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Hydrodynamics of gas-solid turbulent fluidized beds Ellis, Naoko 2003

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H Y D R O D Y N A M I C S O F G A S - S O L I D T U R B U L E N T F L U I D I Z E D B E D S by Naoko Ellis B . S c , The University o f Waterloo, 1990 M . E . S c , The University o f Western Ontar io , 1993 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y i n T H E F A C U L T Y O F G R A D U A T E S T U D I E S Department o f Chemical and Biological Engineer ing W e accept this thesis as conforming to the required standard T H E U N I V E R S I T Y ' O F B R I T I S H C O L U M B I A February 2003 © N a o k o El l i s , 2003 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of C h e m i c a l < * . B T o l r f l i c a ) ^ g ? n e e r i n g The University of British Columbia Vancouver, Canada Date Feb<^/Q3 DE-6 (2/88) A B S T R A C T Many commercial fluidized bed processes (e.g. catalytic and gas-solid reactions, drying) operate i n the turbulent fluidization flow regime owing to its excellent gas-solids contacting, favourable heat transfer, and relatively l ow axial dispersion o f gas. The flow characteristics o f turbulent fluidized beds, having transient voids and a diffuse bed surface, have not been wel l defined, and there have been relatively few previous studies on the fundamental hydrodynamics o f this industrially important flow regime. In this research project, four different size fluidized beds — 0.11 m , 0.29 m , 0.61 m and 1.56 m i n diameter — wi th F lu id Cracking Catalyst and a commercia l catalyst, all involv ing Geldart G r o u p A particles, have been used to investigate the effect o f reactor size, system pressure and temperature on U c , the superficial gas velocity corresponding to the onset o f the turbulent fluidization flow regime, and on the local flow structure for different superficial gas velocities beyond U c . The transition velocity, U c , from the bubbl ing to the turbulent f low regime was deduced by measuring the pressure fluctuations in the bed using gauge and differential pressure transducers. Results show a different trend o f co lumn diameter, D , on U c between shallow ( H / D < 3) and deep beds ( H / D > 3). U c from differential pressure measurements was a stronger function o f the height o f the pressure cell compared to the effect o f radial posi t ion for the 1.56 m fluidization column. T h e transition velocity decreased wi th increasing system pressure (to 0.4 M P a ) confirming findings by earlier investigators. Increasing temperature (to 240°C) led to a decrease i n the transition velocity. The amplitude o f the differential pressure fluctuations indicated very little change i n v o i d size wi th changing temperature for the range investigated. U c f rom differential pressure signals decreased wi th increasing height above the distributor plate. This impl ied greater homogeneity at the top o f the bed. Spectral analysis o f differential pressure signals at different axial positions revealed a shift towards lower frequencies wi th increasing height. Once the turbulent fluidization flow regime was achieved, the dominant frequency becomes less sensitive to height. A x i a l pressure profiles indicated diffuse bed surfaces. The gauge pressure i n the freeboard increased wi th increasing superficial gas velocity due to solids entrainment. T h e bed expansion depended on the configuration o f the solids collection and return system. In systems where the solids circulation rate was not controlled, the characterization o f the overall operating conditions i n terms o f bed i i voidage becomes difficult. Increases i n both absolute pressure and temperature were found to increase bed voidage, wi th pressure having a greater influence than temperature. L o c a l voidages were measured experimentally by means o f optical fiber and capacitance probes. The signals indicated continuous probability distribution functions and rapid fluctuations, indicating a breakdown o f the discrete-two-phase structure, i.e., discrete dense and dilute phases, a c o m m o n feature o f the bubbl ing bed flow regime. Cycle times obtained from rescaled range analysis o f voidage signals suggested a range o f cycle frequencies similar to those detected by the dominant peak from spectral analyses. A recendy established optical velocity probe capable o f simultaneously measuring particle velocity and voidage was used to delineate the change i n the local two-phase flow structure when the superficial gas velocity was increased beyond U c . V o i d velocities deduced from cross-correlation o f voidage signals obtained from two identical optical voidage probes were shown to become increasingly sensitive to the threshold value separating the dense and dilute phases. Hence the utility o f the two-phase theory i n characterizing v o i d dynamics i n the turbulent fluidization flow regime became limited. De-nois ing voidage fluctuation signals using a nonlinear wavelet transform through soft thresholding was shown to be successful i n pre-condit ioning the signal for cross-correlation o f bivariate time series. This study provides further understanding o f the hydrodynamics o f the turbulent fluidization flow regime using equipment o f substantial size to determine transition velocities and provide hydrodynamic data wh ich are meaningful for industrial-sized fluidized beds. 111 T A B L E O F C O N T E N T S H Y D R O D Y N A M I C S O F G A S - S O L I D T U R B U L E N T F L U I D I Z E D B E D S A B S T R A C T i i T A B L E O F C O N T E N T S iv L I S T O F T A B L E S x i L I S T O F F I G U R E S x i i A C K N O W L E D G E M E N T S xxv C H A P T E R 1 1 I N T R O D U C T I O N 1 1.1 F l o w regimes and transitions between regimes 3 1.2 Turbulent fluidization flow regime 4 1.3 Outstanding issues 4 1.4 Research objectives 6 1.5 Thesis layout 7 C H A P T E R 2 10 E Q U I P M E N T A N D M A C R O S C O P I C H Y D R O D Y N A M I C S 10 2.1 Introduction 10 2.1.1 B e d expansion 10 2.1.2 A x i a l voidage profile 10 2.2 Particulate material 11 2.3 C o l u m n I: 0.29 m diameter fluidization co lumn 13 2.3.1 Pressure transducers and data acquisition system 13 2.3.2 B e d expansion 17 2.3.3 B e d voidage 17 2.3.4 In-bed inventory o f solids 19 2.3.5 Solids circulation rate • 23 2.3.6 A x i a l voidage distribution 23 2.4 C o l u m n II: 0.61 m diameter co lumn 23 2.4.1 Pressure balance i n circulation loop 27 2.4.2 Expanded bed height 29 2.4.3 B e d density 29 iv 2.5 C o l u m n III: 1.56 m diameter fluidization co lumn 29 2.5.1 Traversing arm design and construction 32 2.5.2 Pressure measurements 32 2.5.3 B e d expansion 35 2.5.4 A x i a l voidage pro file 3 5 2.5.5 Voidage profile 35 2.6 C o l u m n I V : 0.11 m diameter co lumn 38 2.6.1 Instrumentation (hot unit) 38 2.6.2 B e d expansion (hot unit) 38 2.6.3 B e d voidage (hot unit) 40 2.7 Conclusions 45 C H A P T E R 3 47 R E G I M E T R A N S I T I O N A N D S C A L E E F F E C T 47 3.1 Regime transition 47 3.2 Observat ion o f current knowledge and its gaps 51 3.2.1 Regime transition 51 3.2.2 Scale effect 52 3.3 Exper imental approach 52 3.3.1 Pressure measurement method 56 3.3.2 E r r o r analysis 56 3.4 Results 58 3.4.1 Effect o f axial probe location and static bed height o n U c 58 3.4.2 Effect o f co lumn diameter on U c 61 3.4.3 Effect o f particle properties on U c 68 3.4.4 Effect o f system pressure on U c 70 3.4.5 Effect o f temperature o n U c 75 3.4.6 C o m b i n e d effects o f pressure and temperature o n U c 77 3.4.7 U c correlation 80 3.5 Conclusions and recommendations 84 C H A P T E R 4 86 V O I D A G E M E A S U R E M E N T S 86 4.1 Introduction 86 4.2 L o c a l voidage measurement 86 v 4.3 Voidage in turbulent fluidized beds 88 4.3.1 Radial voidage distribution 88 4.3.2 Dense phase voidage 91 4.4 Opt ica l probe measuring method principles 92 4.5 Opt ica l voidage probe used i n this study 95 4.5.1 Opt ica l probe calibration 97 4.5.2 Exper imental calibration o f optical voidage probe 98 4.5.3 Glass w indow 101 4.6 Capacitance probe 104 4.7 Results 109 4.7.1 Opt ica l fiber probe 109 4.7.2 Radial voidage profile 109 4.7.3 Scale effect on radial voidage profile " - 116 4.7.3.1 Results from 0.61 m diameter fluidization co lumn 120 4.7.3.2 Results from 1.56 m diameter fluidization co lumn 120 4.7.3.3 Scale effect 123 4.7.4 Dense phase voidage 127 4.7.5 Capacitance probe measurements 127 4.8 Conclusions 130 C H A P T E R 5 132 V E L O C I T Y M E A S U R E M E N T S 132 5.1 Introduction 132 5.1.1 V o i d velocity 132 5.1.2 Particle velocity 133 5.2 Opt ica l fiber probe 134 5.3 Data acquisition and analysis 136 5.4 Results 139 5.4.1 Particle velocities in 0.61 m diameter co lumn 139 5.4.2 Effect o f superficial gas velocity on particle velocity 144 5.4.3 Particle velocity and voidage 147 5.4.4 Particle velocities i n the 0.29 m diameter co lumn 152 5.4.5 V o i d velocities in the 0.29 m diameter co lumn 152 5.5 Conclusions and recommendations 156 v i C H A P T E R 6 160 S I G N A L A N A L Y S E S A N D I N T E R P R E T A T I O N 160 6.1 Introduction 160 6.2 Frequency analysis o f pressure fluctuations i n fluidized beds 160 6.2.1 Fourier transform 162 6.2.2 Exper imental data analysis 162 6.2.3 Crossing frequency 164 6.2.4 Sensitivity o f threshold value to crossing frequency 167 6.2.5 Effect o f air-feed system 170 6.2.5.1 Experimental investigation o f dominant frequency from air-feed system 170 6.3 Cross-correlation function 172 6.3.1 Correlat ion function coefficient o f voidage signal 172 6.4. Autocorrela t ion 174 6.5 Coherence structure and characterization 176 6.5.1 Coherence function from pressure measurements 184 6.5.2 Coherence function from optical probe voidage measurements 184 6.6. Chaotic analysis 190 6.6.1 Hurs t exponents 191 6.6.2 Cycle time and V statistic 191 6.6.3 Results from pressure signals 193 6.6.4 Results from voidage signals 197 6.7 Conclusions 200 C H A P T E R 7 203 M U L T I S C A L E R E S O L U T I O N 203 7.1 Introduction 203 7.2 Turbulence - two phase flow 203 7.3 Mul t ip le scales i n fluidized beds 205 7.3.1 K o l m o g o r o v scale o f turbulence 206 7.3.2 T ime scale 206 7.4 Turbulence energy decomposit ion - phase space 207 7.5 Wavelet analysis 207 7.5.1 Wavelets and turbulence 208 7.6 Analysis method 209 v i i 7.6.1 Appl ica t ion o f wavelet transform to de-noising signals 209 7.6.1.1 Crude method 209 7.6.1.2 Thresholding 211 7.6.2 L o c a l intermittency measure 211 7.6.2.1 Wavelet analysis applied to particle velocity 214 7.6.2.2 Wavelet analysis applied to voidage fluctuation 221 7.6.3 Qualitative analysis using wavelet 231 7.7 Mul t ip le scales in turbulent fluidized beds 234 7.8 Conclusions 235 C H A P T E R 8 237 C O N C L U S I O N S 237 N O M E N C L A T U R E 242 R E F E R E N C E S 250 A P P E N D I X A 274 C O L U M N III: 1.56 M D I A M E T E R F L U I D I Z A T I O N C O L U M N 274 A . 1 R i g modification 274 A . 1.1 Cyclone inlet area 274 A.1 .2 Distr ibutor plate and pressure drop 274 A . 1.3 Solids storage 274 A . 2 Traversing arm design and construction 278 A . 3 Commiss ion ing the rig 278 A . 4 Pressure measurements 280 A . 5 Summary o f operating conditions 280 A P P E N D I X B 284 V E L O C I T Y M E A S U R E M E N T D A T A A N A L Y S E S 284 B . l Cross-correlation 284 B.2 G r o u p number 286 B.3 E l imina t ion criteria 289 B.4 Peak detection 289 B.5 Dense-phase-associated particle velocity 290 B.6 Binary coding 293 B.7 Opt ica l fiber voidage probes 298 B.8 Conclusions wi th respect to data analysis method 305 v i i i A P P E N D I X C 306 F O U R I E R A N D W A V E L E T T R A N S F O R M A T I O N S 306 C l Fourier transform 306 C . 2 Wavelet analysis 307 C.2.1 Introduction to wavelet transformation 307 C.2.2 Compar ison o f wavelet transform to windowed Fourier transform 309 C.2.3 Different types o f wavelet transform 312 C.2.3.1 Continuous wavelet transform 312 C.2.3.2 Discrete wavelet transform 312 C.2.4 Details and approximations 313 C. 2.5 Thresholding 314 A P P E N D I X D 319 H Y D R O D Y N A M I C A N D C F D M O D E L L I N G 319 D . l Introduction 319 D . 2 Primary forces acting on a fluidized particle 319 D . 3 Forces acting on solids in gas-solid multiphase flows 320 D . 3.1 D r a g Forces 321 D.3.2 Particle inertia 322 D.3.3 Electrostatic forces 323 D.3.4 Other forces 324 D . 4 Hydrodynamic modell ing 324 D.4.1 Discrete particle model 325 D.4.2 Con t inuum model 326 D.4.3 Kine t i c theory o f granular flow 327 D.4.4 Restitution coefficient, e 330 D.4.5 Radial distribution function, g 0 331 D.4.6 Solids pressure, P a 332 D.4.7 Particle shear viscosity, \xs 334 D.4.8 Solids phase (bulk) viscosity: Xs 336 D . 5 Turbulence i n two-phase flow 336 D.5.1 Gas phase turbulence 336 D.5.2 Particle phase turbulence 337 i x D . 6 Turbulent two-phase flow models applied to fluidized beds 337 D . 7 Mode l l ing turbulent fluidized beds 338 D . 8 Simulat ion using C F X 339 D.8.1 Computer speed and capacity 340 D.8.2 Computat ional techniques 340 D.8.3 Geometry and grid generation 340 D.8.4 Boundary and conditions 342 D.8.5 C o m m a n d file 342 D.8.6 User Fortran 343 D.8.6.1 U S R I N T 343 D.8.6.2 U S R C V G 343 D.8.6.3 U S R T R N 343 D.8.6.4 U S R B C S 343 D . 8 . 6 . 5 C V I S 344 D.8.7 Parameters 344 D.8.8 Convergence 345 D.8.9 Typica l result 345 D.8.10 Future studies 348 D . 9 Conclusions 348 x L I S T O F T A B L E S Table 2.1 Particle properties. 11 Table 2.2 Coefficients for the Modi f i ed Richardson-Zaki equation. 21 Table 3.1 Particle properties used in 0.29 m diameter column. 70 Table 3.2 Published exponents for Equat ion 3.2. 71 Table 4.1 Summary o f reported hydrodynamic parameters i n turbulent fluidized beds. 89 Table 4.2 Summary o f literature data on radial voidage distribution i n turbulent fluidized beds. 90 Table 5.1 M A T L A B ® functions written for data analysis. 137 Table 5.2 Average voidage. D=0.61 m, H 0 = 2 m, F C C I V . 141 Table 5.3 Moments o f particle velocity distributions. D=0.29 m , 2=0.78 m , r /R=0 .55 , F C C I. 154 Table 6.1 Transducer positions for Figure 6.22. 183 Table A .1 Exper imental conditions. 283 Table B . l Effect o f threshold determination methods on threshold voidage values. U=0.69 m / s , D=0.61 m , z=0.80 m , r /R=0 .09 , f=30,147 H z . 298 Table B.2 Effect o f threshold determination methods on voidage value and crossing frequency. D=0.29 m , U=0.69 m / s , r /R=0 .70 , z=0.78 m, F C C I. 299 Table D . l Summary o f fluid and particle characteristic parameters based on typical F C C used i n those parts o f this work carried out at U B C . 320 Table D . 2 D r a g coefficients. 321 Table D . 3 Radial distribution functions. 332 Table D . 4 Sol id phase elastic modulus. 332 Table D . 5 Particle shear viscosity expressions i n the literature. 335 Table D . 6 G r i d quality for Aug02-geo02. 342 x i LIST OF FIGURES Figure 1.1 Gas-sol id fluidization flow regimes. (Adapted from Grace, 1986) 2 Figure 2.1 Particle size distribution o f spent F C C particles. 12 Figure 2.2 Progressive change in particle size distribution in 1.56 m diameter fluidization column. F C C II. 12 Figure 2.3 Schematic o f 0.29 m diameter, 4.5 m tall fluidization co lumn at U B C . 14 Figure 2.4 Photograph o f 0.29 m diameter co lumn wi th P V C pip ing for air supply. W o o d e n enclosure on the top level contains bag filters. 15 Figure 2.5 Schematic o f 0.29 m diameter fluidization co lumn depicting axial distances (in m) o f ports relative to distributor plate. 16 Figure 2.6 A x i a l gauge pressure profile for 0.29 m column. H 0 =0.51 m . D=0.29 m , F C C I. 18 Figure 2.7 Expanded bed height calculated from gauge pressure profiles in Figure 2.6. D=0.29 m , F C C I. 18 Figure 2.8 Deteriri ination o f bed pressure drop. U=0.96 m / s , H 0 = 1 . 2 m , D=0.29 m , F C C I. 20 Figure 2.9 Time-mean bed voidage vs. U . D=0.29 m , F C C I. 20 Figure 2.10 Time-mean bed voidage vs. superficial gas velocity. Determinat ion o f effective terminal velocity, U * , in modif ied Richardson-Zaki equation. H 0 =0 .6 m , D=0.29 m , U c =0.62 m / s (2=0.31 m , D P ) . 21 Figure 2.11 Height o f dense bed corresponding to voidage at m i n i m u m fluidization vs. superficial gas velocity. D=0.29 m , F C C I. 22 Figure 2.12 Solids circulation flux vs. superficial gas velocity. D=0.29 m , H 0 = 1 . 0 m , F C C I. 24 Figure 2.13 A x i a l voidage profile from time-mean D P measurements. D=0 .29 m , H 0 = l . l m , F C C I. 24 Figure 2.14 Schematic diagram o f location (in m) o f pressure ports i n 0.61 m column. 25 Figure 2.15 Loca t ion (in mm) o f pressure transducers and optical fibre probes for dynamic measurements i n 0.61 m diameter fluidization column. 26 Figure 2.16 Distr ibutor plate pressure drop measured i n empty column. D=0.61 m . 28 Figure 2.17 Pressure profile for circulation loop for D=0.61 m , H 0 = 2 m , F C C I V . 28 x i i Figure 2.18 Expanded bed height and height o f dense bed corresponding to voidage at s m f calculated from axial gauge pressure profiles. D=0.61 m, H 0 = 2 m , U c =1.12 m / s ( 2 = 1 . 5 5 m , D P ) , F C C I V . 30 Figure 2.19 Time-mean bed density vs. superficial gas velocity for D=0.61 m , H 0 =2 .0 m , axial location o f D P taps: 0.73-1.55 m, F C C I V . U c at 2 = 1.55 m from D P fluctuations. 30 Figure 2.20 Loca t ion o f pressure transducers and traversing probe arms i n 1.56 m column. 31 Figure 2.21 Distr ibutor plate pressure drop measured i n empty 1.56 m column. 33 Figure 2.22 Frequency spectrum analysis o f gauge pressure fluctuations i n empty bed. D=1.56 m, U = l . l m / s , z = 0 . 2 m , r /R=0 .9 . 33 Figure 2.23 B e d and distributor pressure drop for 1.56 m fluidization column. U=0.43 m / s , H 0 =0.9 m, F C C II. 34 Figure 2.24 Schematic diagram o f the tip o f a traversing probe arm. 34 Figure 2.25 Calculated expanded bed height from time-mean gauge pressure profile. D=1.56 m, F C C II. 36 Figure 2.26 Height o f dense bed corresponding to voidage at rrrinimum fluidization vs. superficial gas velocity. U c deduced from gauge pressure signals. D=1.56 m , F C C II. 36 Figure 2.27 A x i a l voidage profile from time-mean D P measurements. D=1 .56 m , F C C II. 37 Figure 2.28 Voidage calculated from D P method and optical probe signal. D=1.56 m, z=0.85 m, H 0 =0.9 m. A l l sensors positioned at r /R=0 .9 . U c (z =0.84 m , DP)=0.39 m / s , F C C II. 37 Figure 2.29 Schematic diagram o f 0.11 m diameter hot unit. A l l dimensions are i n metres. 39 Figure 2.30 Effect o f system pressure on expanded bed height at r o o m temperature. D=0.11 m, Catalyst C , H 0 =0 .7 m . 41 Figure 2.31 Effect o f temperature on bed expansion at a system pressure o f 0.2 M P a . D=0.11 m , Catalyst C , H o =0 .7 m . 41 Figure 2.32 Effect o f system pressure and temperature on time-mean bed voidage deduced from D P signals. D=0.11 m , U=0.40 m / s , Catalyst C . 42 Figure 2.33 Compar i son o f experimental voidage data with predictions from literature correlations. Catalyst C . A m b i e n t conditions. 43 Figure 2.34 Exper imental voidage measurement at 240°C compared to correlation predictions. D=0.11 m , H 0 =0 .7 m, Catalyst C. 44 Figure 3.1 Definit ions o f transition velocities U c and U k based on standard deviation o f pressure fluctuations. Adapted from Yerushalmi and Cankurt (1979). 48 xi i i Figure 3.2 Typica l standard deviation o f pressure fluctuations and bed density measurements. Pressure fluctuation measurement: z =1.50 m , Az=0.10 m . B e d density: z =1.14 m , Az=0.82 m. D=0.61 m, F C C I V , H=1.67~1.77 m. 54 Figure 3.3 B e d density measurements, z =1.85 m (z, o w c r=1.55 m , z u p p c r =2.14 m), Az =0.59 m , D=0.61 m , F C C I V , d =98 urn. H=1.67~1.77 m.Figure 3.4 Standard deviation o f optical fiber voidage probe signal. z=1.55 m , r /R=0 .09 , D=0.61 m , F C C I V , H=1.67~1.77 m. 54 Figure 3.4 Standard deviation o f optical fiber voidage probe signal. z=1.55 m , r /R=0 .09 , D=0.61 m , F C C I V , H = 1 . 6 7 ~ 1 . 7 7 m . 55 Figure 3.5 Typica l plot o f standard deviation o f D P fluctuations vs. U . D=0.29 m , H 0 =0 .60 m, F C C I. Az=0.064 m for z=0.18, 0.31, 0.43 m; and Az=0.13 m for z=0.59 m D P port locations. 59 Figure 3.6 Typica l plot o f standard deviation o f gauge pressure fluctuations vs. U . D=0.29 m , H 0 =0.51 m , F C C I. 59 Figure 3.7 Effect o f pressure port location on U c f rom D P signals. D=0.29 m , F C C I. 60 Figure 3.8 Effect o f aspect ratio H / D on U c from gauge pressure signals. D=0.29 m , F C C I. 62 Figure 3.9 U c obtained in this study from gauge pressure signals as a function o f co lumn diameter. F C C . 64 Figure 3.10 U c based on gauge pressure fluctuations vs. bed aspect ratio for the three columns investigated in this work together wi th data from B i (1994). F C C . 64 Figure 3.11 Compar ison o f experimental U c obtained from D P signals to published data for H / D > 3 . 66 Figure 3.12 Standard deviation o f D P signals and voidage plotted against superficial gas velocity. D=0.29 m , F C C I, H 0 =0.51 m , z=0.31 m. 66 Figure 3.13 P lo t o f U c vs. corresponding bed voidage, s c. F C C . 67 Figure 3.14 Standard deviation o f D P signals plotted a s a function o f U . D = 1 . 5 6 m , H 0 = 2 m , F C C II. 67 Figure 3.15 Cumulative distribution o f particle size based on mass fraction. 69 Figure 3.16 Compar ison o f expanded bed height from axial pressure distribution for F C C and Catalyst Cr . D=0.29 m , H 0 =0.6 m. 69 Figure 3.17 Effect o f particle properties on axial profiles o f U c f rom D P signals. H n =0 .60 m, D=0.29 m. 71 Figure 3.18 Archimedes number vs. particle Reynolds number based o n U c compared to published correlations based on Equat ion 3.2 and Table 3.2. D=0.29 m . 72 xiv Figure 3.19 Effect o f system pressure on U c . D=0.11 m , z=0.9 m , H0=0.7 m , Catalyst C fluidized wi th N 2 . 74 Figure 3.20 Effect o f system pressure on U c . Compar ison o f this work (D=0.11 m, Catalyst C , fluidizing air: N 2 , T = 2 0 °C) to others. 76 Figure 3.21 Effect o f temperature on U c . D=0.11 m , Catalyst C . 78 Figure 3.22 Standard deviation o f gauge pressure signals against volumetric gas flow rate. D=0.11 m , Catalyst C , P=0.2 M P a . 78 Figure 3.23 Effect o f gas viscosity and system pressure on Q C J transition based on volumetric flow rate. D=0.11 m , Catalyst C . Subscript T denotes system temperature. 79 Figure 3.24 Compar i son o f predictions by Equat ion 3.10 wi th experimental U c . Catalyst C . D=0.11 m diameter column, H 0 =0 .7 m . D=0.29 m diameter column, H 0 =0 .6 m. 81 Figure 3.25 Compar i son o f predictions by Equat ion 3.11 wi th experimental U c . Catalyst C . D=0.11 m diameter column, H 0 =0 .7 m. D=0.29 m diameter co lumn, H0—0.6 m . 81 Figure 3.26 Compar i son o f U c data from this work to literature data for fluidized bed o f Geldart G r o u p A particles from gauge pressure signals. 82 Figure 3.27 Compar ison o f predictions by Equat ion 3.19 wi th experimental U c . F C C . 82 Figure 3.28 Compar ison o f predictions by Equat ion 3.18 and 3.19 wi th experimental U c from gauge pressure signals. F C C I, D=0.29 m. 83 Figure 4.1 Reflective-type optical fiber probe response curves for various fiber configurations (adapted from K r o h n , 1987). 93 Figure 4.2 Probe tip in relation to particle size. Reflective optical fiber probe detecting (a) swarm o f particles; and (b) single particles (adapted from Matsuno et al., 1983). 94 Figure 4.3 Opt ica l fiber probe for measuring local particle concentrations: the probe is shown detecting a swarm o f particles. 96 Figure 4.4 Schematic o f local voidage measurement apparatus and configuration. 96 Figure 4.5 Schematic o f optical probe calibration equipment applying "drop-trap" technique. 99 Figure 4.6 Response curve for calibration o f optical probe using F C C I without glass window. The line represents the calibration curve o f Issangya (1998). 100 Figure 4.7 Response curve for calibration o f optical probe using F C C I and coke particles with glass window. 102 Figure 4.8 Response signal o f experimental calibration curves for F C C II wi th glass window in water-solids system.Figure 4.9 Signal obtained from optical probe without glass window. xv (Dotted line represents the max imum calibrated value.) D=0.29 m, U=0.15 m / s , 2=0.15 m, r /R=0 .0 , F C C I. 102 Figure 4.9 Signal obtained from optical probe without glass window. (Dotted line represents the max imum calibrated value.) D=0.29 m , U=0.15 m / s , z=0.15 m , r /R=0 .0 , F C C I. 103 Figure 4.10 Setting the upper intensity i n dense bed: (a) without window; (b) wi th window. 105 Figure 4.11 Signal obtained from optical probe wi th glass window. (Dotted line represents the max imum calibrated value.) D=0.29 m, U=0.15 m / s , z=0.15 m, r / R = 0 . 0 , F C C I. 105 Figure 4.12 Schematic o f needle-type capacitance probe. 107 Figure 4.13 Signal response o f capacitance probe wi th F C C II i n water-solids suspensions. 107 Figure 4.14 Effect o f volumetric solids fraction on the effective relative dielectric permittivity o f a wa te r -FCC system. A l l models assume K p = 14 and K h = 80 for F C C and water, respectively, based o n Louge and Op ie (1990). 108 Figure 4.15 Radial voidage distributions. H 0 =0.51 m, D=0.29 m , F C C I. U c (z =0.43 m , D P ) = 0.49 ± 0 . 0 1 5 m / s . 111 Figure 4.16 Cross-sectional average voidage from local radial voidage measurements from optical probe. H 0 =0 .51m, D=0.29 m , F C C I. 112 Figure 4.17 Compar ison o f cross-sectional average voidage from optical signal to that from D P . H 0 =0.51 m , D=0.29 m , z=0.27 m F C C I. 112 Figure 4.18 Radial profile o f normalized time-mean average voidage. H 0 = l . l m , D=0.29 m, F C C I, U = 0 . 4 0 m / s . 114 Figure 4.19 Radial profile o f normalized time-mean average voidage. H 0 = l . l m , D=0.29 m, F C C I, U=0.80 m / s , U c (z =0.85 m , D P ) = 0 . 7 3 m / s . 114 Figure 4.20 Radial profile o f voidage fluctuation represented by standard deviation o f local voidage measured by optical probe. D=0.29 m, H 0 =0 .8 m , z=0.40 m , U c =0.75 m , F C C I. 115 Figure 4.21 Probabili ty distribution function o f local voidage measured by optical probe. U c D P (z =0.85 m)= 0.727 ± 0.039 m / s , H 0 = l . l m , D=0.29 m , r /R=0 .0 , z=0.40 m , F C C I. 117 Figure 4.22 Probabili ty distribution function o f local voidage measured by optical probe. U c D P (z =0.85 m)= 0.727 ± 0.039 m / s , H 0 = l . l m , D=0.29 m , r /R=0 .0 , z=0.78 m , F C C I. 117 Figure 4.23 Contour plot o f time-mean local voidage measured by optical probe. D=0.29 m, F C C I, H 0 = 1.1 m , U = 0 . 4 m / s . 118 Figure 4.24 Contour plot o f time-mean local voidage measured by optical probe. D=0.29 m , F C C I, H 0 = 1.1 m , U = 0 . 9 m / s 118 xv i Figure 4.25 Contour plot o f time-mean local voidage measured by optical probe. D=0.29 m , F C C I, H 0 = 1 . 5 m , U = 0 . 4 m / s 119 Figure 4.26 Contour plot o f time-mean local voidage measured by optical probe. D=0.29 m, F C C I, H 0 = 1 . 5 m , U = 0 . 9 m / s 119 Figure 4.27 Radial profile o f time-mean voidage from optical probe signals. H 0 = l . l - 1 . 3 m , D=0.61 m , 2=0.8 m , F C C III, U c =0.83 m / s (z=0.8m, D P ) . 121 Figure 4.28 Radial profile o f time-mean voidage from optical probe signals. H 0 = 2 m , D=0.61 m , 2=1.55 m , F C C I V , U c =1.12 m / s (z=1.5 m, D P ) . 121 Figure 4.29 Radial profile o f time-mean voidage from optical probe signals. H 0 =1 .7 m , D=0.61 m , U=0.85 m / s , z=0.8 m , F C C III, U c = 0 . 7 7 m / s (z=0.36 m , D P ) . 122 Figure 4.30 Radial profile o f time-mean voidage from optical probe signals. z=0.84 m , D=1.56 m, H 0 = 1 . 2 m , F C C II, U c (z=0.84 m , DP)=0.39 m / s . 124 Figure 4.31 Probabili ty density o f voidage obtained from optical probe signals measured at r /R=0 .90 and 0.0. D=1.56 m, H 0 = 1 . 2 m , F C C II, z=0 .84m. 124 Figure 4.32 Radial profile o f time-mean voidage from optical probe signals. D=1.56 m , z=0.84 m , H 0 =2 .2 m , U c (z=0.85 m , DP)=0.53 m/s, F C C II. 125 Figure 4.33 Effect o f U on time-mean voidage and D P fluctuation at r /R=0 .0 . D=1.56 m, z=0.84 m , H 0 =2 .2 m , U c (z=0.85 m , DP)=0.53 m / s , F C C II. 125 Figure 4.34 Radial profile o f normalized time-mean voidage. Compar i son o f experimental data to other publications. Particle properties and operating conditions listed i n Table 4.2. 126 Figure 4.35 Effect o f U / U c on radial profile o f normalized time-mean voidage. F C C . 128 Figure 4.36 Probabili ty density o f voidage from optical probe signals. D=0.29 m , z=0.527 m , U=0.78 m / s , F C C I, H 0 =0 .8m. 129 Figure 4.37 Probabili ty distribution o f voidage measured by optical probes. D=0.29 m ( F C C I). D = 1 . 5 6 m ( F C C I I ) . . 129 Figure 4.38 Probabili ty density o f voidage from capacitance and optical probe signals. D=0.61 m , U=0.86 m / s (capacitance); U=0.85 m / s (optical), H 0 = 2 m , z=1.55 m , F C C III, r /R=0 .83 . 131 Figure 5.1 Details o f optical fiber velocity probe. 135 Figure 5.2 Schematic o f optical velocity probe tip showing measurement volume and elimination o f 'b l ind 2one' by addition o f glass cover. 135 Figure 5.3 Typica l optical signal obtained by two identical voidage probes separated by 0.01 m. D=0.29 m , z=0.78 m , U=0.90 m / s , r /R=0 .70 , H 0 =1.5 m , F C C I. 137 xv i i Figure 5.4 Schematic o f the optical fiber velocity probe system for simultaneous measurement o f local solids concentration and particle velocity. 138 Figure 5.5 A x i a l profile o f time-mean voidage determined from differential pressure signals. D=0.61 m , H 0 = 2 m , F C C I V , U c ( D P at z =1.55 m)=1.12 m / s . 140 Figure 5.6 Cumulative void-associated particle velocity profile. D=0.61 m , U=1.56 m / s , z=1.55 m , H 0 = 2 m , F C C I V . 140 Figure 5.7 Probabili ty distribution o f voidage. D=0.61 m , U=0.82 m / s , z=1.55 m , H 0 = 2 m, F C C I V . 141 Figure 5.8 Radial profile o f time-mean void-associated particle velocity ( © ) a n d voidage (A)distr ibutions: (a) U=1.56 m / s ; (b) U=0.82 m / s . D=0.61 m , z=1.55 m , H 0 = 2 m , F C C I V . 142 Figure 5.9 Cumulative void-associated particle velocity occurrence at (a) r /R=0 .09 and (b) r /R=0.50 . D=0.61 m , H 0 = 2 m , F C C I V . 143 Figure 5.10 W a l l measurements o f gauge pressure and standard deviation o f pressure fluctuation. D=0.61 m , H 0 = 2 m , F C C I V . 145 Figure 5.11 Effect o f U on average particle velocities. r /R=0 .09 , D=0.61 m , H 0 = 2 m , F C C I V , U c = 1.12 m / s ( D P at z =1.55 m). 145 Figure 5.12 Standard deviation o f particle velocities. D=0.61 m , z=1.55 m, r /R=0 .09 , U c =1.12 m / s ( D P at z= 1.55 m), F C C I V . 146 Figure 5.13 Probabil i ty distribution o f particle velocities for (a) U=0.42 m / s , and (b) U=1.00 m / s at radial positions o f 0.94, 0.50, and 0.09. D=0.61 m, z=0.80 m , F C C I V . 148 Figure 5.14 Particle velocity and voidage distribution for U=0.42 m / s at radial positions o f 0.94, 0.50, and 0.09. D=0.61 m , z=0.80 m, F C C I V . 149 Figure 5.15 Particle velocity and voidage distribution for U=1.00 m / s at radial positions o f 0.94, 0.50, and 0.09. D=0.61 m, z=0.80 m, F C C I V . 150 Figure 5.16 Particle velocity and voidage distribution for U=1.56 m / s at radial positions o f 0.94, 0.50, and 0.09. D=0.61 m, z= l .55 m, F C C I V . 151 Figure 5.17 Dis t r ibut ion o f particle velocities associated wi th dense-phase. D=0.29 m , r /R=0.70 , z = 0 . 7 8 m , H 0 = 1 . 0 m , F C C I. 153 Figure 5.18 V o i d velocity distribution for (a) r /R=0 .0 , and (b) r /R=0 .70 . D=0.29 m , z=0.78 m, Az=0.02 m , H 0 =1.5 m, F C C I. 155 Figure 5.19 Average v o i d velocity. D=0 .29m, z=0.78 m, Az=0.02 m , H 0 =1 .5 m , F C C I. 157 xvi i i Figure 5.20 Radial distribution o f average v o i d frequency. D=0 .29m, z=0.78 m , Az=0.02 m , H 0 =1.5 m, U c (z=1.16 m , AP)=0.85 m / s , F C C I. 157 Figure 6.1 Power spectral density functions o f pressure fluctuations. U=0.65 m / s , H = l . l m , r / R = l , F C C I. (n identifies recurrent "natural frequency") 163 Figure 6.2 Effect o f expanded bed height on natural frequency from A P signals wi th comparison to calculated values based on Equat ion 6.1. D=0 .29m, F C C I. 165 Figure 6.3 Effect o f superficial gas velocity on major frequency from D P signals. D=0.29 m, H , ,= 1.1 m, F C C I. 165 Figure 6.4 Varia t ion o f dominant frequency, f D P , wi th superficial gas velocity. D=1.56 m, H 0 =2.2 m. 166 Figure 6.5 Strouhal number vs. Froude number correlation for TJ > U c , F C C . 166 Figure 6.6 Radial profiles o f voidage and crossing frequency. D=0.29 m , H 0 = l . l m , U=0.70 m / s , F C C I. 168 Figure 6.7 Effect o f superficial gas velocity and height on crossing frequency. D=0.29 m , H 0 = l . l m , U c =0.68-0.73 m / s , r /R=0 .0 , F C C I. 168 Figure 6.8 Radial profiles at different superficial gas velocities o f crossing frequency calculated from threshold value o f time-mean voidage. D=0.29 m , H 0 = l . l m , z=0.78 m , F C C I. 169 Figure 6.9 Effect o f superficial gas velocity on crossing frequency calculated from threshold value o f time-mean voidage. D=0.29 m, H 0 = l . l m , z=0.78 m , r / R=0 .0 , F C C I. 169 Figure 6.10 Fast Fourier Transform o f pressure fluctuations: (a) A P at z=0.15 m ; (b) D P across grid; (c) A P i n windbox. D=0.29 m , H„=T.5 m, U=0.19 m / s . 171 Figure 6.11 Cross-correlation function o f optical voidage probe signals. D=0.29 m , H 0 =1.5 m, distance between probes=0.01 m , r /R=0 .70 , U=0.90 m / s , F C C I. 173 Figure 6.12 Varia t ion o f correlation function coefficients wi th superficial gas velocity. D=0.29 m , H 0 =1 .5 m , r /R=0 .35 , U =0.75 m / s , H 0 =1.5 m, z l o w c r p r o b c =0.77 m , F C C I. 173 Figure 6.13 Effect o f optical probe separation distance on cross-correlation function coefficient, (a) U=0.40 m / s ; (b) U=0.90 m / s . D=0.29 m, H 0 =1.5 m , z , o w c r p r o b c =0.77 m , F C C I. 175 Figure 6.14 Autocorrela t ion function o f voidage signal. D=0.29 m , U=0.90 m / s , z=0.78 m, r /R=0 . 0 , H 0 = l . l m , F C C I . 177 Figure 6.15 Radial profile o f characteristic time o f autocorrelation function from voidage measurements. D = 0 . 2 9 m , U = 0 . 9 0 m / s , H 0 = 1.1 m, F C C I. 177 xix Figure 6.16 Radial profile o f time-mean voidage for data presented i n Figure 6.15. D=0.29 m , U = 0 . 9 0 m / s , H „ = l . l m , F C C I. 178 Figure 6.17 Effect o f U on Tc. r /R=0 .0 , D=0.29 m , H 0 = l . l m , F C C I. 178 Figure 6.18 Coherence function and standard deviation vs. superficial gas velocity. (Adapted from C a i et al., 1990; D=0.139 m, d p =280 urn, probe separation distance=0.1 m) 181 Figure 6.19 Incoherent-output power spectral density (defined i n Equa t ion 6.10) from gauge pressure fluctuations for two superficial gas velocities. D=0.29 m , z ^ O . 2 1 m, z 2=0.34 m, H 0 = 1 . 5 m . 183 Figure 6.20 Typica l coherence function. D=0.29 m , U=0.87 m / s , r / R = 0 . 0 , z=0.40 and 0.46 m , H 0 = 1 . 5 m , F C C I. 185 Figure 6.21 Average coherence function from gauge pressure signals. D=0.29 m , H 0 = l . l m , U c =0.73 m / s , F C C I.Figure 6.22 Average coherence function from D P signals. D=0.29 m, H 0 = l . l m , c h l locations, U c (Az =0.845 m) = 0.72710.039 m / s , F C C I. 185 Figure 6.22 Average coherence function from D P signals. D=0.29 m , H 0 = l . l m , c h l locations, U c (Az =0.845 m) = 0.727±0.039 m / s , F C C I. 186 Figure 6.23 Average coherence function and correlation function coefficient. D=0.29 m , r /R=0 .0 , U c =0.75 m / s , probe separation distance=0.063 m , z=0.40 m and 0.463 m , H 0 =1 .5 m, F C C I. 186 Figure 6.24 Power spectra density o f voidage data at U=0.65 m / s . D=0.29 m , r / R=0 .0 , z=0.46 m, H 0 =1 .5 m, F C C I. 188 Figure 6.25 Coherence function o f voidage data at U=0.65 m / s . D=0 .29 m , r /R=0 .0 , probe separation distance=0.063 m, z=0.40 m and 0.463 m , H 0 =1 .5 m , F C C I. 188 Figure 6.26 Radial profile o f average coherence function. D=0.29 m , Az=0.01 m , H 0 =1 .5 m, F C C I. 189 Figure 6.27 Effect o f U on average coherence function form voidage measurements. D=0.29 m , z=0.77 m and 0.78 m , distance between probes=0.01 m , H 0 =1 .5 m , F C C I. 189 Figure 6.28 Var ia t ion o f the rescaled range wi th sub-period length for gauge pressure fluctuation. Sampling frequency=500 H z , sampling duration=200 s, U=0.39 m / s , D=0.29 m , z=0.65 m, H 0 =0.97 m , F C C I. 192 Figure 6.29 Var ia t ion o f the Hurs t exponents f rom D P signals wi th superficial gas velocity. D=0.29 m , H 0 = l . l m , z =0.59 m , Az =0.12 m , sampling frequency=100 H z , sampling duration=100 s. • 194 xx Figure 6.30 A x i a l profiles o f cycle time from (a) D P , and (b) A P signals. D=0.29 m , H 0 =1.5 m, r / R = l , F C C I . 196 Figure 6.31 Var ia t ion o f cycle time with dimensionless height for U > U c f rom D P signals. 198 Figure 6.32 Var ia t ion o f cycle time regularity wi th dimensionless superficial gas velocity. A x i a l positions: D=0.29 m (z/H=0.64); D=0.61 m (z /H=0.87) ; D=1.56 m (z/H=0.62). 198 Figure 6.33 Radial profile o f Hurs t exponents for U=0.40 and 0.90 m / s . D=0.29 m , z=0.78 m , H 0 = l . l m , F C C I. 199 Figure 6.34 Var ia t ion o f max imum Hurs t exponent f rom optical voidage probe signals wi th superficial gas velocity. D=0.29 m , z=0.40 m, U c =0.75 m / s , r /R=0 . 0 , H 0 =1 .5 m , F C C I. 201 Figure 6.35 Varia t ion o f cycle time wi th superficial gas velocity for optical voidage probes signals. D=0.29 m , z=0.40 m , r /R=0 .0 , H „ = 1 . 5 m, U c =0.75 m / s , F C C I. 201 Figure 7.1 Original and de-noised signals. 210 Figure 7.2 De-nois ing signal using Daubechies 3 wavelet level 5. 212 Figure 7.3 De-nois ing signal using Daubechies 3 wavelet level 5 wi th soft thresholding method. 212 Figure 7.4 Compar i son o f v o i d velocity distribution between cut-off method (O); and db3 level 5 wavelet transform with soft thresholding ( A ) (data o f Figure 7.6a). 213 Figure 7.5 Voidage fluctuation captured by optical velocity probe. Sampling frequency, 28,741 H z , D=0.61 m, U=1.56 m / s , r /R=0 .09 , z=1.55 m, z=1.55 m , H 0 = 2 m , F C C I V . 215 Figure 7.6 Particle velocity fluctuation o f data from Figure 7.10 based on cross-correlation o f 4096 data points, representing 142.5 ms. D=0.61 m , U=1.56 m / s , r /R=0 .09 , z=1.55 m , H 0 = 2 m, F C C I V . 215 Figure 7.7 Contour plot o f L I M for 6 levels depicting passage o f energetic microstructure centred around scale 3. U=0.42 m / s , r /R=0 .09 , D=0.61 m , z=1.55 m , H 0 = 2 m , F C C I V . 217 Figure 7.8 Contour plot o f L I M for 6 levels depicting passage o f energetic microstructure centred at all scales o f analysis. U=0.82 m / s , r /R=0 .09 , D=0.61 m , z=1.55 m , H 0 = 2 m , F C C I V . 218 Figure 7.9 Contour plot o f L I M for 6 levels depicting passage o f energetic microstructure mostly at small scales o f analysis. U=1.56 m / s , r /R=0 .09 , D=0.61 m , z=1.55 m , H 0 = 2 m, F C C I V . 219 Figure 7.10 Effect o f superficial gas velocity on probability distribution o f L I M at: (a) level 1; and (b) level 6. D=0.61 m, r /R=0 .09 . z=0.80 m for U=0.42 m / s ; z=1.55 m for U=0.82 and 1.56 m / s , H 0 = 2 m , F C C I V . 220 Figure 7.11 Effect o f scale on probability distribution o f L I M j . D=0.61 m , r /R=0 .09 . z=0.80 m for U=0.42 m / s ; z=1.55 m for U=0.82 and 1.56 m / s , H 0 = 2 m , F C C I V . 222 xxi Figure 7.12 Voidage fluctuation signal from optical velocity probe and probability distribution o f L I M at 6 scales. U=0.57 m / s , r /R=0 .09 , D=0.61 m , z=0.80 m , H 0 = 2 m , F C C I V . 223 Figure 7.13 Voidage fluctuation signal from optical velocity probe and probability distribution o f L I M at 6 scales. U=0.82 m / s , r /R=0 .09 , D=0.61 m , z=1.55 m , H 0 = 2 m , F C C I V . 224 Figure 7.14 Voidage fluctuation signal from optical velocity probe and probability distribution o f L I M at 6 scales. U=1.56 m / s , r /R=0 .09 , D=0.61 m, z=1.55 m , H 0 = 2 m , F C C I V . 225 Figure 7.15 Effect o f U on probability distribution o f L I M at 6 scales for r /R=0.94 . D = 0.61 m , . z= 1.55m, H 0 = 2 m , F C C I V . 226 Figure 7.16 Compar ison o f L I M j o f 6 scales for probe in various radial posi t ion and phases: (a) r /R=0 .94 ; (b) r /R=0 .09 , high-density phase; (c) r /R=0 .09 , low-density phase; (d) r /R=0.09 , fluctuating phase. D=0.61 m, U = 1.56 m/ s , z=1.55 m , H 0 = 2 m , F C C I V . 227-230 Figure 7.17 Continuous wavelet transform using Mor le t wavelet, (a) U=0 .32 m / s ; and (b) 1.0 m/ s . D=0.29 m, z=0.77 m, r /R=0 .0 . (lowest scale corresponding to 50 H z ) 232 Figure 7.18 Dis t r ibut ion o f energy i n the time-frequency plane o f voidage signal using continuous wavelet transform wi th Mor le t wavelet during defluidization. D=1 .56 m , r / R = 0 . 5 , z=0.84 m , H n = 2 . 0 m , F C C II. 233 Figure A . l Photograph o f the 1.56 m fluidization co lumn standing beside heavy tech building at C S I R O Minerals, Clayton. 275 Figure A . 2 Isometric view o f cyclones and top o f 1.56 m fluidization co lumn. 276 Figure A . 3 Schematic diagram showing bubble caps on distributor o f 1.56 m diameter fluidization column. 276 Figure A . 4 Schematic o f bubble cap (in mm) as originally installed. 277 Figure A . 5 Photograph taken upward from the plenum chamber o f the 64 m m sockets installed to reduce the open area o f air inlet and the central bubble cap removed from service. 277 Figure A . 6 Photograph o f a probe arm socket depicting the interlocking angle mechanism. 279 Figure A . 7 Photograph o f a traversing probe arm #2 positioned at the centre o f an empty 1.56 m diameter column. 279 Figure A . 8 Photograph o f the scaffold supporting frame and a massive amount o f silicone sealant after a welding failure. 281 Figure A . 9 Compar ison o f pressure profile f rom two data logging systems. E r r o r bars depict m a x i m u m error o f 10,000 sample size. D=1.56 m / s , U=0.43 m / s , H 0 = 1 . 2 m , F C C II. 282 Figure B . l Log i c flow sheet for data cross-correlation and elimination. 285 xxn Figure B.2 (Original) Typical raw signal; (a) One void isolated from Figure 5.6; (b) Binary coding; (c) Cut-off method. D=0.61m, U=0.57 m/s, r/R=0.17, 2=0.80 m, f=29,378 Hz. 287 Figure B.3 Comparison of data processing method with respect to fraction of data groups eliminated. Data from Figures 5.6 (a) and (c). 287 Figure B.4 Effect of group number on percentage of data eliminated for void-associated particle velocities. Threshold voidage=0.62, D=0.29 m, U=0.42 m/s, r/R=0.55, 2=0.78 m, FCC I. 288 Figure B.5 Effect of group number on average velocity and solid fraction of void-associated particles. D=0.29 m, U=0.42 m/s, r/R=0.55, z=0.78 m, FCC I. 288 Figure B.6 Comparison of void-associated particle velocity distribution between cross-correlation and peak-picking methods. D=0.29 m, U=0.42 m/s, 2=0.78 m, r/R=0.55, f= 13,357 Hz, FCC I. 291 Figure B.7 Comparison of void-associated particle velocity distribution between cross-correlation and peak-picking methods. U=0.69 m/s, D=0.29 m, z=0.78 m, r/R=0.55, f=12,059 Hz, FCC I. 292 Figure B.8 Comparison of the positive and negative void-associated particle velocity distribution between cross-correlation and peak-picking methods. U=0.69 m/s, D=0.29 m, z=0.78 m, r/R=0.55, f=12,059 Hz, FCC I. 292 Figure B.9 Probability distribution function of local voidage measured by optical velocity probe and determination of threshold value corresponding to boundary between dilute and dense phases. U=0.69m/s, D=0.29 m, z=0.78 m, r/R=0.55, f=12,059 Hz, FCC I. 294 Figure B.10 Logic flow sheet for binary coding signals. 295 Figure B . l l Voidage signal from two fibers. Broken lines denote the threshold values from Methods (a), (b), (c), and (d). U=0.69 m/s, D=0.29 m, z=0.78 m, r/R=0.55, f=12,059 Hz, FCC I. 297 Figure B.12 Velocity distribution applying Method (d) binary coding. U=0.69 m/s, D=0.61 m, z=0.80 m, r/R=0.09, f= 30,147 Hz, FCC IV. 297 Figure B.13 Probability distribution of voidage indicating threshold values from Methods (a), (b), (d), and (e). D=0.29 m, U=0.69 m/s, r/R=0.70, z=0.78 m, FCC I. 300 Figure B.14 Voidage fluctuation measured by optical voidage probe. D=0.29 m, U=0.69 m/s, r/R=0.70, z=0.78 m, FCC I. 300 Figure B.l5 Probability distribution of void velocity and its effect of threshold voidage expressed as crossing frequency. D=0.29 m, U=0.69 m/s, z=0.78 m, r/R=0.70, Az=0.01 m, FCC I. 301 X X l l l Figure B.16 Voidage signals depicting v o i d velocity evaluation method o f Matsuura and Fan (1984). D = 0 . 2 9 m , U=0.90 m / s , r /R=0 .70 , z=0.78 m , H 0 =1 .5 m , F C C I. . 303 Figure B.17 Voidage signals processed by cut-off method exemplifying the erratic movement o f voids. D=0.29 m , U=0.90 m / s , r /R=0 .70 , z=0.78 m , H 0 =1 .5 m , F C C I. 303 Figure B.18 V o i d velocity wi th voidage fluctuation. X error bars representing periods o f signal considered for cross-correlation. Threshold voidage value=0.704 from M e t h o d (a), D=0.29 m, H 0 =1 .5 m , U=0.69 m / s , r /R=0 .70 , z=0.78 m , F C C I. 304 Figure B.19 Effect o f group number on cumulative v o i d velocity distribution. D=0.29 m, U=0.90 m , r /R=0 .70 , z=0.78 m , H 0 =1.5 m , F C C I. 304 Figure C l Typica l shapes o f (a) sine wave; (b) real part o f Mor le t wavelet; and (c) Mexican hat wavelet. 308 Figure C.2 Phase space associated wi th different transforms: (a) Fourier transform, (b) windowed Fourier transform, and (c) wavelet transform. (Adapted from Farge, 1992) 310 Figure C.3 (a) Funct ion f wi th support [-2*1 ,2 '^ )piecewise constant on [k2 ^° , (k + 1)2 *° ) . (b) Magnificat ion o f a port ion o f f. O n every pair o f intervals,' f is replaced by its average (-^ f 1 ) ; the difference between f and f1 is g 1 , a linear combinat ion o f Haar wavelets. (Adapted from Daubechies, 1992) 315 Figure C.4 Discrete wavelet decomposit ion and wavelet tree using Haar wavelets o f voidage fluctuation from optical probe. D=0.29 m, U=0.90 m / s , r / R = 0 . 0 , H 0 = l . l m , z=0.78 m , F C C I. 316 Figure C.5 Discrete wavelet decomposit ion o f voidage fluctuation from optical probe using Haar wavelet. D=0.29 m, U=0.90 m / s , r /R=0 .0 , H 0 = l . l m , z=0.78 m. 317 Figure D . l Mode l l ing geometry for 2 D simulation o f a turbulent fluidized bed. Green rectangle depicts three solids, i.e., areas, that are set as 3 D patch to set static bed height o f F C C . The 2 D patch highlighted wi th pink shows the secondary inlet patch to feed solids back i n to the column. T o p o f the co lumn geometry is not shown. 341 Figure D . 2 Mass residual o f gas phase wi th iteration. R u n # Oct022-m01. 346 Figure D . 3 Simulated voidage profile o f 2 D fluidized bed operated at atmospheric pressure, U=0.5 m / s . Initial bed height 1.0 m. Coefficient o f restitution 0.9. R u n # Aug02-m01,m02,m04. 