scale intensity PDF and relative flow structures for sand fluidized in: (a) slugging and; (b) turbulent fluidization flow regimes................................................. 66 Figure 3.5 – Examples of gray-scale intensity PDF and relative flow structures for FCC fluidized in bubbling flow regime. ..................................................................................................... 68 Figure 3.6 – Examples of gray-scale intensity PDF and relative flow structures for FCC fluidized in turbulent fluidization flow regime.................................................................................... 69 Figure 3.7 – Time-average entropy, skewness and kurtosis for gray-scale PDFs obtained at 72 fps over 10 s as a function of superficial gas velocity. ............................................................... 70 Figure 3.8 – Sample time-average voidage distributions around probe inserted at 0.56 m above the distributor (right side) and the corresponding distribution with the probe removed (left side): (a) sand, Ug = 0.50 m/s; (b) FCC, Ug = 0.50 m/s......................................................... 73 Figure 3.9 – Comparison of radial profiles of time-average voidage obtained by borescopy and other measurement techniques for sand fluidized at Ug = 0.50 m/s. ...................................... 75 Figure 3.10 – Comparison of radial profiles of time-average voidage obtained by borescopy and other measurement techniques for FCC fluidized at Ug = 0.40 m/s....................................... 76 Figure 3.11 – Comparison of cross-sectional average voidage for sand as a function of height for: (a) Ug = 0.40 m/s; (b) Ug = 0.50 m/s; (c) Ug = 0.60 m/s........................................................ 78 Figure 3.12 – Comparison of cross-sectional average voidage for FCC as a function of height for: (a) Ug = 0.30 m/s; (b) Ug = 0.40 m/s; (c) Ug = 0.50 m/s........................................................ 79 xvi  Figure 3.13 – Overall bed average voidage results for: (a) FCC; and (b) sand. ........................... 80 Figure 3.14 – Percent deviations from cross-sectionally and longitudinally averaged voidages: a) for FCC (Ug = 0.30 to 0.50 m/s); and b) for silica sand (Ug = 0.30 to 0.60 m/s). ................... 82 Figure 4.1 – Radial profiles of time-average solid velocity at three levels for FCC, Ug = 0.30 m/s. Only particles with deviation from vertical motion by ≤ 30˚ are included. ........................... 89 Figure 4.2 – Radial profiles of time-average solid velocity at three levels for FCC, Ug = 0.40 m/s. Only particles with deviation from vertical motion by ≤ 30˚ are included. ........................... 90 Figure 4.3 – Radial profiles of time-average solid velocity at three levels for FCC, Ug = 0.50 m/s. Only particles with deviation from vertical motion by ≤ 30˚ are included. ........................... 91 Figure 4.4 – Radial profiles of time-average solid velocity at three levels for FCC, Ug = 0.60 m/s. Only particles with deviation from vertical motion by ≤ 30˚ are included. ........................... 92 Figure 4.5 – Radial profiles of time-average solid velocity at three levels for FCC based on vertical components of velocity vectors, Ug = 0.30 m/s. ....................................................... 94 Figure 4.6 – Radial profiles of time-average solid velocity at three levels for FCC based on vertical components of velocity vectors, Ug = 0.40 m/s. ....................................................... 95 Figure 4.7 – Radial profiles of time-average solid velocity at three levels for FCC based on vertical components of velocity vectors, Ug = 0.50 m/s. ....................................................... 96 Figure 4.8 – Radial profiles of time-average solid velocity at three levels for FCC based on vertical components of velocity vectors, Ug = 0.60 m/s. ....................................................... 97 Figure 4.9 – Comparison of radial profiles of time-average solid velocity at three levels for FCC obtained by volume-based and crossing-based analysis, Ug = 0.40 m/s. For the volume-based data, the cells were of height 30 mm centred at the level (z-value) of interest in each case. 101 xvii  Figure 4.10 – Overall percent deviation of particle vertical velocities for different superficial gas velocities: a) Velocities for particles with a deviation angle of less than 30 degrees from the vertical; b) Vertical components of the velocities............................................................... 102 Figure 4.11 – Effect of the sampling time on the time-average particle velocity measured by the borescopy for FCC: Experiment a) Ug = 0.40 m/s, z = 0.40 m, r/R = 0.77; experiment b) Ug = 0.60 m/s, z = 0.40 m, r/R = 0; experiment c) Ug = 0.30 m/s, z = 0.24 m, r/R = 0.33. ........... 103 Figure 4.12 - Count number for RPT in 8 hours and PEPT in 3.5 hours sampling time for different annuli with different filtering criteria, FCC, Ug = 0.40 m/s, z = 0.40 m. ............... 104 Figure 4.13 – Examples of probability distribution function of solid velocity for FCC. Only particles deviating from vertical motion by ≤ 30˚ are included for the borescope, RPT and PEPT. ................................................................................................................................ 105 Figure 4.14 – Radial profiles of time-average solid velocity at three levels for FCC excluding zero velocities. .................................................................................................................. 113 Figure 4.15 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.40 m/s. ................................................................................................................................... 116 Figure 4.16 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.50 m/s. ................................................................................................................................... 118 Figure 4.17 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.60 m/s. ................................................................................................................................... 119 Figure 4.18 – Radial profiles of time-average solid velocity at three levels for sand based on vertical components of velocity vectors. ............................................................................ 120 xviii  Figure 4.19 – Effect of the sampling time on time-averaged particle velocity measured by the borescope. Sand: a) Ug = 0.40 m/s, z = 0.40 m, r/R = 0.77; b) Ug = 0.60 m/s, z = 0.40 m, r/R = 0.33; c) Ug = 0.60 m/s, z = 0.56 m, r/R = 0.60; d) Ug = 0.50 m/s, z = 0.56 m, r/R = 0.33. ... 121 Figure 4.20– Sample probability distribution functions of solid velocity for sand. ................... 122 Figure 4.21 – Solid velocity time series obtained by: a) Optical probe; b) Borescope. Note that the traces are not continuous, but broken into bursts of duration 1 s for the borescope and 0.5 s for the optical probe. ....................................................................................................... 123 Figure 4.22 – PEPT and RPT measured tracer velocities crossing the z = 0.56 m level during the entire sampling period. ...................................................................................................... 124 Figure 5.1 – Radial profiles of time-average solids mass flux at three levels for FCC fluidized at Ug = 0.30 m/s. ................................................................................................................... 131 Figure 5.2 – Radial profiles of upward and downward time-average solids mass flux at three levels for FCC fluidized at Ug = 0.40 m/s. ......................................................................... 132 Figure 5.3 – Radial profiles of time-average solids mass flux at three levels for FCC fluidized at Ug = 0.50 m/s. ................................................................................................................... 135 Figure 5.4 – Radial profiles of time-average solids mass flux radial profiles at three levels for FCC fluidized at Ug = 0.60 m/s. ......................................................................................... 136 Figure 5.5 – Radial profiles of time-average particle momentum flux at three levels for FCC fluidized at Ug = 0.30 m/s. ................................................................................................. 138 Figure 5.6 – Radial profiles of time-average particle momentum flux at three levels for FCC fluidized at Ug = 0.40 m/s. ................................................................................................. 139 Figure 5.7 – Radial profiles of time-average particle momentum flux at three levels for FCC fluidized at Ug = 0.50 m/s. ................................................................................................. 141 xix  Figure 5.8 – Radial profiles of time-average particle momentum flux at three levels for FCC fluidized at Ug = 0.60 m/s. ................................................................................................. 142 Figure 5.9 – Net vertical mass flux over entire measurement time period (10 s for borescope, 3.5 h for PEPT, and 8 h for RPT) and cross-section at three levels and four superficial gas velocities for fluidized FCC. See text for discussion of points surrounded by shaded zones. .......................................................................................................................................... 143 Figure 5.10  – Count number per unit time for PEPT and RPT at different radial positions for FCC. ................................................................................................................................. 146 Figure 5.11 – Radial profiles of upward and downward time-average solids mass flux at three levels for sand fluidized at Ug = 0.40 m/s. .......................................................................... 149 Figure 5.12 – Radial profiles of upward and downward time-average solids mass flux at three levels for sand fluidized at Ug = 0.50 m/s. .......................................................................... 152 Figure 5.13 – Radial profiles of upward and downward time-average solids mass flux at three levels for sand fluidized at Ug = 0.60 m/s. .......................................................................... 153 Figure 5.14 – Radial profiles of upward and downward time-average solids momentum flux at three levels for sand fluidized at Ug = 0.40 m/s. ................................................................. 154 Figure 5.15 – Radial profiles of upward and downward time-average solids momentum flux at three levels for sand fluidized at Ug = 0.50 m/s. ................................................................. 155 Figure 5.16 – Radial profiles of upward and downward time-average solids momentum flux at three levels for sand fluidized at Ug = 0.60 m/s. ................................................................. 156 Figure 5.17 – Net mass flux over entire measurement time period (3.5 h for PEPT, and 8 h for RPT) and cross-section at three levels for different superficial gas velocities and fluidized sand. .................................................................................................................................. 159 xx  Figure B.1 – Radial profiles of time-average solid velocity at three levels for FCC using volume-based approach for RPT and PEPT, Ug = 0.30 m/s. ............................................................ 195 Figure B.2 – Radial profiles of time-average solid velocity at three levels for FCC using volume-based approach for RPT and PEPT, Ug = 0.40 m/s. ............................................................ 196 Figure B.3 – Radial profiles of time-average solid velocity at three levels for FCC using volume-based approach for RPT and PEPT, Ug = 0.50 m/s. ............................................................ 197 Figure B.4 – Radial profiles of time-average solid velocity at three levels for FCC using volume-based approach for RPT and PEPT, Ug = 0.60 m/s. ............................................................ 198 Figure B.5 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.40 m/s. ................................................................................................................................... 201 Figure B.6 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.50 m/s. ................................................................................................................................... 202 Figure B.7 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.60 m/s. ................................................................................................................................... 203 Figure D.1− Type A Axisymmetric; and type B square-nosed slugging schematics. Adapted from Yang (2003). ..................................................................................................................... 208 Figure E.1− Effect of distributor plate on particle velocity data obtained by borescopic high-speed PIV .......................................................................................................................... 214  xxi  List of Symbols A  strength of the radioactive source, Bq Ap  area of the borescopic image occupied by particles, px2 Atot  total area of the borescopic image, px2 cj  multiplicand for PEPT instantaneous particle velocity determination, -  C  γ-ray counts detected by RPT detector, - dS  mean deviation of γ-ray trajectories from point m, mm D  column diameter, m DS  sum of the distances of γ-ray trajectories from point m, mm dsauter  Sauter mean particle diameter, μm dfibre  external diameter of optical probe fibres, μm dprobe  external diameter of optical probe, mm E  error of cross-correlation, m/s f  sampling frequency necessary for optical probes, kHz f,  upwards or downwards momentum fluxes due to tracer particle motion through a cell, kg/s2m xxii  fi  probability that a γ-ray interacts with the detector crystal, - fmin  required sampling frequency for optical probe maximum detectable velocity, kHz  fopt  final fraction of γ-ray sample, - F,  upwards or downwards momentum fluxes due to all particles motion through a cell, kg/s2m Fs  solid momentum flux, kg/s2m Fsc  average solid momentum flux at centre of the bed, kg/s2m g,  upwards or downwards mass fluxes due to tracer particle motion through a cell, kg/m2s G,  upwards or downwards mass fluxes due to all particles motion through a cell, kg/m2s Gs  solid mass flux, kg/m2s Gsc  average solid mass flux at centre of the bed, kg/m2s h  height coordinate in X-ray images, m H   Shannon entropy, bit Hs  static bed height, m I  transmitted intensity, - xxiii  I0  incident intensity, - IA,B  time-series of the electric signals associated with the two light-receiving fibres,V Ip  interval of measurable velocities using optical probe, m/s Iw  interval of measurable velocities in wall region using optical probe, m/s j  cross-sectional area cell at a certain level i, - J  total number of cells, - Js  solid circulation flux, kg/m2s l  path length, m Le  effective distance between receiving ends of optical probe, m mp  mass of a single particle, kg M  multiplicand for time-lag, - Mp   total mass of all particles in the bed, kg ms  minimum distance point, mm n  total number of classes of distribution, - n  external unit vector locally perpendicular to the solid angle, mm n,  number of times the tracer particle passes upwards or downwards, - xxiv  N  initial sample size, - p  X-ray path length, m pi   probability of class i of distribution, -  Pi  PEPT tracer particle location vector, mm r  distance between tracer and geometric centre of the detector, mm S  initial γ-ray set, -   S(j)  cross-sectional area of the jth cell, m2 Stot  cross-sectional area of the column, m2 T  sampling time, s Tint  integration time, s Uc  superficial gas velocity at transition to turbulent fluidization flow regime, m/s Ug  superficial gas velocity, m/s Ums  minimum slugging velocity, m/s Ut  terminal settling velocity in air at 25˚C, m/s v,  upwards or downward vertical component of tracer particle velocity, m/s vp  local instantaneous particle velocity, m/s xxv  v'p   fluctuating component of particle velocity, m/s v p   mean component of particle velocity, m/s vpc  average solid velocity in the centre of the bed, m/s vp,min  minimum particle velocity measurable by optical probe, m/s vp,max  maximum particle velocity measurable by optical probe, m/s vpw  average solid velocity in the wall region, m/s vp,x, vp,y, vp,z coordinates of instantaneous vector of tracer particle velocity, m/s w  positron camera resolution, mm x,y,z  spatial coordinates of with reference to the centre of the distributor plate, m X  values of a population, - Y   correction for deviation from the two-phase theory of fluidization, - β  angle of internal friction, deg β2  kurtosis, - βd  bubble drift volumetric fraction, - βw  bubble wake volumetric fraction, - dΣ  elementary solid angle, strd xxvi  δi(m)  distance of ith γ-ray trajectory from point m, mm  Δ  location precision for PEPT, mm t   time lag between successive tracer detections, ms x   tracer particle displacement, m ε  voidage, - ε'   fluctuating component of voidage, - ε    mean component of voidage, - εb  bulk voidage, - εmf  voidage at minimum fluidization, - ϕ  photopeak ratio, - ΦIAIB  cross-correlation function, V2 γ1  skewness, - γ2  normalized kurtosis, - μm  attenuation coefficient of solid material, m2/kg  μ  mean of a probability distribution function, - μ4  fourth moment about the mean, -  xxvii  ν  number of γ-rays emitted per disintegration, - Ψp  solid area fraction, - ρ  gas density, kg/m3 ρb  bulk density, kg/m3 IAIB  cross-correlation coefficient, V2 ρp  particle density, kg/m3 σ  standard deviation, -  σvp  PEPT tracer particle velocity uncertainty, m/s τ  dead-time per recorded pulse, s τl  time-lag between two signals of optical probes, s  ζ  total detector efficiency, - Ω  solid angle subtended by the detector surface, strd    xxviii  List of Acronyms CCD  charge coupled device  CFB  circulating fluidized bed CFD  computational fluid dynamics ECT  electrical capacitance tomography FCC  fluid cracking catalyst FFT  Fast Fourier Transform LDA  laser doppler anemometer OID  object-to-intensifier distance  PDF  probability distribution function PEPT  positron emission particle tracking PIV  particle image velocimetry Poly  Ecole Polytechnique PSRI  Particulate Solid Research Inc. RPT  radioactive particle tracking SID  source-to-intensifier distance TFB  travelling fluidized bed UBC  University of British Columbia UC  University of Calgary UCL  University College London UoB  University of Birmingham USask  University of Saskatchewan UWO  University of Western Ontario xxix  XCT  X-ray computed tomography xxx  Acknowledgements I would like to thank Dr. John Grace, who was more than a technical supervisor for me. From his approach in solving extremely complex problems, I learned critical thinking, endeavour for excellence, and interpersonal skills. It was a great honour for me to work with such a great leader. His supervision justified all the difficulties I faced: leaving my hometown and travelling across the ocean. My special thanks go to my co-supervisor, Dr. Naoko Ellis. Her technical advice was absolutely practical and useful for the success of my project. Her support during extremely difficult steps of my project was unique and precious. I am also grateful to my committee members, Dr. Xiaotao Bi and Dr. Bud Homsy, for their useful comments and support. I am extremely grateful to Dr. Ray Cocco and Dr. S.B. Reddy Karri for their great support during my time at PSRI and afterwards. I was really lucky to work with such a high-calibre team of scientists. I would like to thank Dr. David Parker and Dr. Paola Lettieri for their support during my experiments at UoB and UCL. Words cannot express my gratitude to my family members: Rakhshi, Avaz, Anis and Faran, for their encouragement and virtual presence during every second of this path. I would like to thank my beloved Silvia that supported me with her beautiful smile since the night I was packing to come to Vancouver. Her trust and encouragement were beyond any physical description. I would also like to thank Rizzi family: Lucia, Gigi, Giacomo and Manuela for their great support and encouragement. xxxi  I would like to thank all my friends specially: Nima, Giuseppe, Anna, Bashir, Iman, Dario, Mara, Ramona, Andrew, James, Maziar, Hamid and Sebastiano. Their unlimited love and support accompany me in every second. Great gratitude is owed to my friend and aunt, Marilena and her family. Her genuine and pure way of conducting matters, and her great support and encouragement will accompany me in all the stages of personal and professional life. Special thanks go to Subhashini and Amir for their help with CFD modeling of my unit. I would also like to thank Ciprian and his beautiful family, and Jaber family: only God knows how much they have done for me. I also thank Linus and Nicola and their beautiful program on Radio Deejay. They may not know it, but their voices made most of my days. My gratitude also goes to all FRC group and my previous supervisors, Drs. Piero Salatino and Roberto Solimene. I am also grateful to Natural Sciences and Engineering Research Council of Canada for an RTI grant, which made it possible to build the equipment, and for Discovery grant funding which assisted in supporting my graduate studies and in covering the costs of transportation, insurance and equipment operation.     xxxii  Dedication    Dedicated to my family:  Silvia, Rakhshi, Avaz, Anis and Faran 1  Chapter 1: Introduction Gas fluidization is the unit operation by which granular solids are transformed into fluid-like state through suspension in a vertically-flowing gas stream. This process brings into intimate contact solid and gas phases, producing unique features such as: 1) excellent heat transfer; 2) close to isothermal behaviour, even for highly exothermic reactions; 3) ease of solids handling and processing; 4) efficient solids mixing; 5) ability to feed and disperse some liquid; and 6) flexibility in treating wide ranges of particle properties. Gas-solid fluidized beds are used in a broad range of industrial processes (Kunii and Levenspiel, 1991) including application in emerging technologies such as carbon capture, UV photocatalytic oxidation, and production of ultra-pure solar grade silicon. Local particle velocity, solid flux, gas motion and voidage distribution, often collectively referred to as “hydrodynamics”, profoundly influence the performance of gas-fluidized beds, from heat and mass transfer to chemical conversion and selectivity. Despite the extensive efforts of many researchers and practicing engineers, design and scale-up of gas-fluidized beds are still challenging, often relying on empirical correlations (Yang, 2003). Lack of fundamental knowledge of physical phenomena occurring in these systems and accurate experimental data leading to valid hydrodynamic models are among the factors that cause uncertainties with design and scale-up. As a result, fluidized beds are commonly eliminated from consideration, as these uncertainties compromise the risk tolerances in a corporate culture.  Various invasive and non-invasive experimental techniques have been proposed for the hydrodynamic study of fluidized beds (reviewed by Yates and Simons, 1994; Werther, 1999; van 2  Ommen and Mudde, 2008). However, except for our group’s recent work on voidage distribution (Dubrawski et al., 2013), the accuracy of many of these techniques has not been challenged by comparing results obtained by alternative techniques under identical operating conditions. This makes it difficult to investigate the merits and reliability of each measurement technique. In the present work a novel travelling fluidized bed (TFB) facility, designed and built to provide identical operation in different physical settings, was employed to directly compare alternate experimental measurement techniques for hydrodynamic characterization of gas-fluidized beds. Operating with the same equipment, with the same particles and under the identical operating conditions eliminates differences due to discrepancies between equipment, particles and operating conditions as sources of variation in data. 1.1 Importance of hydrodynamics of gas-fluidized beds Hydrodynamic parameters studied in this thesis include local particle velocity, solids mass and momentum flux, time-average voidage distribution and pressure fluctuations. The performance of gas-fluidized beds is closely related to these parameters as discussed in the next sections.   1.1.1 Voidage distribution, solids velocity and flux Voidage distribution and solids motion/flux are of extreme importance, as they influence many aspects of gas-fluidized bed performance:  In fluidized bed reactors, vertical movement of solid particles can transport reaction components and catalysts upward and downward in the bed, affecting axial dispersion, conversion and selectivity (Nguyen et al., 1977; Kunii and Levenspiel, 1991). 3   Many processes involve contact between solids with different densities (e.g. in the production of titanium or zirconium, drying of solids). Solids movement and velocity influence mixing processes and staging of the solids.  Erosion of in-bed tubes and other components in fluidized beds, as well as particle attrition, are directly related to particle motion, affecting the velocity and frequency of impact (Lyczkowski et al., 1993).  Heat exchange between immersed surfaces and fluidized beds, operating in any flow regime, depends on the frequency of particles reaching the surface and their velocity (Werdermann and Werther, 1994). Local heat transfer coefficients also depend strongly on the local void fraction around immersed surfaces (Ozawa et al., 1998; Di Natale et al., 2010). Di Natale et al. (2010) state that the difficulty of measuring the void fraction profile around the immersed object is the main factor leading to the lack of a fully-valid mechanistic model for heat transfer.  The solids circulation rate is a key parameter in determining the performance of circulating fluidized beds (Pugsley et al., 1992).   Measurement of solids mass flux entrained from the bed is extremely important in determining the loss of solids not captured by cyclones. 1.1.2 Pressure fluctuations Pressure measurements provide a simple and practical method for determining or estimating key hydrodynamic properties of gas-fluidized beds: 4   The maximum standard deviation of pressure fluctuations across the bed as a function of superficial gas velocity is commonly accepted as an indicator of the transition from bubbling to the turbulent fluidization flow regime, caused by break-up of bubbles or slugs into transient voids (Johnsson et al., 2000; Ellis, 2003).   Axial pressure profiles along fluidized beds provide information on the hold-up of particles in different sections of the bed. For circulating fluidized beds, pressure measurements are used to determine the solids inventory in the riser section and also to obtain quick information about flow instabilities and disturbances in the cyclone and the standpipe from dynamic measurements of the pressure loop (Werther, 1999). 1.2 Computational Fluid Dynamics (CFD) model validation  Balance equations for conservation of mass, momentum and energy, in combination with transport equations and constitutive laws, are the basis for CFD models, where a computer numerically solves the resulting coupled non-linear system of partial differential equations.  CFD models hold great promise for the design and understanding of gas-fluidized beds, but their prediction ability remains limited (Grace and Taghipour, 2004; Panday et al., 2014). Kashiwa and Yang (2002) reported instances of success and failure of CFD applied to circulating fluidized bed reactors. They note that gas-solid hydrodynamics in the turbulent fluidization flow regime is not still completely understood, with a lack of adequate physical models able to describe the dynamics of different operating flow regimes being a major cause of CFD failure in predicting the behaviour of fluidized beds. Panday et al. (2014) presented the first part of the most recent Challenge Problem project to benchmark the state of the art in CFD models employed to 5  simulate the hydrodynamic behaviour of gas-fluidized beds. For two sets of bed material, different parameters such as pressure profile, particle velocity and solid flux were obtained experimentally at different operating conditions for a CFB. Different modellers have simulated CFB systems and compared their blindly-generated simulation results with experimental data. Failures and successes of different model types (Eulerian-Eulerian, Eulerian-Lagrangian) have been discussed and suggestions for future prospects in CFD modeling presented.   Grace and Taghipour (2004) advocated “close cooperation at the planning stage between the modeller and experimentalists”. They also suggest that experiments must cover an extensive range of operating conditions and physical variables to provide benchmarks for testing CFD models. A CFD model is “validated” only when it can predict an extensive array of experimental data obtained at different operating conditions. Kashiwa and Yang (2002) note that there are difficulties in obtaining standardized experimental data. They state that to be accurate and reliable, the experimental data should be verified by different independent research groups under similar operating conditions. Some indication of the value of systematic errors that are inevitable in experimental works could be produced by using different measurement techniques that measure the same variables in the same experimental apparatus under identical operating conditions (Grace and Taghipour, 2004). Grace and Li (2010) discussed the mutual benefit resulting from collaboration between experimentalists and numerical and reactor modellers. 1.3 Hydrodynamic measurements in gas-fluidized beds Performing reliable and accurate measurements in gas-fluidized bed is extremely important to gain a deeper understanding of these systems and for testing of CFD and other mechanistic models. However, intrinsic features of industrial gas-fluidized beds, such as their optical opacity 6  and their harsh abrasive environment, caused by continuous motion of solids that can erode and block any immersed measurement instrument, make it extremely challenging to obtain reliable experimental data. High temperature, high pressure and chemically aggressive atmosphere often add to the challenge. Although research groups around the world have been developing a variety of sophisticated measurement techniques for the hydrodynamic study of gas-fluidized beds, based on both invasive and non-invasive methods (Yates and Simons, 1994; Werther, 1999), a number of issues still need to be considered:  Each technique delivers only specific data that represent only a portion of the global hydrodynamic behaviour of the system, for example local particle velocity, but not local voidage. This results in a limited database for model validation.  Consider for instance, two experimental measurement techniques that deliver the same hydrodynamic information owned by two different research groups, X and Y. Group X has applied and tested the technique in its possession on an experimental fluidization facility (consisting of a column, auxiliary components, instrumentation and particles) differing in multiple aspects from the facilities utilized by the research group Y.  In fact, researchers purposely ensure that their equipment is unique in order to avoid being seen as being unoriginal or derivative of other groups. While this is entirely comprehensible, the individualistic approach makes it impossible to directly compare the results obtained by different measurement techniques and different research groups, since discrepancies may be simply associated with differences in equipment (geometry, scale, material of construction, electrical grounding, etc.), variations in particle properties (mean size, size 7  distribution, density, shape, roughness, dielectric constant, moisture content, etc.), gas properties (e.g. humidity) and/or operating conditions (temperature, pressure, flow rate of gas), as well as unique features of the analytical measurement technique deployed. As a result, there is no standard for establishing limits and merits of each measurement technique, nor for quantification of the systematic errors associated with them. In fact, no single technique nor experimental facility is regarded as a “gold standard”.   