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Electromagnetic induction sensing of individual tracer particles in a circulating fluidized bed Goldblatt, William M. 1990

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Electromagnetic Induction Sensing of Individual Tracer Particles in a Circulating Fluidized Bed by  William M . Goldblatt B.Sc, Colorado School.of Mines, 1972 M.Sc, Colorado School of Mines, 1974 M.E., City College of New York, 1981  A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F T H E REQUIREMENTS F O R T H E D E G R E E O F D O C T O R OF PHILOSOPHY in T H E F A C U L T Y O F G R A D U A T E STUDIES Department of Chemical Engineering We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A October, 1990 © Wilham Goldblatt, 1990  i' ,  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  department  purposes  may be granted  or by his or her representatives.  by the head of my  It is understood  that  publication of this thesis for financial gain shall not be allowed without permission.  Department The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  6 /?'6re/Q*-y /?9 I  copying or my written  Abstract Understanding the trajectories of particulate solids inside a flow-through reactor, such as the riser of a recirculating fluidized bed, is a basic requisite to accurately modelling the reactor. However, these trajectories, which are complicated by gross internal recirculation, are not readily measurable. Conventional means of measuring the residence time distribution can be applied to closed boundaries, such as the exit of the riser. Doing so, however, does not directly provide the details of the trajectories within the riser. In order to determine these trajectories, meaningful measurements must be made at the open boundaries between the adjacent axial regions which, in total, make up the riser. Transient tracer concentration measurements at open boundaries are ambiguous because, as tracer material recirculates past the sensor, its concentration is repeatedly recorded, with no distinction as to which region (above or below the boundary) it has just resided in. A method designed to eliminate this ambiguity at open boundaries is reported in this thesis. By repeatedly introducing single tracer particles into the riser, and measuring the time of passage through each axial region, the residence time distributions for each region can be obtained from the frequency density of these times. approach is being able to sense individual tracer particles.  The crux of this  The major thrust of this  investigation has been to find a practical means to this end. The final sensor considered in this investigation is based on electromagnetic induction: a magnetic primary field induces an eddy current in a conductive tracer particle, and the resulting secondary field is sensed, indicating the presence of the tracer particle in the sensing volume.  Noise,  resulting from direct coupling between transmitter and receiver coils, electrostatics, and vibrations, determines the sensitivity of the device. The final prototype sensor is limited in sensitivity to relatively large tracer particles, and it is incapable of measuring tracer velocity.  Nevertheless, the trajectory of large particles is of practical significance for  circulating fluidized beds. Limited tests were conducted in a 0.15 m ID x 9.14 m tall acrylic riser where the tracer particles were injected opposite the solids re-entry point, and were sensed by a single sensor located at an open boundary 7.5 m downstream. At each of the two superficial gas velocities considered, and above a threshold solids flux, the time-of-flight frequency density between the injector and the sensor for these large tracer particles does not change with increasing flux of the fine solids.  This result is  incongruous with obvious changes in the macro-flow structure occurring in the riser. Recommended changes in the sensor would allow measurement of the direction and speed of the tracer, as it passes by the sensor, as well as potentially reducing noise. With these improvements, it would be useful to install multiple sensors along the full length of  n  the riser. The information obtainable from such a configuration would greatly enhance understanding of the detailed trajectories within the riser.  in  Table of Contents  ABSTRACT  ii  List of Tables  vii  List of Figures  "vu^  ACKNOWLEDGEMENTS  x  1  Introduction  1  1.1  Circulating Fluidized Beds (CFB)  2  1.2  Residence Time Distribution Techniques in the C F B  6  1.3  2  3  1.2.1  Previous Measurements  10  1.2.2  Single Particle vs. Pulse Response  12  Electro-magnetic Induction (EMI)  15  1.3.1  Other Applications and Their Relevance  15  1.3.2  Special Considerations in the C F B  24  Our Early Approaches to E M I Sensing  31  2.1  Calculated Response of a Circumferential Loop  31  2.2  Permanent Magnet Tracers  35  2.3  Inducing and Sensing a Magnetic Dipole  40  2.3.1  Decoupling Primary Field  41  2.3.2  Resonant Transmitter Circuit  53  2.3.3  Nonlinear Methods  57  Present Configuration  65  3.1  Sensor and Associated Electronics  65  3.2  Calculated Response of a Diametral Loop  72  3.3  Exciting Field Due to the Circumferential Transmitter  76  3.4  Originality  77  3.4.1  Successful Decoupling due to Diametral Design  81  3.4.2  Phase of Response Considerations  83  3.4.3  Effective Shielding From Electric Field Fluctuations  86  iv  3.5  3.6  4  87  3.5.1  Global vs. Local Indications  87  3.5.2  Minimum Tracer Size  88  3.5.3  Noise  . . . ;  90  Recommendations  93  3.6.1  Resolving Local Indicators  93  3.6.2  Scale-Up  3.6.3  Local Flow Rate Determination  94 .-  98  Experimental Work  100  4.1  Validation of the EMI Technique  100  4.1.1  Method  101  4.1.2  Results  105  4.1.3  Discussion  114  4.2  5  Limitations of the EMI Technique  Application of the Technique in the C F B  115  4.2.1  Apparatus  115  4.2.2  Particulate and Tracer Properties  120  4.2.3  Experimental Procedure  124  4.2.4  Results  126  4.2.5  Discussion  129  Summary  135  5.1  Implications of This Work  135  5.2  Recommendations for Future Work  5.3  Overall Conclusions  .  137 140  Bibliography  145  A  Dipole Moment of a Non-Permeable Thin Shell Based on U  154  B  Derivation of Equations Used in Sections 2.1 and 3.2  156  e  B.l  Translating the Origin from the Dipole to the Centre of the Circumferential Loop  156  B.2  Integrands and Inner Integrals of Equation 2.4  157  B.3  Justification of the form of Equation 3.1  159  C  Calculation of Superficial Gas Velocity (U ) from Orifice Measurements 160  D  Multiplication of Two Sinusoids Followed by Integration  g  v  .  162  E  Terminal Velocity Calculation for a Sphere  164  F  Data from C F B Tests and Statistical Evaluation of Results  165  F.l F.2  Can the Results of Runs #7a and #7b be considered to come from the same Population?  165  Which of Runs 1 Through 7a Share the Same Probability Law?  166  vi  List of Tables  2.1  M for Spheres Compared to £  4.1  Oscilloscope Signal During Drop Tests  Ill  4.2  Properties of F-75 Ottawa Sand (Burkell, 1986)  121  4.3  Schedule of Experimental Runs  127  F.l  Number of Observations by Time Intervals  168  F.2  Measured Peak Times, Run l-7b  169  r e s  i d l / M o for Materials of Figure 2.2. u a  vii  .  40  List of Figures  1.1  Schematic of a Circulating Fluidized Bed Combustor (Grace, 1990).  1.2  Regime Map of Solids-Gas Flow (Grace, 1990).  1.3  Typical Density Profiles in a C F B with Abrupt Exit (Brereton, 1987).  .  7  1.4  Effect of Coils Relative Positions on Coupling (Grant and West, 1965).  .  18  1.5  Real and Imaginary Parts of Response Function as a Function of Response Parameter | i f a | and of Relative Permeability 2  2  . .  5  /i/// 0  (Grant and West,  1965) 1.6  19  Transient Approach — Transmitter and Receiver Alternately on (Grant and West, 1965)  22  2.1  Response of Circumferential Case, R\  2.2  Typical Demagnetization Curves of Various Permanent Magnet Materials  oop  = 0.095m  Stablein (1982) 2.3  Satellite Receiving Loop Perpendicular to Plane of, and Tangent to TransSatellite-Sector  45 Receiving Loop ("figure-eight") Parallel to Plane of Cir-  cumferential Transmitter Loop 2.5  47  Cross-Section of Centerline Transmitter/External Satellite Loop Receiver (transmitter is perpendicular to plane of page)  2.6  59  Shearing Correction of a Magnetization Curve (Chikazumi and Charap, 1964)  2.9  52  Waveform of Current with Sinusoidal Applied Voltage to a Non-Linear Conductor (adapted from Ashworth et al., 1946)  2.8  51  Two External Axial Transmitters with Four Receiver Loops in Nulled Positions (showing resultant exciting field at P)  2.7  36 39  mitter Coil 2.4  3  '.  61  Assumed Magnetization Curves in Dilute Samples of Three Sizes of Ferromagnetic Particles (Bean, 1955)  64  3.1  Coil Form and Receiver Coil Winding  66  3.2  Block Diagram of Present Coil Relative to Supporting Electronic Circuits.  69  3.3  Transmitter Circuits for Security Application (taken directly from Fitzgerald, 1979)  : .  70  vm  3.4  Receiver Circuits for Security Application (taken directly from Fitzgerald, 1979)  71  3.5  Velocity Component of Response Diametral Case. Coil Rad. = 0.095m.  73  3.6  Moment Component of Response Diametral Case. Coil Rad. = 0.095m.  74  3.7  Magnetic Field Strength in Plane of Transmitter from Near Field Equation (3.4)  78  3.8  Ratio of Imaginary Response to Exciting Field for a Sphere at 6 kHz.  85  3.9  Locus of Particle Diameters and Conductivites Giving the Same as, or 10% of the Response of a 6.35 mm Aluminum Shell at 6 k Hz  91  3.10 Response of Circumferential Case, R^^ = 0.19 m  95  3.11 Velocity Component of Response Diametral Case. Coil rad. = 0.19 m.  .  96  3.12 Moment Component of Response Diametral Case. Coil rad. = 0.19 m.  .  97  4.1  Jig for Releasing Particles from Reproducible Positions in Rapid Succession  4.2  102  Velocity of 6.35 mm Diameter A l Shell Calculated on the Basis of Equation (4.1) with V^tij = 0  4.3  104  Sketch of Characteristic Oscilloscope Trace for a Typical Tracer PassThrough  107  4.4  Actual Oscilloscope Traces for Local Response Tests.  108  4.5  Scaled Circulating Fluidized Bed (Brereton, 1987)  116  4.6  Schematic of Tracer Injector  118  4.7  Cumulative PSD of F-75 Ottawa Sand  122  4.8  Choking Regime for Sand in 0.15m Diameter Riser (data points from Br-  4.9  ereton, 1987).  128  Time-of-Flight Histograms C F B Tests  130  ix  Acknowledgements  I would like to thank Harrison Cooper for generously loaning me a crucial piece of equipment, without which I might not have succeeded. I am grateful to John Grace for supporting me and riding along on this journey of exploration, many roads of which ended nowhere. My thanks to the men in the machine shop for their invaluable advice, and for stepping aside so that, with my own hands, I could give form to my ideas. To my way of thinking, fabrication is to invention, as mathematics is to process modelling, and I still cannot fathom how others forego this synergy. Last, and most important of all, I am grateful my family has sustained my spirit throughout this endeavor. This time has been a rewarding experience for each of us, and we have achieved far more than the pages of this thesis can ever reflect. My youth, with all its curiosity and enthusiasm, could well have been spent before the final chapter, had it not been for a small voice, repeatedly making inquiries and suggestions — rejuvenating me. Although his questions sometimes disturbed me because either I did not know their answers, or he too readily understood that which I was sure would be too complex for him, I thank my son for his participation, and hope he too will come to realize that curiosity is the fountainhead of innovation.  x  In the rampant storm, I listen for a faint whisper. But I do not hear it, shrouded in the wind and thunder. If I am to perceive the message, I must now learn how to listen.  xi  Chapter 1 Introduction  The purpose of this investigation has been to develop a novel sensor capable of obtaining solids residence time data within individual axial regions of a flow reactor. A technique of obtaining a residence time distribution by monitoring individual tracer particles over many solo passages through the regions of interest would eliminate the ambiguity associated with the open boundaries of such regions. Although conventional pulse-response tracer methods have been widely used to evaluate the flow between two open, and monitored boundaries, (e.g. see Wen and Fan, 1975), the model-dependent conclusions are limited in their applicability (Levenspiel, 1972). In its prototype form, the device developed in this study is capable of sensing only large tracer particles because certain characteristics of high-velocity particulate processes adversely affect the device's signal to noise ratio. In order to prove the usefulness of the device, it was tested in a cold model circulating fluidized bed (CFB). The solids circulating around a C F B are typically much smaller than these tracer particles.  Nevertheless,  the C F B was still chosen because some or all of the fuel fed to C F B combustors, for example, may be of a comparatively large particle size. In addition, agglomeration can occur in some C F B processes, or other oversized lumps may occur for other reasons (e.g. chips of refractory falling off the wall). Hence, an understanding of how large particles pass around or through the combustor and where they spend their time is important in developing a realistic model of the process.  1  Chapter 1. Introduction  2  In order to put this specific application in perspective, a brief overview of the circulating fluidized bed follows. Previous reviews have been presented by Yerushalmi (1982), Yerushalmi and Avidan (1985), and Grace (1990), while gas-solids reactions in C F B systems are covered by Reh (1986).  1.1 The  Circulating Fluidized Beds ( C F B ) C F B provides a means of contacting particulate solids with a high velocity gas  stream, and then continuously recycling the solids through an external loop for additional contacting.  