347 xxiv A C K N O W L E D G E M E N T S The complet ion o f this degree wou ld not have been possible i f it were not for those people who truly believed i n my potential and provided me with opportunities; who unconditionally supported me i n my endeavour; who took the time to let me discover; and w h o gave me the hugs when I needed them most. T o Prof. J o h n Grace, Prof. J i m L i m and Prof. Xiaotao B i , who enriched my learning by sharing with me their unremitting wealth o f knowledge, invaluable guidance, and tremendous opportunities, I am so deeply indebted. Thei r unfailing confidence i n me gave me the latitude to explore and develop concepts i n my research. Grateful appreciation is expressed to Seng L i m for his professionalism and hospitality while at C S I R O , where the work for scale-up was conducted. Terry Joyce and Ross Close have taught me skills and technical expertise in the operation and construction o f the apparatus that I have never learned in school. Prov id ing enormous assistance through technical support were Peter, A l e x , Robert, Horace and Q i . I recognize and appreciate the assistance o f the support staff and faculty at the department. Special thanks to L o r i and Helsa for their proficiency in keeping me on track. Financial support from the N S E R C , and U B C Graduate Fel lowship F u n d is also gratefully acknowledged. Jonathan Taylor, Fel ix Herrmann, Mar t in Rhodes, Masayuki H o r i o and Cedric Briens have allowed me to leap forward into new directions through insightful discussions, sparkling dialogues, and thought-provoking questions. Thei r knowledge and insights are reflected i n this thesis. F o r their guidance and support, I acknowledge Profs. Bruce B o w e n , Far iborz Taghipour and Ian Gartshore. X X V I extend my gratitude to Sijin W e n , Lauren Briens, X u q i Song, H i r o s h i Mor ikawa , Jian X u , Pierre Constantineau, A l f i Zakhar i and Peter Wi t t for their generosity i n sharing their expertise and experiences. I thank A b b a , G o r k e m , Ian, and Ar tu ro for making a difference i n my life. The constant encouragement from K i m , Eddie , Masato, Kathy, Robyn , Gar th , F u m i k o and Ikuko was the source o f continual energy. Thank-you. Y o u all have been such amazing cheerleaders i n my life. In particular, I acknowledge B o b for his generous sense o f humour that pulled me out o f the tunnel o f hopelessness. Countless numbers o f people have supported me throughout the endeavour i n so many helpful indirect ways. T o Jay, K e l l y - A n n , Joy, G i l l , A n n e , Harriet, L i z , Y u r i , Diana , Shigeko, T o m , and Peter, my array o f unique mentors, I thank-you. E n o u g h thanks cannot be said to my family, Pat, M i k i , E r i c a and A l i c i a , for their love and support through all the many challenging times they were subjected. Y o u have demonstrated how true understanding and patience translated into everyday life, and coped wi th the absence o f a M o m . Thank-you for always braving a smile. I am, as I am sure they are too, look ing forward to getting back to a normal family life. This work is dedicated to Isabelle whose remarkable strength, determination and love carried me this far. She knew all along that some day this task w o u l d be completed. I know she is smiling with me now. Whi le others are not specifically mentioned, their support and assistances have been truly appreciated. x x v i T o keep your edge you have to feel insecure. . . Gay Laliberte Founder, Cirque du Soleil xxvn C H A P T E R 1 I N T R O D U C T I O N Gas-sol id fluidization is a unit operation which brings two phases, one comprised o f solid particles, into intimate contact. F luidized beds have been widely used i n industry owing to their excellent gas-solids contacting and favourable heat and mass transfer characteristics. T h e advantages o f high gas throughputs, overcoming the tendency o f sticky particles to agglomerate, and more efficient contact between gas and solids, led the way to high-velocity fluidization (Avidan, 1980). The merit o f a gas-fluidized bed operated in the turbulent fluidization flow regime was initially discovered through industrial experience, where an increased gas flow rate resulted i n a higher efficiency during the F lu id Cracking Catalyst (FCC) regeneration process. In fact, many practical fluidized beds operate beyond the terminal settling velocity o f individual particles (Grace, 1992). Presently, commercial fluid bed catalytic reactors such as those used in the product ion o f acrylonitrile and chlorinated hydrocarbons, and F C C regenerators, operate in the turbulent fluidization flow regime wi th superficial gas velocities ranging between about 0.5 and 0.8 m / s . In many industrial fluidized bed applications where min imiz ing entrainment and maximizing gas throughput lead to increased reactor performance, the turbulent fluidization flow regime is a viable operating mode. Turbulent fluidization is commonly characterized by the 'gradual' disappearance o f discrete bubbles and voids, wi th the bed surface no longer clearly defined due to considerable entrainment o f the solids into the freeboard. Some o f the early photographs showing a flow pattern distinctively different from that o f the bubbl ing flow regime were reported by Matheson et al. (1949) and Zenz and Othmer (1960). Breakdown o f large bubbles into smaller transient voids assists i n increasing the homogeneity o f turbulent fluidized beds. Compared to bubbl ing beds, turbulent fluidized beds are characterized by: (1) higher gas throughput; (2) improved gas-solids contact; (3) higher gas-to-solid mass and heat transfer rates; and (4) additional conversion i n the freeboard (Venderbosch, 1998). Turbulent fluidization also defines a transition regime between the low velocity bubbl ing bed and highly entraining flow in circulating fluidized beds, as depicted i n Figure 1.1. Understanding this flow regime is critical to the design and operation o f many fluidized bed processes and applications. Chapter 1 Introduction 2 F i g u r e 1.1 G a s - s o l i d fluidization flow reg imes . ( A d a p t e d f rom G r a c e , 1986) Chapter 1 Introduction 3 1.1 Flow regimes and transitions between regimes A s fluid enters the bot tom o f a vessel containing a bed o f solids, several flow regimes are observed with increasing fluid throughput. A bed is fluidized when the factional force between particle and fluid counterbalances the weight o f the particles, initially occurring at the m i n i m u m fluidization velocity, U m f . F lu id passes through the interstitial space between the fluidizing particles, and expands the bed homogeneously, leading to a 'fluidlike' state o f solids. W i t h a further increase i n fluid flow, the superficial gas velocity passes through the m i n i m u m bubbl ing velocity, U m b , i.e., the transition between Figure 1.1 (a) and (b), where two distinct phases, the bubble phase and the emulsion phase, are present. The bubbl ing regime is one o f the most studied flow regimes in gas-solid fluidization. Bubble coalescence and break-up take place as fluid flow is increased. Eventually, the bubbles become large enough to occupy a considerable fraction o f the cross-section o f small diameter columns, wi th slug flow observed, as shown i n Figure 1.1 (c). A further increase i n gas flow makes bubbles (slugs) unstable, and bubble splitting becomes dominant. A l t h o u g h the definitions relating to the turbulent fluidization flow regime are controversial (e.g. Rhodes, 1996), the smoothness i n fluidization prevailing beyond transition, Figure 1.1 (d), is what is considered as the defining characteristic o f the turbulent fluidization flow regime. Bubbles no longer retain their usual spherical-capped shape and character as in the bubbl ing regime. Instead there are transient voids zig-zagging their way to the surface. The high frequency o f v o i d splitting is one o f the most significant characteristics o f turbulent fluidization. This breakdown not only improves gas-solid contacting, but also increases macrornixing. Moreover , the upper surface o f the bed becomes increasingly diffuse, wi th substantial entrainment o f solids out o f the top. Further increasing the fluid flow and efficient return o f entrained solids enables the bed to be operated in the fast fluidization flow regime. In some cases, the lower region o f the fast fluidization regime has similar hydrodynamics to those o f the turbulent fluidization flow regime; however, the upper region o f the bed exhibits a core-annulus structure wi th strands o f solids, a characteristic unique to fast fluidization. Pneumatic conveying represents the upper limit o f fluid flow. Transit ion velocities are used to help distinguish between different flow regimes; however, they are subjected to confusion and controversy when flow regime characteristics are not clear. Moreover , transitions between the respective regimes are often not sharp. Chapter 1 Introduction 4 1.2 Turbulent fluidization flow regime The term 'turbulent fluidization' has seen its share o f controversy mainly due to the subjective observations by many earlier researchers (Johnsson et al., 1992). The dynamics o f the fluidized state are governed (Zijerveld et a l , 1998) by: • superficial gas velocity • size o f the facility • solids holdup • gas distributor design • solids properties « gas properties • axial solids distribution • solids mass flux. In addition, numerous definitions exist for a flow regime between bubbl ing and fast fluidization. Challenges arise when a particular phenomenon is referred to as a 'turbulent fluidized bed' without reporting on the details o f operating conditions and material properties. F o r instance, Trnka et al. (2000) identified several states o f gas-solid fluidized beds, including two for turbulent beds, namely intermediate turbulence and fully turbulent beds, using a three-dimensional space diagram o f pressure fluctuations obtained from spectral analysis. Based on Zijerveld et al. (1998), the turbulent fluidization flow regime is divided into an intermediate turbulent bed and a turbulent bed, characterized through chaos analysis o f pressure fluctuations. Furthermore, transition to turbulent fluidization has been denoted as type I, a sharp transition as bubble wakes become open, rather than closed, and type II, gradual transition through intermittent slug-like structures (Bi et al., 1995). A l though standardization o f these definitions is important, the flow characterization pertaining to fluid-particle interactions must be established not only to distinguish between flow regimes, but also to assist in defining transitions. 1.3 Outstanding issues U n t i l recently, the majority o f work on the turbulent fluidization flow regime has dealt wi th the transitional velocities (Rhodes and Geldart, 1986; Brereton and Grace, 1992; Chehboun i et al., 1994; B i et al., 1995). T o extend and validate current predictions o f transition velocities against realistic operating conditions o f industrial reactors, knowledge must be extended wi th respect to the influence o f pressure (see Lanneau, 1960; Y a n g and Chitester, 1988; C a i et al., 1989; Tsukada et al., 1993; Marzocchel la and Salatino, 1996; N e w t o n et al., 2001), temperature (see C a i et al., 1989; Foka Chapter 1 Introduction 5 et a l , 1996; Peeler et a l , 1999) and equipment scale (see C a i et al., 1989; Sun and Chen , 1989; El l i s et a l , 2001). Very l imited work has been reported on the detailed hydrodynamics and flow structure for units operating i n the turbulent fluidization flow regime. Extending the current knowledge o f macroscopic hydrodynamics, e.g., obtained by characterizing axial and radial profiles o f voidage using local measurements, should clarify the features which contribute to favourable gas-solid contacting. There is enough evidence that 'bubbles' i n a traditional bubbl ing fluidization sense break down (Lanneau, 1960; R o w e and MacGi l l iva ry , 1980; Lee and K i m , 1989). L o c a l v o i d size and rise velocity have been investigated in the turbulent fluidization flow regime as analogous to the bubbl ing regime (Lanneau, 1960; Yamazak i et a l , 1991; L u et a l , 1997; Farag et a l , 1997a; Tax i l et a l , 1998). However , Tax i l et al. (1998) found little correlation between the v o i d chord length and rise velocity, suggesting breakdown o f the two-phase theory, and the limitations in characterizing turbulent fluidized bed hydrodynamics through extension o f bubble characteristics studied extensively in the bubbl ing flow regime. Departure from the familiar terminology o f the two-phase theory, i.e., dense and dilute phases, to describe the system i n terms o f distribution o f voidage may be required to fully characterize the hydrodynamics o f the turbulent regime. In turbulent fluidized beds, coalescence and splitting o f voids exist as competing mechanisms. Attempts to explain gas-solid interactions based on turbulence characteristics may contribute to our understanding o f this complex phenomenon. V a n den A k k e r (1998) highlighted the occurrence o f coherent structures i n multiphase systems. Coherent structures o f the vorticity field giving organized patterns containing most o f the energy may be a result o f local differences i n mixture density. Investigations o f factors contributing to energy dissipation, turbulence and chaos are much needed (Hartman et a l , 2001). A l though challenges exist in obtaining concrete experimental data pertaining to such structures, careful experimentation wi th numerical model l ing may also extend our understanding. W i t h the advent o f increased computational capabilities, computational fluid dynamics ( C F D ) is emerging as a promising new tool in hydrodynamic modell ing. Whi l e it is n o w a standard tool for single-phase flows, it is still at the development stage for multiphase systems, such as fluidized beds. W o r k is required to make C F D suitable for fluidized bed reactor model l ing and scale-up purposes. T w o different approaches have been applied in early attempts to apply C F D model l ing to gas-solid Chapter 1 Introduction 6 fluidized beds: two-fluid models treating fluid and solid phases as interpenetrating continuum phases; and Euler ian/Lagrangian models wh ich treat the fluid phase as a cont inuum, and the particle phase as Lagrangian, solving Newton ian equations o f mo t ion for each particle. D u e to computational limitations, the Euler ian/Lagrangian mode l is normally l imited to a number o f particles o f order 10 7. Fo r small particles, such as typical catalyst particles o f diameter 75 um, it becomes difficult to simulate any meaningful reactor volume. Therefore, the two-fluid model is the preferred choice for simulating macroscopic hydrodynamics. B y pursuing fundamental studies o f parameter validation, and experimentally validating the hydrodynamics predicted by the two-fluid model , wh ich incorporates coupling terms, C F D can become a significant contributor to reactor model l ing and scale-up o f industrial fluidized beds. 1.4 Research objectives The research presented i n this thesis addresses some o f the issues outlined above. K e y objectives are to: • Conduc t experimental investigation on the transition from bubbl ing to the turbulent fluidization flow regime, and the effect o f pressure, temperature and scale on the transition velocity, U c . Four different fluidization columns o f diameter 0.11, 0.29, 0.61, and 1.56 m are used i n this study. O n e o f these is a high-temperature unit wi th pressures ranging from 0.1 to 0.4 M P a absolute pressures and temperatures from 20 to 2 4 0 ° C . T h e effect o f scale on regime transition is investigated wi th two relatively large columns owned by C S I R O Minerals, Australia. This organization has complementary ongoing research interests, and they have recently embarked upon a research program to study the effect o f temperature on the transition velocity o f turbulent fluidization (Peeler et al., 1999). • Obta in local measurements i n these fluidization columns using optical fiber probes, measuring both voidage and velocity, and a capacitance probe, measuring voidage. A novel optical velocity probe developed at the Fluidizat ion Research Centre at U B C is applied to measure particle velocity and voidage, and hence particle flux, simultaneously i n turbulent fluidized beds o f F C C particles. Bivariate local voidage measurements from two identical optical fiber voidage probes are also obtained to investigate the fluid-particle interactions. • Provide experimental evidence relating to the flow structure o f the turbulent fluidized bed using various analysis methods, such as statistical, spectral, wavelet and chaos analyses. Turbulent fluidized beds have been reported to exhibit unique chaotic characteristics (Bai et Chapter 1 Introduction 7 a l , 1999). Further exploration o f various data analysis methods applied to experimental data may broaden understanding o f the complexity o f the flow dynamics. • Investigate the effect o f particle size distribution on the transition velocity, U c . However , particles used in this study only pertain to Geldart G r o u p A particles. 1.5 Thesis layout Chapter 2 summarizes the detailed design o f the four fluidization columns used in this work, as wel l as the macroscopic hydrodynamics obtained from pressure measurements. The time-mean pressure measurements at the wall o f a fluidized bed provide information about the overall bed voidage, and estimation o f bed expansion. Operating conditions characterized by superficial gas velocity, solids circulation rate, distributor plate pressure drop, and initial bed inventory are described. Details on the design and construction o f traversing probe arms used to obtain local measurements inside the largest co lumn (1.56 m diameter) are included. This chapter also summarizes the properties o f the particulate materials used i n this study. Chapter 3 focuses on the transition from the bubbl ing to the turbulent fluidization flow regime. The transition velocity, U c , is defined as the superficial gas velocity at wh ich the standard deviation o f pressure fluctuations reaches a maximum. The effects o f initial solids inventory, and location o f pressure transducer ports on U c are reported from the cold mode l U B C unit. The effect o f scale on the transition velocity is determined from measurements obtained i n the 0.61 and 1.56 m diameter columns at C S I R O , i n comparison to the data obtained at U B C from a 0.29 m diameter column. The effect o f particle properties on U c is reported for two different catalysts having similar densities. Finally, the effect o f system pressure and temperature o n transition velocity is discussed based on results obtained in the hot unit. Chapter 4 presents a detailed description o f the two identical optical voidage probes used to measure the local voidages in four fluidization columns, and on the capacitance probe used in the two C S I R O columns. The design, calibration and placement o f a quartz cover at the tip o f the optical voidage probe are discussed. Reported results include radial profiles, probability distributions, standard deviations o f local voidages, and the effect o f scale on such measurements. Compar ison o f the optical voidage probe and capacitance probe measurements highlights the difference in the measuring volume o f the probes. Chapter 1 Introduction 8 In Chapter 5, experimental results f rom the optical fiber velocity probe i n the 0.29 and 0.61 m columns are reported. Cross-correlation o f signals between the two fibers al lowed velocities to be determined i n turbulent fluidized beds. The high-speed data acquisition, ~29 k H z , for the particle velocity measurement required condit ioning o f the data prior to cross-correlation. The effects o f different pre-condit ioning techniques on the resulting velocity measurements are shown to be substantial. Simultaneous measurements o f voidage and particle velocity reveal changes i n flow dynamics wi th superficial gas velocity, and with radial location. A n attempt is made to deduce vo id velocity, simultaneously wi th particle velocities, highhghting the difference in the physical scale o f these measurements, and the requirement for further data condi t ioning to obtain the velocity o f voids, wh ich are themselves o f transitory character. Chapter 6 presents analysis o f the pressure and voidage measurements obtained in Chapters 2 through 5, using various statistical, spectral and chaotic analysis methods. Particular focus is placed on methods which help delineate structural changes as the bed undergoes transition to the turbulent fluidization flow regime. Spectral analysis highlights dominant frequencies present i n the signals, while rescaled range analysis can deduce cycle times inherent in signal fluctuations. The data are further analyzed wi th a coherence function, wh ich characterizes the coherence o f a pair o f signals at a given frequency. The significance o f the physical length scale to the scale o f interest is emphasized. In Chapter 7, wavelet analysis, a relatively new analysis tool, wh ich finds numerous applications including the interpretation o f non-linear data, is employed in an effort to gain physical insight into the gas-solid turbulent fluidized bed. Wavelet analysis allows the decomposi t ion o f data into different frequency components, wi th the positions and scales then resolved as independent variables. This method can deal wi th the multiple levels o f scales present in fluidized beds, namely the macro-, meso- and micro-scales, wh ich affect signals at various temporal and spatial resolutions. Wavelet transformation is also applied to non-linear de-noising to remove high frequency fluctuations resulting from local particle variations in distinguishing v o i d movements for v o i d velocity calculations. L o c a l Intermittency Measure (LIM) applied i n turbulence research is extended to search for coherent structures. Finally, Chapter 8 provides a summary o f experimental findings, interpretations o f data analysis, and future perspectives related to advancing the understanding o f fluid-particle interactions as wel l as v o i d and particle dynamics i n turbulent fluidized beds. Chapter 1 Introduction 9 Appendix A lists further details on the modifications and commiss ioning o f the 1.56 m diameter fluidization column. Appendix B discusses the analysis methods employed for pre- and post- processing o f data i n deducing the velocity measurements. Cross-correlation is performed on the raw data as well as on data that had been pre-processed wi th binary coding and cut-off methods. Appendix C summarizes the background on the Fourier and wavelet transformations applied i n Chapters 6 and 7. Discussions on the continuous and discrete wavelet transformation, and details on the thresholding method are included. Appendix D reviews forces on solids in gas-solid fluidized beds, mcluding interparticle and fluid-particle interaction terms. C F D simulation was attempted using the two-fluid mode l to simulate turbulent fluidized bed o f F C C particles. However , definitive results were not obtained owing to time constraints. CHAPTER 2 EQUIPMENT AND MACROSCOPIC HYDRODYNAMICS 2.1 Introduction Four separate experimental systems were used i n this study. Details o n particle characteristics, configuration, air supply, operation, challenges encountered in large-scale units, and instrumentation are presented i n this chapter and i n Append ix A . The macroscopic hydrodynamics obtained through pressure measurements are also summarized as a preface to more localized voidage measurements presented in Chapter 4. 2.1.1 Bed expansion D u e to the fluctuating and diffuse bed surface i n turbulent fluidized beds, it is not possible to determine bed expansion solely by visual observation. C o m m o n l y , the bed voidage, deduced from the mean pressure drop, is used to characterize the bed expansion. A v i d a n and Yerushalmi (1982) related changes i n slope o f the expansion curve, for a 0.15 m diameter co lumn, to regime transitions. However , Geldart and Rhodes (1985), employing a similar G r o u p A powder i n their 0.29 m column, observed gradual changes as the transition occurred wi th no indicat ion o f any discernible abrupt variation as a result o f entry to the turbulent regime. A modified Richardson-Zaki equation was applied to both G r o u p A particles (Avidan and Yerushalmi, 1982) and G r o u p B particles (Lee and K i m , 1990) to correlate the average bed voidage with the superficial gas velocity wi th in the turbulent fluidization regime. A v i d a n (1980) introduced the concept o f the effective terminal cluster velocity, U t , such that: - ^ = e n (2-1) u ; It should also be noted that the pressure drop method i n obtaining voidage has been criticized (Werther and W e i n , 1994) as yielding too high solids fraction values due to the acceleration o f solid material i n the region close to the distributor. 2.1.2 Axial voidage profile A x i a l voidage distributions in turbulent fluidized beds are characterized by a smooth increase o f gas volumetric concentration i n the freeboard wi th the voidage remaining at ~0.65 to 0.75 in the bed. In 10 Chapter 2 Equipment and Macroscopic Hydrodynamics 11 the turbulent flow regime, the voidage is a strong function o f height (Venderbosch, 1998). A s the gas velocity increases, the average solids concentration measured by optical fibre probes decreases in the bed. In examining the effect o f static bed height on the axial voidage distribution, both H o r i o et al. (1992a) and Venderbosch (1998) reported that the decrease i n hold-up shifted towards higher heights. A l though the axial voidage distribution along the co lumn and bed expansion may not uniquely characterize turbulent fluidized beds, they provide vital information i n designing fluidized bed reactors operating in the turbulent fluidization flow regime. 2.2 Particulate material T w o different types o f solids and several different particle size distributions for each were investigated i n this study. The particle properties are tabulated i n Table 2.1. Spent F C C particles were donated by Chevron Texaco Corp . in Burnaby, and by a local refinery i n Vic to r ia , Australia. Particle size distributions o f F C C samples are shown i n Figure 2.1, while those for Catalysts C and C r are shown i n Figure 3.15. In the largest fluidization column, considerable entrainment o f fines was observed. This is depicted by the change in particle size distribution, shown i n Figure 2.2. Table 2.1 Particle properties. Identity FC C I F C C II F C C III F C C IV Particle density, k g / m 3 1560 .1450 1450 1450 Bu lk density, k g / m 3 860 740 820 N A M e a n diameter, u m 78 58 81 98 Identity Catalyst C Catalyst Cr Particle density, k g / m 3 1580 1580 B u l k density, k g / m 3 1093 N A Mean diameter, u m 41 33 Chapter 2 Equipment and Macroscopic Hydrodynamics 12 50 100 150 200 Mean particle size, um —o— F C C I — • — F C C I I - • - F C C I I I F C C I V 250 Figure 2.1 Particle size distribution of spent FCC particles. I n i t i a l d i s t r i b u t i o n A f t e r o n e w e e k - - F i n a l d i s t r i b u t i o n A — B a g filter c o n t e n t Mean particle size, um Figure 2.2 Progressive change in particle size distribution in 1.56 m diameter fluidization column. FCC II. Chapter 2 Equipment and Macroscopic Hydrodynamics 13 In order to alleviate electrostatic effects i n the fluidizing system, the catalysts were mixed with approximately 0.5 weight% o f Larostat 519 particles supplied by P P G Industries Inc. In addition, the columns were grounded at multiple points. 2.3 Column I: 0.29 m diameter fluidization column The 0.29 m diameter, 4.5 m tall Plexiglas vessel is located at the Universi ty o f Bri t ish Columbia . It is equipped wi th 58 sampling ports. The distributor is an a luminium perforated plate containing 98 holes o f 5.6 m m diameter arranged in an equilateral triangular configuration with a 32 m m pitch, resulting in an open area ratio o f 3.7%. A second supporting distributor wi th the same number o f holes o f 64 m m diameter is located below the first plate wi th a 38 mic ron stainless screen mesh sandwiched between the two plates to prevent particles from falling into the windbox. The disengaging section at the top o f the column, expanded to 0.4 m I D , abruptly converges to a 0.1 m exit duct connected to two external cyclones i n series. A schematic diagram o f the 0.29 m diameter co lumn appears i n Figure 2.3. Solids circulation is not controlled, but rather determined through a pressure balance between the return leg and the column. There are two flapper valves installed in the return leg to prevent gas from escaping up the standpipe. Flu id iz ing air is supplied by a Roots blower wi th a max imum capacity o f 425 N m 3 / h @ 69 kPa. A s shown i n Figure 2.4, fluidizing air is supplied through 0.15 m P V C piping. The air flow rate is controlled by the by-pass line located close to the blower, and calculated from the pressure drop across an orifice plate. 2.3.1 Pressure transducers and data acquisition system B o t h steady-state and dynamic pressure measurements were obtained by 20 gauge and differential pressure transducers ( O M E G A PX140) positioned at regular intervals along the column, as shown i n Figure 2.5. Pressure taps were mounted flush wi th the wal l o f the co lumn wi th 38 u m mesh stainless steel screens glued over the entrance to prevent solids from entering the pressure sensing lines. Modif icat ions were incorporated to prevent clogging o f the sampling ports resulting in better accuracy (Werther, 1999). A l iquid manometer was used to calibrate the pressure transducers. Their linear response characteristics were incorporated into the calibration equations. Pressure signals were logged into a computer via an A / D converter ( D A S 0 8 - E X P 3 2 ) . Chapter 2 Equipment and Macroscopic Hydrodynamics expanded section 0.4 m I D 6 cyclones 0.16 m I D return legs i 0.051 m I D solids re-entry level 0.051 to 0.18 m above distributor Figure 2.3 Schematic of 0.29 m diameter, 4.5 m tall fluidization column at U B C . F i g u r e 2.4 P h o t o g r a p h o f 0.29 m d iamete r c o l u m n w i t h P V C p i p i n g for air supp ly . W o o d e n enc losure o n the top leve l con ta ins b a g filters. Chapter 2 Equipment and Macroscopic Hydrodynamics 16 Figure 2.5 Schematic of 0.29 m diameter fluidization column depicting axial distances (in m) of ports relative to distributor plate. Chapter 2 Equipment and Macroscopic Hydrodynamics 17 Data acquisition was performed through a program written i n V i s u a l Basic and the L A B T E C H ® software, N o t e b o o k pro ver. 10.12, for steady-state and dynamic pressure measurements, respectively. 2.3.2 Bed expansion In many fluidized beds operated i n the turbulent fluidization flow regime, solids circulation is not controlled, but it is determined by the superficial gas velocity and by the overall pressure balance wi th in the system. In the 0.29 m diameter column, an increase in the superficial gas velocity resulted in an increase in the overall bed voidage, consequently i n bed expansion. O n c e in the turbulent fluidization flow regime, the bed surface becomes increasingly diffuse, wi th considerable fluctuations, rendering determination o f the bed level by visual observations impossible. The c o m m o n method used to deduce the expanded bed height is to plot the time-mean gauge pressure (single-point pressure) against the height o f the transducer ports, as exemplified in Figure 2.6, where the intercepts o f the two slopes correspond to the level o f the expanded bed. The effect o f initial static bed height on bed expansion is shown in Figure 2.7. T h e increases in expanded bed heights wi th U for the initial static bed heights o f 1.5 m and 0.51 m are not observed for H 0 =0.80 m. The differences in trend are attributed to the solid return leg, wh ich constrains the entrained solids flow. The sudden expansion at higher U was observed to depend on the overall 'smoothness' o f the solids flow, i.e., solids being efficiently returned through the dipleg, which seemed to be affected by the humidity o f the air i n the laboratory from wh ich fluidizing air was drawn into the blower. In fact, the upper l imit o f the experiment was set by the capacity o f the dipleg solids throughput, and not the blower. 2.3.3 Bed voidage A momentum balance on a cross-sectional slice o f a fluidized bed can be expressed (Gidaspow, 1994) as d I 9 ?\ dP do / \ 4 ( T w g + T w J -(q^I + ^ - j = - — - - - g ( e g e + e . O 5 (2.2) where the terms from the left are: net rate o f momentum outflow for gas/solids; fluid pressure gradient; gradient o f solids normal stress; gravitational force; and force due to wal l shear. F o r a fully developed flow and ignoring wal l shear and solid stress, the momen tum balance can be simplified to: Chapter 2 Equipment and Macroscopic Hydrodynamics 1 8 6n 1 Axial distance above distributor, m F i g u r e 2.6 A x i a l gauge pressure profde for 0.29 m c o l u m n . H0=0.51 m . D=0.29 m , F C C I. B 2.0 0.4 0.6 0.8 U, m/s 1.0 1.2 O H o = 0 . 5 1 m H o = 0 . 8 0 m * H = 1 . 5 m F i g u r e 2.7 E x p a n d e d b e d he igh t c a l cu l a t ed f rom gauge pressure profi les i n F i g u r e 2.6. D=0.29 m , F C C I. Chapter 2 Equipment and Macroscopic Hydrodynamics 19 ' - — * g(egs+es£s) (2-3) dz F r o m the time-mean gauge pressure profile, a least-squares linear fit can be performed to deduce the slope, i.e., d P / d z . In order to systematically include or exclude pressure data points near the diffuse bed surface, the standard deviation o f each data point is compared to the root mean standard error o f the curve fit, as shown in Figure 2.8. Since the pressure measurements do not display a c o m m o n variance, a weighted regression using Reduced Square-Chi o f the standard deviation o f the pressure fluctuation was performed. A s a result, the error imposed on the fitted parameter was minimized. The time-mean bed voidage for three different initial static bed heights calculated from the above procedure is shown in Figure 2.9. A s indicated by arrows in the figure, the trend wi th increasing bed height changes wi th U > U c for H 0 =0.51 and 1.5 m . ( U c is defined as the superficial gas velocity at wh ich the standard deviation o f pressure fluctuations reaches a max imum, and is described further in Chapter 3). However , this trend is not always consistent, as exemplified by the plot for H 0 =0.80 m. This is attributed to the varying in-bed inventory o f solids due to increasing entrainment o f solids in the freeboard as wel l as the solids in the return system. Variations o f bed voidage wi th superficial gas velocity are next analyzed using a modified Richardson-Zaki equation as proposed by A v i d a n (1980). F r o m a plot o f U versus voidage on a logarithmic scale, A v i d a n (1980) chooses the slope, n , to represent the homogeneity o f the fluidized bed. The superficial gas velocity o f the extrapolation o f slope to S = l is said to give the effective terminal cluster velocity, U t , through Equat ion 2.1 as shown i n Figure 2.10. The resulting coefficients are listed i n Table 2.2. A s H 0 is increased, both exponents are seen to decrease. 2.3.4 In-bed inventory of solids In order to correct for the solids contained in the freeboard and return loop, the mass o f solids remaining in the dense bed (Rhodes and Geldart, 1986) is used, i.e., M b = A ? b c d A = H A ( l - e ) 9 s (2.4) g Figure 2.11 depicts the height o f the dense bed corresponding to voidage at m i n i m u m fluidization, expressed as H ' = H ( l - s ) / ( l - 8 m f ) , based on Equat ion 2.4. The bed height representing the amount o f solids remaining in the dense bed, H ' , indicates a slight decrease approaching U c , beyond which a Chapter 2 Equipment and Macroscopic Hydrodynamics 20 OH 3 OJ u a 3 o o U=0.96 m / s data points Linear fit o f 4 data points • •Upper 9 5 % Confidence L i m i t • •Lower 9 5 % Confidence L i m i t - Linear fit o f 3 data points 0.4 0.8 1.2 Axial height, m Figure 2.8 Determination of bed pressure drop. U=0.96 m/s, H0=1.2 m, D=0.29 m, F C C I. A H =0.51 m O HQ=0.80 m X H = 1 . 5 m U , m / s Figure 2.9 Time-mean bed voidage vs. U . D=0.29 m, F C C I. Chapter 2 Equipment and Macroscopic Hydrodynamics 21 0.4 0.6 0.8 1 U, m/s Figure 2.10 Time-mean bed voidage vs. superficial gas velocity. Determination of effective terminal velocity, U*, in modified Richardson-Zaki equation. H0=0.6 m, D=0.29 m, Uc=0.62 m/s (z =0.31 m, DP). Table 2.2 Coefficients for the Modified Richardson-Zaki equation. H 0 , m U*, m/s n 0.6 1.76 1.82 1.2 1.23 0.76 1.5 1.16 0.41 Chapter 2 Equipment and Macroscopic Hydrodynamics 22 1.4 1.2 1.0-1 0.8 0.6 0.4 0.2 -I 0.0 o * * * ooo o ou O U , m / s A H Q = 0 . 5 1 m O H = 0 . 8 0 m ^ H = 1 . 5 m — i 1 1 1 1 1 1 1 1 1 1 — 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Figure 2.11 Height of dense bed corresponding to voidage at minimum fluidization vs. superficial gas velocity. D=0.29 m, F C C I. Chapter 2 Equipment and Macroscopic Hydrodynamics 23 steeper decrease is observed. This implies that the net decrease i n solids remaining i n the dense bed occurs at U > U c , i n agreement wi th the findings o f Rhodes and Geldart (1986). 2.3.5 Solids circulation rate The solids circulation rate was measured using the flapper valve by estimating the collected solids in the dipleg over a given time interval. Mor ikawa (1999) and Mor ikawa et al. (2001) reported an extensive study on entrainment from this column. In Figure 2.12, a typical range o f solids circulation rates is given to provide information about the system. 2.3.6Axial voidage distribution F r o m the eight differential pressure transducers located along the co lumn, the cross-sectional average voidage is calculated as represented i n Figure 2.13. A s a result o f increased entrainment at higher gas velocities, the average dense bed voidage increases while the freeboard voidage slightly decreases. The time-mean voidage at the axial posit ion closest to the distributor plate possibly reflects the jetting effect. Furthermore, the lower voidage indicated at the lower axial locations for U=0.94 m / s may be due to the influence o f solids re-entering the co lumn at axial distances between 0.051 and 0.18 m above the distributor plate. Increasing superficial velocity has been shown to cause the bed surface to become more diffuse. 2.4 Column II: 0.61 m diameter column The 0.61 m diameter, 9.8 m tall fluidization co lumn is located at C S I R O Minerals, Clayton, Australia. B o t h perforated plate and bubble cap type distributor plates are available. A single external cyclone o f 1.2 m diameter is located at the top to return solids to the fluidization column-at an average distance o f 0.88 m above the distributor plate via a return leg. The solids circulation rate is controlled by aeration gas via a distributor at the base o f the loopseal. A s shown i n Figure 2.14, the co lumn is fitted wi th multiple pressure taps to moni tor the pressure balance i n the circulation loop. Addit ional ly , as shown i n Figure 2.15, multiple ports were available to accommodate insertion o f optical probes, fast response pressure transducers and capacitance probes. The 0.61 m fluidized bed co lumn was modif ied to operate in the turbulent fluidization flow regime wi th F C C particles. The inlet o f a single cyclone o f 1.2 m diameter was reduced from 0.146 m 2 to 0.032 m 2 by inserting a 280 m m by 540 m m metal plate to ensure that the inlet velocity o f gas was Chapter 2 Equipment and Macroscopic Hydrodynamics 24 Figure 2.12 Solids circulation flux vs. superficial gas velocity. D=0.29 m, H0=1.0 m, FCC I. Q B o W) o > G 05 <U s I 0.0 0.4 0.8 1.2 1.6 Height of probe above distributor, m • U = 0 . 2 5 m / s U = 0 . 5 2 m / s o U = 0 . 9 4 m / s Figure 2.13 Axial voidage profile from time-mean DP measurements. D=0.29 m, H 0=l.l m, FCC I. Chapter 2 Equipment and Macroscopic Hydrodynamics 25 P10(10.0)i 9.78 P8 (9.50) 7.78-P7(6.i 5.78-P6 (4.82) solids re-entry level 0.63 to 1.18 m above distributor 3.78-Scale: 2 cm = 1m 0.41 ID P9(9.78)|— 1.20 ID "0.61 ID 9-6.78 P11 (6.42) 5.78 PI 2 (5.69) 0.25 ID '3.78 Figure 2.14 Schematic diagram of location (in m) of pressure ports in 0.61 m column. Chapter 2 Equipment and Macroscopic Hydrodynamics Optical probe Optical probe 4820 3155 2745 2170 1500 1600 1760 850 750 745 420 305 190 Manometer Manometer Manometer Pg5 D P 3 Pe4 D P 2 Pg3 _Pg2_ D P I Pel -I i Digital / I manometer Figure 2.15 Location (in mm) of pressure transducers and optical fibre probes for dyi measurements in 0.61 m diameter fluidization column. Chapter 2 Equipment and Macroscopic Hydrodynamics 27 sufficient to capture entrained particles i n an efficient manner. The distributor plate contained 523 holes o f 6.4 m m i n diameter on a 25.4 m m triangular pitch. The pressure drop across the distributor plate for an empty fluidization co lumn is shown in Figure 2.16. T h e high pressure drop results from the fabric placed under the distributor to prevent solids from falling into the windbox. T w o Roots blowers wi th max imum capacities o f 30,000 N m 3 / h @ 20 kPa and 10,000 N m 3 / h @ 60 kPa supply the fluidizing air for both the 1.56 m and 0.6 m diameter fluidization columns. The air flow rate is calculated by measuring the gauge and differential pressures and the thermocouple readings across an orifice plate. T w o separate pressure logging systems for dynamic and steady-state pressure measurements were used on the 0.61 m fluidization column. F o r the steady-state pressure measurements, differential pressure transducers (Sensym 30 mb to 1000 mb; Rosemount 375.65 mb; Taylor 373.65 mb; Honeywel l 100 mb) were used. Pressure taps were mounted flush wi th the wal l o f the co lumn and fitted wi th cigarette filters to prevent solids from entering the pressure sensing lines. The data acquisition system was configured to sample at 100 FIz. For the dynamic measurement system, five S U R S E N S E ™ ultra low pressure sensors from Data Instruments (model D C A L 4 0 5 D N , ± 5 in . F I 2 0 F.S.) and five Sensym Signal Condi t ioned Pressure Transducers (models 142SC01D, 0-1 psid and 142SC05D, 0-5 psid) were calibrated and connected to the pressure taps via 15 m m stainless steel sintered filters. Between the author's two visits (13 month apart) to C S I R O , the particle size distribution o f the F C C particles fluidized i n the 0.61 m diameter co lumn changed. The two lots are identified as F C C III and I V i n Section 2.2. 2.4.1 Pressure balance in circulation loop Figure 2.17 shows the pressure balance for the bubbl ing and turbulent fluidization flow regimes in a 0.61 m diameter co lumn circulation loop. A t U=0.26 m / s , entrainment o f solids was minimal . W h e n U was increased to 1.56 m / s , there was considerable entrainment as reflected by the pressure profile. Efficient return o f solids through the cyclone and dipleg is observed wi th solids accumulating at the loopseal. Chapter 2 Equipment and Macroscopic Hydrodynamics 28 63 < 24-20-16-12 8^ O o o o 28 — i 1 • 1 1 1 1 1 ' 1 1 — 0.3 0.4 0.5 0.6 0.7 0.8 0.9 U , m / s Figure 2.16 Distributor plate pressure drop measured in empty column. 0=0.61 m. s-C •a c «8 a u C « X 13 105 110 115 120 Absolute pressure, kPa — A — U=1.56 m/s: riser —A— IJ=1.56 m/s: return leg - Q — U=0.26 m/s: riser —•— U=0.26 m: return leg Figure 2.17 Pressure profile for circulation loop for D=0.61 m, H 0=2 m, F CC IV. Chapter 2 Equipment and Macroscopic Elydroclynamics 29 2.4.2 Expanded bed height F r o m the axial pressure profiles, expanded bed height is calculated for each superficial gas velocity as shown i n Figure 2.18. The initial F C C static bed height was approximately 2 m . The expanded bed height data reflect the large storage capacity o f the loopseal and return leg system. It also shows an initial increase wi th superficial gas velocity, followed by a slight decrease. A s deduced from a D P transducer located between 1.50 and 1.60 m above the distributor plate, U c =1.12 + 0.05 m / s . Increasing U results i n a decrease i n the dense bed height corresponding to the m i n i m u m fluidization voidage without a noticeable change in its slope near U c , as shown in Figure 2.18. This implies that the mass o f solids remaining i n the dense bed continually decreases wi th increasing U , and that U c does not solely correspond to the loss o f solids. 2.4.3 Bed density Variations o f the time-mean suspension density wi th superficial gas velocity are shown i n Figure 2.19. B e d densities at U > U c in the 0.61 m column indicate very efficient return o f entrained solids, as the corresponding voidage remains below 0.6 at U=1.56 m / s . This suggests that there are statistically steady suspension densities resulting from pressure balance i n the circulation loop at U > U C . This seems contrary to the earlier investigations where the existence o f the turbulent fluidization flow regime as an independent regime was questioned, e.g. Rhodes (1996), that the transition is caused by the transfer o f solids from the bed to the freeboard wi th the exposure o f the pressure probe to the freeboard. 2.5 Column III: 1.56 m diameter fluidization column The 1.56 m diameter, 15 m tall cold-model is also located at C S I R O D i v i s i o n o f Minerals i n Clayton. F lu id iz ing air is supplied through a 0.95 m air duct, a p lenum chamber expanding the diameter to 1.56 m, and a distributor plate consisting o f 18 bubble caps. T w o external cyclones in parallel at the top o f the co lumn separate gas and solids and feed solids back to the co lumn through return legs equipped wi th flapper valves. Aerat ion via a distributor at the base o f the loopseal controls the solids circulation rate. In order to operate this rig in the turbulent fluidization regime wi th Geldart G r o u p A solids, the distributor plate and cyclone inlet area were modif ied. The locations o f the pressure transducers and traversing probe arms are shown i n Figure 2.20. Further details on the modifications and commissioning o f the 1.56 m diameter fluidization co lumn are reported i n Append ix A . Chapter 2 Equipment and Macroscopic 2.0 30 Figure 2.18 Expanded bed height and height of dense bed corresponding to voidage at smf calculated from axial gauge pressure profiles. D=0.61 m, H0=2 m, Uc=1.12 m/s (z =1.55 m, DP), FCC IV. 800 n , 0.45 C/3 G v -o v Figure 2.19 Time-mean bed density vs. superficial gas velocity for D=0.61 m, H0=2.0 m, axial location of DP taps: 0.73-1.55 m, FCC IV. U c at z =1.55 m from DP fluctuations. Chapter 2 Equipment and Macroscopic Hydrodynamics 31 circles represent location of steady-state pressure logging ports solids re-entry level 0.2 to 0.8 m above distributor upper traversing probe arm lower traversing probe arm distributor unit: m 3.60 O high speed pressure logging ports 1.80 1.71 O 1.85 1.75 1.01 O 0.84 1.20 1.10 0.90 0.80 0.50 O 0.095 o 0.20 -0.30 O windbox Figure 2.20 Location of pressure transducers and traversing probe arms in 1.56 m column. Chapter 2 Equipment and Macroscopic Hydrodynamics 32 The distributor pressure drop was measured i n an empty co lumn for an open area ratio o f 3%, as shown in Figure 2.21. After mstalling 5 m m spacers, the final open area ratio was reduced to 2.3% without a significant increase i n distributor pressure drop. A s shown i n Figure 2.22, frequency analysis o f the gauge pressure measurements in die 1.56 m diameter fluidization co lumn without any Solids exhibits two smaU-amplitude wide band peaks. Peaks at these frequencies increased in amplitude with increasing superficial gas velocity, and are attributed to the inherent frequency o f the blower, and /o r natural frequency o f the air supply system. A s indicated i n Figure 2.23, the ratio o f distributor plate pressure drop to bed pressure drop was experimentally shown to be between 10 and 30% for the range o f superficial gas velocities studied, ensuring a uniform distribution o f gas; however, no bubble caps were located i n the centre o f the distributor which likely contributed to a preferential flow o f gas towards the wall , as discussed in Chapter 4. 2.5.1 Traversing arm design and construction In order to measure pressure and voidage simultaneously at various radial positions in the bed, two stainless-steel traversing probe arms were designed and fabricated for a differential pressure transducer and to ho ld optical and capacitance probes. A s shown in Figure 2.24, the probe arm consisted o f either an optical probe for probe arm #1 or both the optical and the capacitance probes for probe arm #2, a differential pressure transducer, and two 15 | i m sintered filters as pressure ports. The support structure at the end o f the probe arm was designed to have m i i i i m u m interference between different measuring probes, and was made o f 64 m m O D stainless steel tube, 60 m m in length. The probe arms, made o f 38 m m O D stainless steel tube wi th a total length o f ~850 m m , were inserted into the rig 0.84 m and 1.8 m above the distributor at 90° to each other. 2.5.2 Pressure measurements T w o separate systems for dynamic and steady-state pressure measurements were used on the 1.56 m diameter fluidization column. Fo r the steady-state pressure measurements, differential pressure transducers o f X T C M o d e l 341 Series - smart Pressure transmitter f rom M o o r e Product (model type: 3 4 1 D D 1 S 2 B N 1 N N 2 N , 4-20 m A D C , 10-450" H 2 0 programmable) were programmed to register a m a x i m u m o f 100 mbar (for 0.4-2 volt). Pressure taps were mounted flush wi th the wal l o f the column and were fitted with cigarette filters to prevent solids from entering the pressure sensing lines. The data acquisition system was configured to sample at 1 H z , and was installed in a portable Chapter 2 Equipment and Macroscopic Hydrodynamics o 3 3.0 A 2.0 1.5 A fin 1.0 < 0.5 A 0.0 o o o o o o o ° o ° o 0.4 0.8 1.2 U, m/s 1.6 Figure 2.21 Distributor plate pressure drop measured in empty 1.56 m column. 