While non-invasive techniques are often applied in academic research, invasive techniques such as optical and capacitance probes may be good candidates for performing measurements in industrial units that currently are commonly monitored exclusively by temperature, pressure and overall concentration change measurements. Development of advanced probes for obtaining direct information on instantaneous hydrodynamic features of commercial gas-fluidized beds could be useful for improving their performance, reliability and control. However, the degree of their interference with the local hydrodynamics of fluidized bed needs to be assessed in order to evaluate the reliability of invasive measurement techniques.  Except for our group’s recent work on voidage measurements (Dubrawski et al., 2013) there have been few attempts to compare different measurement techniques in the past. Wright et al. (2001) used X-ray computer assisted tomography, X-ray digital fluoroscopy and radioactive particle tracking (RPT) to measure different parameters of a single fluidized bed column, without any direct quantitative comparison of results. Mabrouk et al. (2005) deployed both RPT and optical probes to measure voidage profiles in gas-solid fluidized beds of diameter 50, 78, and 152 mm, and found good qualitative agreement between the results from these two techniques. 8  Pugsley et al. (2003) compared electrical capacitance tomography with fibre optical probe voidage data in the same riser and between two slightly different bubbling fluidized beds. Ellis (2003) used both optical and capacitance probes to determine voidage profiles in columns of different diameters, operating in the bubbling and turbulent fluidization regimes. The profiles differed substantially, with discrepancies attributed to the much larger measuring volume of the capacitance probe. Song et al. (2006) compared the radial voidage profiles in the reactor section of FCC particles in a cold model of a fluid coker obtained by capacitance and optical probes. These two measurement techniques gave very similar results. Werther et al. (1996) compared a laser doppler anemometer (LDA) and a single fibre reflection probe to measure solid velocity in the dilute zone of a circulating fluidized bed riser. These experiments were performed under identical conditions with the same equipment. However, the comparison could not be performed for high-solid-concentration flows since LDA is effective only for dilute suspensions. Panday et al. (2014) compared the time-average solid velocity in a CFB obtained by a dual multi fibre optical probe with data obtained by high-speed particle image velocimetry. Good agreement was observed between the results of the employed techniques, but the comparison was limited to one operating condition and few locations. Holland et al. (2008) compared voidage profiles and bubble frequencies obtained by magnetic resonance imaging (MRI) and electrical capacitance volume tomography (ECVT), with fair agreement among the results. However, the bed material employed for the MRI study differed slightly from that employed for ECVT. Pore et al. (2015) compared positron emission particle tracking (PEPT), MRI and X-ray radiography to measure the length of a single jet in a packed bed at different gas velocities, observing agreement among the jet lengths obtained by all three techniques in most cases, but with appreciable differences at the lowest superficial gas velocities.   9  1.4 Research objectives In this research project, a novel “travelling fluidized bed” (TFB), together with its auxiliary components and solid material, whose characteristics are described in the next chapter, was transported to different laboratories in possession of advanced hydrodynamic measurement techniques in order to: 1. Directly compare quantitative results obtained by alternate particle velocity measurement techniques. Four different experimental techniques  radioactive particle tracking (RPT) a non-invasive method practised at the Ecole Polytechnique (Poly); Positron emission particle tracking (PEPT), a non-invasive technique developed at the University of Birmingham (UoB); optical fibre probes, an invasive technique deployed at the University of British Columbia (UBC); and borescopic high-speed particle image velocimetry (PIV), an invasive measurement method owned and operated by Particulate Solid Research Inc. (PSRI)  are used for this purpose. Radial profiles of time-average particle velocity and the probability distribution function of solid velocity obtained by all four techniques are directly compared, and the reasons underlying observed discrepancies are considered. 2. Further analyze the data obtained by RPT, PEPT and borescopy in order to obtain information on local solid mass and momentum flux. A novel approach is suggested to obtain solid flux from non-invasive particle tracking techniques, and the results are directly compared with data measured by borescopy. The ability and accuracy of these techniques in measuring solid flux is discussed by taking into account the intrinsic physical principles associated with each method. 10  3. Investigate the accuracy of invasive probes in determining key hydrodynamic features of gas-fluidized beds and the degree of their interference with measurements. Invasive probes are among the few hydrodynamic measurement techniques that can be deployed in industrial units, and their degree of interference with hydrodynamic measurements has not been fully investigated. Direct comparison of results from invasive probes with data obtained by other techniques provides an indication of the degree of their interference with measurements. In addition, fast X-ray imaging is employed to investigate the effect on time-average voidage distribution when an intrusive probe is inserted into the field of view. 4. Study the change in flow structures corresponding to the transition from bubbling to the turbulent fluidization flow regime using statistical analysis of X-ray images and pressure fluctuations.  5. Obtain cross-sectional time-average voidages at different operating conditions using pressure drop and X-ray images and radial profiles of time-average voidage based on borescopic imaging, that together with the distribution map of solid velocity and flux obtained by the methods mentioned in points 1 and 2, and radial profiles of time-average voidage from previous work (Dubrawski et al., 2013), provide an extensive experimental hydrodynamic database for validation of CFD and other models.                                                 Note that although MRI is proving to be another helpful hydrodynamic measurement technique for fluidized beds  (Holland et al., 2008; Müller et al., 2008; Kawaguchi, 2010), it could not be employed in this study due to bed material and equipment size limitations. 11  1.5 Conclusion This work represents a unique attempt to characterize key hydrodynamic properties of a single gas-fluidized bed system utilizing an array of alternate experimental techniques under identical operating conditions. The work is mostly intended to determine the accuracy of different hydrodynamic measurement techniques in order to provide insights for: (1) experimentalists employing similar techniques; and (2) modellers when comparing their predictions with experimental data as a benchmark for model validation.    12  Chapter 2: Experimental equipment and measurement methods The travelling fluidized bed (TFB) unit was previously employed in different laboratories in Canada for voidage characterization (Dubrawski et al., 2013). The author of this thesis first compiled and further analyzed the already available voidage results and compared them with those obtained by pressure drop. The project was then extended in order to characterize the TFB in terms of particle velocity, solid mass and momentum flux, and fluidization flow regime at the same operating conditions as Dubrawski et al. (2013). This chapter provides details of the TFB unit, physical properties of the solid particles used during the experiments and the methodology associated with the experimental measurement techniques employed during this work. The entire TFB apparatus, accompanied by the author, travelled to different research laboratories for experimentation using alternative sophisticated instrumentation, while maintaining identical operating conditions. 2.1  Travelling fluidized bed equipment The travelling fluidized bed apparatus (Figure 2.1) and its auxiliary components were designed to be a robust test platform in order to be easily disassembled, transported and remounted, ensuring identical operation in different locations. Supply, conditioning and control of the fluidizing gas were provided using four modular boards that slide out of the transportation crate as shown in Figure 2.2. Key features of the equipment include:   A cylindrical fluidization vessel consisting of a 0.96 m long x 0.133 m i.d. dense bed section, surmounted by a 1.36 m long x 0.190 m i.d. freeboard section, with an inclined 13  transition in between angled at 30˚ to the vertical.  A windbox with a perforated distributor plate (49 perforations on a circular pattern) that can be changed, without having to remove particles, in order to control the distributor pressure drop over a broad range of gas flow rates. Three grid plates with different orifice diameters (1.5, 2.0 and 2.5 mm) could be employed to maintain the distributor plate pressure drop for operation at different superficial velocities. The grid plate with 2.5 mm diameter orifices was used for all cases of this study, except that some particle velocity results are compared in Appendix E with those corresponding to the grid plate with 1.5 mm orifices.  An internal cyclone of 63.5 mm diameter with a 3/8˝ (O.D. 17.15 mm) schedule 40 pipe dipleg to return particles to the dense bed.   Eighteen sample ports in the dense bed region and six additional ports along the height of the freeboard section for insertion of probes. All ports were of diameter 1/4˝ NPT (nominal O.D. 13.6 mm).  A robust gas delivery system enabling researchers to connect either house air or a manifold connecting six compressed gas cylinders.  Parallel inline electric gas heaters (2 x 1000 Watt PraxAir) for adjusting the fluidizing gas temperature.   High-quality instrumentation including two 0-14 kPa absolute pressure transducers, three 0-35 kPa absolute pressure transducers, two high-pressure static pressure transducers (0-14  1.4 MPa), two differential pressure transducers (0-14 and 0-35 kPa), two Hoskin Scientific Limited temperature sensors (0-50ºC), and a relative-humidity sensor.   A wiring break-out box connecting the instrumentation to a NI USB 6215 data acquisition module.  Figure 2.1 − Traveling fluidized bed (TFB) column: a) assembled; b) exploded modular view The fluidizing cylinder air or compressed laboratory air, passes through an oil and water filter, and then is heated to the desired temperature (25˚C), with its velocity measured by four sonic (a) (b) Dense bed section Freeboard Internal cyclone 15  nozzles, calibrated against an orifice flow meter using the ASME standard and found to be in almost perfect calibration.   Figure 2.2 − Schematic of fluidizing gas delivery system 16  2.2 Solid (particulate) materials The two particulate materials tested were spent fluid cracking catalyst (FCC) and silica sand. Their key physical properties are provided in Table 2.1. These particles travelled with the equipment as a further measure towards identical operating conditions at each participating location. Figure 2.3 shows the cumulative particle size distributions (PSD) of both types of particles determined by a Malvern Instruments MasterSizer 2000, obtained before and after the experiments. The results indicate that the FCC particles became somewhat coarser, likely due to the entrainment of a small portion of small particles; whereas the sand particles became slightly finer, presumably due to attrition. However, as indicated in Table 2.1, the change in Sauter mean diameter was quite small (~ 9% for FCC and 6% for sand particles).   Table 2.1 – Experimental particle properties FCC Sand Supplier W.R. Grace Lane Mountain LM50 Sauter mean diameter, dsauter (μm) Before experiments: 98 After experiments:107 Before experiments: 312 After experiments:292 Particle density, ρp (kg/m3) 1560 2644 Bulk density, ρb (kg/m3) 851 1250 Minimum fluidization velocity, Umf (m/s) a 0.00606 0.0796 Minimum bubbling velocity Umb (m/s) b 0.028 (= Umf) Terminal settling velocity in air, Ut (m/s) c 0.44 0.73 Geldart classification Group A Group B Composition silica-alumina zeolite, trace metals 99.9% SiO2 Shape Nearly spherical Irregular a Calculated at 298 K and 1 atm using the correlation given by Grace (1982) b Measured as the minimum velocity at which the bubbles appear in the snapshots obtained by the X-ray imaging  c Calculated iteratively using drag coefficient as a function of Reynolds of particles  17  Particle diameter (m)10 100 1000 10000Volume (%)020406080100FCC after experimentsSand after experimentsFCC before experimentsSand before experiments Figure 2.3 – Cumulative particle size distribution. 2.3 Experimental operating conditions The experimental operating conditions were nearly identical at all measurement locations. The only minor difference consisted in using building compressed air instead of cylinder air for RPT and PEPT due to the prolonged total duration of each single run (8 h for RPT and 3.5 h for PEPT). Three different measurement heights were tested for measuring hydrodynamic features of the TFB operating at different superficial gas velocities, as indicated in Table 2.2. Table 2.2 – Experimental operating conditions Superficial gas velocities, Ug (m/s) FCC: 0.30, 0.40, 0.50, 0.60; Sand: 0.40, 0.50, 0.60 Static tapped bed height (m) FCC: 0.80 Sand: 0.82 Measurement heights, z (m) 0.24, 0.40, 0.56 Operating temperature (ºC) 25 ± 2 18  2.4 Measurement techniques 2.4.1  Voidage measurements The voidage measurement techniques employed in the first phase of the project consisted of electrical capacitance tomography (ECT) at the University of Saskatchewan (USask), X-ray computed tomography (XCT) at the University of Calgary (UC), optical fibre probes at the University of British Columbia (UBC), Ecole Polytechnique of Montreal (Poly) and University of Western Ontario (UWO) , radioactive particle tracking (RPT) at Poly and pressure drop at UBC. ECT and XCT represent non-invasive measurement techniques where the voidage is calculated respectively from the mixture capacitance and X-ray attenuation measurements, as reported by Dubrawski et al. (2013). All the optical probes used had dimensions much larger than particles diameter. However, the calibration method differed at each research laboratory (Dubrawski et al., 2013). RPT is mainly intended to measure particle velocity in gas-fluidized beds. However, the research group at Poly suggested a method which assumes that the voidage corresponding to the cell with the highest number of counts and lowest tracer velocity is equal to loose bulk voidage. The voidage in each individual cell is then determined by normalizing with respect to the voidage of the cell with the highest count. Details of the pressure drop measurements, performed by the author, are given in Section 2.4.4.                                                 This university has subsequently been renamed Western University. 19  2.4.2 Particle velocity measurements 2.4.2.1 Optical fibre probes (a) Fundamentals of optical fibre technique Optical fibre probes have been used widely for hydrodynamic characterization of gas-fluidized beds due to their simplicity and low cost. In order to measure the particle velocity, the optical probe should contain at least three fibres (or fibre bundles). A typical schematic showing three vertically aligned optical fibres is given in Figure 2.4. The central fibre illuminates the particles that pass close to the tip of the probe while the two outer fibres capture the light reflected by the particles.   Figure 2.4 – Optical fibre probe system configuration and schematic. For a particle moving with a constant speed along the direction connecting the two light-receiving fibres, the velocity (vp) is determined by: Signal Processing Probe Fluidization direction Optical Probe insertion (top view) Dipleg   20  ( )  ( ) 1/epllLa vb M f     (2.1) where f is the sampling frequency, τl is the particle transit time, Le is the effective distance between the light-receiving fibres (Figure 2.4) determined by calibration, and M is a positive integer which, when multiplied by the inverse of the frequency, provides the time lag between the two signals. τl is a discrete function of the frequency, with its value corresponding to the time lag between the two light-receiving fibres signals obtained by cross-correlation, as summarized by Ellis (2003) and Liu et al. (2003). Cross-correlation of signals obtained by the light-receiving fibres (A BI I ) is defined in Equation 2.2 as given by Bendat and Piersol (1986). The cross-correlation coefficient function (A BI I ) measures the degree of linear dependence between the two signals for different time lags τl.            01( )( )limA BA BA BTI I l A B lTI I l A BI I lA Ba I t I t dtTI t I tb           (2.2)  where IA and IB are the time-series of the signals associated with the two light-receiving fibres and σA and σB are the respective standard deviations. The time lag that maximizes the cross-correlation coefficient function is taken to represent the particle transition time and utilized for determining the particle velocity according to Equation 2.1. Sampling frequency and integration period are important parameters for determining accurate solid velocity. Their choice is dictated by the necessity of capturing instantaneous values of 21  particle velocity within a certain range of measurable values, according to the following equations (Liu et al., 2003):  ,, ,2( )( )ep minintp max p maxmineLa v Tv v Eb fL E       (2.3) where vp,min, vp,max, Tint and fmin are minimum and maximum measurable particle velocities, integration time and required sampling frequency, respectively. The parameter E represents the error, defined as the difference in velocity between two adjacent points in proximity of the maximum cross-correlation (Herbert et al., 1994), dictating the accuracy in determining the maximum solid velocity: 1 11eE f LM M        (2.4) Rearrangement of Equation 2.4 provides the relationship between sampling frequency and maximum measurable particle velocity for a given E, as indicated by Equation 2.3.  High particle velocity corresponds to low τl, and therefore to low M, as given by Equation 2.1. Equation 2.1 indicates that the higher the sampling frequency, the greater the multiplicand (M) corresponding to the transition time of a high-velocity particle, resulting in an increase of the number of points near the maximum cross-correlation coefficient and lower error (E).  22  A short Tint corresponds to a high vp,min; however, if the integration time is too long, no instantaneous velocity is detected since the signals would result from multiple particles moving with different velocities.  (b) Optical fibre methodology utilized for TFB experiments Measurements were obtained at the levels indicated in Table 2.2, at each of which the probe was inserted from ports located on the column perimeter (Figure 2.4) to measure the solid velocity at different radial locations along a diameter.  To calibrate the probe, as reported by Liu et al. (2003), a disc with a particle affixed was rotated at a known angular velocity, with the line connecting the light-receiving fibres aligned parallel to the direction of particle motion, simulating the movement of particles in the bed. A stepper motor and optical encoder were used to precisely control the rotation speed. Over a range of known linear velocities, using the cross-correlation method described before, the time lag between pairs of signals allows the effective distance (Le) between receiving ends of the probe to be determined.  Table 2.3 – Optical probe propertiesUnit PV-4A Measurement heights 3 (z = 0.24, 0.40 and 0.56 m) Probe type Fibre size similar to dsauter Sampling time, s 40 (80 × 0.5 s intervals) Probe specifications 3-fibre parallel dprobe: 4 mm dfibre: 280 μm Sampling frequency, kHz 15.6 (wall region) 62.5 (other positions) Glass window Yes Le, mm 0.38 Integration period, s 0.13 (wall region), 0.033 (other positions) Cross-sectional positions 7 23  Table 2.3 summarizes the properties of the optical probe and the data acquisition methodology employed in this study. For most radial positions, a sampling frequency of 62.5 kHz was employed. The exception was in the region close to the column wall, where, since the velocities were smaller in magnitude, the sampling frequency was lower, 15.6 kHz. Continuous data acquisition for 40 s was not compatible with the capabilities of the computer in use; therefore, the data were collected during 20 intervals of 2.09 s for the wall region (r/R = 0.83) and 80 × 0.52 s intervals for all other radial positions. Each interval was then divided into 16 sub-intervals that represent the integration time over which the signals were cross-correlated as indicated in Table 2.3. In agreement with those reported by Liu et al. (2003), values of Tint employed in this study could result in obtaining velocities of more than one particle, depending on their velocity.  The obtainable magnitude of velocities with a maximum tolerance for error (E) of 10% for the wall region are included in the interval Iw = [0.0058 m/s, 0.66 m/s] and for the other radial positions in the interval Ip = [0.023 m/s, 2.64 m/s]. Solid velocities corresponding to a maximum cross-correlation coefficient greater than 0.5 are considered to be valid, as in previous work by Liu et al. (2003).  In order to obtain a valid cross-correlation, the particles must move almost vertically in the measurement volume of the optical probes. If a particle is moving with too great a deviation angle with respect to the vertical direction, it is not detected in the second light-receiving fibre field of view, and no valid cross-correlation is then possible. The maximum deviation angle for which the particle movement is traceable by the optical probe is extremely important when comparing the results with other measurement techniques. For this purpose, experiments were carried out where the particles were poured vertically in front of the optical fibre probe mounted 24  with different inclination angles with respect to the vertical direction. The cross-correlation success at different deviation angles was quantified by considering the percentage of data that present a maximum cross-correlation coefficient greater than 0.5.  Figure 2.5 shows that for both FCC and sand particles, there was a sharp decrease in the percentage of valid velocity vectors for angles of deviation to the vertical exceeding 30 degrees. Deviation angle (deg)0 10 20 30 40 50 60 70Valid data fraction (%)020406080100FCCSand Figure 2.5 – Sensitivity to measurement angle of optical probe. 2.4.2.2 Borescopic high-speed Particle Image Velocimetry (PIV) (a) Fundamentals of borescopy A high-speed borescopic PIV system, owned and operated by Particulate Solid Research Inc. (PSRI) in Chicago, has been deployed to investigate the solid motion and cluster characteristics 25  of gas-fluidized beds (Cocco et al., 2010). This PIV system utilizes a high-speed, high-resolution Phantom v7.3 camera with a resolution up to 800 × 600 pixels. The video camera was coupled with an Olympus R100-038-000-50 industrial rigid borescope of 6 mm diameter in order to perform high-speed PIV measurements at different radial and axial locations inside the travelling fluidized bed. A Xenon light and an oil filled light pipe supplied intense light to the tip of the borescope to illuminate the particles and generate high-quality images. In order to prevent particles from blocking the illumination source, an optical spacer (Melles Griot) is fitted to the borescope. Vision Research Phantom Camera Control Software (ver. 9) is utilized for image downloading. This novel technique (Figure 2.6) facilitates optical access to the interior of a dense fluidized bed, which is otherwise impossible due to the opacity of the system.  Figure 2.6 – Borescopic high-speed PIV system configuration for TFB experiments. 26  (b) Borescopic high-speed PIV for TFB experiments The image capture rate was 3000 frames/s, with an exposure time of 10 μs. This rate was high enough to capture the highest particle velocities in the system. The total sampling period of the high-speed PIV was selected considering the number of data that had to be produced, memory needed for their storage and the time required for analysis. With axial-symmetry assumed for each measurement location, the total sampling period was 10 s, resulting from 10 one-second intervals of continuous acquisition. Each video corresponding to 1 s of data sampling occupied 0.5 GBytes of memory. Properties of the borescopic high-speed PIV system are summarized in Table 2.4. Table 2.4 – Borescopic high-speed PIV system properties Camera Phantom v7.3 Measurement heights 3 (z = 0.24, 0.40 & 0.56 m) Frame rate 3000 frames/s Sampling time 10 (10×1 s intervals) Camera resolution 256×256 pixels Borescope diameter 6 mm Exposure time 10 μs Region of interest 1.5 × 1.5 mm Cross-sectional positions 9 Glass window Yes FCC catalyst particles are often subject to substantial electrostatic forces which can cause particles to adhere to the tip of the borescope, blocking the view of the solid motion. Significant improvement was obtained by rubbing the borescope tip with an antistatic sheet (PSRI proprietary) every 2-3 runs, largely preventing particle adhesion.  Sand particles did not present any problem of adhesion to the borescope tip, but since they are white, the produced images were characterized by low contrast, resulting in poor particle boundary distinction. Antipolar filters mounted on the borescope window did not improve the 27  image quality. The best solution in terms of the image contrast was achieved by colouring all particles using a PSRI proprietary dark red dye which had negligible influence on the density of the particles, but may have altered the surface properties. The analysis of the high-speed PIV data consisted of conversion of the videos into consecutive grayscale images and determination of solid displacement for each pair of consecutive images using an open source Matlab code called PIVlab, developed by Thielicke and Stamhuise (2013), where the particle velocity is determined using a multiple pass interrogation method, based on a grid-refining scheme described by Raffel et al. (1998). The following points summarize the main steps for calculating the solid displacement from consecutive frames:  1. A region of interest of about 2 mm × 2 mm was chosen. A mask was used to prevent interference from outside regions.  2. An interrogation area as large as 1.5 mm × 1.5 mm capable of capturing the greatest particle displacement within the region of interest was chosen. 3. A standard interrogation was performed based on the cross-correlation peak detection from successive images. 4. The results of Step 3 were used as estimates for the next higher resolution level. The estimated displacement data were projected onto the next smaller interrogation area, and this procedure was repeated until the final image resolution was reached. 5. Each velocity vector refers to the displacement of the particles present in a dimension equal to the smallest pass at a certain position. 6. In regions where no particles were present, the software assigned a “Not a Number” (NaN) velocity value, which was then ignored in time averaging. The results containing 28  the instantaneous velocity vectors and the relative positions were saved into consecutive text files. Velocities more than three standard deviations from the mean were removed. 7. A Matlab code was then employed to calculate the time-average particle velocity at each radial position. As with RPT and PEPT, two values were calculated, one averaging the vertical component of all measured velocities and the other where only values with a deviation angle with respect to the vertical direction less than 30° were included, in order to compare with the optical probe data.   The choice for the final interrogation pass size depends on the particle image density. Below a certain number of particles present in the pass (typically N < 4), the displacement detection rate decreases significantly, as pointed out by Raffel et al. (1998).  Figure 2.7 shows typical images analyzed by PIVlab for both bed materials and the corresponding velocity maps. The vectors are present only in the region of interest where the image is in focus.   29     Figure 2.7 – Velocity vectors obtained by PIVlab in a region of interest for: (a) FCC; (b) sand.  2.4.2.3 Radioactive particle tracking (RPT) RPT experiments were carried out by the previous student involved in the TFB project (Dubrawski et al., 2013). However, the author was deeply involved in the interpretation and analysis of the RPT data especially for obtaining particle velocity and solid flux. Velocity magnitude, m/s Velocity magnitude, m/s 30  (a) Fundamentals of RPT Proton-deficient nuclides are unstable, spontaneously decaying to a more stable form, releasing their excess energy by emitting electrons and γ-rays. This principle is deployed by RPT in which an array of scintillation detectors is used to view a single radioactive particle and track its motion. The number of γ-ray counts C, recorded by a detector during a sampling time T from a point radioactive source of strength A placed inside the fluidized bed, depends on the distance between the source and the detector. It can be expressed by the following relationship (Larachi et al., 1996): 31iT ACAr nf dr          (2.5) where ν is the number of γ-rays emitted per disintegration; ζ is the total efficiency, i.e., the probability that the γ-ray emerges from the reactor without scattering and interacts with the detector; τ the dead-time per recorded pulse, ϕ the peak-to-total ratio; r the distance between the source and a point P on the outer surface of the detector crystal; fi the probability of non-interaction of γ-rays emitted within the elementary solid angle dΣ with the bed material and interaction with the detector; Ω the solid angle subtended by the detector surface; and n the external unit vector locally perpendicular to the solid angle. A given number of counts in one detector implies that the particle is located on an iso-count nearly-spherical surface. In principle, the position of the tracer particle can be determined as the intersection of the iso-count surfaces corresponding to three different detectors positioned around 31  the fluidized bed column. However, to achieve better accuracy in particle location, more than three detectors are generally employed. The number and the spatial configuration of the detectors array are essential for obtaining the maximum resolution of the RPT system. Theoretical models based on Monte-Carlo simulations are used to find the optimal arrangement of the detectors as indicated by Roy et al. (2002). Three methods have been employed in the RPT technique to determine the location of the tracer particle using the number of counts recorded by the detectors. A detailed description of each location algorithm was given by Larachi et al. (1996). In the first, the detector is considered as a “virtual point” and the distance from the tracer particle as a polynomial function of the number of counts. For each detector, a polynomial is fitted to the calibration data obtained by locating the tracer at known locations in the column, and the position is computed using a weighted least-squares approach. The second method employs a rigorous phenomenological approach in which a map of detector counts versus tracer position is generated by Monte Carlo calculation and is adjusted to calibration measurements. The location of the tracer is then determined by a least-squares search for the grid point on the map which best matches the registered counts in the detectors. The third method differs from the second method, with the least-squares search replaced by a direct and faster back-projection neural network model.  (b) RPT methodology utilized for TFB experiments In this study, sodium iodide (NaI) scintillation detectors, whose details are given by Larachi et al. (1996), were arranged in a spiral pattern along the column covering the full height of the dense bed section. The coordinates of these detectors are listed in Table 2.5.  32  Figure 2.8 provides a plan view of the detector arrangement. The centre of the distributor plate was chosen as the (x,y,z) = (0,0,0) origin for the system.  Figure 2.8 – Plan view showing NaI detectors deployed around TFB column (adapted from Dubrawski et al., 2013).  Table 2.5  – Origin and RPT detector locations  x (mm) y (mm) z (mm) Centre of distributor grid plate 0 0 0 Detector 1 240.3 0 91.8 Detector 2 0 238.2 221.5 Detector 3 218.8 0 331.1 Detector 4 0 201 459.8 Detector 5 237.4 0 607.2 Detector 6 0 241.1 724.3 Detector 7 221.1 0 827.3 Detector 8 0 241.2 956.2 The first localization approach outlined in the previous section is deployed to determine the tracer position as a function of time during the experiments. The coefficients of the polynomial z = 91.8 mm z = 221.5 mm z =331.1 mm z = 459.8 mm z = 956.2 mm z = 827.3 mm z = 724.3 mm z = 607.2 mm33  function were determined by calibrating the detectors to locate the tracer at 73 specific locations in the dense bed section, for each superficial gas velocity and each bed material. Several tracers were considered based on previous experience. Gold is much denser than the particles employed in this study. Any form of powder/epoxy combination was rejected due to radiation embrittlement of epoxy resin. Pure scandium, obtained from Alfa Aesar and characterized by a half-life of 83.3 days (Larachi et al., 1996), was selected as the tracer particle. The half-life of the tracer particle was long enough that any change in signal strength over the measurement period could be ignored. Samples were cut mechanically under magnification to provide the particle sizes of interest. The samples were irradiated to 200 µCi at McMaster University in Hamilton, Ontario. Since pure scandium has a density of 2990 kg/m3, the tracer was immersed in epoxy resin (density ≈ 750 kg/m3) post-irradiation to decrease the net particle density, in order to better match that of the experimental bed particles. Since tracer particles smaller than 400 µm could not be handled safely, scandium particles as small as ~250 µm in diameter were dipped into epoxy, making nearly spherical tracer particles of ~400 µm diameter, with a composite density of ~2000 kg/m3. Physical properties of the tracer particle are reported in Table 2.6. Single tracer particles from the same batch were used for both the FCC and sand particle experiments.  Table 2.6 –RPT tracer particle physical properties  RPT Tracer dsauter (μm) 400 ρp (kg/m3) 2000 Ut (m/s) 2.35 shape spherical 34  NaI detection amplifiers were calibrated to accommodate the voltage range for scandium, with the upper and lower limits of the amplifiers set at 4.4 and 9.8 V. The measuring region was then set to between 5.0 and 6.5 V, with the remainder filtered out.   The duration of each test was 4 hours; whereas, the time interval between each successive data acquisition (Δt) was 10 ms. Each test was repeated, yielding a total sampling period of 8 h.  The radial profile of particle velocity was correlated at the same measurement heights as those obtained from invasive probes using a Matlab code. The most important steps for correlating the radial profiles include: (i) The tracer position coordinate matrix was fed into the program, with the instantaneous particle velocity calculated from successive positions of the tracer particle as: 1,1,,1i ip xi ip p yp zi ix xtvy yv vtvz zt                     (2.6) (ii) When and only when the tracer crosses a specific measurement level, the coordinates of the tracer particle were saved. Velocity components were then calculated from successive positions. Outliers more than 3 standard deviations from the mean were filtered out. (iii) Two types of averaging were conducted: for the first type, the vertical components of velocity of all particles crossing the plane of interest were averaged; in the second 35  method, only the velocity vectors with small deviation angles (< 30°) with respect to the vertical direction were considered, in order to provide direct comparison with the optical probe data. (iv) The column cross-sectional area was divided into four concentric areas of equal cross-sectional area. Later, dividing the area into five concentric annuli was also tested. The velocity vectors of the tracer crossing each measurement plane with its centre inside each of the concentric areas were counted and averaged in each case. The alternative volume-based algorithm, commonly used to determine the solid motion in fluidized beds from particle tracking techniques, divides the whole column into a mesh consisting of small cells of finite volume (e.g. 30 mm × 30 mm × 30 mm) and calculates the local time-average velocity considering the tracer velocity every time that it is inside the cell of interest during the data sampling period (Larachi et al., 1996). In this study, however, the crossing-level algorithm described by (i-iv) above was mainly employed for the following reasons:   The particle tracking data must be comparable to those obtained by the invasive techniques in terms of the measurement volume. The optical probe and the borescope produce zero-volume point measurements at the levels of interest and condition (ii) stated in the algorithm produces a similar measurement volume corresponding to a zero-width plane.   If instead of requiring the condition (ii) stated above, we calculate the velocity of the tracer when it is present in an annulus of a finite (e.g. 30 mm) thickness, the number of experimental velocity vectors increases substantially. However, considering a certain 36  region, since the slowly moving particles spend more time therein compared to the high-velocity ones, the time-average solid velocity is then biased towards low-velocity vectors. This condition is totally absent in optical probe data since the velocity vector corresponding to a certain particle is calculated exclusively once due to the cross-correlation criteria. The borescopic PIV analysis has the tendency to count low-velocity vectors more often than other ones. However, taking into account the sampling frequency of each measurement technique, in order to make particle tracking techniques data obtained from volume-based approach comparable to those of borescopy, the height of the cell must be chosen in a way to result in the same proportion between the number of slow and fast particles. This is not trivial, since unlike RPT and borescopy, as reported in the next section, the PEPT sampling frequency is variable in time.  2.4.2.4 Positron emission particle tracking (PEPT) (a) Fundamentals of PEPT Positron emission particle tracking (PEPT), similar to RPT, allows non-invasive observation of a single radioactive tracer particle within the domain of the fluidized bed. The physical principle of PEPT differs slightly from RPT since the radioactive particle contains neutron-deficient nuclei that undergo β-decay, accompanied by positron emission. Any positron emitted by β-decay combines with its antiparticle (electron) generating two back-to-back 0.511 MeV γ-rays. The difference in emission mechanism, which is based on single photon emission for RPT and dual photon emission for PEPT, affects the method of detection and arrangement of sensors for particle tracking (Larachi et al., 1996).  37  The algorithm for tracer particle tracking was developed by the Positron Imaging Centre of the University of Birmingham (Parker et al., 1993, 2002). The essential ideas for the interpretation of the results of this study follow.  Simultaneous detection of γ-rays resulting from positron annihilation delineates a trajectory called Line of Response (LoR). The position of the annihilation site (radioactive particle) must in principle lie along the LoR. Ideally, the position of a stationary particle can be detected from the intersection point of only two LoRs. However, some detected events are corrupt (due to scatter, random coincidences, etc.) and due to the finite spatial resolution of the detector and positron range, the LoRs surround the true position of the tracer at a certain instant. The PEPT algorithm rejects these corrupt trajectories and locates the tracer particles based upon the set of remaining LoRs. Starting with a small set, S, containing N sequential LoRs, the minimum distance point, mS, is calculated as the point in space that minimizes the sum: ( )S iSD m  (2.7) where δi(m) is the distance of the ith trajectory from point m. The mean deviation of these trajectories from mS is defined as: SSDd N  (2.8) The minimum distance point is considered as the first estimate of the tracer location. Trajectories that lie furthest from mS are considered to be corrupt and are removed from the set. The 38  discarded trajectories are those for which δi (mS) is larger than k∙dS, where k is a fixed parameter whose optimal value is 1.2 for most situations (Parker et al., 1993). The minimum distance point is then re-evaluated from the new set of LoRs. This iteration process continues until a predefined fraction, fopt, of the sample S remains. The final mS position is calculated from the last fraction of N (fopt×N), with precision Δ given by the average perpendicular distance from this point to each LoR in the final set. For a stationary particle, Δ is given (Leadbeater et al., 2012) by: Δoptwf N   (2.9) where w is the intrinsic spatial resolution of the detection camera of around 8 mm (Parker et al., 2002; Leadbeater, 2014). The value of fopt depends on the proportion of corrupt events, and it is determined for each bed material considering the maximum location accuracy of a stationary tracer inserted in the bed as a function of final fraction of γ-rays (Leadbeater et al., 2012).  From Equation 2.9 it can be observed that for a stationary particle, as expected, the higher the sample size the smaller the error in tracer location. With moving tracers, the LoRs in each set of events are distributed along the particle trajectory. Therefore, the final set of LoRs does not converge into a single point, but surrounds a volume around the minimum distance point given by location precision Δ. The value of N must be reduced for moving tracer particles to deal with the movement. An exact theoretical argument for optimising N as a function of particle speed has not been found (Leadbeater and Parker, 2013). Therefore, the logic presented in the next section has been taken into account for selecting an adequate value of N for each experimental run.  39  (b) PEPT methodology utilized for TFB experiments Experiments were conducted using the ADAC Forte dual-headed gamma camera owned by the Positron Imaging Centre of the University of Birmingham (Figure 2.9). This camera consists of two gamma camera heads mounted on a motorized gantry which permits the face-to-face separation of the detectors to be varied from 250 to 800 mm. Each head contains a single NaI crystal, 16 mm thick and approximately 500 × 400 mm2, optically coupled to an array of 55 photomultiplier tubes. A detailed description of the positron camera can be found in the literature (Stein et al., 1996; Parker et al., 2002; Leadbeater et al., 2012).  Figure 2.9 – PEPT system configuration for TFB experiments. For both bed materials used in our TFB experiments, an optimum fraction fopt = 0.12 was obtained as the value that minimized the standard deviation of a stationary tracer location. The PEPT detector and camera 40  fopt obtained for the stationary particle was applied to the analysis with moving tracer at all superficial gas velocities (Parker et al., 1993).  For each superficial gas velocity, data were acquired with the system operated for a total of 3.5 hours, comprising three runs lasting 1 hour and a final run lasting 30 minutes. For each experimental run, the average coincidence rate, i.e., rate at which both pairs of γ-rays are simultaneously detected, was noted. Assuming that the uncertainty in location for a moving particle follows the same formalism as for a stationary particle, Δ was calculated for different values of N. Small values of N result in more detected positions of the moving tracer, but may result in a significant decrease in location precision due to lack of enough LoRs for the calculation. High N provides enough LoRs for the particle location, but may reduce the precision due to movement of the tracer particle during the time defined by the set size.  In this study, the initial sample size was chosen considering that its value should result in a reasonable localization rate and that the distance travelled between successive locations must be greater than 2Δ (with Δ obtained from Equation 2.9) for all tracer velocities greater than 0.01m/s. For each run, data for which the measured Δ was greater than three times the standard deviation of the location uncertainties were rejected.  The analysis of the raw data was performed using overlapping sets to increase position sampling, with each set of LoRs starting one-fifth of the way through the previous set (Stein et al., 1996). Note that the resulting tracer locations, unlike RPT, are not equally spaced in time, but each corresponds to a precise time given by the average of the times of the annihilation vectors used in each set, producing data of the form (x,y,z,t). Once the raw data are analyzed with specific criteria given by the input parameters such as N, fopt and number of overlapping sets, a matrix 41  with instantaneous spatial positions of the tracer particle and the location precision is generated. From successive tracer locations, the instantaneous tracer particle velocity can be calculated. For overlapping sets, the tracer particle velocity is obtained by comparing 11 consecutive locations and performing a weighted rolling average of six estimates of the resulting velocities: 5 4 1 3 25 4 1 3 22 3 1 4 52 3 1 4 50.1 0.15 0.250.25  0.15 0.1i i i i i ipi i i i i ii i i i i ii i i i i iP P P P P Pvt t t t t tP P P P P Pt t t t t t                                                                          (2.10) Here pv and iP represent the particle velocity and location at instant ti. The rest of the algorithm for deriving the radial profile of time-average solid velocity at each superficial gas velocity was exactly the same as that used for RPT.  Equation 2.10 indicates that pv is calculated as a weighted combination of positions at different instants. Since the instantaneous location uncertainty, given by the average perpendicular distance from the mS point to each LoR, is available for all tracer locations, the accuracy in any single velocity determination could be determined using an error propagation formula based on the assumption of independent successive measurements, valid for our experiments:                                                 For RPT, Equation 2.6 was preferred to the weighted rolling average method used for PEPT, since the RPT sampling rate was fixed at 100 Hz and in certain cases was much slower than for PEPT. Therefore, Equation 2.10 could result in loss of instantaneous information for RPT. Nevertheless, the 6-point averaging method was tested for RPT, but it did not result in any improvement of the results in terms of comparison with the data from the other techniques. 42   52 25pj i jvjc       (2.11) The coefficients cj are the multiplicands, whereas Δi+j is the location uncertainty associated with the 11 tracer positions used to determine the particle velocity in Equation 2.10.  Neither sand nor FCC particles could be activated enough for the PEPT experiments. Therefore, Dowex SBR strong base (OH- form) anionic exchange resin beads for FCC and Aluminium oxide, superactivated base form (gamma-alumina) for the sand experiments were used as tracer particles. The properties of the tracer particles for different runs are given in Table 2.4. The size of the resin tracer particle matched well the average size of the FCC particles, but the particle density was considerably lower. The gamma-alumina tracer was slightly bigger and denser than the sand particles. All tracers were radio-labelled using an indirect activation approach, involving the exposure of the tracer to a dilute aqueous solution of 18F with a half-life of 110 minutes (Leadbeater et al., 2012), prepared by direct bombardment of ultrapure water at the University of Birmingham cyclotron. One tracer was employed during experiments corresponding to 4-9 hours operation. Therefore, there was appreciable loss of signal strength from the beginning to the end of each experimental run, but not enough to affect tracer particle localization within acceptable spatial resolution.    43  Table 2.7 – Properties of radioactive tracer particles in the PEPT experiments  Dowex SBR  resin beads (used with FCC fluidized bed) γ -Al2O3 (used with sand fluidized bed) First day run radioactivity (mCi) 1.20 1.34 Second day run radioactivity (mCi) 0.205 0.598 dsauter (μm) 100 300 ρp (kg/m3) 1100 3000 Ut (m/s) 0.31 0.91 Shape Spherical Irregular 2.4.3 Solid flux measurements Results provided by PEPT, RPT and borescopy can be further analyzed to obtain two other important hydrodynamic parameters: solid mass flux and momentum flux. 2.4.3.1 Borescopy methodology for determining solid flux Local instantaneous solid mass (Gs) and momentum (Fs) flux are defined as: 2( ) ( )[1 ( )]( ) ( )[1 ( )]s p ps p pG t v t tF t v t t     (2.12) where ρp, vp(t) and ε(t) represent the particle density, instantaneous particle velocity and voidage, respectively. The borescopy delivers mainly local instantaneous 2-D snapshots of particles at the surface of the borescope recorded at 3000 frame/s as shown in Figure 2.7. Due to reflectance of the light by particles close to the borescope tip, the depth of field is extremely small. Determination of voidage, a 3-D quantity, is possible if the total area of the plane covered by particles in each frame (Ap) and depth of field can be determined (Hoomans et al., 1996; Ouyang and Li, 1999). Different methods may be deployed to determine Ap (Casleton et al., 2010). Global thresholding and edge detection are among the methods frequently used for this purpose. 44  Edge detection was extremely challenging for the images obtained in this study because of the absence of distinguishable edges between particles. Thresholding transforms grayscale images into binary images using an intensity-based criterion. In-focus particles have a higher intensity than out-of-focus ones since they are closer to the light source. In this method a threshold is chosen as the intensity above which particles are considered to be in-focus, and therefore the relative pixels are transformed to intensity equal to 1 in a binary image, whereas all other pixels below the threshold value are considered to represent voids (zero intensity). Determination of a suitable threshold is therefore extremely important for this method.  The most popular thresholding technique is the Otsu (1975) method, which assumes that the intensity distribution of the image is bimodal, and determines the threshold value that maximizes the variance between the two modes. However, this method failed in our case because of the absence of a bimodal intensity distribution when the image corresponds to the borescope tip entirely occupied by dense phase or voids (Figure 2.10).      Figure 2.10 – Example of Otsu method failure applied to a snapshot corresponding to an extremely dilute flow. 45  In this study the threshold for different images was chosen based on the average image grayscale intensity. For this purpose, grayscale images of both bed solid materials obtained by the borescope and a series of relative binarized images using different threshold values were provided to a panel of judges. For each image, each judge, based on visual inspection, selected the binary image best representing the original grayscale image, considering the constraint of zero-depth of field. The results of the survey were then collected, and for each image the threshold value obtained from the weighted average was used to find a correlation that could be implemented as the thresholding algorithm. As shown in Figure 2.11, a linear correlation provides a good representation of the data. The error bars on each data point represent the ± 90% confidence interval based on the scatter among different judgments.  FCCGrayscale intensity0 10 20 30 40 50 60 70Threshold value0.080.120.160.200.240.28Regression line, R2=0.86SandGrayscale intensity0 20 40 60 80 100 120 140Threshold value0.200.240.280.320.360.400.44Regression line, R2=0.93 Figure 2.11 – Borescopic threshold as a function of average image grayscale intensity                                                  Members of UBC Fluidization Research Centre and PSRI, actively engaged in fluidization hydrodynamic research.  46  Figure 2.12 shows selected examples of frames obtained by the borescope and the binarized image based on the linear correlation.                                      Figure 2.12 –Binarization of images obtained by borescope based on average intensity threshold for: (a) FCC; and (b) sand particles. Once binarized, the solid area fraction (Ψp) in each image defined as the total area occupied by the particles (Ap) divided by the area of the image (Atot) is calculated: pptotAA   (2.13) The voidage (ε) is a 3D measurement of the empty space, dependent on the particle volume concentration. Therefore, the 2D solid area fraction must be transformed into a 3D volume void fraction (ɛ). Different approaches have been proposed for obtaining ε from Ψp, mostly arising from 2D flow simulations. For FCC particles, we used the Hoomans et al. (1996) correlation: 47  3/2213p     (2.14) Equation 2.14 was derived based on a comparison between a hexagonal (two-dimensional) lattice and an FCC (three-dimensional) unit cube assuming equal distance between particles.  Since Equation 2.14 was evaluated specifically for FCC particles, for sand particles, more physically reasonable results (all ε ≥ εmf) could be obtained from a correlation of Ouyang and Li (1999): 3/2213p     (2.15) This correlation was obtained by comparing a two-dimensional hexagonal lattice with a three-dimensional hexagonal packed structure in which the layer space is 4/√3 times the lattice space. Particle velocity and voidage obtained for each frame were used to determine solid mass and momentum flux for ascending and descending particles, given by Equation 2.12. 2.4.3.2 PEPT and RPT methodology for determining solid flux A simple novel algorithm has been implemented for inferring solid mass and momentum flux based on the results obtained by RPT and PEPT. Providing that the tracer particle is representative of the bed material, the solid flux can be obtained from the particle tracking data as follows: Let subscript i denote the height of interest. Let j denote the cross-sectional area cell, numbered outwards from the centre from 1 to J, where J is the total number of cells. 48  Let mp be the mass of a single particle (such as the tracer particle), Mp be the total mass of all particles in the bed, v(i, j) be the measured vertical component of the tracer velocity as it crosses level z within cell j in an upwards direction, v(i, j) be the measured vertical component of the tracer velocity as it crosses level i within cell j in a downwards direction, n(i, j) be the number of times the tracer particle passes upwards through cell j at level i, n(i, j) be the number of times the tracer particle passes downwards through cell j at level i, T be the total time over which the measurements are taken, and S(j) be the cross-sectional area of the jth cell. The total cross-sectional area of the column (Stot) is then simply:  1JtotjS S j  (2.16) The upwards and downwards mass fluxes due to a tracer particle rising and descending through cell (i, j) [ ] and upwards and downward mass fluxes due to all particles through cell (i, j) [ ] are given by: ( , )( , )[ ( ) ]( , )( , )[ ( ) ]( , )( , ) ( / ) ( , )[ ( ) ]( , ) ( , ) ( / ) ( , )[ ( ) ]pppp ppp pm n i jg i jS j Tm n i jg i jS j TM n i jG i j M m g i jS j TM n i jG i j M m g i jS j T                    (2.17) The net particle mass flux through cell (i, j) [Gs(i, j)] and its integral over the whole cross-section [Gs(i)] are then defined as:  ),(,jig ),(,jiG 49     ( , ) ( , ) ( , )1( ) ,sJs sj itotG i j G i j G i jG i G i j S jS       (2.18) The net mass flux over the whole cross-section at height i [G (i)] should be 0 at each level for conservation of mass, with negligible entrainment and return of particles respectively above and below level i. An analogous method is used to obtain the momentum flux. Upwards and downwards momentum fluxes due to the tracer particle passing through cell (i, j) [ ] and upwards and downwards momentum fluxes due to all particles in the bed through cell (i, j) [ ] are defined as:                     ,,,,,. ( / ) ,,. ( / ) ,pppp ppp pm v i jf i jS j Tm v i jf i jS j TM v i jF i j M m f i jS j TM v i jF i j M m f i jS j T                      (2.19) Equations 2.16 to 2.19 are implemented in Matlab, with the cross-section divided into eight annuli of equal area, assuming axial-symmetry and counting the ascending and descending particles when they cross the same measurement levels as were used for the borescope measurements.  jif , , ,F i j 50  2.4.4 Dynamic pressure measurement Differential pressure transducers, situated at different sections of the column wall, were employed to obtain: 1) dynamic pressure fluctuations; and 2) time-average pressure drops.  The maximum standard deviation of pressure fluctuations across the bed as a function of gas velocity is generally accepted to indicate the transition from bubbling to the turbulent fluidization flow regime, as reported in the literature (Johnsson et al., 2000; Ellis, 2003). Ignoring the acceleration term and with p >> , we can use the time-average pressure drop, (ΔPi,i+1), between two axial positions separated by Δzi,i+1 to estimate the average voidage in the intervening volume, i.e. , 1, 1, 11 i ii ip i iPg z    (2.20) Microswitch USA, differential transducers provided by OMEGA Engineering Inc. were situated on the column wall providing dynamic pressure measurements between ports at 0.16 m intervals covering the height of the dense bed section. Data were obtained at a sampling rate of 100 Hz for 60 s intervals. The pressure probes were purged with air at a velocity of 0.5 m/s in order to prevent particles from entering the sampling tube. 51  2.4.5 Fast X-ray imaging (a) Fundamentals of fast-X-ray imaging X-rays are electromagnetic waves generated using an X-ray tube: a vacuum tube across which a high voltage is imposed in order to accelerate electrons released from a hot cathode. The high velocity electrons then collide with the anode to release high-energy photons. X-ray imaging has been applied extensively for hydrodynamic study of gas-fluidized beds. For example, X-rays have been deployed to investigate instantaneous and time-average voidage distribution, bubble size and velocity, interaction of bubbles with immersed surfaces and the voidage distribution around bubbles (Rowe and Everett, 1972; Yates, 1996; Yates et al., 2002; Lettieri and Yates, 2013). In this technique, a rotating anode is used to produce a high-energy cone-shaped pulsed X-ray beam (50-150 kV) which is flashed into the fluidized bed vessel. The fluidized bed attenuates the flashed X-ray beams, and the transmitted beams are collected on an X-ray image intensifier, optically coupled with a high-speed charge coupled device (CCD) camera that can acquire images at up to 72 frames/s. The image intensifier comprises a scintillator input window, a photocathode, electron optics, a luminescent screen and an output window, all contained in an evacuated enclosure. The spatial resolution of the system is 100 μm. The configuration of the X-ray system deployed for this study is shown schematically in Figure 2.13.  The voltage applied between the cathode and anode determines the acceleration of the electrons, and hence the energy spectrum of the X-ray beams. The voltage must be chosen adequately for the studied system depending on the geometry and physical characteristics of the materials 52  present. If the voltage is too low, the X-ray beam will have insufficient power to penetrate the column and fluidized bed, resulting in a poor-quality image. Extremely high voltages result in insufficient attenuation of the X-ray beam, leading to a poor-contrast image, lacking specific details. The brightness and resolution of the image depend also on the applied current, which represents the number of electrons hitting the anode.      53    Boundary of insertion port Schematic of optical probe a) Side view   Figure 2.13 – X-ray system configuration and optical probe insertion schematic. Source to Intensifier Distance (SID): 0.78 m, Object to Intensifier Distance (OID): 0.10 m.  X-ray source Inserted probe Insertion port b) Top view p1 p2 p3 SID OID Image intensifier Fluidized bed column 54  The images collected on the image intensifier and recorded by the CCD camera need to be processed in order to be able to obtain quantitative hydrodynamic information. Factors that need to be taken into account are:  Non-uniform image intensity Image intensity varies over the cone-beam, with higher intensities associated with the beams passing through the edges of the column. The variation in intensity is due to differences in path length, p, due to the diverging conical shape of the X-ray beam and the geometry of the studied system. From Figure 2.13 it can be observed that the differences between the distance travelled by three sample beams with p3 ˂ p2 ˂ p1, result in different degrees of beam attenuation through the object.   Geometric image lack of sharpness Since the focal spot, defined as the area of the anode on which electrons impinge, has a finite size, a penumbra is formed at the edges of the image resulting in geometric lack of sharpness. The smaller the focal spot, the smaller the penumbra, hence the better the image resolution. However, there is a trade-off between obtaining a small focal spot and the X-ray power, since concentrating a high power beam into a small area may cause the anode to melt. The size of the penumbra can be reduced by increasing the source-to-intensifier distance (SID).    Pin-cushion distortion The curvature of the X-ray image intensifier introduces a pin-cushion distortion due to non-linear magnification across the image, with the image magnified more at its periphery than at its centre. The pin-cushion distortion can be reduced by decreasing the object-to-55  intensifier distance (OID) and increasing SID. Different approaches can be used to correct this distortion (Soimu et al., 2003; Yoneyama et al., 2006; Park et al., 2009).  X-rays, passing through the system are attenuated by the particulate material based on absorption, reflection and scattering. The degree of attenuation depends on the chemical nature of the bed material, as well as the voidage along the path and the path length. The X-ray beam that emerges from the fluidized bed is amplified by the image intensifier that produces a grayscale image recorded by a CCD camera synchronized with the X-ray source. Attenuation of X-ray beams follows the Beer-Lambert equation: 0 exp( )m bI I l    (2.21) where I is the transmitted intensity, I0 the incident intensity, μm the attenuation coefficient of the particulate material, ρb its bulk density and l the path length of the X-ray beam through the object. X-ray attenuation by the column walls was negligible in this study since images of the empty column were characterized by the maximum intensity I0. Equation 2.21 can be expanded as follows neglecting second and higher order terms as reported by Yates et al. (2002): 0 0( )(1 )m pI I I l      (2.22) Here ε represents the average voidage along the path length and ρp the particle density. The average voidage corresponding to each path length can be obtained once a reference image of the packed bed with known voidage has been acquired for both particulate materials. 