The advantages of the C F B compared with lower velocity particulate-gas  contacting schemes are a relatively high throughput of gas without significant bypassing,  near uniformity of temperature and solids composition throughout the reactor, a  reduced tendency for particle agglomeration, the potential for staged addition of gaseous reactants at different levels, and independent control of solids hold-up. Compared to dilute pneumatic conveying, the temperature is more uniform in the C F B due to greater refluxing of solids and higher suspension densities. The  major components of the C F B , as shown schematically (Grace, 1990) in Fig-  ure 1.1, are the riser, where the particulates and gas are intimately contacted, the cyclone, where the gas and particulates are separated, and the standpipe/control valve, through which the particulates are reintroduced into the bottom of the riser. Since this investigation is concerned specifically with particulate motion in the riser, further discussion is focussed on this component. The riser is operated at a superficial gas velocity substantially above that of a conventional bubbling fluidized bed, but generally below that of a pneumatic transport line. A regime map (Grace, 1990), Figure 1.2, shows the typical operating conditions of the  Chapter 1.  Introduction  3  Flue gas to Superheater, Ecooomizef, Atrheater, Baghouse  Cooling waterwall  Cyclone  Standpipe Sec. air Fuel, Sorbent  Primary a i r Drain  Figure 1.1: Schematic of a Circulating Fluidized Bed Combustor (Grace, 1990).  Chapter 1. Introduction  4  C F B relative to other particulate/gas processes. The C F B is operated in what is known as the fast fluidization regime, which is characterized by a core/annular structure. Based on observations of flow in cold, scaled-down physical models, numerous researchers (e.g. Brereton, 1987; Ishii et al, 1989; Rhodes et al, 1990; Ambler et al, 1990) have constructed mathematical models of this core/annular structure. Measurements by capacitance probes (Brereton, 1987; Herb et al, 1989), X-rays (Weinstein et al, 1985), solids sampling probes (Bierl et al, 1980), and fibre optic probes (Hartge et al, 1988) have been used to support this concept. The core region, according to the model, contains an upward-moving gaseous continuous phase interspersed with solids, both as individual particles and as loose clusters of particles. On the other hand, in the thin annular region adjacent to the riser's wall, there is a downflow of dense strands of solids, having a wide range of local voidages and descent velocities.  The interfaces between the two regions  varies randomly both with time and position, the annular region intermittently disappearing altogether at some axial positions in the riser, especially at low solids flux and high gas velocities. There is a continual interchange of solids, as well as gas, across the interface between the core and annulus. The generally-accepted decaying density profile (Figure 1.3, Brereton, 1987) along the riser length, has been used to substantiate the notion that there is a net flux of solids from the core to the annular region (Brereton, 1987; Senior, 1989). Furthermore, the abrupt exit geometry, commonly used in C F B combustors, causes separation of some of the solids from the gas stream "at the exit, feeding solids into the annulus at the top of the riser and resulting in an increase in solids hold-up there. In fact, the density profile throughout the length of the riser is affected by the exit geometry (Figure 1.3).  The interchange between the annulus and core can also be influenced by  such aspects of wall geometry as protrusions or baffles. This interchange is important for  Chapter 1.  Introduction  Figure 1.2: Regime Map of Solids-Gas Flow (Grace, 1990).  5  Chapter 1. Introduction  6  heat transfer as well as in affecting the effectiveness of the riser as a chemical reactor. Means of predicting or measuring this inter-region transfer are not. at present, readily available or proven. The core-annulus model is probably not appropriate for the full length of the riser, especially considering the extensive turbulence apparent at the entrance, as well as the exit. These regions, together with the core/annulus region, have a profound effect on how particles travel through the riser, and therefore each region must be individually characterized, in order to comprehend the riser in total. Investigating the solids residence time in these regions, with unknown flows through their boundaries and recycle external to the riser itself, requires a special tool capable of keeping an accurate account of tracers entering and leaving each region. Developing such a tool has been the objective of this investigation.  1.2  Residence T i m e Distribution Techniques in the C F B  Grace and Baeyens (1986) present a table summarizing techniques that have been used in studying solids mixing in all types of fluidized beds.. Within this general class of reactors, experimenters either seek to measure local particle movements, or to identify gross solids mixing. Local techniques include the measurement of trajectories of tagged radioactive particles by Kondukov et al. (1964) and by Lin et al. (1985). Local particle velocities have been measured using fibre optic techniques (Oki et al, 1977; Ishida et al., 1980; Ishida and Hatano, 1983), while local solids mass flux have been determined using hot wire anemometry (Marsheck and Gomezplata, 1965; Turton and Levenspiel, 1989) or by measuring the temperature distribution around a heated wire (Valenzuela and Glicksman, 1984). Schmalfeld (1976) has measured the momentum of moving particles  7  Chapter 1. Introduction  to  /  or  O  O f— ZD CO. CO Q  e x i t  Legend  A  Symbol Ugjm/s] G ( k g / m s )  txi  2  s  O A  //  oc  Abrupt  7.1  45 73  > o cn <  O ui X  s o l i d s r e e n t r y  0  .100  200  300  400  500  SUSPENDED SOLIDS DENSfTY , kg/m3  Figure 1.3: Typical Density Profiles in a CFB with Abrupt Exit (Brereton, 1987).  Chapter 1. Introduction  8  on a small piezo probe. Gross solids mixing lias been investigated using various tracer techniques such as coloured particles (Brotz, 1956; Mori and Nakamura, 1966), radioactive-tagged particles (May, 1959; Chmielewski and Selecki, 1977; Santos and Dantas, 1983; Baillie, 1986), heated particles (Borodulya et ai, 1982; Meunier et al., 1989), and magnetic tracer particles (Rowe and Sutherland, 1964).  Several investigators have incorporated mass  and/or heat transfer into their tracer experiments.  Bellgardt and Werther (1986) have  used a pulse of sublimating solid carbon dioxide pellets to induce temporal and spatial changes in both bed temperature and gas composition. Haider and Basu (1989), using a tethered sublimating particle, measured its weight loss in order to determine the mass transfer rate. Dry et al. (1987) "reacted" a pulse of heated gas with the cold solids in the bed, measuring the temperature response at the outlet.  Turton and Levenspiel (1989)  injected a pulse of ferromagnetic tracers, whose measurable magnetic properties changed upon contact with the hot bed. The core/annulus concept of the C F B has been substantiated in the literature by local measurements of solids density, solids flux, and/or particle velocity in the riser. Alternatively, residence time distribution (RTD) measurements can also serve to elucidate this structure, as evidenced for example by a bimodal response to a pulse injection of tracer (Roberts, 1986; Ambler et al., 1990; Patience, 1990). However, in addition, R T D measurements can provide clues oil how the solids mix, and the structure of internal recirculation; such information cannot be derived from local measurements without significant assumptions. If RTD information can be obtained in several axial regions within the riser, as opposed to a lumped or overall RTD, then much more detail of the solids motion would be available.  Enough information might be available to determine the  most probable trajectory of the tracer particles as they traverse the riser and to show  9  Chapter 1. Introduction  the effect of tracer density and size on this trajectory. Studies have also been conducted to measure the nature of gas movement through the CFB (Cankurt and Yerushalmi, 1978; Adams, 1988; Bader et al, 1988; Brereton et al, 1988). These studies indicate that there is relatively little axial mixing of the gas, except close to the wall. There is evidence (Grace et al, 1990) of significant radial concentration gradients of various gas species along the length of a riser, in which a reaction is occurring. Gas RTD experiments are simpler than those with solids because there is little possibility of external recirculation back through the return leg, a concern in solids RTD experiments. Also, since the extent of backmixing for the gas is so much less than that for the solids, measurements of gas-tracer concentration at points within the riser are not nearly as suspect as similar measurements of solids-tracer concentration. In the following sections, earlier pertinent solids RTD studies are reviewed briefly, and the pulse/response approach is compared to the single particle technique, adopted in this investigation. As already noted, the single particle tracers actually used in this study are considerably larger, and have a different density than the circulating solids. This is in contrast to the other investigations, where the tracer particles were carefully chosen to be as aerodynamically similar to the circulating material as possible. The reason for this discrepancy between the two approaches is that there is a basic difference in the goals of this investigation compared to those of the earlier studies.  Here, the  RTD and the flow patterns of the circulating solids are not being sought, but rather a new experimental technique aimed at finding the RTD of only the large particles in a circulating bed of fines.  This will shed light on the flow of large particles in such  CFB applications as combustors, gasifiers, calciners, and dryers, where there may well be large isolated particles in a medium of fine recirculating solids. The importance of determining the history of large particles as they pass through the riser is suggested  Chapter 1. Introduction  10  by other investigations, such as those of Basu and Haider (1989) and Haider and Basu (1988). That is not. to say that the single-particle technique could not be used to measure theflowof fines. Indeed, in the following sections, the case is made for the selection of the single/particle method over the pulse technique, regardless of the particles being studied. However, refinement of the technique developed in this work will be required before this technique can be used, with an acceptable signal-to-noise ratio, to determine RTD's for particles of size comparable to the mean size of those in the CFB system. Other sensors already exist for detecting much smaller individual particles, compared to the 6 mm tracer spheres used in this study. For example, Lin et al. (1985) tracked a single radioactive tracer as small as 500 pm in diameter in a 140 mm diameter bubbling fluidized bed. Similarly, Masson et al. (1981) used a 200 pra diameter radioactive source in their experiments in a 180 mm square bed. Ironically, the latter investigators embedded their source in a much larger particle, so that they could study the circulation of large isolated spheres. Using a 28 mm diameter electromagnetic sensing coil (compared to the 162 mm diameter coil used here), Waldie and Wilkinson (1986) sensed a ferromagnetic tracer particle 3 mm in diameter, as it passed up the spout of a spouted bed. Their approach, based on the change of inductance in the coil, as a permeable tracer particle passes through it (Bohn, 1968), does not have the same potential for sensitivity or noise rejection as the two coil configuration used in the present investigation. The development of the latter configuration, which is really the essence of this investigation, is still in its infancy.  1.2.1  Previous Measurements  The importance of RTD measurements in understanding the riser has not stimulated much research in this area. This may be due, in part, to the absence of a viable technique,  11  Chapter 1. Introduction  which is not fraught with ambiguity, at the open boundaries, within the riser. Some researchers (Roberts, 1980; Kunitomo and Hayashi, 1988; Ambler et al, 1990; Patience, 1990) have circumvented this problem by injecting a pulse, or step change in tracer at the closed inlet, and making their response measurements at the closed exit of the riser. However, this has only allowed them to determine an overall R T D for the entire riser, yielding no details on individual regions and, therefore, at best, they can only fit their results to a model, which embodies their perception of those details. For example, Ambler et al. (1990) formulated a steady state mass balance based on a model of a dilutesuspension, upward-flowing core, and dense, downward-flowing annulus. By assuming certain characteristics of these two phases (e.g.  core slip velocity equal to terminal  settling velocity of a single particle, voidage of annulus equal to minimum fluidization voidage, no recirculation of gas between annulus and core), they calculated the upward and downward fluxes of solids as functions of riser length. Using this information, they solved a set of partial differential equations, which describe the flow of a pulse of tracer through the core/annulus structure (Jagota et al., 1973). The solution gave the mass fraction of tracer in both the core and annulus as a function of axial position and time, the sole fitting parameter being the annulus-to-core solids interchange coefficient, as a function of axial position. Assuming the interchange coefficient was constant over the bottom of the riser and zero elsewhere, they were able to predict the times of the two peaks in the measured bimodal response to a pulse of radioactive tracer. Other researchers, attracted by the prospect of detailed mixing information, have injected a pulse of tracer at one point in the riser and measured the response at one or more levels downstream, and, in one case, upstream, but still within the riser (Avidan, 1980; Bader et al., 1988; Kojima et al, 1989; Rhodes et al, 1990). Avidan (1980) injected a pulse of ferromagnetic particles at a point approximately midway between a pair of  Chapter 1. Introduction  12  upstream sensors and a pair of downstream sensors. Using the time of appearance of the first "substantial" quantity of tracer at the downstream and upstream sensors closest to the injection point, he calculated, to an order of magnitude, the upward and downward velocities for the respective phases of a core/annulus model. Alternatively, he used the responses registered at the two downstream sensors to determine the axial dispersion coefficient, based on the change in variance between the two responses (Aris, 1959). Similarly, Kojima et al. (1989) also calculated axial dispersion coefficients and particle upward velocities. These measurements were made using two sets of fibre optic probes and dye-treated tracer particles, and were performed on the axis of the riser, in contrast to Avidan's measurements, which were averaged across the cross-section of the riser. Both Bader et al. (1988) and Rhodes et al. (1990) used the same technique, a salt tracer and solids-sampling probes, sampling both near the wall and at the axis of the riser, downstream of the injection point. Bader et al. (1988) refrained from fitting a model to their data, but inferred a substantial interchange between the core and annulus in order to account for the long tail they observed in the response curves. Rhodes et al. (1990) used the variance of the response curve to calculate an axial dispersion coefficient.  