3 0.005 0.004 §2 0.003 £ 0.002 0.001 0.000 5 10 15 Frequency, Hz 20 Figure 2.22 Frequency spectrum analysis of gauge pressure fluctuations in empty bed. D=1.56 m, U=l.l m/s, z=0.2 m, r/R=0.9. Chapter 2 Equipment and Macroscopic Hydrodynamics 34 S3 % a o u U u EC u 0.2 0.3 0.4 U, m/s Figure 2.23 Bed and distributor pressure drop for 1.56 m fluidization column. U=0.43 m/s, H0=0.9 m, FCC II. Optical probe 15 um stainless steel sintered filter -=L~ Capacitance probe 64 mm OD stainless steel tube 38 mm OD stainless steel tube to gauge pressure transducer Differential pressure transducer Figure 2.24 Schematic diagram of the tip of a traversing probe arm. Chapter 2 Equipment and Macroscopic Hydrodynamics 35 hut located next to the rig. F o r the dynamic measurement system, five transducers each o f 1) S U R S E N S E ™ ultra low pressure sensors from Data Instruments: mode l no. D C A L 4 0 5 D N (± 5 in . H 2 0 F.S.), and 2) Sensym Signal Condi t ioned Pressure Transducers: mode l no. 142SC01D (0-1 psid) and mode l no. 142SC05D (0-5 psid) were calibrated and connected to the pressure taps via 15 u m stainless steel sintered filters. T o minimize reduction i n transducer response amplitude, the transducer volume was made as small as possible (~ 6 cm 3 ) , and the transducer-data acquisition card cable length was shortened to reduce noise; therefore, the data acquisition board and the computer were positioned on the platform o f the supporting structure o f the rig. Pressure fluctuations were recorded by the data acquisition card C I O - D A S 0 8 (Computer Boards, Inc.) wi th a P e n t i u m ™ 233 computer using the data acquisition software L A B T E C F 1 ® N o t e b o o k P ro ver. 10.1, sampling at 100 H z for periods o f 100 s. 2.5.3 Bed expansion The expanded bed height, H , and height representing solids remaining i n the bed, H ' , both estimated from axial pressure profiles, are shown i n Figures 2.25 and 2.26. In both cases there are insignificant change for H 0 =0.9 m, compared to H 0 =2 .2 m where a decreasing trend is observed at U > U c . This may be due to the H 0 =0.9 m run not reaching high enough U . 2.5.4 Axial voidage profile B y assuming that the friction and acceleration terms are negligible and assuming identical response times for transducers logged at 1 H z , voidages can be calculated from the pressure drop measurements. A s a result o f increased entrainment at higher gas velocity, the average dense bed voidage increases as the freeboard voidage decreases slightly, as shown i n Figure 2.27. This profile is dependent on the solids re-circulation rate, wh ich could not be measured. 2.5.5 Voidage profile The voidages calculated from D P measurements at the wal l i n Figure 2.28 appear to exhibit a two-stage increase wi th gas velocity. Voidages calculated from D P signals o n the traversing probe arm resulted in consistendy higher values unti l the gas flow exceeded 0.47 m / s ; at this point both D P measurements showed similar voidages indicative o f increased bed homogeneity at gas velocities beyond U c . The differences in voidages obtained from these D P measurements may be attributed to the location o f the traversing probe arm i n relation to the solids injection port from the return leg. The co lumn diameter may significandy affect the entrainment flux, thereby influencing the solids Chapter 2 Equipment and Macroscopic Hydrodynamics 3.5-3.0 A % 2.5 A | 2.0 A "g 1.5 « W 1.0 A 0.5 O U, o o ° o o 0 0 IL 0.2 0.4 U , m / s 0.6 O HQ=0.9 m A H =2.2 m 0.8 36 Figure 2.25 Calculated expanded bed height from time-mean gauge pressure profile. D=1.56 m, FCC II. O H =0.9 m o A H =2.2 m Figure 2.26 Height of dense bed corresponding to voidage at minimum fluidization vs. superficial gas velocity. U c deduced from gauge pressure signals. D=1.56 m, FCC II. Chapter 2 Equipment and Macroscopic Hydrodynamics 37 Q o v 8 O > c u s i s • H = 0 2.2 m, U =0.25 m / s o H = 0 2.2 m, U =0.53 m / s H = 0 1.2 m, U =0.24 m / s • H = 0 1.2 m, IJ: =0.51 m / s V e r t i c a l c o o r d i n a t e , m F i g u r e 2.27 A x i a l v o i d a g e prof i le f rom t i m e - m e a n DP measu remen t s . D=1.56 m , F C C II. « -T-< c > c s I E D P rail O D P t r a v e r s i n g p r o b e a r m A O p t i c a l p r o b e U , m / s F i g u r e 2.28 V o i d a g e c a l c u l a t e d f rom DP m e t h o d a n d o p t i c a l p robe s i g n a l . D=1.56 m , z=0.85 m , H 0 =0.9 m . A l l sensors p o s i t i o n e d at r /R=0.9 . U c ( z =0.84 m , DP)=0.39 m / s , F C C II. Chapter 2 Equipment and Macroscopic Hydrodynamics 38 flow i n the region near the return leg. Tasirin and Geldart (1998) reported a decrease i n total entrainment rate wi th increasing co lumn diameter; however, since their largest co lumn size was only 0.152 m , their results may not correctiy predict the trend when the co lumn diameter is increased to 1.56 m. Further comparison can be drawn from the dense bed voidages shown in Figure 2.9 (D=0.29 m), Figure 2.19 (D=0.61 m), and Figure 2.28 (D=1.56 m). However , as indicated in Figure 2.9, the bed voidage is influenced by the static bed height. Information on the solids circulation rate, the solids hold-up in the return system, and the in-bed solids inventory must be taken into consideration to compare the effect o f scale on bed voidage. 2.6 Column IV: 0.11 m diameter column A hot mode l unit study was conducted to investigate the effects o f pressure and temperature on the hydrodynamics o f turbulent fluidized beds using commercial Catalyst C . The unit, residing at an industrial research facility (contract work), is constructed o f stainless steel wi th a diameter o f 106 m m for a height o f 2 m above the distributor, wi th an expansion to a diameter o f 212 m m for a further height o f 1 m at the top. A schematic is shown i n Figure 2.29. A single stage internal cyclone wi th a return leg O D o f 22 m m captures and returns entrained particles. T h e solids inventory was maintained at 7 kg for all runs. Gas leaving the top o f the unit is cooled before being discharged via a filter. A sintered plate is used as the distributor plate wi th nitrogen as the fluidizing gas. The fluidizing gas is heated to a preset temperature upstream using an electrical heater. 2.6.1 Instrumentation (hot unit) There are six equally spaced ports on the wal l starting 300 m m above the distributor. Ni t rogen gas is purged at 0.05 N m 3 / h through a T-junction in order to prevent solids f rom entering the pressure transducers. T w o differential and three gauge pressure transducers are located as shown i n Figure 2.29 to measure pressure fluctuations in the hot unit. A Keyence N R - 2 5 0 data acquisition card acquires data at a rate o f 10 H z for periods o f 7 minutes. 2.6.2 Bed expansion (hot unit) O w i n g to the l imited number o f pressure transducers i n the hot unit, a second method o f analysis was adopted to estimate the expanded bed height. F r o m the time-mean differential pressure drop across a certain interval i n the middle o f the dense bed, and across another section extending from the lowest pressure tap to a tap i n the freeboard, the fol lowing equation was used: Chapter 2 Equipment and Macroscopic Hydrodynamics 39 V 0.21 D P l r ~3 1.2 0.11 P g : 0.9 P g ; D P h ~7FT V 0.3 Pre-heater (Units: m) Figure 2.29 Schematic diagram of 0.11 m diameter hot unit. A l l dimensions are in metres. Chapter 2 Equipment and Macroscopic Hydrodynamics 40 A P t t j H = ~ ~ ^ Z b e d + 2 b o t t o m probe (2-5) ^ i bed Since this method relies on a single pressure drop measurement across the bed, it is much more prone to error than the method based on the gauge pressure measurement profile, as shown in Figure 2.6. However , this is a c o m m o n method applied in industrial units to estimate the overall bed voidage. Figure 2.30 plots the expanded bed height against superficial gas velocity at r o o m temperature. A s the absolute pressure in the vessel increases, the bed expansion rado increases for the same superficial gas velocity owing to the increase in gas density. Changing the temperature had less effect on the expanded bed height, as indicated in Figure 2.31. The increase i n temperature increases the gas viscosity and decreases the gas density. Moreover , the elevated temperatures may affect the role o f the hydrodynamic and interparticle forces, as reported for the stability o f a fluidized bed at mi r i imum fluidization by Lettieri et al. (2001). Further investigation is required before any conclusions can be drawn. 2.6.3Bed voidage (hot unit) The effect o f system pressure and temperature on the time-mean bed voidages is presented in Figure 2.32. The results show some increase in voidage wi th increasing pressure, wi th voidage being approximately proport ional to P 0 0 8 for a given superficial gas velocity. W i t h an increase in the absolute pressure o f the column, voidage tended to increase wi th increasing bed temperature as shown i n Figure 2.32. The data are compared with voidage correlations in Figure 2.33. The fol lowing voidage correlation by C a i et al. (1989) incorporates a co lumn size effect:: ^0.0653 (2.6) 'o.7% + 8 S , 4 x l 0 ~ n D v A r 2 y However , this correlation overpredicts the voidage for both columns, wi th the trend for co lumn size not consistent wi th the experimental trend. The empirical correlation o f K i n g (1989) U + l e = (2.7) U + 2 gives better predictions. W h e n the difference in gas density due to the effect o f pressure and temperature is taken into consideration, the simple correlation o f K i n g (1989) underestimated the voidage, as portrayed i n Figure 2.34. Chapter 2 Equipment and Macroscopic Hydrodynamics 41 X 1.2 • P= =0.1 MPa A P: =0.2 MPa P = =0.3 MPa O V-=0.4 MPa U, m/s Figure 2.30 Effect of system pressure on expanded bed height at room temperature. D=0.11 m, Catalyst C, H0=0.7 m. 0.2 0.3 0.4 U, m/s • T = 20 ° C o T = 160 ° C T = 240 ° C Figure 2.31 Effect of temperature on bed expansion at a system pressure of 0.2 MPa. D=0.11 m, Catalyst C, H0=0.7 m. Chapter 2 Equipment and Macroscopic Hydrodynamics 42 F i g u r e 2.32 Effec t o f sys t em pressure a n d temperature o n t i m e - m e a n b e d vo idage d e d u c e d f r o m D P s igna l s . D=0.11 m , U=0 .40 m / s , Ca ta lys t C . Chapter 2 Equipment and Macroscopic Hydrodynamics 43 O D=0.29 m, H =0.6 m • D=0.29 m, H =1.0 m ' o A D=0.29 m, H =1.5 m • D=0.11 m, H =0.7 m •K ing Correlation (1989) -Ca ie t al. (1989): D=0.29 m -Ca i et al. (1989): D=0.11 m 0.05 0.1 0.5 1 U , m /s F i g u r e 2.33 C o m p a r i s o n o f e x p e r i m e n t a l vo idage data w i t h p r ed i c t i ons f rom literature corre la t ions . Ca ta lys t C . A m b i e n t c o n d i t i o n s . Chapter 2 Equipment and Macroscopic Hydrodynamics 44 v « -a c > •0 OJ e V e H 0.6 P=0.2 MPa P=0.3 MPa P=0.4 MPa ••King (1989) - Cai et al. (1989) - C a i et al. (1989) - C a i etal. (1989) P=0.2 MPa P=0.3 MPa P=0.4 MPa 0.4- -1 1 1—i—f— 0.1 -> • — i — 0.5 U , m /s F i g u r e 2.34 E x p e r i m e n t a l vo idage measu remen t at 2 4 0 ° C c o m p a r e d to cor re la t ion p r ed i c t i ons . D=0.11 m , H 0 = 0 . 7 m , Ca ta lys t C . Chapter 2 Equipment and Macroscopic Hydrodynamics 45 2.7 Conclusions Four different fluidization columns used i n this study are described. Macroscopic hydrodynamics were determined based on time-mean pressure measurements. T w o different types o f catalysts belonging to Geldart G r o u p A were used, wi th their properties listed i n Table 2.1. The operating conditions are summarized i n Table A . l i n Append ix A . » A x i a l pressure profiles indicated diffuse bed surfaces wi th higher gauge pressure in the freeboard wi th increasing superficial gas velocity due to solids entrainment. The solids circulation rate was not controlled for the two smaller diameter columns. F o r the two larger columns, adjusting the fluidizing air to the loopseal controlled the solids circulation rate, but this rate could not be measured. • Increasing the initial static bed height changed the bed expansion vs. superficial gas velocity trend. In the 0.29 m diameter fluidization column, flow i n the solids return system seemed to affect the overall bed expansion. Occasionally the expanded bed height decreased gradually wi th increasing U , indicating accumulation o f solids in the return leg system. This was only noticed in the 0.29 m unit as the Plexiglas unit allowed visual observations o f solids flow, and because o f the material o f the column, the system was much more susceptible to electrostatic charges wh ich are k n o w n to be sensitive to the humidity o f the fluidizing air. • The dense bed height corresponding to voidage at m i n i m u m fluidization calculated from the bed pressure drop allowed the characterization o f the fluidized bed without the effect o f the solids contained i n the freeboard and return system i n order to isolate the in-bed inventory o f the solids. T h e decrease i n the dense bed height corresponded wel l wi th the superficial gas velocity at U c for the 0.29 m diameter fluidization column. However , i n the 0.61 m diameter co lumn and i n some cases in the 1.56 m diameter column, a gradual decrease in dense bed height was observed without any noticeable change at U c . • The modif ied Richardson-Zaki equation was applied to the bed voidage measurements. However , consistency o f the exponents was questionable as the bed voidage was sensitive to the 'smoothness' o f operation. Moreover , i n a system where the solids circulation rate cannot be controlled, it is difficult to characterize the overall operating conditions. Thus, it was not possible to draw any conclusions. • Increases i n both absolute pressure and temperature caused increases i n bed voidage, wi th pressure having greater influence than temperature. F o r measurements at ambient pressure and temperature condit ion, bed voidage was better correlated by the empirical correlation o f Chapter 2 Equipment and Macroscopic Hydrodynamics 46 K i n g (1989) than other approaches. However , the correlation o f C a i et al. (1989) indicated better predictions for increased pressure and temperature, accounted for by the particle Reynolds number and Archimedes number. Further study o f the effect o f scale is required under high pressure and elevated temperature operating conditions. C H A P T E R 3 R E G I M E T R A N S I T I O N A N D S C A L E E F F E C T 3.1 Regime transition Regime transition from bubbling to turbulent fluidized flow has been based on visual observation, bed expansion, voidage fluctuations, and pressure fluctuations. A still photograph o f F C C particles fluidized i n a two-dimensional bed i n Zenz and Othmer (1960) shows a breakdown o f bubbles at a gas velocity o f 0.91 m / s (3 ft/s). A number o f reports have been published i n the past two decades analyzing definitions o f the turbulent fluidized flow regime (see reviews such as B i et a l , 2000; Smolders and Baeyens, 2001). A s discussed by Grace (2000), this flow regime has adopted the name 'turbulent' f rom the chaotic appearance o f its voids movement, and is not necessarily based on a sound description o f the physics o f the phenomenon. Consequendy, this regime has been subject to much controversy and there remains no clear definition o f its hydrodynamic structure. In gas-solid fluidization, there exists a transitional regime between bubbl ing and fast fluidization, i.e., between the superficial gas velocity at which a max imum bubble size is attained and the transport velocity at which the dilute phase transport state is reached. The competing mechanisms o f increasing homogeneity due to the break-up o f bubbles/voids , and increasing heterogeneity owing to the formation o f clusters, determines where the transition, U c , lies. In investigating the transition from bubbling to turbulent fluidization, Yerusha lmi and Cankurt (1979) identified two transition velocities: U c , the superficial gas velocity at wh ich the pressure fluctuations reach a maximum; and U k , the velocity at wh ich the pressure fluctuations begin to level off, as depicted i n Figure 3.1. O n e point o f controversy is how the 'transition velocity' should be defined. A s summarized by Rhodes (1996), early work contributing to the definition o f the flow regime was ambiguous owing to the lack o f reporting important details, such as the measurement method o f U c , and the solids circulation rate. K e h o e and Dav idson (1970) reported greater homogeneity o f the bed through breakdown o f distinct bubbles as an important characteristic o f the onset o f turbulent fluidization. However , A b e d (1984) demonstrated that the hydrodynamic structure o f the bed i n the turbulent regime is radially non-homogeneous. 47 Chapter 3 Regime Transition and Scale Effect Figure 3.1 Definitions of transition velocities U c and U k based on standard deviation of pressure fluctuations. Adapted from Yerushalmi and Cankurt (1979). Chapter 3 Regime Transition and Scale Effect 49 The factors contributing to the confusion that exists even today are mainly: 1) lack o f details regarding the method by which the regime was identified; and 2) no clear agreement between researchers o n what constitutes the turbulent flow regime. Furthermore, the issue o f whether U c or U k should demarcate the onset o f the turbulent flow regime has gained more attention than understanding the hydrodynamic structure o f the flow regime once it has been reached. The different schools o f thought regarding this transition can be categorized into two classes, as suggested by Sun and Chen (1989): 1) it is related to gas-solid contact characteristics in the fluidized bed; or 2) it is based on the axial expansion and entrainment characteristics o f the whole reactor. These two interpretations are discussed further i n this chapter; however, the reason for clarifying the definition needs to be addressed first. W h e n designing a gas-solid fluidized bed reactor, one requires a reactor mode l wh ich is capable o f coupling the contact mode and the kinetics (Levenspiel, 2002). The contact mode, i.e., the hydrodynamics, o f the fluidized bed dictates key parameters such as phase hold-up, velocity profiles, mixing and residence time distribution. It is critical to know when the transition to the turbulent regime occurs wi th respect to reactor modell ing. T h e overall reactor mode l depends on the kinetics and the contact mode, wh ich i n turn depend on the velocity, solids circulation rate, and operating conditions, including pressure and temperature. In other words, i f the gas velocity is being increased from the bubbl ing fluidized flow regime, one needs to be able to predict the velocity at wh ich breakdown o f the two-phase theory occurs. W i t h this in mind, the fol lowing summarizes the reported characteristics and perceived definitions i n the area o f turbulent fluidization flow regime in the two categories, followed by the author's experimental findings. The first types o f characterization o f the turbulent fluidized bed relate to the local contacting characteristics o f the bed. The most noticeable change i n the bed i n going from the bubbl ing to the 'turbulent flow regime is the break-up o f bubbles. This phenomenon is we l l documented from local voidage measurements using capacitance and optical fiber probes (Lanneau, 1960; Massimilla, 1973; Lancia et al., 1988). The condit ion at which bubble splitting becomes prevalent throughout the bed depends on particle properties and operating conditions. The bubble break-up characterized by a decrease in pressure fluctuations is the basis in marking the transition using pressure fluctuation measurements. Sun and C h e n (1989) correlated U c values based o n the not ion that once a gas velocity has reached the point where max imum bubble size is attained just above the distributor, bubble splitting wi l l be dominant throughout the bed. A s summarized by Brereton and Grace (1992), bo th differential and gauge pressure fluctuations have been analyzed i n terms o f standard deviation, average fluctuations, peak-to-peak, and r.m.s. about mean, and these can give different Chapter 3 Regime Transition and Scale Effect 50 values. Through the statistical analysis o f pressure fluctuations plotted against superficial gas velocity, a m a x i m u m point, denoted as U c , is attained, indicating a change i n the bed structure. However , it was not unt i l the study o f B i and Grace (1995) that the discrepancies between reported U c values from pressure fluctuations were analyzed i n terms o f the effect o f measurement methods. U c is generally considered to be the superficial velocity at wh ich the onset o f the turbulent fluidized flow regime occurs, when distinct bubbles start splitting at high frequency resulting i n smaller voids and a decrease i n the standard deviation o f the pressure fluctuations. Beyond U c , there is some indication that the fluidized bed can no longer be modelled by simple two-phase models like those applied to bubbl ing fluidized beds (see Foka et a l , 1996). O n the other hand, some researchers have concentrated on the axial solids distribution i n interpreting what constitutes a transition. A c c o r d i n g to Geldart and Rhodes (1985), the transition is due to the two competing mechanisms o f increasing bubble size, and bed depth, and decreasing bed height because o f greater entrainment o f particles as the gas velocity is increased. U k has been interpreted (Yerushalmi and Cankurt, 1979) as the gas velocity corresponding to the onset o f the turbulent flow regime where solids rearrange into distinct clusters, wi th strong interaction between the dense and lean phases. Moreover , U k obtained from the pressure fluctuations is generally taken as the gas velocity at wh ich the pressure fluctuations reach a plateau. The analysis o f Geldart and Rhodes (1985) suggested that U k is, in fact, the gas velocity at wh ich the bed surface falls below the top differential pressure tap used to indicate the bed surface. Regardless o f whether or not the pressure tap is submerged i n the bed, the increase i n gas velocity results i n a decrease in the time-mean differential pressure as a result o f the expansion o f the bed. T h e transition velocity, U k , is reported to be dependent on the solids return efficiency (i.e., cyclone efficiency), measurement technique, measurement location, and particle properties. F o r a system wi th an efficient solids return system, U k is not reached unti l a much higher gas velocity (Geldart and Rhodes, 1985). Thus, it has been criticized as having no physical meaning and as only an experimental artefact due to the use o f a differential pressure transducer (Chehbouni et a l , 1994). H o r i o et al. (1992a) examined the inflection point o f dz/ds to conf i rm the finding o f Yerushalmi and Cankurt (1979) that the transport velocity, U t r , is the transition gas velocity between turbulent and fast fluidization. B y analyzing the local voidage measured by optical probes, they concluded that Chapter 3 Regime Transition and Scale Effect 51 the clusters in the turbulent regime were not completely suspended by the gas. Schnitzlein and Weinstein (1988) suggested that the levelling-off o f pressure fluctuations coincided wel l wi th the levelling-off o f the bed voidage. Some researchers (see B i and Fan, 1992) have supported U k as the onset o f transport. In that case, the range between U c and U t r (~U k ) should constitute the turbulent fluidization flow regime. N o t e that this second method o f interpretation is based on the time-averaged distribution o f solids, wh ich neglects the complex dynamic behaviour o f the fluidized bed (Zijerveld etal . , 1998). Some questions that arise from a mechanistic understanding o f the phenomena relate to: • physical meaning o f U k ; • significance o f clusters; • competing mechanisms o f increase i n expanded bed height f rom increased gas flow vs. decrease i n bed inventory due to significant entrainment. The change in local and macroscopic structures o f the bed i n passing through the turbulent regime can be viewed as starting from U c , wi th a gradual transition from the continuous phase being a dense phase containing dispersed voids to the continuous phase being the gas phase wi th dispersed solid clusters. This transitional regime, called the turbulent fluidization flow regime, exhibits unique hydrodynamic features resulting i n significant advantages when fluidized beds operating i n this mode are used as reactors. 3.2 Observation of current knowledge and its gaps Pressure fluctuations i n fluidized beds depend on particle properties, bed geometry, flow conditions, pressure and temperature conditions (M'chirgui et al., 1997). Numerous studies have used pressure fluctuations to indicate the quality and /o r flow regime o f fluidization (e.g. B a i et a l , 1996; Schouten and van den Bleek, 1998; X u et a l , 1998). F r o m an industrial point o f view, the use o f simple pressure measurements i n the reactor to determine the fluidization quality or regime is convenient and attractive. 3.2.1 Regime transition Transi t ion from the bubbl ing to the turbulent regime has been commonly characterized by the transitional velocity, U c , defined as the velocity at wh ich the standard deviation o f pressure fluctuations, obtained wi th either single or double probes measuring either gauge or differential Chapter 3 Regime Transition and Scale Tiffed 52 pressure, reaches a max imum as the superficial gas velocity is increased. However , due to the effect o f the measurement method on U c , it has been difficult to compare reported values i n a standardized manner as pointed out by Brereton and Grace (1992) and B i and Grace (1995). Pressure fluctuations i n fluidized beds are considered to originate f rom multiple physical phenomena such as bed oscillations and the formation/r ise/erupt ion o f voids (Bi et a l , 1995). Gauge pressure measurements from a single probe reflect more global phenomena i n the bed as opposed to the more localized phenomena measured by the dual (differential pressure) probes. B y using closely spaced dual probes, higher frequency pressure waves reflecting the v o i d behaviour resulting from their formation, coalescence, eruption or rising may be studied. In the latter measurements, a decreasing standard deviation o f the differential pressure fluctuations denotes a more homogeneous bed. A c c o r d i n g to this interpretation, U c , indicates where the bed starts to become more homogeneous as the gas velocity increases. However , considerable scatter i n data has been reported, making it difficult to predict the transition velocity wi th confidence for a given geometry, operating conditions and solids characteristics. Moreover , reported transition velocities are column- and solids-specific. 3.2.2 Scale effect Al though they are util ized i n a number o f industrial processes, there are only a few reported studies o f scale-up effects i n turbulent fluidized beds. In the bubbl ing flow regime, conversion tends to decrease due to inefficient gas-solid contacting from increased v o i d size when the co lumn diameter is increased. In order to alleviate this problem, Edwards and A v i d a n (1986) ensured bubble suppression by increasing the proportions o f fine catalyst particles. M o n i t o r i n g the local vo id behaviour while increasing the co lumn diameter should provide invaluable insight into how units can be scaled up without loss o f conversion or yield. The effect o f co lumn diameter on U c provides a convenient benchmark for designing new reactors. C a i (1989) reported, after using Geldart A and B particles in columns o f diameter 0.05, 0.14, 0.28 and 0.48 m , that U c was unchanged with increasing co lumn diameter beyond a certain scale. Further hydrodynamic investigation o f this trend may clarify the relationship between homogeneity o f the bed and U c . 3.3 Experimental approach For the remainder o f this chapter, the transition velocity, U c , refers to the superficial gas velocity at wh ich the max imum standard deviation o f pressure fluctuations is attained. Reference to local Chapter 3 Regime Transition and Scale Effect 53 voidage fluctuations is made where deemed necessary. However , i n view o f the interest in estabHshing a general correlation for U c and its applicability to industrial operating conditions, pressure fluctuations are the main focus. The standard deviation is calculated according to: n i x - ( Ix) - 1 ; — — • t3-1) n(n - 1 ) where x is the instantaneous value and n the number o f determinations. F o r all experimental measurements pertaining to the determination o f transition velocity through pressure fluctuations, a sampling frequency o f 100 H z and a sampling duration o f 100 s were used for consistency. A n F F T analysis o f the pressure signals revealed that most peaks observed were wi th in 10 H z . Thus, a sampling frequency o f 100 H z was considered sufficient. Sampling durations o f 100 s and 200 s were compared and these indicated at most a 1.9 % difference i n the standard deviation o f pressure fluctuation for steady-state operations. Thus, the sampling frequency and duration were considered acceptable. N o t e that the standard deviation o f pressure fluctuation shown i n Figure 3.2 indicates a rather broad maximum, i.e., a transition which was not at all sharp. This was especially so i n larger diameter columns. The error involved in deducing the max imum point, indicative o f U c , through curve fitting is investigated i n Section 3.3.2, while alternative ways o f deducing U c are examined i n Chapter 6. The study conducted in this work pertains to bubbl ing fluidized beds and the transition to the turbulent flow regime. A s exemplified i n Figure 3.2, bed density reaches a plateau before steadily deceasing at U « 1 m / s . The standard deviation from differential pressure (DP) signals within the bed indicates a gradual transition. Moreover , when the bed density f rom a D P cell wi th one port located above the expanded bed height is plotted against U , Figure 3.3, it shows a sudden drop at around U=0 .8 m / s , followed by a plateau. The physical meaning o f this drop is related more to the location o f the bed surface rather than to any change in bed dynamics. W h e n the local voidage fluctuation is plotted, as shown i n Figure 3.4, the change occurs around U = l . l m / s . This demonstrates that different definitions o f the transition velocity can result i n values for this parameter. Chapter 3 Regime Transition and Scale Effect 0.08 54 cn Q 0.02 800 600 4 200 400 -a cc c CU -0 -d CU PQ Figure 3.2 Typical standard deviation of pressure fluctuations and bed density measurements. Pressure fluctuation measurement: z =1.50 m, Az=0.10 m. Bed density: z =1.14 m, Az =0.82 m. D=0.61 m, FCC IV, H=1.67~1.77 m. 250 w C CU Ti Figure 3.3 Bed density measurements, z =1.85 m (zlower=1.55 m, zupper-2.14 m), Az=0.59 m, D=0.61 m, FCC IV, d=98 urn. H=1.67~1.77 m. Chapter 3 Regime Transition and Scale Effect 55 1.6 ' 5 1-2 0.4 o o o o o o o o o o ° o % o o 1 1 0.4 0.8 1 1 1.2 1.6 U , m / s Figure 3.4 Standard deviation of optical fiber voidage probe signal. z=1.55 m, r/R=0.09, D=0.61 m, FCC IV, H=1.67~1.77 m. Chapter 3 Regime Transition and Scale Effect 56 3.3.1 Pressure measurement method T o date, most predictive correlations are o f the general form: (3.2) where A r = e8(eP-ee)gdp (3.3) Fitted values o f a and b have been tabulated by H o r i o (1997). Correlations o f this form suggest that U c is solely influenced by the gas and particle properties, wi th pressure and temperature also entering A s summarized by B i et al. (2000), the factors that affect U c include: • probe location • type o f transducer • particle size distribution • solids circulation rate • pressure probe resistance • D P pressure port spacing • static bed height • co lumn diameter • particle characteristics • operating conditions (pressure and temperature) • internals (e.g. baffles) A number o f these have been examined (Bi and Grace, 1995). In this chapter, a further study is conducted to determine the role o f other factors such as probe location, static bed height and co lumn diameter. 3.3.2 Error analysis A s shown i n Figure 3.2, the plot o f standard deviation o f pressure fluctuations vs. superficial gas velocity does not necessarily produce sharp peaks which can be identified unambiguously as U c . U c was determined through a second-order polynomial curve fitting o f the data, fol lowed by solving for the maximum. The confidence level from a purely statistical point o f view was examined to obtain through their influence on gas properties. Chapter 3 Regime Transition and Scale Effect 57 error bars on the curve fit o f data. This procedure was recommended by the U B C Statistical Consul t ing and Research Laboratory ( S C A R L file #01-01-004). For the number o f superficial gas velocity data, I, let y ; be the value o f the standard deviation o f the pressure fluctuation corresponding to the i t h gas velocity x ;. Th rough the quadratic polynomial regression model , the regression parameters are estimated from the data, and expressed as: y = p o + p i X + p 2 x 2 (3.4) The value o f x wh ich maximizes y i s obtained by differentiating equation (3.4) wi th respect to x and setting the result to 0, giving Pi Through the Delta method, an approximation o f the variance o f x m a ! i is expressed as: (3.5) rz V p ,p a r ( p j 2 c o v ( p i > p 2 ) < v a r j p j var 9 Pr P iP 2 P 2 (3.6) The statistical software J M P I N ver. 4.0.3 from S A S Institute was used to perform the regression and to estimate the parameters. Covariance was calculated from: c o v ^ p , ) = corr(p 1 ,f$2)*s.c{^ )s.e.(f52) (3.7) The statistic (3.8) has an approximately standard normal distribution. Hence the approximate confidence interval for x m a x can be expressed as: ( X m a x - Z a / 2 V V " ( X m a x ) ! Xmax + Z a / 2 (Xmax )) ( 3 - 9 ) Through this statistical method, the 95% confidence interval for the example in Figure 3.2 was calculated to be (1.07 m / s , 1.17 m/s) . F r o m Figure 3.4, it is clear that this range coincides wel l wi th the superficial gas velocity at which the local voidage fluctuation drops precipitously. The error associated wi th curve fitting was approximately 4 to 7%. Those results wi th errors greater than 10 % o f the predicted U c suggested standard deviation curves too broad to determine maxima, and thus were discarded. Chapter 3 Regime Transition and Scale Effect 58 V a n O m m e n et al. (1999) considered factors affecting the accuracy o f probe-transducer systems in gas-solid fluidized beds, and provided guidehnes wi th respect to probe diameter and length for m i n i m u m distortion o f pressure signals. F o r the frequencies o f interest, they recommended that the probe diameter be between 2 and 5 m m , and transducer volumes be 2500 m m 3 or less. Care was taken i n this study to nhnimize the transducer volume and probe length. The majority o f transducers used in the U B C co lumn had a tube diameter o f 3.2 m m and length o f about 0.1 m (equivalent to a transducer volume o f —810 mm 3 ) , except for the transducers connected to the freeboard, wh ich had lengths o f around 0.3 m. The maximum volume encountered in this study was for a gauge pressure (AP) cell mounted at the end o f a traversing probe arm at C S I R O i n order to obtain pressure measurements at the centre o f the 1.56 m diameter column. T h e calculated volume i n this case was approximately 6700 m m 3 . Wire mesh and sintered filters were used at U B C and C S I R O , respectively, at the tip o f the pressure probe to prevent F C C particles from entering the transducers. These filters inevitably caused some dampening o f the pressure signals. It was assumed that the signal frequencies were linearly filtered, and thus had no affect on the location o f the max imum standard deviation wi th respect to superficial gas velocity. Fluctuations o f the fluidizing air flow, supplied by the Roots blower at U B C , as a result o f the blower performance and temperature variations in the feed line were estimated to cause pressure fluctuations between 0.5 to 3.6 % o f the mean. 3.4 Results 3.4.1 Effect of axial probe location and static bed height on Uc The effect o f the axial probe location on U c i n the 0.29 m diameter co lumn is depicted in Figures 3.5 and 3.6 for D P and A P , respectively. A s indicated, U c deduced from D P is quite sensitive to the axial posi t ion o f the probe, as opposed to those from A P , wh ich show very similar maxima. The difference i n U c obtained from differential vs. gauge pressure measurements is due to their reflecting local and global phenomena i n the bed, respectively, as noted above. T h e trend confirms the findings o f B i and Grace (1995), and is extended i n Figure 3.7, illustrating the effect o f probe location as wel l as static bed height. Chapter 3 Regime Transition and Scale Effect 0.6 59 p o o M C ^ '> o — Xi 63 -a c CD 0.4 J, 0.2 0.0 A A A A A w * "** *S o** — I 1 1 1 1 1 ' 1 1 1— 0.2 0.4 0.6 0.8 1.0 1.2 o z=0.59m A z=0.43m z=0.31m z=0.18m U , m / s Figure 3.5 Typical plot of standard deviation of DP fluctuations vs. U . D=0.29 m, H0=0.60 m, F C C I. Az=0.064 m for z=0.18, 0.31, 0.43 m; and Az=0.13 m for z=0.59 m DP port locations. Figure 3.6 Typical plot of standard deviation of gauge pressure fluctuations vs. U . D=0.29 • z=0.21 m o 2=0.34 m A 2=0.46 m O 2=0.65 m z=0.91 m ffl 2=1.16 m U , m / s m, H0=0.51 m, F C C I. Chapter 3 Regime Transition and Scale Effect 1.0 0.8 A 0.6 A 0.4 O • v * fflffl - O O A V A A • V port spac ing 1 1 = 6.4 c m ^ i 1 1 • — ^ port spac ing = 12.7cm 0.2 0.4 0.6 0.8 1.0 1.2 Height of probe above distributor, m V A o H Q = 0 . 6 m H Q = 0 . 7 m H Q = 0 . 9 m H =1.1 m o H =1.5 m o Figure 3.7 Effect of pressure port location on Uc from DP signals. D=0.29 m, FCC I. Chapter 3 Regime Transition and Scale Effect 61 It can be seen that U c values obtained from pressure fluctuation measurements are influenced by local phenomena i n the fluidized bed, and that the break-up o f voids starts f rom the top o f the expanded bed, as indicated by the decreasing U c deduced from probes at higher elevations. F r o m these findings, it is strongly recommended that when reporting U c , the type o f pressure transducer, location o f probes and static bed height be specified. Moreover , since U c deduced from gauge pressure signals seems to reflect the overall change i n a fluidized bed, it is simpler to compare U c f rom gauge pressure signals for the reason mentioned above. The effect o f static bed height on U c measured by gauge pressure signals is shown in Figure 3.8. It has been reported that U c measured by gauge pressure signals is unaffected by the H / D ratio providing that it is above 1 (Cai, 1989) or 4 (Grace and Sun, 1991) for F C C particles. The trend is certainly represented i n Figure 3.8, where at H / D ~ 3, U c becomes less sensitive to the aspect ratio, H / D . 3.4.2 Effect of column diameter on Uc Reliable knowledge about the effect o f co lumn diameter on U c is important to the design and operation o f high-velocity fluidized bed reactors. C a i (1989) employed Geldart A and B particles in four columns o f diameter 0.05 to 0.48 m , and reported that U c becomes independent o f column diameter beyond a certain diameter. Based on J in et al. (1986), his data were correlated by r 1 i ° - 2 7 U„ I H-e2o I f 0.211 2.42 x l O " 3 10.27 • + V J D 0.27 D 1.27 v d p y e s 2 o v e g j p i n m ] (3.10) This correlation accounts for the effects o f temperature and pressure up to 4 4 0 ° C and 600 kPa, respectively. Sun and Chen (1989) proposed a correlation for U c based on the m a x i m u m bubble diameter. U c = 1 . 7 4 d ; ' m f 1 - 6 m f 0.5 TT + U m f (3.11) where 2.25 0.6D d b , m a x + 0 . 6 D •d b .max (3.12) Chapter 3 Regime Transition and Scale Effect 62 Figure 3.8 Effect of aspect ratio H / D on U C from gauge pressure signals. D=0.29 m, FCC I. Chapter 3 Regime Transition and Scale Effect 63 \ — e m f d b,rrvax Q g and = 1.32 (3.13) V e l - E m f The correlation was based on G r o u p A particles fluidized in a co lumn o f diameter 0.8 m . However , none o f these correlations has been validated for co lumn diameters exceeding 0.8 m. Exis t ing correlations are overwhelmingly derived from experiments conducted i n laboratory-scale fluidized beds operating at atmospheric temperature and pressure, conditions remote from those o f most industrial-scale fluidized beds. Figure 3.9 compares predictions from various correlations wi th experimental results obtained in columns o f diameter 0.29, 0.61 and 1.56 m. Equat ion 3.14 does not produce a comparable U c nor does it predict the observed effect o f co lumn diameter. U c appears to be affected by the reactor diameter, at least up to D=1.56 m , in disagreement wi th previous conjecture (Cai, 1989) that U c should remain insensitive to D for diameters beyond 0.5 m . The effect o f H / D may become increasingly significant i n larger columns where greater heights may be needed to reach the max imum stable bubble size. U c is plotted against the aspect ratio (FI /D) i n Figure 3.10. Different trends are observed for shallow ( H / D < 3) and deep ( H / D > 3) beds. N o t e that the difference in mean particle diameter (see Table 2.1 in Chapter 2) i n the two columns may have contributed to the lower U c values i n the 1.56 m diameter column. However , wi th the usual exponents on the Archimedes number i n equations o f the form o f Equat ion 3.2, the effect o f the particle diameter variation is not able to fully explain the drop i n U c in passing from the 0.61 m diameter co lumn to the 1.56 m diameter column. Interpretation o f U c as the velocity at wh ich the max imum bubble size is attained may explain U c being independent o f pressure tap location above the level where bubbles /voids have reached their max imum sizes. Chapter 3 Regime Transition and Scale Effect 1.0 64 0.8 H 0.6 A 0.4 0.2 0.0 0.0 • • s o B \ t \ X O 0.4 0.8 1.2 D, m 1.6 • H / D = =4.4 o H / D = =3.7 • H / D = =3.3 • H / D : =2.3 • H / D : =2.1 o H / D = =1.0 Ca i correlation (1989) •Sun & Chen (1989) 2.0 Figure 3.9 U C obtained in this study from gauge pressure signals as a function of column diameter. FCC. 1.0 0.8-.* 0.6-£ ° 0.4 0.2 0.0 - • o 8 GO • o this work: D=1.56 m • o A this work: D=0.61 m O this work: D=0.29 m • o • B i (1994) D=0.10 m i 1 i 1 i 1 2 4 6 Bed height to diameter ratio, H / D Figure 3.10 U C based on gauge pressure fluctuations vs. bed aspect ratio for the three columns investigated in this work together with data from Bi (1994). FCC. Chapter 3 Regime Transition and Scale Effect 65 U c data for deep beds ( H / D > 3) are compared wi th published data (Schnitzlein and Weinstein, 1988; Grace and Sun, 1991; B i , 1994; Chehbouni et a l , 1995a) wi th F C C particles as the bed material i n Figure 3.11. Experiments conducted at different static bed heights i n the three columns studied in this work confi rm that U c , based on differential pressure fluctuations increases wi th decreasing height. This implies that homogeneity o f the bed is attained at the top o f the bed first; the entire bed is not wel l into the turbulent flow regime until the gas velocity is wel l beyond that required for turbulent fluidization at the bed surface. The scatter in the measured U c for a given co lumn probably originates from different static bed heights, or different particle size distributions i n the case o f Grace and Sun (1991). Excep t for the data o f Chehbouni et al. (1995a), U c correlates reasonably well wi th z / D . Inclusion o f the location o f the D P cell in the correlation reduces the dependence o f U c on the specific co lumn geometry. In order to account for the difference i n static bed height, the time-mean voidage calculated from D P s from which U c is obtained is considered in characterizing the bed condit ion. B y plotting voidage and standard deviation from the same D P as in Figure 3.12, s c, the voidage at wh ich the max imum standard deviation occurs, is obtained by extrapolation. A s s u m i n g that £ c represents the cross-sectional average voidage at a given D , the effect o f co lumn diameter may be removed. Thus, as shown in Figure 3.13, an attempt was made to correlate the voidage wi th U c . D u e to the scatter and the l imited number o f data, it is impossible to obtain a clear relationship. Whi ls t most studies on U c are conducted wi th D < 0.4 m (Bi and Grace, 1995), it is o f interest to see whether U c deduced from pressure transducers mounted on the wal l is indeed representative o f the pressure fluctuation occurring throughout the cross-section o f a large-scale reactor. The traversing probe arm constructed at C S I R O for this purpose allowed pressure measurements at the centre o f the 1.56 m diameter reactor. Figure 3.14 presents the standard deviation o f differential pressure fluctuations. U c deduced from the standard deviation o f pressure fluctuations at r /R=0 .9 and at the centre appear to be similar, indicating that U c , though affected by height, is insensitive to radial location. The increased frequency o f voids in the centre o f the co lumn even at lower gas velocities is indicated by a relatively steep rise i n the standard deviation o f pressure signals as the gas velocity is increased. Beyond U c , increased homogeneity o f the bed is observed, as indicated by the limited spread i n the measured standard deviations. Chapter 3 Regime Transition and Scale Effect 66 1.2 0.8 s u p 0.4 0.0 A this work (D=0.61 m) O this work (D=0.29 m) A Bi (D=0.10 m, 1994) O Grace & Sun (D=0.10 m, 1991) • Schnitzlein & Weinstein (D=0.15 m, 1998) X Chehbouni et al. (D=0.082 & 0.20 m, 1995) o A o o o X A I i 0 8 A o X X 4 6 Dimensionless height of probe, z /D 10 Figure 3.11 Comparison of experimental U c obtained from DP signals to published data for H/D>3. 0.5 Q O c o V -a u C5 d CS •w C/3 0.4 ^  0.3 J 0.2 A 0.1 A 0.0 0.0 o o o o o A ' G3D O o c o 0 o 0.2 0.4 0.6 U, m/ s "oT 1.0 0.8 -I 0.6 cm C J 0.4 o 0.2 0.0 1.0 Figure 3.12 Standard deviation of DP signals and voidage plotted against superficial gas velocity. D=0.29 m, FCC I, H0=0.51 m, z=0.31 m. Chapter 3 Regime Transition and Scale Effect 1.0 n 67 0.8-0.6 0.4-0.0 * A O O o 0.5 1.0 U , m / s 1.5 A D =0.29 m 0 D =0.61 m D =1.56 m 2.0 Figure 3.13 Plot of U c vs. corresponding bed voidage, sc. FCC. • D P I : z= 0.85 m, r/R= =0.9 o DP2: 2= 1.15 m, r/R= =0.9 A DP3: 2= 1.80 m, r/R= =0.9 A DP4: 2= 1.80 m, r/R= =0.0 Figure 3.14 Standard deviation of DP signals plotted a s a function of U. D=1.56m, H0=2 m, FCC II. Chapter 3 Regime Transition and Scale Effect 68 3.4.3 Effect of particle properties on Uc The effect o f fines and mean particle size on the 'quality' o f fluidization has been the subject o f several studies owing to reports suggesting increased chemical conversions wi th higher proportions o f fines (e.g. Yates and N e w t o n , 1986). B a i et al. (1996) have shown the effect o f different relative fractions o f binary mixtures o f F C C particles and silica sand on U c . The i r results correlated well wi th U c predicted from C a i (1989) correlation, Equat ion 3.10, by accounting for the binary distribution in terms o f equivalent particle diameter and particle density. The mixture o f the narrower and higher mass mean particle diameter sand particles wi th F C C particles showed a .much higher U c for more than 50% mass fraction o f sand to F C C particles. This signified that there was very little effect o f the particle size distribution (PSD) o f sand on U c when the mixture consisted o f more than 50% F C C particles. Judd and Goosen (1989) indicated a decrease i n gauge pressure fluctuations when the reactor diameter increased from 0.05, 0.14 to 0.29 m , wi th a lower U c for powders o f smaller mean diameter (mass and Sauter means) and larger P S D . In many studies, the change i n P S D results i n a change i n mean particle diameter, and the independent effects o f P S D and particle mean diameter cannot therefore be distinguished. Grace and Sun (1991) reported on the enhanced chemical conversion obtained by broadening the P S D yet keeping the mean particle size constant. U c for F C C particles having a wider P S D indicated an earlier onset o f the turbulent fluidization flow regime. This was attributed to the change in the gas flow through the dense phase producing smaller voids for w ide r -PSD fluidized beds. In this work, particles displaying a density close to that o f F C C particles (1560 k g / m 3 ) were chosen to obtain experimental values o f U c . The particle size distribution is plotted i n Figure 3.15 i n comparison to the F C C particles, wi th properties listed in Table 3.1. Catalyst C had two different size distributions. B o t h batches o f catalysts had the same range o f particle size, but Catalyst C r had a higher content o f size cut between 32 and 45 um, resulting i n a smaller mean diameter. Experiments were conducted in a 0.29 m diameter co lumn wi th an initial static bed height o f 0.60 m for each set o f particles. The expanded bed height calculated from the time-average axial pressure measurement, Figure 3.16, indicated much more entrainment for Catalyst C r than for F C C particles. W i t h Catalysts C and Cr , the return leg often filled up very quickly, indicating that a considerable por t ion o f the bed had been transferred to the return leg. Chapter 3 Regime Transition and Scale Effect 69 C/3 cn > 3 a u —o— F C C A Catalyst C Catalyst Cr ~\ ' 1 1 r — • 1 • 1 • r 20 40 60 80 100 120 140 Diameter, jam Figure 3.15 Cumulative distribution of particle size based on mass fraction. 