56  (b) X-ray imaging for TFB experiments The X-ray generation system used in this study provided X-ray pulses as brief as 500 μs in duration, with a maximum intensity of 450 mA at a voltage that could be varied from 50 to 150 kV. A latest generation 0.30 m X-ray image intensifier, optically coupled with a 1024 × 1024 pixel high-speed CCD camera was employed to collect the images corresponding to the X-rays transmitted from the fluidized bed at 72 frames/s. The values of current and voltage employed in this study were chosen based on visual inspection of the images corresponding to the fluidized bed operating at different superficial gas velocities (current = 150 mA, voltage = 80 kV for FCC and 55 kV for sand).  To correct for non-uniform image intensity with both particulate materials, an image of a packed bed with the same current and voltage values as indicated above was acquired and subtracted from single images obtained from the fluidized bed at different superficial gas velocities. A global correction method applying a barrel distortion (Ojanen, 1999), with appropriate distortion parameter to each single image, is employed to correct for the pin-cushion distortion, as shown in Figure 2.14 for a sample perforated plate with holes of 2 mm diameter arranged on a 10 mm square pitch. SID and OID values were chosen (SID = 0.78m, OID = 0.10 m) considering the geometry of the system in order to limit pincushion distortion and geometric lack of sharpness.  57   Figure 2.14 – Pincushion distortion correction: (a) original image; (b) corrected image. The red grid is intended to check the alignment of the points. The following paragraphs report how X-ray imaging was employed to study and characterize the TFB. All algorithms for image processing and analysis were implemented in Matlab. (c) Degree of interference of invasive probes The degree of interference of invasive probes with the flow patterns was investigated in terms of time-average voidage distribution. To achieve this, both FCC and sand fluidized beds was operated at different superficial gas velocities (Ug), and images of the same section of the column were obtained under the operating conditions of interest, with and without the presence of the optical fibre probe described in Section 2.4.2.1(b). The probe was inserted at 0.56 m above the distributor plate with its tip situated at the column centre. The probe axis was perpendicular to the X-ray source axis as indicated in Figure 2.13 (b). (a) (b) 58  (d) Fluidization flow regime transitions The transition from bubbling to turbulent fluidization flow regime was studied by qualitative and quantitative statistical analysis of the images corresponding to the same section of the column where the pressure fluctuations were measured for the same purpose.  Kurtosis, skewness and Shannon entropy of time series of fluidized beds local hydrodynamic parameters represent statistical tools, sometimes used for demarcation of the various flow regimes (Ellis et al., 2003; Zhong et al., 2009; Duan and Cong, 2013). All X-ray images obtained for a certain Ug at 72 frames/s for 10 s were considered, with the grayscale intensity probability distribution function (PDF) of each frame analyzed in terms of these statistical parameters:  Kurtosis: Kurtosis (β2) is defined as the standardized fourth population moment about the mean:   442 2 42XX    (2.23) where <> is the expectation operator, μ is the mean, μ4 is the fourth moment about the mean, and σ is the standard deviation. Since the normal distribution has a kurtosis of 3, the normalized kurtosis (γ2 = β2 − 3) is often used so that a normal distribution has a kurtosis of zero. De Carlo (1997) compared sample distributions characterized by positive and negative normalized kurtosis with the normal distribution. A distribution with positive kurtosis is characterized by heavier tails and a higher peak compared to one with a normal distribution, whereas a distribution with a negative kurtosis has lower tails and a flatter shape. A simple example of negative kurtosis is the 59  continuous uniform (rectangular) distribution (γ2 = −1.2). For symmetric distributions, positive kurtosis indicates extra weight in the tails, whereas negative kurtosis denotes lighter tales than in normal distributions.  Skewness The degree of asymmetry of a PDF is quantified by the skewness coefficient (γ1):    331 3/2 32XX   (2.24) where μ3 is the third moment about the mean The coefficient γ1 is positive or negative according to whether the tail of the distribution points to the right or left.  Shannon Entropy The entropy (H) of each frame grayscale intensity PDF was calculated according to the definition given by Shannon (2001): 21logni iiH p p    (2.25) where pi represent the probability of class i of the distribution from a total of n classes. The entropy defined by Equation 2.25 is characterized by different properties such as: 1. H = 0 if and only if all pi’s but one (having a value of unity) are equal to zero, i.e., only when the PDF of the grayscale image presents one single intensity. 60  2. For a given n, H reaches a maximum and is equal to log2n when all pi’s are equal. This corresponds to an image with all grayscale intensities of equal weight. Entropy defined by Equation 2.25 represents the degree of randomness of the PDF and increases as flow structures become more uniform. (e) Cross-sectional  time-average voidage The time-average cross-sectional voidage at each superficial gas velocity was obtained from the analysis of X-ray images, and these values were compared with the results obtained by pressure drop (Equation 2.20), borescopy and the other techniques employed by Dubrawski et al. (2013). 61  Chapter 3: Flow regime characterization, voidage distribution and interference of invasive probes with flow structures This chapter addresses several subjects important for understanding the later chapters. It first deals with the flow regimes for the chosen operating conditions and particles. Then it adds to the earlier work (Dubrawski et al., 2013) by comparing two other methods for determining voidage. Finally, X-rays are used to investigate the extent to which invasive probes interfere with the hydrodynamics they are supposed to study.  3.1 Fluidization flow regime In this section, the travelling fluidized bed is characterized in terms of fluidization flow regimes associated with the superficial gas velocities employed in this study. Sub-section 3.1.1 analyzes pressure fluctuations, a well-known method to characterize different fluidization flow regimes and to determine the onset of the turbulent regime. Section 3.1.2 provides an alternative viewpoint where quantitative and qualitative analyses of the snapshots obtained by X-ray imaging are employed to determine the flow regimes associated with the operation of the TFB. 3.1.1 Pressure fluctuations for flow regime determination Pressure fluctuations in bubbling fluidized beds are generally attributed to passage of bubbles and compression waves originating from bubble coalescence, splitting, eruption and flowrate fluctuations (Bi, 2007). Transition from the bubbling to the turbulent fluidization flow regime corresponds to the breakdown of bubbles into smaller transient voids. It is widely accepted that the onset of the transition to the turbulent fluidization flow regime occurs at Uc, the superficial 62  gas velocity at which the standard deviation of pressure fluctuations reaches a maximum (Bi and Grace, 1995). Differential pressure transducers filter out most pressure signals due to pressure waves (Bi et al., 1995), so fluctuations are almost entirely attributable to local phenomena such as passing bubbles. This is in agreement with previously reported findings (Bi et al., 1995; Ellis, 2003; Zhu and Zhu, 2008), showing that the break-up of bubbles and the transition to the turbulent fluidization flow regime starts at higher elevations, then migrates downwards in the fluidized bed. Figure 3.1 suggests that the superficial velocity at the onset of turbulent fluidization is ~0.68 m/s for FCC and ~0.78 m/s for sand particles. Quadratic polynomial regression line (R2 = 0.83 for FCC and 0.92 for sand) have been added to the plots in order to depict the qualitative trend. The amplitude of pressure fluctuations was greater for sand particles, for which particle density was higher and larger bubbles were observed. FCCUg (m/s)0.2 0.4 0.6 0.8 1.0Standard deviation (kPa)0.00.20.40.60.81.0SandUg (m/s)0.4 0.6 0.8 1.0Standard deviation (kPa)1.01.21.41.61.8 Figure 3.1 – Standard deviation of differential pressure fluctuations for measurements between z = 0.56 and z = 0.72 m for: (a) FCC; and (b) sand. For the sand particles, the presence of square-nosed slugs visually observed from the X-ray images for some of the superficial gas velocities of this study (see Section 3.1.2), was consistent 63  with the pressure fluctuation data and the relative Fast Fourier Transform (FFT) analysis presented in Figure 3.2. This figure indicates a more periodic pressure fluctuation time-series for the sand, with the frequency confined to a narrower range of lower frequencies, more characteristic of slug flow, compared to FCC which was characterized by more chaotic pressure fluctuation time-series. SandTime (s)0 5 10 15 20P (kPa)-101234567Ug = 0.50 m/s, Sand, z=0.40 m - 0.56 m  FCCTime (s)0 5 10 15 20P (kPa)-2-1012345Ug = 0.50 m/s, FCC, z=0.40 m - 0.56 m0 2 4 6 8 100.00.10.20.30.40 10 20 30 400.000.020.040.060.080.100.120.140.160.18 Amplitude (kPa2/Hz)Frequency (Hz) Amplitude (kPa2/Hz)Frequency (Hz)Figure 3.2 – Pressure fluctuation data and FFT analysis for sand and FCC at Ug = 0.50 m/s between z = 0.40 and z = 0.56 m 3.1.2 X-ray imaging for flow regime determination As outlined in Chapter 2, X-ray imaging was employed to visualize the internal flow structures 64  of the TFB operating at different superficial gas velocities. The images presented in this section correspond to superficial gas velocities that span between the bubbling and turbulent fluidization flow regimes. Figure 3.3 provides snapshots depicting the flow structures established in the sand fluidized bed operating at low superficial gas velocities corresponding to the bubbling and slugging fluidization flow regimes for the same height interval where the differential pressure measurements were performed [0.56 - 0.72 m]. The gray-scale intensity PDF associated with each snapshot representing the number of pixels corresponding to each gray-scale intensity is also reported. The figure indicates that at low superficial gas velocities (≤ 0.25 m/s), distinct bubbles are present and square-nosed slugs are not fully formed. The observed probability distribution functions appear to be tailed and bimodal, with most counts concentrated on low-intensity pixels represented by the dense phase. The tail represents higher intensity pixels represented by bubbles and slugs occupying a fraction of the snapshot. Figure 3.4 provides examples of the flow structures and relative gray-scale intensity PDF of sand fluidized at higher superficial gas velocities corresponding to square-nosed slugging and transition to the turbulent fluidization flow regime. Bimodal PDFs were observed for the square-nosed slugging regime (e.g. Ug = 0.40 m/s), but, compared to the results indicated in Figure 3.3, the probability distribution function is spread over a wider range of gray-scale intensities due to greater slugs present in the snapshot. The PDFs associated with higher superficial gas velocities close to or greater than Uc are characterized by more symmetric close-to-uniform shapes, representing more homogenous flow structures. 65                         (a) Sand Ug= 0.15 m/sGrayscale intensity0 50 100 150 200 250Count0.02.0e+44.0e+41.0e+51.5e+52.0e+52.5e+53.0e+5 (a) Sand Ug= 0.15 m/sGrayscale intensity0 50 100 150 200 250Count0.02.0e+44.0e+41.0e+51.5e+52.0e+52.5e+53.0e+5                                                                  (b) Sand Ug= 0.25 m/sGrayscale intensity0 50 100 150 200 250Count05000100001500030000400005000060000700008000090000(b) Sand Ug= 0.25 m/sGrayscale intensity0 50 100 150 200 250Count0500010000300004000050000Figure 3.3 – Examples of gray-scale intensity PDF and relative flow structures for sand fluidized in: (a) bubbling and; (b) slugging flow regimes. 66                                                             (a) Sand Ug= 0.45 m/sGrayscale intensity0 50 100 150 200 250Count0.08.0e+31.6e+44.0e+46.0e+48.0e+41.0e+51.2e+5 (a) Sand Ug= 0.45 m/sGrayscale intensity0 50 100 150 200 250Count050001000030000                                                           (b) Sand Ug= 0.65 m/sGrayscale intensity0 50 100 150 200 250Count02000400060008000(b) Sand Ug= 0.85 m/sGrayscale intensity0 50 100 150 200 250Count0200040006000 Figure 3.4 – Examples of gray-scale intensity PDF and relative flow structures for sand fluidized in: (a) slugging and; (b) turbulent fluidization flow regimes. 67  Figures 3.5 and 3.6 represent the flow structures and corresponding PDFs associated respectively with the FCC fluidized bed operating in the bubbling and turbulent flow regimes. Generally, the qualitative trends observed for sand were also observed for FCC, with tailed bimodal gray-scale intensity PDFs corresponding to bubbling and more uniform shapes associated with the turbulent fluidization flow regime.   The transition from bubbling to the turbulent fluidization flow regime, visually observable in Figures 3.3 to 3.6, was also analyzed quantitatively by digital image analysis. For this purpose, all images obtained at 72 frames/s over 10 s when operating at a certain Ug were considered, with the gray-scale intensity PDF of each frame analyzed in terms of three statistical parameters − kurtosis, skewness and Shannon entropy. The average values of kurtosis, skewness and entropy for all images corresponding to each superficial gas velocity were calculated using Matlab. The results are shown in Figure 3.7. It can be observed that the skewness and kurtosis decrease with increasing superficial gas velocity when the bed is operated at low superficial gas velocities (Ug < 0.3 m/s for FCC and < 0.4 m/s for sand) in the bubbling regime and reach more uniform values at greater Ug. Entropy presents increasing behaviour, reaching a plateau at Ug ≥ 0.55 m/s for FCC and at Ug ≥ 0.70 m/s for sand.    68                                                              FCC Ug= 0.08 m/sGrayscale intensity0 50 100 150 200 250Count0.08.0e+31.6e+42.4e+44.0e+46.0e+48.0e+41.0e+51.2e+5FCC Ug= 0.08 m/sGrayscale intensity0 50 100 150 200 250Count08e+32e+44e+46e+48e+41e+5                                                                                                FCC Ug= 0.42 m/sGrayscale intensity0 50 100 150 200 250Count050002000025000FCC Ug= 0.36 m/sGrayscale intensity0 50 100 150 200 250Count0500010000250003000035000 Figure 3.5 – Examples of gray-scale intensity PDF and relative flow structures for FCC fluidized in bubbling flow regime. 69                                                    FCC Ug= 0.53 m/sGrayscale intensity0 50 100 150 200 250Count02000400060008000FCC Ug= 0.53 m/sGrayscale intensity0 50 100 150 200 250Count02000400060008000                                                    FCC Ug= 0.63 m/sGrayscale intensity0 50 100 150 200 250Count02000400060008000FCC Ug= 0.63 m/sGrayscale intensity0 50 100 150 200 250Count02000400060008000 Figure 3.6 – Examples of gray-scale intensity PDF and relative flow structures for FCC fluidized in turbulent fluidization flow regime. 70  FCCUg (m/s)0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7entropy, skewness1234567Kurtosis051015202530SandUg (m/s)0.0 0.2 0.4 0.6 0.8 1.0entropy, skewness02468Kurtosis020406080100Average entropy Average Skewness Average kurtosis Figure 3.7 – Time-average entropy, skewness and kurtosis for gray-scale PDFs obtained at 72 fps over 10 s as a function of superficial gas velocity. Time-average data provided in Figure 3.7 confirm the conclusions that could be drawn from the visual inspection of the frames obtained by X-rays and the respective gray-scale PDFs reported in Figures 3.3 to 3.6:  Images corresponding to low superficial gas velocities mainly in bubbling fluidization flow regime (Figures 3.3 and 3.5) are characterized by tailed (bubble) and asymmetric PDFs, with most data confined to a narrow window of intensities (emulsion phase). At these velocities, most images are characterized by bubbles occupying a small fraction of the total field of view which is mostly occupied by emulsion phase of low gray-scale intensity, leading to PDFs which are not clearly bimodal, but characterized by high kurtosis and skewness, with small entropy relative to uniform distributions.  71   At higher superficial gas velocities, as shown in Figures 3.4 and 3.6, the PDFs are more nearly symmetric, devoid of heavy tails and with data spread over a larger interval of gray-scale intensities (approaching the uniform distribution) resulting in low kurtosis, low skewness and high entropy. This is expected since once the turbulent fluidization flow regime is reached, voids are small and transitory, with flow structures then being more uniform. Figure 3.1 indicates that the standard deviation of the pressure fluctuations reaches a nearly constant value between Ug = 0.5 and 0.7 m/s for the FCC, and between Ug = 0.6 and 0.8 m/s for the sand particles, representing the superficial gas velocity intervals corresponding to transition to the turbulent fluidization flow regime. While average kurtosis and skewness reached constant values for Ug < Uc for both materials (at ~0.3 m/s for FCC and ~0.4 m/s for sand), it is notable that the average entropy reached a maximum plateau at gas velocities very close to Uc derived from pressure fluctuations as shown in Figure 3.6. This finding confirms the suitability of the Shannon entropy of dynamic hydrodynamic features of fluidized beds for studying flow regime transitions, as proposed elsewhere (Kang et al., 1999; Duan and Cong, 2013). 3.2 Degree of interference of invasive probes with local hydrodynamics Figure 3.8 presents some X-ray images of the time-average voidage distribution in sand and FCC with the 4-mm diameter optical probe described in Section 2.4.2.1 inserted 0.56 m above the distributor and a corresponding image with the probe removed at the same operating conditions, in each case for a total sampling time of 20 s. The left image represents the time-average voidage distribution in the column without the probe; the right 72  image represents the corresponding voidage distribution in the same section of the column with the probe inserted. Note that the small circular region in the contour map images [r/R = 0, z = 0.06 m] is the insertion port situated on the column wall, represented in Figure 2.13, plugged with a high-density plastic tap which attenuates the X-ray beam, resulting in difficulty in distinguishing the tip of the probe.  Figure 3.8 indicates that the presence of the probe in the region of interest had a small influence on the voidage distribution, producing slight qualitative and quantitative differences. For some cases the voidage distribution around the inserted probe spread over a larger area with slight loss of symmetry compared to the case where there was no intrusive probe. However, the average voidage in the viewing window did not change significantly (<2%) once the probe was inserted. The results do not indicate total absence of interference of the probe with local hydrodynamics since the voidage profiles were not completely identical. Moreover, the interference should be studied also in terms of other hydrodynamic parameters, such as particle velocity, as well as conducting tests at other measurement positions (e.g. near the distributor) and employing probes of different sizes and shapes. CFD models could also be useful to compare with the results of this study and to investigate the interference of invasive probes with other hydrodynamic parameters. 73             Figure 3.8 – Sample time-average voidage distributions around probe inserted at 0.56 m above the distributor (right side) and the corresponding distribution with the probe removed (left side): (a) sand, Ug = 0.50 m/s; (b) FCC, Ug = 0.50 m/s. 3.3 Voidage distribution Radial profiles of time-average voidage obtained by electrical capacitance tomography (ECT), X-ray computerized tomography (XCT), radioactive particle tracking (RPT) and three different custom-made optical probes were reported by Dubrawski et al. (2013). Figures 3.9 and 3.10 compare the radial profiles of time-average voidage obtained by the borescopy and the overall average profile obtained by averaging the results of all of the other aforementioned voidage measurement techniques. The tables containing the voidage values of single measurement techniques deployed by Dubrawski et al. (2013), are provided in Appendix A. The error bars in these figures refer to the 90% confidence interval obtained Optical probe inserted at z = 0.56 m  Bolt (a) (a) (b) (b) Insertion port 74  when averaging the results of all techniques at a certain location for a specific superficial gas velocity. The error bars were significantly wider (up to 43%) for those cases where the average values were obtained from the results of only two techniques. RPT results, especially at the wall, differed substantially from the data obtained by the other techniques, mainly because it imposed a value of εb at the wall.  In Figures 3.9 and 3.10, for both bed materials, the qualitative trend of the radial profiles obtained by the borescopy was similar to that of the other techniques in most cases, with greatest voidage in the centre of the column where the voids tend to favour. There is an exception in some cases for sand where a quasi-flat radial profile of time-average voidage was obtained by the borescopy in the middle section (z = 0.40 m) of the bed, with square-nosed slugs fully established occupying the entire cross-section of the column. This trend was less noticeable at the lowest measurement level since the slugs are not completely formed there, and at the highest level due to the break-up of slugs aided by the presence of the internal cyclone dipleg. For the sand particles in most cases, the voidages obtained by borescopy are greater than the corresponding average values derived from the other techniques, whereas there is no consistent trend for FCC.  Generally, voidage values obtained by borescopy fall in the interval represented by the error bars of the average values obtained from the data of the alternative measurement techniques. A partial exception was at the lowest measurement level where for some radial positions, the borescopy data lie above the confidence intervals from the other techniques. However, the percent deviation of the borescopy data from the average results of the other techniques was less than 15% for sand and less than 10% for FCC particles in most cases.  75  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.00.550.600.650.700.750.80Previous resultsBorescopyz = 0.40 mTime-average voidage0.500.550.600.650.700.750.80z = 0.56 m0.550.600.650.700.750.800.85 Figure 3.9 – Comparison of radial profiles of time-average voidage obtained by borescopy and other measurement techniques for sand fluidized at Ug = 0.50 m/s. 76  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.00.450.500.550.600.650.700.750.80Previous resultsBorescopyz = 0.40 mTime-average voidage0.30.40.50.60.70.80.9z = 0.56 m0.30.40.50.60.70.80.9 Figure 3.10 – Comparison of radial profiles of time-average voidage obtained by borescopy and other measurement techniques for FCC fluidized at Ug = 0.40 m/s.  77  In order to investigate the effect of height, the average voidage at different measurement levels obtained by X-rays, pressure drop and borescopy are next compared to the cross-sectional average voidage results obtained by other measurement techniques reported by Dubrawski et al. (2013).  The cross-sectional average voidage at a certain level was obtained from X-ray images considering only the beam passing through a (central) diameter attenuated by the solids, with the corresponding time-average voidage then calculated based on Equation 2.22. Since the borescopy provides point voidage measurements (Section 2.4.2.2), assuming that each measurement point is representative of a certain annular cell centered at a given radial position, the cross-sectional average voidage was evaluated by a numerical integration. Average voidages at different heights in the column were also obtained from pressure drop data using Equation 2.20. Details of the other voidage evaluation techniques listed above are given by Dubrawski et al. (2013).  Figures 3.11 and 3.12 report the cross-sectional average voidage results for sand and FCC particles respectively. The average cross-sectional voidage values obtained by all the measurement techniques generally do not significantly change with increasing height, with the greatest coefficient of variation (~10%) for FCC fluidized at Ug = 0.50 m/s. This effect is expected since on one hand, the size of the voids increases as a function of distance from the distributor plate, and on the other hand, larger voids travel faster than the smaller ones resulting in nearly constant voidage axial profile.  78  (a) Sand, Ug = 0.40 m/sz (m)0.0 0.2 0.4 0.6 0.8 1.00.450.500.550.600.650.700.750.800.85Pressure dropUBC Probe UWO Probe RPTXCTECT Poly ProbeFast XrayBorescopy(b) Sand, Ug = 0.50 m/sCross-sectional time-average voidage0.450.500.550.600.650.700.750.800.85(c) Sand, Ug = 0.60 m/s0.500.550.600.650.700.750.800.85 Figure 3.11 – Comparison of cross-sectional average voidage for sand as a function of height for: (a) Ug = 0.40 m/s; (b) Ug = 0.50 m/s; (c) Ug = 0.60 m/s. 79  (a) FCC, Ug = 0.30 m/sz (m)0.0 0.2 0.4 0.6 0.8 1.00.500.550.600.650.700.750.800.85Pressure dropUBC Probe UWO Probe RPTXCTECT Poly ProbeFast XrayBorescopy(b) FCC, Ug = 0.40 m/sCross-sectional time-average voidage0.450.500.550.600.650.700.750.80(c) FCC, Ug = 0.50 m/s0.40.50.60.70.80.9 Figure 3.12 – Comparison of cross-sectional average voidage for FCC as a function of height for: (a) Ug = 0.30 m/s; (b) Ug = 0.40 m/s; (c) Ug = 0.50 m/s. 80  Figure 3.13 shows that for FCC, the overall bed average voidage measured by most of the techniques increases with increasing superficial gas velocity. The UBC optical probe was an exception with the overall voidage at Ug = 0.30 m/s slightly higher than at the two higher superficial gas velocities. RPT and, to a lesser extent, XCT, presented the minimum value at Ug = 0.40 m/s and maximum voidage at the highest superficial gas velocity.   For sand particles, except for RPT, which produced a decreasing trend, and ECT, which did not produce a clear trend, the overall bed average voidage obtained by the other measurement techniques generally increased with increasing superficial gas velocity. These results are consistent with the behaviour of a bubbling fluidized bed where the size of the bubbles and voids is expected to increase as the superficial gas velocity increases (Geldart, 1972).  SandUg (m/s)0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65Overall average voidage0.580.600.620.640.660.680.700.720.740.76Pressure dropUBC Probe UWO Probe RPTXCTECT Poly ProbeFast XrayBorescopyBed expansionFCCUg (m/s)0.25 0.30 0.35 0.40 0.45 0.50 0.55Overall average voidage0.560.580.600.620.640.660.680.700.720.74 Figure 3.13 – Overall bed average voidage results for: (a) FCC; and (b) sand. 81  As shown in Figures 3.9 to 3.13, the agreement among the results obtained by the different measurement techniques was far from perfect. To compare the results of the measurement methods at different superficial gas velocities, the overall volumetric average voidages from each technique are compared to the overall averages provided by all measurement techniques for each superficial gas velocity in terms of the percent deviation in Figure 3.14. The percent deviation from the overall voidage for most of the techniques varies with the superficial gas velocity, giving some insight into the scatter between the results of the techniques at each operating condition.  For FCC, the UWO probe consistently provided the most positive percent deviations compared to the other measurement techniques. None of the techniques produced consistently lower overall average voidages. The highest scatter is observed at the lowest superficial gas velocity. For sand, RPT and fast X-ray produced the highest-magnitude overall percent deviations compared to the other techniques, with the X-ray imaging results being consistently lower than those of the other techniques. The overall scatter is minimum at the lowest Ug, opposite to the trend for FCC.  Except for the cases mentioned above, all the measurement methods generally gave similar results, with deviations less than about ±6%. Dividing the data into ‘invasive’ and ‘non-invasive’, further insight into the relative accuracy of individual techniques may be obtained from the average percent deviations in Figure 3.14. Here both differential pressure measurement and bed expansion are included as non-invasive methods for estimating the voidage.  82  (a) FCCUg (m/s)0.25 0.30 0.35 0.40 0.45 0.50 0.55Percent deviation (%)-15-10-5051015(b) SandUg (m/s)0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65Percent deviation (%)-15-10-50510Pressure dropUBC Probe UWO Probe RPTXCTECT Poly ProbeFast XrayBorescopyBed expansion Figure 3.14 – Percent deviations from cross-sectionally and longitudinally averaged voidages: a) for FCC (Ug = 0.30 to 0.50 m/s); and b) for silica sand (Ug = 0.30 to 0.60 m/s). If we assume that the overall averages obtained by considering the results of all measurement techniques provide accurate estimates, the invasive techniques tend to systematically overestimate the voidage, with slightly higher absolute deviations compared to non-invasive methods, which present a slight tendency to underestimate the voidage. However, the small absolute values of the percentage deviation (<4% for FCC and ~2% for sand) indicate that invasive probes do not unduly reduce the accuracy of fluidized bed voidage measurements (Table 3.1). Overall, the mean percent deviation from the averages at all velocities provided by the different measurement techniques is less than 7% for all superficial velocities, demonstrating that alternate 83  techniques may be employed to make voidage measurements and giving an indication of the accuracy of experimental data which is applicable when evaluating the validity of CFD codes and other predictive models. However, it should be noted that this scatter was in terms of the overall voidage, whereas single-technique voidage results differed substantially at each measurement location, as reported by Dubrawski et al. (2013) and shown in previous figures. Table 3.1 – Average percent deviations from overall average voidage (%). Ug (m/s) 0.30 0.40 0.50 0.60 Average FCC Invasive 6.64 4.72 0.16 - 3.84 FCC non-Invasive -3.32 -2.36 -0.053 - -1.91 Sand Invasive 2.12 2.22 2.96 2.13 2.36 Sand non-Invasive -1.27 -1.48 -1.97 -1.42 -1.54 An extensive discussion regarding the reasons underlying the differences among the results of different voidage measurement techniques is given in Dubrawski et al. (2013). Factors such as different calibration methods for optical fibre probes, difficulties in obtaining a radioactive tracer particle that truly represents the bed material, the necessity of running the RPT experiment for long periods (hours) in order to capture the voidage distribution based on the movement of a single particle, and differences in measurement volumes (e.g. along the diameter of the column for fast X-ray, optical probes and the borescope, or over the entire cross-section for tomographic techniques and radioactive particle tracking) are among the reasons for the observed discrepancies. It should be noted also that since the borescopy has a very small depth-of-field and its images are mainly 2-dimensional, the voidage determination relies on the correlations given by Equations 2.14 and 2.15 which resulted from CFD simulations. Uncertainties resulting from the conversion of solid area fraction to void fraction and determination of an adequate threshold value should also be taken into account. 