1.2.2 Single Particle vs. Pulse Response The obvious fault with measuring the pulse response within the riser, as opposed to at the exit, is that the tracer can recirculate back past the sensor, which cannot differentiate between tracer material leaving the region for the very first time, that returning to the region after being outside of it, and that leaving the region for a second or succeeding time. This limitation is the crux of the open boundary problem. Because measurements at an open boundary cannot exclude time spent by the tracers outside of the region, Nauman  Chapter 1. Introduction  13  (1984) stated that measurement of RTD in an open system is impossible, at least using inert tracers.  However, these response measurements, at both the exit and at open  boundaries, if interpreted with caution, can serve to delineate certain flow malfunctions, such as bypassing and stagnant regions. These considerations are crucial to the operation and design of any reactor. The use of age-distribution curves, especially the intensity function of Naor and Shinnar (1963), to uncover bypassing and stagnancy, is discussed by Himmelblau and Bischoff (1968), with specific examples given by Bischoff and McCracken (1966). In addition to the inherent ambiguity associated with open boundaries, there may also be a problem in interpreting the results of the pulse-response technique even at the closed exit, due to time-fluctuating flow. The flow of solids through the L-valve into the riser of the cold model C F B , used in these experiments, fluctuates in a pronounced stickslip flow, under some operating conditions (especially for group B particles in the Geldart classification). Using a stochastic mixing model, Krambeck et al. (1969) interpreted the results of various tracer experimental techniques in quasisteady flow systems, of which the C F B is an example. They concluded that the pulse-response method, as it is typically conducted (i.e. the concentration response to a pulse in inlet tracer flow rate), has no probabilistic interpretation. Only when the tracer flow-rate response to a concentration impulse is measured does the resulting density function correspond to the "true" residence time density. Even intuitively, the application of the pulse-response method to the C F B is questionable. If the pulse of tracer is injected into the base of the riser at the instant the solids stick in the L-valve, the resulting response will presumably be very different from that obtained when tracer is injected while a slug of solids slips through the L-valve into the riser. It has been observed that the frequency of stick/slip flow is typically of the  Chapter 1.  Introduction  14  same order as the inverse of the pulse injection time, 1 sec . -1  The single particle tracer technique, adapted in this investigation, avoids this quasisteady flow problem because the individual tracer spheres are separately injected into the riser over a long time span (i.e. compared to the fluctuations in the flow). This permits the tracers to experience the same temporal fluctuations in the solids density, at the base of the riser, as the solids entering the base of the riser. The single tracer particles could even be introduced into the L-valve and their entry into the riser could be monitored by a sensor located at the solids re-entry point. The single particle technique originates from the probabilistic interpretation of RTD. Seinfeld and Lapidus (1974) indicate that, at steady state, which, as just noted, is not always possible for the C F B , the RTD is the same, regardless of whether it is determined by a large number of individual particles introduced separately at different times, or with all of the tracer particles entering at the same instant. In the technique developed in this thesis, as a single-particle tracer passes by a sensor, which delineates a region, the corresponding time is logged, giving a time increment (since the previous signal) spent in the axial region either just above, or just below the sensor. After the residence times of many visits to a given region have been recorded, the accumulated data can be used to prepare a histogram, with the height of a given bar in the histogram corresponding to the number of visits to the region falling within the respective time interval, divided by the total number of all visits recorded for that region. This quotient is further divided by the time interval in order to conform to the residence-time density convention that the area of an element of width dt is interpreted as the probability that the residence time is between t and (t + dt). The total area under such a histogram is equal to unity. Clearly, the single-particle approach circumvents the open-boundary limitations because it can account for the tracer's whereabouts, by region, during the whole time the  Chapter 1. Introduction  15  tracer is in the riser. Although the hmited prototype sensor described in this thesis was not able to differentiate the direction the tracer was travelling, it was able to distinguish first-time passage through the region between injector and sensor, a feat beyond the pulse-response methods.  1.3  Electro-magnetic Induction (EMI)  The single-particle sensor developed in this investigation is based on the principles of electromagnetic induction. When a conductive tracer particle enters an alternating primary magnetic field, eddy currents are induced in the particle which, in turn, generate a comparatively weak secondary field, having the form of a magnetic dipole. The receiver coil of the sensor is designed to sense the presence of this secondary field. Electromagnetic induction (EMI) is the basis of a geophysical exploration technique, as well as some security devices.  In this section, these applications are discussed in order to introduce  the principles of EMI. Afterwards, the application of EMI to sensing in the C F B is briefly considered, in order to demonstrate that the magnetic fields inherent in the method do not interfere with what is being measured; nevertheless, the method is susceptible to considerable noise resulting from the nature of the C F B .  1.3.1  Other Applications and Their Relevance  Geophysics  The electromagnetic prospecting technique employed in applied geophysics (Grant and West, 1965; Telford et al., 1976; Wait, 1982; Kaufman and Keller, 1985), utilizes a time-varying primary field which is transmitted from above the earth's surface and has a frequencj usually less than 5 kHz. As in the sensor developed here, this field r  Chapter 1. Introduction  16  induces a secondary field in a buried conductor, which is then sensed at a receiver. These low frequencies allow the primary field to penetrate the earth without being completely damped by marginally conductive regions above the buried conductor. The free-space wavelength at these frequencies (> 60 km) is very large compared to the distances between the transmitter, conductor, and receiver. Therefore, wave propagation (i.e. radiation) does not occur in this quasi-static regime; in order to radiate effectively, a system of conductors must have dimensions of the order of a wavelength or more. Furthermore, the phase of the primary field is Uniform throughout the region. It is therefore possible to assume that the displacement current, indicative of charge accumulation and essential for the concept of electromagnetic wave propagation, is negligible compared to the electric current density, and that all of the conductive body is being uniformly acted upon by the primary field. As a result of these assumptions, the same magnetic vector potential used to calculate a static magnetic field may also be used to derive the field around a slowly alternating magnetic dipole (Plonsey and Collin, 1961). Based on these assumptions, magneto-static field equations have been used exclusively throughout this thesis. Also, electric field effects, such as capacitive coupling and fluctuations in the permittivity of the intervening space, are assumed to have no direct effect on this technique, and are not considered here. Throughout the rest of this text, unless otherwise noted, terms such as fields, moments, permeability, etc. refer to magnetic properties. In the geophysical method, the transmitter of the primary field, the buried conductor, and the receiver of the response can be considered analogous to a set of coils, which are coupled together strictly inductively. This model allows the receiver's response to be evaluated using simple circuit theory, thereby avoiding complex electromagnetic field theory.  Chapter 1. Introduction  17  The response field of the conductor coil, the secondary field, has the same frequency, but differs in amplitude and phase from the primary field. The receiver coil, energized by both the secondary and primary fields simultaneously, indicates the presence of the conductor coil by a change of amplitude and/or phase in its signal compared to that generated when no conductor is present.  Grant and West (1965) have shown that the  ratio of the two signals at the receiver is: EMFRC EMF  hrchcR  R T  cr + ia 1+ a  2  (1.1)  where: subscripts R, C , and T represent receiver, conductor and transmitter, respectively. EMF^  =  E M F in coil A due to current flow in coil B  k*AB  —  coefficient of coupling between coils A and B  a  =  UJ  =  angular frequency • 2TT/  L  C  =  self inductance of the conductor  R  =  resistance of the conductor  C  B  LJL JR C  C  The first term in brackets in (1.1), called the coupling coefficient, is the ratio of the transmitter-receiver coupling through the conductor coil to that directly between transmitter and receiver coils. Its value depends upon the relative positions of the three coils as shown in Figure 1.4 coils. The second term in Equation 1.1, called the response function, is a complex function of the response parameter, a. The response parameter depends only on the conductor coil's electrical properties and the frequency of the primary field. A buried conductor in the form of a conducting, permeable solid sphere is a specific case of the preceding general development. Resorting to field theory in this case, Grant and West (1965) determined that the secondary field generated by such a sphere in a  Ciiapter  1. Introduction  Transmitter  Transmitter  k  TR  +  Receiver  Receiver  Transmitter  k + TC  Transmitter-receiver 1 Transmitter-circuit J  Transmitter  c o u p (  Receiver  Receiver  k CR  ;  '*  Circuit-receiver coupling  Figure 1.4: Effect of Coils Relative Positions on Coupling (Grant and West, 1965)  Chapter 1.  19  Introduction  Figure 1.5: Real and Imaginary Parts of Response Function as a Function of Response Parameter \K a \ and of Relative Permeability p/p . (Grant and West, 1965) 2  2  0  20  Chapter 1. Introduction  uniform primary field has in-phase and quadrature (i.e.  90° out of phase) components  which are functions of a response parameter, K a , and the sphere's permeability, p. 2  2  This complex response is incorporated in the response function for a sphere: x  i  Y  M  =  + Ka) + M  1  2  sinh  2  ( K a ) - (2/i + p )Ka cosh(Ka) 0  \p (\ + K a?) - p] sinh(Ka) + (p - po)Ka cosh(Ka)  %  0  2  ^' '  where  p  =  free space permeability = Air X 1 0  Ka  =  (^^p )* (1 + *) (K is commonly known as the wave number)  u>  =  2 7 r / , [radians/sec]  cr  =  conductivity of sphere, [mhos/m]  0  -7  H/m  -  a = radius of sphere, [m] The real and imaginary parts of the response function have been plotted by Grant and West (1965) as a function of the modulus of the response parameter, | J f a | . The plot is 2  2  reproduced in Figure 1.5 (with a minor correction of the original, where the parameter labels of the imaginary curves were in the wrong order). The resulting dipole moment of the secondary field generated by such a solid sphere is given in Equation (2.3) below. Similarly, the response of a spherical shell of a non-permeable, conducting material can be determined from the magnetic potential, U , derived by Wait (1969).  The dipole  e  moment, m,h u, generated by such a shell in a uniform primary field, Hoe , twt  t  is inferred  from U in Appendix A and is shown to be given by: e  -mshen = -2irb H e^  (l - —  3  0  V  where  b  =  a  = a,p Arb, [s]  Ar  =  shell thickness [ml «  a,  =  conductivity of shell, [mhos/m]  radius to outside of shell, [m] 0  (—*—)  7  )  3 -f tctu) J  (1.3)  Chapter 1. Introduction  21  There is a wide variety of geophysical instruments (Grant and West , 1965) which make use of electromagnetic induction, each exploiting the underlying principle in a different manner. Two methods are potentially pertinent to the application of tracersensing in the present context: 1. Quadrature sensing: In this case, the quadrature (i.e. imaginary) component is comparatively insensitive to the relative position of the transmitter and receiver compared to the in-phase component. 