1.2 1.0 0.6 0.4 O o oooo o°coO GD O O C P A i ' 1 > 1 > 1 < 1 > r—* 1— 0.0 0.2 0.4 0.6 0.8 1.0 1.2 A Catalyst Cr O F C C U , m / s Figure 3.16 Comparison of expanded bed height from axial pressure distribution for FCC and Catalyst Cr. D=0.29 m, H0=0.6 m. Chapter 3 Regime Transition and Scale Effect 70 Therefore, when U c is plotted against the vertical coordinate as i n Figure 3.17, the selected probe heights o f 0.18 and 0.43 m ensured that the probe was always located wi th in the fluidized bed. The difference in U c between Catalysts C and C r was min imal wi th the error bars for a 95% confidence interval from curve fitting overlapping. The particle Reynolds number corresponding to U c from D P signals is plotted against the Archimedes number for mass mean particle diameters in Figure 3.18. Since the effect o f height on U c is not predicted by the correlation i n the form o f A r and Re p , the results are not readily compared wi th those o f previous studies. A n attempt was made to correlate U c deduced from D P fluctuations wi th height, but this was not successful. The addition o f fines to improve the 'quality' o f fluidization is a c o m m o n practice, and one o f the easiest variables to change from the reactor-design point o f view. A d d i t i o n o f fines has an effect on the quantity o f fines associated with voids (Grace and Sun, 1990), thus affecting pressure fluctuations, and thus the measured value o f U c . Table 3.1 Particle properties used in 0.29 m diameter column. Particle F C C I Catalyst C Catalyst C r Density, k g / m 3 1560 1580 1580 A r (mass mean) 23.5 3.94 2.06 d p (mass mean), u m 75.1 41.2 33.3 d s m (Sauter mean), u m 57.4 40.6 36.5 3.4.4 Effect of system pressure on Uc The effect o f system absolute pressure on the bed hydrodynamics including U c is o f vital importance i n designing fluid bed reactors, especially wi th the increasing application o f pressurized systems for coal combust ion and gasification (Yates, 1996). F o r G r o u p A powders, an increase in system pressure has been shown to increase the voidage i n the dense phase leading to less stable, smaller bubbles. Since the gas density increases with pressure, it is expected, according to correlations o f the form o f Equa t ion 3.2, that U c should decrease wi th increasing pressure. N o t e that viscosity is virtually unaffected by pressure. Chapter 3 Regime Transition and Scale Effect B c - p • F C C o • Catalyst C - 1 - o Catalyst Cr Figure 3.17 Effect of particle properties on axial profiles of U c from DP signals. H0=0.60 D=0.29 m. Table 3.2 Published exponents for Equation 3.2. Source a b Applicable range Lee and K i m (1988) 0.700 0.485 0.44 < A r < 4.4x10 7 L e u e t al. (1990) 0.568 0.578 H o r i o (1992a) 0.936 0.472 54 < d p < 2600 u m Nakajima (1991) 0.633 0.467 Tsukada (1995) 0.791 0.435 B i and Grace (1995) D P data 1.243 0.447 3 < A r < 3 x l 0 7 B i and Grace (1995) A P data 0.565 0.461 3 < A r < 2 x l 0 5 Chapter 3 Regime Transition and Scale Effect A A r based on mass mean d Leu et al. (1990) - — - M o n o (1991) Tsukada (1995) - - - B i & Grace (1995) D P data Figure 3.18 Archimedes number vs. particle Reynolds number based on U c compared published correlations based on Equation 3.2 and Table 3.2. D=0.29 m. Chapter 3 Regime Transition and Scale Effect 73 C a i et al. (1989) examined the effect o f pressure up to 0.8 M P a for eight different powders including F C C particles i n a 0.28 m diameter column. The resulting correlation for U c , Equa t ion 3.10, includes the viscosity and density o f gas relative to those measured for air at standard conditions, i.e., 2 0 ° C and 0.1 M P a . A s the pressure increased, the amplitude o f pressure fluctuations was found to decrease. The findings are consistent wi th the findings i n the bubbl ing flow regime showing that bubble size decreases at elevated pressure making the fluidization much smoother (Hoffmann and Yates, 1986). It is expected that the increased bubble break-up w i l l result i n a decrease i n U c . Tsukada et al. (1993) examined the pressure effect on U c for F C C particles i n a 0.05 m diameter C F B . F o r pressures up to 0.7 M P a , U c was found to be proport ional to P ~ 0 3 . However , the solids circulation rate was found to be insensitive to the pressure at the regime transition. This implies a structural change wi th in the bed. Simultaneous optical probe measurements indicated a decrease i n bubble fraction from 0.4 to 0.3 wi th increasing pressure. A study o f transition velocity at pressures up to 7.2 M P a was recendy reported by N e w t o n et al. (2001) using 13 different powders, including six Geldart G r o u p A powders. U c was determined through visual inspection o f the images taken by X- ray imaging i n 0.127, 0.254 and 0.42 m diameter columns. F o r G r o u p A powders, the correlation o f Sun and Chen (1989) showed the best fit. The results for pressures higher than 3 M P a indicated very little effect o f pressure o n U c . A s a part o f an industrial contract project, the author explored the effects o f pressure and temperature on the hydrodynamics i n a 0.11 m diameter vessel (Column I V i n Chapter 2). Data were sampled at a frequency o f 10 H z wi th 4000 points (duration ~7 minutes) collected for analysis. Figure 3.19 shows decreasing U c and decreasing amplitude o f pressure fluctuation wi th increasing system pressure, consistent wi th the findings o f C a i et al. (1989). The effect o f pressure on the l rdnimum fluidization velocity, U m f , has been reported to be more prominent for larger particles (Yates, 1996). This is because the flow around smaller particles is dominated by viscous forces from the gas phase. A n increase i n pressure has been reported to decrease the apparent kinematic viscosity o f the dense phase ( K i n g et a l , 1981), possibly due to adsorption o f gas on particles promoting increased cohesion (Piepers and Rietema, 1989). The resulting increase i n interparticle forces in the dense phase may be the cause o f dense phase Chapter 3 Regime Transition and Scale Effect 74 0.2 0.3 0.4 U, m/s • 0.1 M P a o 0.2 M P a 0.3 M P a • 0.4 M P a F i g u r e 3.19 E f fec t o f sys t em pressure o n U c . D=0.11 m , z=0.9 m , H0=0.7 m , Cata lys t C fluidized w i t h N 2 . Chapter 3 Regime Transition and Scale Effect 75 expansion at high pressure causing a lower effective dense phase viscosity. Clif t et al. (1974) suggested that a decrease i n the apparent kinematic viscosity o f the dense phase contributes to the instability o f voids. This explanation can be extended to explain the early onset o f U c at higher pressure where voids are smaller and fluidization smoother as pressure is increased. The effect o f system pressure on U c is summarized i n Figure 3.20. F o r the calculation o f U c using the correlations by C a i et al. (1989), Sun and Chen (1989) and B i and Grace (1995), gas viscosity, U m f and Smf are all assumed to be independent o f pressure ( K u n i i and Levenspiel , 1991; Yates, 1996) for G r o u p A powders. Values o f 0.565 and 0.461, for a and b, respectively, were taken in applying Equat ion 3.2 for U c obtained from gauge pressure fluctuations (Bi and Grace, 1995). The calculations were based on a co lumn diameter o f 0.106 m , and therefore do not reflect the range o f vessel size represented i n the plot. However , the overall trend is wel l predicted. The effect o f co lumn diameter and pressure are not isolated for the N e w t o n et al. (2001) results represented by triangles in Figure 3.20 for D=0.42 m. Since most U c correlations are deduced from experimental data obtained from relatively small vessels, the effects o f vessel size and pressure on U c should be studied to extend correlations to systems and conditions c o m m o n i n fluidized bed combustors and gasifiers. 3.4.5 Effect of temperature on Uc Changing temperature affects gas properties, i.e., gas density decreases while gas viscosity increases with increasing system temperature. The viscosity o f air at elevated temperature was estimated from: 1 . 4 6 x l 0 " 6 (273.15 + T ) 1 ' 5 0 4 \i = ^ - (3.15) g (273.15 + T ) + 120 (Svoboda and Hartman, 1981). Chehbouni et al. (1995b) examined the effect o f temperatures up to 4 2 5 ° C on U c and found that U c decreased wi th increasing temperature for Geldart A powders, and increased for Geldart B powders in a 0.2 m diameter vessel. Extending the temperature to 9 6 0 ° C , Peeler et al. (1999) reported similar trends for two powders i n their 0.08 m riser. O n the other hand, an increase i n U c was observed for two types o f F C C particles when the temperature was increased from 50 to 2 5 0 ° C in a 0.15 m diameter vessel (Cai et al., 1989). The max imum amplitude o f gauge pressure fluctuations decreased wi th increasing temperature, indicating smaller voids and smoother fluidized bed operation as the system temperature increased. Chapter 3 Regime Transition and Scale Effect 76 This work (z=0.3 m): D=0.11 m A This work (z=0.9 m): D=0.11 m EB Tsukada et al. (1993): D=0.05 m O Newton et al. (2001): D=0.13 m A Newton et al. (2001): D=0.42 m e Cai etal. (1989): D=0.28 m - Cai et al. (1989) Equation 3.10 Sun and Chen (1989) Equation 3.11 — • Bi and Grace (1995) Equation 3.2 with a=0.565, b=0.461 T—rr-j 1 1 1 1—i—i—IT] 1 1 1 1—i—r"T' 'i "|— 0.1 1 10 System pressure, MPa Figure 3.20 Effect of system pressure on U c . Comparison of this work (D=0.11 m, Catalyst C, fluidizing air: N 2 , T=20 °C) to others. Chapter 3 Regime Transition and Scale Effect 11 Recent studies o n the influence o f temperature on the dense phase properties o f fluidized beds o f F C C particles (Lettieri et al., 2001; Formisani et al., 2002) indicate the contributions from thermal modifications o f particle properties, and fluid dynamic effects. Temperature increase was found to influence the interparticle forces wh ich stabilized looser fixed structures. A s a result, voidages i n the fixed state, at m i n i m u m fluidization, and in the dense phase o f a bubbl ing fluidized bed increased linearly wi th temperature (Yamazaki et al., 1986; Formisani et al., 2002). This suggests that temperature may influence dense phase structure through particle-particle interaction even in high-velocity fluidized beds. Exper imental findings for temperatures o f 20, 160 and 2 4 0 ° C at 0.2 and 0.4 M P a are presented i n Figure 3.21. F r o m the ideal gas law, gas density is inversely proport ional to absolute temperature. However , the change i n gas density does not linearly affect the amplitude o f the pressure fluctuations, wh ich is a measure o f the relative bubble size, indicating that the influence exerted by gas density change does not affect the size o f voids. N o t e that the effect o f temperature on U c is more pronounced at the lower system pressure. 3.4.6 Combined effects of pressure and temperature on Uc In order to examine the effect o f gas viscosity on U c , the standard deviation o f gauge pressure fluctuations is plotted in Figure 3.22 for system temperatures o f 20, 160 and 2 4 0 ° C against the volumetric flow rate at standard conditions, i.e., 2 0 ° C and 0.1 M P a pressure. B y plotting i n this manner, the change i n gas density wi th temperature is compensated. I f a correlation o f the form o f Equat ion 3.2 applies, then Q C ^ ' ; 2 B ( 3 - 1 6 ) The dependence o f Q c on viscosity is therefore given by f . . V - 2 b (3.17) Q c 2 , 20 Q c T ^ g20 where the subscript 20 denotes conditions at 20°C . Unfortunately the data do not include an atmospheric pressure system. F r o m Figure 3.23, it is concluded that the effect o f temperature represented by the gas viscosity term has less influence on Q c as pressure is increased. This may suggest less change i n the apparent kinematic viscosity o f dense phase at higher pressures. Chapter 3 Regime Transition and Scale Effect 78 0.3 s 0.2 H • A A A 0.1-A P=0.2 M P a A P=0.4 M P a 50 100 150 200 Temperature, °C 250 Figure 3.21 Effect of temperature on U c . D=0.11 m, Catalyst C. Figure 3.22 Standard deviation of gauge pressure signals against volumetric gas flow rate. D=0.11 m, Catalyst C, P=0.2 MPa. Chapter 3 Regime Transition and Scale Effect 79 5 U 0.5 0.5 o o 20 0.8 o P =0.2 MPa A P =0.3 MPa P =0.4 MPa Figure 3.23 Effect of gas viscosity and system pressure on Q c , transition based on volumetric flow rate. D=0.11 m, Catalyst C. Subscript T denotes system temperature. Chapter 3 Regime Transition and Scale Effect 80 Experimental data for U c from the hot unit for temperatures o f 2 0 ° C at 0.1, 0.2, 0.3 and 0.4 M P a , and o f 160 and 2 4 0 ° C at 0.2, 0.3 and 0.4 M P a are compared to predictions based on the correlations by C a i et al. (1989), Equat ion 3.10, and Sun and Chen (1989), Equa t ion 3.11, i n Figures 3.24 and 3.25, respectively. Figure 3.24 indicates that the correlation by C a i et al. (1989), though based on operating temperatures o f 50 to 500°C and pressures o f 0.1 to 0.8 M P a , overestimates the transition velocity. Better predictions were obtained from the Sun and C h e n correlation (1989) based on G r o u p A particles fluidized i n a 0.8 m diameter column. 3.4.7 Uc correlation Based on the extensive experimental study on U c from different co lumn sizes, a correlation is proposed taking into account the effect o f the aspect ratio, H / D , on U c deduced from gauge pressure signals. A s noted in Section 3.4.1, the effect o f H / D o n U c becomes less significant for H / D >~3. In Figure 3.26, U c for higher aspect ratios is compared to other studies where confirmation o f H / D > 3 can be verified. The linear fit on log-log coordinates gives R e c = 0.371 A r 0 ' 7 4 2 (3.18) wi th R 2 =0.989. The exponent b=0.742 is much higher than those previously published, as listed i n Table 3.2. This is attributed to this correlation only mcluding Geldart G r o u p A particles, and restricting the data to only include U c from high H / D and those deduced from gauge pressure fluctuations. Fo l lowing the procedure used by D u n h a m et al. (1993), a correlation is proposed for U c obtained from gauge (single point) signals measured in the lower H / D fluidized beds as: 0.183 ln(d pg,)+0.83 (3.19) This correlation is compared to the experimental data obtained i n columns o f three different diameters in Figure 3.27. C o m b i n i n g the two correlations, i.e., Equations 3.18 and 3.19, the overall prediction o f U c is plotted in Figure 3.28 i n comparison wi th the experimental data, resulting i n an overall root-mean-square deviation o f 0.12. The discontinuity shown between the two correlations is a function o f the A r number, and is a result o f l imited data available for correlating U c . Re = 0 .459Ar 0 4 5 4 F o r the purpose o f refining the proposed correlations by comparison wi th other studies, it is recommended that the standard deviation o f gauge pressure signals be reported along wi th the Chapter 3 Regime Transition and Scale Effect 0.8 T : 81 0.6 "„ 0.4 0.2 A 0.0 o o • D =0.29 m, T= 20°C o D =0.11 m , T = 20°C • D =0.11 m, T= 160°C D =0.11 m , T= 240°C 0.0 0.2 0.4 0.6 0.8 Predicted U from Equation 3.10 (Cai et al., 1989), m/s Figure 3.24 Comparison of predictions by Equation 3.10 with experimental U c . Catalyst C. D=0.11 m diameter column, H0=0.7 m. D=0.29 m diameter column, H0=0.6 m. • D =0.29 m , T= :20°C o D =0.11 m , T= :20°C • D =0.11 m , T= :160°C D =0.11 m, T= =240°C 0.0 0.2 0.4 0.6 0.8 Predicted U by Equation 3.11 (Sun and Chen, 1989), m/s Figure 3.25 Comparison of predictions by Equation 3.11 with experimental U c . Catalyst C. D=0.11 m diameter column, H0=0.7 m. D=0.29 m diameter column, H0=0.6 m. Chapter 3 Regime Transition and Scale Effect 82 10 ~ l 1—i—i—r • O 10 100 D=0.29 m (FCC) D=0.61 m (FCC) D=0.29 m (Cat C) D=0.11 m (Cat C) B i (1994) D = 0 . 1 0 m (FCC) Ca i (1989) D=0.05,0.14, 0.28, 0.48 m (FCC) A r F i g u r e 3.26 C o m p a r i s o n o f U c da ta f rom this w o r k to l i terature data for f l u i d i z e d b e d o f Ge lda r t G r o u p A par t ic les f rom gauge pressure s igna l s . F i g u r e 3.27 C o m p a r i s o n o f p red ic t ions b y E q u a t i o n 3.19 w i t h e x p e r i m e n t a l U c . F C C . Chapter 3 Regime Transition and Scale Effect 83 Figure 3.28 Comparison of predictions by Equation 3.18 and 3.19 with experimental U c from gauge pressure signals. F C C I, D=0.29 m. Chapter 3 Regime Transition and Scale Effect 84 information on expanded bed height, particle density and mean diameter, and gas density and viscosity. 3.5 Conclusions and recommendations Experimental work has been conducted to extend the knowledge o f the transition velocity, U c , using two different powders and four experimental columns. The effect o f pressure and temperature was also studied. Transit ion velocities based on pressure fluctuations were determined in columns much larger than those used i n most academic research laboratories. The diameter o f the co lumn has been shown to affect the transition to the turbulent flow regime o f fluidization. • The transition velocity, U c , was found to decrease as the co lumn diameter was increased from 0.29 m through 0.61 m to 1.56 m , and wi th decreasing static bed height o f F C C particles. • In practice, most pressure measurements are obtained at the co lumn wal l for convenience. The validity o f the assumption that the wal l measurements are representative o f the cross-section and give the transition velocity applicable at the centre was confirmed experimentally. • U c f rom D P signals was shown to increase as the location o f the sensor descended towards the distributor plate. This implies that, as the superficial gas velocity is increased, homogeneity is attained at the top o f the bed first, as indicated by its lower U c value, before the rest o f the bed reaches the turbulent flow regime. The transition velocity decreased wi th increasing system pressure (to 0.4 MPa) confirming the fmdings o f others. The trend is wel l predicted on the basis o f the change in gas density wi th increasing pressure. • The transition velocity was shown to decrease wi th increasing temperature (to 240°C) for the results obtained i n this work. The amplitude o f the differential pressure fluctuation indicated very little change in v o i d size wi th changing temperature. • Better predictions were obtained by the Sun and Chen correlation for U c obtained from gauge pressure signals for increased system pressures (to 0.4 M P a ) and for elevated temperature (to 240°C) . • Correlations are proposed for predicting U c in fluidized bed o f Geldar t G r o u p A particles deduced from gauge pressure signals: R e c = 0.371 A r ' 0.742 (3.18) for H / D > 3, and (3.19) Chapter 3 Regime Transition and Scale Effect 85 for H / D < 3. Further studies • Further investigation o f U c is required based on DP signals. T h e effect o f height on U c should be taken into account when correlating U c . • In an attempt to prevent the results from being co lumn specific, s c and U c have been correlated. M o r e data are required before a reliable correlation can be obtained. C H A P T E R 4 V O I D A G E M E A S U R E M E N T S 4.1 Introduction Voidage is the volumetric fraction o f gas i n a gas-solid system. Knowledge o f the time-mean voidage provides information useful for setting operating conditions and for overall reactor design, while local instantaneous voidage measurements extend understanding o f the complex local flow structure i n fluidized beds. In a fluidized bed reactor, information on local voidage encompasses determining effects o n mass and heat transfer phenomena, and reaction rates (Louge, 1996). O w i n g to the transient nature o f multiphase flow, the instantaneous local voidage measurement method must be able to distinguish the two phases quantitatively and capture signals at relatively high frequencies. Measurement techniques for voidage include non-invasive methods, such as X-rays , computer-assisted tomography ( C A T ) , positron emission tomography ( P E T ) , capacitance tomography, gamma ray transmission densitometry, and invasive techniques including capacitance and optical probes. Visual izat ion techniques such as Laser Dopp le r Anemomet ry ( L D A ) are mostly restricted to very dilute systems where the laser can penetrate into the flow o f interest, or the wal l region, where backscatter can be used. W i t h the progress o f Computat ional F lu id Dynamics ( C F D ) i n model l ing the hydrodynamics o f multiphase flows, detailed experimental measurements o f the flow structure w i l l play an essential role i n validating C F D models. Thus, information on local voidage w i l l help to elucidate the dynamics o f multiphase flow and to test the validity o f theoretical models. 4.2 Local voidage measurement Voidage measurements have been executed wi th various instruments as reviewed by Nieuwland , et al. (1996), Louge (1996) and Werther (1999). Some essential features o f the equipment capable o f measuring voidage (Werther and Molerus , 1973a) are: • disturb the bed as litde as possible; • measure local variations; • respond rapidly to changes in voidage; • have adequate mechanical strength; • be movable wi th in the bed; 86 Chapter 4 Voidage Measurements 87 • be compatible wi th the bed solids. F o r measurements in dense particle phase systems the choice becomes limited. Since reflective-type optical probes are k n o w n to be simpler and less intrusive than most other types o f probes (Lischer and Louge, 1992), they have been employed by numerous researchers to determine voidage i n fluidized beds (e.g. R e h and L i , 1990; Lischer and Louge; 1992, C o c c o et a l , 1995; Farag et a l , 1997b). Because o f their compact size, the measurements are localized with m i n i m u m disturbance to the flow dynamics (Zhang et a l , 1998). A s the light intensity depends on the reflection and penetration o f the emitting light, the measuring volume is a function o f the solids concentration at the tip o f the probe. Thus, careful calibration is critical to obtaining the measurements wi th high accuracy and precision. Est imat ion and model l ing o f the effective measuring volume o f a single-fiber reflection probe have been reported by Rensner and Werther (1991, 1993). A capacitance probe measures voidage through the dielectric constant i n the capacitance sensor volume. Thus, signals reflect the change i n capacitance due to a change i n the local solids concentration i f the dielectric constants o f the phases differ significantly. Since the probe itself potentially contributes to the capacitance, wh ich varies slighdy wi th temperature, the 'guarded' capacitance probe is capable o f suppressing the capacitance from the probe body (Hage and Werther, 1997a,b), especially for applications involv ing high temperatures. Thus, as summarized by Louge (1997), the 'guarded' capacitance probe is reported to reduce the problem wi th stray o f response, and wi th increasingly defined measuring volume. However , the sensitivity o f the probe to static electricity, and to change i n humidity (Herbert et a l , 1994) has also been acknowledged. Very few cases are k n o w n in which voidage has been measured successfully under the harsh conditions o f industrial high-temperature fluidized bed systems. Recently Johnsson and Johnsson (2001) detected bubbles in a 850°C C F B boiler wi th a two-fiber reflective type optical probe. A n y technological advancements i n hydrodynamic measurement methods w i l l certainly be embraced by the fluidization community. In the case o f invasive probes i n general, the influence o f the presence o f a probe o n the flow structure has generally been neglected, but this assumption needs to be confirmed. Chapter 4 Voidage Measurements 88 4.3 Voidage in turbulent fluidized beds The ongoing interest and need to clarify changes i n bed structure and flow development through the "gradual" disappearance o f discrete bubbles and voids i n turbulent fluidization has been addressed i n only a few publications pertaining to the hydrodynamics o f this flow regime. A s listed in Table 4.1, most hydrodynamic studies comprising voidage measurements have been conducted in much smaller columns than industrial scale reactors. The effect o f scale on the local flow structure i n turbulent fluidized beds must be investigated i n order to ensure that excellent contacting between gas and solids can be achieved when the co lumn diameter is increased. M o n i t o r i n g the local v o i d behaviour while increasing the co lumn diameter should provide valuable insights into how units can be scaled up without loss o f conversion or yield. 4.3.1 Radial voidage distribution The inhomogeneity o f the solids holdup in the turbulent fluidized bed was investigated using capacitance probes by A b e d (1984). D o w n w a r d flow along the wall , and accelerated upward flow o f higher voidage closer to the centre o f the co lumn were reported. F r o m point measurements, the probability density function was computed to obtain hydrodynamic parameters such as vo id phase fraction and dense phase voidage (emulsion v o i d fraction). A closer look at the radial density profiles reveals that, despite passing into the turbulent flow regime, the gas continued to favour flowing in the core o f the fluidized bed, and a different momentum transport mechanism predominated near the walls. Us ing Geldart group B particles and a capacitance probe, Werther and W e i n (1994) showed a shift to higher voidage i n the central region as the gas velocity increased from 0.38 to 2.05 m / s . M o r e recendy, W a n g and W e i (1997) reported - ^ ^ = 0.908 + 0.276 where s m represents the cross-sectional average voidage. The radial voidage distributions i n larger columns (D=0.71 m at z=0.23 and 0.36 m by L u et al., 1996; D=0.47 m at z=0.36 m by W a n g and W e i , 1997) show flatter profiles surrounding the centre o f the co lumn compared to smaller columns (e.g. D=0.15 m by A b e d , 1984; D=0.09 m by L i et al., 1990; D=0.076 m by Issangya, 1998; D = 0 . 0 9 m by X u et al., 1999) due to less wal l effect on the voids i n larger columns. Table 4.2 89 O N GO N a Q a T3 O T3 V - 3 3 CO u <U u O cs cn <U 5 C O CN N O T h C N o o o 0 0 o Tt-N O CU X O i-i C L CU o G 'o 03 CL, Oj C J 13 0 o N O C N 3 03 C J G a 03 co co co L O o o C O o CN N O CL) CU H U 3 3 cn XJ ' o o o cO O X 0 0 o C O C O N O L O N O CO m N O C N O T J -N O CN O CU X o u CL, n cj X c d 13 u • d C L o C J cn 03 X C L "9 ' o C N C N 03 03 z L O o L O oo L O o N O CN o CL) X 0 »-, C L C J X cd »—H . 03 U •a CL, 0 u 0 U > 'en CL) T3 cn • a 'Cl O C N C N 03 CL) 03 N oi 6 03 O N O CN © C N o N O ' © ' o T i -to CN C O CN oo" © ' Tt-" o © L O L O Tt" o L O N O cO © L O o CL) X o U C L H CL) X C Q "3 O • d C L o a o • d o 03 C J cn 03 X C L "2 ' o > C N C N C J 03 w o3 IX, U O cu U N > ' cn CL) - 0 cn • -H - d ^ ' o > L O L O L O 0 0 L O C O L O o L O " O 0 0 L O 0 0 T - H 0 0 C N o I C N C O o CN cj X O u Cu u C J X i d "o3 u • d C L O a o • d C J 03 U O CL) U N > 'cn •5 ' C 5 > t--C N C N <U ( 5 0 a 03 X N N O C O o ^ co" O CN o N O L O C N © O N —^—' t~~ r - oo o ©' C J o u Cu t-i CL) X cd "o3 o 'd C L o "2 'o > C N C N 3 h-1 N O 0 0 C O CN o L O C N CN o CL) X O U C L n C J — ' i d "oi U • d cu o o "° ^ ^ G O C J 03 > C J - d ' o > 0 0 C N C N 03 H C J §1 cu L O o C O o C N o o CN L O CL) X O u C L CL) c d "o3 U • d C u o C J 03 - d ' o > o o o CN •3 u 0 0 o oo" o CN CN o U U X C N O CU X o u Cu u cu X c d "o3 O • d cu o ^ -u 03 i-g x Pi G C J T3 o o CN 03 CU 03 90 o 5* •Si-te •3 u £> N 3 53 C 3 c o •-H 'C •*-> • d V OJO cs T 3 O > "3 c o cs •*-» cs T3 u t-l 3 cs u o • M cs £ S 3 C/5 cs H L O 00 O Q a •3 o 43 I T ) I O V 00 L O S O CN O 1) t-i a , u 0 03 'u OS a , os u CS bjo +-> a; a o 00 '•3 o 00 T f L O 00 T f CN L O T f LT) CS o n CU u u c OS 'u OS cu os o t-l cu <u - 3 11-3 'oi u '3 C u 0 T f 00 Cs T3 1) 1-3 O CN Cs oi CJ CN 4 so O 00 r o o o so O u G os -w 'u oi CU OS u T f Cs Cs •9 OS t-l •5 > 4) S O O o CN o so O Cs T f o L O o - 3 o t-l cu H u - 3 113 i — l os o •3 C u o so Cs Cs I 3 Cs O S O 00 L O o L O C s 00 r o TI-LT) Tt-t-l C u t-i 4) I * 3 'os <_> •3 CU 0 r--Cs Cs '1 OS a OS 00 r o O SO T f O o r o T f o o so o o u 0 t-i u 1-3 OS o •3 C u 0 oo Cs Cs OS fcuO G OS o r o L O o T U L O T f L O Cs O o i-l OJ 1 3 "oi u •3 CU 0 Cs Cs Cs 3 L O o o L O o CN CN O t-l cu 1) u 3 OS ' u OS CU os u Cs Cs Cs O OS 1-3 U 00 © o CN © u tU Cs T-H © t-i 1-3 | i3 "-j O '3 CU O o o CN ST IPQ CN O L O CN o L O so 00 CN O 1) t-i CU u 1-3 113 13 u '3 CU o o o CN 0 Chapter 4 Voidage Measurements 91 summarizes the published work on radial voidage distributions in turbulent fluidized beds. This earlier work is referred to below. 4.3.2 Dense phase voidage It has been shown (Chaouki et al., 1999) that as the gas velocity is increased i n the turbulent regime, the volume fraction o f voids increases while the dense phase voidage increases from that o f m i n i m u m fluidization. The dense phase voidage is often a key parameter i n inventory control, process model ing and pressure balance i n fluidized bed operations (K ing , 1989). The measured average v o i d fraction has been used to calculate the dense phase voidage (Yamazaki et al., 1991), suggesting expansion o f the dense phase during transition from the bubbl ing to the turbulent regime. Similarly, Werther and W e i n (1994), using Geldart G r o u p B particles, observed a significant increase o f dense phase voidage wi th increasing gas velocity. The dense phase voidage was obtained from the probability density distribution o f capacitance probe signals. However , no clear influence o f radial posi t ion was observed for the particles under investigation. In both o f these studies, point density measurements were analyzed to deduce the phase fractions from probability density functions. The threshold value i n the probability distribution function strongly influences the resulting phase fraction, especially for high velocity fluidization (Bi, 1994), so that reliance on this method alone is questionable. Lee and K i m (1989) indirecdy measured the dilute phase fraction, and calculated the interstitial gas rise velocity and voidage in the dense phase from measurements o f tracer gas concentration i n the dense and dilute phases using Geldart group B particles. C a i et al. (1988) and W a n g et al. (1997) conducted collapse tests i n a co lumn which physically separates the bed and freeboard, making it possible to eliminate accumulation o f entrained particles on top o f the bed surface as it collapsed. The effect o f particle mean size on the performance o f the fluidized bed was studied using this configuration. Once entrained and carried over to the freeboard, these particles had no means o f returning to the bed, thereby changing the particle mean size i n the bed f rom the initial condition. The dense phase voidage was independent o f the gas velocity between 0.1 and 0.5 m / s , in agreement wi th Yamazak i et al. (1991). N o direct measurements o f the dense phase voidage have been reported for superficial gas velocities beyond 0.5 m / s , possibly due to the difficulty o f conducting experiments such as collapse tests i n high velocity fluidized beds. Chapter 4 Voidage Measurements 92 O n e method o f deducing the local v o i d fraction is by inserting probes w h i c h can differentiate local solids concentrations, and thus obtaining the cumulative v o i d contact time wh ich is then divided by the total sampling time. The signals are averaged wi th respect to time, and the time fraction o f the probe in voids is considered to be the local v o i d fraction. Opt ica l fiber probes have revealed an increase in the non-uniformity o f local v o i d fractions across the radius i n turbulent fluidized beds, wi th increasing height (Nakajima et a l , 1991; Farag et a l , 1997a; Z h a n g et a l , 1997), and gas velocity (Nakajima et a l , 1991; Zhang et a l , 1997). However , once again, difficulty exists i n setting a threshold to distinguish the phases, thus resulting i n ambiguity and l imit ing the accuracy o f the reported phase fractions. 4.4 Optical probe measuring method principles V o i d s i n turbulent fluidized beds are k n o w n to be intermittent and transient i n nature. Because o f their simplicity and affordability, fiber optic voidage probes are often chosen to measure voidage fluctuations and distribution. B o t h emissive and reflective optical measurement systems can be used to deduce the solid volume concentration. However , emission is not suitable for dense suspensions (Louge, 1996; Werther, 1999). Reflective optical fiber probes work on the principle that a small volume o f particles is il luminated and the reflected light intensity is correlated to the volumetric concentration wi th in a local measuring volume at the tip o f the probe. Voidage fluctuations i n a turbulent fluidized bed were investigated i n this project to yield instantaneous local solid concentrations. I f the instantaneous bed density measurements reflect the characteristics o f the passing voids, analysis o f the signals should give very localized hydrodynamic information. Voidage measurements using miniature optical fiber probes are slighdy invasive, yet they provide insight into the physical phenomena o f the fluidized bed. A c c o r d i n g to K r o h n (1987), different fiber configurations result i n different characteristic responses (see Figure 4.1). Thus, the design o f optical probes must reflect the size o f particles o f interest. A s depicted i n Figure 4.2, the signal from the reflective-type optical probe w i l l capture particle movement when the measuring volume o f a probe is comparable i n size wi th the particles. Alternatively, i f the measuring volume is large enough to contain a large number o f particles, signals transmitted from the probe represent swarms o f particles. Chapter 4 Voidage Measurements 93 Sing le C o a x i a l H e m i s p h e r i c a l R a n d o m F i b e r p a i r C o a x i a l S ing le D i s t a n c e F i g u r e 4.1 Ref lec t ive- type o p t i c a l fiber p robe response curves for var ious fiber conf igura t ions (adapted f rom K r o h n , 1987). Chapter 4 Voidage Measurements 94 0 0 measuring area time Figure 4.2 Probe tip in relation to particle size. Reflective optical fiber probe detecting (a) swarm of particles; and (b) single particles (adapted from Matsuno et al., 1983). Chapter 4 Voidage Measurements 95 4.5 Optical voidage probe used in this study The two identical reflection type optical fiber probes, P C - 4 Powder Voidmeter , used for voidage measurements i n this work were supplied by the Institute o f Chemica l Metallurgy o f the Chinese Academy o f Science in Beijing, China. A schematic diagram o f the configuration for the optical fiber probe is shown i n Figure 4.3. The probe contains a bundle o f fibers projecting light onto a swarm o f particles interspersed wi th Hght-receiving fibers wh ich measure the intensity o f the light reflected from the particles. The bundle diameter is 4 m m , length is 600 m m , and individual fiber diameter is 15 um. The fibers are arranged i n an alternating array o f emitting and receiving layers. Because the particle diameter is much smaller than the bundle diameter, light is reflected by many particles i n the measurement volume, al lowing the probe to detect the instantaneous solids volume concentration from the output voltage, after suitable calibration. The measuring volume o f the reflective-type optical probe is dependent on the solids concentration at the tip. Thus , careful calibration o f the response signal to the solids concentration is required for accurate measurement o f voidage. This is discussed i n the next section. The local voidage measurement system includes a reflective optical fiber probe, light source, photo-multiplier, A / D converter and data acquisition system (Figure 4.4). T h e P C - 4 Powder Voidmeter allows auto-adjustment o f the photomultiplier i n order to compensate for variation o f the light source through re-adjustment using the reference light. The emitting and receiving diode circuits can be adjusted separately al lowing the control o f the sensitivity, m a x i m u m signal output and offset value. Before and after each set o f runs, the voidmeter was calibrated against a dense bed (to give ~5 V ) and the 'black box' , a tube painted black to prevent reflection o f light, representing the no solid condi t ion (set at ~ 0 V ) . A n y shifts o f the upper and lower settings were corrected through the calibration equation, having the form o f Equat ion 4.5, when converting the voltage signals to local voidages. Measurements o f instantaneous voidage fluctuations were captured through voltage output logging using L A B T E C H ® N o t e b o o k 10.1 sampling at 100 H z for periods o f 100 s. Chapter 4 Voidage Measurements 96 Fiber configuration (enlarged section) To receiver F i g u r e 4.3 O p t i c a l fiber p robe for m e a s u r i n g l o c a l par t i c le concen t ra t ions : the p robe is s h o w n de tec t ing a s w a r m o f par t ic les . Probe tip Opt ica l fibers Emi t t ing light Reflected light \ I. Reference light Light source Photomult ipl ier A / D converter F i g u r e 4.4 S c h e m a t i c o f l o c a l vo idage m e a s u r e m e n t apparatus a n d con f igu ra t i on . Chapter 4 Voidage Measurements 97 4.5.1 Optical probe calibration A s emphasized by numerous researchers (e.g. A m o s et a l , 1996; Z h a n g et a l , 1998), one o f the disadvantages o f otherwise simple and relatively inexpensive reflective-type optical fiber probe is the difficulty in obtaining an accurate calibration o f voidage as a function o f reflected light intensity, especially i n gaseous suspensions. D u e to the nature o f heterogeneous suspensions in gaseous media, an accurate and reproducible calibration procedure has been elusive (Herbert et a l , 1994). Zhang et al. (1998) reviewed the calibration methods employed by earlier researchers. M o r e recent researchers prefer that the calibration be done i n the med ium o f interest. Thus, extrapolating calibration results f rom a l iquid fluidized bed to a gas-solid riser (Hartge et a l , 1986) has been criticized for not considering the difference in refractive index between water and gas. Furthermore, the method o f calibration must reflect the required scale and flow dynamics. F o r instance, the average cross-sectional voidage measured by pressure transducers was used to calibrate the optical probe response by T u n g et al. (1989). Calibration against time-mean values may introduce uncertainties (Lischer and Louge, 1992) when measuring instantaneous values. Calibrat ion against a capacitance probe (Lischer and Louge, 1992; Herbert et a l , 1994) introduces a difference in measuring volume and shape, no doubt altering the calibration. Furthermore, use o f linear relationships for comparison between different measuring volumes is questionable (Zhang et a l , 1998). Mathematical simulation using a Mon te Carlo method was carried out by Lischer and Louge (1992). The influences o f particle size, numerical aperture o f the optical fibers, and the ratio o f the refractive indices o f the particles and the suspending medium were tested. A m o s et al. (1996) investigated the probe reflection curve and response function for a fiber diameter o f 1 m m , and concluded that the relation o f the fiber diameter to the effective penetration o f light i n to the suspension was the controll ing variable. Thus, the inclusion o f particle diameter was necessary. Bergougnoux et al. (1999) and Bel l ino et al. (2001) improved on the Mon te Carlo simulation by incorporating such factors as: the volume fraction o f suspension; scattering properties o f particles (i.e., refractive index, size and shape); geometric properties o f the sensor (i.e., fiber diameter and distances between emitting and receiving fibers), for a bundle o f fibers wi th a central emitting fiber surrounded by two bundles o f receiving fibers. Calibration o f local particle concentration has been examined theoretically by L i u (2001). Chapter 4 Voidage Measurements 98 Elirrrinating the 'bl ind zone' (e.g. Figure 5.2), and obtaining a monoton ic reflective function by placing a protective quartz w indow in front o f the probe tip, suggested by C o c c o et al. (1995), were confirmed by the simulation results (Liu, 2001). F o r a typical fiber diameter o f 40 um for a mult i -fiber optical probe, a window thickness o f 80 um resulted in a nearly linear calibration curve. 4.5.2 Experimental calibration of optical voidage probe Measurement o f voidage i n turbulent fluidized beds requires that the voidage probe capture the full spectrum o f voidages, i.e., from dense bed to 100% void . The calibration was accomplished wi th the same particles and the same suspending medium, i.e., air as were used i n the fluidization experiments. The optical probe system had to be turned on for half an hour or so before calibration for the system to stabilize. Failure to do so resulted i n shifting signals. T h e F C C particles were put in a container designated for dense bed calibration to set the upper voltage, while a 'black box ' supplied by the Institute o f Chemica l Metallurgy was used to set the lower voltage. The black box was a tube wi th an inner coating o f black paint to absorb all visible light emitted from an optical fiber probe, thus providing conditions equivalent to no solid suspension. A n iterative procedure was adopted to adjust the upper and lower voltages to enhance the probe sensitivity by setting the full-scale limits o f the probe. Calibrat ion was conducted i n the same unit as was used by L i u (2001) based on the dropping/ t rapping techniques described by Issangya (1998) and Issangya et al. (2000). The calibration set-up, shown i n Figure 4.5, is comprised o f an incipiently fluidized hopper section at the top where solids are introduced, a 12.7 m m I D tube to develop the solids flow, a pair o f externally connected slide valves to trap the solids, and a collection vessel at the bot tom. O n c e a steady fall o f solids is attained, the optical probe signals are recorded at 100 H z for 10 s before trapping the solids between the slide valves by simultaneously shutting the two valves. T h e collected solids are weighed to calculate the volumetric solids concentration, wh ich is correlated to the recorded signal. B y changing the feeding tube i n the hopper and the flow o f aeration air, a wide range o f solids concentrations could be attained. The optical probe was calibrated using the F C C I particles with and without the glass w indow (see Figure 4.6). However , this method produced considerable scatter o f the equivalent voidage calculated from the captured solids between the slide valve. This was considered to be mainly due to the imperfect closing o f the slide valve, and fluctuation o f the downflow o f solids. Ano the r difficulty encountered was the presence o f electrostatic charges, which caused solids to adhere to the tip o f the probe. Chapter 4 Voidage Measurements 700 mm 12.7 m m I D Plexiglas downer 12.7 m m I D Copper downer optical probe 152 mm < • incipiendy fluidized hopper ^ aeration < — 1500 m m sUde valve 32 m m separation collection vessel Figure 4.5 Schematic of optical probe calibration equipment applying "drop-trap': technique. Chapter 4 Voidage Measurements 100 0.4 -! 1 1 1 1 1 0 0.2 0.4 0.6 0.8 1 Normalized signal Figure 4.6 Response curve for calibration of optical probe using FCC I without glass window. The line represents the calibration curve of Issangya (1998). Chapter 4 Voidage Measurements 101 Anothe r method was devised to measure the signal response to reflect the solid concentration using F C C and coke particle mixtures. B o t h F C C and coke particles were sieved using screen sizes o f 90 and 150 u m wi th a mean particle size o f 120 um. Different concentration mixtures were obtained by combining a k n o w n ratio o f the two types o f solids, F C C reflecting light and coke particles absorbing light, and detected by the optical voidage probe. Compared to the response from the bare probe, the results wi th the glass w indow at the tip o f the probe show a near-linear response to the equivalent voidage calculated from the concentration o f F C C i n mixture, as shown in Figure 4.7. The near-linearity is further supported by examining the effect o f the glass w indow in the following section. In addition, the optical probe wi th the glass w indow (see below) was placed i n a beaker where F C C II particles were suspended i n water through stirring. A s the refractive index o f water differs from that o f air, i.e., 1.33 and 1 i n vacuum, respectively, quantitative calibration cannot be obtained through suspension in l iquid media. However , the trend shown i n Figure 4.8 suggests an improved linearity o f response, comparable to that reported by L i u (2001). 4.5.3 Glass window O n e o f the difficulties encountered wi th voidage measurements using the optical fiber probe was accumulation o f static charges, not completely eliminated by the addition o f Larostat 519, an anti-static agent. The presence o f static electricity was evident f rom touching the exterior surface o f the Plexiglas co lumn and having solids congregate around this point, hearing sparks at the top o f the column, and observing flashes o f light at the tip o f the optical probe. The well-reported problem o f electrostatic charges (e.g. Zhang et al., 1998; Geldart, 1986) could affect the optical measurement i n turbulent fluidized beds as the operating gas velocities are not high enough to sustain the solids i n dilute suspension, or to sweep the particles away from the probe tip. Another phenomenon that was noticed was the probe response signal exceeding the pre-set max imum value. A s shown i n Figure 4.9, despite setting the upper and lower voltages to dense bed and black box values, once the probe was placed i n the bubbl ing fluidized bed, the signals frequendy reached values beyond the maximum. A t a superficial velocity o f 0.15 m / s wi th the probe i n the centre, it is expected that the optical probe wi l l pick up the movements o f voids passing the tip. However , the signal obtained is difficult to comprehend in terms o f v o i d dynamics. Chapter 4 Voidage Measurements 102 CUD « 'o > c JU > '3 a 1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.0 0.2 0.4 0.6 Normalized signal 0.8 1.0 Figure 4.7 Response curve for calibration of optical probe using FCC I and coke particles with glass window. 