84  3.4 Overall comment and conclusions X-ray imaging was deployed to visualize the internal flow structures of the travelling gas-fluidized bed (TFB) operating at different superficial gas velocities. Average Shannon entropy associated with the gray-scale intensity probability distribution function of the images obtained from the X-ray system provided an alternative parameter to the standard deviation of pressure fluctuations for detecting the transition from bubbling to turbulent fluidization flow regime. Uc was found to be ~0.68 m/s for FCC and ~0.78 m/s for the sand particles. The degree of interference of a 4-mm diameter intrusive optical probe (used for particle velocity measurements) inserted into the fluidized bed was investigated by analysis of the time-average voidage in a region of the bed operated with and without the probe present. Qualitative differences were observed between the two cases. However, the average voidage in the investigated window did not significantly change (<2%) once the probe was inserted.  The agreement among the voidage distributions obtained by borescopic and X-ray imaging and the voidage data obtained from several other experimental techniques (electrical capacitance tomography, X-ray tomography, radioactive particle tracking, pressure drop, optical probes) presented in previous work on the same system operating under identical conditions was far from  perfect. Quantitative comparison of the overall voidage results obtained by each technique indicated that invasive probes did not unduly reduce the accuracy of voidage measurements. 85  Chapter 4: Results and discussion: particle velocity  In this chapter, the probability distribution functions (PDF) and time-average radial profiles of particle velocity are compared at different measurement heights for different superficial gas velocities obtained by four alternative techniques: optical fibre probe, RPT, PEPT and borescopic high-speed PIV. The results are discussed separately for each bed material, taking into account the physical principles upon which each technique is based. 4.1 Particle velocity: FCC 4.1.1 Radial profiles of time-average particle velocity Time-average particle velocity radial profiles for fluidized FCC obtained by all four techniques mentioned above, for different superficial gas velocities at different levels above the distributor plate are compared in this section. Axial-symmetry is assumed for the data in each of these plots. In order to take into account the vertical alignment of optical probe fibres, the borescopy, PEPT and RPT data presented in this section result from considering two cases: (a) only the velocity vectors associated with solid motion with a deviation angle with respect to the vertical direction of 30 degrees or less; and (b) the vertical component of all velocity vectors of particles that crossed the measurement height. The radial profiles corresponding to each of the aforementioned approaches are given in separate figures. The lines connecting the data points, obtained by spline interpolation, are intended to facilitate the distinction of the results associated with different measurement techniques and should not be considered as an actual interpolation of the data between the measurement points. Even though all the measurement heights were included inside the field of view of the PEPT camera, solid velocity results obtained by PEPT at 0.24 m above 86  the distributor are excluded from the graphs since these results fail to satisfy the physical constraint that for a steady-state measurement with negligible entrainment, the technique must produce a nearly-zero time-average solid mass flux over the whole cross-section due to mass conservation.  The error bars for the RPT, borescopy and optical probe represent 90% confidence intervals obtained by considering the whole sample of velocity vectors. For PEPT, since the location precision was given for each instantaneous tracer position, the uncertainty in the solid velocity was determined using the error propagation formula reported in Chapter 2. The resulting error bars for PEPT are based on the average value of velocity uncertainty. Even if the average value of velocity error for PEPT is small (due also to the six-point-averaging method), it should be noted that the standard deviation of the error is substantial, leading to uncertainties up to 0.2 m/s. The best statistical reproducibility was delivered by the borescopy which provided a large amount of data, producing nearly zero-width confidence intervals for all measurements. RPT, PEPT and the optical probe provided wider, but reasonable, average confidence intervals, in the range of 10-20%.  Figures 4.1 and 4.2 correspond to FCC operating in the bubbling fluidization flow regime (Ug = 0.30, 0.40 m/s) based on the pressure fluctuation data provided in Chapter 3. The results of borescopy, RPT and PEPT were obtained using approach (a) mentioned above. Radial profiles provided by each of the four techniques show net upward solid velocity in the centre of the column due to the movement induced by the wakes and drift caused by rising bubbles, accompanied by corresponding downward velocities near the wall. For both superficial gas velocities, PEPT consistently produced downward solid velocities near the wall of higher 87  magnitude compared to the average velocities obtained by the other techniques (2 - 4 times greater). For the other radial positions, good agreement was mostly observed among all four techniques. The exception was in the centre of the column at 0.40 m above the distributor, where PEPT results were up to 3 times greater than the average derived from the other three techniques.  For Ug = 0.30 m/s, the average solid velocity in the centre of the bed (vpc), obtained by considering the results of all of the techniques, is significantly higher (~93%) in the middle-section (z = 0.40 m) compared to the lower one (z = 0.24 m). A similar, but less pronounced trend (~31% increase) was observed also for Ug = 0.40 m/s. For a given measurement level, it is also noticeable that vpc for Ug = 0.40 m/s is generally greater than for Ug = 0.30 m/s. Both of these trends are expected, since for a bubbling fluidized bed the bubble rise velocity increases with both  superficial gas velocity and distance from the distributor plate (Geldart, 1972).  For Ug = 0.30 m/s, when comparing the upper levels, it could be observed that vpc at z = 0.56 m is lower (~30%) than at z = 0.40 m, whereas for Ug = 0.40 m/s, no difference is observed. This may be due to the presence of the internal cyclone trickle valve at z = 0.70 m which could break the bubbles, hence decelerating the particles as they travel to the upper levels. However, note that this sensitivity was mainly due to PEPT and, to a lesser extent, to optical probe results since vpc values obtained by RPT and borescopy at these two levels were nearly identical.    For Ug = 0.30 m/s, the absolute value of solid velocity in the wall region (r/R = 0.93), obtained by averaging the results from all four techniques (vpw), for the two upper levels (z = 0.40 and 0.56 m) were very similar and greater (~60%) than at the lowest height. For Ug = 0.40 m/s, vpw reached the highest magnitude in the upper level (z = 0.56 m) while the other heights gave similar values. Note that the bed expanded to a height of 1.03 m for Ug = 0.30 m/s and 1.1 m for 88  Ug = 0.40 m/s, and therefore the levels located 0.40 and 0.56 m above the distributor were both distant from the top and the bottom of the fluidized bed. Hence the observed trend of the downward solid velocity might be expected since, for a continuous solid circulation pattern, vpw should present the lowest values at the top and the bottom of the fluidized bed where particles are changing their direction of motion. Note that since optical probe results at r/R=0.93 were not available, a linearly extrapolated value was employed in that case to estimate vpw. Figures 4.3 and 4.4 present the radial profiles of time-average solid velocity obtained when the fluidized bed was operated with a superficial gas velocity close to Uc (0.68 m/s). The results of the borescopy and the particle tracking techniques were obtained by considering only the velocities of the particles travelling with a deviation angle of less than 30˚ from the vertical direction. The shapes of the curves are similar to those for lower superficial gas velocities (Figures 4.1 and 4.2), suggesting that the vertical motion of the voids occurs mostly in the central region of the bed. The maximum vpw and minimum vpc for both superficial gas velocities generally occurred at the lowest level (i.e. z = 0.24 m). Similar to the previous figures, PEPT returned the highest-magnitude solid velocities at the wall for all cases.  Comparison of the results of bubbling and turbulent flow regime reveals that for all measurement levels, vpc obtained for Ug close to Uc was greater (up to 40%) than at lower superficial gas velocities, reflecting higher void velocities. vpw values at z = 0.24 m obtained at higher superficial air velocities were greater (by ~45%) than those obtained for the bubbling flow regime, whereas the opposite trend was observed at the two higher measurement heights, with differences of up to 17%.   89  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.15-0.10-0.050.000.050.100.150.200.25Optical probe Borescope RPT PEPT z = 0.40 mTime-average particle velocity (m/s)-0.6-0.4-0.20.00.20.40.60.8z = 0.56 m-0.6-0.4-0.20.00.20.4 Figure 4.1 – Radial profiles of time-average solid velocity at three levels for FCC, Ug = 0.30 m/s. Only particles with deviation from vertical motion by ≤ 30˚ are included. 90  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.2-0.10.00.10.20.30.4Optical probe Borescope RPT PEPT z = 0.40 mTime-average particle velocity (m/s)-0.4-0.20.00.20.40.6z = 0.56 m-0.4-0.3-0.2-0.10.00.10.20.30.4 Figure 4.2 – Radial profiles of time-average solid velocity at three levels for FCC, Ug = 0.40 m/s. Only particles with deviation from vertical motion by ≤ 30˚ are included. 91  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.4-0.20.00.20.40.6Optical probe Borescope RPT PEPT z = 0.40 mTime-average particle velocity (m/s)-0.4-0.20.00.20.40.60.8z = 0.56 m-0.6-0.4-0.20.00.20.40.6 Figure 4.3 – Radial profiles of time-average solid velocity at three levels for FCC, Ug = 0.50 m/s. Only particles with deviation from vertical motion by ≤ 30˚ are included. 92  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.3-0.2-0.10.00.10.20.30.40.5Optical probe Borescope RPT PEPT z = 0.40 mTime-average particle velocity (m/s)-0.3-0.2-0.10.00.10.20.30.40.5z = 0.56 m-0.4-0.20.00.20.40.6 Figure 4.4 – Radial profiles of time-average solid velocity at three levels for FCC, Ug = 0.60 m/s. Only particles with deviation from vertical motion by ≤ 30˚ are included. 93  Figures 4.5 to 4.8 are similar to Figures 4.1 to 4.4, but instead of filtering out particles travelling with deviations exceeding 30˚ from the vertical direction (approach a), the vertical components of all the velocity vectors (approach b) for particles crossing a certain level obtained by borescopy, RPT and PEPT are considered. The overall qualitative trends are similar for the two approaches, i.e. net upward and downward solid velocity respectively in the core and wall region. However, for many cases, the radial profiles of particle velocity derived from the RPT, PEPT and borescopic high-speed PIV change appreciably as a result of switching from approach (a) to approach (b).  As shown in Figure 4.5, for the lowest superficial gas velocity, the results associated with approach (a) are in better agreement at the lowest measurement height, and vice versa for the middle-section (z = 0.40 m) where the PEPT results are closer to those obtained by the other three techniques. Both approaches gave similar levels of agreement at the upper measurement level. For Ug = 0.40 and 0.50 m/s, better agreement between the results is observed at z = 0.24 m and 0.40 m when approach (b) is used, and vice versa for z = 0.56 m (Figures 4.6 and 4.7). For Ug = 0.60 m/s, approach (a) provides better agreement at the lower heights (z = 0.24 and 0.40 m) as shown in Figure 4.8.    94  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.15-0.10-0.050.000.050.100.150.200.25Optical probe Borescope-Vertical Vertical PEPT-Vertical z = 0.40 mTime-average particle velocity (m/s)-0.6-0.4-0.20.00.20.40.6z = 0.56 m-0.6-0.4-0.20.00.20.4 Figure 4.5 – Radial profiles of time-average solid velocity at three levels for FCC based on vertical components of velocity vectors, Ug = 0.30 m/s. 95  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.10-0.050.000.050.100.150.200.25Optical probeBorescope-Vertical RPT-Vertical PEPT-Vertical z = 0.40 mTime-averaged particle velocity (m/s)-0.4-0.20.00.20.40.6z = 0.56 m-0.4-0.3-0.2-0.10.00.10.20.30.4 Figure 4.6 – Radial profiles of time-average solid velocity at three levels for FCC based on vertical components of velocity vectors, Ug = 0.40 m/s. 96  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.3-0.2-0.10.00.10.20.30.4Optical probe Borescope-Vertical RPT-Vertical PEPT-Vertical z = 0.40 mTime-average particle velocity (m/s)-0.3-0.2-0.10.00.10.20.30.40.5z = 0.56 m-0.4-0.20.00.20.40.6 Figure 4.7 – Radial profiles of time-average solid velocity at three levels for FCC based on vertical components of velocity vectors, Ug = 0.50 m/s. 97  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.2-0.10.00.10.20.30.40.5Optical probe Borescope-Vertical RPT-Vertical PEPT-Vertical z = 0.40 mTime-average particle velocity (m/s)-0.3-0.2-0.10.00.10.20.30.40.5z = 0.56 m-0.4-0.20.00.20.40.6 Figure 4.8 – Radial profiles of time-average solid velocity at three levels for FCC based on vertical components of velocity vectors, Ug = 0.60 m/s. 98  Agreement among the profiles of time-average solid velocity obtained by the four techniques is no better than fair, with significant quantitative differences observed in some cases, especially between PEPT and the other three experimental techniques. In most cases PEPT produced downward velocities of higher magnitude than for the other three techniques near the wall region (up to 8 times greater) and, to a lesser extent in some cases, higher upward velocities at the centre of the column (up to 3 times greater).  The volume-based alternative analysis method described in Section 2.4.2.3 was not preferred, since: a) it confers more weight to the low tracer velocities due to their higher counts in the volume of interest; and b) it produces results which have some dependencies on the height of the measurement volume.  Figure 4.9 provides an example of how the results change for both particle-tracking data once the volume-based analysis is considered with a cell height of 30 mm. The results confirm a decrease in the velocity magnitude for both RPT and PEPT due to the higher weight given to low velocities when calculating time-average values. RPT results were less sensitive to this methodology than PEPT, possibly because the tracer particle employed by RPT is significantly larger than the bed material producing mainly velocity vectors of low magnitude. In general, there was no improvement in agreement among the different profiles as a result of taking volume-based averaging rather than crossing-based data and averaging. Hence the volume-based averaging method was abandoned and the crossing-based approach preferred, due to greater similarity with the manner of determining velocity by the optical probe. Borescopy is a volumetric technique, but, as also indicated in Section 2.4.2.3, for a fair comparison, the height of the cell for volumetric analysis of RPT and PEPT should be chosen to be consistent with the 99  interrogation window of the borescope, taking into account the differences of sampling frequency. This option is far from trivial since PEPT is characterized by a variable sampling rate. All results associated with the volume-based methods are reported in Appendix B for interested readers. Statistical analysis using the analysis of variance (ANOVA) was performed to test the null hypothesis, i.e., to see whether all measurement techniques can be considered to be from the same population. If the null hypothesis is rejected, the results associated with each technique are characterized by different mean values (Montgomery and Runger, 2010). For a sample of cases, the analysis of variance was performed on the population of solid velocities obtained by each measurement technique at a given location and a given superficial gas velocity, using OriginPro software. It was observed that only for a limited number (13%) of the 24 cases examined was there strong evidence that null hypothesis was true, most of which were at the lowest measurement height where PEPT was excluded from the analysis. The rejection of the null hypothesis in most cases using one-way ANOVA implies that the differences among the time-average values obtained by alternative techniques are not only due to random errors but also related to the statistically-called “treatment effect” which is based on the systematic errors associated with each measurement technique. The treatment effects associated with each measurement technique contribute to produce different populations of solid velocity and are, at least in part, discussed in Section 4.1.3. Note also that the one-way ANOVA assumes that all populations are characterized by similar standard deviations. Since the degree of similarity of standard deviations is subjective, Welch correction to the ANOVA analysis was also applied, giving similar results to those of one-way ANOVA. Fisher’s least significant difference (LSD) 100  method (Montgomery and Runger, 2010) was also performed to compare the means of all pairs of techniques. It was observed that in most cases (~80%) the time-average solid velocities obtained by two measurement techniques could be considered to be taken from the same population with 95% confidence. These cases tended to be observed when the interval of confidence of one of the measurement techniques embedded the value of the mean and interval of confidence of the other technique. Tables of typical results of ANOVA corresponding to two instances of acceptance or rejection of the null hypothesis are given in Appendix C.  101  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.2-0.10.00.10.20.30.4Optical probe Borescope RPT PEPT RPT- volumePEPT- volumez = 0.40 mTime-average particle velocity (m/s)-0.4-0.20.00.20.40.6z = 0.56 m-0.4-0.3-0.2-0.10.00.10.20.30.4 Figure 4.9 – Comparison of radial profiles of time-average solid velocity at three levels for FCC obtained by volume-based and crossing-based analysis, Ug = 0.40 m/s. For the volume-based data, the cells were of height 30 mm centred at the level (z-value) of interest in each case. 102  The discrepancies among the results were quantified by calculating the absolute percent deviation of each result from the average obtained from the results produced by all four measurement methods (equally weighted) at each superficial gas velocity and each spatial position. For a given superficial gas velocity, the deviation of each technique results from the overall mean value was calculated by averaging the absolute deviations obtained at all spatial positions, and the results are given in Figure 4.10 for both filtering criteria. It can be observed that, even when the lowest measurement height is excluded from the analysis, PEPT for most of the cases presents the highest magnitude of deviation (~2 times greater) compared to the other three techniques which present similar absolute deviations. Both filtering criteria produce similar overall absolute percent deviations.  30 degreeUg (m/s)0.3 0.4 0.5 0.6Overall average percent absolute deviation (%)20406080100120Vertical componentsUg (m/s)0.3 0.4 0.5 0.6Overall average percent absolute deviation (%)30405060708090100Optical probeBorescopeRPTPEPTFigure 4.10 – Overall percent deviation of particle vertical velocities for different superficial gas velocities: a) Velocities for particles with a deviation angle of less than 30 degrees from the vertical; b) Vertical components of the velocities. 103  The data collected by the borescope for periods of 10 and 15 s are compared in Figure 4.11. These results indicate that the data are not very sensitive to the sampling duration over this limited range. FCCExperimenta b cTime-average velocity-0.10.00.10.20.3Sampling duration: 10 secondsSampling duration: 15 seconds Figure 4.11 – Effect of the sampling time on the time-average particle velocity measured by the borescopy for FCC: Experiment a) Ug = 0.40 m/s, z = 0.40 m, r/R = 0.77; experiment b) Ug = 0.60 m/s, z = 0.40 m, r/R = 0; experiment c) Ug = 0.30 m/s, z = 0.24 m, r/R = 0.33. For RPT, the count number, defined as the number of times the tracer was detected in a certain defined annulus, depended significantly on the radial position, but also, to a minor extent, on the filtering criteria. PEPT count number appears to have been nearly insensitive to the filtering criteria and to be nearly constant over the column cross-section. The count number would decrease if, instead of considering the vertical components of all velocity vectors, a limit of 30˚ deviation angle from the vertical were to be included as one of the data filtering criteria. However, as shown in Figure 4.12, a sufficiently large count number was obtained for both particle tracking techniques (RPT and PEPT), even with the deviation angle from the vertical included as a filtering criterion. 104  r/R0.0 0.2 0.4 0.6 0.8 1.0Counts100100010000RPT RPT Vertical componentsPEPT PEPT Vertical components Figure 4.12 - Count number for RPT in 8 hours and PEPT in 3.5 hours sampling time for different annuli with different filtering criteria, FCC, Ug = 0.40 m/s, z = 0.40 m. 4.1.2 Probability distribution function of solid velocity Probability distribution functions (PDF) of the solid velocity at different positions obtained by each measurement technique, considering only the particles moving with a deviation angle from vertical less than 30˚ for the borescope, RPT and PEPT are plotted in Figure 4.13. Note that for all of the cases, there was remarkable similarity between the PDFs of the two non-invasive techniques (RPT and PEPT). The PDFs of solid velocity obtained by the borescope were shifted towards lower magnitude velocities producing a different shape compared to the PDFs of the other techniques for most cases. The PDFs of solid velocity associated with the optical probe were generally more similar to those produced by the non-invasive techniques than to the borescope data. 105  FCC, Ug = 0.40 m/s, z = 0.40 m, r/R = 0Particle velocity (m/s)-2 -1 0 1 2010203040Optical probeBorescopeRPTPEPTFCC, Ug= 0.40 m/s, z = 0.40 m, r/R = 0.6Particle velocity (m/s)-2 -1 0 1 2Probability (%)010203040FCC, Ug = 0.50 m/s, z = 0.56 m, r/R = 0.6Particle velocity (m/s)-2 -1 0 1 205101520253035FCC, Ug = 0.60 m/s, z = 0.56 m, r/R = 0Particle velocity (m/s)-2 -1 0 1 2Probability (%)01020304050 Figure 4.13 – Examples of probability distribution function of solid velocity for FCC. Only particles deviating from vertical motion by ≤ 30˚ are included for the borescope, RPT and PEPT. 106  FCC, Ug = 0.30 m/s, z = 0.40 m, r/R = 0.6Particle velocity (m/s)-2 -1 0 1 205101520253035Optical probeBorescopeRPTPEPTFCC, Ug= 0.50 m/s, z = 0.40 m, r/R = 0.6Particle velocity (m/s)-3 -2 -1 0 1 2 3Probability (%)05101520253035FCC, Ug = 0.40 m/s, z = 0.56 m, r/R = 0Particle velocity (m/s)-2 -1 0 1 2Probability (%)01020304050FCC, Ug = 0.60 m/s, z = 0.40 m, r/R = 0.6Particle velocity (m/s)-2 -1 0 1 2051015202530 Figure 4.13 (cont’d) – Examples of probability distribution function of solid velocity for FCC. Only particles deviating from vertical motion by ≤ 30˚ are included for the borescope, RPT and PEPT 107  4.1.3 Discussion Consideration of the unique characteristics of each of the four measurement techniques helps to explain the quantitative differences in the particle velocity data. The next section discusses the general differences among the experimental techniques regardless of the bed material used. Specific factors that need to be considered for each bed material are then discussed in Sections 4.1.3 (b) and 4.2.3. a) General factors leading to quantitative differences in results Features of the measurement technique which contributed to the differences for both bed materials include the following:  The optical probe and borescopic probe are both intrusive, and therefore interfere to some extent with the flow field being measured, with the nature and extent of the interference depending on such factors as probe shape, size, orientation and roughness, as well as the prevailing direction, velocity and particle volume fraction of the local gas-solid flow.   The sampling rate of the RPT system is fixed at 100 Hz, whereas the PEPT velocity detection rate is variable and could reach sampling rates of 500 Hz. Suppose that the tracer displacement during two time-steps Δt1 and Δt2 are Δx1  and Δx2  , respectively, where Δt1 + Δt2 = Δt = 10 ms. RPT detects the mean tracer movement associated with Δt given by ( Δx1  + Δx2  ) / Δt, whereas PEPT can detect two velocity vectors Δx1  /Δt1 and Δx2  /Δt2. Generally ( Δx1  + Δx2  ) / Δt ≠ mean ( Δx1   / Δt1, Δx2  / Δt2) resulting in different velocity evaluations for PEPT and RPT.  108   In order to be accepted as providing valid cross-correlation measurements, particles had to pass the optical probe nearly vertically. No such restriction applies to the PEPT, RPT and borescopic probe techniques.  The four methods have different dependencies on particle volume fraction. In a given time interval, the optical probe returns a particle velocity irrespective of whether there are only a few or many particles passing in the correct direction during that interval. The velocities can therefore be considered to be “volume-fraction-independent”. Hence the optical probe is, for example, indifferent to whether the particle is travelling in the dense or dilute phase when it accepts a cross-correlation as giving a valid velocity. The borescopy presents a slight volume-fraction dependency since the PIV algorithm needs a sufficient number of particles within the measurement volume for an accurate velocity determination (Raffel et al., 1998). At low particle volume fractions, longer image collection times are needed, resulting in much larger image files (i.e., longer analysis times). Extremely dilute regions provide more freedom of movement in three-dimensional space, resulting in cases where particles present in one frame escape from the field of view in the next frame. Otherwise, the borescope dependency on volume fraction is weak since, providing there are some particles within the measuring volume, their number is not important. On the other hand, in the RPT and PEPT methods, over a long analysis time period, the tracer particle passes more times through regions of high flux than through low-flux regions. Thus the measurements may be more accurate in high-flux regions because of normalizing over more data, but the values over long time periods should be “flux independent”. With optical and borescopic probes, the borescope has a larger measuring volume, resulting in some spatial averaging that is not a consideration for the optical probe. Also, the detection 109  of movement of particles far from the tip of the borescope is difficult because of its short focal length. This happens mostly when dilute phase passes the borescope, and is less of a factor for the optical probe, which relies on the intensity of reflected light, and to a much lesser extent on focus.  The average resolution of the PEPT system given by location uncertainty was between 2.7 and 4.3 mm for different runs, which was of the same order as the distance travelled by the particle during one time step at lower particle velocities (<0.06 m/s). This may result in poor accuracy of detecting low particle velocities. Instantaneous location uncertainty of RPT data was not available, but RPT applied to systems similar to the TFB presented a spatial resolution of around 6 mm, which is thought to provide similar inaccuracy as described for PEPT (Rasouli, 2014).  Considering PEPT, an exact theoretical principle for optimizing N as a function of particle speed needs to be implemented in order to improve the data analysis. Also, unlike for RPT, the half-life of the PEPT tracer was shorter than the sampling duration, which may result in different accuracies in particle localization during the experiments.   An ideal radioactive tracer particle only represents a single average size and density of the bed material; on the other hand, the optical probe and borescope measure the velocities of all particles present in the bed.   Friction along the tip of the borescope and optical probe may also have affected particle movement.  The measurement volumes of the invasive and non-invasive techniques differed. Particle tracking techniques measure the time-average velocity in annuli of a given width, whereas the probing techniques perform point measurements. 110  b) Discussion specific to results obtained from FCC fluidized bed The following insights could be deduced by considering the results presented in Section 4.1, focusing on the physical principles upon which each measurement technique is based:  The PEPT and RPT methods assume that the tracer particle travels in a manner that is perfectly representative of the other particles in the bed. However, as shown in Table 2.6, even though similar in shape, the diameter and density of the tracer particle used for RPT differed substantially from those of the main FCC particles, with the tracer particle being significantly larger and denser. For PEPT measurements, the tracer particle size and shape were well matched, but its density differed considerably. These differences can produce different circulation patterns, likely resulting in greater acceleration of the PEPT tracer particle, but greater resistance to following the bulk particle motion for the RPT tracer particle than for FCC particles, hence failing to accurately follow the motion of the bed material. Close matching of all physical properties (density, diameter and shape) of the tracer particle with the bulk solid is vital for obtaining very accurate data. A tracer particle that perfectly follows the bulk particle motion cannot be simply achieved by adjusting its diameter and density in order to obtain the same terminal settling velocity as the bulk solid particles. The terminal settling velocity for the case of interest is more strongly dependent on particle diameter than on particle density, whereas, as reported by Rowe and Nienow (1976), the effect of density ratio is considerably more important than that of size ratio in causing solid segregation in gas-fluidized beds.   Electrostatic and van der Waals forces may have caused some particles to adhere to both the optical and borescopic probe surfaces, causing significant loss of data. Perhaps as a 111  result, the FCC particles gave low optical fibre cross-correlation, with 35% valid data compared to 65% for sand. Closer matching between the optical fibre diameter and particle diameter for the sand may also have been a contributing factor.  The optical probe is incapable of measuring velocities close to 0 because of the need to cross-correlate signals from two fibres. This restriction is absent for the other three techniques. Better agreement, especially between the borescope and the optical probe radial profiles of time-average solid velocity was obtained in some cases when particle velocities whose magnitudes were smaller than 0.023 m/s were excluded from the signal analysis (Figure 4.14). This improvement was observed exclusively for FCC particles characterized by a significant proportion of zero-magnitude velocity data due to adhesion problems discussed above (up to 50% for borescopy). PEPT and RPT are less sensitive to the effect of zero-magnitude velocities since, to cross the measurement level and be counted, the tracer must possess a minimum vertical velocity. As discussed above and observable in the PDFs of solid velocity (Figure 4.13), the borescopy tends to be biased towards nearly-zero velocities, while the PEPT and RPT method of post-processing produces results comparable with the optical probe. If instead of the level-crossing approach, the volume-based method was used for PEPT and RPT post-processing, the results would shift towards smaller magnitudes (Appendix B).  