2. Transient method: In this case, the receiver senses only when the primary field is shut off, revealing a conductor by its characteristic decay (Figure 1.6). Both of these approaches have been devised in order to reduce the direct coupling between the transmitter and receiver. Such coupling can overwhelm the signal coming from the conductor. As discussed briefly in Section 1.3.2 below, and in Section 2.3.1, where various attempts at resolution are described, direct coupling has been the major source of noise in this work.  Security  In order to protect stores and libraries from theft, many different systems have been proposed (e.^.  Picard, 1934; Fearon, 1974; Novikoff, 1978; Richardson, 1981). Items  are tagged with a detectable target which interacts with a primary field, generating a secondary field, which is then sensed by a receiver. In some instances, the target may consist of an antenna and diode, which generates harmonics of the primary field, or an antenna and capacitor, which resonates, absorbing energy from the primary field. Another approach, described by Anderson et al. (1983), depends upon magnetomechanical coupling in amorphous metal targets. This results in each target having an identifiable  Chapter 1.  22  Introduction P r i m a r y field at r e c e i v e r  T r a n s m i t t e r  o f f  Primary field at conductor  •g o it.  Total field at conductor  Decay O h « i c  due to l o s s  Total field at receiver 2  emf induced.  in receiver decaying  <due  t o  f i e l d )  t Receiver  o f f  Figure 1.6: Transient Approach — Transmitter and Receiver Alternately on (Grant and West, 1965)  23  Chapter 1. Introduction  signature in its response. There are also simpler techniques, which utilize induced magnetization in a highly permeable target; these are particularly relevant to the present effort to develop a viable tracer detector and will now be described. In the coupled-coils model discussed in the previous section, electric currents, in the conductor coil, are responsible for a secondary field. In a highlj permeable target, magr  netic domain movement, as well as possible eddy currents, account for the secondary field. This induced magnetization resulting from domains aligning with the applied field, is non-linear in nature.  Therefore, when such a target is excited by a sinusoidal pri-  mary field, it responds with a non-sinusoidal secondary field.  This non-linear effect,  as it pertains to the development of the present tracer detector, is discussed further in Section 2.3.3, below. As indicated by Fourier series analysis technique, a non-sinusoidal signal can be considered to consist of harmonics. Some of these security systems limit their detection to the higher order harmonics, rather than monitoring at the same frequency as the primary field. As in the quadrature and transient system employed in geophysical exploration, the underlying purpose of harmonics detection is to reduce the overwhelming signal, at the receiver, due to the primary field, as compared to that due to the secondary field (i.e. emanating from the target). In addition, to be reliable, a security system must be able to differentiate between common ferromagnetic objects (eg. key chains, umbrellas, etc.) and the much smaller target, in order to avoid false alarms. Picard (1934) utilized the ratio of a higher order harmonic to the fundamental in the response, in order to accomplish this differentiation. In order to further reduce the coupling between the transmitter and receiver, Picard (1934) proposed that either coil be wound in a "figure eight" configuration, so as to obtain a null. In the case of a "figure eight" receiving coil, both lobes of the coil are exposed to  24  Chapter 1. Introduction  the same exciting field generated by the transmitter coil and each lobe therefore responds with an E M F of equal magnitude, but opposite sign. Therefore, the net signal from this receiver-coil configuration is zero. However, an imbalance occurs when the presence of the target causes one lobe to experience a slightly different exciting field (i.e. prirmuy plus secondary field) than the other lobe. This configuration was adopted in the final sensing coil for this, as well as two other reasons, which are discussed in the next section.  1.3.2  Special Considerations i n the C F B  When the EMI methods discussed in the previous section are applied to tracking tracers in the C F B , there are two concerns that warrant special attention. First, the primary magnetic field, which is the basis of the device, must not appreciably affect the hydrodynamics of particles in general, or the trajectory of the tracer particle, in particular. Secondly, the signal due to the tracer must be greater than the undesired signals, or noise, due to such C F B attributes as mechanical vibrations, and a plethora of highly charged particles moving through space. Furthermore, the signal-to-noise ratio is limited by an especially weak signal from a relatively small tracer particle, in comparison to geophysical and security applications. Let us now briefly discuss these two considerations.  Magnetic Field-Hydrodynamic Interactions  It is first assumed that the sensing device does not effect the flow of the particles, which are commonly highly charged due to electrostatic effects. In terms of the primary magnetic field, B, the force on a charge, Q, travelling at a velocity, v, is the Lorentz force, expressed by: F= L  Q v x B  Chapter 1. Introduction  Since B varies sinusoidally with time, so does F'i, and, therefore, on average, it has no net effect on the particles' trajectories at the velocities and frequencies of operation. Because of its shielding, the sensor affects the surrounding electric field. This field results from both the cloud of charged particles, and the accumulation of charge on the inside wall of the plastic riser. The presence of the grounded, conducting shield, both around the circumference, as well as across the diameter of the riser, alters this electric field. The resultant field is complex; however, it is most intense at the interface between the plastic wall and shielded sections.  I have not observed any evidence of particle-  flow distortion at this interface, nor is there any accumulation of particles there, when the flow of solid particles is shut off.  Furthermore, numerous researchers (e.g. Beck  and Wainwright, 1969; Tardos and Pfeffer, 1980; Irons and Chang , 1982; Mathur and Klinzing, 1984; Nieh et a/., 1986; Riley and Louge, 1989) have purposely introduced capacitance-measuring surfaces, either directly into the solid-gas flow or just outside the non-conductive wall, with negligible ill-effect on the hydrodynamics. Therefore, the assumption of minimal interference of the sensor appears to be reasonable. The second assumption, regarding interaction, is that there is no significant magnetic force on a tracer particle as it passes through, and interacts with, the primary field. As discussed in Section 1.3.1, the tracer particle can be modelled as a secondary coil, in which eddy currents are induced. According to Lenz's law, the field resulting from these eddy currents (i.e. the secondary field) opposes the exciting field and the force, 8 F, on  26  Chapter 1. Introduction  an incremental length, S£, of the secondary coil is shown by Matthews (1980) to be  S  F= I,  SI  I.  x B  where I  =  current in the secondary coil  B  =  primary magnetic field  s  The value of I, depends upon the component of B which is normal to the plane of the secondary coil. However, the component of 8 F which applies a body force to the coil (called levitation), depends upon the component of B parallel to the coil. Because the spherical tracer particle used here is small compared to the dimensions of the exciting coil, it is assumed that the primary field, B, is uniformly directed within the immediate neighborhood of the tracer.  Hence, B only has a component normal to the induced  current rings in the tracer. Therefore, neglecting the earth's weak magnetic field, the magnetic force on the tracer is negligible.  The reason that the sinusoidal argument,  applied earlier to charged particles, was not invoked here, is because the current I has both a real and quadrature component relative to B, and therefore the time-averaged value of LB 1  is non-zero.  This is the Lorentze force, where Q v has been interpreted as a current element, I dl. I is the  charge flow per second, or the charge contained in length  , which equals:  I — nq v where n — number of free charges, q, per unit length. The Lorentz force on all the charges in length  d£ is:  d F= - (ndiq) [v x 5) d F= I [dl x B  Chapter 1. Introduction  27  Signal-to-Noise Concerns  To reiterate what was stated in Section 1.3.1, direct coupling between the transmitter and receiver is the foremost source of unwanted noise. The first term of Equation (1.1) is a ratio of coefficients of coupling, each of which represents a geometric mean of two fractions: kB A  where k  A  (k k )^ A  B  — fraction of the total flux generated by coil A passing through coil B.  kg — fraction of the total flux generated by coil B passing through coil A. Because of the limited size of the present tracer particle (d = 6.35mm) compared to p  the transmitter coil(171.5mm ID), kxc is small. Also, because the induced field is small, kcR is likewise small. However, when the receiver is wound in a "figure eight", as in the final configuration, direct coupling between transmitter and receiver, krR, is also reduced, as described for security systems in Section 1.3.1. Furthermore, the "figure eight" configuration can also serve to increase the coupling between the tracer and the receiver, kcRThis improvement in coupling, compared to more conventional circumferential receiver coils, is described in Section 3.2. The particular "figure eight" form of the receiver coil adopted here, incorporates a diametral leg across the riser, and it is this feature, which makes it especially sensitive to a second source of noise, vibrations.  These vibrations may be due to either parti-  cle impacts on the diametral leg, or to riser-wall vibrations, due, for example to blower pulsations, which are then transmitted to the coil. These vibrations are probably converted to electrical noise in this coil because the diametral leg is physically distorted, by vibrations and/or particle impacts, upsetting the null between transmitter and receiver. An alternate explanation is that when wound, the wire of the coil is forced around four  Chapter 1. Introduction  28  corners at the ends of the diametral leg, and, at these pinch points, vibrations ma}' cause fluctuations in the spacing between the closely packed wires. Fitzgerald (1989) has indicated that these fluctuations may cause large variations in the coils inductance, thereby generating noise in the receiving-coil circuit. This noise has been reduced by multiplying the receiver's signal by an out-of- phase signal, as described in Section 3.1. A third source of noise in this application is the prominence of electrostatic charging under the present experimental conditions. According to the Biot-Savart law, a magnetic field accompanies each charged particle as it travels through the riser. However, the noise due to these practically static fields is eliminated, since all but signals of the primary field's frequency are filtered out, when the receiver's signal is processed. A much more troublesome aspect of this phenomena is that extensive electric discharging occurs, presumably due to charge accumulation on the inside wall of the plastic riser. These discharges occur erratically and radiate an electro-magnetic wave spanning a wide frequency spectrum. Direct discharges to the sensing coil, and random fluctuations in the surrounding electric field resulting from the fluctuating electrostatic phenomena can both be somewhat alleviated. However, the radiated energy from the discharges is intercepted by the receiving coil, as if it were an antenna. That portion of the spark impulse energy, at the operating frequency, cannot be differentiated from an authentic signal due to a tracer. Radios, operating in or near gasoline powered automobiles, suffer from a similar source of interference; the ignition system. This noise is typically attacked at the source by various schemes (ARRL Handbook, 1987). Because the source of discharge is ubiquitous, these solutions are not directly applicable. However, it is apparent that, when operating on humid days, the discharges are less frequent, and some researchers (e.g. Ambler, 1988) have purposely humidified fluidizing air for this reason. Wrapping the column with grounded aluminum foil does not appear  Chapter 1. Introduction  29  effective (Grace and Baeyen, 1986). Indeed, information from Corion Technologies (1989) indicates that this approach results in confinement and amplification of the electric field between the foil and the charge accumulated on the wall. This field can then increase to such high levels as to result in discharges within the riser. There are several other techniques, such as charge neutralizes (Corion Technologies, 1989) and antistatic additives (Louge, 1990), which purport to eliminate electrostatic problems, but these have not been investigated here. I have found, however, that a grounding device, placed in the return leg for an electrostatic-related problem (see Section 3.1) was effective in resolving that problem. When automobile-radio interference cannot be resolved at the source, further measures to suppress noise are directed at either accessories to the radio, such as noise limiters or noise blankers, or sampling the noise with a separate "noise antenna" and using that signal to cancel the noise entering through the "signal antenna" (ARRL Handbook, 1987). This latter measure is incorporated in the "figure eight" receiving coil. The two halves of the "figure eight" are actually two separate antennas connected in counter series. When the two are exposed to radiated energy, of a comparatively large wavelength, they should respond with equal but opposite sign voltages, thereby canceling out the noise. Nevertheless, despite my best efforts, electrostatic effects still persisted as a source of noise. Initially there was concern that'the varying dielectric in the sensing volume, due to fluctuations in solids concentration, would be another source of noise. It was soon realized that this was not a consideration since, as discussed briefly in Section 1.3.1, under the so-called quasi-static assumption, these fluctuations in the dielectric do not interfere with the magnetic fields. Of course, these fluctuations do affect the electrostatic field, which is a source of noise due to the resultant fluctuating electric field around the sensing coil,  Chapter 1. Introduction  as well as discharges, as discussed above.  