0.6 0.8 Voidage 1.0 Figure 4.8 Response signal of experimental calibration curves for FCC II with glass window in water-solids system. Chapter 4 Voidage Measurements 103 1 1 0 -I , 1 60 70 80 Time, s Figure 4.9 Signal obtained from optical probe without glass window. (Dotted line represents the maximum calibrated value.) D=0.29 m, U=0.15 m/s, z=0.15 m, r/R=0.0, FCC I. Chapter 4 Voidage Measurements 104 A s shown i n Figure 4.4, the signal obtained through the photomult ipl ier is the relative intensity between the reflected light and the reference light, i.e., l = _ ^ _ ( 4 2 ) 1 re fe rence Since the intensity is converted to voltage, when the signal intensity is higher than I r c f c r c n C (., as shown i n Figure 4.10 (a), the relative intensity becomes larger than 1, translating to a voltage beyond 5 V . However , when a quartz glass w indow o f 0.5 m m thickness, custom made by Canadian Scientific Glass B lowing , covered the probe tip, as depicted in Figure 4.10 (b), the signal intensity was always less than the max imum reference intensity. Figure 4.11 shows the difference i n the measured voltage for the same operating condit ion as in Figure 4.9, but wi th the glass w indow covering the tip. Evidendy, the 'b l ind zone' was eliminated and the probe response was altered. The basis for the linear response o f the probe with the 'bl ind zone' being eliminated is reported by L i u (2001). The routine measurement o f local voidage using the optical voidage probe involved obtaining the upper and lower voidage limits, wi th the black box and dense phase, respectively. Linearity was then assumed to be val id for voidages between these two limits. The 0.29 m Plexiglas co lumn was covered wi th black curtains to ensure there was no external light permeating through the co lumn to give erroneous results. 4.6 Capacitance probe A s noted before, capacitance probes measure the dielectric constant between two poles, wi th the signal being a function o f the solids concentration between the poles. B y maintaining the voltages o f the guard and sensor at the ground voltage, the probes and guard circuit reported by Acree and Louge (1989) did not induce electrostatics, nor did they attract charged particles. A s highlighted by Wiesendorf and Werther (2000), the linear relationship between voidage and capacitance signal generally applies wel l for gas-solid suspensions, although linearity may not ho ld for systems at high temperature due to the relative dielectric constant o f solids being affected by increasing temperature. Disadvantages o f capacitance probes include the measuring volume being not we l l defined, and the sensitivity o f the capacitance probe to humidity (Zhang et a l , 1998). The output signal o f the capacitance probe i n voltage, is given by V = Q ; r (4.3) [ga in ]xC Chapter 4 Voidage Measurements 105 Window thickness * I. CO C V tl -a <u -w CJ CJ a CJ •d CD N o ^signal / Distance Distance Figure 4.10 Setting the upper intensity in dense bed: (a) without window; (b) with window. 60 70 Time, s I 80 Figure 4.11 Signal obtained from optical probe with glass window. (Dotted line represents the maximum calibrated value.) D=0.29 m, U=0.15 m/s, z=0.15 m, r/R=0.0, FCC I. Chapter 4 Voidage Measurements 106 where Q s is the constant charge amplitude supplied by the amplifier. T h e effective relative dielectric permittivity, K e f f , is a function o f local voidage, particle size, sphericity, and particle size distribution for particles o f negligible conductivity (Louge and Opie , 1990). I f the gain and charge are constant, then K c f f can be expressed as: K [ f f o c - c c ^ (4.4) e C 0 V K J where C is the capacitance between the probe surface and ground. The capacitance probe used i n this study was developed in-house at C S I R O and used exclusively i n the 1.56 and 0.61 m diameter columns. The probe schematic presented i n Figure 4.12 has a very similar design and construction to the one used also at C S I R O and reported by Whi te and Zakhar i (1999). The probe is connected to a capacitance meter wi th a driven-shield to minimize electrical noise such as stray and cable capacitances. Initially, the upper and lower capacitance response limits were set by placing the probe into the co lumn prior to injecting solids, i.e., i n air for the upper voidage limit, and into the static bed i n the co lumn after solids injection. Calibration o f the capacitance probe wi th F C C particles suspended i n water was conducted to obtain the response and to extrapolate the results to the gas-solid system. The capacitance probe was placed in a beaker where F C C particles were suspended i n water by means o f stirring. Figure 4.13 depicts the normalized response vs. volumetric solids concentration i n water. T h e effect o f solid concentration on the effective relative dielectric permittivity o f a suspension, K e f f , is presented i n Figure 4.14 and compared to calibration models applied to the water-solids system. T h e relative dielectric permittivity o f F C C material, K p , is estimated to be 14 for all models, based on the findings o f Louge and Op ie (1990). A t very dilute conditions, the effective relative dielectric permittivity, K c f f , o f a FCC-wa te r suspension is seen to be wel l represented by the linear model . However , the capacitance response becomes fairly insensitive to the volumetric solid fraction beyond 0.03, as depicted in Figure 4.14. The discrepancies between measured response and the models are attributed to the difficulty i n assessing the wetting behaviour o f porous F C C wi th an unknown amount o f water penetration into the pores. Therefore, as suggested by Wiesendorf and Werther (2000), the linear signal response was taken to be adequate for measurements i n gas-solids suspensions, and thus applied i n this case. Chapter 4 Voidage Measurements 107 Probe tip: 3 mm x 1 mm OD Earthed outer sheath, 6 mm OD x 0.25 mm wall thickness and 250 mm long SS tube Earth Driven shield Co-axial cable, to signal processing with BNC connector Figure 4.12 Schematic of needle-type capacitance probe. > « c _gjD y N £ la 0 Z 1.00 Q 0.99 0.98 0.97 0.96 0.95 0.0 0.1 0.2 0.3 Volumetric solid fraction 0.4 0.5 Figure 4.13 Signal response of capacitance probe with F C C II in water-solids suspensions. Chapter 4 Voidage Measurements 108 O da ta 90 M a x w e l l (1892) • l inear m o d e l ser ies m o d e l M e r e d i t h & T o b i a s (1960) K ^ - = 3 K p - 2 s ( K p - K h ) K h 3 K h + e ( K p - K h ) K e f f = e K h + ( l - E ) K p 1 K e f f = K . s 1 - s - + — h p X - 2 ( l - e ) + Y-2.133Z K h ~ X + ( l - e ) + Y-0.906Z w h e r e X = 2 K h + K p K h - K p Y = 0.409(1-s) 7 / 3 6 K h + 3 K p 4K h +3K p Z = (l-S) 10/3 3 K h _ 3 K p 4K h +3K p o o o o o o S 70 50 0.00 0.05 0.10 0.15 V o l u m e t r i c s o l i d f rac t ion 0.20 F i g u r e 4.14 Ef fec t o f v o l u m e t r i c so l ids f ract ion o n the effective relat ive d ie lec t r ic pe rmi t t i v i ty o f a w a t e r - F C C sys tem. A l l m o d e l s a s sume Kp = 14 a n d K h = 80 for F C C a n d water , respect ive ly , b a s e d o n L o u g e a n d O p i e (1990). Chapter 4 Voidage Measurements 109 The temperature o f the fluidizing air ranged from 18 to 66°C , a range wh ich was considered to be small enough that there was negligible change i n the relative dielectric constant o f F C C (Wiesendorf and Werther, 2000). 4.7 Results 4.7.1 Optical liber probe L o c a l voidages were captured by the optical fiber voidage probes by sampling at 100 H z for durations o f 100 s. Voltage signals were converted to voidages by f T T T T V (4.5) 1- •e v - v 0 v V m f - v o y where V 0 is the voltage signal obtained from the black box where negligible light is reflected, representing a voidage o f 1, and V m f is the signal when the probe is immersed i n a container o f static solids representing closely the voidage at m i n i m u m fluidization. The power n was taken as 1 for a linear response o f voltage against voidage. The two end points, V 0 and V m f , were calibrated several times during experimental runs to detect any shift i n signal output. In general, al lowing sufficient time to warm up the equipment resulted i n stable V 0 and V m f readings. Occasionally when converting voltage measurements to voidage signals, signals were recorded outside the range set by the two end points, i.e., the black box and dense phase limits. Dis t inc t ion criteria were set between noisy signals, i.e., electrical spikes, and the shifts i n the range o f signals were observed to be mostiy linear. F o r a given set o f data, V m a x and V m m were plotted chronologically for each set to assess against the V m f and V 0 values. A n y gradual shifts or isolated shifts were further investigated by plott ing the probability distribution curve for each set. Da ta points o f probability <0.5 % for the lower l imit (if V m i n < V 0 ) , or > 99.5 % for the upper l imi t (if V m a x > V m f ) were considered to be outliers. Otherwise, probability distribution curves for data sets before and after the one under investigation were assessed to examine i f any shift i n output could be observed. O n average, a 3% difference in voidage was observed by re-adjusting the signal limits, wi th as high as 7.6% within the data set studied. 4.7.2 Radial voidage profile The time-mean local voidage was calculated from Chapter 4 Voidage Measurements 110 1 T I N e = - J s t d t = - 5 : e t i (4.6) 1 o JN i=i Figure 4.15 represents a typical radial voidage profile at three axial levels i n a 0.29 m diameter co lumn containing F C C I particles with a static bed height o f 0.51 m . A t the level closest to the distributor plate, the flow was not fully developed, as signified by the asymmetric distribution. The return leg re-introducing entrained solids into the co lumn was posit ioned at 90° to the plane o f the plot i n Figure 4.15 at z between 0.051 and 0.18 m which may affect the local voidage at z=0.15 m. A t the next level o f z=0.27 m , better symmetry is observed. A n increase i n gas velocity clearly increases the local voidage at most radial locations. The difference in voidage measurement near the wal l represented by r /R=-0 .98 and 0.98 are likely due to the probe insertion from one side. The optical voidage probe was inserted into the co lumn at r / R = l and extended to measure voidage at r / R — 0 . 9 8 . The short distance between the tip o f the probe and the wal l may have disturbed the local flow. Asymmetry o f the radial voidage profile is observed at the level o f z=0.40 m. This may be due to the effect o f solids movement near the fluctuating expanded bed surface. The cross-sectional average voidage, s m , was obtained by integration o f the polynomial curve fit o f local time-mean voidage over the co lumn cross-section. • 1 R 1 e m = - T I 2 s r d r = J 2ecpdcp (4.7) R o o where (p=r/R. Figure 4.16 depicts the cross-sectional average calculated from the data shown in Figure 4.15. The trend is as expected, wi th the overall cross-sectional voidage remaining relatively constant wi th in the bed, and starting to increase close to the top o f the expanded bed, i.e., at z=0.40 m. U c measured from the standard deviation o f D P reading located between z=0.40 and 0.463 m is 0.495 ±0 .015 m / s , beyond which point a sudden increase i n cross-sectional average voidage is observed at z=0.40 m i n Figure 4.15. Cross-sectional average voidages from the optical probe are compared wi th those from D P measurements at z=0.27 m i n Figure 4.17. Cross-sectional average voidages from the optical probe tend to be somewhat higher than from D P signals. This may be due to the D P measurements being Chapter 4 Voidage Measurements u So 3 > b/j *-u > JJ Sc xj ' o > CJ fee CJ > 0.9 0.8 0.7 CJ 0.6 V 0.70 u s 2 0.65 o > CJ M ts •CJ > cj £ 0.60 0.554 0.0 0.5 1.0 0.70 0.65-^ 0 . 6 0 .§ 0.55 H 0.50 (a) z=0.40 m — • — U=0.31 m /s o U=0.40 m /s Mi U=0.50 m /s - v - U=0.61 m/s (b) z=0.27 m — • — U=0.29 m/s o U=0.42 m /s U=0.50 m /s - v - U=0.58 m /s j * \ y / . - A " o ° ' • ¥ (c) z=0.15 m - • - U=0.28 m /s O U=0.39 m /s r • 1 A U=0.49 m /s — V — U=0.62 m /s • p-—""'^ \ u 1 1 • 1 • 1 1 1 -1.0 -0.5 0.0 0.5 1.0 r / R F i g u r e 4.15 R a d i a l vo idage d i s t r ibu t ions . H 0 = 0 . 5 1 m , D=0 .29 m , F C C I . U c ( I =0.43 m , = 0.49 ± 0.015 m / s . Chapter 4 Voidage Measurements 112 O > CU 5JD rt u u I C _o u <u cc • cn cn O u 0.80 0.75 A 0.70 0.65 A 0.60 A 0.55 9 9 • A • A A • • 0.3 i 1 0.4 0.5 0.6 • z=0.15 m A z=0.27 m 9 z=0.40 m U , m / s Figure 4.16 Cross-sectional average voidage from local radial voidage measurements from optical probe. H0=0.51m, D=0.29 m, FCC I. 0.65 OS • 1—1 O > . cu cu c o +-> cj cu CO CC CO o 1-u 0.60 4 0.55 4 V X V • • 1 0.3 i 1 0.4 0.5 1 1 0.6 )K D P measurement V E 0 < r / R < l m • e - K r / R < 0 U , m / s Figure 4.17 Comparison of cross-sectional average voidage from optical signal to that from DP. H0=0.51 m, D=0.29 m, z=0.27 m FCC I. Chapter 4 Voidage Measurements 113 more influenced by v o i d dynamics near the wal l where the D P ports are posit ioned compared to the vo id dynamics closer to the axis o f the column. Figure 4.18 and 4.19 portray normalized time-mean voidage profiles, s / s m . F o r an initial static bed height o f 1.1 m , U c measured through D P fluctuations between axial heights o f 0.53 and 0.65 m was 0.657 + 0.040 m / s . Thus, the normalized voidage profiles for gas flow rates o f 0.40 and 0.80 m / s represent below- and beyond-U c values. In the bubbl ing flow regime, the highest voidage does not necessarily occur at the co lumn axis. In fact, Werther and Molerus (1973b) reported coalescence and evolution o f bubbles i n bubbl ing fluidized beds depicting the highest frequency o f bubbles at r / R ~ 0.6 to 0.7. Beyond U c , the max imum voidage shifts closer to the axis. The profile between r / R = 0 . 7 to near the wal l seems insensitive to height and gas velocity, while that towards the co lumn axis varies wi th axial position and gas velocity when H 0 = l . l m. Similar profiles obtained by A b e d (1984) have been employed (Geldart and Rhodes, 1985; W a n g and W e i , 1997) to support the idea o f the existence o f flow heterogeneity i n turbulent fluidized beds. The macroscopic non-uniformity observed i n radial distribution o f time-mean voidage is interpreted as not having unique enough features to call the turbulent fluidization flow regime an independent regime by some researchers (e.g. X u et al., 1999). However , the not ion o f a turbulent fluidized bed becoming increasingly homogeneous beyond a certain transition originated qualitatively through photographs such as those o f Zenz and Othmer (1960) and K e h o e and Dav idson (1970). In order to quantitatively analyze the breakdown o f larger voids into smaller transient voids, the scales o f time and space must reflect the hydrodynamics o f interest. Figure 4.20 indicates a decrease i n voidage fluctuations wi th increasing gas flow rate. G i v e n that the average voidage increases wi th increasing gas flow rate, this denotes an increase i n the lower l imit o f the voidage. Furthermore, the voidage fluctuations gradually decrease from the wal l inwards, signifying the influence o f the denser structure. Chapter 4 Voidage Measurements 1.2 114 2=0.15 m • 2=0.46 m o 2=0.65 m r / R Figure 4.18 Radial profile of normalized time-mean average voidage. H 0=l.l m, D=0.29 m, FCC I, U=0.40 m/s. 2 =0.15 m • 2 =0.46 m o 2 =0.65 m r / R Figure 4.19 Radial profile of normalized time-mean average voidage. H 0=l.l m, D=0.29 m, FCC I, U=0.80 m/s, U c (z =0.85 m, DP)=0.73 m/s . Chapter 4 Voidage Measurements 115 0.16 • U=0.40 m/s • U=0.51 m/s A U=0.59 m/s O U=0.71 m/s U=0.80 m/s r / R Figure 4.20 Radial profile of voidage fluctuation represented by standard deviation of local voidage measured by optical probe. D=0.29 m, H0=0.8 m, z=0.40 m, Uc=0.75 m, FCC I. Chapter 4 Voidage Measurements 116 Figure 4.21 presents the evolution o f the probability density function at z=0.40 m and at the co lumn axis wi th the superficial gas velocity. The function is a non-linear gas-solid distribution as reported by C u i et al. (2000). The shift in voidage distributions from U < U c to those beyond U c is clearly shown at this level. F r o m U=0.60 to 0.79 m / s , the cumulative probability distribution o f local voidage remains nearly unchanged. This is also indicated by the relatively unchanged average bed voidage around U c , as shown i n Figure 2.9 (H 0 =0.8 m), also reported by Lanc ia et al. (1988) and Tannous et al. (1996). The plateau o f average voidage wi th increasing U may indicate competing mechanisms o f v o i d spHtting, coalescence and acceleration. A t z=0.78 m in Figure 4.22, the voidage probability distributions exhibit wider spread wi th increasing U than i n Figure 4.21, where the data were measured simultaneously. These results indicate a monotonical ly increasing gas flow at r / R = 0 wi th increasing height at all gas velocities between 0.4 and 0.9 m / s . This supports the trend displayed i n Figure 4.15 for a lower static bed height o f 0.51 m. The contour plots shown in Figure 4.23 through Figure 4.26 are based on 64 and 80 cells o f time-mean voidage for static bed heights o f 1.1 and 1.5 m , respectively. T h e qualitative observations suggest higher time-mean voidage around r /R=0 .5 for b e l o w - U c , than for beyond-U c . The effect o f static bed height on the voidage mapping for U=0.9 m / s indicates an increased dispersion o f voidage for deeper beds. In other words, for H ^ L l m, there seems to be a definite pattern o f higher voidage toward the axis, while for H n =1 .5 m , the higher voidage areas are more dispersed, suggesting possible local circulating flows. This , however, cannot be confirmed without making velocity measurements. 4.7.3 Scale effect on radial voidage profile The published work summarized in Table 4.2 does not elucidate the effect o f scale on the radial voidage profile, as very limited data are available i n this respect f rom reactor sizes comparable to industrial scale units. T o a certain point, the increase in reactor size increases the max imum bubble diameter attainable from coalescence, d b m a x , as expressed by M o r i and W e n (1975), d b m a x = 0 . 6 5 2 [ A ( U - U m f ) ] a 4 (4.8) Chapter 4 Voidage Measurements 117 . 3 C r3 O X) c o 3 ft c <u o .Si 7 3 3 '5 E « 3* —•— U=0.40 m/s — o — U=0.51 m/s — • — U=0.60 m/s — A — U=0.71 m/s — — U=0.79 m/s — T — U=0.90 m/s 0.6 0.7 Voidage Figure 4.21 Probability distribution function of local voidage measured by optical probe. U c DP (z =0.85 m)= 0.727 ± 0.039 m/s, H 0 =l . lm, D=0.29 m, r/R=0.0, z=0.40 m, FCC I. 0.6 0.7 0.8 Voidage — • — U=0.40 m/s — o - U=0.51 m/s • U=0.60 m/s — A — U=0.71 m/s — ; — U=0.79 m / s — T — U=0.90 m/s Figure 4.22 Probability distribution function of local voidage measured by optical probe. U c DP (z =0.85 m)= 0.727 ± 0.039 m/s, H 0 =l . lm, D=0.29 m, r/R=0.0, z=0.78 m, FCC I. Chapter 4 Voidage Measurements 118 Figure 4.24 Contour plot of time-mean local voidage measured by optical probe. D=0.29 m, FCC I, H 0= 1.1 m, U=0.9 m/s Chapter 4 Voidage Measurements 119 Figure 4.26 Contour plot of time-mean local voidage measured by optical probe. D=0.29 m, FCC I, H0=1.5 m, U=0.9 m/s Chapter 4 Voidage Measurements 120 where A is the reactor cross-sectional area. U c is considered to be the superficial gas velocity at which the max imum bubble size is attained by coalescence. Increasing U beyond U c results i n bubble break-up being more dominant than coalescence (Sun and Chen , 1989; C a i et al., 1990). Equat ion 4.8 then no longer applies. A s conversion in a fluidized bed catalytic or gas-solid reactor is affected immensely by gas-solid contacting, moni tor ing the local v o i d behaviour wi th increasing co lumn diameter should provide valuable knowledge into scale-up effects. The same optical voidage system used at U B C was used to acquire voidage data from reactor diameters o f 0.61 and 1.56 m at C S I R O . 4.7.3.1 Results from 0.61 m diameter fluidization column Similar radial voidage profiles were observed for the 0.61 m and 0.29 m diameter columns. A s depicted i n Figures 4.27 and 4.28, the max imum time-mean voidage occurred near r /R=0 .5 for U < U c , while it was closer to the column axis for U > U c . This trend is consistent wi th other runs, as wel l as that reported by Nakajima et al. (1991) in a 0.20 m diameter co lumn. Moreover , the profile was similar for a given gas flow rate at two levels, z=0.8 and 1.55 m . This provides a strong indication that i n the turbulent fluidized bed flow regime, the radial voidage profile examined through time-mean local voidage measurements becomes fully developed at z / D « 1.3. A s shown i n Figure 4.29, the cross-sectional voidage calculated from local voidages based on optical probe signals was i n good agreement wi th that from D P measurements. 4.7.3.2 Results from 1.56 m diameter fluidization column In order to obtain simultaneous measurements o f D P , A P , and voidages from optical and capacitance probes i n the co lumn o f diameter 1.56 m , traversing swivel arms were designed and constructed as described i n Chapter 2. The effect o f the swivel arms o n the flow was not investigated; however, due to the relative size, i.e., 1.56 m diameter vs. a 0.064 m diameter head attached to a 0.038 m diameter tube, wi th the optical voidage probe at the tip o f the arm measuring local light reflection, the blockage effect was likely rninimal. The radial positions were determined from the penetration length and the swivel angle, which covered the desired radial positions on a fan-shaped plane rather than a line connecting the wal l and the co lumn centreline. Chapter 4 Voidage Measurements 121 a 0.9 4 U= ^ 0.63 m/s o u= =0.71 m/s A u= :0.75 m/s Figure 4.27 Radial profile of time-mean voidage from optical probe signals. H0=l.l-1.3m, D=0.61 m, z=0.8 m, FCC III, Uc=0.83 m/s (z=0.8m, DP). U= 1.31 m/s o u = 1.42 m/s A u = 1.56 m/s Figure 4.28 Radial profile of time-mean voidage from optical probe signals. H0=2 m, D=0.61 m, 2=1.55 m, FCC IV, Uc=1.12 m/s (z=1.5 m, DP). Chapter 4 Voidage Measurements 122 O data cross-sec. ave. voidage from optical probe —-— cross-sec. ave. from D P 0.70 r / R Figure 4.29 Radial profile of time-mean voidage from optical probe signals. H0=1.7 m, D=0.61 m, U=0.85 m/s, z=0.8 m, F C C III, U c=0.77m/s (z=0.36 m, DP). Chapter 4 Voidage Measurements 123 The radial profile for H 0 = 1 . 2 m at z=0.84 m is shown i n Figure 4.30. F o r both superficial gas velocities, the trend shows increased voidage near the wall. This was attributed to the centre o f the co lumn being non-uniformly aerated. The increase i n U naturally increased the voidages. T w o points from these data are chosen to examine the probability density o f voidages portrayed i n Figure 4.31. The time-mean voidages are 0.69 and 0.72 for r / R = 0 . 9 and 0.0, respectively. However , the profiles o f the probability density distribution indicate a slight difference between the two radial positions, wi th less high-density phase and an increased presence o f voids near the wall . A l though these two measurements were obtained from different runs, the trend was confirmed to be reproducible. F o r a deeper bed, i.e., H0=2.2 m , the general trend o f radial profile is represented by that for U=0.62 m / s i n Figure 4.32. F o r r / R = 0 . 0 the time-mean voidage peaked at around U c as demonstrated i n Figure 4.33. This trend was also indicated for r /R=0 .23 and 0.50. After examining the probability density distribution o f voidages for U > U c at r /R=0 .8 , 0.6 and 0.0, it was concluded that fewer voids and a denser dense phase were detected at gas velocities beyond U c . Curiously, the trend did not reflect the increase i n gas flow rate. F r o m the cross-sectional averaged voidage based on D P measurements against gas velocity, e.g. Figure 2.27, albeit at a different H 0 , an overall increase i n voidage is evident. F o r the 1.56 m diameter co lumn, the axial posi t ion o f the return leg was between 0.2 and 0.8 m. A t higher gas velocities resulting i n increased entrainment, more solids were re-injected into the column. W i t h the traversing probe arm posi t ion at 0.84 m the results may have reflected the influence o f the remrning solids resulting i n lower local voidages. In fact, when time-mean voidages were compared for the probe swinging from the left to the right, it was observed that for U > U c the probe positioned closer to the return leg indicated a lower voidage. 4.7.3.3 Scale effect The normalized radial profiles o f time-mean voidage are compared to several o f the works listed in Table 4.2 i n Figure 4.34. It shows that the profiles are quite similar for co lumn diameters ranging from 0.076 to 0.71 m. D u e to the non-uniform aeration i n the 1.56 m diameter co lumn, data from the largest co lumn are not included. Therefore, there is not enough evidence to say whether the radial profile in Figure 4.34 is valid when co lumn diameter is scaled-up beyond 0.71 m. Nevertheless, the results provide an indication o f the radial variation o f the flow structure. Chapter 4 Voidage Measurements 124 0.75 0.70 4 0.65 0.60 o A • • A A O O o OO o o g3 0.0 0.2 0.4 0.6 0.8 r / R O U=0.39 m/s A U=0.50m/s 1.0 Figure 4.30 Radial profile of time-mean voidage from optical probe signals. z=0.84 m, D=1.56 m, H0=1.2 m, FCC II, Uc (z=0.84 m, DP)=0.39 m/s. 6 Voidage Figure 4.31 Probability density of voidage obtained from optical probe signals measured at r/R=0.90 and 0.0. D=1.56 m, H0=1.2 m, FCC II, z=0.84 m. Chapter 4 Voidage Measurements 125 v CUD cs • o o > C CS s i a 0.70 0.65 J 0.60 J 0.55 4 0.50 0.45 o u= 0.45 m/s • u= 0.62 m/s r /R Figure 4.32 Radial profile of time-mean voidage from optical probe signals. D=1.56 m, z=0.84 m, H0=2.2 m, Uc (z=0.85 m, DP)=0.53 m/s, FCC II. 0.7 v cS o > c cS (U s I CU s 0.6 0.5 A OA A 0.3 O ° o -O -o o o O i A ° o • • A A A A A . A -i 0.0 1 ' 1 0.1 0.2 i 0.3 0.4 0.5 0.6 1.0 40.8 J.0.6 4 0.4 40.2 J.0.0 cs PH Q o c o -*-» cS o * d CS - o G CS •!-> en U, m/s Figure 4.33 Effect of U on time-mean voidage and DP fluctuation at r/R=0.0. D=1.56 m, z=0.84 m, H0=2.2 m, Uc (z=0.85 m, DP)=0.53 m/s, FCC II. Chapter 4 Voidage Measurements 126 A B a i et al. (D=0.076 m , 1999) • X u et al. (D=0.09 m , 1999) + L i et al. (D=0.09 m , 1990) • A b e d (D=0.15 m , 1984) — Bayle et al. (D=0.19 m , 2001) O Chaouk i et al. (D=0.2 m , 1999) o This work (D=0.29 m) 0 Wang and Wei (D=0.47 m , 1997) A This work (D=0.61 m) X L u e t a l . (D=0.71m, 1996) Equation 4.1 Wang and W e i (1997) 0.0 I — - r — , , , 1 0 0.2 0.4 0.6 0.8 1 r / R Figure 4.34 Radial profile of normalized time-mean voidage. Comparison of experimental data to other publications. Particle properties and operating conditions listed in Table 4.2. Chapter 4 Voidage Measurements 127 Figure 4.35 presents the effect o f normalized superficial gas velocity o n the normalized radial profile o f time-mean voidage. The voidage near the axis increases wi th increasing normalized superficial gas velocity. F o r the range o f co lumn diameters under investigation, the effect o f co lumn diameter on the radial voidage profile is shown to be less significant compared to the effect o f U , as the profile for U / U c = 1 . 3 9 and D=0.61 m is similar to that for U / U c = 1 . 3 8 and D=0.15 m i n Figure 4.35. 4.7.4 Dense phase voidage The strong interaction between the dense and dilute phases is one o f the characteristics o f turbulent fluidized beds. Devia t ion from the two-phase theory prediction has been reported by Nakajima et al. (1990) through local bubble fraction measurements using an optical probe. Chaouk i et al. (1999) estimated the dense phase voidage to be the lower l imit o f the probability distribution function o f local voidage measured wi th a capacitance probe. Thei r findings suggest that the dense phase voidage increases wi th increasing gas velocity while the dilute phase voidage remains constant beyond U c for F C C particles. Figure 4.36 depicts the probability density o f voidage at three radial locations. The voidage distributions indicate heterogeneity across the radius. The voidage value at zero probability, s c, shifts wi th radial posi t ion wi th the value corresponding to r /R=0 .0 . Accordingly , the peaks o f the voidage probability, representing the maximum crossing voidage, shift wi th radial posit ion. The broad probability distribution function for r / R = 0 . 0 supports the not ion o f breakdown o f a two-phase structure. The breakdown o f the two-phase structure is further illustrated i n Figure 4.37, where the voidage distribution is compared for columns o f diameter 0.29 and 1.56 m. A t similar normalized superficial gas velocities, the voidage distribution i n the larger co lumn exhibits a broad b imodal distribution, while that i n the smaller co lumn appears to be unimodal . The wal l effects may be the cause o f this difference i n voidage distributions. 4.7.5 Capacitance probe measurements The local voidage was also measured using the capacitance probe, wh ich recorded the local dielectric constant i n the 0.61 and 1.56 m diameter fluidized beds. A linear relationship between the capacity response and the solids concentration was assumed as explained i n Section 4.6. Chapter 4 Voidage Measurements 128 1.6 0.4 — • — U / U c = l . l l ( D = 0 . 2 9 m ) — • - • U / U c = 1 . 2 7 (D=0.61 m) — A — U / U c = 1 . 3 9 (D=0.61 m) U / U c = 1 . 3 8 (D=0.15 m) Abed(1984) o U / U =1.52 (D=0.076 m) Baiet al. (1999) 0.0 0.2 OA 0.6 0.8 1.0 r / R Figure 4.35 Effect of U / U c on radial profile of normalized time-mean voidage. FCC. Chapter 4 Voidage Measurements 129 0.12 0.00 4 r / R = 0 . 0 <r /R=0.56 r / R = 0 . 9 8 0.7 0.8 Voidage Figure 4.36 Probability density of voidage from optical probe signals. D=0.29 m, z=0.527 m, U=0.78 m/s, F C C I, H0=0.8m. — D = 0 . 2 9 m z / H = 0 . 4 5 U / U = 1 . 4 H / D = 2 . 1 r / R = 0 . 0 £ = 0 . 6 8 — D = 1 . 5 6 m z / H = 0 . 5 3 U / U =1.2 H / D = 1 . 0 r / R = 0 . 9 s=0.74 0.4 0.5 o!6 0 J ol8 0.9 L0 Voidage Figure 4.37 Probability distribution of voidage measured by optical probes. D=0.29 m (FCC I). D=1.56 m (FCC II). Chapter 4 Voidage Measurements 130 The probability density distributions o f the voidage measured by the capacitance and optical probes, compared i n Figure 4.38, exhibit significandy different profiles. Time-mean voidage was calculated to be 0.58 and 0.57 from capacitance and optical probe signals, respectively. T h e broader peaks imply that the measured capacitance o f the gas-solid mixture covers a larger measuring volume than the optical measurement. 4.8 Conclusions L o c a l voidage measurements were obtained experimentally through the use o f optical fiber and capacitance probes i n 0.29, 0.61 and 1.56 m diameter columns for fluidized beds o f F C C particles, operated i n the bubbl ing and turbulent fluidized bed flow regimes. The signals showed continuous distributions o f probability distribution and rapid fluctuations, indicating a breakdown i n the two distinct phases (discrete dense and dilute phases) usually assumed i n the bubbl ing bed flow regime. • Symmetry o f the radial voidage profile was confirmed for z / H = 0 . 5 i n the D=0.29 m column. • Cross-sectional average voidages obtained from optical probe measurements compared wel l wi th those derived from differential pressure measurements for D=0.61 and 1.56 m. • Time-mean radial voidage profiles tended to be different for the bubbl ing and turbulent fluidization flow regimes: for U ^ U c there was a max imum voidage at a non-axis position; on the other hand, for U > U c , the max imum voidage was at the co lumn centre. • The standard deviation o f voidage decreased wi th increasing superficial gas velocity. • Contour plots o f time-mean voidage from optical probe signals for the D=0.29 m column showed that static bed height and superficial gas velocity affect the overall flow structure. • A comparison o f voidage distributions for D=0.29 m and 1.56 m revealed a bimodal distribution for the larger co lumn and a unimodal one for the smaller column. The breakdown o f the two-phase structure for the smaller co lumn is presumably due to a greater wal l effect. • Results f rom the optical probe and capacitance probe differed substantially. This is attributed to the fact that the measuring volume o f the capacitance probe is m u c h larger than that o f the optical probe. Further analyses on the local voidage measurements are pursued i n Chapter 6. Chapter 4 Voidage Measurements 131 • Capaci tance p robe - O p t i c a l p robe Voidage Figure 4.38 Probability density of voidage from capacitance and optical probe signals. D=0.61 m, U=0.86 m/s (capacitance); U=0.85 m/s (optical), H0=2 m, z=1.55 m, FCC III, r/R=0.83. CHAPTER 5 VELOC ITY MEASUREMENTS 5.1 Introduction O n e o f the more fundamental measurement quantities related directly to the physics o f two-phase flows is the velocity o f each phase. Numerous studies have been reported o n direct measurements o f particle and /o r bubb le /vo id velocities i n fluidized beds, often in attempts to verify hydrodynamic theories and models that can depict the complex flow dynamics (e.g. H o r i o et a l , 1992b; Seville et a l , 1995; Z h u et a l , 2001). This chapter deals wi th the experimental v o i d and particle velocity measurements for obtaining reliable data to contribute to the understanding o f the local heterogeneity o f the two-phase flow structure. 5.1.1 Void velocity Many hydrodynamic studies o f the turbulent fluidization flow regime have adopted the terminology applied i n the bubbl ing flow regime where the dense phase forms a continuous phase and the gas phase remains discontinuous. O n e o f the first reports published o n the v o i d velocity i n or close to the turbulent fluidization flow regime was by Lanneau (1960) using dual capacitance probes positioned 0.076 m apart i n a 0.076 m diameter column. Beyond a superficial gas velocity o f 0.6 m, the voids were reported to be small, rapid, and losing their identity, making the measurement unattainable. The trend is such that the bubble phase velocity approaches the superficial gas velocity as U is increased. Lee and K i m (1989) analyzed the cross-correlation o f two pressure fluctuation signals to deduce the v o i d rise velocities i n a turbulent fluidized bed. Thei r fluidized bed o f glass beads i n a 0.1 m diameter co lumn encountered the slugging regime prior to the turbulent flow regime. The reported average vo id rise velocity remained around 1.6 m / s once i n the turbulent fluidization flow regime. In measuring the slug rise velocity, the correlation o f pressure fluctuations at the wall , approximately equal to cross-sectional average pressures, seems to be a viable choice. However , once i n the turbulent fluidized flow regime, due to the transient nature o f voids, the average v o i d velocity may not be obtainable from a cross-correlation o f the gauge pressure signals. Similarly, Yamazak i et al. (1991) found a max imum v o i d rise velocity at U c =0.55 m / s , followed by a plateau at a superficial gas velocity o f around 0.8 m / s for a bed o f F C C catalyst particles (D=0.2 m). Ege (1995) reported on the bubble rise velocity i n 0.3 and 0.5 m diameter columns with F C C particles using two optical fiber probes. Considerable scatter i n the radial profile o f v o i d rise velocity 132 Chapter 5 Velocity Measurements 133 was observed for both columns at a superficial gas velocity o f 0.55 m / s . In general, the v o i d rise velocity decreased wi th increasing distance from the grid. This was shown to coincide wi th decreasing v o i d length, and decreasing v o i d frequency. L o c a l measurements have been reported i n investigating bubble characteristics such as rise velocity and chord length (e.g. Zhang et al., 1997; L u et al., 1997). L u et al. (1997) found an increase in the average v o i d chord length wi th increasing height from z=0.15 to 0.85 m , while there was no significant difference i n the v o i d rise velocity for the three superficial gas velocities under investigation (0.59, 0.78, 0:98 m/s ) . The results o f T a x i l et al. (1998) indicate significant scattering o f lengths and velocities, wi th 15% o f the voids having chord lengths greater than the co lumn diameter o f 0.2 m. Compar i son o f the v o i d lengths reported by L u et al. (1997, D=0.71 m) wi th those o f Tax i l et al. (1998) reveals a 3-fold difference, highlighting the challenge i n identifying v o i d structure and dynamics due to the distorted and transient nature o f the voids i n turbulent fluidized beds. 5.1.2 Particle velocity L o c a l particle velocity measurements coupled wi th the volumetric solid concentration can provide vital information on the heterogeneity o f the flow. However , very few reports pertain to the turbulent fluidization flow regime, especially for G r o u p A particles, due to the experimental difficulty i n obtaining reliable results f rom experiments conducted i n dense phase beds. V a n den M o o r t e l et al. (1998) reported on the velocities o f particles i n a circulating fluidized bed. Their superficial gas velocity o f 1 m / s for G r o u p A glass beads (p p = 2400 k g / m 3 , d p = 120 um) almost certainly corresponds to the turbulent fluidization flow regime, and this is consistent wi th the reported solid circulation flux o f 0.22 k g / m 2 s . However , i n order to capture the particle movement wi th a phase Dopp le r particle analyzer, the volume fraction was restricted to 1.5%, resulting i n a very dilute suspension, implying a situation where no distinct voids are present and particles are carried upwards by the gas as a dilute suspension. Reported lateral instantaneous particle velocities ranged from -0 .9 to 2.5 m / s . Denes (1995) used a reflective fiber optical probe, consisting o f fibers o f diameter 50 p m , in a bubbl ing fluidized bed o f particles o f size range 600 to 2500 u m with superficial gas velocities up to 1.3 m / s . The average particle velocity increased wi th both height and superficial gas velocity. However , possibly due to the blockage o f a 0.02 m diameter area i n the centre o f the distributor plate i n a 0.1 m diameter column, the radial profile o f the average local particle velocity exhibited higher values (0.46 m/s ) at the wal l than i n the centre (0.33 m/s ) for U = 1.0 m / s and z / D — 1. N o details on the optical probe used to determine the velocities were Chapter 5 Velocity Measurements 134 provided. A reflective fiber optical probe wi th seven receiving fibers was applied to a bubbl ing bed o f F C C particles wi th fluorescent-coated F C C as tracer particles by Tayebi et al. (1999). B y detecting tracer particles that give uniquely intense signals, two-cUmensional local particle and vo id velocities were measured. The results showed tracer particle velocities i n all directions up to 0.92 m / s for U = 0.065 m / s . The fiber orientation provides the advantage o f al lowing the mot ion o f particles in different directions to be determined. In this study, a novel velocity probe developed at U B C is used to report on the local velocities o f voids and particles i n turbulent fluidized beds. 5.2 Optical liber probe T w o types o f probes were employed in this study. The first is the multi-functional optical fiber probe designed at U B C by L i u (2001) and manufactured by the Institute o f Chemica l Metallurgy i n Beijing, China , for simultaneous measurement o f local instantaneous voidage, particle velocity and solids flux. This probe was originally used i n a high density circulating fluidized bed, but is intended for a wide range o f two-phase systems. A s shown i n Figure 5.1, the probe contains three 0.26 m m diameter fibers; one light emitting, and two light receiving, wi th a physical centre-to-centre separation distance o f 0.53 m m , and an effective separation distance o f 0.18 m m between adjacent fibers. Since the diameter o f the fibers is similar to the mean size o f the F C C particle used in this work (75 um), single particle movements can be detected. Mathematically, by acquiring data at a frequency higher than 27.8 k H z , this method can capture one-dimensional axial particle velocities up to 5 m / s travelling over the effective separation distance o f 0.18 m m . In order to prevent particles from occupying the b l ind zone (see L i u , 2001; C u i et a l , 2001), a glass cover was placed over the probe tip, as depicted i n Figure 5.2. This helps to ensure a linear relationship between the signal and voidage measurements. Details o f the optical velocity probe and the verification o f velocity measurements can be found i n L i u (2001), L i u et al. (2003a), and L i u et al. (2003b). The second type o f sensor utilizes two identical optical fiber voidage probes separated by a known distance to obtain voidage fluctuations, thus capturing the lag time between the signals from the two probes. The detailed concept o f the optical voidage probe is covered i n Chapter 4. A s shown i n Figure 4.2, the size o f the fibers relative to that o f the particles affects the measurements. In this case, the diameter o f the fiber bundle is much larger than that o f the particles. Chapter 5 Velocity Measurements 1 to photo-multiplier i i light f rom source ' ^ to photo-multiplier side view 0.53 mm front view receiver o f reflected light 1 T 0.26 m m ^ ' hght ^pro jec tor Figure 5.1 Details of optical fiber velocity probe. light in light out A g light out measuring region glass cover blind zone Figure 5.2 Schematic of optical velocity probe tip showing measurement volume and elimination of 'blind zone' by addition of glass cover. Chapter 5 Velocity Measurements 136 A s a result, this type o f optical probe receives light reflected from a swarm o f particles, as typified in Figure 5.3, and cannot distinguish signals from individual particles. D u e to the sufficient separation o f the two probes, the effective distance between the probes is considered to be identical to the physical separation distance as there is no overlapping measuring volume i n this case. However , correlation o f the signals f rom the probes becomes poor as the distance between the two probes is increased. This method is advantageous for capturing v o i d movements f rom acquisition o f data at much lower frequencies than those required by the particle velocity probe described i n the previous paragraph. The drawback is the relatively poor correlation o f signals, especially i n turbulent fluidized beds due to considerable distortion and deviation in the shapes, sizes and directions o f mot ion o f voids and particles travelling between the two probes. A s indicated by the traces i n Figure 5.3, the irregularity o f the voidage fluctuation signals makes the analysis difficult, inevitably leading to some uncertainty and error. 5.3 Data acquisition and analysis The optical fiber velocity probe and the high-speed data acquisition card were supplied by the Institute o f Chemica l Metallurgy i n Beijing, China . The high-speed data acquisition software for the optical velocity probe is written in Turbo C based on a program written by L i u (2001) without the user interface. The typical sampling rate was between 13 and 30 k H z wi th durations o f 60 to 140 s. A s shown i n Figure 5.4, two signals from fibers A and B are acquired at high speed, followed by off-line analysis o f the cross-correlation between the signals and conversion to voidage. In order to pursue the analysis i n an unbiased manner, pre- and post- processing o f data was carried out according to the algorithms, written in M A T L A B ® , listed i n Table 5.1. Cross-correlation was performed on the raw data as wel l as on data that had been pre-processed wi th binary coding and cut-off methods. Further details oh the pre-conditioning o f data and analysis methods are described i n Append ix B . Chapter 5 Velocity Measurements 137 Figure 5.3 Typical optical signal obtained by two identical voidage probes separated by 0.01 m. D=0.29 m, z=0.78 m, U=0.90 m/s, r/R=0.70, H0=1.5 m, FCC I. Table 5.1 MATLAB® functions written for data analysis. File name Function corr_fun.m performs cross-correlation on group number elirninate.m imposes elimination criteria on correlated data dense.m extracts data points related to dense-phase binary.m converts raw data into binary code based o n assigned threshold value Chapter 5 Velocity Measurements 138 voidage off-line calibration and averaging Figure 5.4 Schematic of the optical fiber velocity probe system for simultaneous measurement of local solids concentration and particle velocity. Chapter 5 Velocity Measurements 139 5.4 Results 5.4.1 Particle velocities in 0.61 m diameter column The time-average overall axial voidage profile from the wal l mounted differential pressure (DP) transducer for the velocity measurement runs performed in the 0.61 m diameter co lumn is shown i n Figure 5.5. The results indicate an increased difference i n time-mean voidage at z=1.55 m compared to z=0.80 m wi th increasing superficial gas velocity. Figure 5.6 depicts the cumulative void-associated particle velocity profile for U=1.56 m / s , z=1.55 m. A s the optical fiber velocity probe is moved towards the centre, the profile shifts to higher velocity, coinciding wi th an increase i n time-average voidage. Figure 5.7 exhibits a typical probability distribution o f voidage at four different radial positions. A s the optical probe is traversed towards the axis o f the column, the voidage distribution changes from dominandy representing the dense phase to a b imodal distribution o f dense and dilute phases. A further increase i n superficial gas velocity results i n a radial profile resembling a core/annulus structure i n a circulating fluidized bed. F o r all o f the superficial gas velocities examined, a b imodal distribution, suggesting dense and dilute phases, is present near the centre. Radial profiles o f average void-associated particle velocity and voidage for superficial gas velocities o f 1.56 and 0.82 m / s are shown i n Figure 5.8. The method o f distinction between the vo id - and dense-phase-associated particle velocities is discussed i n A p p e n d i x B . A t the measurement height o f 1.55 m , the cross-sectional time-average voidages for the two velocities are similar, i.e., 0.88 and 0.87, respectively. The particle velocity profile is rather scattered for 11=0.82 m / s , wh ich is very close to U c , as determined according to the pressure fluctuations. It is concluded that the average velocity may not necessarily be representative o f the flow conditions given the considerable fluctuations i n both pressure and solids velocities. The curves in Figure 5.9 display a shift i n void-associated particle velocity distribution wi th superficial gas velocity as wel l as wi th position. F o r both r /R=0 .09 and 0.5, particle velocity is higher for z=0.80 m (at U=0.81 m/s ) than for z=1.55 m (at U=0.82 m/s ) . The operating conditions expressed i n terms o f average pressure drop measurements along the axial height, and the average Chapter 5 Velocity Measurements 140 <D 4 V " a u O 3 o « U C s IB 5 0.4 cm. O U = 1 . 5 6 m/s • U=0.82 m/s A U = 0 . 5 2 m/s X U = 0 . 2 6 m/s cm 0.6 0.8 Time-mean Voidage Figure 5.5 Axial profile of time-mean voidage determined from differential pressure signals. D=0.61 m, H 0=2 m, F C C IV, U c (DP at z =1.55 m)=1.12 m/s. Void-associated particle velocity, m/s Figure 5.6 Cumulative void-associated particle velocity profile. D=0.61 m, U=1.56 m/s, z=1.55 m, H 0=2 m, F CC IV. Chapter 5 Velocity Measurements 141 0.6 0. Voidage 1.0 0.6 0.8 1.0 Voidage = : 3 £ x •3 « 0 6 4 0.4 r / R = 0 . 6 6 0.6 0.8 Voidage 1.0 s s s 8 6 0.4 r / R = 0 . 9 4 0.6 0.8 1.0 Voidage F i g u r e 5.7 P r o b a b i l i t y d i s t r i b u t i o n o f vo idage . D=0.61 m , U = 0 . 8 2 m / s , z=1.55 m , H 0 = 2 m , F C C I V . T a b l e 5.2 A v e r a g e vo idage . D=0.61 m , H 0 = 2 m , F C C I V . Voidage comparison r / R = 0.5 r /R=0 .09 2=0.80 m (U=0.81 m/s) 0.76 0.66 z = 1 . 5 5 m ( U = 0 . 