As mentioned above, most of the discrepancy between PEPT and the other three techniques was observed at the lowest measurement level (z = 0.24 m) in the bed, where PEPT consistently produced much lower magnitude velocities compared to the other techniques. In fact, at this measurement level, the PEPT results failed to satisfy the physical constraint that for steady-state measurement, the technique must produce a nearly-zero time-average 112  solid mass flux over the whole cross-section due to mass conservation. This suggests that in the PEPT facilities, the camera field of view was smaller than the nominal size indicated in the literature (Stein et al., 1996; Leadbeater et al., 2012). Therefore, the PEPT results associated with this height have been excluded for the FCC data. 113  Ug = 0.40 m/s, z = 0.40 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.4-0.20.00.20.40.6Optical probeBorescope RPT PEPT Ug = 0.60 m/s, z = 0.40 mTime-average particle velocity (m/s)-0.3-0.2-0.10.00.10.20.30.40.5Ug = 0.50 m/s, z = 0.56 m-0.6-0.4-0.20.00.20.40.6 Figure 4.14 – Radial profiles of time-average solid velocity at three levels for FCC excluding zero velocities. 114  4.2 Particle velocity: Sand 4.2.1 Radial profile of time-average particle velocity for sand Radial profiles of time-average particle velocity obtained by all four experimental techniques with sand particles are reported in this section. Axial-symmetry is again assumed in each of the plots. The borescopy, PEPT and RPT data in these plots result from considering only the velocity vectors associated with solid motion with deviation angle with respect to the vertical direction of 30 degrees or less in order to be directly comparable with the optical probe data.  The error bars for the RPT, borescopy and optical fibre probe represent 90% confidence intervals obtained by considering the whole sample of velocity vectors for each measurement location. For PEPT the uncertainty in solid velocity is again determined using the error propagation formula, as for FCC. All the operating superficial gas velocities investigated were less than Uc (0.78 m/s), the superficial gas velocity corresponding to onset of the turbulent fluidization flow regime, obtained from pressure fluctuation data (Chapter 3), and above Ums (0.16 m/s), the minimum slugging velocity, calculated from the correlation given by Stewart and Davidson (1967). As visually observed from X-ray images (Chapter 3), typical of large Geldart B particles of small angle of internal friction (Thiel and Potter, 1977; Chen et al., 1997) satisfying the slugging criteria described by Grace (1982), sand particles exhibited a square-nosed slugging behaviour with dense plugs occupying the entire cross-section of the bed moving upwards and solids raining from the bottom into the slug, producing in most cases an unusual trend with pronounced negative time-average solid velocity in all radial positions. However, although the measured 115  velocities were mostly negative, solids flux data presented in Chapter 5 show that upward and downward mass fluxes averaged over time and the cross-section were in balance, as expected when entrainment fluxes are low. Because this flow regime is not widely studied, details of square-nosed slugging characteristics are reviewed in Appendix D. This flow regime, mainly observed in laboratory and pilot scale fluidized beds and of interest for a few applications (Noordergraaf et al., 1987; van Putten et al., 2007), provides a useful platform for satisfying the main objective of the study, which is to compare experimental results and features of a number of the most advanced particle velocity measurement techniques for operation under identical operating conditions.     For Ug = 0.40 m/s, the results obtained by RPT, optical probe and the borescopy are in good qualitative and quantitative agreement at the lowest measurement level (z = 0.24 m), where these three techniques provide downward solid velocity near the wall and upward velocities in the centre of the bed, typical of bubbling fluidized beds (Figure 4.15). The poorest agreement among the results was observed at 0.40 m above the distributor plate, where a quasi-flat radial profile was observed for all four techniques, with PEPT providing the most negative values; and RPT and borecope results close to zero and the optical probe results lying in the middle. As mentioned above, negative velocities were observed at most radial positions in the upper sections of the bed because of the establishment of square-nosed slug flow and particle “raining” inside the slugs. For all three measurement levels, the profiles obtained by RPT and borescopy are quite close to each other as shown in Figure 4.15. .  116  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.4-0.3-0.2-0.10.00.10.20.3Optical probe Borescope RPT PEPT z = 0.40 mTime-average particle velocity (m/s)-0.8-0.6-0.4-0.20.00.2z = 0.56 m-0.8-0.6-0.4-0.20.00.20.4 Figure 4.15 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.40 m/s. 117  For Ug = 0.50 m/s (Figure 4.16), agreement among the results of the borescope, RPT and optical probe at the lowest measurement height is slightly worse than for Ug = 0.40 m/s, where some signs of downward solid velocity in the core region are observable from the optical probe radial profile. At the upper measurement section (z = 0.56 m), there is poor agreement among the results in the wall region relative to the central region where the profiles obtained by all four techniques were much closer to each other. Similar to the behaviour shown in Figure 4.15 for z = 0.40 m, PEPT produced negative values of greater magnitude than the other techniques for most cases with Ug = 0.50 m/s in Figure 4.16.  For Ug = 0.60 m/s (Figure 4.17), radial profiles of solid velocity at z = 0.24 and 0.40 m presented similar behaviour as for Ug = 0.50 m/s. At the upper measurement level, solid raining in the central region of the bed was less prominent than for the two lower superficial gas velocities investigated. Figure 4.18, reports the equivalent of the radial profiles of solid velocity at the lowest measurement level reported in Figures 4.16 and 4.17, where, instead of averaging all the velocity vectors corresponding to particles moving with a deviation angle of less than 30˚ from the vertical direction (approach a), the vertical components of all velocity vectors of particles crossing the measurement level (approach b) are considered to obtain local time-average results for the borescopy, PEPT and RPT. Except for the few cases shown in Figure 4.18, there is little difference in the results of these two approaches, suggesting that the contributions from non-vertical particle velocities were minimal. In fact the sensitivity to the filtering approach was observed only for the lowest measurement height where the square-nosed slugging was not completely established. 118  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.4-0.3-0.2-0.10.00.10.20.3Optical probe Borescope RPT PEPT z = 0.40 mTime-average particle velocity (m/s)-1.0-0.8-0.6-0.4-0.20.00.2z = 0.56 m-0.8-0.6-0.4-0.20.00.2 Figure 4.16 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.50 m/s. 119  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.3-0.2-0.10.00.10.20.3Optical probe Borescope RPT PEPT z = 0.40 mTime-average particle velocity (m/s)-1.0-0.8-0.6-0.4-0.20.00.20.4z = 0.56 m-0.8-0.6-0.4-0.20.00.20.4 Figure 4.17 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.60 m/s. 120  Ug = 0.60 m/s, z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.3-0.2-0.10.00.10.2Optical probe Borescope-Vertical RPT-Vertical PEPT-Vertical Ug = 0.50 m/s, z = 0.24 mTime-average particle velocity (m/s)-0.3-0.2-0.10.00.10.2 Figure 4.18 – Radial profiles of time-average solid velocity at three levels for sand based on vertical components of velocity vectors. The velocity data collected by the borescope for periods of 10 and 15 s are compared in Figure 4.19. As for FCC, the data were obtained for 10 seconds in one experiment and an additional 5 seconds in a separate run. Compared to FCC, more scatter between the results obtained with different sampling times was observed for sand particles, suggesting greater statistical uncertainty, possibly due to the aliasing effect and instability of the square-nosed slugging flow regime. 121  SandExperimenta b c dTime-average velocity (m/s)-0.2-0.10.00.10.2Sampling duration: 10 secondsSampling duration: 15 seconds Figure 4.19 – Effect of the sampling time on time-averaged particle velocity measured by the borescope. Sand: a) Ug = 0.40 m/s, z = 0.40 m, r/R = 0.77; b) Ug = 0.60 m/s, z = 0.40 m, r/R = 0.33; c) Ug = 0.60 m/s, z = 0.56 m, r/R = 0.60; d) Ug = 0.50 m/s, z = 0.56 m, r/R = 0.33. The count number radial profile for RPT and PEPT presented similar behaviour as was discussed for FCC in Section 4.1.1, with PEPT results being nearly constant over the column cross-section and insensitive to the filtering criteria, and RPT count number being slightly sensitive to the filtering criteria and considerably greater in the wall region compared to other radial positions. 4.2.2 Instantaneous solid velocity and probability distribution function Probability distribution functions (PDF) of the solid velocities at different axial and radial positions obtained by each measurement technique are plotted in Figure 4.20. All four techniques detected particles raining inside the slugs giving bimodal PDFs, where upward velocities are induced by rising square-nosed slugs. The optical probe and PEPT detected downward velocities of greater magnitude compared to RPT and the borescopy, especially at the middle-section of the column (z = 0.40 m). PEPT, borescopy and the optical probe detected similar upward velocities, whereas the RPT data are more scattered, i.e., have more prominent “tails”. 122  Sand, Ug = 0.60 m/s, z = 0.56 m, r/R = 0Particle velocity (m/s)-2 -1 0 1 2051015202530Optical probeBorescopeRPTPEPTSand, Ug = 0.50 m/s, z = 0.40 m, r/R = 0.6-3 -2 -1 0 1 2 3Probability (%)0510152025Sand, Ug = 0.40 m/s, z = 0.24 m, r/R = 0-1.5 -1.0 -0.5 0.0 0.5 1.0 1.50102030405060 Figure 4.20– Sample probability distribution functions of solid velocity for sand. Figure 4.21 shows instantaneous particle vertical movement in the core region of the bed captured by the optical probe and the borescope. As mentioned in Chapter 2, the sampling consisted of multiple periods of only 1 s duration for the borescopy and only 0.5 s duration for 123  the optical probe. Therefore, continuous data giving a complete picture of the slugging and the solid raining phenomenon are not available in either of those cases. Nevertheless, the plots still portray the intermittency of upward velocities associated with the roof and floor regions of slugs interspersed with downward motion caused by particles raining inside the voids. Note that the actual time intervals between successive bursts (random for the optical probe and 5.67 s for the borecopy) are not represented in the plots in order to facilitate the visualization of the slugging phenomena.   Figure 4.21 – Solid velocity time series obtained by: a) Optical probe; b) Borescope. Note that the traces are not continuous, but broken into bursts of duration 1 s for the borescope and 0.5 s for the optical probe. Figure 4.22 presents the instantaneous velocities of the tracer passing the z = 0.56 m level for the two particle tracking techniques (RPT and PEPT). It can be observed that PEPT presents a higher density of data points for upward velocities, with almost a constant value and more scattered downward velocities characterized by greater magnitudes. RPT, as indicated also in the PDFs, provided more symmetrical velocity vectors with respect to zero and a smaller count frequency compared to PEPT. 124  PEPT, Sand Ug = 0.50 m/s, z = 0.56 m, count/t = 955 (1/h)Time (s)0 2000 4000 6000 8000 10000 12000 14000Particle velocity (m/s)-3-2-1012RPT, Sand Ug = 0.50 m/s, z = 0.56 m, , count/t = 475 (1/h)0 5000 10000 15000 20000 25000 30000Particle velocity (m/s)-2024Figure 4.22 – PEPT and RPT measured tracer velocities crossing the z = 0.56 m level during the entire sampling period. 125  4.2.3 Discussion specific to sand results  The following factors, in addition to the general factors presented in Section 4.1.3 may be, at least in part, responsible for the quantitative differences observed among the sand particle velocity results provided by the four measurement techniques:  The shape, diameter and the density of the tracer particle used for RPT differed substantially from those of the bulk bed material (sand), with the RPT tracer particle being spherical rather than of irregular shape and considerably larger and less dense (see Table 2.6). For the PEPT measurements, the tracer particle size and shape were well matched, but its density was higher (see Table 2.7). As for FCC, these differences in properties may have affected the measurements, preventing the tracers from accurately representing the motion of the sand particles. As shown in Figure 4.22, the count frequency obtained by PEPT was more than twice that of RPT. This result may be due to less “mobilization” of the RPT tracer particle and also differences of tracer radioactivity and sampling rates of the two particle tracking techniques. Note also that the terminal velocity (Ut) of the RPT and, to a lesser extent, the PEPT tracers was greater than that of the bulk sand which may lead to higher magnitude velocities when particle raining occurs. Sand particles may also have abraded the tracer particles and modified their shape during the operation of the system.  The sand particles exhibited square-nosed slug flow; with raining of particles inside the slugs (extremely dilute region) playing a prominent role (Figures 4.15 to 4.18). Downward particle velocities in the interior of the column were detected when flux-independent or concentration-independent measurement techniques encountered such a 126  flow. There was significantly better agreement between the results of RPT, borescope and optical probe in the lower region of the bed (z = 0.24 m), where the square-nosed slugs had not yet formed and the upward movement of the particles in the core of the bed was dominant (moving with bubble noses and wakes). The profiles obtained by all four techniques are closer in the upper region (z = 0.56 m) compared to the middle-height (z = 0.4 m). The presence of the cyclone dipleg at a higher level (z = 0.7 m) may have contributed to slug break-up and prevention of particle raining.  The Fast Fourier Transform (FFT) analysis performed on the time-series of pressure fluctuations of the system suggests a dominant frequency in the range of 0.40-0.43 Hz for passage of slugs, as given for example in Figure 3.2, corresponding to a time-interval between arrival of slugs of 2.3 to 2.5 s, though with surrounding peaks of higher frequency. The time interval between successive acquisitions (of duration of 1 s) was 5.67 s for the borescopy, i.e., one measurement every 6.67 s. This may have led to some aliasing in the borescope data, with successive measurements tending to favour one phase. The optical probe data would not present the same aliasing issue since its data capture was done randomly over a much longer sampling period. RPT and PEPT data samplings were continuous for long periods of time, again preventing the aliasing problem. 4.3 Overall comment and conclusions The overall quantitative agreement between the results of the four particle-velocity techniques was at best fair for FCC and disappointing for sand particles. Careful attention is needed to specifics of each instrument and each analytical technique used to make hydrodynamic 127  measurements in systems as complex as fluidized beds, subject to bubbling, slug flow and the turbulent fluidization flow regime. The results from this and other chapters, suggest that probe intrusiveness is less of a factor when determining particle motion than matching all key tracer particle physical properties (size, density, shape) in non-intrusive techniques. Particle tracking techniques require close matching of all three of these particle properties to be assured for accurate determination of particle motion by following the motion of tracer particles.   128  Chapter 5: Results and discussion: solid flux As discussed in Chapter 1, solid flux is a crucial hydrodynamic parameter determining important aspects of the gas-fluidized beds such as bed-to-surface heat exchange, solid circulation rate and erosion of in-bed tubes.  In gas-solid flows, the instantaneous local particle velocity and voidage can be expressed as summations of a mean value and a fluctuating component: ( ) ( )( ) ( )p p pv t v v tt t     (5.1) The local instantaneous local solid mass flux can be expressed as: ( ) ( )[1 ( )] [ ( )][1 ( ( ))]s p p p p pG t v t t v v t t            (5.2) Time average solid flux, can be obtained by integration of Equation 5.2 over a sufficient time interval (T): 01( ) [ (1 ) (1 )]Ts s p p pG G t dt v vT         (5.3) The final term in the square brackets of Equation 5.3 represents the covariance term obtained by the time-average of the product of the fluctuating terms. This term is generally non-zero due to the strong correlation between the solid velocity and suspension concentration, as confirmed by Zhu et al. (1991) and Bi et al. (1996). Thus, the time-average mass flux cannot be determined from separate measurements of solid velocity and voidage, making it important to perform 129  measurements that provide both parameters simultaneously. This concept is extendable to momentum flux measurements as well.  This chapter provides the radial profiles of time-average solid flux obtained from RPT, PEPT and borescopy. Given the significant difference between the fluidization flow regimes associated with each bed material, i.e., FCC and sand, the results of solid mass and momentum flux are presented in separate sections. 5.1 Solids flux: FCC 5.1.1 Radial profiles of time-average mass and momentum flux Radial profiles of vertical solid mass flux for fluidized FCC obtained by RPT, PEPT and borescopy are given in this section. As for the FCC particle velocity data presented in Section 4.1.1, solid flux results obtained by PEPT at 0.24 m above the distributor were again excluded from the graphs since these results failed to produce a nearly-zero time-average solid mass flux integrated over the whole cross-section as shown later in this section. Figures 5.1 and 5.2 present radial profiles of solids mass flux for FCC fluidized in the bubbling flow regime for three levels and two superficial air velocities. All three techniques provided results of the same order and, in most cases, the qualitative trends are as expected, i.e., highest-magnitude upward flux at the centre, due to the void motion, and highest-magnitude downward flux in the wall region due to net downward particle movement there.  For both gas velocities, the magnitudes of the solid mass flux obtained by PEPT are consistently greater than those provided by the other two techniques, with the highest absolute values in the 130  core region of the bed for the ascending particles and in the region close to the wall for descending ones. Solid mass fluxes based on the borescopy technique lie between the fluxes derived from the two particle tracking techniques (RPT and PEPT) in most cases.  The solid circulation flux, Js, in a bubbling fluidized bed can be estimated by considering the solids upward flow associated with bubble wake and drift as given by Geldart (1986):  w(1 )( ) ( 0.38 )s p mf g mf dJ U U Y        (5.4) where Y is a correction for deviation from the two-phase theory of fluidization, βw and βd are values of wake and drift volumetric fraction respectively, and the factor 0.38 for drift flux is derived from experimental evidence that the particles carried up in the drift travel on average at about 38% of the bubble velocity (Yang, 2003).  The order of magnitude of solids mass flux obtained by all measurement techniques was in agreement with the solid circulation flux, Js, given by Equation 5.4 where Y, βw and βd were estimated to be ~0.9, ~0.4 and ~0.9, respectively, based on the Archimedes number (Geldart, 1987).  131  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-80-60-40-20020406080z = 0.40 mTime-average mass flux [kg/(m2 s)]-150-100-50050100150200BorescopeRPTPEPTz = 0.56 m-150-100-50050100150200 Figure 5.1 – Radial profiles of time-average solids mass flux at three levels for FCC fluidized at Ug = 0.30 m/s. 132  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-100-50050100z = 0.40 mTime-average mass flux [kg/(m2 s)]-150-100-50050100150BorescopeRPTPEPTz = 0.56 m-150-100-50050100150200 Figure 5.2 – Radial profiles of upward and downward time-average solids mass flux at three levels for FCC fluidized at Ug = 0.40 m/s. 133  Comparing the results at different measurement levels, we find that for Ug = 0.30 m/s the magnitude of solid flux in the central region, Gsc, obtained by averaging the results of all three techniques increased (by ~17%) as a function of height between z = 0.24 m and 0.40 m. Little difference (~6%) was observed between the Gsc at the middle and upper measurement levels. For Ug = 0.40 m/s, the maximum mass flux in the core region of the bed was observed at the highest level (z = 0.56 m), with percent difference of 30% compared to the other two heights characterized by similar Gsc.  For the highest measurement level, Gsc increased slightly as the superficial gas velocity increased from 0.30 to 0.40 m/s, with differences of ~13%; whereas no significant difference was observed between the values at the other measurement levels.  The aforementioned effects are generally expected, since bubbles grow in size and rise faster with increasing superficial gas velocity and distance from the distributor, resulting in greater solid mass flux induced by bubble wakes and drift (Geldart, 1972). Figures 5.3 and 5.4 represent radial profiles of mass flux obtained at superficial gas velocities close to (Ug = 0.50 m/s) and at (0.60 m/s) Uc obtained by pressure fluctuations, reported in Chapter 3. Similar qualitative trends were observed as in the previous figures when the superficial gas velocities were increased further, with upward mass flux in the central region of the bed and downward flux near the wall. For both superficial gas velocities, the average solids flux in the central region of the column reached its maximum value at the highest level (z = 0.56 m), with differences of up to ~45% compared to the other two heights.  134  Comparing the results obtained for Ug = 0.50 and 0.60 m/s, we observe that Gsc increased slightly (~10%) for this increase in superficial gas velocity in the middle-section of the bed (z = 0.40 m), and to a negligible extent (~4%) for the lowest level (z = 0.24 m). The value of Gsc at the upper level obtained at Ug = 0.60 m/s was significantly (~38%) higher than for Ug = 0.50 m/s.  Comparison of the average core region mass fluxes for the bubbling fluidization flow regime (Ug = 0.30 and 0.40 m/s) with those obtained at higher superficial gas velocities (0.50 and 0.60 m/s) reveals consistently higher magnitude (up to 25% higher) values at the superficial gas velocities closer to the Uc suggesting more solid movement due to larger and faster voids.    135  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-120-100-80-60-40-200204060z = 0.40 mTime-average mass flux [kg/(m2 s)]-150-100-50050100150BorescopeRPTPEPTz = 0.56 m-150-100-50050100150200 Figure 5.3 – Radial profiles of time-average solids mass flux at three levels for FCC fluidized at Ug = 0.50 m/s. 136  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-80-60-40-200204060z = 0.40 mTime-average mass flux [kg/(m2 s)]-150-100-50050100150BorescopeRPTPEPTz = 0.56 m-150-100-50050100150200250 Figure 5.4 – Radial profiles of time-average solids mass flux radial profiles at three levels for FCC fluidized at Ug = 0.60 m/s. 137  Radial profiles of momentum flux obtained for the bubbling fluidization flow regime (Ug = 0.30 and 0.40 m/s) are provided in Figures 5.5 and 5.6. Most profiles obtained by the three measurement techniques presented the highest-magnitude upward and downward momentum flux in the core and wall regions, respectively. For most cases, the momentum flux radial profiles obtained by borescopy and RPT are quite similar. However, results derived from the PEPT measurements are significantly greater than those from the other two techniques. For both superficial gas velocities tested, the average momentum flux in the core region of the column (Fsc) obtained by averaging the results from all three measurement techniques were significantly higher (up to 200%) for the middle level (z = 0.40 m) than for the lowest measurement height (z = 0.24 m). This is mainly due to the fact that PEPT momentum flux at the middle-section was up to ~4 times greater than the other two techniques results, whereas the PEPT values at the lowest measurement height were excluded, as explained above.  For Ug = 0.30 m/s, Fsc at the upper level was ~36% lower than that at the middle-level, whereas, for Ug = 0.40 m/s, negligible (~4%) difference was observed between the Fsc values at the upper and the middle measurement height. The presence of the internal cyclone dipleg at z = 0.70 m, may have caused bubbles to break and decelerate, resulting in lower upward particle momentum fluxes. As for the mass flux, the average momentum flux in the core region for each measurement level generally increased as a function of the superficial gas velocity, indicating higher momentum transfer due to larger and faster bubbles.   138  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-40-20020406080z = 0.40 mTime-average momentum flux [kg/(ms2)]-100-50050100150BorescopeRPTPEPTz = 0.56 m-120-100-80-60-40-20020406080 Figure 5.5 – Radial profiles of time-average particle momentum flux at three levels for FCC fluidized at Ug = 0.30 m/s. 139  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-40-20020406080100z = 0.40 mTime-average momentum flux [kg/(ms2)]-60-40-20020406080100120BorescopeRPTPEPTz = 0.56 m-100-80-60-40-20020406080100 Figure 5.6 – Radial profiles of time-average particle momentum flux at three levels for FCC fluidized at Ug = 0.40 m/s. 140  The trend observed for lower superficial gas velocities was similar to that for superficial gas velocities close to and at Uc, with RPT and borescopy results again in better agreement compared to PEPT (Figures 5.7 and 5.8). The magnitude of momentum flux results obtained by PEPT was significantly greater than for the other two techniques. Comparison of the average momentum flux results in the core region obtained at each measurement level indicates that the values associated with Ug = 0.60 m/s are consistently greater than those for Ug = 0.50 m/s with differences of 13-40%.  Comparing the results of the bubbling fluidization flow regimes with those where the superficial gas velocities were closer to the onset of fluidization, we find that momentum transfer at the two highest superficial gas velocities (Ug = 0.50 and 0.60 m/s) was significantly (23-130%) greater than at the two lower Ug values (0.30 and 0.40 m/s), suggesting more efficient momentum transfer due to the faster and larger voids. The net solid mass flux integrated over the whole cross-section, calculated using Equation 2.18, is plotted as a function of height in Figure 5.9. Since the borescopy provides point flux measurements, the net flux over the whole cross-section has been evaluated by assuming that each measurement point is representative of a certain annular cell with the radial position at its centre. The results indicate that, except for PEPT at the lowest measurement height where the net mass flux is consistently negative and an order of magnitude higher than the other ones (highlighted in red since excluded from further analysis), the other techniques generally produce a reasonably low net mass flux over the cross-section, confirming adequate overall mass conservation. 141  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-60-40-200204060z = 0.40 mTime-average momentum flux [kg/(ms2)]-100-80-60-40-20020406080100120BorescopeRPTPEPTz = 0.56 m-100-80-60-40-20020406080100120 Figure 5.7 – Radial profiles of time-average particle momentum flux at three levels for FCC fluidized at Ug = 0.50 m/s. 142  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-20-1001020304050z = 0.40 mTime-average momentum flux [kg/(ms2 )]-60-40-20020406080100120140BorescopeRPTPEPTz = 0.56 m-100-50050100150 Figure 5.8 – Radial profiles of time-average particle momentum flux at three levels for FCC fluidized at Ug = 0.60 m/s. 143  Ug= 0.40 m/sz (m)0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60-15-12-9-6-3036Ug= 0.50 m/sz (m)0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60Net Mass flux (kg/(m2 s))-16-12-8-4048Ug= 0.60 m/sz (m)0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60-20-15-10-505RPTPEPTBorescopeUg=0.30 m/sz (m)0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60Net Mass flux (kg/(m2 s))-12-10-8-6-4-20246 Figure 5.9 – Net vertical mass flux over entire measurement time period (10 s for borescope, 3.5 h for PEPT, and 8 h for RPT) and cross-section at three levels and four superficial gas velocities for fluidized FCC. See text for discussion of points surrounded by shaded zones. 144  5.1.2 Discussion The following points may, at least in part, explain the observed discrepancies in the flux profiles derived from the three measurement techniques:  As shown in Table 2.6, the RPT tracer particle was significantly larger and denser than the FCC particles. The tracer particle deployed for the PEPT measurements had virtually the same diameter as the bulk bed material, but a significantly lower density. As mentioned in Chapter 4, these differences in physical properties have a considerable impact on the circulation patterns influencing velocity fluctuations and acceleration. Better matching of all particle/tracer properties is extremely important for producing a reliable picture of bulk solid motion based on the movement of a single particle. The observed higher upward flux obtained by PEPT in the central region and downward flux close to the wall compared with the RPT and borescopic measurements is an indication of more pronounced circulation of the PEPT tracer particle.   As shown in Figure 5.10, counts over time obtained by PEPT measurements were, in average, ~2 times greater than for RPT. The greater count frequency of PEPT is another indication of less “mobilization” of the RPT tracer particle than for PEPT, as discussed in Chapter 4. As reported in Chapters 2 and 4, tracer particle radioactivity (less for RPT than for PEPT), detection instrumentation (fixed sampling rate for RPT and variable for PEPT) and the localization algorithm based on different physical principles of RPT and PEPT also differed greatly, contributing to different count frequencies.   Figure 5.10 indicates that the RPT tracer residence time is not uniformly distributed throughout the cross-section with the tracer particle spending most of its time in the wall 145  region. In fact, the count frequency was an order of magnitude greater in the wall region compared to an equal area in the central part. This may be related to the tracer adherence to the wall for periods during the sampling time, due to electrostatic forces, producing a count number substantially greater in a layer close to the wall of ~300 µm thickness. When the tracer particle moves closer to (or adheres to) the wall, its high activity (chosen for this experiments due to non-optimum arrangement of detectors) could result in saturation of the detector(s) positioned close to its position, with consequent loss of detector sensitivity in locating the tracer. This may have caused the tracer to undergo apparent oscillations back and forth across the measurement level close to the wall due to the inherent location uncertainty of the system.   The borescope has a very small depth-of-field. The voidage determination relies on the correlation given by Equation 2.14 which resulted from CFD simulations for FCC particles. Uncertainties result from the conversion of solid area fraction to void fraction.  Even though measurements were not performed all the way to the wall, the general trend of the particle motion profiles indicates downward solid motion near the wall, suggesting that the no-slip boundary condition often employed in CFD simulations, is not applicable as a wall boundary condition for the particles.   