Chapter 2  O u r Early Approaches to E M I Sensing  2.1  Calculated Response of a Circumferential Loop  Many different sensing loop configurations were considered in this study, and each will be briefly described in this chapter.  In order to illustrate how a loop responds to an  approaching tracer particle, two sensing loops will be examined in detail. The circumferential loop, wound around the outside circumference of the riser, allows a straightforward illustration of the theory. The diametral loop, consisting of two "D" loops back-to-back with their common leg passing along a diameter of the riser, was the ultimate loop of this investigation and it will be discussed in the next chapter. In both of these configurations the plane of the loop is perpendicular to the axis of the riser (i.e. z-axis) and the derivation given here addresses this geometry. Other arrangements require different axis transformations, but the derivation is similar. A voltage (i.e. EMF), indicating the presence of the tracer, is induced in the sensing loop when there is a time rate of change in the magnetic field lines cutting through the loop. In both the permanent-magnet, and the induced-dipole approaches investigated here, these field lines originate at the tracer, which is modelled as a magnetic dipole. The expression for the far field of the dipole, with the coordinates fixed on the tracer, is (Grant and West, 1965):  B= 4T  IV + -*)  21  31  (2.1)  Chapter 2.  32  Our Early Approaches to EMI Sensing  where p  — magnetic permeability of free space(practically the same as in the riser)  0  m  z  =  z-component of the magnetic dipole moment (i.e. parallel to the axis of the riser) unit vectors in two orthogonal directions  p  2  =  x +y 2  2  A sensing loop, in a plane parallel to the p-plane (and perpendicular to the axis of the riser), responds to an approaching dipole as a function only of the z-component of the dipole's field, evaluated in the plane of the loop. Faraday's law gives the response as: = y f B-dS= dt ./loop  EMF  I ^dS ./loop dt  (2.2)  since the loop is fixed in space. The particles in the riser travel predominantly in the axial direction, and therefore it is assumed that the tracer/dipole has only a z-component of velocity, and the integrand in Equation (2.2) becomes: dB  dB  dt  dm  z  z  Px  dB  z  dz  dt  dz  dt  z  z  where ^ = V  dm  = velocity of the dipole  For the case of a permanent-magnet tracer, having only a translational velocity, the dipole moment is constant and therefore dm/dt = 0. For the induced-dipole case, the moment for a spherical tracer is (Grant and West, 1965): m  z  where  = -27rrJ il • H e 0  iu,t  (X + iY)  (2.3)  33  Chapter 2. Our Early Approaches to EMI Sensing  r  =  radius of the tracer particle  He  =  exciting field at the tracer's location  (A' +iY)  =  in-phase (X) and quadrature (Y) components of the induced  p  tui  0  moment (w.r.t. the exciting field) — functions of ui and tracer properties, as shown in Equation (1.2).  Therefore, the value of ^j*-, for the induced-dipole case, is: dm  z  —-— =  dt  icum,  We will discuss m in more detail in Section 2.2 for permanent magnet tracers and in z  Section 3.4.2 for induced dipole tracers. The integration in Equation (2.2) can be made more manageable by translating the origin from the center of the dipole to the riser's centerline, where it intersects the plane of the loop. The spatial variables in Equation (2.1), (z, p), are now expressed in terms of the new variables; (r, v, zi, R, 8). The basis of the transformation is given in Appendix B . l , and the final result is: z p  = Z\ 2  =  r - [2R (cos 6 cosv + sin 8 sin v)]r + R 2  2  where (R, 8, z{) are the position coordinates of the dipole relative to the new origin.  The incremental area in Equation (2.2) becomes: dS = rdrdv and the response of the circumferential loop to the tracer's field is then: EMF  C  = V  Pz  I [ ^rdrdv Jv Jr OZ  + iu> I [ m ^rdrdv z  Jv Jr  Om  z  (2.4)  Chapter 2.  34  Our Early Approaches to EMI Sensing  where the second term on the right hand side is zero for a permanent-magnet dipole. The transformed integrands, as well as expressions for the inner integrals in Equation (2.4), are derived in Appendix B.2. The outer integrals of Equation (2.4) can be evaluated using a numerical (e.g. quadrature) technique. In order to evaluate Equation (2.4), only those field lines which pass just once through the area encircled by the loop are counted. Because each field line of the dipole forms a closed loop, only those lines passing through the encircled area, which then go on to pass through the area in the same plane, but outside the loop, contribute to the integral. Since for these field lines, the absolute value of / B -dS is the same for both the interior and exterior crossings  1  , Equation (2.4) can be determined by evaluating it over the  area external to, and in the same plane as, the loop; in any case, Equation (2.1) is applicable only to the far field and could not be used for determining the field in the near neighborhood of the tracer dipole. Therefore, for the circumferential loop the ranges of integration in Equation (2.4) are: #loop < r < oo 0< v <  2TT  where R\ -p is the radius of the loop. QO  Due to symmetry considerations: EMF  C  =  f(R,zi)  This result follows directly from Maxwell's equation, y- B= 0. Applying the divergence theorem gives: 1  y-BdV-^B-dS-Q Therefore:  fB-dS-f  Jt  ./interior  B -dS+ I  ./exterior  B -dS - 0  Chapter 2.  35  Our Early Approaches to EMI Sensing  Figure 2.1 is a plot of the two integrals in Equation (2.4) showing the relative contribution of each to  2.2  EMF . C  Permanent Magnet Tracers  An early approach to sensing single tracer particles was to simply use small fragments (of the order of 200-500/x) chipped from a powerful permanent magnet.  These candi-  date tracers, passing through a sensitive flat coil of 1000 turns of 36 gauge wire, would then produce the anticipated signal on an oscilloscope.  This effort quickly encountered  irresoluble difficulties that led to its eventual abandonment. First, the very weak signal from a small tracer required a multiple-turn sensing coil in order to obtain a significant signal. The signal from such a coil was very sensitive to the coil's motion (presumably in the earth's weak, yet pervasive field).  In light of  the vibrations inherent in the riser, significant magnetic shielding and/or signal filtering would be required to isolate the coil, from outside sources of magnetic fields. Furthermore, 60 Hz electromagnetic radiation, which permeates our environment, was unfortunately of the same order as the frequency of the response produced by a magnet tracer approaching the sensing coil at an anticipated velocity of 10 m/s, thereby reducing the effectiveness of filtering as a remedy. The second difficulty was due to electrostatically charged particles, prominent in high velocity beds, producing false signals.  As observed in the Biot-Savart law, a charge  travelling through space generates a magnetic field, as if it were a small element of a current-carrying conductor. The field lines are circular loops centered about the moving charge and lying in planes perpendicular to the charge's velocity. If the particles only had axial velocity, they would make no contribution to the E M F of a sensing loop in the  Chapter 2.  Our Early Approaches to EMI Sensing  36  Velocity Component IiVpz-nizPo/Air = 1*' integral Equation (2.4).  Moment Component I umi po/4ir = 2 integral Equation (2.4). nd  2  z  Figure 2.1: Response of Circumferential Case, h\  = 0.095m.  Chapter 2. Our Early Approaches to EMI Sensing  37  lateral plane; however, in the fast bed, particles are known to have radial, and azimuthal velocity components at times, constituting a potential source of noise. Thirdly, as Equation (2.4) shows, the signal from a permanent magnet would be velocity dependent. At times, when the tracer particle might be incorporated in a slowmoving cluster, especially in the low sensitivity region near the centre of the column, its signal would be greatly reduced. The fourth difficulty with using permanent-magnet tracers was a lower-than-expected moment, m, for some candidate materials because of a shape-dependent demagnetizing effect. The value of the moment had been initially calculated only on the basis of the residual induction, ^  r e s  id  u a  l ) which is the positive ordinate intercept of the material's  hysteresis curve. This approach seemed reasonable, since it was assumed that the magnetic field intensity within the tracer, - f f t i ; the abscissa, was equal to the externally a c  u a  applied field (in excess of the earth's field), ^ p p d > which is zero in this case. The a  Ue  moment was then obtained by:  B  = Mo (^actual +  M  )  (-) 2  5  and by assuming # ttial = 0  ;  ac  TO = \irrlM 3  = l 3 residual 3 po OT  (  g  for  a  s p h e r e  )  where M = magnetic dipole moment per unit volume. However, this, approach did not account for the demagnetizing field, which depends primarily on the shape of the magnet. Taking into account demagnetization, the magnetic field intensity is: ^actual = ^applied "  D  ( -°)  M  2  where D = the demagnetization factor = 0.333 for a sphere. Therefore, when ^ p p a  1 U e a  =  Chapter 2. Our Early Approaches to EMI Sensing  38  0, Equation (2.5) and (2.6) give:  B  =  Po (l ~ -p) #actual  =  -^o^actual  (  for  a  sphere)  (2.7)  Equation (2.7) is the operating line for a spherical magnet, and it intersects hysteresis curve in the second quadrant at the operating point (Hop,  Bop).  the  The actual  moment per unit volume for a spherical magnet is then:  M =  ^  -  H  o  (2.8)  p  Po  Examples of operating points, are illustrated in a graph by Stablein (1982) and are shown in Figure 2.2, where the operating line marked "2" is for a sphere. The values of the operating point for each of the six materials have been interpolated from the graph and are shown in Table 2.1. The calculated values of M from Equation (2.8) and (2.5) are also included in this table in order to show the effect of the demagnetization field on the moment per unit volume, M. Note that material #2, with the highest residual induction, results in the lowest M, when it is in the shape of a sphere. In conclusion, selecting a magnetic tracer involves consideration of the demagnetization curve (i.e.  the second quadrant of the  hysterisis curve) and not simply the residual induction; the actual moment per unit volume may be equal to, or considerably less than, that based on 5  r e s  j j (  u a  i.  For the four reasons discussed, the permanent-magnet scheme was eventually abandoned in favour of the induced-dipole approach, which eventually allowed resolution of the various obstacles.  Chapter 2.  Our Early Approaches to EMI Sensing  Figure 2.2: Typical Demagnetization Stablein (1982)  39  Curves of Various Permanent Magnet Materials  (1) hard ferrite; (2)AlNiCo, high B grade; (3) AINiCo, high H grade; (4) alloy: (5) RECo alloy; (6) RE{Co, Cu, Fe ) alloy. T  5  e  7  Mn-Al-C  Chapter 2.  Our Early Approaches io EMI Sensing  Table 2.1: M for Spheres Compared to 5  Materials  Hop,  1 2 3 4 5 6  -1.03 -4.91 -1.18 -1.40 -2.42 -2.72  B p,  A/m  x x x x x x  0  10 10 10 10 10 10  5  4  5  5  5  5  Wb/m  0.26 0.12 0.29 0.35 0.60 0.67  2  res  40  i d l J p o for Materials of Figure 2.2. ua  M  sphere>  3.1 1.5 3.5 4.2 7.2 8.0  x x x x x x  /  A  10 10 10 10 10 10  5  5  s  s  5  5  m  ^residual// "' 1  3.1 9.6 6.0 4.7 7.4 8.2  x x x x x x  10 10 10 10 10 10  A  /  m  5  5  s  5  5  5  Inducing and Sensing a Magnetic Dipole Although the permanent-magnet scheme was not adopted in the end, due to its inherent hmitations and the final configuration is quite simple in principle, the intervening effort was an extended evolutionary process.  Many different configurations were considered,  each of them directed at overcoming the shortcomings of its predecessor, but each also introducing new obstacles to be resolved. The development, from the permanent-magnet tracer to the diametral coil, represents the major part of our effort in this investigation. It represents a quest to reduce noise, mostly due to the primary field, to a level such that the minute signal generated by the tracer particle could be discerned. This long, and often frustrating labor usually produced configurations in which the noise level was several orders of magnitude greater than the signal sought. Ironically, such results did not necessarily signify that a given configuration was intrinsically valueless.  Seemingly  minor modifications could reduce noise dramatically — the trick was finding the right modification. Even though none of the intermediate concepts reached fruition in terms  Chapter 2.  