8 2 m/s ) 0.77 0.71 Chapter 5 Velocity Measurements 142 1.0 0.8 4 0.6 0.4 0.2 A 0.0 ® -A -A -o A ® © o -0.0 0.2 1.0 0.9 <u bfj 0.8 | <u 5J0 c\5 u V 0.7 <| 0.6 (a) U=1.56 m/s © Velocity -A— Voidage 0.4 0.6 0.8 1.0 r / R (b) U=0.82 m/s © Velocity -A— Voidage « o > u V r / R Figure 5.8 Radial profile of time-mean void-associated particle velocity (#)and voidage (A)distributions: (a) U=1.56 m/s; (b) U=0.82 m/s. D=0.61 m, z=1.55 m, H0=2 m, FCC IV. Chapter 5 Velocity Measurements 143 2 4 Void-associated particle velocity, m / s (a) r/R=0.09 U=0.57 m / s , 2=0.80 m - • - 0=0.81 m / s , 2=0.80 m U=0.82 m/s , 2=1.55 m U=1.56 m / s , 2=1.55 m Figure 5.9 Cumulative void-associated particle velocity occurrence at (a) r/R=0.09 and (b) r/R=0.50. D=0.61 m, H 0=2 m, FCC IV. Chapter 5 Velocity Measurements 144 local voidage measurements at four spatial locations (i.e., combinat ion o f z=0.80 and 1.55 m, and r /R=0 .09 and 0.5) are examined i n Table 5.2. The results from Figure 5.9 compared to the values i n Table 5.2 conf i rm that fewer particles are mov ing much faster as they travel mostly upward wi th the voids near the co lumn axis The cumulative velocity distribution, Figure 5.9, also indicates numerous occurrences o f particle velocity close to 0 for z=0.80 m , particularly for r /R=0 .09 . This is attributed to being close to the solids return posit ion, as illustrated i n Figure 2.14, and is supported by the decrease in time-average voidage at these locations. The particles re-entering the fluidized bed have little axial momentum, and they frequendy change directions. The effect o f the solids return o n the hydrodynamics in the turbulent fluidized bed intensifies wi th increasing solids circulation rate. 5.4.2 Effect of superficial gas velocity on particle velocity In order to examine the effect o f superficial gas velocity on particle velocity, data have been analyzed for eight superficial gas velocities between 0.82 and 1.56 m / s , as shown i n Figure 5.10. B y choosing these particular runs, the change in hydrodynamics is investigated as U varies f rom below U c to beyond U c . Figure 5.11 indicates that the void-associated particle velocity exhibits a steady increase wi th increasing U , despite the max imum standard deviation from the gauge pressure being attained at around 1 m / s . The dense-phase-associated particle velocities do not rise unt i l U is beyond U c . A s reported i n Chapter 4, one o f the characteristic changes i n the local structure, once wi th in the turbulent fluidization flow regime, occurs in the dense phase. A further analysis o f the data yields the standard deviation o f the particle velocity fluctuation reported i n Figure 5.12. This may indicate, though quite scattered, that the fluctuation o f the dense-phase-associated particles generally increases wi th U . N o t e that at 11=1.56 m / s , the signals from the dense to the dilute phases are still distinguishable, i.e., there are two major peaks i n the pd f o f voidage, wi th the standard deviation o f the pressure fluctuation decreasing, and the particle movement becoming less dominated by v o i d dynamics. The particle velocity fluctuations originate f rom collisions between particles and interactions wi th the gas phase i n the form o f shear stress, and are characteristics o f the particle phase turbulence. In essence, the trend beyond U c can be interpreted as particles i n the dense phase becoming increasingly spaced apart, gaining turbulent energy by having less energy loss as a consequence o f inelastic particle-particle collisions. Once local pressure gradients and fluctuations Chapter 5 Velocity Measurements 145 !4 116 112 CA a 108 c o J3 "o 104 100 • z=0.075mz A z=2.14m X =0.73 m X z=3.16m ® z=1.48 m — stdev z=1.55 m 0.7 0.9 • • G @ A I a * 1.1 1.3 U, m/s 1.5 0.06 0.055 0.05 0.04 1.7 e o V T3 58 0.045 | Figure 5.10 Wall measurements of gauge pressure and standard deviation of pressure fluctuation. D=0.61 m, H0=2 m, FCC IV. a y "y > "y ON 3 void-associated - 75% quantile 25% quantile X- dense-phase-associated Figure 5.11 Effect of U on average particle velocities. r/R=0.09, D=0.61 m, H0=2 m, FCC IV, U c =1.12 m/s (DP at z =1.55 m). Chapter 5 Velocity Measurements 146 9 void-associated particle velocity )K dense-phase-associated particle velocity Figure 5.12 Standard deviation of particle velocities. D=0.61 m, z=1.55 m, r/R=0.09, Uc=1.12 m/s (DP at z=1.55 m), F C C IV. Chapter 5 Velocity Measurements Ul due to voids become reduced, the extra lift exerted o n particles f rom the Saffman force should decrease. Assuming that the majority o f voids are travelling vertically, the reduction i n the lift force may further promote radial movement o f particles. 5.4.3 Particle velocity and voidage Another set o f data is examined next to interpret the results based on a continuous distribution o f voidage rather than separated into binary phases. F o r consistency, a group number o f 200 was chosen for this analysis o f the data, wi th the probability distribution o f particle velocities measured at superficial gas velocities o f 0.42 and 1.00 m / s i n the 0.61 m diameter column. Figure 5.13 (a) depicts a close-to-symmetrical probability distribution o f particle velocities for U=0.42 m / s . A t U=1.00 m / s , Figure 5.13 (b), the distribution becomes increasingly skewed and asymmetric, especially for die central location. M o r e negative particle velocities were recorded near the wall than i n the core for U=1.00 m / s . B y plott ing the particle velocity against voidage, the change i n two-phase flow dynamics becomes obvious. Figure 5.14 shows that most particle movement is associated wi th denser voidage for the radial positions r /R=0 .94 and 0.50, while the particle dynamics exhibit a near binary voidage region near the centre-most radial position. The lack o f particle movement for s « 0.7 indicates that the distinction between being in a v o i d and in the dense phase is clear, similar to typical vo id characteristics i n bubbl ing fluidized beds. W i t h U increased to 1.00 m / s , Figure 5.15 shows more intermediate voidage data, while particle velocities shift toward more to the positive domain for r /R=0 .09 . This confirms that as the superficial gas velocity is increased to the turbulent fluidized bed flow regime, particles are found over a wide spectrum o f concentrations, i.e., the distinction between the dense and dilute phases becomes increasingly diffuse. Voidage and particle velocity data were also obtained at the higher superficial gas velocity o f 1.56 m / s , though at a different level, z=1.55 m , and the results are shown i n Figure 5.16. There is very little distinction between the structures detected at r /R=0 .50 and 0.09 both for the voidage and particle velocity distributions. E v e n near the wall , the voidage is widely distributed. It is quite noticeable that a significant number o f particle velocities are positive. A further increase in the superficial gas velocity should reveal the local structural change as the transition to the fast fluidization flow regime is approached. Chapter 5 Velocity Measurements 148 r /R=0 .94 r /R=0 .50 • r /R=0.09 -4 -2 0 2 4 Pa r t i c l e ve loc i t y , m / s (a) U=0 .42 m / s 40 o I ' 1 • 1 ' 1 • 1 • 1 1 1 -6 -4 -2 0 2 4 6 Pa r t i c l e ve loc i t y , m / s (b) U=1.00 m / s F i g u r e 5.13 P r o b a b i l i t y d i s t r i b u t i o n o f par t ic le ve loc i t ies for (a) U = 0 . 4 2 m / s , a n d (b) U=1.00 m / s at r a d i a l pos i t i ons o f 0.94, 0.50, a n d 0.09. D=0.61 m , z=0.80 m , F C C I V . Chapter 5 Velocity Measurements 149 0.8 A cu ts. 1 0-7 A > 0.6-1 0.5 A X " • i • • • « • • • ,1 • 8 m m I it o X o -4 -2 0 2 P a r t i c l e v e l o c i t y , m / s o r / R = 0 . 9 4 X- r / R = 0 . 5 0 • r / R = 0 . 0 9 F i g u r e 5.14 Pa r t i c l e ve loc i ty a n d vo idage d i s t r i b u t i o n for U = 0 . 4 2 m / s at r a d i a l pos i t i ons o f 0.94, 0.50, a n d 0.09. D=0.61 m , z=0.80 m , F C C I V . Chapter 5 Velocity Measurements 150 1.0 A 0.9 4 o r / R = 0 . 9 4 r / R = 0 . 5 0 • r / R = 0 . 0 9 1 1 l 1 I 1 l 1 l 1 I 1 1 -6 -4 -2 0 2 4 6 Particle velocity, m/s Figure 5.15 Particle velocity and voidage distribution for U=1.00 m/s at radial positions of 0.94, 0.50, and 0.09. D=0.61 m, z=0.80 m, FCC IV. Chapter 5 Velocity Measurements 151 Figure 5.16 Particle velocity and voidage distribution for 11=1.56 m/s at radial positions of 0.94, 0.50, and 0.09. D=0.61 m, z=1.55 m, FCC IV. Chapter 5 Velocity Measurements 152 5.4.4 Particle velocities in the 0.29m diameter column Veloci ty measurements using the optical fiber velocity probe wi th high-speed data acquisition have been analyzed to obtain the effect o f superficial gas velocity o n the one-climensional particle velocities associated wi th voids and dense phase i n a 0.29 m diameter column. The procedures are described i n Append ix B . For the data set f rom the optical velocity probe used for the 0.29 m diameter column, sampling frequencies o f up to 13,357 H z were acquired for the fiber separation o f 0.18 m m . This means that particle velocities beyond 2.4 m / s could not be captured. A s this may not be sufficient for the conditions under study, only particle velocities primarily associated wi th the dense phase are analyzed in this section. The dense-phase-associated particle velocity distribution is shown i n Figure 5.17 wi th statistical moments calculated in Table 5.3. The mean particle velocity distribution approaches zero with increasing U , while the skewness o f particle velocity distribution decreases, indicating increasing symmetrical distribution o f the probability distribution function. H i g h kurtosis numbers (=3 for Gaussian distribution) may suggest intermittency i n the dense-phase-associated particle velocities. Changes i n the dense-phase-associated particle velocity distribution may indicate a different solids circulation pattern in the fluidized bed. Unfortunately, the data at hand for the 0.29 m diameter co lumn did not allow verification o f the trend beyond U c , around 0.7 m / s . 5.4.5 Void velocities in the 0.29 m diameter column The method described i n Section B.7 i n Append ix B using optical voidage probes was adopted to capture the v o i d velocities i n the 0.29 m diameter column. T h e cut-off method using the threshold value set by M e t h o d (a) i n Section B.6 was used to eliminate fluctuations corresponding to the dense-phase prior to performing the cross-correlation. The group number was set at 300, which for a sampling frequency o f 1,000 H z , represented 0.3 s correlating segments. The distance between the two probes was varied from 0.01 to 0.04 m . Figures 5.18 (a) and (b) portray the v o i d velocity distribution for r / R = 0 . 0 and 0.7. These indicate increasing skewness at the centre posit ion compared to r /R=0 .70 . T h e transition velocity, U c , was determined to be 0.82 m / s from gauge pressure measurements at z=0.65 m. Thus, at a superficial Chapter 5 Velocity Measurements 153 (a) U=0.42 m/s (b) U=0.50 m/s -0.5 0.0 0.5 1.0 Particle velocity, m/ s •1.0 -0.5 0.0 0.5 Particle velocity, m / s (c) U=0.60 m/s (d) U=0.69 m/s Particle velocity, m/s 1.5 -1.0 -0.5 0.0 0.5 1.0 Particle velocity, m/ s Figure 5.17 Distribution of particle velocities associated with dense-phase. D=0.29 m, r/R=0.70, z=0.78 m, H0=1.0 m, FCC I. Chapter 5 Velocity Measurements 154 Table 5.3 Moments of particle velocity distributions. D=0.29 m, z=0.78 m, r/R=0.55, FCC I. Moments U=0.42 m/s U=0.50 m/s U=0.60 m/s U=0.69 m/s Mean 0.06717 -0.009676 -0.01798 -0.02198 Std D e v 0.218 0.207 0.236 0.218 Std E r r M e a n 0.00954 0.00804 0.00538 0.00553 upper 95% Mean 0.0859 0.00610 -0.00742 -0.0111 lower 95% M e a n 0.0484 -0.0255 -0.0285 -0.0328 Sample N u m b e r 520 663 1917 1557 Sum Weights 520 663 1917 1557 Sum 34.9 -6.41 -34.5 -34.2 Variance 0.0474 0.0428 0.0556 0.0476 Skewness 3.24 -1.40 0.554 -0.494 Kurtosis 26.9 22.5 26.1 25.8 Coef. variance 323 -2138 -1311 -993 Chapter 5 Velocity Measurements 155 (a) r/R=0.0 U=0.41 m / s — U=0.60 m / s U = 0 . 6 9 m / s U=0.90 m / s Void velocity, m/s -5 0 5 Void velocity, m/s Figure 5.18 Void velocity distribution for (a) r/R=0.0, and (b) r/R=0.70. D=0.29 m, z=0.78 m, Az=0.02 m, H0=1.5 m, FCC I. Chapter 5 Velocity Measurements 156 gas velocity o f 0.90 m / s , the standard deviation o f pressure fluctuations is on the decrease. The increased number o f occurrences o f negative v o i d velocities, particularly at U=0.90 m / s and r /R=0 .70 , was verified by exarnining the original data and wi th the peak picking method. This, coupled wi th the dense-phase-associated particle velocity distribution i n the previous section, may suggest void- induced downward flow o f solids at r /R=0 .7 . Further analysis can be conducted to study the gas mix ing behaviour, wh ich is not only associated wi th v o i d movement, but is also related to a back-mixing phenomenon. In Figure 5.19, the average v o i d velocity is plotted against the superficial gas velocity for three radial positions. V e r y crudely, the results can be interpreted as showing the average v o i d velocity increasing at r /R=0 .70 , and decreasing near the wal l wi th increasing superficial gas velocity. The vo id velocities are wi t i i in the same range as the findings o f T a x i l et al. (1998) i n a 0.2 m diameter co lumn wi th F C C particles o f 95 um mean diameter. However their study merely mentions downflowing voids " f rom time to time", without indicating any negative velocities i n the reported data. The average v o i d frequency is plotted i n Figure 5.20 against radial posi t ion for four superficial gas velocities. T h o u g h very much threshold-value dependent, the frequencies are similar to those reported by Bayle et al. (2001), Tax i l et al. (1998) and Ege (1995). Ege (1995) indicated v o i d frequencies as high as 20 H z for a 0.3 m diameter co lumn wi th F C C particles o f 65 um mean diameter fluidized at U=0.55 m / s . Bayle et al. (2001) presented v o i d frequencies up to 6 H z at U=0.80 m / s i n a 0.2 m diameter co lumn wi th F C C particles o f 95 um mean diameter. This underlines the strong dependency o f the v o i d frequency on the analysis method. The frequency range indicated i n Figure 5.20 is comparable to the major frequency f rom the differential pressure fluctuation signals reported i n Chapter 6 (Figure 6.3), wh ich provides evidence that the D P signals can capture the v o i d dynamics. 5.5 Conclusions and recommendations Exper imental work has been conducted to capture simultaneous measurements o f local voidage, particle velocity and v o i d velocity in 0.29 and 0.61 m diameter columns for F C C particles, operated i n the bubbl ing and turbulent fluidized bed flow regimes. The results conf i rm previous reports that v o i d movement is erratic and transient in the turbulent fluidized bed. Chapter 5 Velocity Measurements 157 x o > o > cu l-l -8 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 o O o A O A A A A A O 0.4 0.6 0.8 U , m/s 1.0 A r / R = ^0.35 O r / R = •0.70 * r / R = ^0.96 Figure 5.19 Average void velocity. D=0.29m, z=0.78 m, Az=0.02 m, H0=1.5 m, FCC I. 2.0 N E >> o c <u 3 cr o > cu w <U 1.5 A 1.0 0.5 0.0 O o o # • • • o • U=0.50 m / s U=0.69 m / s U=0.81 m / s o U=0.90 m / s 0.0 0.2 0.4 0.6 0.8 1.0 r / R Figure 5.20 Radial distribution of average void frequency. D=0.29m, z=0.78 m, Az=0.02 m, H0=1.5 m, U c (z=1.16 m, AP)=0.85 m/s, FCC I. Chapter 5 Velocity Measurements 158 Particle velocity • The void-associated particle velocity distribution shifted to higher velocities wi th increasing height, as wel l as wi th increasing superficial gas velocity. • The average particle velocity associated wi th voids increased monotonical ly wi th increasing superficial gas velocity, while that associated wi th the dense-phase only started to increase beyond U c . • The standard deviation o f particle velocity fluctuations for dense-phase associated particle velocities increased slighdy beyond U c . • The relationship between simultaneously measured particle velocities and voidages indicated a change i n the local two-phase flow structure when the superficial gas velocity exceeded U c . • Radial variations o f voidage and void-associated particle velocity indicate a core/annulus structure at the highest superficial gas velocity examined (i.e., 1.56 m/s ) . Void velocity • Considerable scatter in the v o i d velocity was detected for both the bubbl ing and turbulent fluidization flow regimes. • The v o i d frequency range corresponded closely wi th the major frequencies f rom a frequency analysis o f D P signals (in Chapter 6). • The v o i d velocity distribution became wider as the superficial gas velocity increased. The effect o f solids flux from the return leg was found to be significant w i th respect to the hydrodynamics o f the bed, especially for a larger co lumn at higher solids net mass fluxes. The major drawback to the current velocity measurement system is the l imitat ion o f obtaining only a one-dimensional velocity due to having two receiving fibers. The assumption o f measuring a known flow direction i n a turbulent fluidized bed may not be justified i n certain positions i n the dense bed, such as those close to the solids return leg. B y applying an optical probe like the one reported by Tayebi et al. (1999) (seven-fiber probe), it wou ld be possible to deduce the max imum cross-correlation for the two-dimensional flow. However , such a probe w o u l d inevitably be more intrusive and therefore perturb the flow more than a two-fiber probe. The present work is significant as it provides important experimental evidence regarding the dynamic nature o f the flow structure. Chapter 5 Velocity Measurements 159 Further studies • Acquis i t ion o f additional data on particle and vo id velocities f rom different co lumn diameters wou ld enhance the knowledge o f the effect o f co lumn size o n the velocity distribution. In particular, the effect o f scale on the chord length o f voids w o u l d provide insight into the size o f voids i n the turbulent fluidization flow regime where bubble diameter correlations are no longer valid. • Simultaneous measurement o f v o i d velocities at two axial locations can reveal v o i d growth and coalescence wi th varying superficial gas velocity. • The design and fabrication o f an optical probe capable o f simultaneously measuring particle and v o i d velocities, and voidage, wou ld lead to experimental data that could advance understanding o f how particle velocities are affected by v o i d dynamics. • Compar i son o f results obtained from vo id velocity measurements and a simultaneous gas mix ing study wou ld be helpful i n interpreting data. • A computer program should be written to detect the passing o f voids and to cross-correlate the signals according to the group number reflective o f each vo id . • A d d i t i o n o f fluorescent F C C particles to the bed o f regular F C C particles w i l l 'tag' some particles wi th in the system. The unique reflective properties w i l l help validate the particle velocity measurements. • Tracking the particle velocity at the top o f the expanded bed should enable the change in particle momen tum and flow structure to be studied, especially near the transition from the turbulent to the fast fluidization flow regimes. • Radial particle transport mostly depends on particle-particle collisions and particle acceleration due to eddy and particle interactions. I f the configuration o f the optical velocity probe could be such that the radial particle velocity can be measured without disturbing the particle flow, vi tal information could be obtained on the radial solids flux. This may be accomplished by simultaneously measuring the voidage to cUscriminate single particles hitting the probe and changing directions from particles in the dense phase mov ing radially as a result o f momentum exchange. CHAPTER 6 SIGNAL ANALYSES AND INTERPRETATION 6.1 Introduction The complex hydrodynamics o f multiphase flows cannot be represented by time- or volume-averaged parameters alone for the design and scale-up o f such systems (Mudde et a l , 1997). Various statistical analysis methods have been employed, as demonstrated i n Chapters 2 through 5. In this chapter, the linear analysis techniques such as frequency (FFT) , cross-correlation, and autocorrelation analyses, as wel l as nonlinear analysis techniques including chaos analysis, are applied to gain further insight into the nature o f the flow structure, and to extract dynamically meaningful information. 6.2 Frequency analysis of pressure fluctuations in fluidized beds Pressure fluctuations in gas-solid fluidized beds have often been investigated owing to their relative ease o f measurement, even under challenging industrial conditions. Pressure measurements can be used to infer stability, quality o f fluidization, flow structure and regime transitions (e.g. Trnka et a l , 2000). Pressure signals reflect complex phenomena, including effects o f absolute pressure, temperature, gas turbulence, and the formation, coalescence and eruption o f voids. T ime , frequency, and state-space analyses o f such measurements have been interpreted i n terms o f both macro-flow and detailed structures o f gas and solids flow (Johnsson et a l , 2000). It is commonly held that a fundamental frequency exists for a fluidized bed o f given geometry, particle and fluid properties, and flow conditions. However , the origin o f the pressure fluctuations requires further inquiry. O n e o f the strong associations between pressure fluctuations and the behaviour inside a fluidized bed at low gas velocities is the movement o f bubbles. Thei r eruptions at the surface o f the bed instigate pressure waves wh ich propagate throughout the bed. Fan et al. (1984) suggested that the frequency o f pressure fluctuations is affected by the mean bubble residence time, average windbox pressure, p lenum volume, co lumn cross-sectional area, and bed mass, indicating that the bed surface is not the only source o f fluctuations. A s reviewed by M'ch i rgu i et al. (1997), studies show that the fundamental frequency i n a fluidized bed is strongly affected by the static bed height (e.g. V e i i o o p and Heertijes, 1974; Baskakov et a l , 1986). Analysis o f pressure 160 Chapter 6 Signal Analyses and Interpretation 161 signals from a fluidized bed at m i n i m u m fluidization has shown distinct pressure waves, propagating upwards and downwards, originating from bubble formation and from bubble eruptions at the bed surface (van der Schaaf et al., 1998). Kage et al. (2000) identified three principal frequencies from the power spectra o f pressure signals i n a p lenum chamber corresponding to the natural frequency o f the fluidized bed, the bubble eruption frequency and the bubble generation frequency. The latter two were confirmed from local voidages, determined by an optical probe, and visualization o f bubble eruption by a video camera. However , their study was restricted to the bubbl ing fluidization regime. The macroscopic behaviour o f a fluidized bed inferred from pressure measurements has been elucidated by local measurements. Simultaneous measurements o f gauge pressure and voidage using an optical probe ( X u et al., 1998) indicated that the pressure waves did not correspond to the heterogeneous flow structure. B i et al. (1995) reported that gauge pressure measurements tend to reflect more macroscopic behaviour o f fluidized beds, whereas differential pressure measurements, wi th the separation distance between the two ports o f the order o f a few centimetres, are able to differentiate between the dense and dilute phase behaviour. E v e n wi th closely spaced differential pressure probes, the information from pressure probes differed f rom that corresponding to local optical fibre probes measurements. In the turbulent fluidization regime, pressure fluctuations are commonly employed to delineate a transition velocity, U c , at wh ich the standard deviation attains a max imum. This is commonly taken to indicate the onset o f the turbulent fluidization flow regime. U c has been reported to be influenced not only by the fluid and particle properties, but also by co lumn geometry, static bed height and the location o f the measurements (Cai, 1989; D u n h a m et al., 1993; B i and Grace, 1995). Reported values o f U c tend to be empirical and geometry-specific. Industrial fluidized beds often operate at gas velocities corresponding to the turbulent fluidization flow regime. M o n i t o r i n g fluidization quality in commercial scale units using pressure measurements can be a convenient method o f ensuring excellent contacting between the gas and solids. It is crucial to ensure that the natural frequency o f the structure differs appreciably from the major frequency range o f the bed, for vibrations tend to be increasingly significant as units are scaled-up (Pell, 1990). Thus, understanding the source and propagation o f pressure waves and the fundamental frequency o f a given unit is crucial, especially for scale-up. Chapter 6 Signal Analyses and Interpretation 162 In order to further investigate the origin o f these fluctuations and their effect o n scale-up, turbulent fluidization experiments were conducted i n this work i n four different columns. T h e macroscopic behaviour o f the fluidized beds mferred from the pressure waves is compared below to local measurements obtained using optical fibre probes. 6.2.1 Fourier transform The Fast Fourier Transform, F F T , transforms rime domain functions into frequency domain representations. A l t h o u g h this is a well-established method o f analysis i n engineering (Chatfield, 1996), the transform is briefly reviewed i n Append ix C i n order to highlight the difference between the Fourier transform and the wavelet transform discussed in the next chapter. 6.2.2 Experimental data analysis In order to examine the pressure waves i n a turbulent fluidized bed, simultaneous pressure signals were recorded at 8 different vertically aligned locations, the windbox and across the distributor plate o f the 0.29 m diameter column. Ampl i tude spectra o f gauge and differential pressure signals obtained by F F T analysis from vertically aligned pressure probes are shown i n Figure 6.1 for a superficial gas velocity o f 0.65 m / s . The following criteria were used: • Frequencies less than 0.5 H z are taken as the leakage o f the Fast Fourier transformation depending on the window function; therefore, peaks below 0.5 H z are ignored. • Since the typical frequency range o f interest in fluidized beds is 0-10 H z , frequencies above 10 H z are not considered. • T h e combined results o f differential pressure, D P , and gauge pressure, A P , signals enable peaks related to predominantly global phenomena to be differentiated f rom those reflecting local voids. The amplitude o f the strong peak present throughout the bed (and even i n the windbox) i n the spectra o f gauge pressure signal remains relatively constant suggesting global pulsations resulting from particle oscillations. The recurrent peaks o f gauge pressure signals i n Figure 6.1 indicated by " n " provide die experimentally determined fn. This "natural frequency," characteristic o f global dense phase movement, has been predicted by Ver loop and Heertjes (1974) based on a balance o f frictional and gravitational forces i n gas-solid fluidized beds as: ( 1 _ e ) ( e P - e j g ( 2 - e ) ( f - ^ p +eef. H e (6.1) Chapter 6 Signal Analyses and Interpretation 0.10 163 0.00 0.10 % 0.08 % 0.06 —^» % 0.04 ^ 0.02 0.00 0.10 — 3 OH £ < 0.08 0.06 0.04 0.02 z=0.591 m Az=0.128m 0.00 0.10 £ 0.08 z=0.432 m Az=0.064 m 0.08 0.00 0 z=0.336 m windbox absolute pressure fluctuation 2 4 6 8 10 Frequency, Hz 2 4 6 8 Frequency, Hz 10 (a) DP signals (b) AP signals Figure 6.1 Power spectral density functions of pressure fluctuations. U=0.65 m/s, H=l. l m, r/R=l, FCC I. (n identifies recurrent "natural frequency") Chapter 6 Signal Analyses and Interpretation 164 wh ich can be simpKfied for o p » o f to f n = y / g ( 2 - e ) / H e 12%. Figure 6.2 summarizes the effect o f expanded bed height on the observed natural frequency from gauge pressure signals. The predicted fn f rom Equat ion 6.1 gives better predictions with increasing bed height. The amplitude o f the power spectral density function from differential pressure fluctuations confirms that vigorous fluctuations in the windbox are largely filtered out, wi th D P signals then reflecting local phenomena between the two ports. The broadband peak at around 3.2 H z increases in intensity and shifts towards 2.8 H z before diminishing beyond 1.10 m above the distributor plate. The frequency o f the major peak from the D P signals, f D P , can be attributed mainly to voids wh ich coalesce mov ing upward, thus exhibiting decreased f D P and increasing intensity. Gauge pressure signals support this trend, wi th the intensity o f peaks increasing wi th height. The eruption o f voids at the top o f the bed is difficult to identify owing to the diffuse bed surface i n a turbulent fluidized bed. Further frequency analysis o f D P signals using an F F T smoothing function was pursued to study the effect o f U on f D P in Figure 6.3. This confirms the v o i d growth wi th increasing height for U < U c . Beyond U c , the fluidized bed becomes increasingly homogeneous, while f D P continues to decrease. A similar trend was observed by Tax i l et al. (2000) where the dominant frequency from D P signals continued to decrease far beyond U c . The f D P peaks for the 0.61 and 1.56 m diameter columns were increasingly clear, especially for deeper beds, probably due to larger voids under these conditions. A s portrayed i n Figure 6.4, the same trend o f decreasing f D P as U approaches U c is present; however, f D P reaches a plateau around U c , possibly because o f the competing phenomena o f v o i d growth and splitting. The major frequencies from D P signals i n columns o f different diameter are compared i n Figure 6.5 in terms o f the Strouhal number, Sr, based on expanded bed height and U c , versus the Froude number, based on superficial gas velocity and co lumn diameter. P lot t ing i n this manner yields a good correlation wi th other data reported in the turbulent flow regime. T h e data indicate that f D P increases wi th decreasing gas velocity and wi th increasing co lumn diameter for U > U c . 6.2.3 Crossing frequency In order to conf i rm the source o f the fluctuations observed i n the F F T spectra, the dynamic behaviour o f local voids was also captured using optical fibre probes. Probabil i ty distribution curves Chapter 6 Signal Analyses and Interpretation 165 • This work A Verloop & Heertjes (1974) H , m Figure 6.2 Effect of expanded bed height on natural frequency from AP signals with comparison to calculated values based on Equation 6.1. D=0.29m, FCC I. 44 34 c Q 14 o ^ m ° m o o U =0.73 m/s c \ o 1 1 0.2 0.4 0.6 0.8 1.0 * z=0.305 m o z=0.845 m U , m/s Figure 6.3 Effect of superficial gas velocity on major frequency from DP signals. D=0.29 m, H 0 =l. l m, FCC I. Chapter 6 Signal Analyses and Interpretation 3.5 -i 1 3.0 A 2.5 2.0 O A O O u , o A z=1.8 m , r / R = 0 . 0 O 2=0.84 m, r /R=0 .31 —i 1 1 1 1 1 ' 1 ' 1 <— 0.2 0.3 0.4 0.5 0.6 0.7 0.8 U , m/s Figure 6.4 Variation of dominant frequency, fDP, with superficial gas velocity. D=1.56 m, H0=2.2 m. This work (D=1.56 m) This w o r k (D=0.61 m) This w o r k (D=0.286 m)) T a x i l et al. (2000) (D=0.19 m) Bat et al. (1999) (D=0.102 m) 0.2 0.4 0.6 0.8 Froude number, Ft = V/^gD Figure 6.5 Strouhal number vs. Froude number correlation for U > U c , FCC. Chapter 6 Signal Analyses and Interpretation 167 o f the voidage at given conditions reveal b imodal distributions, even for gas velocities wel l beyond U c . It is difficult, however, to distinguish between small frequent voids and large sparse voids from a cumulative function. Therefore, the data were analyzed in terms o f a crossing frequency, i.e., the number o f times the signal passes through a threshold value over a given time, expressed as: (number o f crossings) / 2 f c =" : : ( 6 - 2 ) duration o f time series The threshold value for counting was set to give the max imum number o f crossings, which corresponds to the threshold value setting o f method (d) i n Figure B.9 i n Append ix B. Figure 6.6 plots radial profiles o f both the average local voidage and the average crossing frequency from Equat ion 6.2 at two levels. The average crossing frequency remains similar when v o i d activity is dominant, i.e., for 0 < r / R < 0.6, z=0.40 and 0.78 m , implying that flow is fully developed and that any excess gas is carried by the dense phase, as indicated by the increase in average voidage. Higher fc towards the wal l indicates frequent signal fluctuations in the dense phase. T h e effect o f U on the crossing frequency i n comparison wi th f D P i n Figure 6.3 is shown for the 0.29 m co lumn i n Figure 6.7. The overall trend o f fc resembles that o f the f D P wi th respect to U . Moreover , fc is o f the same order o f magnitude as f D P for measurement intervals o f 0.1 m or less. T h e discrepancy between fc and f D P is due to fc being a localized measurement, and cannot be fully integrated to be compared to f D P at the wall . The latter is considered to reflect the cross-sectional v o i d activities. Use o f two traversing probe arms i n the 1.56 m diameter co lumn (see Chapter 2) allowed pressures and voidages to be measured simultaneously at various radial positions. T h e crossing frequency from optical probe measurements showed a decrease i n fc wi th increasing U , imply ing larger voids as U approached U c . Further investigation is required to determine v o i d dimensions directiy in confirming the breakdown o f voids while maintaining high gas throughput for U > U c . 6.2.4 Sensitivity of threshold value to crossing frequency Further investigation into the crossing frequency revealed the sensitivity o f the resulting crossing frequency to the threshold value. Taking the threshold value as the time-mean voidage, the crossing frequency was calculated as shown in Figure 6.8, where the radial variations o f crossing frequency indicate a more profound influence o f U , compared to Figure 6.6. Furthermore, the trend o f crossing frequency wi th increasing U at the co lumn centre shown in Figure 6.9, indicates a reversal o f the trend compared to the dominant frequency deduced from DP, shown i n Figure 6.3. The sensitivity to the threshold value is caused mainly by the signal repeatedly crossing the threshold value. Thus, it may not necessarily pick up the dominant frequency present i n the signal. Chapter 6 Signal Analyses and Interpretation 0.75 O z=0.40 m —•—^ z=0.40 m A z=0.78 m —A—/ z=0.78 m £ 0.65-1 0.504 0.45 -r 0.0 0.2 0.4 0.6 r / R 10 CO 0.8 1.0 168 Figure 6.6 Radial profiles of voidage and crossing frequency. D=0.29 m, H 0 =l . l m, U=0.70 m/s, FCC I. 8 t/3 6 - 1 ^ 4 2\ 0 X X X z=0.46 m O z=0.78 m • z=0.91 m o o T CX a 0 . 2 0 . 4 0 . 6 U , m / s 0 . 8 1 . 0 Figure 6.7 Effect of superficial gas velocity and height on crossing frequency. D=0.29 m, H 0 =l . l m, Uc=0.68-0.73 m/s, r/R=0.0, FCC I. Chapter 6 Signal Analyses and Interpretation 10 169 N X 7 6-5-— i > 1 • 1 1 1 ' 1 • 1— 0.0 0.2 0.4 0.6 0.8 1.0 r / R —•-- U=0.40 m / s o U=0.71 m / s A U=0.90 m / s Figure 6.8 Radial profiles at different superficial gas velocities of crossing frequency calculated from threshold value of time-mean voidage. D=0.29 m, H 0 =l . l m, z=0.78 m, FCC I. 8 N X 44. o o n o o o 0.2 0.4 0.8 1.0 0.6 U , m/s Figure 6.9 Effect of superficial gas velocity on crossing frequency calculated from threshold value of time-mean voidage. D=0.29 m, H 0 =l . l m, z=0.78 m, r/R=0.0, FCC I. Chapter 6 Signal Analyses and Interpretation 170 Crossing frequencies wi th two different threshold values have been sought and compared with the dominant frequencies deduced from D P . The sensitivity o f the threshold value to the crossing frequency causes ambiguity i n the analysis. Thus, evidence o f the origin o f f D P f rom F F T is further pursued through analysis o f voidage signals wi th respect to the cycle time i n Section 6.6. 6.2.5 Effect of air-feed system O n e o f the main concerns raised in assigning peaks from the frequency analysis o f pressure fluctuations is the origin o f the fluctuations. A s i n previous sections, pressure measurements i n fluidized beds reflect natural oscillation o f the bed as wel l as b u b b l e / v o i d dynamics. The air-feed system may also be important, affecting the boundary conditions for numerical model l ing (Johnsson et a l , 2002). Roots blowers, i n particular, have been reported to be a source o f pressure fluctuations (Dhodapkar and K l i n z i n g , 1993). F o r example, Chyang and L i n (2002) found that the characteristic frequency resulting from a Roots blower was comparable to the simultaneous pressure measurements in 0.29 and 0.10 m diameter fluidization columns. The existence o f this characteristic frequency was confirmed to be independent o f the static bed height and windbox volume, and to be a function o f the blower impeller speed. The influence o f the pressure pulsations became less significant wi th increasing superficial gas velocity, possibly due to an increased pressure drop across the distributor plate. In most reported cases o f laboratory-scale fluidized beds attached to in-house pressurized air systems, the effect o f air-feed system may not be significant (Johnsson et a l , 2002). However , i n industrial-scale fluidized beds, the entire air-feed system may contribute to the transient effects o f pressure and flow fluctuations. 6.2.5.1 Experimental investigation of dominant frequency from air-feed system Simultaneous pressure fluctuations i n the windbox, across the distributor plate, and at the bot tom o f the bed were measured for F F T analysis in a 0.29 m diameter co lumn wi th a static bed height o f 1.5 m. The peaks in Figure 6.10 (b) and (c) at around 13.5 H z are for data obtained in the windbox and at the distributor plate. The signal at the frequency o f 13.5 H z was only present i n the windbox. A s the blower impeller speed is fixed and the gas flow rate is controlled by the by-pass line, the peak corresponding to the blower should remain constant. Moreover , by using the fluidizing gas from the compressed bui lding air supply, the peak at 13.5 H z was not observed from fluidizing at U=0.19 m / s . It was concluded that the peak at 13.5 H z was due to the air-feed system. M o r e importantiy, the frequency o f the air-feed system did not interfere wi th the frequency range o f interest for bed dynamics. Chapter 6 Signal Analyses and Interpretation 171 0.020 0.000 5 10 Frequency, Hz Figure 6.10 Fast Fourier Transform of pressure fluctuations: (a) AP at z=0.15 m; (b) DP across grid; (c) AP in windbox. D=0.29 m, H0=1.5 m, U=0.19 m/s. Chapter 6 Signal Analyses and Interpretation 172 6.3 Cross-correlation function F r o m bivariate time series, cross-correlation coefficients can provide empirical indications o f possible relationships between the variables. The cross-correlation coefficient function is defined as: Q i ("0 C . , . 2 = , 1 2 (6-3) V C I , ( ° ) C I 2 ( 0 ) which satisfies, for all T, - i<e n <i (6.4) 1 2 C] i is the covariance functions at arbitrary fixed values o f t =t and t 2 = t +T, defined by: C I ) l 2 = E [ ( x ( t > - x w ) ( y ( t + x ) - y ( t + T) ) ] (6.5) E [ ] represents the expected value over the index t and t+T. A typical cross-correlation function is shown i n Figure 6.11. The value o f X at wh ich o, j is a m a x i m u m represents the lag between the two signals. In Chapter 5, the same analysis method was applied to obtain the time shift to calculate the velocity at wh ich particles or voids passed the tip o f two optical fibers. T h e value o f p x y measures the linear dependence between two signals for a displacement o f T i n signal 2 relative to signal 1. A t T=0, p x y represents the correlation coefficient. The correlation function coefficient is calculated for local voidage signals obtained from optical voidage probes. However , it must be noted that the cross-correlation function fails when the linearity assumption is not val id (Bendat and Piersol, 1971). 6.3.1 Correlation function coefficient of voidage signal A Plexiglas plate wi th 10 equally spaced 4 m m holes was mounted o n the exterior o f the co lumn 0.77 m above the distributor plate. This allowed two identical optical voidage probes to be inserted into the co lumn a k n o w n distance apart. The multi-fiber probes are capable o f capturing the reflected light intensity from swarms o f particles. The correlation w i l l be stronger i f the scale length o f the measurements matches the size o f voids. Thus, the cross-correlation function is a function o f the probe distance, v o i d velocity, sampling frequency, and size o f voids. T h e distance between the two probes was varied from 10 to 50 m m i n 10 m m increments. Intuitively, voids o f chord length close to or larger than the separation distance o f the probes should give higher cross-correlations. A s shown i n Figure 6.12, most maxima o f cross-correlation function indicate higher values for smaller probe separation distance. F o r a separation distance o f 0.01 m , the highest correlation occurs near U=0.7 m / s , wh ich is close to U c obtained though gauge pressure signals. A s the separation distance Chapter 6 Signal Analyses and Interpretation 173 0.0 1.0x10 2.0x10' x, sec 3.0x10 Figure 6.11 Cross-correlation function of optical voidage probe signals. D=0.29 m, H0=1.5 m, distance between probes=0.01 m, r/R=0.70, U=0.90 m/s, FCC I. 0.9 0.8 A 0.7 A 0.6 0.5 A • A °A cf O • O • • A O A • © A Az= 0.01 m O Az= :0.03 m Az= •0.04 m • Az= ^0.05 m 0.4 0.6 0.8 1.0 U , m/s Figure 6.12 Variation of correlation function coefficients with superficial gas velocity. D=0.29 m, H0=1.5 m, r/R=0.35, Uc=0.75 m/s , H0=1.5 m, z l o w e r p r o b e =0.77 m, FCC I. Chapter 6 Signal Analyses and Interpretation 174 increased, the max imum occurred at different gas velocities. However , owing to the scatter, definite trends are difficult to identify. Figure 6.13 (a) and (b) represent cross-correlation function coefficients for U=0.40 and 0.90 m / s , respectively. The high correlation coefficients indicate the coherence between the probe distance and the size o f voids. However , owing to the l imited and fixed distances between the probes, this method is considered to be disadvantageous in deducing the length scale o f voids. The increased scatter o f the cross-correlation function coefficient for the shortest distance i n the bubbl ing regime (Figure 6.13 (a)) may suggest that the probe interferes with the flow. 6.4. Autocorrelation The autocorrelation function o f random data relates the influence o f values at any time to values at a future time (Bendat and Piersol , 1971). It is useful i n detecting non-randomness i n data, and to identify an appropriate time series mode l for periodic signals (Box and Jenkins, 1976). A n y deterministic data w i l l have an auto-correlation function that persists over all time displacements, as opposed to random data, whose auto-correlation function approaches zero over large time displacements. The function is defined as: 1 N-T Z X , X i + T y^=^w ( 6- 6) Ni=i i f it is calculated directly, or it may be calculated by the inverse transform following F F transformation o f signal. This function has been applied to various fluidized bed systems to assess the quality or to detect the deterministic nature o f the data, wh ich might be masked i n a random background (Saxena and Waghmare, 2000; Johnsson et a l , 2000). The characteristic shape o f the autocorrelation function for a purely random process fluctuates randomly about zero indicating that the process at any instant has no 'memory ' o f the past (Tsonis, 1992). A chaotic system can be characterized by a characteristic time, T c , wh i ch signifies the time over wh ich the system retains previous information. This particular statistical method was applied to voidage measurements f rom optical probes. A s shown i n Figure 6.14, the autocorrelation function rapidly decays wi th lag time, 1, and oscillates Chapter 6 Signal Analyses and Interpretation 175 1.0 0.8 0.4 0.2 • • o A • O • 0.01 0.02 0.03 Az, m 0.04 0.05 (a) A r/R= =0.0 O r/R= =0.35 r/R= =0.70 (b) • r/R= =0.0 o r/R= =0.35 * r/R= =0.70 Figure 6.13 Effect of optical probe separation distance on cross-correlation function coefficient, (a) U=0.40 m/s; (b) U=0.90 m/s. D=0.29 m, H0=1.5 m, z l o w c r p r o b e =0.77 m, FCC I. Chapter 6 Signal Analyses and Interpretation 176 about zero implying a random signal. The radial profile o f the characteristic time o f autocorrelation function, xc, is illustrated i n Figure 6.15 for U=0.9 m / s at axial heights o f 0.40 and 0.78 m above the distributor. Since the signal strongly reflects the v o i d dynamics, the lower the value o f xc, i.e., the faster the autocorrelation function decays, implies higher intensity o f v o i d mot ion . The simultaneous measurement o f the two signals allows the change i n v o i d mo t ion intensity wi th height to be determined. The similarity i n T c for the outer region o f 0.5 < r / R < 1.0 suggests less change i n vo id dynamics compared to the core region. Furthermore, the radial profile o f the time-mean voidage shown i n Figure 6.16 indicates very little change i n voidage between z=0.40 m and z=0.78 m. This suggests coalescence o f voids between the two axial positions i n the core region. In fact, the standard deviation o f D P at these two levels indicates an increasing trend, suggesting U < U c . ; U c is measured at 0.73 m / s at z=0.85 m from gauge pressure fluctuations. The effect o f U on T c , shown in Figure 6.17, indicates considerable scatter for measurements at the higher level. This may reflect the complex dynamics o f v o i d coalescence and splitting at higher posit ion. The decrease i n xc at the lower posit ion implies increased intensity o f the v o i d mot ion wi th increasing superficial gas velocity. The underlying assumption o f the autocorrelation function is that there is a linear functional relationship between the data points. The autocorrelation function may not be appropriate for signals produced by nonlinear systems (Karamavruc and Clark, 1997). Thus , the purpose o f applying the autocorrelation function w i l l be to assess the deterministic nature o f voidage fluctuations. 