146  Ug = 0.40 m/s z = 0.40r/R0.0 0.2 0.4 0.6 0.8 1.0Count/t (1/h)020406080100120140160180PEPT upwardRPT upwardPEPT downwardRPT downward Figure 5.10  – Count number per unit time for PEPT and RPT at different radial positions for FCC. 5.2 Solids flux: Sand 5.2.1 Radial profiles of time-average mass and momentum flux Given the presence of the square-nosed slugging regime, radial profiles of upwards and downwards fluxes are reported separately on the same graph, with ascending and descending particles associated with each technique represented by similar symbols pointing in opposite directions. Several factors contributed to uncertainty in deriving fluxes from the borescopic measurements for sand. Upward movement of particles was associated with dense plugs travelling close to the tip of the borescope, covering the entire field of view. On the other hand, particle raining occurs in the dilute phase, resulting in less accurate results due to the zero-depth of field and other characteristics of the borescopic PIV, as discussed in Chapter 4. This was 147  reflected also in the net mass flux over the cross-section, where the borescope consistently produced positive values. There was also uncertainty in voidage evaluation from borescopic images due to the conversion of solid area fraction to voidage, as indicated in Section 2.4.3.1. The possibility of aliasing added to the uncertainties. As a result, the author was not confident with the solid flux results obtained by borescopy. Therefore only results derived from RPT and PEPT are included in this section.  Figure 5.11 presents radial profiles of solid mass flux for the lowest superficial gas velocity (0.40 m/s). Both RPT and PEPT presented quasi-flat radial profiles of solid upward mass flux at the upper levels of the column (z = 0.40 and 0.56 m), due to the presence of square-nosed slugs occupying the entire column cross-section. Partial exceptions were for RPT that provided unusual upward flux of greater magnitude in the wall region than at the other radial positions; and at the lowest measurement level where PEPT presented higher upward mass flux in the core region of the column, mainly because the slugs were not completely formed at this height.  Upwards and downwards mass fluxes obtained by RPT are consistently lower in magnitude than those obtained by PEPT. Downward solid mass fluxes obtained by PEPT presented nearly-uniform profiles over the entire cross-section for the middle section (z = 0.40 m); slightly more pronounced downward fluxes were observed near the wall at the lowest and highest measurement levels. RPT provides enhanced downward mass flux in the wall region compared to the other radial positions, which were characterized by similar values of mass flux.  Table 5.1 reports the cross-sectional time-average upward and downward mass flux obtained by each measurement technique and the overall mass flux obtained by averaging the results of both techniques at a given level and superficial gas velocity for sand particles. The coefficient of 148  variation is defined as the ratio of standard deviation of the data obtained by the different techniques at a given height and Ug, and the overall average. The average scatter among the results in terms of the coefficient of variation is around 45%. It is observed that in general for Ug = 0.40 m/s, the cross-sectional average mass flux obtained by considering both measurement techniques did not present a significant dependency on the measurement height between z = 0.24 m and z = 0.40 m with differences < 7%. The average upward and downward mass fluxes in the upper measurement level were ~22% greater than at the other two measurement heights.  Figure 5.12 represents the radial profiles of solid mass flux for Ug = 0.50 m/s. The trends are similar for Ug = 0.40 and 0.50 m/s, with a slight (~14%) increase in overall cross-sectional average upward mass flux when moving from z = 0.40 m to the upper level (z = 0.56 m) and negligible differences among the profiles at the two lower measurement levels. The scatter among the data in terms of the coefficient of variation is around 34%.   Figure 5.13 displays the mass flux profiles for the highest superficial gas velocity (0.60 m/s). As also given in Table 5.1, unlike the lower superficial gas velocities, the cross-sectional upward and downward mass fluxes obtained by averaging the results from both techniques increased consistently in magnitude as a function of measurement height (up to ~28%). For most cases, there was little difference between the cross-sectional average mass fluxes obtained at the two higher superficial gas velocities (Ug = 0.50 and 0.60 m/s). A partial exception was for the upward mass flux at the highest measurement level (z = 0.56 m) where the data obtained at Ug = 0.60 m/s were slightly (~12 %) greater than at Ug = 0.50 m/s. On the other hand, the mass fluxes obtained at Ug = 0.40 m/s were consistently lower in magnitude than those at higher superficial gas velocities, with differences up to 46%. 149  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-150-100-50050100150RPT UpwardPEPT UpwardRPT DownwardPEPT Downwardz = 0.40 mTime-average solid mass flux [kg/(m2 s)]-200-150-100-50050100150200z = 0.56 m-200-150-100-50050100150200 Figure 5.11 – Radial profiles of upward and downward time-average solids mass flux at three levels for sand fluidized at Ug = 0.40 m/s. 150  Table 5.1 – Cross-sectional time-average upward and downward mass flux for sand  z (m) RPT PEPT Overall Coefficient of variation (%)  Ug = 0.40 m/s Upward mass flux, kg/(m2s) 0.24 43 87 65 47 Downward mass flux, kg/(m2s) 0.24 -42 -92 -67 53 Upward mass flux, kg/(m2s) 0.40 43 77 60 39 Downward mass flux, kg/(m2s) 0.40 -44 -81 -63 41 Upward mass flux, kg/(m2s) 0.56 47 100 74 51 Downward mass flux, kg/(m2s) 0.56 -48 -105 -76 52  Ug = 0.50 m/s Upward mass flux, kg/(m2s) 0.24 71 97 84 22 Downward mass flux, kg/(m2s) 0.24 -69 -103 -86 29 Upward mass flux, kg/(m2s) 0.40 66 108 87 34 Downward mass flux, kg/(m2s) 0.40 -66 -116 -91 39 Upward mass flux, kg/(m2s) 0.56 70 129 99 42 Downward mass flux, kg/(m2s) 0.56 -70 -131 -100 43  Ug = 0.60 m/s Upward mass flux, kg/(m2s) 0.24 75 78 76 3 Downward mass flux, kg/(m2s) 0.24 -75 -90 -83 13 Upward mass flux, kg/(m2s) 0.40 64 109 87 37 Downward mass flux, kg/(m2s) 0.40 -66 -118 -92 41 Upward mass flux, kg/(m2s) 0.56 71 151 111 51 Downward mass flux, kg/(m2s) 0.56 -69 -148 -108 51 Radial profiles of solid momentum flux obtained at each superficial gas velocity are plotted in Figures 5.14 to 5.16.  Substantial differences were observed between the RPT and PEPT downward solid momentum flux radial profiles, especially at the middle level (z = 0.40 m). For most cases PEPT provided negative values of up to 4 times greater magnitude compared to RPT. The difference in the downward momentum profiles at the lower level (z = 0.24 m) was less pronounced, while at the upper level (z = 0.56 m), there were significant differences close to the wall.  151  The upward momentum flux profiles of both techniques were in better agreement with quasi-flat profiles obtained at all measurement heights representing the movement associated with dense plugs. A partial exception was at the lowest measurement height where in most cases PEPT and to a lesser extent RPT presented momentum flux of higher magnitude in the core region.    As shown in Table 5.2, in most cases the cross-sectional average upward momentum flux increased (by 14-79%) with increasing measurement height, indicating increasing velocity of the dense plugs associated with the square-nosed slugs.  For Ug = 0.40 m/s, the magnitude of downward momentum flux increased with increasing height (up to 67%). For Ug = 0.50 m/s and 0.60 m/s, the downward momentum fluxes, were significantly greater (up to 3 times greater) in magnitude at the middle height (z = 0.40 m) compared to the lowest measurement height, whereas there was little difference between the middle and highest heights. Overall, the downward momentum flux was of greater magnitude at the two upper levels where the slugs were fully formed, resulting in enhanced particle raining.  Considering each measurement height, the magnitude of the momentum flux consistently increased (by up to 76%) with increasing superficial gas velocity, indicating more momentum exchange for higher superficial gas velocities, as noted also for FCC.     152  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-200-150-100-50050100150200RPT UpwardPEPT UpwardRPT DownwardPEPT Downwardz = 0.40 mTime-average solid mass flux [kg/(m2 s)]-300-200-1000100200300z = 0.56 m-300-200-1000100200 Figure 5.12 – Radial profiles of upward and downward time-average solids mass flux at three levels for sand fluidized at Ug = 0.50 m/s. 153  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-400-300-200-1000100200300RPT UpwardPEPT UpwardRPT DownwardPEPT Downwardz = 0.40 mTime-average solid mass flux [kg/(m2 s)]-200-150-100-50050100150200z = 0.56 m-300-200-1000100200300 Figure 5.13 – Radial profiles of upward and downward time-average solids mass flux at three levels for sand fluidized at Ug = 0.60 m/s. 154  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-80-60-40-2002040Borescope UpwardRPT UpwardBorescope DownwardRPT Downwardz = 0.40 mTime-average particle momentum flux [kg/(ms2)]-140-120-100-80-60-40-200204060z = 0.56 m-200-150-100-50050100 Figure 5.14 – Radial profiles of upward and downward time-average solids momentum flux at three levels for sand fluidized at Ug = 0.40 m/s. 155  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-80-60-40-200204060Borescope UpwardRPT UpwardBorescope DownwardRPT Downwardz = 0.40 mTime-average particle momentum flux [kg/(ms2)]-250-200-150-100-50050100z = 0.56 m-250-200-150-100-50050100 Figure 5.15 – Radial profiles of upward and downward time-average solids momentum flux at three levels for sand fluidized at Ug = 0.50 m/s. 156  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-200-150-100-50050100150Borescope UpwardRPT UpwardBorescope DownwardRPT Downwardz = 0.40 mTime-average particle momentum flux [kg/(ms2)]-300-200-1000100200300z = 0.56 m-300-200-1000100200 Figure 5.16 – Radial profiles of upward and downward time-average solids momentum flux at three levels for sand fluidized at Ug = 0.60 m/s. 157  The net solid mass flux integrated over the whole cross-section is plotted as a function of height in Figure 5.17. RPT results are close to zero for all of the cases, reflecting the need for the upwards and downwards fluxes to be equal under steady state operating conditions, with the tracer particle not entrained from the system. The highest deviations from zero were observed for the PEPT in the lowest and middle measurement level (z = 0.24 m and 0.40 m) where disagreement among the time-average solid velocity profiles was also significant (see Section 4.2.1). Unlike FCC, the PEPT measurements at the lowest measurement level did not produce a consistent deviation from the net cross-sectional value obtained at the other measurement heights, and therefore the results were not discarded. This may be attributable to differences between FCC and sand tracers’ radioactivity and different level of γ-ray scattering by the bulk solids.          158  Table 5.2 – Cross-sectional time-average upward and downward momentum flux for sand  z (m) RPT PEPT Overall Coefficient of variation (%)  Ug = 0.40 m/s Upward momentum flux, kg/(ms2) 0.24 21 22 21 2 Downward momentum flux, kg/(ms2) 0.24 -20 -46 -33 55 Upward momentum flux, kg/(ms2) 0.40 13 22 18 35 Downward momentum flux, kg/(ms2) 0.40 -14 -96 -55 106 Upward momentum flux, kg/(ms2) 0.56 25 28 27 9 Downward momentum flux, kg/(ms2) 0.56 -26 -118 -72 90  Ug = 0.50 m/s Upward momentum flux, kg/(ms2) 0.24 30 25 27 14 Downward momentum flux, kg/(ms2) 0.24 -29 -52 -40 41 Upward momentum flux, kg/(ms2) 0.40 26 37 31 25 Downward momentum flux, kg/(ms2) 0.40 -25 -161 -93 103 Upward momentum flux, kg/(ms2) 0.56 34 43 39 15 Downward momentum flux, kg/(ms2) 0.56 -39 -147 -93 82  Ug = 0.60 m/s Upward momentum flux, kg/(ms2) 0.24 34 20 27 38 Downward momentum flux, kg/(ms2) 0.24 -35 -46 -40 19 Upward momentum flux, kg/(ms2) 0.40 51 46 49 8 Downward momentum flux, kg/(ms2) 0.40 -50 -187 -119 81 Upward momentum flux, kg/(ms2) 0.56 51 63 57 15 Downward momentum flux, kg/(ms2) 0.56 -55 -168 -112 72 159  Ug = 0.50 m/sMass flux (kg/(m2 s))-12-8-404Ug= 0.40 m/sz (m)0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60-6-5-4-3-2-1012RPTPEPTUg= 0.60 m/s-14-12-10-8-6-4-20246 Figure 5.17 – Net mass flux over entire measurement time period (3.5 h for PEPT, and 8 h for RPT) and cross-section at three levels for different superficial gas velocities and fluidized sand. 160  5.2.2 Discussion The following factors, together with those identified in the discussion reported for solid velocity data in Chapter 4, likely contributed to the discrepancies among the observed radial profiles and deviations from the requirement that the net vertical flux be 0 at any level, providing that entrainment of the tracer particle does not occur:  As reported in Tables 2.6 and 2.7, the terminal velocities of the RPT and, to a lesser extent, of PEPT tracer particles were greater than for the sand particles which may cause, on the one hand, enhanced downward movement when particle raining occurs and, on the other hand, more resistance to acceleration in the upward movement associated with the slugs. However, the terminal velocity is not the only property to consider since it only accounts for a combination of tracer density and diameter given in the drag coefficient expression. As also discussed in Chapter 4, the effect of density difference is considerably more important than that of size difference when considering solid segregation in gas-fluidized beds. The tracer particles employed by RPT and PEPT differed significantly in terms of density which can produce different circulation patterns, even though they had similar terminal velocities.       Momentum flux reflects, to a certain extent, the behaviour in terms of time-average solid velocity since it is a product of mass and velocity. The degree of agreement among the radial profiles of time-average solid velocity is similar to that of time-average momentum flux. For instance, the greatest magnitude of solid downward velocity observed at z = 0.40 m from PEPT was reflected in the downward momentum flux profile for all superficial velocities investigated. The reasons underlying the discrepancies observed for 161  solid velocity profiles given in Chapter 4 likely also explain, at least in part, the differences in solid momentum flux profiles.  Particle raining inside the square-nosed gas slugs was of higher absolute velocity than the upward solid movement between the gas slugs. PEPT, characterized by variable sampling rates and, in some cases, faster sampling than RPT, captures particle raining more often compared to RPT.  The number of counts per unit time for RPT and PEPT differed for the sand experiments, but to a lesser extent than for the FCC experiments. In most cases RPT presented the highest count density in the wall region, similar to what was observed for FCC (Figure 5.10) due to the possible saturation of the detectors when the tracer particle was in the wall region and consequent loss of sensitivity, as discussed in Section 5.1.2. This may explain why RPT produced high unphysical upward fluxes near the wall, a result observed in the radial profiles of solid flux.  5.3 Overall comment and conclusions All the techniques considered, provided mass and momentum flux of the same order, but there were significant differences in some cases mainly for sand particles. Different physical properties of tracer particles and the bed material, low spatial resolution of the particle tracking systems, differences in the tracer localization instrumentation and uncertainty in determining the depth of field of the borescope are among the factors that likely contributed to the observed discrepancies. The novel procedure suggested for obtaining solid flux from particle tracking methods provided reasonable results.  162  The data presented in this chapter, complementing the results of the previous chapters, provide experimental hydrodynamic benchmark data intended to be uniquely useful for testing of CFD codes and other hydrodynamic models. However, the type of analysis method employed and the limitations of each measurement technique must be taken into account when comparing the experimental data with model predictions. 163  Chapter 6: Conclusions and recommendations This work represents a systematic effort to compare different experimental techniques in measuring key hydrodynamic features of gas-fluidized beds. The findings provide benchmark information related to the limitations and relative merits of each technique in measuring certain hydrodynamic parameters and an experimental database useful for testing CFD and other models. This chapter summarizes the conclusions of the work and provides some recommendations for future work.  6.1 Conclusions Key conclusions are summarized as follows:  The degree of interference of the intrusive optical probe (used for particle velocity measurements) inserted into the fluidized bed was found to be small in terms of the time-average voidage in a region of the bed operated with and without the probe present obtained by X-ray imaging.  Visual X-ray images indicated gradual transition to the turbulent fluidization flow regime in the same range of gas velocities as inferred from the results obtained from pressure fluctuations for the onset of turbulent fluidization flow regime.   Quantitative measurements of cross-sectional average voidage from the X-ray images are consistent with voidage data obtained from an array of other experimental techniques such as electrical capacitance tomography, X-ray tomography, radioactive particle tracking, borescopy, pressure drop, optical probes presented in Dubrawski et al. (2013) and extended by Tebianian et al. (2014). 164   Optical fibre probes, radioactive particle tracking, positron emission particle tracking and borescopic high-speed PIV deployed to investigate local particle velocities in the “travelling fluidized bed” operated under identical conditions at four different research laboratories with the same FCC (Geldart Group A powder) and silica sand (Geldart Group B powder) gave similar overall qualitative trends, but significant quantitative differences in measured results.  For FCC particles, after discarding the results of PEPT at the lowest measurement height due to physical inconsistency, fair agreement was observed among radial profile time-average solid velocity radial profiles obtained by four alternative techniques. However, significant quantitative differences were observed in some specific cases, especially between PEPT and the other three techniques.   For sand particles, significant quantitative differences were observed for solid velocity measurements among the time-average data provided by all four techniques, especially in the middle section (z = 0.40 m) of the bed.  Likely reasons for the observed differences among the results of the considered techniques for both bed materials include invasiveness of two of the methods, significant differences between the physical properties of tracer particles and the bulk bed material, differences in sensitivity to the angle of travel and concentration of particles in the measurement zone, differences in acceptance algorithms, spatial resolution of the particle tracking systems, differences among RPT and PEPT tracer localization algorithms and differences in measurement volume.  For most of the cases examined for FCC particles, the solid velocity data obtained by RPT, borescopy and optical probes and, to a much lesser extent, by PEPT exhibited at 165  best fair agreement, delineating the range of particle velocities to be expected in this physical system at different superficial gas velocities.   Optical fibre probes may be used to produce benchmark particle velocities for CFD validation using the crossing method analysis, while borescopy can be employed when volume-based analysis is preferred. RPT and PEPT results, obtained from tracking the motion of a tracer particle which properly matches the key physical properties of the bulk solids, may be analyzed based on either the crossing or volume-based approach. These particle-tracking-derived velocities are most suitable when working with a narrow particle distribution and when a non-uniform size distribution cannot be implemented in the CFD software.    The scatter among the data obtained for sand, observed especially in the middle section (z = 0.40 m) of the column, makes it challenging to employ the results as a benchmark for CFD validation. However, direct comparison of the results provided useful information for the future deployment of these techniques in investigating particle velocities and fluxes in gas-fluidized beds.   A novel procedure, based on the number of times the tracer particle crosses a given level, was utilized for deriving solid flux from particle tracking methods.   For both bed materials, all three techniques generally provided mass and momentum fluxes of the same order, but there were significant differences in some cases. In addition to the factors mentioned for solid velocity, uncertainty in determining the depth of field of the borescope is among the factors that likely contributed to the observed discrepancies. 166   The results from this study suggest that probe intrusiveness is less of a factor when determining particle motion than the matching all key tracer particle physical properties (size, density, shape) in the non-intrusive tracking techniques.  The general trend of the particle velocity and flux profiles indicated downward solid motion approaching the wall, indicating that the no-slip particle boundary condition, often employed in CFD simulations, is not applicable.    Borescopic measurements for obtaining particle velocity in extremely dilute regions are challenging due to the possibility of losing particles from the field of view during successive frames, failing to provide cross-correlation.  It is absolutely necessary to perform measurements using the same equipment under identical operating conditions when different techniques should be directly compared. As shown in Appendix E, borescopic particle velocity measurements at the same section of the TFB provided different results when different distributor plates were used.  6.2 Recommendations for future work The results of this work may be useful in developing new measurement techniques for monitoring the performance of commercial units. The following points represent general recommendations for future studies:  When using particle tracking techniques, near-perfect matching of the key physical properties of the tracer and the bed material (particle size, density and shape) is essential to minimize measurement discrepancies and uncertainties. Matching the terminal settling velocity (Ut) of the tracer with that of the bed particles of mean size, for instance by 167  decreasing the diameter of a denser tracer particle, does not necessarily improve the tracer representativeness of the bed material; since, as reported by Rowe and Nienow (1976), the effect of density difference is considerably more important than that of particle size difference when considering solid segregation and vice versa when considering Ut.  It is preferable that more than one experimental technique results be used in validation studies of CFD and other models. The comparison must be performed with different hydrodynamic parameters over an extensive array of operating conditions (Grace and Taghipour, 2004).  CFD models could be useful for investigating the effect of intrusive techniques on local hydrodynamics of gas-fluidized bed. It would be useful to run simulations where, for example, a probe is inserted in the domain and one calculates the time-average solid velocity in the proximity of the probe tip.  The square-nosed slugging flow regime observed for sand particles provided unstable behaviour which made it challenging to obtain reliable data. It would be useful to add another Geldart B powder to the study to have a more complete experimental benchmark. Performing studies with Geldart D particles would also be useful.    It would be preferable to use continuous data sampling for the borescope in order to eliminate possible aliasing problem when examining either slugging flow regime.  The PIV program owned by NETL (Cocco et al., 2010), where single particles are detected and their movement followed in time, should be tested. With this algorithm the borescopic data could be analyzed according to the crossing method. However, the efficiency of this software for dense phase flow needs to be investigated. 168   Solids mass and momentum should be measured using the optical flux probes employed by Liu et al. (2003) and Kim et al. (2004), and the results should then be compared the data with those obtained in this study.  Employ multi-fibre optical probe to measure particle velocity and compare the results to those obtained by particle tracking data analyzed using the volume-based approach and borescopy.  It would be useful to repeat some measurements (e.g. pressure fluctuations and bed expansion) using the dyed sand as the bed material and compare the results with those obtained with the uncoloured sand.  More work is required to characterize the field of view of the PEPT detection camera. It would be useful to perform some more particle velocity measurements where the lowest extreme of the camera’s field of view is well above the distributor. 169  References Bendat, J.S., Piersol, A.G., 1986. 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(2013) at different radial positions are compared with voidage values acquired by borescopy.  Table A.1 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.40 m/s, z = 0.24 m Radial voidage distribution, Sand, Ug = 0.40 m/s, z = 0.24 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Poly Probe) r/R (Borescope) UBC probe XCT RPT UWO Probe Poly Probe Borescope -0.95 -1.00 -1.00 -0.90 -0.93 0.57 0.58 0.53 0.67 0.60 0.61 -0.90 -0.93 -0.86 -0.50 -0.78 0.58 0.64 0.64 0.68 0.63 0.69 -0.75 -0.86 -0.71 0.00 -0.60 0.60 0.65 0.64 0.68 0.59 0.71 -0.50 -0.79 -0.57  -0.33 0.63 0.65 0.63 0.72  0.68 0.00 -0.72 -0.43  0.00 0.70 0.66 0.63 0.74  0.69 0.50 -0.66 -0.29  0.33 0.63 0.66 0.62 0.73  0.68 0.75 -0.59 -0.14  0.60 0.57 0.68 0.62 0.71  0.71 0.90 -0.52 0.00  0.78 0.58 0.70 0.61 0.64  0.69 0.95 -0.45 0.14  0.93 0.56 0.70 0.62 0.58  0.61  -0.38 0.29    0.71 0.62     -0.31 0.43    0.72 0.63     -0.24 0.57    0.73 0.63     -0.17 0.71    0.74 0.64     -0.10 0.86    0.74 0.64     -0.03 1.00    0.73 0.53     0.03     0.73      0.10     0.73      0.17     0.74      0.24     0.74      0.31     0.74      0.38     0.73      0.45     0.73      0.52     0.72      0.59     0.70      0.66     0.69      0.72     0.68      0.79     0.66      0.86     0.64      0.93     0.63      1.00     0.62     179  Table A.2 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.40 m/s, z = 0.40 m Radial voidage distribution, Sand, Ug = 0.40 m/s, z = 0.40 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Poly Probe) r/R (Borescope) UBC probe XCT RPT UWO Probe Poly Probe Borescope -0.95 -1.00 -1.00 -0.90 -0.93 0.64 0.59 0.53 0.71 0.60 0.67 -0.90 -0.93 -0.86 -0.50 -0.78 0.65 0.68 0.79 0.76 0.61 0.79 -0.75 -0.86 -0.71 0.00 -0.60 0.69 0.69 0.80 0.73 0.63 0.73 -0.50 -0.79 -0.57  -0.33 0.70 0.70 0.83 0.76  0.75 0.00 -0.72 -0.43  0.00 0.73 0.70 0.85 0.74  0.70 0.50 -0.66 -0.29  0.33 0.69 0.70 0.84 0.73  0.75 0.75 -0.59 -0.14  0.60 0.66 0.69 0.85 0.72  0.73 0.90 -0.52 0.00  0.78 0.63 0.68 0.87 0.72  0.79 0.95 -0.45 0.14  0.93 0.63 0.68 0.85 0.70  0.67  -0.38 0.29    0.68 0.84     -0.31 0.43    0.68 0.85     -0.24 0.57    0.69 0.83     -0.17 0.71    0.69 0.80     -0.10 0.86    0.69 0.79     -0.03 1.00    0.68 0.53     0.03     0.68      0.10     0.68      0.17     0.68      0.24     0.68      0.31     0.69      0.38     0.69      0.45     0.68      0.52     0.69      0.59     0.68      0.66     0.67      0.72     0.67      0.79     0.66      0.86     0.66      0.93     0.66      1.00     0.65            180  Table A.3 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.40 m/s, z = 0.56 m Radial voidage distribution, Sand, Ug = 0.40 m/s, z = 0.56 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Poly Probe) r/R (Borescope) UBC probe XCT RPT UWO Probe Poly Probe Borescope -0.95 -1.00 -1.00 -0.90 -0.93 0.68 0.63 0.53 0.72 0.63 -0.95 -0.90 -0.93 -0.86 -0.50 -0.78 0.68 0.68 0.75 0.72 0.68 -0.90 -0.75 -0.86 -0.71 0.00 -0.60 0.72 0.69 0.81 0.74 0.76 -0.75 -0.50 -0.79 -0.57  -0.33 0.74 0.70 0.83 0.75 0.73 -0.50 0.00 -0.72 -0.43  0.00 0.74 0.70 0.83 0.73 0.71 0.00 0.50 -0.66 -0.29  0.33 0.72 0.70 0.83 0.74 0.73 0.50 0.75 -0.59 -0.14  0.60 0.73 0.70 0.85 0.72 0.76 0.75 0.90 -0.52 0.00  0.78 0.70 0.70 0.79 0.71 0.68 0.90 0.95 -0.45 0.14  0.93 0.70 0.71 0.85 0.70 0.63 0.95  -0.38 0.29    0.70 0.83     -0.31 0.43    0.71 0.83     -0.24 0.57    0.71 0.83     -0.17 0.71    0.71 0.81     -0.10 0.86    0.70 0.75     -0.03 1.00    0.71 0.53     0.03     0.71      0.10     0.70      0.17     0.70      0.24     0.70      0.31     0.70      0.38     0.70      0.45     0.71      0.52     0.72      0.59     0.72      0.66     0.72      0.72     0.71      0.79     0.71      0.86     0.71      0.93     0.70      1.00     0.70       181  Table A.4 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.50 m/s, z = 0.24 m Radial voidage distribution, Sand, Ug = 0.50 m/s, z = 0.24 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Poly Probe) r/R (Borescope) UBC probe XCT RPT UWO Probe Poly Probe Borescope -0.95 -1.00 -1.00 -0.90 -0.93 0.58 0.62 0.53 0.63 0.63 0.61 -0.90 -0.93 -0.86 -0.50 -0.78 0.60 0.68 0.67 0.66 0.64 0.75 -0.75 -0.86 -0.71 0.00 -0.60 0.62 0.69 0.66 0.65 0.63 0.76 -0.50 -0.79 -0.57  -0.33 0.65 0.70 0.68 0.70  0.75 0.00 -0.72 -0.43  0.00 0.69 0.72 0.68 0.72  0.72 0.50 -0.66 -0.29  0.33 0.64 0.73 0.69 0.74  0.75 0.75 -0.59 -0.14  0.60 0.62 0.75 0.72 0.72  0.76 0.90 -0.52 0.00  0.78 0.60 0.76 0.71 0.68  0.75 0.95 -0.45 0.14  0.93 0.59 0.76 0.72 0.65  0.61  -0.38 0.29    0.77 0.69     -0.31 0.43    0.76 0.68     -0.24 0.57    0.76 0.68     -0.17 0.71    0.76 0.66     -0.10 0.86    0.76 0.67     -0.03 1.00    0.77 0.53     0.03     0.78      0.10     0.78      0.17     0.78      0.24     0.77      0.31     0.76      0.38     0.76      0.45     0.75      0.52     0.74      0.59     0.73      0.66     0.73      0.72     0.73      0.79     0.71      0.86     0.69      0.93     0.68      1.00     0.67       182  Table A.5 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.50 m/s, z = 0.40 m Radial voidage distribution, Sand, Ug = 0.50 m/s, z = 0.40 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Poly Probe) r/R (Borescope) UBC probe XCT RPT UWO Probe Poly Probe Borescope -0.95 -1.00 -1.00 -0.90 -0.93 0.60 0.61 0.53 0.65 0.60 0.77 -0.90 -0.93 -0.86 -0.50 -0.78 0.62 0.68 0.76 0.69 0.62 0.74 -0.75 -0.86 -0.71 0.00 -0.60 0.65 0.69 0.77 0.70 0.65 0.77 -0.50 -0.79 -0.57  -0.33 0.67 0.70 0.77 0.69  0.75 0.00 -0.72 -0.43  0.00 0.69 0.70 0.79 0.72  0.76 0.50 -0.66 -0.29  0.33 0.64 0.70 0.79 0.73  0.75 0.75 -0.59 -0.14  0.60 0.62 0.70 0.79 0.72  0.77 0.90 -0.52 0.00  0.78 0.60 0.70 0.78 0.71  0.74 0.95 -0.45 0.14  0.93 0.61 0.70 0.79 0.72  0.77  -0.38 0.29    0.70 0.79     -0.31 0.43    0.71 0.79     -0.24 0.57    0.70 0.77     -0.17 0.71    0.70 0.77     -0.10 0.86    0.70 0.76     -0.03 1.00    0.70 0.53     0.03     0.69      0.10     0.69      0.17     0.69      0.24     0.70      0.31     0.70      0.38     0.70      0.45     0.71      0.52     0.71      0.59     0.71      0.66     0.71      0.72     0.71      0.79     0.71      0.86     0.71      0.93     0.70      1.00     0.69     183  Table A.6 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.50 m/s, z = 0.56 m Radial voidage distribution, Sand, Ug = 0.50 m/s, z = 0.56 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Poly Probe) r/R (Borescope) UBC probe XCT RPT UWO Probe Poly Probe Borescope -0.95 -1.00 -1.00 -0.90 -0.93 0.63 0.66 0.53 0.72 0.74 0.64 -0.90 -0.93 -0.86 -0.50 -0.78 0.65 0.72 0.66 0.72 0.75 0.73 -0.75 -0.86 -0.71 0.00 -0.60 0.70 0.72 0.62 0.74 0.69 0.70 -0.50 -0.79 -0.57  -0.33 0.71 0.72 0.62 