Our Early Approaches to EMI Sensing  41  of a working sensor, amongst them may he the seed for future sensors waiting to be germinated with that right modification. For this reason, and also so that others may learn from our experiences, our effort, as it evolved, is now outlined. Some of the configurations described in this section were only evaluated through calculations, when their failings were recognized; others (eg. those shown in Figures 2.4 and 2.5) were pursued all the way to working models, at which point they demonstrated noise levels which were orders of magnitude above the anticipated tracer signal.  2.3.1  Decoupling P r i m a r y Field  Loop T r a n s m i t t e r / L o o p Receiver  The simplest induction configuration consists of a circumferential transmitter and receiver. For this case, Bohn (1968) shows that, based on Neumann's formula, the mutual inductance between the two coils is expressed by:  MR T  where  = poN N /T r T  Ry  T  (jf ~ ) K  R  F  2E_  Chapter 2.  Our Early Approaches to EMI Sensing  A  =  number of turns in the respective coil  r  =  radius of the respective coil  Po  =  AT x 1 0  I  =  axial distance between the two coils  F  =  elliptic integral of the first kind  7  42  H / m = permeability of free space  -7  ° y/l-K*sm f3  J  E  =  2  elhptic integral of the second kind JJ y/1-  K* Si*  2  3d0  The elhptic integrals can be expanded as an infinite series (Sokolnikoff and Redheffer, 1958). When K  2  < 1, these expansions are:  1.3.5...(2,-1)  ,f  2-4-6...2n  E(K,-) = V ' 2/ •  -  ---K 2 2  2  Jo  H n 8d6-—  f  2  S1  Jo  l-3-5-..(2n-3)^ 2-4-6...2n  sin*6d6...  2  2- 4 Jo f f  s  i  n  ^  w  _  Jo  The signal at the receiver, assumed to be an open loop, due to direct coupling with the transmitter is: EMF  = -M ^-I e dt  iwi  RT  TR  T  =  -iwM I e  iwt  TR  T  Chapter 2.  Our Early Approaches to EMI Sensing  43  where Ie  =  lwt  T  time-varying current in the transmitter  Evolving directly from the permanent-magnet approach, however, two-coil configurations were initially considered without regard to the direct coupling between the transmitter and the sensor coils. The simplest arrangement in this category consisted of two concentric, but spaced, parallel loops, whose common axis was either concentric with, or perpendicular to the axis of the riser. The above calculations revealed that the strong coupling between the coils would result in a very small ratio of tracer signal to transmitter signal (i.e. noise), no matter how the coils were spaced or sized. This can be inferred from Equation (1.1), where an analogy is made to coupling between three coils. The first term on the right hand side of that equation, the coupling coefficient is:  k  TR  where  kAB =  (^fcs)^  k  =  fraction of total flux from coil A, which passes through coil B  ks  =  fraction of total flux from coil B, which passes through coil A  A  As the transmitter and receiver coils are moved apart, kxR decreases. However, even for the strongest tracer signal, when the tracer is near the receiver and therefore kcR is relatively large, the value of kxc  becomes small, since the transmitter is distant from the  tracer (the subscript C represents the conductive tracer). The two coefficients, k^R and  kxc,  roughly compensate for each other, so that the coupling coefficient, and therefore  the signal-to-noise ratio, remain relatively unchanged with coil spacing. Although reducing the diameter of a horizontal receiver coil does effect an increase in the coupling coefficient, for an axial spacing between transmitter and receiver coils, the  Chapter 2.  Our Early Approaches to EMI Sensing  44  increase is minimal. Furthermore, because the smaller coil now intrudes into the flow, a new source of noise is introduced, due to the relative motion between the two coils, as the receiver coil is buffeted by the flow. Calculations for the general case of two concentric spaced loops indicated that, although the signal-to-noise ratio is unacceptable, the strongest signals would occur when the tracer is either near the transmitter, or near the receiver. This symmetry pointed the way to a later geometry, the coaxial-line and loop, in which the strongest part of the exciting field is positioned away from the receiver, hence reducing the region of low sensitivity. Satellite-Sector Sensing L o o p s In the next development, I considered the shape of the tracer's induced field compared to the field lines generated by the transmitter. It was only when this new perspective was adopted that the orientation of the two loops was considered, relative to each other, as a means to obtain a null, thereby minimizing unwanted noise due to the overwhelming exciting field. The concept of decoupling the receiver from the primary field was incorporated in two variations of the previously discussed two-loop theme. Known as satellite-sector configurations, these variations involved having several satellite-sector sensing loops around the periphery of the column. In the first case, I considered satellite-sector loops which were tangential to and in a plane perpendicular to that of the circumferential transmitter loop. This configuration is shown in Figure 2.3, for one sector. Although the near-field around the transmitter was not calculated, due to the complexity of the calculation, it was assumed that, due to the symmetrical position of the receiver loop relative to the transmitter loop, there would be negligible coupling between them. As the tracer approached the plane of the transmitter  Chapter 2.  Our Early Approaches to EMI Sensing  45  Figure 2.3: Satellite-Receiving Loop Perpendicular to Plane of, and Tangent to Transmitter Coil (solids and gas flow in the cross-hatched area)  Chapter 2.  Our Early Approaches to EMI Sensing  46  loop, the radial component of its field lines would be normal to the receiver loop, thereby inducing a signal. When the tracer was in the plane of the transmitter loop, the signal would go to zero, because its field would be symmetric relative to the receiver. Comparing the signals from individual sectors would allow a rough estimation of the tracers radial and azimuthal position.  Though the signal-to-noise ratio of this arrangement would  have been better than the two-loop configuration discussed previously, this approach was eventually abandoned because:  (a) It depended upon the relatively weak radial component of the tracer's induced field for coupling to the receiver (b) The sectors could not be physically positioned relative to the transmitter accurately enough to reduce their coupling to the order of the minute tracer signal.  The second variation incorporating decoupling, also had a transmitter coil wound around the circumference of the riser, but the plane of the receiver satellite-sectors was parallel to the plane of the transmitter. In order to attain a null in this configuration (Figure 2.4), the receiver loop had to be accurately positioned, so that the fluxes (i.e. / B • ds) from the interior and exterior of the transmitter loop just balanced as they cut the receiver loop.  The near-field equations, rather than the simplified dipole far-field  equation used previously (Equation (2.1)), were required to determine the precise null position of the receiver loops. The advantages of this configuration were:  (a) effective null due to positioning of the receiver loops, as well as "bucking" the two receiver loops against each other (our first "figure eight" arrangement);  Chapter 2. Our Early Approaches to EMI Sensing  48  (b) transmitter and receiver external to the riser and physical!}' "locked" together in a coil form; (c) receiver coupled to strongest (i.e. axial) component of tracer's field. However, when this configuration was tested, there was still enough noise at the receiver loop to overwhelm the tracers' signal.  At least some of this noise could be  atrributed to insufficient accuracy in positioning the loops in the exact null position. In the diametral receiver, which was eventually developed successfully, this problem was remedied by incorporating adjusters to distort the receiver loops, in order to obtain the null. Conceptually, this satellite variation was insensitive to a tracer particle travelling in the vertical plane of symmetry dividing the two receiving loops. In such a case, the signals from the two loops would be equal, and would therefore add up to a zero total response, because of the "counter" series connection of the two loops. Furthermore, the exciting field, generated by the circumferential transmitter loop, is weakest at the centre, resulting in a relatively weak induced moment in a tracer at, or near, that position.  Solenoid Transmitter  In order to make this section complete, brief mention is made of the solenoid, as a source of the exciting field.  The field deep within a solenoid is very uniform, and therefore  the signal from a tracer within such a field depends only on its position relative to the receiver loop. The receiver loop located within a long solenoid would be shielded from outside noise.  A null might be attained if the receiver was a rectangular loop, whose  plane was warped to conform to the inside curvature of the solenoid.  Unfortunately,  this solenoid's geometry involved construction complexities (e.g. parasitic capacitance at high IM, length/diameter > 3, wire length < 0.1A), which were inappropriate at this  Chapter 2. Our Early Approaches to EMI Sensing  49  stage of the project, since the simpler loop-transmitters could not be made to work. The advantage of a uniform field could, however, be attained instead by two axialry displaced concentric loops (i.e. Helmholtz coils), without suffering the inherent complexities of the solenoid. In practice, the fine transmitter, described in the next section, superseded the solenoid, and it too provided a nearly uniform field in the neighborhood of the receiver loop. In any event, the benefits of a uniform field were of secondary importance, compared with the problem of coupling between transmitter and receiver. Hence, the solenoid configuration was not pursued further. Line Transmitter/Loop  Receiver  Because of the low signal-to-noise ratio, as well as the potential added noise of a loop inside the riser, the two loop arrangement evolved into the centerhne wire/circumferential loop configuration. This new geometry not only would uncouple the transmitter from the receiver (providing that the former was maintained perpendicular to the plane of the latter), but also place the strongest part of the exciting field far away from the receiver thereby reducing kxR. The transmitter's field fines, in this case, are coaxial circles around the centerhne, in planes parallel to that of the receiver loop, and are expressed by (Plonsey and Collin, 1961): Vol 27TT  (2.9)  where / = current through the transmitter wire. The centerhne wire would also present a small cross-sectional obstruction to any buffeting from the turbulent flow, and its tension could be adjusted so that the vibrating frequency, at which the wire might respond to the turbulence, would not interfere with the desired signal. It was assumed, at this time in the development, that the field would be a function only of radial position, and would be  Chapter 2.  Our Early Approaches to EMI Sensing  50  uniform axially. This was considered a benefit, in light of the discussion in the previous section regarding a solenoid transmitter. As shown in Section 2.3.2 below, this perception of an axial-independent field was only an approximation, the accuracy of which depended upon the operating frequency. The centerhne transmitter /circumferential receiver was abandoned because none of the flux lines emanating from the tracer cut through the receiver loop, when the tracer was in the plane of the receiver. Even when the tracer was not in this plane, symmetry dictated that each of its flux line would cut through the receiver loop at two points, and therefore no signal would be induced in the receiver. In order to circumvent this symmetry problem, we considered an external satellitesector loop receiver instead of the circumferential receiver (Figure 2.5). Although there would still be no signal when the tracer was in the plane of the receiver, or, in a vertical plane, which bisects the sector, a signal would be expected whenever the tracer was elsewhere. This arrangement was modified to improve the coupling between the tracer and the receiver, by adapting the tangent satellite, discussed previously and shown in Figure 2.3, to the centerhne transmitter configuration. However, once again, due to symmetry, no signal would be induced in the receiver when the tracer was in the vertical plane, bisecting the coil. In the next evolutionary step, I opted to remove the transmitter from the flow and replace it with two wires parallel to the riser, but outside of it, as shown in Figure 2.6. These two external transmitters would provide a strong resultant exciting field, due to superposition of the individual fields of each wire, in which the current flows in the direction opposite to that in the other wire. The four receiver coils are placed so as to be uncoupled from the resultant exciting field.  ' 2. r  a Ppi-o,  »o ,  E  S  Chapter 2.  Our Early Approaches to EMI Sensing  52  Figure 2.6: Two External Axial Transmitters with Four Receiver Loops in Nulled Positions (showing resultant exciting field at P)(solids and gas flow in the cross-hatched area).  Chapter 2.  Our Early Approaches to EMI Sensing  53  Instead of the four receiver coils, shown in Figure 2.6, satellite-sector receiver loops, such as the one shown in Figure 2.5, could be used, with the two external transmitters. Here again, the sector is coupled to the tracer through a relatively weak component of the latter's field, and is not coupled at all when the tracer is in the sector's plane.  