6.5 Coherence structure and characterization Turbulence leads to the presence o f localized coherent structures, i.e., organized patterns containing most o f the energy. The coherence according to Rob inson (1991), is i n general terms defined as: "a three-dimensional region o f the flow over wh ich at least one fundamental flow variable (velocity component,- density, temperature, etc.) exhibits significant correlation wi th itself or wi th another variable over a range o f space and /o r time that is significantly larger than the smallest local scales o f the flow". Turbulent signals i n the context o f component analysis and pattern recognition for the study o f turbulent coherent motions have been characterized through a variety o f statistical analysis tools, such as auto- and cross-correlation coefficients, and spectra and coherence functions. However , the capability o f the statistical approaches to deduce dynamic and quantitative information about the turbulent flow structure is questionable (Ferre and Giral t , 1993; Kev lahan et al., 1993), due to the necessity to distinguish between global and local self-similarities i n characterizing coherent Chapter 6 Signal Analyses and Interpretation 1.0-n 177 0.8-0.6-0.4-X, s Figure 6.14 Autocorrelation function of voidage signal. D=0.29 m, U=0.90 m/s, z=0.78 m, r/R=0.0, H 0 =l . l m, FCC I. Figure 6.15 Radial profile of characteristic time of autocorrelation function from voidage measurements. D=0.29 m, U=0.90 m/s, H 0 =l . l m, FCC I. Chapter 6 Signal Analyses and Interpretation 178 H § 0.65 A o > c cu - A — 2=0.40 m -O—2=0.78 m Figure 6.16 Radial profile of time-mean voidage for data presented in Figure 6.15. D=0.29 m, U=0.90 m/s, H 0 =l . l m, FCC I. 44 34 ^ 24 A A A A A A 0.2 0.4 0.6 U , m / s 0.8 A 2=0.40 m * 2=0.78 m 1.0 Figure 6.17 Effect of U on Tc. r/R=0.0, D=0.29 m, H 0 =l . l m, FCC I. Chapter 6 Signal Analyses and Interpretation 179 structures. Furthermore, the analysis tool must be able to characterize quasi-periodic repeating patterns o f the coherent mot ion i n the flow (Robinson, 1991). F o r single-phase flow, coherent mot ion has been described as a burst-sweep process where the violent outward ejections o f low-speed fluid are followed by the rapid mrushing sweeps o f high-speed fluid ( M c C o m b , 1990). Mul t ip le bursts occurs per sweep o f fluid velocity o f 30-60 times that o f mean flow velocity. A s a result, the coherence mot ion is reported to be responsible for most turbulence product ion i n the near-wall region and for increased drag and mixing. Recent experimental and numerical investigations show that this bursting process is more intermittent i n space than i n time (Robinson, 1991). A recent summary by V a n D e n A k k a r (1998) portrays coherent structures i n multiphase systems. These may originate from the slip velocity created from the density difference between the two phases, or the shear over no-slip walls. Regardless o f the origin, the local turbulence and vorticity levels may intensify as a result o f local differences i n mixture density. T h e resulting flow regimes wi th typical phase re-distributions are a consequence o f energetically favourable structures i n multiphase flows. The interactions o f particles and coherent structures in a turbulent boundary layer were summarized by Hetsroni (1989), albeit only for very dilute cases. Coherent structures i n bubble columns have been investigated through particle image velocity measurements (e.g. Tzeng et al., 1993, C h e n et al., 1994) and through Laser-Doppler Velocimetry (Groen et al., 1996; Mudde , et al., 1997). In a recent review, Joshi et al. (2002) attributed the increased number o f publications dealing wi th the dynamics o f bubble columns using C F D to progress i n computational power fuelling further understanding o f circulation cells and coherent structures. Perhaps due to the difficulty in making velocity measurements i n dense-phase gas-solid fluidized beds, the analysis f rom the viewpoint o f turbulent fluctuations or vort ical structures has not been as c o m m o n as for gas-liquid bubble columns. Transient wave-like flow patterns were reported through image analysis o f a two-dimensional circulating fluidized bed by K o n o et al. (1999), without any quantitative analysis. The coherence function defined as: y',(f) = | G " ( f ) | 2 S I ( M ' G I I ( f ) G „ ( f ) (Bendat and Piersol , 1971) was applied for regime identification by V i a l et al. (2001) and Letzel et al. (1997) i n bubble columns and airlift reactors, and by C a i et al. (1990) i n a gas-solid turbulent Chapter 6 Signal Analyses and Interpretation 180 fluidized bed. The ratio o f the auto power spectral density and cross power spectral density in the frequency domain characterizes the coherence between two signals reflecting the instantaneous flow structure: the ratio is then 1 for totally analogous signals at a given frequency; and 0 for signals being completely different. Moreover , the ratio is a measure o f linearity between two related signals (Bendat and Piersol , 1971). In order to characterize the flow structure at a given gas flow rate, Ca i et al. (1990) arbitrarily proposed the average coherence function as: Y j = 7 -V i^y( f )d f (6.8) with f and f2 as 0 and 10 H z , respectively. A s shown i n Figure 6.18, the average coherence function exhibited a peak close to U c , determined by the max imum standard deviation f rom gauge pressure fluctuations, when plotted against the superficial gas velocity. The trend i n the average coherence function between A and B is attributed to enhanced bubble variations wi th increasing gas velocity. W i t h the increase i n standard deviation for this sub-region, the dominant bubble mechanism is coalescence. Once into the sub-region between B and C , it was explained that the bubble size was o f the same order o f magnitude as the probe separation distance, i n this case 0.1 m . This is called the transition region where signal similarity improves without much variation i n pressure fluctuations. Po in t C was found to be insensitive to port separation distances up to 0.3 m . Further increasing the superficial gas velocity decreases the average coherence function represented i n the C - D sub-region. The variation o f bubbles is enhanced, represented by the decrease in coherence function. A s well , bubble break-up becomes predominant as indicated by the decrease i n standard deviation o f pressure fluctuations. A s examined i n Section 6.2, major frequencies from gauge pressure signals are always below 10 H z for gas-solid fluidized beds. Thus, the average coherence function calculated between 0 and 10 H z covers almost all o f the phenomena reflected by pressure fluctuation. However , by using gauge pressure to calculate the coherence function, one picks up not only frequencies reflecting vo id movements, but also global pulsations o f the bed and other local and non-local phenomena within the bed (see, for example, Figure 6.1 (b)). Ano the r aspect for consideration is the probe separation distance. C a i et al. (1990) claimed to have observed the same trend as i n Figure 6.18 for separation distances up to 0.3 m. The length scale o f coherent structure may change considerably and rapidly once i n the turbulent flow regime. The initial decrease i n average coherence function may represent this change i n length scale; however, it becomes difficult to assess i f the decreasing trend is due to a change in v o i d characteristics, or to a change in global circulation frequency. Despite these Chapter 6 Signal Analyses and Interpretation 181 0.0 0.2 0.4 0.6 0.8 1.0 U, m/ s Figure 6.18 Coherence function and standard deviation vs. superficial gas velocity. (Adapted 'from Cai et al., 1990; D=0.139 m, dp=:280 um, probe separation distance=0.1 m) Chapter 6 Signal Analyses and Interpretation 182 comments, the coherence function appears to be promising in identifying and characterizing the coherence structure i n turbulent fluidized beds. Moreover , the three main types o f statistical functions in expressing the joint properties o f two signals are: joint probability density function; cross-correlation functions; and cross-spectral density functions, p rovid ing information regarding the joint properties in the amplitude, time and frequency domains, respectively. A s indicated in Section 6.3, dynamic phenomena i n fluidized beds exhibit frequency dependency through pressure signals, making cross-correlation unsuitable (Bendat and Piersol , 1971). Thus , the coherence function based on power spectral and cross-spectral density functions seems to be a viable choice, and is pursued further. Ano the r approach has been taken to express the coherence related to the power spectral density function from bivariate pressure fluctuation measurements. The coherent-output power spectral density ( C O P ) and incoherent-output power spectral density (IOP) are defined (van der Schaaf et al., 1998; van der Schaaf, 2002) as: C O P ( f ) = Y ^ y O y y (6.9) I O P ( f ) = ( l-^ y)o y y (6.10) where O represents the power spectral density o f time series measured at posi t ion y. The above definitions distinguish the power spectral density from fast pressure fluctuations, C O P , from that due to gas bubbles or turbulence, I O P . F r o m the standard deviation o f I O P , the characteristic bubble scale was calculated i n a bubbl ing fluidized bed, while that for voidage i n the dense bed region o f the circulating fluidized bed rise was estimated from the pressure signal. T h e power-law fall-off i n the I O P characterizes the gas bubble dynamics. The I O P was applied to gauge pressure measurements from the turbulent fluidized bed o f diameter 0.29 m in Figure 6.19 for U=0.33 and 0.87 m / s . Based on van der Schaaf (2002), the standard deviation o f I O P is correlated to the average bubble diameter: D b ~ — (6-H) e s g ( i - e m f ) F o r the case shown i n Figure 6.19, increasing U led to a decrease in characteristic length scale from 1.36x10 to 1.24x10 m . A l though the physical meaning o f this characteristic length is unclear, especially in the context o f turbulent fluidized beds where voids are transient, the standard deviation o f I O P suggests a decreasing value wi th increasing U . Further study on the effect o f probe Chapter 6 Signal Analyses and Interpretation 183 N 0.14 0.014 o 1E-3 4 U=0.33 m / s U=0.87 m / s i i—i i i i ~i—i—i i i |— 10 f, Hz Figure 6.19 Incoherent-output power spectral density (defined in Equation 6.10) from gauge pressure fluctuations for two superficial gas velocities. D=0.29 m, z^O.21 m, z2=0.34 m, II =1.5 m. Table 6.1 Transducer positions for Figure 6.22. Channel identification z, m Az, m chl 0.305 0.064' ch2 0.432 0.064 ch3 0.591 0.128 ch6 0.845 0.128 Chapter 6 Signal Analyses and Interpretation 184 separation distance on this characteristic length scale may reveal the physical significance o f this parameter. F o r the purpose o f this study, the average coherence function is applied to characterize the change i n bed dynamics wi th U . 6.5.1 Coherence function from pressure measurements A s shown i n Figure 6.20, the coherence function o f two pressure measurements exhibits a fall-off at f « 3 H z . Assuming that most bed dynamic coherence can be captured between 0 and 10 H z , and following the method described by C a i et al. (1990), the average coherence function is calculated by integrating the function between 0 and 10 H z . Figure 6.21 portrays the effect o f superficial gas velocity on the average coherence function at various heights from simultaneous measurements o f five gauge pressure transducers. A s separation distance increases, the coherence functions suggest decreased similarity between signals in the 0 to 10 FIz frequency range. The trend f rom this work is similar to that shown i n Figure 6.18 from C a i et al. (1990), although wi th much smaller dips. D i p s are, however, indicated for three cases, namely separation distances o f 0.13, 0.25, and 0.45 m , for U close to U c . A t a separation distance o f 0.70 m, the average coherence function remains below 0.2, wi th a slight increase for U > 1.0 m / s , attributed to the' decrease i n power spectra at high U . A t such a l ow coherence function, conclusions other than that the signals are incoherent are difficult. Figure 6.22 reveals that the average coherence function based on D P signals is lower than from gauge pressure signals. This may be because the D P signals reflect more local phenomena. The detailed locations o f the transducers are listed i n Table 6.1. The higher value o f the average coherence function for the lower D P pair o f pressure taps, i.e., between channels 1 and 2 for U beyond 0.7 m / s i n Figure 6.22, may reflect the v o i d break-up mechanism becoming predominant at higher axial positions. The overall trend o f decreasing average coherence function wi th increasing superficial gas velocity indicates decreasing coherence o f the two signals captured by D P measurements. 6.5.2 Coherence function from optical probe voidage measurements In this section, coherence function analysis is extended to optical probe voidage measurements, reflecting local behaviour o f voids, to provide further insight into bed dynamics. Figure 6.23 plots the average coherence function and correlation function coefficient defined by Equa t ion 6.3. The absolute value o f the coherence function is a function o f the probe separation distance. A c c o r d i n g to C a i et al. (1990) i f the v o i d size matches the probe separation distance, the two signals w i l l exhibit a high correlation. Chapter 6 Signal Analyses and Interpretation 1.0 n 185 T 1— i — i i i | 1 1 r 1 — i — i i t | r 1 10 f, H z Figure 6.20 Typical coherence function. D=0.29 m, U=0.87 m/s, r/R=0.0, z=0.40 and 0.46 m, H0=1.5 m, FCC I. 0.8 C o c a U c V u V o u CJ it. 3 0.6 0.4 0.24 0.0 • • • s s I fil • • A A A I • A o O o • o O o o o • • • • « 0.4 • Az =0.127 m • Az =0.254 m Az =0.445 m • Az =0.699 m 0.8 U , m/s 1.2 Figure 6.21 Average coherence function from gauge pressure signals. D=0.29 m, H 0 =l. l m, Uc=0.73 m/s, FCC I. Chapter 6 Signal Analyses and Interpretation 186 G O u G CU cu C U n cy JS o CJ <u WD CS cu 3 • chl-ch2 A ch3-ch6 U , m/s Figure 6.22 Average coherence function from DP signals. D=0.29 m, H 0 =l . l m, chl locations, U c (Az =0.845 m) = 0.727±0.039 m/s, FCC I. G O -*-> cu C y CJ C cu u cu JS o u cu wo CS W l CU U , m/s Figure 6.23 Average coherence function and correlation function coefficient. D=0.29 m, r/R=0.0, Uc=0.75 m/s, probe separation distance=0.063 m, z=0.40 m and 0.463 m, H0=1.5 m, FCC I. Chapter 6 Signal Analyses and Interpretation 187 W h e n the average coherence function i n Figure 6.23 reaches a peak, the dominating v o i d dynamics i n the bed are coherent wi th a length scale o f 0.063 m , the distance between the two probes. F r o m the cross-correlation o f the signals, the v o i d rise velocity was calculated to be approximately 0.63 m / s . The power spectral density o f the voidage measurement corresponding to the peak in Figure 6.23, i.e., at U=0.65 m / s , is shown i n Figure 6.24. N o obvious dominant frequency can be distinguished. However , as depicted i n Figure 6.25, the coherence function o f the same data including the second probe signal at U=0.65 m / s , indicated a strong peak at 3.2 H z , very close to the dominant frequency obtained from D P signals as indicated in Figure 6.3, albeit for a different static bed height. This indicates a useful method from which to deduce the coherent cycle from bivariate time series measured at the appropriate length scale. A further increase i n U resulted in a decrease i n coherence between two measurements. A t this point, it is not clear whether the decrease i n coherence is related to an unsuitable length scale set by the distance between the measuring probes alone, or due to increased turbulence intensifying the v o i d dynamics. A s the measurements were from optical voidage probes, bed dynamics at the particle level could not be picked up. Further investigation is pursued wi th the same optical voidage probes 0.01 m apart. A s shown i n Figure 6.26, much higher average coherence function values result as the probe separation distance is decreased from 0.063 m to 0.01 m. In all cases, the average coherence function was smallest near the wal l o f the column. The coherence function at U=0.9 m / s for r /R=0 .70 d id not indicate any dominant frequency between 0 and 10 H z . Rather, the distribution was very broad reflecting the broad range o f frequencies o f voidage fluctuation for this operating condit ion. T h e effect o f U on the average coherence function, shown i n Figure 6.27, indicates scattering o f points at r / R = 0 . A s the average over the frequency range o f 0 to 10 H z is arbitrary, the averages for 0 to 30 H z and 0 to 100 H z were calculated for comparison, wi th hardly any change. In this section, the applicability o f the coherence function to pressure and voidage signals has been investigated. Stronger coherence was indicated mainly in the bubbl ing fluidization regime when the v o i d length scale was similar to the probe separation distance. In the turbulent fluidized bed exhibiting erratic v o i d movements, the coherence function alone may not be sufficient to capture trends at different frequencies. In order to detect the 'footprints' o f the coherence structure (Toyoda et a l , 1993) from experimental measurements, the length scale(s) o f the phenomena o f interest need to be considered carefully. Chapter 6 Signal Analyses and Interpretation 188 If/14 1 10 f, H z Figure 6.24 Power spectra density of voidage data at U=0.65 m/s. D=0.29 m, r/R=0.0, z=0.46 m, H0=1.5 m, FCC I. 0.64 0.44 0.24 0.0 f, H z Figure 6.25 Coherence function of voidage data at U=0.65 m/s. D=0.29 m, r/R=0.0, probe separation distance=0.063 m, z=0.40 m and 0.463 m, H0=1.5 m, FCC I. Chapter 6 Signal Analyses and Interpretation 0.8 189 C o •a 0.6 u C g 0.4 u cu o o & 0.2 u 0.0 o A X " A i 0.0 1 0.2 1 1 0.4 - 0.6 0.8 1.0 -O-U=0.40 m/s - A — U=0.90 m/s r / R Figure 6.26 Radial profile of average coherence function. D=0.29 m, Az=0.01 m, H0=1.5 m, FCC I. Figure 6.27 Effect of U on average coherence function form voidage measurements. D=0.29 m, z=0.77 m and 0.78 m, distance between probes=0.01 m, H0=1.5 m, FCC I. Chapter 6 Signal Analyses and Interpretation 190 6.6. Chaotic analysis In the study o f non-linear dynamics, irregular but deterministic systems have been investigated in recent decades through chaotic analysis. A l though the conventional method o f characterizing fluidized bed hydrodynamics has been to use time-averaged properties, such as average v o i d diameter, v o i d rise velocity, average solids holdup and bed voidage, time-dependent components have gained more attention in recent years. Schouten et al. (1996) argue that all o f the analytical methods considered above neglect the time-dependent dynamic behaviour o f the fluidized bed, and that the analysis must take account aperiodicity and nonlinearity o f the dynamics, leading to chaos analysis. Fo l lowing the hypothesis o f Stringer (1989) that a fluidized bed is a chaotic dynamic system, several researchers (Daw and Ha low, 1991; Schouten et a l , 1992; Skrzycke et a l , 1993) have experimentally confirmed this. Chaos analysis has been applied to scale-up, transition detection and regime identification. The dynamics o f a chaotic system are fully represented by the "attractor" i n phase space (Hi lborn, 1994). A n attractor can be estimated from the time series o f only one o f the system's characteristic variables, wi th pressure fluctuations most commonly used i n fluidized bed studies. Spectral analysis has also been used to obtain the dominant frequency o f the fluctuations (Jin et a l , 1986; Lee and K i m , 1988; Chehboun i et a l , 1994). C a i et al. (1990) used the coherence function on signals from two pressure transducers. The signal variations were related to the movement o f bubbles, and the coherence function plotted against a gas velocity showed higher values at wh ich two signals were similar at frequency / . The K o l m o g o r o v entropy, one o f the chaotic invariants, seems to be sensitive to changes i n operating conditions, resulting i n its use i n examining the change i n dynamics i n fluidization regimes and transition from fixed bed to dilute transport flow (Zijerveld et a l , 1998; Ba i et a l , 1999). Increasing the solid loading o f F C C i n a C F B , H u i l i n et al. (1997) observed less 'chaos' i n the system through the correlation dimension, suggesting that solids dampen the turbulence and reduce the complexity o f the flow. A l though pressure measurements have been the most c o m m o n parameter i n characterizing the flow i n a fluidized bed, due to the propagation o f pressure waves affecting the local pressure measurements (Bi et a l , 1995), pressure fluctuations measured i n the bed do not truly represent localized phenomena. In order to reveal the local behaviour, voidage measurements should be better for chaotic analysis than pressure measurements. In this section, deterministic chaos theory is Chapter 6 Signal Analyses and Interpretation 191 applied to time-dependent data o n pressure and voidage fluctuations as a quantitative tool to characterize the behaviour o f a turbulent fluidized bed. 6.6.1 Hurst exponents Hurst (1951) introduced the rescaled range (R/o") analysis for the time series o f natural phenomena. The Hurs t exponent describes the self-similarity o f a signal and reveals the detail differences in different scales (Tsonis, 1992). The 'fractality' i n a time series can be expressed by < H « ^ (6,2, a( t , t ) and R ( t , i ) = m a x c ( t , i ) - m i n c(t , i ) (6.13) 0<i<T 0<i<I where c(t, i) is the cumulative departure o f x ( t+T H ) from the mean; max(c) and m i n (c) are the max imum and l runimum value o f c over the subperiods, T H ; and cr is the standard deviation. A detailed procedure for obtaining the Hurs t exponent is reported by Bnens et al. (1997). T h e rescaled range analysis has been found to be useful in characterizing fluidized bed systems (Hey et al., 1995; Karamavruc and Clark, 1997; Bnens et al., 1997; B a i et al., 1997; Tax i l et al., 2000). A Hurs t exponent o f 0.5 mdicates a pure Brownian mot ion , or random walk; for H = 0 , the position becomes mdependent o f time (Tsonis, 1992). F o r H > 0.5, the posi t ion follows a biased random walk where the next position is more likely to repeat the present event, and the system is considered to be nonlinear or chaotic. A typical plot o f the rescaled range analysis is shown i n Figure 6.28. T w o distinct Hurst exponents can be deduced from a signal for the bubbl ing regime, suggesting bifractal flow behaviour (Bai et a l , 1999). T h e m i n i m u m Hurs t exponent, the slope at higher T (or lower frequency), is found to be less than 0.5 for measurements in the bubbl ing flow regime, indicating the pressure fluctuations are less likely to repeat the present pattern, i.e., it is an antiper sis tent system. This may be attributed to vo id coalescence and splitting. O n the other hand, the max imum Hurst exponent, the slope at smaller T (or higher frequency), is observed to be higher than 0.5, representing a divergent system. 6.6.2 Cycle time and Vstatistic The cycle time o f a system can be obtained through Hurs t analysis f rom a break in the plot o f log(R/o~) vs. log(x) (Peters, 1994). The method has been applied to obtain the average cycle time Chapter 6 Signal Analyses and Interpretation 192 Figure 6.28 Variation of the rescaled range with sub-period length for gauge pressure fluctuation. Sampling frequency=500 Hz, sampling duration=200 s, U=0.39 m/s, D=0.29 m, z=0.65 m, H0=0.97 m, FCC I. Chapter 6 Signal Analyses and Interpretation 193 used to calculate the delay time to reconstruct the phase space o f further chaotic analysis (Hay et a l , 1995). M o r e recently, Briens and Briens (2002) have compared this method to the V statistic (Peters, 1994) to detect cycle times i n various multiphase systems. A s a part o f the on-going collaboration between Lauren Briens and the author, some analysis is pursued here based o n methods described by Briens (2000). Detect ion o f the break i n the log(R/O") vs. log(t) curve is enhanced by using the V statistic suggested by Peters (1994). V T = ^ - ^ (6.14) The V statistic, derived from the rescaled range analysis, was applied to the local heat transfer i n a circulating fluidized bed ( K i k u c h i and Tsutsumi, 2001) reporting increasingly uni form and deterministic gas-solid flow structure wi th increasing circulating solid mass flux. T h e underlying assumption in the V statistic is that the intersection o f the slope is between Hurs t exponents higher and lower than 0.5. B o t h exponents indicate values lower than 0.5 when there is no cycle i n the signal, or a cyclic signal without slope switching from smaller to larger than 0.5 (Briens and Briens, 2002). F o r such cases, the P statistic is used to determine the cycle time (Briens, 2000), where (6.15) Here y is an exponent between 0 and 1. O n e advantage o f the cycle time analysis through rescaled range analysis is that as long as it is a linear operation, the Hurs t exponent is tolerant to the minor shifts i n the calibration constants o f the measuring probes (Briens and Briens, 2002). The detailed procedure for calculating the regularities is given i n Briens and Briens (2002). The regularity o f a cycle time is defined as: V T A t _ P T A t Ff T where T is the cycle time, and A t is the sampling time interval. 6.6.3 Results from pressure signals The Hurs t exponent from D P signals is presented in Figure 6.29. B i m o d a l plots as i n Figure 6.28 lead to two Hurs t exponents. A peak in the m i n i m u m Hurs t exponent is indicated, consistent wi th the findings o f B a i et al. (1999). In the bubbl ing fluidization flow regime, the m i n i m u m Hurs t Chapter 6 Signal Analyses and Interpretation 194 © Maximum Hurst exponent A Minimum Hurst exponent C <u C o a x •*-» CO 3 E U , m / s Figure 6.29 Variation of the Hurst exponents from DP signals with superficial gas velocity. D=0.29 m, H 0 =l . l m, z =0.59 m, Az =0.12 m, sampling frequency=100 Hz, sampling duration=100 s. Chapter 6 Signal Analyses and Interpretation 195 exponent decreases to below 0.5, implying a convergent system. This can be attributed to the splitting and coalescence o f bubbles reflecting reversing phenomena. T h o u g h not showing as clear a trend as i n Figure 6.29, Tax i l et al. (2000) reported a similar trend for Hurs t exponents i n their 0.19 m diameter co lumn wi th F C C particles. The max imum Hurs t exponent, reflecting higher frequency phenomena, is shown to be consistently above 0.5 for D P signals measured at the wall , suggesting a divergent system. A t around U ^ O . 7 6 m / s , the difference between the two Hurs t exponents becomes smaller, suggesting less phase segregation near U c . The cycle time calculated from the intercept o f the two slopes o f Hurs t exponents represents a lag time caused by a dominant periodic component o f a signal (Fan et al., 1993). This is also indicated in Figure 6.28. The variation o f the cycle time wi th the axial posi t ion o f the pressure taps for D P and gauge pressure signals appear in Figures 6.30 (a) and (b), respectively. Three superficial gas velocities are chosen as representative U values, corresponding to U < U c , U « U c , and U > U c . Increasing U increases the cycle time for all superficial gas velocities at D P locations close to the distributor, indicating gradual growth i n voids due to coalescence wi th height. The range o f cycle time o f 0.3-0.55 s corresponds wel l to the dominant frequency detected from F F T o f D P signals o f 1.5-3 H z , e.g. see Figure 6.3. A t z = l . l m for U ^ l . O m / s , the trend in cycle time reverses, suggesting dominance o f v o i d splitting over coalescence. The bed above this point becomes dominated by smaller voids, contributing to the increased homogeneity o f the turbulent fluidized bed. The trend shown from gauge pressure signals, Figure 6.30 (b), indicates two distinct regions: one nearer the distributor corresponding closely to the natural frequency o f the bed, and the other indicating much lower cycle times. A s signals from gauge pressure reflect global phenomena i n a fluidized bed, the origin, propagation, and attenuation o f pressure waves may be picked up. Fo l lowing the analysis o f B i et al. (1995), the higher cycle time near the bo t tom o f the fluidized bed may indicate pressure waves much lower i n frequency than the natural frequency o f the bed, implying that the bed is acting "as a wave propagation medium". O n the other hand, at z=0.46 m and beyond, the imposed pressure waves have frequencies higher than the natural frequency o f the bed resulting in oscillatory mot ion. Oscillations are dampened by energy loss f rom interparticle collisions, and friction between particle-gas or the wall , but sustained by the continuous supply o f pressure waves. In a turbulent fluidized bed, it is extremely difficult, i f not impossible, to pin-point Chapter 6 Signal Analyses and Interpretation ^ ^  ^^^^^ Q^MA / \ O ^,.A m o \ A " • • • \ OA c i 0.3 0.4 0.5 0.6 Cycle time, s (a) DP signals — • — U =0.49 m / s - o - u =0.72 m / s A u =1.00 m / s 0.7 0.8 (b) AP signals - • - U = 0 . 4 9 m / s -O~U=0.72 m / s —A— U=1.00 m / s 0.8 1.0 1.2 Cycle time, s 1.6 Figure 6.30 Axial profiles of cycle time from (a) DP, and (b) AP signals. D=0.29 m, H 0 m, r/R=l, FCC I. Chapter 6 Signal Analyses and Interpretation 197 the factors contributing to the pressure fluctuation owing to the complex dynamics. However , extending the analysis o f such pressure waves from fluidized beds at m i n i m u m fluidization or m i n i m u m bubbl ing velocities (Musmarra et a l , 1995; B i et a l , 1995; van der Schaaf, 2002) may provide insight into the understanding o f energy supply and dissipation. The effect o f co lumn diameter on the cycle times calculated from the rescaled range analysis o f D P signals is illustrated in Figure 6.31. By comparing the cycle time variation wi th normalized axial probe height wi th expanded bed height, i.e., z / H , it is seen that there is a shift in trend in cycle time at certain axial heights for U > U c . This implies that once i n the turbulent fluidization flows regime, cycle time shifts to smaller values with height reflective o f v o i d splitting for the three columns i n this study. T h e cycle time for the 0.61 m diameter co lumn is indicated to be much larger than for the two other columns. This can be attributed to the distributor plate design, as wel l as the particle size distribution, wh ich was widest for the 0.61 m diameter column. The cycle time regularity, defined in Equat ion 6.16, for D P signals obtained from the three columns are represented by Figure 6.32. The regularity from the rescaled range analysis indicates a decline wi th increasing TJ, except for the one point for the 1.56 m diameter co lumn at U / U c = 1 . 2 4 , wh ich is considered to be inconclusive for the amount o f information at hand. 6.6.4 Results from voidage signals The rescaled range analysis is extended to voidage signals in this section. A s noted by Briens et al. (1997), increasing the measurement volume wi th different measuring probes increases the Hurs t exponent, implying increasingly persistent behaviour o f phenomena occurring globally. The voidage signals obtained from optical voidage probes reflect much smaller measuring volumes than A P or D P signals, as discussed i n Chapter 4. Thus, more localized behaviour should be revealed. Figure 6.33 illustrates radial profiles o f the Hurs t exponents for U=0.40 and 1.0 m / s . The m a x i m u m Hurs t exponent remains close to 0.5 for U=0.40 m / s near the co lumn axis indicating random motion. Though their Hurs t exponents were much higher, B a i et al. (1999) reported a similar radial profile for the bubbl ing flow regime. However , i n the turbulent fluidization flow regime, both maximum and m i n i m u m Hurs t exponents indicated values above 0.5, increasing towards the wall. Figure 6.33 indicates smaller differences between max imum and m i n i m u m Hurs t exponents near the wall implying less phase separation than in the core o f the column. Chapter 6 Signal Analyses and Interpretation 198 N 1.0 0.84 0.6 0.4 0.24 0.0 o o 1X k A o 6 o A 0.4 0.6 0.8 1.0 i 1.2 —o— D=0.29 m — A — D=0.61 m D=1.56 m Cycle time, s Figure 6.31 Variation of cycle time with dimensionless height for U > U c from DP signals. 0.35 "y >, U 0.304 0.25 0? •c 3 y v 0.20 S 0.15 4 0.10 A ^ ^ i 1 • 1 • 1 r o 1 1 1 1 —o— D=0.29 m —A— D=0.61 m D=1.56 m 0.4 0.6 0.8 1.0 u/u 1.2 1.4 Figure 6.32 Variation of cycle time regularity with dimensionless superficial gas velocity. Axial positions: D=0.29 m (z/H=0.64); D=0.61 m (z/H=0.87); D=1.56 m (z/H=0.62). Chapter 6 Signal Analyses and Interpretation 199 - • - H : m a x U=0.40 m / s — • — H : m i n U=0.40 m / s - • - H : m a x U=0.90 m / s —o— H : m m U=0.90 m / s Figure 6.33 Radial profde of Hurst exponents for U=0.40 and 0.90 m/s. D=0.29 m, z=0.78 m, H 0 =l. l m, FCC I. Chapter 6 Signal Analyses and Interpretation 200 The m a x i m u m Hurs t exponent, H m a x , f rom the local voidage measurements shows a sudden drop wi th increasing superficial gas velocity, see Figure 6.34, indicating a change i n the high frequency fluctuations. The velocity at wh ich this abrupt drop occurs may correspond to the transition into the turbulent fluidization flow regime. The drop i n H m a x also corresponds to a slight decrease i n Figure 6.29 from D P measurements. The sensitivity o f the H m a x f rom voidage signals to the change i n local fluctuation may suggest a viable means o f deducing the transition velocity, U c . The cycle time deduced from rescaled range analysis for voidage signals is shown i n Figure 6.35. Considerable scatter o f cycle time is observed wi th no definite trend indicated by the transition, as shown i n Figure 6.34. The general trend o f decreasing cycle time wi th increasing U indicates increasing cycle frequency o f voidage fluctuations. The range o f cycle frequency, i.e., reciprocal o f cycle time, indicates close correspondence wi th the range o f frequencies observed from F F T o f D P signals, as shown i n Figure 6.4. Thus wi th the optical signal capmring the local v o i d movements, f D P reflects v o i d dynamics. Moreover , the superiority o f the rescaled range analysis i n deducing cycle time over the crossing frequency is highlighted. 6.7 Conclusions Various statistical, spectral and chaotic analysis methods were employed to interpret pressure and voidage data i n fluidization columns o f diameter 0.29 ; 0.61 and 1.56 m . The results may be summarized as follows: • Pressure signals were examined to study the hydrodynamic behaviour o f turbulent fluidized beds i n columns o f different diameter. The natural frequency o f the bed based on gauge pressure signals decreased wi th increasing bed height. F F T analysis o f D P signals at different axial positions revealed a shift towards lower frequency distributions wi th increasing height, due to an increase i n v o i d sizes for U < U c . Once i n the turbulent fluidization flow regime, f D P became less sensitive to height. This trend was supported by the crossing frequency, defined i n Equa t ion 6.2, deduced from local voidage measurements via an optical fibre probe wi th in the bed. Figure 6.5 gives a graphical correlation for the pressure fluctuation frequency wh ich includes the influence o f co lumn diameter and gas velocity i n the turbulent fluidization flow regime. • T h e correlation function coefficient was applied to characterize simultaneous voidage signals from two identical optical voidage probes. Higher correlation function coefficients were obtained for a probe distance similar to the length scale o f the voids. O n c e i n the turbulent Chapter 6 Signal Analyses and Interpretation 0.6 201 Figure 6.34 Variation of maximum Hurst exponent from optical voidage probe signals with superficial gas velocity. D=0.29 m, z=0.40 m, Uc=0.75 m/s, r/R=0.0, H0=1.5 m, FCC I. Figure 6.35 Variation of cycle time with superficial gas velocity for optical voidage probes signals. D=0.29 m, z=0.40 m, r/R=0.0, H0=1.5 m, Uc=0.75 m/s, FCC I. Chapter 6 Signal Analyses and Interpretation 202 fluidization flow regime, less radial variation o f the correlation function coefficient was observed, possibly indicating a narrow range o f physical length scale o f voids i n the turbulent bed. This method o f deducing the length scale is not considered to be practical, without a priori knowledge o f the length scale to be detected, as the physical separation distance o f probes dictates what scales can be detected. • The autocorrelation function was applied to assess the non-randomness o f voidage measurements from optical probes. The autocorrelogram i n Figure 6.14 suggests a chaotic signal from a system which 'forgets' previous information. Simultaneous voidage measurements at two axial locations indicate longer lag times for the higher probe posit ion indicating v o i d coalescence being dominant as voids rise at U=0 .9 m / s . Further analysis using autocorrelation function was not pursued as it is based o n the underlying assumption o f a linear relationship between data points, wh ich is unlikely for v o i d dynamics i n turbulent fluidized beds. T h e coherence function measures the coherence o f a set o f signals at a given frequency. Strong coherence was indicated between the two probes when their separation distances corresponded to the length scale o f the voids, wh ich occurred i n the bubbl ing flow regime. Once i n the turbulent fluidization flow regime, the coherence function declined with increasing TJ. A s for the autocorrelation function, the probe separation dictates the length scale to be detected. • Rescaled range analysis was applied to pressure and voidage signals. T h e m i n i m u m Hurs t exponent indicated a max imum at U « U c . Cycle times calculated f rom the V and P statistics indicated a shift i n cycle time at U > U c . This may suggest that at a certain height above the distributor plate, v o i d splitting may become more dominant than coalescence. Cycle time obtained from voidage signals indicated a range o f cycle frequencies similar to those detected by the dominant peak from Fast Fourier Transformation o f pressure signals. It strongly suggests that F F T peaks from D P signals reflect v o i d dynamics, as supported by cycle times obtained from voidage signals. CHAPTER 7 MULTISCALE RESOLUTION 7.1 Introduction This chapter continues the exploration o f the hydrodynamic complexity o f the turbulent fluidized flow regime from a multiscale resolution viewpoint. Nonl inear dynamics and their implications with respect to the flow were discussed through chaotic analysis i n the previous chapter, shedding light on the challenges o f understanding dynamics from observations o f systems where non-linearities are important. It is important to determine whether or not the rapid inversion o f continuous and discontinuous phases between low- and high-density phases in turbulent fluidized bed can be explained or modeled through energy-based hypotheses and the dominance o f one phase over the other between two phases (L i et al., 1998). Here, both velocity and voidage fluctuations are analyzed and interpreted as footprints for the flow structure i n an attempt to understand the system from an energy dissipation point o f view. The analysis tool used for this task is wavelet analysis, a technique which is being widely recognized as a powerful tool to interpret the physics o f non-linear data (Ross and Pence, 1997). N o t i n g that the quantification o f dynamics drawn from experimental data is basically bounded by the underlying theory, the fundamental equations governing the two-phase flow based on fluid dynamics are discussed i n Append ix D . 7.2 Turbulence — two phase flow Single-phase turbulence from a statistical fluid mechanic viewpoint is characterized as highly non-linear (inherent i n the Navier-Stokes equations), subject to irregular fluctuations o f velocity, cascading energy, and intermittency o f the dynamically active regions (e.g. A r g o u l et al., 1989; M c C o m b , 1990). Turbulent events include acceleration, deceleration, rotation or vortex, or a constant velocity experienced by eddies. The Reynolds number dictates the ratio o f the nonlinear convective motions, inducing flow instability, to the linear dissipative damping, wh ich converts kinetic energy into thermal energy (Farge et al., 1996). Gas-particle interaction is an important research topic steadily gaining i n attention owing to its dominant influence on heat and mass transfer i n gas-solid flows, as encountered i n many industrial processes. The structure and mot ion o f turbulence are gready influenced by the presence o f turbulent eddies o f different sizes and orientations. Eddies affect the transfer o f momentum found 203 Chapter 7 Multiscale Resolution 204 i n turbulent flow. Instantaneous shear stresses near the wal l are key factors i n the product ion o f turbulent eddies in concurrent-upward gas-solid flows. A s Townsend (1976) stated: the necessary connection between diffusion and the supply o f energy to the turbulent mot ion is a fundamental characteristic o f turbulent flow. The primary eddies are produced by an energy source and are dissipated into smaller eddies. T h e eddies responsible for macroscopic transport are mainly the large-scale ones wh ich contain the major por t ion o f the turbulent energy (Zethrasus et a l , 1992). Bai rd and Rice (1975) attempted to connect the energy dissipation rate per unit mass o f fluid by applying the K o l m o g o r o v ' s theory o f isotropic turbulence. The behaviour o f the suspended solids i n a turbulent two-phase fluid depends largely on the concentration o f the particles, and on the size o f the particles relative to the scale o f turbulence o f the fluid (Hinze, 1959). The particles can dampen or enhance the gas turbulence. A c c o r d i n g to Sinclair and Jackson (1989), the interactions can be categorized as: • Interaction between particles and gas resulting from the difference between their mean velocity fields, leading to drag forces that propel the non-random part o f the particle mot ion. • Interaction o f the particles wi th the fluctuating component o f the gas velocity. This may cause a flux o f kinetic energy i n either direction between the fluctuating components o f velocity o f the two phases, either damping the fluctuations o f gas velocity and stimulating fluctuations i n particle velocity, or vice versa. • Interactions o f the fluctuating part o f the particle mo t ion wi th the mean particle mot ion through interaction between the particles. These generate stresses i n the particle assembly and give rise to its apparent viscosity. • Interactions between the turbulent fluctuations o f gas velocity and the mean mot ion o f the gas, generating the wel l -known Reynolds stresses. K e y features o f fluidized beds such as bubbles and slugs can be traced to inertial instability i n the gas phase, as we l l as the solid phase (Dasgupta et a l , 1994). M o t i o n o f the particles can be partitioned into three components: the mean and the fluctuating velocities associated wi th the organized mot ion o f collections o f particles; and fluctuations at the level o f individual particles. F r o m the previous investigation o f particle-turbulence interaction by Hets roni (1989) and given the operating conditions o f turbulent fluidized bed systems, turbulence due to the influence o f particles should be suppressed. Chapter 7 Multiscale Resolution 205 7.3 Multiple scales in fluidized beds In systems such as a fluidized bed where muldple scales o f dynamics are omnipresent, it is surprising to see how few studies have adopted a multiscale point o f view. In L i (2000), extending a paper o f L i et al. (1998), eight parameters emerge, namely 8f, sc, fd, U g f , U g c , U d f , U d c , d c l , together with three scales o f interaction associated wi th the heterogeneous gas-solid flow. T h e three scales are a macro-scale o f the overall processing unit; a meso-scale o f clusters or bubbles; and a micro-scale o f individual particles. The macroscale i n a fluidized co lumn is the co lumn geometry represented by the macroscopic variables such as pressure, temperature and volume. It is characterized by radial and axial heterogeneity. Fluctuations in the mot ion o f the two phases and the interactions between the dense and dilute phases are observed. K e y phenomena originate f rom instabilities o f shear flow associated with the presence o f the co lumn walls, wi th the largest eddy size being the co lumn diameter. The macroscopic length scale o f the flow is much larger than the particle diameter, so that a cont inuum description o f the suspension can be assumed. In the intermediate (meso) length scale, lengths o f interest (e.g. bubble diameter, cluster size) that are larger than the diameter o f the particles but l imited by the averaging volume are considered. This mesoscale range deals wi th what is usually called a " loca l " measurement w i th respect to the solids such as f rom optical fiber probes. L i (2000) proposes a particle-fluid compromis ing interaction scheme where both 'ordered' and 'irregular' behavioural changes occur. The smallest (micro) scale is characterized by the particle diameter and the separation between neighbouring particles, but is still much larger than the gas molecular mean free path. F o r G r o u p A and B solids, the flow at the microscale level is no longer turbulent but viscous and dominated by molecular effects. Variations i n gas velocity result f rom streamline deformation around a particle. Individual particle velocities differ as a result o f interactions such as collisions or due to fluctuations i n the interstitial gas velocity. A t the smallest scale, viscous dissipation forces become important and tend to damp the eddy mot ion. Interactions at the micro-scale can be particle-dominated in a dense-phase cluster, or fluid-dominated wi th in a dilute phase. Chapter 7 Multiscale Resolution 206 7.3.1 Kolmogorov scale of turbulence The hypothesis o f K o l m o g o r o v depicts the cascading o f energy f rom the largest scales to the smallest through the non-linear terms o f the Navier-Stokes equations ( M c C o m b , 1990). A t the smallest scale o f turbulence, viscous forces dominate over inertial forces resulting i n dissipation o f turbulent kinetic energy where the velocity gradients are large. In an open system, the external forces act only on the largest scales. F o r an intermediate range o f scales, K o l m o g o r o v states that the energy cascaded from the larger scales is transferred to the small scale at a constant rate (Farge et a l , 1996). In dilute suspensions, discrete particles only respond to turbulent eddies larger than the particle diameter. F o r eddies o f size (7.1) and smaller, where O" is the rate o f energy dissipation per unit mass, the kinetic energy o f turbulent mot ion is dissipated as heat. Reade and Coll ins (2000) suggest that the K o m o g o r o v scale dominates the particle clustering process since motions o f this scale contain most o f the fluid vorticity responsible for centrifuging the particles. O n the other hand, Crowe (2000) suggests that the K o m o g r o f f scale is no longer appropriate for a fluid-particle flow since the presence o f the particles provides surfaces that can support stresses. 7.3.2 Time scale The parametric dependence on the small-scale particles can be characterized by the Stokes number, S t = - ^ T 18 i ( \ Q IL fd 1 p Q V 1 J (7.2) Small scale dissipative eddies contribute to the local non-uniform particle distribution which is most pronounced when the ratio o f the particle response time, T p, to the K o l m o g o r o v time scale, x^, is close to unity. This phenomenon o f local vorticity centrifuging particles out o f regions o f high vorticity into regions o f high strain is called "preferential particle concentration." However , for large values o f the particle Stokes number, e.g. S t s s^Re^ , particles become less correlated, thus increasing the coll is ion frequency (Reade and Col l ins , 2000). The particle relaxation time is defined as the time taken for a particle at rest to be accelerated to wi thin ~ 6 3 % o f the fluid velocity. In a dilute two-phase suspension, particle velocities follow the Chapter 7 Multiscale Resolution 207 fluid eddy velocides when the oscillation period or eddy time scale is much larger than the particle relaxation time, dpK/eg+i) x , » p p g- (7.3) c 36u W h e n the two times scales are o f the same order o f magnitude, particles fluctuate less as a result o f interactions wi th eddies. However , the presence o f many discrete particles i n a turbulent flow mdirecdy influences the fluid-velocity field i n the interspace between particles, consequendy changing the length and time scales, and hence the energy spectrum o f the fluid. 7.4 Turbulence energy decomposition - phase space In employing functions to characterize the flow phenomena, one must understand the intrinsic structure o f the field to be analyzed. Farge (1992) points this out i n model ing turbulent flows where an appropriate segmentation o f the energy density i n phase space must be identified to understand the interactions o f the dynamically relevant quantities. F o r example, i f a signal is composed o f superimposed waves, the wave number through the Fourier spectrum is the appropriate analyzing function for characterizing the phenomena. O n the other hand, a different analyzing function must be employed for a flow field composed o f superposed point vortices. O n l y when an appropriate decomposit ion o f the flow field is obtained, can the flow dynamics be meaningfully interpreted. 7.5 Wavelet analysis The wavelet transform, W T , is an analysis tool for decomposing data into different frequency components, and then for resolving the positions and scales as independent variables. It is capable o f isolating singular sequences o f events related to particular scales (Daubechies, 1992; Hlawatsh and Boudreaux-Bartels, 1992; W e n g and L a u , 1994). Through wavelet analysis, a one-dimensional time series is transformed into a two-dimensional region displaying wavelet coefficient amplitudes as a function o f both time and frequency. This enables time localization o f spectral components to be interpreted (Hlawatsch and Boudreaux-Bartels, 1992). A wide range o f applications o f wavelet transforms is found in geophysics, image analysis, seismology and fluid dynamics. Recendy, wavelet transformations have been gaining attention i n studies o f single-phase turbulence. In single phase turbulent flow, the W T has been applied to analyze the intermittent nature and multiscale aspects o f the turbulent flow (Farge et al., 1996); i n investigations o f intermittency and the passage o f turbulent coherent structures (Camussi and Guj , 1997); and i n characterizing local turbulent or eddy structures ( K a m i et al., 2001). The potential efficacy o f wavelet transformation i n understanding the local Chapter 7 Multiscale Resolution 208 structure o f turbulence has been highlighted, e.g. by Farge et al. (1996), Camussi and Guj (1997), Chainais et al. (1999), K a t u l et al. (2001), in identifying the points o f intermittency i n large and small-scale turbulence; in displaying fractal characteristics o f cascading phenomenon; and i n analyzing the physics o f nonlinear data (Ross and Pence, 1997). Dynamic behaviour has also been analyzed through wavelet transformation elucidating intermittency, structural resolution, phase separation, turbulent density and energy, and principal time scales i n bubble columns and i n circulating fluidized beds (Bakshi et a l , 1995; Ross and Pence, 1997; L u and L i , 1999; Z h o u et a l , 2000; R e n et a l , 2001; K u l k a r n i et a l , 2001). A c c o r d i n g to R e n et al. (2001), local voidage measurements from a fluidized bed can be decomposed into three scales: micro-scale (particle and fluid), meso-scale (voids, two phase structure), and macro-scale (equipment, global). The wavelet filtering method has been applied to phase decomposit ion o f voidage measurements i n identifying the transition points between dilute and dense phases, enabling the determination o f the volume fraction o f each phase and cluster duration time, without resorting to pre-set threshold values. Pr ior to applying this recent mathematical tool to data form turbulent fluidized bed systems, a brief overview is presented and its apphcability to this project is discussed in A p p e n d i x C , as the method is not yet wel l established compared to Fourier analysis. 