0.74  0.69 0.00 -0.72 -0.43  0.00 0.73 0.73 0.63 0.75  0.83 0.50 -0.66 -0.29  0.33 0.69 0.72 0.68 0.75  0.69 0.75 -0.59 -0.14  0.60 0.66 0.72 0.73 0.74  0.70 0.90 -0.52 0.00  0.78 0.66 0.72 0.72 0.73  0.73 0.95 -0.45 0.14  0.93 0.64 0.72 0.73 0.68  0.64  -0.38 0.29    0.72 0.68     -0.31 0.43    0.72 0.63     -0.24 0.57    0.72 0.62     -0.17 0.71    0.71 0.62     -0.10 0.86    0.70 0.66     -0.03 1.00    0.69 0.53     0.03     0.68      0.10     0.68      0.17     0.68      0.24     0.68      0.31     0.69      0.38     0.69      0.45     0.69      0.52     0.70      0.59     0.69      0.66     0.70      0.72     0.71      0.79     0.71      0.86     0.71      0.93     0.70      1.00     0.69      184  Table A.7 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.60 m/s, z = 0.24 m Radial voidage distribution, Sand, Ug = 0.60 m/s, z = 0.24 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Poly Probe) r/R (Borescope) UBC probe XCT RPT UWO Probe Poly Probe Borescope -0.95 -1.00 -1.00 -0.90 -0.93 0.57 0.61 0.55 0.61 0.62 0.65 -0.90 -0.93 -0.86 -0.50 -0.78 0.60 0.66 0.66 0.58 0.65 0.74 -0.75 -0.86 -0.71 0.00 -0.60 0.61 0.67 0.60 0.62 0.66 0.75 -0.50 -0.79 -0.57  -0.33 0.67 0.69 0.65 0.64  0.74 0.00 -0.72 -0.43  0.00 0.68 0.72 0.64 0.70  0.76 0.50 -0.66 -0.29  0.33 0.66 0.73 0.61 0.66  0.74 0.75 -0.59 -0.14  0.60 0.62 0.74 0.55 0.65  0.75 0.90 -0.52 0.00  0.78 0.58 0.76 0.56 0.62  0.74 0.95 -0.45 0.14  0.93 0.56 0.77 0.55 0.61  0.65  -0.38 0.29    0.78 0.61     -0.31 0.43    0.79 0.64     -0.24 0.57    0.79 0.65     -0.17 0.71    0.78 0.60     -0.10 0.86    0.78 0.66     -0.03 1.00    0.78 0.55     0.03     0.79      0.10     0.78      0.17     0.78      0.24     0.78      0.31     0.78      0.38     0.79      0.45     0.79      0.52     0.78      0.59     0.78      0.66     0.77      0.72     0.76      0.79     0.74      0.86     0.72      0.93     0.70      1.00     0.67            185  Table A.8 – Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.60 m/s, z = 0.40 m Radial voidage distribution, Sand, Ug = 0.60 m/s, z = 0.40 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Poly Probe) r/R (Borescope) UBC probe XCT RPT UWO Probe Poly Probe Borescope -0.95 -1.00 -1.00 -0.90 -0.93 0.62 0.67 0.53 0.62 0.61 0.71 -0.90 -0.93 -0.86 -0.50 -0.78 0.65 0.75 0.71 0.67 0.63 0.76 -0.75 -0.86 -0.71 0.00 -0.60 0.68 0.76 0.73 0.70 0.66 0.74 -0.50 -0.79 -0.57  -0.33 0.68 0.77 0.73 0.70  0.71 0.00 -0.72 -0.43  0.00 0.74 0.77 0.74 0.69  0.73 0.50 -0.66 -0.29  0.33 0.73 0.77 0.74 0.72  0.71 0.75 -0.59 -0.14  0.60 0.70 0.78 0.72 0.74  0.74 0.90 -0.52 0.00  0.78 0.70 0.78 0.75 0.72  0.76 0.95 -0.45 0.14  0.93 0.64 0.78 0.72 0.70  0.71  -0.38 0.29    0.78 0.74     -0.31 0.43    0.77 0.74     -0.24 0.57    0.78 0.73     -0.17 0.71    0.78 0.73     -0.10 0.86    0.77 0.71     -0.03 1.00    0.77 0.53     0.03     0.77      0.10     0.77      0.17     0.77      0.24     0.77      0.31     0.77      0.38     0.77      0.45     0.77      0.52     0.78      0.59     0.78      0.66     0.77      0.72     0.78      0.79     0.78      0.86     0.78      0.93     0.77      1.00     0.75            186  Table A.9– Radial voidage distribution obtained by alternate measurement techniques, sand, Ug = 0.60 m/s, z = 0.56 m Radial voidage distribution, Sand, Ug = 0.60 m/s, z = 0.56 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Poly Probe) r/R (Borescope) UBC probe XCT RPT UWO Probe Poly Probe Borescope -0.95 -1.00 -1.00 -0.90 -0.93 0.68 0.73 0.54 0.74 0.75 0.68 -0.90 -0.93 -0.86 -0.50 -0.78 0.72 0.75 0.62 0.75 0.76 0.72 -0.75 -0.86 -0.71 0.00 -0.60 0.72 0.76 0.61 0.77 0.73 0.76 -0.50 -0.79 -0.57  -0.33 0.74 0.77 0.59 0.78  0.72 0.00 -0.72 -0.43  0.00 0.74 0.77 0.58 0.76  0.67 0.50 -0.66 -0.29  0.33 0.69 0.77 0.60 0.75  0.72 0.75 -0.59 -0.14  0.60 0.70 0.77 0.57 0.74  0.76 0.90 -0.52 0.00  0.78 0.67 0.77 0.54 0.73  0.72 0.95 -0.45 0.14  0.93 0.61 0.77 0.57 0.74  0.68  -0.38 0.29    0.77 0.60     -0.31 0.43    0.77 0.58     -0.24 0.57    0.76 0.59     -0.17 0.71    0.77 0.61     -0.10 0.86    0.77 0.62     -0.03 1.00    0.77 0.54     0.03     0.76      0.10     0.75      0.17     0.74      0.24     0.74      0.31     0.74      0.38     0.74      0.45     0.75      0.52     0.76      0.59     0.76      0.66     0.76      0.72     0.76      0.79     0.75      0.86     0.75      0.93     0.75      1.00     0.74            187  Table A.10 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.30 m/s, z = 0.24 m Radial voidage distribution, FCC, Ug = 0.30 m/s, z = 0.24 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Borescope) UBC probe XCT RPT UWO Probe Borescope -0.95 -1.00 -1.00 -0.93 0.63 0.51 0.68 0.66 0.61 -0.90 -0.93 -0.86 -0.78 0.65 0.56 0.69 0.67 0.67 -0.75 -0.86 -0.71 -0.60 0.67 0.58 0.66 0.68 0.67 -0.50 -0.79 -0.57 -0.33 0.68 0.60 0.61 0.69 0.71 0.00 -0.72 -0.43 0.00 0.65 0.62 0.58 0.67 0.75 0.50 -0.66 -0.29 0.33 0.64 0.64 0.52 0.68 0.71 0.75 -0.59 -0.14 0.60 0.64 0.66 0.50 0.68 0.67 0.90 -0.52 0.00 0.78 0.60 0.67 0.45 0.66 0.67 0.95 -0.45 0.14 0.93 0.63 0.68 0.50 0.65 0.61  -0.38 0.29   0.69 0.52    -0.31 0.43   0.70 0.58    -0.24 0.57   0.72 0.61    -0.17 0.71   0.72 0.66    -0.10 0.86   0.72 0.69    -0.03 1.00   0.71 0.68    0.03    0.71     0.10    0.70     0.17    0.70     0.24    0.70     0.31    0.68     0.38    0.67     0.45    0.67     0.52    0.65     0.59    0.63     0.66    0.62     0.72    0.60     0.79    0.58     0.86    0.56     0.93    0.54     1.00    0.52           188  Table A.11 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.30 m/s, z = 0.40 m Radial voidage distribution, FCC, Ug = 0.30 m/s, z = 0.40 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Borescope) UBC probe XCT RPT UWO Probe Borescope -0.95 -1.00 -1.00 -0.93 0.64 0.61 0.52 0.68 0.61 -0.90 -0.93 -0.86 -0.78 0.65 0.64 0.64 0.70 0.62 -0.75 -0.86 -0.71 -0.60 0.68 0.64 0.59 0.69 0.63 -0.50 -0.79 -0.57 -0.33 0.68 0.65 0.55 0.72 0.68 0.00 -0.72 -0.43 0.00 0.68 0.66 0.54 0.73 0.66 0.50 -0.66 -0.29 0.33 0.68 0.68 0.52 0.72 0.68 0.75 -0.59 -0.14 0.60 0.66 0.69 0.51 0.70 0.63 0.90 -0.52 0.00 0.78 0.65 0.71 0.45 0.68 0.62 0.95 -0.45 0.14 0.93 0.64 0.71 0.51 0.66 0.61  -0.38 0.29   0.71 0.52    -0.31 0.43   0.70 0.54    -0.24 0.57   0.70 0.55    -0.17 0.71   0.70 0.59    -0.10 0.86   0.69 0.64    -0.03 1.00   0.69 0.52    0.03    0.68     0.10    0.68     0.17    0.69     0.24    0.68     0.31    0.68     0.38    0.67     0.45    0.65     0.52    0.64     0.59    0.63     0.66    0.61     0.72    0.60     0.79    0.58     0.86    0.57     0.93    0.55     1.00    0.54           189  Table A.12– Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.30 m/s, z = 0.56 m Radial voidage distribution, FCC, Ug = 0.30 m/s, z = 0.56 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Borescope) UBC probe XCT RPT UWO Probe Borescope -0.95 -1.00 -1.00 -0.93 0.62 0.60 0.45 0.70 0.62 -0.90 -0.93 -0.86 -0.78 0.63 0.65 0.59 0.72 0.60 -0.75 -0.86 -0.71 -0.60 0.67 0.66 0.57 0.71 0.58 -0.50 -0.79 -0.57 -0.33 0.68 0.67 0.55 0.72 0.60 0.00 -0.72 -0.43 0.00 0.73 0.68 0.59 0.73 0.58 0.50 -0.66 -0.29 0.33 0.70 0.69 0.55 0.74 0.60 0.75 -0.59 -0.14 0.60 0.67 0.70 0.53 0.71 0.58 0.90 -0.52 0.00 0.78 0.63 0.70 0.64 0.70 0.60 0.95 -0.45 0.14 0.93 0.63 0.71 0.53 0.67 0.62  -0.38 0.29   0.72 0.55    -0.31 0.43   0.73 0.59    -0.24 0.57   0.73 0.55    -0.17 0.71   0.74 0.57    -0.10 0.86   0.74 0.59    -0.03 1.00   0.74 0.45    0.03    0.75     0.10    0.75     0.17    0.74     0.24    0.74     0.31    0.74     0.38    0.73     0.45    0.72     0.52    0.72     0.59    0.71     0.66    0.70     0.72    0.70     0.79    0.68     0.86    0.67     0.93    0.65     1.00    0.63    190  Table A.13 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.40 m/s, z = 0.24 m Radial voidage distribution, FCC, Ug = 0.40 m/s, z = 0.24 m r/R (UBC & UWO Probes) r/R (XCT) r/R (RPT) r/R (Borescope) UBC probe XCT RPT UWO Probe Borescope -0.95 -1.00 -1.00 -0.93 0.60 0.50 0.45 0.69 0.61 -0.90 -0.93 -0.86 -0.78 0.61 0.52 0.62 0.67 0.68 -0.75 -0.86 -0.71 -0.60 0.62 0.53 0.64 0.70 0.74 -0.50 -0.79 -0.57 -0.33 0.63 0.54 0.63 0.68 0.73 0.00 -0.72 -0.43 0.00 0.65 0.54 0.64 0.71 0.75 0.50 -0.66 -0.29 0.33 0.64 0.56 0.64 0.70 0.73 0.75 -0.59 -0.14 0.60 0.62 0.57 0.59 0.68 0.74 0.90 -0.52 0.00 0.78 0.61 0.57 0.58 0.69 0.68 0.95 -0.45 0.14 0.93 0.61 0.59 0.59 0.66 0.61  -0.38 0.29   0.59 0.64    -0.31 0.43   0.60 0.64    -0.24 0.57   0.60 0.63    -0.17 0.71   0.60 0.64    -0.10 0.86   0.61 0.62    -0.03 1.00   0.61 0.45    0.03    0.62     0.10    0.63     0.17    0.63     0.24    0.64     0.31    0.65     0.38    0.66     0.45    0.66     0.52    0.66     0.59    0.67     0.66    0.67     0.72    0.67     0.79    0.67     0.86    0.66     0.93    0.64     1.00    0.62           191  Table A.14 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.40 m/s, z = 0.40 m Radial voidage distribution, FCC, Ug = 0.40 m/s, z = 0.40 m r/R (UBC & UWO Probes) r/R (RPT) r/R (Borescope) UBC probe RPT UWO Probe Borescope -0.95 -1.00 -0.93 0.62 0.45 0.70 0.61 -0.90 -0.86 -0.78 0.61 0.66 0.70 0.61 -0.75 -0.71 -0.60 0.63 0.69 0.73 0.63 -0.50 -0.57 -0.33 0.65 0.70 0.73 0.65 0.00 -0.43 0.00 0.68 0.70 0.76 0.68 0.50 -0.29 0.33 0.67 0.71 0.72 0.65 0.75 -0.14 0.60 0.66 0.71 0.70 0.63 0.90 0.00 0.78 0.64 0.73 0.67 0.61 0.95 0.14 0.93 0.62 0.71 0.67 0.61  0.29   0.71    0.43   0.70    0.57   0.70    0.71   0.69    0.86   0.66    1.00   0.45   Table A.15 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.40 m/s, z = 0.56 m FCC, Ug = 0.40 m/s, z = 0.56 m r/R (UBC & UWO Probes) r/R (RPT) r/R (Borescope) UBC probe RPT UWO Probe Borescope -0.95 -1.00 -0.93 0.60 0.45 0.71 0.59 -0.90 -0.86 -0.78 0.61 0.57 0.72 0.58 -0.75 -0.71 -0.60 0.65 0.57 0.73 0.61 -0.50 -0.57 -0.33 0.66 0.56 0.73 0.66 0.00 -0.43 0.00 0.68 0.55 0.73 0.59 0.50 -0.29 0.33 0.67 0.56 0.72 0.66 0.75 -0.14 0.60 0.67 0.55 0.71 0.61 0.90 0.00 0.78 0.65 0.54 0.70 0.58 0.95 0.14 0.93 0.61 0.55 0.69 0.59  0.29   0.56    0.43   0.55    0.57   0.56    0.71   0.57    0.86   0.57    1.00   0.45    192  Table A.16– Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.50 m/s, z = 0.24 m Radial voidage distribution, FCC, Ug = 0.50 m/s, z = 0.24 m r/R (UBC & UWO Probes) r/R (Xray) r/R (RPT) r/R (Borescope) UBC probe XCT RPT Borescope -0.95 -1.00 -1.00 -0.93 0.60 0.51 0.45 0.62 -0.90 -0.93 -0.86 -0.78 0.58 0.53 0.54 0.67 -0.75 -0.86 -0.71 -0.60 0.62 0.54 0.51 0.75 -0.50 -0.79 -0.57 -0.33 0.64 0.55 0.55 0.75 0.00 -0.72 -0.43 0.00 0.66 0.56 0.51 0.74 0.50 -0.66 -0.29 0.33 0.65 0.58 0.54 0.75 0.75 -0.59 -0.14 0.60 0.64 0.58 0.48 0.75 0.90 -0.52 0.00 0.78 0.62 0.59 0.43 0.67 0.95 -0.45 0.14 0.93 0.61 0.60 0.48 0.62  -0.38 0.29   0.61 0.54   -0.31 0.43   0.61 0.51   -0.24 0.57   0.62 0.55   -0.17 0.71   0.63 0.51   -0.10 0.86   0.64 0.54   -0.03 1.00   0.65 0.45   0.03    0.66    0.10    0.67    0.17    0.68    0.24    0.68    0.31    0.70    0.38    0.71    0.45    0.72    0.52    0.72    0.59    0.72    0.66    0.72    0.72    0.72    0.79    0.71    0.86    0.69    0.93    0.67    1.00    0.64    193  Table A.17 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.50 m/s, z = 0.40 m Radial voidage distribution, FCC, Ug = 0.50 m/s, z = 0.40 m r/R (UBC & UWO Probes) r/R (RPT) r/R (Borescope) UBC probe RPT Borescope -0.95 -1.00 -0.93 0.61 0.45 0.60 -0.90 -0.86 -0.78 0.62 0.61 0.62 -0.75 -0.71 -0.60 0.63 0.63 0.65 -0.50 -0.57 -0.33 0.66 0.62 0.66 0.00 -0.43 0.00 0.68 0.60 0.69 0.50 -0.29 0.33 0.67 0.60 0.66 0.75 -0.14 0.60 0.66 0.58 0.65 0.90 0.00 0.78 0.63 0.57 0.62 0.95 0.14 0.93 0.63 0.58 0.60  0.29   0.60   0.43   0.60   0.57   0.62   0.71   0.63   0.86   0.61   1.00   0.45  Table A.18 – Radial voidage distribution obtained by alternate measurement techniques, FCC, Ug = 0.50 m/s, z = 0.56 m Radial voidage distribution, FCC, Ug = 0.50 m/s, z = 0.56 m r/R (UBC & UWO Probes) r/R (RPT) r/R (Borescope) UBC probe RPT Borescope -0.95 -1.00 -0.93 0.60 0.45 0.62 -0.90 -0.86 -0.78 0.61 0.78 0.62 -0.75 -0.71 -0.60 0.63 0.83 0.66 -0.50 -0.57 -0.33 0.67 0.85 0.62 0.00 -0.43 0.00 0.70 0.85 0.64 0.50 -0.29 0.33 0.70 0.83 0.62 0.75 -0.14 0.60 0.68 0.84 0.66 0.90 0.00 0.78 0.66 0.81 0.62 0.95 0.14 0.93 0.60 0.84 0.62  0.29   0.83   0.43   0.85   0.57   0.85   0.71   0.83   0.86   0.78   1.00   0.45      194  Appendix B  − Volume-based analysis of PEPT and RPT In this Appendix, experimental particle velocities based on the volume-based analysis method described in Section 2.4.2.3 are compared with level-crossing method data to investigate the effect on the radial profiles of time-average solids velocity. The time-average solids velocity at each radial position has been calculated considering all the velocity vectors associated with the tracer particle located in the corresponding 3-D annular slice (hollow disc) of 0.03 m height terminating 0.015 m above and beginning 0.015 m below the measurement level.  As mentioned in Chapter 2, compared to the level-crossing method, the volume-based approach tends to produce data which are shifted towards slower velocities. For instance, consider two cases, (a) and (b), where equal numbers of tracer particles have speeds of 0.1 and 0.2 m/s. In the volume-based method, the tracer velocity given in (a) will be counted twice as often as the one of case (b) in the time-averaging calculations associated with a certain 3-D annulus.  As shown in Figures B.1 to B.4, the time-average radial profiles of solid-velocity for FCC associated with RPT and PEPT obtained from the volume-based approach are characterized by lower magnitudes compared to the results in Figures 4.1 to 4.4.  The following paragraphs compare the results obtained by the two approaches. Note that the crossing-method refers here to the case when particles with a small deviation angle compared to the vertical are considered in the time-averaging calculations, but the discussion also applies to the case when the vertical components of all velocity vectors are taken into account.   195  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.15-0.10-0.050.000.050.100.150.200.25z = 0.40 mTime-average particle velocity (m/s)-0.3-0.2-0.10.00.10.20.30.4Optical probe Borescope RPT PEPT z = 0.56 m-0.3-0.2-0.10.00.10.20.3 Figure B.1 – Radial profiles of time-average solid velocity at three levels for FCC using volume-based approach for RPT and PEPT, Ug = 0.30 m/s. 196  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.10-0.050.000.050.100.150.200.25z = 0.40 mTime-averaged particle velocity (m/s)-0.3-0.2-0.10.00.10.20.30.4Optical probe Borescope RPT PEPTz = 0.56 m-0.3-0.2-0.10.00.10.20.30.4 Figure B.2 – Radial profiles of time-average solid velocity at three levels for FCC using volume-based approach for RPT and PEPT, Ug = 0.40 m/s. 197  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.2-0.10.00.10.20.30.4z = 0.40 mTime-averaged particle velocity (m/s)-0.3-0.2-0.10.00.10.20.30.4Optical probeBorescope RPT PEPT z = 0.56 m-0.3-0.2-0.10.00.10.20.30.40.5 Figure B.3 – Radial profiles of time-average solid velocity at three levels for FCC using volume-based approach for RPT and PEPT, Ug = 0.50 m/s. 198  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.2-0.10.00.10.20.30.40.5z = 0.40 mTime-averaged particle velocity (m/s)-0.3-0.2-0.10.00.10.20.30.40.5Optical probeBorescope RPT PEPT z = 0.56 m-0.3-0.2-0.10.00.10.20.30.40.5 Figure B.4 – Radial profiles of time-average solid velocity at three levels for FCC using volume-based approach for RPT and PEPT, Ug = 0.60 m/s. 199  For Ug = 0.30 m/s, the volume-based approach produces better agreement, at all radial positions, among the results of PEPT and the other invasive techniques for the middle section of the column (i.e., z = 0.40 m). For the upper measurement level (z = 0.56 m), only the particle velocity at the wall region obtained by PEPT is appreciably affected by the analysis approach, with the PEPT results associated with volume-based analysis closer to the values of the other techniques. However, it should be noted that the optical probe did not measure the particle velocity exactly at the wall due to the limit imposed by the glass window, making it challenging to compare directly the wall region with the other techniques. Note also that the borescopic high-speed PIV has tendency to give greater weight to the nearly zero-velocity particles when producing a time-average value. Compared to the volume-based method, RPT results obtained by the crossing-level approach are closer to the results of optical probe and borescopy for all measurement heights. For Ug = 0.40 and 0.50 m/s, PEPT results at the middle section obtained by the volume-based approach in the central region show better agreement with the invasive-technique particle velocity data. For the other radial positions, PEPT results at z = 0.40 m are in better agreement with optical probe and borescopy data when the crossing-level method is considered. For all the other measurement levels, compared to the volume-based approach, the crossing-level method provides better agreement between the radial profiles of time-average velocity obtained by all four measurement techniques. For Ug = 0.60 m/s, the crossing-level method provides results of RPT and PEPT closer to those of optical probe and borescopy, compared to the volume-based approach, at all measurement levels. 200  For sand particles, RPT results are not very sensitive to the analysis approach. On the other hand, the volume-based method produces time-average solid PEPT velocity results which differ significantly from those obtained from the crossing method, as shown in Figures B.5 to B.7. The overall agreement among the results is still disappointing. It is observed that the negative time-average particle velocity results obtained by PEPT from the crossing-level method in most cases, switched to positive ones when the volume-based approach was considered. This effect is mainly due to the fact that particle raining produces high-magnitude velocities which: (a) are counted less often than the lower-magnitude velocities represented by the upward moving plugs; and (b) cannot be captured entirely by the volume-based method due to the finite size of the cell. The magnitude of the maximum velocity detected by the volume-based approach depends on the height of the cells, since a fast-moving particle represented by two successive positions outside the boundaries of the cell, one above and one below, would not be counted in the averaging calculations.   201  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.20-0.15-0.10-0.050.000.050.100.15Optical probe Borescope RPT PEPT z = 0.40 mTime-averaged particle velocity (m/s)-0.3-0.2-0.10.00.10.20.30.4z = 0.56 m-0.4-0.3-0.2-0.10.00.10.20.30.4 Figure B.5 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.40 m/s. 202  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.20-0.15-0.10-0.050.000.050.100.15Optical probe Borescope RPT PEPT z = 0.40 mTime-averaged particle velocity (m/s)-0.6-0.4-0.20.00.20.4z = 0.56 m-0.6-0.4-0.20.00.20.4 Figure B.6 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.50 m/s. 203  z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.25-0.20-0.15-0.10-0.050.000.050.100.15Optical probe Borescope RPT PEPT z = 0.40 mTime-averaged particle velocity (m/s)-0.5-0.4-0.3-0.2-0.10.00.10.20.3z = 0.56 m-0.6-0.4-0.20.00.20.40.6 Figure B.7 – Radial profiles of time-average solid velocity at three levels for sand, Ug = 0.60 m/s. 204  Overall, the crossing-level approach is more suitable when the results of the particle tracking techniques are compared to those obtained by the optical fibre probes. This is due to the fact that the probing techniques are: (1) characterized by a quasi-zero measurement volume; and (2) in general, do not have a tendency to attribute more weight to the low-velocity particles. The borescope appears to be volumetric, with a tendency to count more often the nearly zero-velocity particles. In fact, the radial profile of time-average velocity obtained by the borescopy is in most cases characterized by smaller-magnitude values than those obtained by the optical probe.  It is also noteworthy that the crossing-level approach is relevant for the solid flux measurements. 205  Appendix C  − Examples of analysis of variance for solid velocity In this Appendix, two sample tables reporting the results of analysis of variance performed on FCC solid velocity data are given. Multiple means comparison was also performed using the Fisher LSD test (Montgomery and Runger, 2010).  Table C.1 – ANOVA results with true null hypothesis, FCC, Ug = 0.50 m/s, z = 0.56 m, r/R=0.6 Descriptive statistics FCC, Ug=0.50 m/s, z = 0.56 m, r/R=0.60 Sample size Mean (m/s) Standard Deviation (m/s) Standard error of Mean (m/s) Borescopy 26764 0.157 1.397 0.009 Optical fibre probe 2404 0.169 0.613 0.013 PEPT 1020 0.139 0.763 0.024 RPT 877 0.135 1.211 0.041 ANOVA FCC, Ug=0.50 m/s, z = 0.56 m, r/R=0.60 DF Sum of Squares (m/s)2 Mean Square (m/s)2 F value Prob>F Factor 3 1.061 0.354 0.200 0.897 Error 31061 55020.970 1.771   Total 31064 55022.030    Mean comparison (LSD test) FCC, Ug=0.50 m/s, z = 0.56 m, r/R=0.60 MeanDiff (m/s) t Value Prob Alpha Sig Optical probe-Borescope 0.012 0.424 0.672 0.05 0 PEPT-Borescope -0.017 -0.409 0.682 0.05 0 PEPT-Optical probe -0.029 -0.591 0.555 0.05 0 RPT-Borescope -0.022 -0.472 0.637 0.05 0 RPT-Optical probe -0.034 -0.640 0.522 0.05 0 RPT-PEPT -0.004 -0.068 0.945 0.05 0     206  Table C.2 – ANOVA results with false null hypothesis, FCC, Ug = 0.30 m/s, z = 0.40 m, r/R=0 Descriptive statistics FCC, Ug=0.30 m/s, z = 0.40 m, r/R=0 Sample size Mean (m/s) Standard Deviation(m/s) Standard error of Mean (m/s) Borescopy 12785 0.123 0.238 0.002 Optical fibre probe 1964 0.290 0.580 0.013 PEPT 686 0.570 0.668 0.026 RPT 467 0.119 0.948 0.044 ANOVA FCC, Ug=0.30 m/s, z = 0.40 m, r/R=0 DF Sum of Squares (m/s)2 Mean Square (m/s)2 F value Prob>F Factor 3 166.548 55.516 419.022 0 Error 15898 2106.315 0.132   Total 15901 2272.863    Mean comparison (LSD test) FCC, Ug=0.30 m/s, z = 0.40 m, r/R=0 MeanDiff (m/s) t Value Prob Alpha Sig Optical probe-Borescope 0.167 18.933 0.00 0.05 1 PEPT-Borescope 0.447 31.315 0.00 0.05 1 PEPT-Optical probe 0.280 17.326 0.00 0.05 1 RPT-Borescope -0.005 -0.269 0.79 0.05 0 RPT-Optical probe -0.172 -9.159 0.00 0.05 1 RPT-PEPT 0.451 20.669 0.00 0.05 1          207  Appendix D  − Square-nosed slugging This Appendix describes the physical phenomena associated with the square-nosed slugging regime, observed during the TFB experiments with sand particles.  The slugging regime in fluidized beds is characterized by voids (slugs), occupying most or all of the cross-section of the column, which rise at regular intervals, dividing the fluidized bed into alternate regions of dense and dilute phase. As indicated by Grace (1982), in order to reach the slugging regime, several different conditions need to be satisfied:  The average bubble diameter should be larger than about 2/3 of the column diameter;  The superficial gas velocity should be higher than the minimum slugging velocity (Ums) defined by the correlation given by Stewart and Davidson (1967);  The superficial gas velocity should be lower than Uc; and  The bed should be sufficiently deep, based on the criteria given by Darton et al. (1977). The slugging flow regime generally occurs in reactors of laboratory scale characterized by bed height-to-diameter ratio (Hs/D) of at least 2. There are basically two types of slugging. Type A slugging, the better-known variety also found in gas-liquid two-phase flows, consists of axial-symmetric round-nosed gas slugs rising through the dense phase which flow downwards in an annular region surrounding the slug close to the wall (Figure D.1). This type of slugging usually occurs with bed materials that fluidize easily (Geldart A and B powders). Type B slugging, mostly observed for cohesive and particles of angular shape in columns with smooth wall, is characterized by slugs that are essentially square-nosed, occupying the entire cross section of the column (see Figure D.1). The upward movement of the interfaces is then slow and largely caused by particles raining from the roofs of the slugs 208  through the dilute region to their floors. Note that the aforementioned criteria, entirely satisfied for TFB experiments with sand particles, represent the necessary conditions for obtaining slug flow, without specifying the type of slugging.  Figure D.1− Type A Axisymmetric; and type B square-nosed slugging schematics. Adapted from Yang (2003).  The majority of the publications about slugging regime deals with axisymmetric slugs observed for small particles; on the other hand the characteristics of the square-nosed slugging regime have been studied by only a limited number of researchers. Thiel and Potter (1977) observed that for the square-nosed slugging regime, the movement of solids is quite similar to that occurring during the measurement of the angle of internal friction (β) for a packed bed: the inter-slug material is pushed upward relative to the walls by fresh gas admitted at the distributor. If the Type (B) Type (A) Solids raining Gas flow Dense plug motion 209  height of the dense plug is greater than the critical height related to the angle of internal friction, the inter-slug material locks and the pressure rises due to the introduction of fresh gas into the system (similar to the force of a piston). When the plug of solids is locked onto the wall, the only way for the gas slug below the dense plug to move upward is by solids raining from its bottom through the slug, decreasing the plug height below the critical height.  Noordergraaf et al. (1987) observed that square-nosed slugging presents certain similarities with the fluidization characteristics of a fluidized bed coal combustor that contains closely packed heat exchanger tubes. They deployed pressure measurements to analyze the flow regime and suggested that the pressure fluctuations are mainly caused by the disintegration of rising plugs, followed by the precipitation of the particles. When the bed level is at a maximum for a given gas velocity, the number of particles in the raining phase is a maximum, and the pressure drop is a minimum. On the other hand, with the bed at its minimum level, the majority of the particles are in the dense plugs and contribute to the pressure drop. Typically the slug frequency in type A slugging bed is of the order of 1 Hz, whereas in a square-nosed slugging bed the main frequency is significantly lower (e.g. 0.4 Hz). The slug rise velocity in a smoothly slugging bed (type A) is approximately twice that in a square-nosed slugging bed. Thiel and Potter (1977) related this effect to the fact that only a fraction of the gas volumetric flow is carried by the translation of the slugs, with the remainder passing through the plugs as a packed bed flow. The higher pressure drop compared to that required to support the weight of the bed material, observed in square-nosed slugging beds, is a direct consequence of this. Chen et al. (1997) proposed a model based on the transformation and dissipation of the potential energy developed by rising solid plugs to describe the pressure drop across the slugging bed and 210  found results similar to those presented by Noordergraaf et al. (1987). They observed that all the potential energy acquired by solids in the dense plugs, up to the time they detach from the roof of the slug, is dissipated as they strike the dense region below, producing a compression effect resulting in a pressure drop larger than that corresponding to the weight-minus-buoyancy of the particles.  Thiel and Potter (1977) reported a close relationship between the type of slug flow and the value of tanβ for the solids. Solids which form a smooth slugging bed are generally characterized by larger tanβ than those that form square-nosed slugs. Materials that exhibit square-nosed slugging in high aspect ratio (Hs/D) beds can form freely bubbling fluidized beds in vessels of lower aspect ratio. Similar findings were indicated by Chen et al. (1997), who provided a diagram in which different types of slugging were related to the density of the particles and particle/column diameter ratio. Their study suggested that an increase in particle size and a decrease in column diameter both favour the formation of square-nosed slugging.  Van Putten et al. (2007) observed that the square-nosed slugging regime in the riser of a circulating fluidized bed, designed for polymerization reactions, presents a number of advantages such as:   Limited entrainment of fines due to the presence of dense plugs moving close to plug flow;  Prevention of sticking of the polymer particles to the column walls, due to continuous passage of dense plugs with a cleaning effect; and  More control of particle residence time and distribution, and possibility of being able to impose an axial temperature profile. 211  These authors studied the effect of riser diameter, gas velocity, solid hold-up and solids flux on the extent of solids mixing and segregation, and solids residence time. The residence time distribution of solids in square-nosed slugging flows presented Peclet numbers above 40, suggesting behaviour close to plug flow. Gibilaro et al. (1998) examined the mechanism of particle raining in square-nosed gas slugs. They described this phenomenon, considering that in the reference frame that moves with it, the dense solid plug may be regarded as an incipiently-fluidized bed with a free lower boundary. Considering a suspended fluidized bed initially having a lower boundary consisting of a horizontal, uniformly distributed layer of particles, the drag force on a particle in the bottom layer should be smaller than that of particles situated deeper in the bed, since the gas velocity at the bottom surface is smaller than inside the bed. The authors observed that, due to this axial drag force gradient, the particles at the bottom of the solid plug start to move downwards relative to the suspended bed, rapidly affecting the particle concentration in the next axial layer, which responds likewise. Particle raining progresses continuously, peeling off one layer after the other between the dense and the dilute phases, until the solid plug deteriorates. They proposed a model in which the rate of particle raining from the bottom of solid plugs corresponded to dynamic wave propagation.     Zhang and Yu (2002) carried out a computational study of slugging flow using a two-fluid continuum model. They concluded that in the slug flow regime, different wall conditions, representing different particle-wall interaction, result in different types of slugging. The no-slip wall condition (rough wall) leads to round-nosed axisymmetric slugs, whereas the full-slip condition (smooth wall) is likely to result in square-nosed slugs. 212  In summary, the square-nosed slugging occurs for fluidized beds of large particles with a small tanβ that satisfies the necessary criteria for slugging. Hydrodynamic characterization of this particular flow regime is important both for lab/pilot scale fluidized beds and few industrial applications.    213  Appendix E  − Brief study of the effect of the distributor geometry The distributor employed in this study, consistent with that utilized by Dubrawski et al. (2013), was characterized by orifices of 2.5 mm diameter with a pressure drops that ranged from 500 to 1750 Pa for the superficial gas velocities of interest. In order to investigate the effect of distributor on the flow structures, borescopic measurements were performed at the lowest measurement level (z = 0.24 m) using the distributor plate with 1.5 mm diameter orifices, characterized by pressure drop that ranged from 1750 to 4980 Pa.  Figure E.1 reports the radial profiles of time-average particle velocity corresponding to FCC fluidized using different distributors. Significant differences occur in terms of the particle velocity magnitude, when the distributor was switched to the one characterized by higher pressure drop. This confirms the importance and necessity of utilizing the same equipment and identical operating conditions to make reliable comparisons of different measurement techniques.  214    Figure E.1− Effect of distributor plate on particle velocity data obtained by borescopic high-speed PIV  FCC, Ug = 0.30 m/s, z = 0.24 mr/R0.0 0.2 0.4 0.6 0.8 1.0-0.10-0.050.000.050.100.150.200.25Borescope, low pressure drop distributor Borescope, high pressure drop distributorFCC, Ug = 0.50 m/s, z = 0.24 mTime-average particle velocity (m/s)-0.050.000.050.100.150.200.250.300.35

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