2.3.2  Resonant Transmitter Circuit  During the early stages of our work, the transmitter was powered by a function generator, which was designed to feed into a 50 Q resistive load. Therefore, the transmitter had to be made part of a circuit which, in total, presented such a load to the generator. The loop transmitter was modelled as an inductance in series with a resistance, with the two in parallel with a parasitic capacitance. The resistance, due primarily to a skin effect, and, for solenoids, a proximity effect (Dwight, 1923), is frequency-dependent. The parasitic capacitance, inherent in the coil spacing, and its dimensions, is most readily determined by measurement (Langford-Smith, 1953). In order to produce the strongest possible exciting field, for the given signal source, the impedance of the load was matched to that of the source (Durney, 1982), so that  RL  = RG  XL -- XQ  where RL  =  resistance of the load (i.e. transmitter)  XL  =  reactance of the load  RG  =  resistance of the generator = 50 Q,  XQ  — reactance of the generator = 0  In order to accomplish this match, two capacitors were added to the load, one, C,, in series, and the other, C , in parallel. The parasitic capacitance is included in the.latter. p  Chapter 2.  Our Early Approaches to EMI Sensing  54  If the load's resistance, RL, and inductance, L, are known, the values of (7„ and C can p  be calculated, for a given frequency, by simultaneously solving:  = 50 n  Attempts to obtain matching, at frequencies in the range 50-100 kHz, were unsuccessful, due to the sensitivity of the load impedance to slight variations in the two capacitances. Under some circumstances, a 1% increase in C would increase the resistance of p  total load tenfold, with the reactance increasing by an even greater factor. The function generator could not withstand such large fluctuations in load. Some time and effort were expended searching for a combination of loop, frequency and capacitance to which the load impedance was less sensitive. Later, when working with line transmitters, this was not nearly such a problem, because a tube-powered radio transmitter was used in place of the function generator, and it was far more forgiving. The load impedance was so sensitive to the value of its components, as well as to frequency, because it was a resonant circuit, with an apparently considerable Q value. Q, the quality factor, ie a measure of the energy stored in the magnetic field generated by the coil relative to the energy dissipated by the coil. The current circulating through the inductor/parallel capacitor combination is many times greater than that leaving the generator, at resonance. Like the pendulum of a clock, where energy is needed only to replace the minute amount lost due to friction, a large amount of electrical energy in the resonant circuit is  Chapter 2.  55  Our Early Approaches to EMI Sensing  transferred back and forth between the capacitor and the inductor, with the dissipated (i.e. resistive) losses being replaced by energy from the generator. In an attempt to attain a match between the load and the generator at the resonant frequency, the load was chosen as a pure resistance of 50 Cl. Any deviations from resonance introduces a reactive component (inductive for higher frequencies, capacitive for lower frequencies), and the sensitivity of the load to these deviations is directly proportional to the circuit's Q value. No benefit could be derived from resonance during the early loop work, because a strong exciting field also resulted in a greater noise level.  Once decoupling of the  transmitter and receiver was considered, then a resonant circuit would become an asset. Resonance was incorporated into the design of the line transmitter arrangements, as shown below. For the non-linear tracer work discussed below, a resonant exciting field reduces harmonic noise, something which was crucial if this approach was to succeed. The line transmitter consisted of a centerhne 6.35 mm O.D. copper tube, surrounded by a 0.1524 m ID copper pipe (which also served to shield the sensors from extraneous noise). The tube and pipe were connected to each other at each end of the riser's length and the exciting signal was fed into the system through a small loop at one end. In this version of the line transmitter, the sensors were small loops passing through the wall of the pipe and protruding into the flow. Like the loop transmitter discus'sed above, this arrangement also had to be properly matched to the source, requiring an appropriate circuit.  However, at reasonance, the  line transmitter incorporated a standing T E M (transverse electromagnetic) wave. As a result, there were points along the line, at half wavelength intervals from either end, where the current was a maximum and the voltage a minimum. A quarter wavelength distance away from these points, the opposite condition existed. This phenomena occurs  Chapter 2.  56  Our Early Approaches to EMI Sensing  only when the line is at its resonant frequency, so that reflections from the two ends constructively interfere with the incoming waves to produce a standing wave. For this configuration (shorted at both ends), resonance occurred when the total length of the pipe was some multiple of a half wavelength.  The sensing loops were obviously placed  at the points of maximum current, and were therefore free from electric field coupling. In order to avoid propagation modes other than by T E M waves, the following constraint was applied (Terman, 1955): / <  , °  7r(a  .,  + b)  (2.10)  v  '  where /  =  operating frequency  a  =  radius of inner conductor  b  =  radius of outer conductor  C  =  speed of light  This limits the operating frequency to a maximum of 1200 MHz for the dimensions given above, corresponding to the minimum axial spacing between sensors of 20 mm. The actual operating frequency we used was 148 MHz. Random variation of the solids concentration, which results in fluctuations of the dielectric constant of the surrounding space, was not important in the neighborhood of the sensing loops, because the electric field was minimal at these voltage-minimum locations. Unfortunately, the voltage-current distribution along these line configurations was also their undoing. The voltage-peak positions were very sensitive to the fluctuating dielectric constant, especially in light of the high Q values of these configurations. This resulted in the line going in and out of resonance randomly, producing overwhelming noise.  Chapter 2. Our Early Approaches to EMI Sensing  57  This problem of noise might be resolved by reverting back to a loop-transmitter configuration. The loop, however, would now be part of a. circuit in which it was actually the center portion of the circuit's inductor. Because of this, the transmitter would retain the desirable attribute of exhibiting a current maximum and a voltage minimum, while the points of voltage maxima would be removed to the circuit's shielded container.  2.3.3  Nonlinear Methods  In Section 1.3.1 above, the use of targets which respond non-linearly to an exciting field, has been described. This approach offered a significantly better chance of detecting the minute field of the tracer in the presence of the overwhelming exciting field. Since the methods investigated up to this point, utilized induced eddy currents in the tracer, it naturally followed that my first attempts to attain a non-linear response would depend upon non-linear (i.e. non-Ohmic) conductivity properties. A non-linear conductor responds to a sinusoidal exciting filed with a non-sinusoidal, harmonic-rich field. This occurs because the eddy currents in the conductor are related to the induced E M F by: I  c  = A •  EMFS  T  where: A and n  — characteristics of the non-Ohmic conductor  I  =  eddy current in the conductor  EMFCT  =  induced E M F in the conductor due to current flow in the transmitter  c  =  -iu)McThe  iut  > with MCT  =  mutual inductance between transmitter and conductor. These eddy cur-  rents, which determine the secondary field (i.e. due to the tracer), are not sinusoidal and  Chapter 2. Our Early Approaches to EMI Sensing  58  therefore have harmonic content (see Figure 2.7). Although there are many non-linear devices in use (e.g. rectifiers, varistors), most depend upon a junction of dissimilar materials (e.^.Cu/CuO) in order to produce the desired effect. Such devices are referred to as non-symmetrical, since the polarity of how they are connected in a circuit is important. However, some materials, such as silicon carbide, have an intrinsic non-linear nature, and their use, in this instance, would avoid the complications of a composite particle (Stansel et al., 1951). Unfortunately, silicon carbide requires an excessively high voltage gradient in order to display its non-linear nature. Such high gradients (10 -10 volts/m) are not achieved in 3  4  our application. Therefore, silicon carbide was eliminated as a candidate for a non-linear response tracer; other materials, exhibiting the same characteristics as silicon carbide, could not be found. Two non-symmetrical devices, when placed with opposing polarity in a circuit, act like a symmetrical material. In order to simulate such a situation, a composite particle consisting of oxide-coated copper particles was fabricated. However, when this composite was placed in a field, no non-linear response was detected. Rather than pursue the non-Ohmic tack further, an entirely different regime of the response function (Figure 1.5) was explored, involving the response of ferromagnetic materials. Ferromagnetic materials exhibit two properties which make them good candidates for tracer particles when using EMI methods. First, the dipole moment per unit volume, M, can be very high for a relatively small actual field,  ii/actual (-^actual  enced within the material, as opposed to the applied, external field,  is the field experi-  .^applied)-  The second  favourable trait of ferromagnetic candidates is the highly non-linear relationship between the dipole moment and  .^actual-  A material having a magnetization relationship such as  that shown by the solid line in Figure 2.8, typical of some soft ferromagnetics, responds to a sinusoidal excitation with a square wave (providing that  i^actual  exceeds H ). c  Upon  Chapter 2.  Our Early Approaches to EMI Sensing  0  1  2  3  4  59  5  wt (rad.)  T  1  1  1  1  1  1  •  1  '  r  ot—<p (rad.) Figure 2.7: Waveform of Current with Sinusoidal Applied Voltage to a Non-Linear Conductor (adapted from Ashworth et al, 1946).  Chapter 2. Our Early Approaches to EMI Sensing  60  Fourier expansion, a square wave decomposes into fundamental and odd harmonics, with the third harmonic having an amphtude one-third that of the fundamental. However, both of these characteristics can be severely curtailed by the effect of the shape of the tracer particle. The expression for the effect of shape on been given in Section 2.2, above.  i? tuai ac  has already  The values of the demagnetization factor, D. for  spheroids and cylinders is given by Bozorth (1951). The effect of the demagnetization field on the magnetization relationship is illustrated in Figure 2.8. At each ordinate value, the curve has been "sheared" over by the amount DM, and the broken line, having a slope of ^ , represents the relationship between M and if iied • The response of such a apP  sheared curve to a sinusoidal excitation is a clipped sinusoid, as long as implied is greater than the saturation field, H,. The clipped sine wave has less harmonic content than the square wave response. For a spherical tracer particle, the shear is so great, resulting in a magnetization curve with a slope of only 3, that the value of M is vastly reduced from what one might expect from such a material.  Furthermore, saturation is not likely to be attained material.  Furthermore, saturation is not likely to be attained with the applied fields used in this study. Hence, clipping would not even occur, and the response would be linear. In order to attain the desired non-linear characteristic, I considered embedding a prolate ellipsoid in a non-magnetic sphere. Although such an arrangement would generate the requisite harmonics, for a sufficiently high aspect ratio, the volume of the ellipsoid" would be so small that the total magnetic moment would be an order of magnitude less than that of a conducting sphere of the same diameter as that of the composite.  Instead, two  alternatives were devised which might improve the response to the order of a conducting sphere, while retaining the harmonic content.  Chapter 2.  Our Early Approaches to EMI Sensing  61  M  Figure 2.8: Shearing Correction of a Magnetization Curve (Chikazumi and Charap, 1964).  Chapter 2.  62  Our Early Approaches to EMI Sensing  First, I considered a multitude of aligned high aspect-ratio particles, uniformly disseminated in the non-magnetic sphere, to replace the single embedded ellipsoid. This would allow a greater volume of responsive material. Grant and West (1965) and Tesche (1951) described the collective response of small conducting spheres disseminated in a spheroidal envelope.  Their analysis has been applied here to elongated ferromagnetic  ellipsoids embedded in a sphere, since magnetization is just another regime of the same phenomena of induced dipoles. Using  D iope enve  = | for a sphere, the ratio of the dipole  moment per unit volume of the envelope, pM„, to the applied field, pM, _ #a  P P  i^  a p P  iied,  is given by:  p  ~ ^  +  I  P+  D  part  (i_p)  where: -ffacts  =  internal field (i.e. at the site of each individual elongated particle) required to attain saturation  M,  =  maximum dipole moment (i.e. saturation) per unit volume of particle  p  =  volume fraction of embedded particles (assumed to be small)  -Dpart  =  demagnetization factor for the individual embedded particles  The value of this ratio for a perfectly conducting sphere is 1.5, and for a ferromagnetic sphere is 3. As discussed above, however, the ferromagnetic sphere would require an astronomical applied field in order to saturate. Assuming H^JM,  is negligible compared  to the other terms in the denominator, an infinite number of combinations of p and D can be found to attain a value of pM /H , a  app  which exceeds the response of the conducting  sphere. However, in order to minimize the amount by which  i/app  must exceed  in  order to attain saturation, low concentrations of very elongated ellipsoids are favoured. Though this solution appeared to resolve the poor response of a solid ferromagnetic tracer sphere, there were some practical difficulties in applying it, such as:  Chapter 2.  