7.5.1 Wavelets and turbulence Wavelet analysis has been shown to be an effective tool i n studying fully developed turbulence (Meyer, 1993). M o d e r n understanding and characterization o f turbulence are built upon considerable research conducted by early researchers in the field such as K o l m o g o r o v , K a r m a n , Prandtl, and Taylor as described by H i n z e (1959), Batcheleor (1967), and Townsend (1976). Turbulent flow is depicted as unsteady, three-dimensional vort ical flow, leading to high dissipation o f energy into heat and rapid dispersion over wide ranges o f frequencies and scales. The statistical approaches to turbulence investigate the partition o f energy, at different scales, i n solving the Navier-Stokes equations (Meyer, 1993). Some o f the statistical tools applied are averaging, characterization o f fluctuations, probability density functions, space and time correlations, spectra, conditional averaging, Lagrangian statistics, and volume averaging (Libby, 1996). The Fourier transform provides a good representation to solve the linear dissipation term, but is not able to represent the nonlinear convection term, wh ich becomes dominant i n high Reynolds numbers (Farge et a l , 1996). W h e n there is spatial intermittency i n the flow, the Fourier transform is capable o f representing the velocity field i n a combinat ion o f plane waves; however, the posit ion i n physical space is not Chapter 7 Multiscale Resolution 209 revealed (Meneveau, 1991). Wavelet analysis, on the other hand, provides the means for "condit ional averaging and seeking atomic decomposit ion o f phase space, defined i n both space and scale" (Farge et al., 1996), enabling flow intermittency to be treated as localized pulses, rather than as extended waves. Numerous publications on various aspects o f turbulent flow based on wavelet analysis have been published. F o r example, see Lewalle et al. (2000) for clarification o f coherent structures and Camussi and Guj (1997) for a study o f intermittency and coherence structures. 7.6Analysis method 7.6.1 Application of wavelet transform to de-noising signals In de-noising signals, the linear band-pass filters based on the frequency domain allow some frequency signals to pass unaltered, while other frequencies are blocked. This method is useful in removing frequencies that are present throughout the signal, but does not allow time localization. De-nois ing signals using wavelets takes advantage o f the their excellent time-frequency localization and multi-resolution analysis. Recogniz ing these features, the method is applied here to transpose voidage signals to different physical scales by means o f frequency decomposit ion. R e n et al. (2001) reported o n the application o f wavelet analysis to decompose voidage signals into three scales o f components: micro-scale (particle size); meso-scale (cluster size); and macro-scale (unit size), thus avoiding the effect o f the pre-set threshold on the resulting cluster-size distribution. The effect o f threshold value i n determining v o i d velocities was raised i n Chapter 5 and reported i n Append ix B . A s investigated i n Section 5.4.5, the cut-off method was applied i n order to remove the interference o f dense phase fluctuations prior to cross-correlating v o i d velocity signals. The resulting velocity was shown to be affected by the threshold value for the cut-off voidage and the number o f data points used for the sectional cross-correlation. The new approach proposed here applies wavelet decomposi t ion to eliminate dense phase fluctuations o f the voidage signals. 7.6.1.1 Crude method O n e way to eliminate signals o f certain frequencies using wavelets is to decompose the signals and reconstruct the signal without certain components k n o w n to contain noise. The one-dimensional Daubechies wavelet, db, is chosen here to demonstrate the reconstruction o f approximation coefficients to show the signals without certain scales. Figure 7.1 compares the original voidage Chapter 7 Multiscale Resolution 211 signal and the reconstruction o f the approximation confidences at specific levels. Since the purpose o f the decomposi t ion is to retain the v o i d fluctuation, yet to eliminate the small-scale fluctuations associated wi th particle dynamics, the appropriate wavelet must be chosen. Increasing levels o f decomposi t ion results i n eliminating the sharpness o f the edges. Moreover , die signal reconstruction from approximation coefficients loses the sharpest features o f the original data, wh ich may wel l be undesirable. 7.6.1.2 Thresholding In recovering signals f rom noisy and incomplete data, both parametric and nonparametric regression models are applied. The former includes linear or polynomial regression, and produces estimators influenced by a priori knowledge o f the functional form o f data. Nonparametr ic regression, on the other hand, seeks to track the average values o f the dependent variables as a function o f the independent variables wi th mmimal assumptions about the form o f the relationship. Nonl inear wavelet estimators have gained considerable attention i n recent years as an approach to nonparametric regression (Ogden, 1997). Further discussion is reported i n Section C.2.5 i n Append ix C . The methodology o f nonparametric regression was applied to de-noise the same signal prior to cross-correlation. Daubechies wavelet N = 3 at level 5, equivalent to the condi t ion on Figure 7.2, was used to decompose the signal. The soft thresholding method was applied wi th threshold equal to -\y21og(n) and rescaling o f the threshold using level-dependent estimation o f the level noise. The resulting reconstructed signal is shown i n Figure 7.3. Compar ing visually wi th the approximation reconstruction i n Figure 7.2, sharper edge jumps are observed. Furthermore, the cross-correlation o f the de-noised signals results in v o i d velocity distribution much closer to the cut-off method as shown in Figure 7.4. The non-linear wavelet method eliminates the dependency on the threshold value i n determining the v o i d edge. Treating high-frequency, small-scale voidage fluctuations from the particle dynamics as noise, and effectively de-noising the signal, wavelet analysis is seen to be successful in pre-conditioning the voidage signals for cross-correlation. 7.6.2 Local intermittency measure The not ion o f intermittency originated from the transition from laminar to turbulent flows where periods o f laminar mot ion and turbulent bursts succeed each other i n a random sequence Chapter 7 Multiscale Resolution 21 5 0 -| 1 1 1 1 1 1 1 1 1 1 0 1 2 3 4 5 T i m e , s Figure 7.2 De-noising signal using Daubechies 3 wavelet level 5. 5 0 i 1 1 1 1 1 1 ' 1 1 1 0 1 2 3 4 5 T i m e , s Figure 7.3 De-noising signal using Daubechies 3 wavelet level 5 with soft thresholding method. Chapter 7 Multiscale Resolution 213 3 £ 0.6 H 0.4-| • T - l 1 0.2 H o / o / ° - ° ' - O - C T jo- - O - O o - 1 1 1 1 1 1 1 1 1 1 1 1— 6 -4 -2 0 2 4 6 - 1 — 1 — i — 8 10 Void velocity, m/s Figure 7.4 Comparison of void velocity distribution between cut-off method (O); and db3 level 5 wavelet transform with soft thresholding (A) (data of Figure 7.6a). Chapter 7 Multiscale Resolution 214 (Schlichting, 1979). In recent years, intermittency has been associated wi th various types o f regular or quasi-deterministic behaviour, termed coherent structures. Coherent structures affect the energy cascade and other aspects o f turbulent flow. They constitute a relatively new area o f study, as summarized by M c C o m b (1990). Various authors have investigated the relationship between temporal and spatial intermittency o f turbulent flows to the presence o f coherent structures through wavelet analysis (Farge et al., 1996; Camussi ' and Guj , 1997; Chainais et al., 1999). Coherent structures are characterized in Chapter 6. Here, some o f the quantitative methods i n characterizing the intermittency through coherent structures are applied. The passage o f highly coherent vortical structures can be characterized by strong velocity gradients considered to be responsible for momentum transfer (Li , 1998) through viscous dissipation o f turbulent kinetic energy. Appl ica t ion o f wavelet analysis i n distinguishing the coherent and non-coherent components o f turbulent flows and characterizing the intermittency related to coherent structures o f energy bursts should provide insight into the flow structures. The local intermittency index based on the non-uniform distribution o f energy i n space represented by scalar x has been defined as: L I M , ( i ) = , , (7.4) |2< 'N where < > denotes the arithmetic average over N data points. This index has been applied to measure intermittency i n turbulent flows (Farge, 1992; Camussi and Gu j , 1997) and to velocity measurements i n a bubble co lumn (Kulkarni et al., 2001). 7.6.2.1 Wavelet analysis applied to particle velocity The experimental data obtained in this project using the optical velocity probe capable o f capturing fluctuations at a particle scale have been analyzed to quantify the presence o f energetic microstructures through the local intermittency index. The bivariate time series o f voidage fluctuation, shown i n Figure 7.5 is converted to "instantaneous" particle velocity fluctuation based on the methodology described in Append ix B . Particle velocities corresponding to 142.5 ms bursts have been calculated via cross-correlation and are shown i n Figure 7.6. T h e resulting velocity fluctuation is decomposed through Deubechies 5 wavelets (db5) for 6 levels. Figure 7.5 Voidage fluctuation captured by optical velocity probe. Sampling frequency, 28,741 Hz, D=0.61 m, U=1.56 m/s, r/R=0.09, z=1.55 m, z=1.55 m, H0=2 m, FCC IV. 44 24 •r, W P o 3 04 > cu 2 P H -4 4 -6 o >\p-o o o o oooo° °ooo°oo' 0 o o ooo I 3 Time, s Figure 7.6 Particle velocity fluctuation of data from Figure 7.10 based on cross-correlation of 4096 data points, representing 142.5 ms. D=0.61 m, U=1.56 m/s, r/R=0.09, z=1.55 m, H0=2 m, FCC IV. Chapter 7 Multiscale Resolution 216 The max imum number o f levels o f decomposit ion depends on the sample size, N , as: max(j) = l o g 2 N (7.5) The detailed coefficient at levels 1 through 6 are reconstructed to calculate L I M according to Equa t ion 7.4. The local intermittency index represents the normalized energy distribution at various scales j . A large magnitude o f L I M signifies high energy variation and content. Thus, the graphical representation o f L I M has been used to identify the passage o f high-energy coherent structures (Kulkarni et a l , 2001). Typica l contour plots for U less than, close to, and larger than, U c are shown in Figures 7.7, 7.8, and 7.9, respectively. Compar ison o f the three plots suggests a general shift i n distribution o f the energetic microstructures at a given measurement location i n time. F o r U < U c , the local intermittency index indicates energy variations across the scale; o n the other hand, at U=1.56 m / s , Figure 7.9 indicates that most o f the energy variations occur at a smaller scale representing higher frequency. Moreover , these structures are much shorter l ived i n Figure 7.9 than i n Figure 7.7 or Figure 7.8. This highlights the change in flow structure i n passing from bubbl ing to the turbulent fluidization flow regime. Probabili ty distributions o f L I M at three superficial gas velocities, U=0.42, 0.82, and 1.56 m / s , are shown i n Figures 7.10 (a) and (b) for the smallest and largest scales, i.e., ) — \ and 6, respectively, for r /R=0 .09 . B y conducting analysis at different scales, certain trends become apparent. A s shown i n Figure 7.10 (a) at the smallest scale o f analysis for r /R=0 .09 , the local intermittency indicates similar distribution among the three superficial velocities. A s the optical velocity probe reflects voidage variations at the particle level, it is plausible that the burst o f energy reflects particle velocity fluctuation. However , it is difficult to pinpoint the relevant frequency. A s shown i n Figure C.2, as the scale, a, is reduced, the frequency band increases wi th superior time localization. T h o u g h this method o f decomposing the signal and quantifying the energy distribution is shown to be effective, it must be noted that the particle velocity data are unsuitable owing to discontinuities due to cross-correlation and elimination criteria. A s reported i n A p p e n d i x B , 20 to 40% o f data are rejected owing to poor correlation o f the two-voidage signals. F o r the above velocity data, zero velocity is assumed when there is poor correlation. Chapter 7 Multiscale Resolution 217 F i g u r e 7.7 C o n t o u r p lo t o f L I M for 6 levels d e p i c t i n g passage o f energet ic mic ros t ruc tu re cen t red a r o u n d scale 3. U=0 .42 m / s , r / R = 0 . 0 9 , D=0.61 m , z=1.55 m , H 0 = 2 m , F C C I V . Chapter 7 Multiscale Resolution 218 i i i i i • i 1 i 0 1 2 3 4 5 6 Scale, j Figure 7.8 Contour plot of L I M for 6 levels depicting passage of energetic microstructure centred at all scales of analysis. U=0.82 m/s, r/R=0.09, D=0.61 m, z=1.55 m, H0=2 m, FCC IV. Chapter 7 Multiscale Resolution 219 Scale, j Figure 7.9 Contour plot of L I M for 6 levels depicting passage of energetic microstructure mostly at small scales of analysis. U=1.56 m/s, r/R=0.09, D=0.61 m, z=1.55 m, H0=2 m, FCC IV. Chapter 7 Multiscale Resolution 220 (b) j=6 - O - U = 0 . 4 2 m / s — x — TJ=0.82 m / s — A — TJ=1.56 m / s Figure 7.10 Effect of superficial gas velocity on probability distribution of L I M at: (a) level 1; and (b) level 6. D=0.61 m, r/R=0.09. z=0.80 m for U=0.42 m/s; z=1.55 m for U=0.82 and 1.56 m/s, H0=2 m, FCC IV. Chapter 7 Multiscale Resolution 221 7.6.2.2 Wavelet analysis applied to voidage fluctuation T o gain better understanding o f the signal fluctuations at the particle level, data from the optical velocity probe sampled at 7333 H z are analyzed using the Daubechies wavelet 5. The local intermittency measure, L I M j , at scale j = l and 6 is compared for three superficial gas velocities, 0.57, 0.82 and 1.56 m / s , for r /R=0 .09 i n Figure 7.11 (a) and (b). A t the larger scale, the three distributions are very similar. However at the small scale, the energy variation due to particle voidage fluctuation increases wi th U as indicated by the shift i n the probability distribution o f L I M j i n Figure 7.11 (a). A s depicted by the voidage signals for three superficial gas velocities o f 0.57, 0.82 and 1.56 m / s i n Figures 7.12 (a), 7.13 (a) and 7.14 (a), respectively, the erratic voidage fluctuations at the measurement scale and frequency captured by the 0.26 m m diameter fiber increases wi th gas velocity. B y employing the time localization capabilities o f the wavelet analysis, a section from each gas velocity trace representing the dense phase is extracted from the L I M values. L I M values from 9.96 to 10.06 seconds i n the time series are plotted i n Figures 7.12 (b), 7.13 (b) and 7.14 (b). Increasing U towards U c increases the L I M , particularly at the smallest scale, i.e., j = l , and the larger scales o f j=5 and 6. Increasing U beyond U c results i n the L I M distribution becoming increasingly uni form i n the high-density phase near the co lumn axis. Ex tend ing U to examine the distribution o f L I M i n clusters wou ld be o f great interest in bridging the transition between turbulent and fast fluidization flow regimes. Nevertheless, the energy variations i n the high-density phase near the axis become increasingly homogeneous wi th increasing scale. O n the other hand, measurements near the wal l reveal an increase i n larger scale energy variations wi th increasing U as shown i n Figures 7.15 (a) and (b). The significance o f these findings can be associated wi th the increasing size o f eddies near the wall , leading to higher energy dissipation affecting the larger scale o f turbulence reflected by the higher energy variation at larger scale. The time series o f L I M j for four different situations i n a!fluidized bed are shown i n Figures 7.16 (a) through (d). The high L I M peaks are l inked to indicate the presence o f coherent structure corresponding to high energy level (Camussi and Guj , 1997). High-energy fluctuations are indicated at r /R=0 .09 , wi th the probe reflecting very fast movement o f regions o f different voidage, e.g. passing o f fast voids. The energetic microstructure is shown at a small scale to pass near the axis while the larger scale is near the wall . Chapter 7 Multiscale Resolution 222 1.004 0.95 0.90 0.85 4 0.80 O Q O O O O O o ooo^QSQS^^Q^-QW^^^ o y*' ll o - O - U = 0 . 5 7 m / s - x - T J = 0 . 8 2 m / s A ' 1 1 1 ' 1 —A— TJ—1.56 m / s i . i i (a) p i 10 15 L I M 20 25 30 (b) j=6 L I M , Figure 7.11 Effect of scale on probability distribution of LI1VI. D=0.61 m, r/R=0.09. z=0.80 m for U=0.42 m/s; z=1.55 m for U=0.82 and 1.56 m/s, PL=2 m, FCC IV. Chapter 7 Multiscale Resolution 223 Figure 7.12 Voidage fluctuation signal from optical velocity probe and probability distribution of L I M at 6 scales. U=0.57 m/s, r/R=0.09, D=0.61 m, z=0.80 m, H0=2 m, FCC IV. Chapter 7 Multiscale Resolution 224 Figure 7.13 Voidage fluctuation signal from optical velocity probe and probability distribution of L I M at 6 scales. U=0.82 m/s, r/R=0.09, D=0.61 m, z=1.55 m, H0=2 m, FCC IV. Figure 7.14 Voidage fluctuation signal from optical velocity probe and probability distribution of L I M at 6 scales. U=1.56 m/s, r/R=0.09, D=0.61 m, z=1.55 m, H 0 = 2 m, FCC IV. Chapter 7 Multiscale Resolution 226 Figure 7.15 Effect of U on probability distribution of L I M at 6 scales for r/R=0.94. D=0.61 m, z=1.55m, H0=2 m, FCC IV. 228 0 0 CN CN 1111111 rO CN o 1 I 1 I 1 I TT N O I 1 I 1 I 1 I 1 I 1 I 1 I CN O 1 I 1 I 1 I I'I'I'I'I CXXO^ttNO o o CN o o o 00 l _ C N C N | _ O S O N C/3 CU ( O w n 3 230 o CO CN LO 00 I— o .3 0 o © 111111 o o © 'I'I'I'I1 © © © © r O C N r H T T © © © U O T © © © © 00 -rj-3 © © r H © ND © © © I— o I 1 I ' I © © © 00 T t © © ( O w n a NO r H i> CJ IH 3 CUD co 3 > W H H >3 CJ C N © © II c 6 CM II C N © II D* l O r H II N tf NO 'x II CU i - j CO 1—' tf _f •a a "3 3 tf 3 o N O © II Q CC - r j 3 CJ co O ft "3 tf IH CO 3 O • TH 4-rt > cu H O O IH ft tf J3 ft W> .3 '•w tf 3 •w cj 3 C3 © © II Di £ "3 CO - H "tf CJ CO NO CJ CO tf J3 ft S CJ •1 "3 C N © ft II Di o u NO r H t-^  CJ IH 3 OX PH CJ CO tf XI ft Chapter 7 Multiscale Resolution 231 7.6.3 Qualitative analysis using wavelet A more qualitative analysis is presented here based on wavelet transform. The scalogram o f a decomposed signal on a wavelet provides information regarding the time and frequency variation o f signals. Ross and Pence (1997) reported on the continuous wavelet transform using the Mor le t wavelet o f the heat transfer coefficients obtained in a bubbl ing bed o f 345 u m particles. Bifurcating and trifurcating structures were revealed in the scalogram. Baksh i et al. (1995) used the wavelet packets basis i n visualizing the contributing physical phenomena o f local gas holdup signals i n gas-l iquid bubble columns. T ime- and scale-localized energy distributions were shown to provide a rigorous tool i n extracting phenomenological features o f the flow. Moreover , wavelet analysis was shown to unify the interpretive results obtained through statistical, spectral and fractal analysis methods. Continuous wavelet transform and the Mor le t wavelet were applied to the voidage data to obtain wavelet coefficients. Figures 3.17 (a) and (b) display the scalogram based on a sampling frequency o f 100 H z for 100 s data, wi th U=0.32 and 1.0 m / s . The bright red colour indicates strong variations o f signal fluctuation related to energy distribution. In the bubbl ing fluidized flow regime, e.g. Figure 7.17 (a), the voidage fluctuation dominates the energy distribution wi th minor amounts o f energy distribution i n the higher frequency range. Compar ison o f the two figures shows increased energy at the higher frequency and more energy dissipation at lower frequency, while the extent o f variations decreases wi th increasing frequency at U=1.0 m / s . In the flow regime o f turbulent fluidization, the voids transfer energy erratically in various frequency ranges. Figure 7.18 shows the energy dissipation during defluidization o f the bed after the air supply has been cut o f f from the 1.56 m diameter column. Bursts o f energy at lower frequency from the vo id dynamics are no longer present, and the energy is mostly dissipated at high frequency from particle fluctuation. The above analyses reveals the effectiveness o f the continuous wavelet transform in displaying the properties o f signals in a time-frequency domain and provid ing insights which aid physical interpretation. Chapter 7 Multiscale Resolution 232 (a) C W T 1 D Wavelet: Morlet ld ( kQ=6, sigma=1) 0.5 | 1.5 ro o C/3 2 CJ5 2 5 3 3.5 4 1 j 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 (b) Positions 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Positions Figure 7.17 Continuous wavelet transform using Morlet wavelet, (a) U=0.32 m/s; and (b) 1.0 m/s. D=0.29 m, z=0.77 m, r/R=0.0. (lowest scale corresponding to 50 Hz) Chapter 7 Multiscale Resolution F i g u r e 7.18 D i s t r i b u t i o n o f energy i n the t ime- f requency p lane o f v o i d a g e s i g n a l u s i n g c o n t i n u o u s wavele t t ransform w i t h M o r l e t wavele t d u r i n g d e f l u i d i z a t i o n . D=1.56 m , r / R = 0 . 5 , z=0.84 m , H 0 = 2 . 0 m , F C C I I . Chapter 7 Multiscale Resolution 234 7.7 Multiple scales in turbulent fluidized beds A s explained in Section 7.3, flow structures in fluidized beds can be divided into three different scales. The dynamic behaviour o f solids and gas influences the interactions at different scales and under different operating conditions. A t the macroscale, the axial voidage distribution indicated a smooth transition from the bed to the freeboard, as shown i n Figure 2.17. The expanded bed height was greatly influenced by the configuration o f the solids collection and return system. A t the macroscopic level, the radial voidage distribution, as depicted i n Figure 4.34, exhibited heterogeneity. The turbulent fluidization flow regime at this scale clearly indicated a smooth transition between a bubbl ing regime and fast fluidization wi th the dense bed expanded by the increasing superficial gas velocity, while an increasing fraction o f the solids inventory was transferred to the freeboard. O n the meso-scale, v o i d dynamics prevail i n the turbulent fluidization flow regime. T h e rise and fall o f pressure fluctuations correspond to occurrences o f v o i d coalescence and splitting. A s depicted in Figure 6.30 (a), the cycle time obtained from DP signals through rescaled range analysis indicated a shift at U > U c . This may suggest that at a certain height above the distributor plate, v o i d splitting becomes increasingly dominant over coalescence. Furthermore, the increased overall voidage at z / H >0.5 from pressure drop measurements, plotted i n Figure 2.13, and the decrease i n standard deviation o f voidage fluctuations from optical probe measurements, shown i n Figure 4.20, suggest an increasingly diffuse bed subject to high frequency voidage fluctuations. Th is is also consistent wi th the average v o i d frequency, shown i n Figure 5.20. N o t e that the amplitude o f such fluctuations decreased wi th increasing voidage as U was increased, resulting i n a decrease i n pressure fluctuations for U > U c . The homogeneity o f the bed, an often-cited characteristic o f the turbulent fluidization flow regime, originates from the breakdown o f the two-phase structure, i.e., dense and dilute phases at the meso-scale, as shown in Figure 4.37. This breakdown occurred gradually wi th increasing U . A t the microscale, i.e., particle level, a significant number o f upward particle velocities are indicated for r /R=0 .09 and 0.50 wi th increasing U , as depicted in Figures 5.14 through 5.16. These particle velocities were associated with higher voidages, especially at r /R=0 .09 . The increase i n voidage, i.e., interstitial gas between particles, may suggest less energy loss as a consequence o f inelastic particle-particle collisions, and an increase i n the turbulent energy o f particles. Chapter 7 Multiscale Resolution 235 H i g h frequency voidage fluctuations, as shown i n Figure 7.14 (a) may be l inked to the passage o f high-energy structures according to Figure 7.16 (d) at the smaller scales, i.e., reflecting fluctuations at the particle level. 7.8 Conclusions Numerous methods have been introduced (Motard and Joseph, 1994) to provide improved signal processing in contemporary science and engineering. A l l are aimed at analyzing and interpreting complex time series. Though it has not been possible to cover them all, some promising methods have been considered i n this and the preceding chapters. In particular, multiresolution analysis has been introduced i n this chapter and applied to local data f rom turbulent fluidized beds. The following observations are made: • De-nois ing voidage fluctuation signals using a nonlinear wavelet transform through soft thresholding was successful in pre-conditioning the signal for cross-correlation o f bivariate time series. A priori knowledge o f the signal must be applied to set the appropriate criteria to eliminate certain frequencies and time domains o f the signal. T h e successful application o f this technique eliminates the necessity to set threshold values i n distinguishing voidage signals from dense to dilute phases, as described i n Chapter 5. • The time- and frequency-localization capabilities o f the wavelet transform enable further analysis o f signal characteristics. L o c a l intermittency measures defined to characterize energy distribution i n space were applied to velocity and voidage fluctuations i n turbulent fluidized beds, revealing the presence and passage o f energetic microstructures wi th different scales. Mult i resolut ion analysis must consider the physical scale for w h i c h the signal was obtained, as wel l as the frequency scale. • Continuous wavelet transformation was applied to visualize the contributing physical phenomena, wh ich can be extracted for further analysis. • Mult i resolut ion analysis can help i n understanding the complex flow dynamics o f fluidized beds. Preliminary indications o f the applicability o f wavelet transform for scalewise decomposi t ion o f signals f rom fluidized beds are promising. A s stated by many wavelet researchers, e.g. Farge, 1992, wavelet transform can be regarded as a tool to better 'see' the phenomena, and from which to conduct further analysis leading to conclusions, rather than a method to present solutions to underlying phenomena. • The presence o f intermittency from velocity and voidage measurements can be qualitatively shown; however, there is no analogy to connect the observations to the flow structure. Chapter 7 Multiscale Resolution 236 Further studies • Further investigations i n applying wavelet transform to reveal complex dynamics i n fluidized beds from specific scale related measurements and decomposi t ion are required to contribute to the maturity o f analysis methods i n fluidization research. • Multiscale analysis has recendy been applied to the bivariate relationship between two time series (Arneodo et al, 1998; Whitcher, et a l , 2000). This indicates progress i n wavelet analysis, and the potential for further advanced analysis methods. CHAPTER 8 CONCLUSIONS F r o m the extensive experimentation presented i n this work involv ing measurements o f gauge and differential pressure, voidage and particle velocity fluctuations as functions o f gas velocity at ambient temperature, at elevated pressure and temperature, and i n four columns o f different diameters, a number o f conclusions have been drawn. The underlying idea o f understanding the complex flow in the turbulent fluidized bed from the perspective o f gas-solids transient flow has been explored. A s a way o f tackling this complexity and gaining insight into the mechanisms involved, various analysis methods have been employed. The findings are collectively summarized i n this chapter. Differences o f op in ion persist wi th respect to what constitutes the turbulent fluidized bed flow regime, even after 20 years o f work by industrial and academic researchers. Furthermore, and perhaps because o f that, definitions o f transition on both ends o f the turbulent fluidized bed flow regime still fuel heated discussions at fluidization conferences. Once , at an international chemical engineering congress, I was asked about my philosophical view o f these transitions as a young researcher getting into this field. Displaying c o m m o n objective proposit ions happens far too infrequently. A s a result, reports characterizing turbulent fluidization lack standardization on reporting methods and do not display acceptance o f some c o m m o n perspectives. F o r example, hydrodynamic characteristics are still reported by some for units considered to be operated as turbulent fluidized beds from observing breakdown o f voids solely by visual observations or through X-rays. C o m m o n understanding o f key operating parameters affecting hydrodynamics and operations should be sought i n the quest for substantiating past fmdings and advancing knowledge i n this field. The realization o f the lack i n standardized terminology, o n system characterization and experimental methodology was apparent through surveying the literature, and thus served as a starting point for this research project. K e y conclusions are summarized as follows. • The transition velocity, U c , was defined as the superficial gas velocity at wh ich the standard deviation o f pressure fluctuations attains a maximum, and was found to decrease as the co lumn diameter increased from 0.29 m through 0.61 m to 1.56 m , and wi th decreasing initial 237 Chapter 8 Conclusions 238 static bed height. Results indicated a different trend i n U c between shallow ( H / D < 3) and deep beds ( H / D > 3). Correlations are proposed for high H / D as: R e c = 0.371 A r 0 ' 7 4 2 T T x 0.183ln(d„e, )+0.83 0.454 f H ^ V p L s ; and for low H/D as: R e r = 0.459 A r u ' ^ | — ID These equations are for Geldart G r o u p A particles wi th U c deduced from gauge pressure fluctuations. • U c from differential pressure signals was found to increase as the locat ion o f the sensor descended towards the distributor plate. This implies that homogeneity o f the fluidized bed was attained at the top o f the bed first, before the rest o f the bed reached the turbulent fluidization flow regime as the superficial gas velocity increased. N o conclusive correlation was obtained for predicting U c from D P signals due to this height effect. • The transition velocity decreased wi th increasing system pressure (up to 0.4 M P a ) , and wi th increasing temperature (up to 240°C) , for a commercial catalyst. T h e correlation by Sun and C h e n (1989) displayed better predictions o f U c for the conditions under investigation than the correlation o f C a i et al. (1989). The effect o f particle size distribution o n U c was wel l predicted by existing correlations based on A r and R e c numbers reflecting the change i n mean particle size. However , discrepancy was observed when existing correlations were used to predict the effect o f co lumn diameter on U c . The validity o f the assumption that the wal l measurements are representative o f the cross-section and give the transition velocity applicable at the centre was confirmed experimentally. • A x i a l pressure profiles indicated diffuse bed surfaces, wi th increasing gauge pressure in the freeboard wi th increasing superficial gas velocity due to solids entrainment. W i t h an efficient solids return system, bed voidage in the 0.61 m diameter co lumn remained at - 0 . 6 , for operation in the turbulent fluidized flow regime. Increases i n both the absolute pressure and bed temperature, investigated i n the 0.11 m diameter co lumn, caused increases in bed voidage, wi th pressure having a greater influence than temperature. Chapter 8 Conclusions 239 • Spectral analysis o f pressure fluctuations revealed dominant peaks amongst a broad range o f frequencies. T h e natural frequency o f the bed based o n gauge pressure signals decreased wi th increased bed height. F F T analysis o f D P signals at different axial positions indicated a shift towards a lower frequency distribution wi th height, due to an increase i n v o i d size for U < U C . This trend was confirmed by local measurements obtained by optical probes, based on the crossing frequency. • A novel probe was employed to capture simultaneous measurements o f local voidage and particle velocity i n a turbulent fluidized bed o f F C C particles. T h e results confi rm previous reports that v o i d movement is erratic and transient. Particle velocity fluctuations increased at U > U c , indicating an increase in particle turbulence. Increasing U led to increasing migration o f solids to wider range o f voidages, and to increasing occurrence o f upward particle velocities at the wall . Particle velocity fluctuations originate f rom collisions and other interactions between particles and from interactions wi th the gas phase. In a dense suspension, interparticle frictional forces dominate over kinetic and collisions forces. It is shown that particle velocity fluctuations increase for U > U c . The trend can be explained as particles i n the dense phase becoming increasingly spaced apart, gaining turbulence energy by higher fluctuations and having less energy loss as a consequence o f inelastic particle-particle collisions. A t U=1.56 m / s , there were more close-to-zero particle velocities and a shift to a higher voidage distribution. Since the optical velocity probe is only capable o f capturing vertical velocities, an increased occurrence o f near zero velocities may indicate increased radial movement o f particles. • The effect o f solids flux from the return leg was found to be significant wi th respect to the hydrodynamics o f the bed, especially for a larger co lumn wi th a highest mass flux. In systems where the solids circulation rate is not controlled, it is difficult to characterize o f the overall operating conditions i n terms o f bed expansion alone. • U s i n g identical optical probes, v o i d velocity was calculated from the cross-correlation o f signals. A t U > U c determination o f the threshold for removing dense-phase voidage fluctuation prior to cross-correlation became extremely sensitive to the resulting velocity distribution. This suggests that treating turbulent fluidized beds as two discrete phases, i.e., voids and dense phases, may not be applicable. A new method is proposed to remove high-Chapter 8 Conclusions 240 frequency voidage fluctuations from the signal based on a non-linear thresholding method involv ing wavelet transformation. This method eliminates the dependency o n the threshold value i n determining the v o i d edge, and is seen to be successful i n pre-conditioning the voidage signals for cross-correlation. • In order to determine the cycle o f v o i d renewal i n characterizing the change occurring at U « U c without differentiating between v o i d and dense phases, rescaled range analysis was employed. The cycle frequency detected i n voidage fluctuations exhibited a change in trend at U w U c wi th cycle frequencies comparable to those represented by the dominant frequency i n the D P fluctuations. In addition, rescaled range analysis used to detect cycle times in pressure fluctuations provided a means o f confirming the change i n v o i d dynamics wi th height. Cycle time from D P fluctuations for U < U c increased monotonical ly wi th increasing height, indicating general dominance i n v o i d growth. A t U > U c , an increase i n cycle time occurred suggesting larger voids closer to the distributor plate unti l a decreasing trend emerges higher i n the bed. This may suggest relative dominance o f v o i d splitting at the higher levels. • Wavelet analysis provided an excellent means o f time-frequency localization o f signals. The local intermittency measure (LIM) calculated based on wavelet coefficients was shown to describe the non-uniform distribution o f energy resolved in time and frequency. The strong velocity gradient considered can be characterized by coherent vort ical structures. Thus, L I M can identify the passing o f energetic structures. A t U > U c , the L I M near the co lumn wal l indicates more frequent passage o f large-scale energetic structures. This may be due to increasing particle velocity fluctuations as particles respond to the movement o f eddies generated near the wall . Wavelet transforms appear to be promising for scalewise decomposi t ion o f signals from fluidized beds. • The coherence function characterizing the coherence between a set o f signals at a given frequency was shown to decrease wi th increasing superficial gas velocity. In the turbulent fluidized bed exhibiting erratic v o i d movements, the coherence function alone may not be sufficient to capture trends at different frequencies. The length scales o f the phenomena o f interest must be considered before making experimental measurements. Chapter 8 Conclusions 241 A preliminary investigation was carried out to simulate a turbulent fluidized bed o f F C C particles using a commercial C F D software package C F X , based on the two-fluid model . D u e to time constraints, a successful simulation was not attained. O w i n g to the difficulty o f conducting precise experimental measurements to obtain such coupl ing terms as solid stress, drag force, and energy dissipation as a result o f particle collisions, it is very difficult to validate the parameters incorporated i n the two-fluid model . M u c h work is needed to make C F D a viable tool for the simulation o f hydrodynamics o f turbulent fluidized beds. N O M E N C L A T U R E A cross-sectional area m 2 A P single-point pressure (referred to as gauge pressure) kPa A * i • i , G ( G p - e ) g d p A r Archimedes number, = •—^ -V-a wavelet scale in Equat ion C.14 a approximate wavelet coefficient a, b coefficients i n Equat ion 3.2 b translation parameter in Equat ion C.14 C signal capacitance p F C 0 capacitance without solids present p F C D drag coefficient C D s drag coefficient o f a single sphere i n an infinite expanse o f fluid C , T covariance function i | i 2 c instantaneous particle velocity m / s D co lumn diameter m D b bubble diameter m D P differential pressure kPa d detailed wavelet coefficients d c, cluster diameter in Table D . 2 m db max m a x i m u m bubble diameter m dj k wavelet coefficient d p mean particle diameter m d s m Sauter mean particle diameter m E expected value e restitution coefficient e c f r effective coefficient o f restitution e w particle-wall restitution coefficient ^ r Froude number based on U , = U-y/gD F r , Froude number based on U c i n Equat ion 3.14, = U c -\/gD 242 Nomenclature 243 f sampling frequency 1 /s fc crossing frequency from Equation 6.10 1/s fc crossing frequency in Table B.2 (with defined threshold value) 1/s fDP major frequency from DP signals 1/s fd volume fraction of dense phase in Table D.2 fn natural frequency from AP signals 1/s G(f) cross-spectral density function G(e) solid pressure function g gravitational acceleration m/s 2 g0 radial distribution function for a uniform distribution of given mean porosity g'0"1 detailed wavelet function g(r) radial distribution function H expanded bed height m H Hurst exponent H ' dense bed height corresponding to voidage at minimum fluidization m H m a x maximum bed expansion m H m a x maximum Hurst exponent H m i n minimum Hurst exponent H 0 initial static bed height m I relative intensity of reflected light to reference light I identity tensor in Equation D.12 IA B(t) time series of relative light intensities from fibers A and B, respectively i time index j wavelet scale K c f f effective relative dielectric permittivity of a suspension in Equation 4.4 K h relative dielectric permittivity of host fluid K p relative dielectric permittivity of particles k wavevector/translation parameter k thermal conductivity W-m2-K k unit vector along line from centre of particle 1 to 2 in Equation D.20 and D.21 Nomenclature 244 kg number o f levels corresponding to scale L 2 (I) set o f square-integrable functions on the interval, I, defined i n Equa t ion 6.1 L I M local intermittency measure denned i n Equat ion 7.4 M largest resolvable wavelet scale M b mass o f solids in the dense bed kg M s mass o f solids kg m mass o f particles in Equat ion D.14 kg m a x Q max imum number o f levels o f wavelet decompositions i n Equa t ion 7.5 m ; thermodynamic mass transfer term i n Equat ion D . 7 kg/m 3 - s m s particle mass loading: mass o f particles/mass o f gas i n computational -domain N number o f data points analyzed i n time series/group number N ' number o f vanishing moments in wavelet n number o f determinants n coefficient used in Equat ion 2.1 P pressure kPa P g g a u g e (single point) pressure kPa P T P statistic defined i n Equat ion 6.15 •Y 3 Q c volumetric flow rate at wh ich standard deviation o f pressure fluctuation k g / m reaches a max imum Q s constant charge amplitude Coulombs d p 9 g U c r radial coordinate R co lumn radius Re Reynolds number based on U c , = R e c Reynolds number i n dense phase i n Table D . 2 R e D Reynolds number based on co lumn diameter, = m m D o g U R e f Reynolds number i n dilute phase i n Table D . 2 Re particle Reynolds number, W 1 Nomenclature 245 ' • • p^ g g Re particle Reynolds number based on relative velocity, = •— ^g Re* Taylor microscale mrbulent Reynolds number -R(t,T) range over the subperiod, T, defined i n Equa t ion 6.13 R T regularity o f cycle time defined i n Equat ion 6.16 (R/a)T rescaled range for the subperiod o f length x Sr Strouhal number based on dominant frequency, =fDpH/Uc St Stokes number, x p / x^ -sigma moment o f wavelet function -T temperature °C T c time required for distance between particles to return to original value s T n time scale i n Equat ion D.23 s T r relaxation time i n Equat ion D.23 s U superficial gas velocity m / s u c transition velocity at wh ich standard deviation o f pressure fluctuations m / s attains a max imum u c superficial gas velocity i n dense phase in Table D . 2 m / s u f superficial gas velocity in dilute phase i n Table D . 2 m / s u d c superficial particle velocity i n dense phase m / s u J f superficial particle velocity i n dilute phase m / s superficial gas velocity i n dense phase m / s superficial gas velocity i n dilute phase m / s u k superficial gas velocity corresponding to levelling out o f pressure m / s fluctuation amplitude wi th increasing U u m b m i n i m u m bubbling velocity m / s m i n i m u m fluidization velocity m / s U P velocity vector o f particles m / s particle terminal settling velocity m / s u; . effective cluster terminal velocity m / s transport velocity m / s V voltage signal V V 0 optical fiber signal in black box V Nomenclature 246 V[k] Fourier transformation o f x[n] v m f optical fiber signal o f dense bed/packed state V v r ratio o f terminal velocity o f a group o f particles to that o f an isolated -particle v x V statistic defined in Equat ion 6.14 -0.5 s v 8 gas velocity m / s particle velocity m / s W j ( k ) wavelet coefficient w[n] window function in Equat ion C.6 X time series data value x(i) signal wavelet transform o f x(i) z set o f integers -z axial distance above distributor m z coordinate i n direction o f flow m z statistic defined i n Equat ion 3.8 coefficient defined i n Equat ion 3.12 z average height between two ports from distributor plate m Symbols P fluid-particle friction coefficient kg/m 3 -s P, regression parameters in Equat ion 3.4 (i=0, 1, 2) -Y exponent for P statistic i n Equat ion 6.15 -ys coll is ion rate o f dissipation per unit volume -autocorrelation function defined i n Equat ion 6.6 -coherence function defined in" Equat ion 6.7 A P pressure drop Pa A P b t J bed pressure drop extrapolated from gauge pressure profile Pa A P t o t a , total pressure drop Pa A t time interval s A z vertical separation between two ports/probes m Aco frequency band H z s voidage -Nomenclature 247 £ 0 compact ion gas phase volume fraction £ time-mean voidage g c voidage corresponding to max imum standard deviadon o f pressure -fluctuations e c voidage i n dilute phase g voidage at zero probability (lower l imit o f voidage) g f voidage i n dense phase g cross-sectional average voidage g voidage at m i n i m u m fluidization £ s solids volume fraction £ s m a x max imum sohds compaction fraction E voidage signal as a function o f time (Equation 4.6) -q eddy size defined in Equat ion 7.1 m 0 granular temperature m 2 / s 2 cp normalized radial coordinate i n Equat ion 4.8, r / R X threshold value used i n Equat ion C.29 X , m f mean free path o f particles m X sohds bulk viscosity p a . s p coefficient o f friction i n Equat ion D .22 p g gas viscosity p a . s I V S a s v i s c o s i t y a t 2 0 ° C Pa-s p sohds shear viscosity p a . s P g/Pf gas density k g / m 3 p gas density at 2 0 ° C and 0.1 M P a k g / m 3 P p / p s particle density k g / m 3 p cross-correlation coefficient function r j standard deviation defined i n Equat ion 3.1 r j sohds normal stress in Equat ion 2.2 Pa X time lag s shear stress tensor Pa x x characteristic time o f autocorrelation function s c xc eddy time scale s xH subperiods i n Equat ion 6.12 Nomenclature 248 \ particle response time s wal l shear due to gas Pa ^ s wall shear due to solids Pa K o l m o g o r o v time scale s ° I A I B cross-correlation function Wj(k) Mothe r wavelet Wj(k) wavelet function in frequency space wavelet basis function ¥ , ( k ) wavelet function i n time space 91 set o f real numbers (-co,co) Operations [a,b) half-open interval {x: a < x < b} (£_ g) L 2 inner product f -L g functions f and g are orthogonal, i.e., (f, g)=0 V gradient V I transpose o f gradient Abbreviations A P single-point (gauge) pressure C F B circulating fluidized bed C F D computational fluid dynamics C O P coherent-output power spectral density defined i n Equa t ion 6.9 C S I R O Commonwea l th Scientific and Industrial Research Organisation C W T continuous wavelet transformation db Deubechies wavelet D E M discrete element method D P differential pressure F C C fluid cracking catalyst F F T fast Fourier transformation I D internal diameter I O P incoherent-output power spectral density defined i n Equa t ion 6.10 Nomenclature L I M local mtermittency measure defined i n Equa t ion O D outside diameter P S D particle size distribution U B C Universi ty o f Bri t ish Columbia Subscripts b bubble g g a s p particle R range s solids x time-series data y time-series data X subperiod R E F E R E N C E S A b b a , L A , A Generalised Fluidized Bed Reactor Model Across the Flow Regimes, P h . 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