t  Our Early Approaches to EMI Sensing  63  1. uniformly packing and aligning elongated particles into a spherical envelope. 2. remaining in the multi-domain regime as the diameter of the elongated particles is reduced to the submicron range. (Single domain particles have a different magnetization curve). 3. avoiding an apphed torque to such a tracer particle, if the particle's long axis is not aligned with the exciting field. A second alternative was then considered in which the elongated multi-domain particles were replaced with single domain spherical particles.  Calculations indicated that be-  cause the embedded particles were the same shape as the envelope, the actual field they experienced would be the same as that apphed to the envelope. These particles, e.g. 20-50 A for iron particles, are known as superparamagnetic particles. Bean (1955) has shown (Figure 2.9) that they exhibit extremely easy magnetization compared to multi-domain particles. This is the preferred response to generate harmonics, via a clipped sinusoid, generated by a relatively small exciting field. Despite the conceptual promise of this alternative, it was put aside for more promising avenues because, like the preceding alternative, it presented practical difficulties in fabricating such a tracer.  Chapter 2. Our Early Approaches to EMI Sensing  64  Figure 2.9: Assumed Magnetization Curves in Dilute Samples of Three Sizes of Ferromagnetic Particles (Bean, 1955). a = large multidomain particles; h = small "superparamagnetic" particles; c = optimum single-domain particles.  Chapter 3  Present Configuration  3.1  Sensor and Associated Electronics  The present sensor consists of two coils, a transmitter, excited at 6 kHz, and a receiver, both wound on a common acrylic form, as shown in Figure 3.1.  The transmitter coil  is a circumferential winding of 68 turns of 30 gauge magnet wire, having a measured impedance of 11 -f 83xfi at 6 kHz; the measured voltage across, and the current through the transmitter are 12.9 v (r.m.s.)  and 160 m.A. (r.m.s.), respectively.  Based on the  impedance measurement, the current in the transmitter lags behind the exciting voltage by 82.5°. The receiver, in order to attain a null relative to the exciting field, as well as to improve response and reject extraneous noise, is wound as a diametral coil. Each of the 100 turns of 36 gauge magnet wire of the receiver coil can be considered two separate loops connected in series, such that a common alternating magnetic field induces an E M F of the same magnitude, but of opposite sign in the two loops. After the initial 50 turns of this coil had been wound, a grounding tap was attached, so that the coil would conform to the input requirements of the local amplifier, which was designed for an input of two coils. The average impedance of each half of the receiver coil (relative to the center tap) is 59 -f lOlzfi. The inductance of both transmitter and receiver were measured with a General Radio Impedance Bridge. The lengths of wires used to wind the receiver coil, 95 m, and the transmitter coil, 38 m, are both much less than 0.08 A, or 4000 m at.6 kHz.  65  Figure 3.1: Coil Form and Receiver Coil Winding  Chapter 3. Present Configuration  67  Hence, the current can be assumed uniform at all points in the coil (ARRL Handbook, 1987). The coils can therefore be treated as magnetic dipoles. This receiver coil might be referred to as a "figure-eight" configuration. Alternatively, the two loops might be said to be connected in counter-series. There are three adjusters incorporated in the coil form, spaced at 120° intervals, so that one side or the other of the receiver coil can be expanded ever so shghtly in order to make the final precise adjustment to null. The diametral wire bundle of the receiver was originally shielded mechanically from the flowing solids by a 8.0 mm OD plastic tube, which was later replaced with a brass tube, providing electrical shielding, as well. The complete sensor assembly, consisting of the coil form with its two coils, two short sections of 0.152 m ID acrylic pipe on which the form is mounted, and two flanges, one at the top and the other at the bottom, has a height of 57 mm. Together with a companion flanged section of pipe 0.398 m high, the assembly replaces a standard 0.46 m long flanged section in the riser. In order to eliminate noise due to the randomly fluctuating electric field within the riser, the coil form/wire bundle, and the local amplifier circuit board, are enclosed in aluminum foil and a sheet metal shield, respectively, the two being electrically connected to ground. The foil has a gap at a point opposite the board so that it does not present a closed loop to the magnetic fields, thus blocking them. The underlying principle of this shield is explained by King et al. (1945). Both the transmitter and receiver coils were designed to replace their counterparts, at a frequency of 6 kHz, in a security system developed at Oregon State University. A prototype was generously loaned to the department by its owner, Harrison Cooper Associates. The underlying principles of this system can be inferred from a description of an earlier circuit given by Fitzgerald (1980).  In the system which used here, the  Chapter 3. Present Configuration  68  components which were germane to this particular application were the oscillator/phase shift circuit, the power amplifier circuit for driving the transmitter coil, the local amplifier circuit and the multipher/filter amplifier circuit. The block diagram in Figure 3.2 shows how these various components were connected to each other. The details of the circuits and the loads that were applied to them in the security prototype are shown in Figures 3.3 and 3.4. The oscillator/phase shift circuit generates two sinusoidal signals, <f> and c6j, which 0  are of equal amplitude and frequency, but out of phase with each'other by an adjustable amount. Part of the signal, <j) , is amplified and used to excite the transmitter coil. 0  The phase of the transmitter current, as well as the resultant exciting magnetic field is approximately 90° out of phase with c6 (lagging), assuming that the power amplifier has 0  no effect on the phase of its input. The receiver coil, modelled as an open loop, responds with a signal which is approximately 90° out of phase with the exciting field. Therefore, assuming the local amplifier does not affect the phase of the receiver signal, the overall phase shift of the signal entering the multiplier circuit is approximately 180° out of phase relative to c6- This signal from the receiver coil is multiplied by the other signal, aV 0  Although a bandpass filter was considered to remove noise at other freqencies, this multiplication process effectively serves this function, as explained in Section 3.2 As well, noise due to direct coupling between the transmitter and receiver coils is eliminated by this approach. The purpose of the integrator/amplifier after the multiplier is to remove the carrier signal by averaging it with a smoothing time constant. The time constant was changed from 220 ms in the original security system, to 14.7 ms in the present application (by replacing the 1.5 pF capacitors with ones of 0.1 pT), in order to improve the circuit's response to relatively fast moving tracer particles.  Oscilloscope M  Integrator  Figure 3.2: Block diagram of present coil relative to supporting electronic circuits. CO  Chapter 3. Present Configuration  70  Transmitter  Amplifier  «*>PUT —I—MA,  E x c i t i n g and S h i f t e d Signals Generator  £_VvV  'VjM—  Figure 3.3: Transmitter Circuits for Security Application (taken directly from Fitzgerald, 1979).  Chapter 3. Present Configuration  71 Remote flmplif i e r  -to  fieri*** USHTS  o-i^f  34,0V.  Mult i p l i e r / l n t e g r a t o r  M«Jt«pU  SUA.  5  -4>  —\  3Wt  y  1—*M  UAA/  BiJC ah «u  W"V\,  1 Receiver s i g n a l to o s c i l l i s c o p e OUTPUT  7-  „ .. 6<^C  o3r  MfSJCM  Figure 3.4: Receiver Circuits for Security Application (taken directly from Fitzgerald, 1979).  Chapter 3. Present Configuration  3.2  72  Calculated Response of a Diametral Loop  Similar to the development given in Section 2.1 for the circumferential coil, for the case of the diametral loop, the calculated response to the tracer passing through one semicircle is equal to the sum of EMF ,  from Equation (2.4), and a contribution due to the field  C  lines cutting through the opposite semicircle. The latter contribution is doubled because not only do these hnes add to the EMF of the semicircle through which the tracer is passing, but they also generate an opposite EMF in the opposite semicircle. As noted in Section 3.1, the two semicircles are connected in "counter" series, so that the absolute value of two opposite values of EMF  are added to obtain the total response.  This  is justified more rigorously in the Appendix B.3. For the tracer located in the region 0 < 8 < 7r, the response of the diametral loop is therefore:  [v P P ? ^rdrdv 00  EMF  D  = EMF  C  + 2  pt  [  Jn JO  OZ  + iu> J-K  Jo  P /*  l o o  P  m ^rdrdv\ J (3.1) z  0m  z  Due to symmetry considerations:  EMF =g(R, ,6) D  Zl  Figure 3.5 and 3.6 are plots of the integrals in Equation (3.1) for several values of 8. Although the values of I in these plots are greater than the corresponding values x  of I2, in order to obtain the values of the integrals, the former are multiplied by the velocity of the tracer particle, V , which is of the order of 10 m/s, whereas the latter are pz  multiplied by the angular frequency, u>, which has a value of 3.76 x 10 s . 4  -1  Therefore,  at the present operating frequencies, the velocity component is insignificant compared to the moment component. The response of a coil, consisting of many loops in series, is approximately the product of the single loop's EMF, derived here, and the number of loops (or turns).  Chapter 3.  Present  74  Configuration  G=37r/8  B=n/2  Figure 3.6: Moment Component of Response Diametral Case. Coil Rad. = 0.095m. I urm p /4TT 2  z  0  =2  n  d  integral Equation (3.1)  Chapter 3. Present Configuration  75  The purpose of the foregoing model is not to predict the amplitude of the signal displayed on the oscilhscope as a tracer particle passes through the sensor. Not only does the signal from the sensor undergo several stages of amplification and multiphcation, but more importantly, the true signal level is effectively masked by integrator circuits near the end of the signal-processing train, which reduce the frequency response to near dc. The effect of these circuits is to produce a signal on the oscilhscope which reflects not only the amplified magnitude of the sensor's signal, but also the rate at which this signal is changing as the tracer passes through the sensing region. Therefore, although the signal at the sensor is not affected by tracer velocity, as described above, the rate at which the tracer "climbs" over the contour determines to what extent the oscilhscope tracer follows the signal. For example, the oscilloscope trace of a slow moving particle will more closely follow the amphfied/multiplied sensor signal than would be the case of a rapidly moving particle; the time constant for the integrator circuits is 14.7 ms. In addition, the model is based on the assumption that the exciting field is uniform throughout space, which is not very realistic for the circumferential transmitter coil used in the final configuration. This model does serve, however, to compare the responses of different coil configurations, to determine the effects of scaling-up a given coil, and to delineate regions of sensitivity for a given coil. The model agrees with the relative magnitude of the responses given in Section 4.1 for tracers passing through various points in the plane of the diametral coil. Although it does not take' account of the downstream signal conditioning, the model is an essential tool for further development of the technique.  Chapter 3. Present Configuration  3.3  76  Exciting Field Due to the Circumferential Transmitter  The induced dipole moment, m ,  of the tracer depends, in part, on the exciting field,  z  Ho e , at the tracer's location (Equation (2.3)). The exciting field, for both the circumlut  ferential and diametral sensing loops discussed above, was generated by a circumferential transmitter coil, as described in Section 3.1. Because the region of interest is in close vicinity to the transmitter coil, it is described by the near-field equation (Ramo and Whinnery , 1953). The assumption that m  z  is uniform in space used in the appendix  to derive analytical expressions for the inner integrals of Equations (2.4) and (3.1), is a simplification.  Especially near the riser wall, this assumption is not valid, and the  distribution of Ho must be taken into account. The z-component of Ho, at a position (r", v", z") relative to the center of the transmitter coil, is given by:  =  — fl - -kP (x) + —k PJx) 2a I 2 8  for  r" < Va - z"  2  2  2  2  W  4 V  ;  2  (3-2)  and  H\  Z NF  =  L ffc-fP (»)-|fc-!P (x) JLa L I 2  4  P (x) + . . . 8  for where  r" > Va - z" 2  2  (3.3)  Chapter 3. Present Configuration  77  k  x  +1  I  =  instantaneous current in the transmitter coil  a  =  radius of circumferential transmitter coil  =  Legendre polynomial of order n  P  n  Equation (3.2) and (3.3) can be expressed relative to the receiver coil, which is parallel to, coaxial with, and displaced a distance I above the transmitter coil, by making the transformation: z  = z -f t  where z' is relative to the receiver coil. In the plane of the transmitter (i.e. z" = 0), the field inside the loop (r" < a) is found by simplifying Equation (3.2):  + for  z" = 0  (3.4)  The series in brackets in Equation (3.4) is plotted in Figure 3.7, showing that the exciting field is much stronger near the wall than near the axis of the riser.  3.4  Originality  Previous fluidization applications of EMI-based techniques (e.g. Cranfield, 1972; Fitzgerald, 1979; Avidan, 1980; Waldie and Wilkinson, 1986; Turton and Levenspiel, 1989) have exclusively used ferromagnetic tracers and a single coil sensor, as opposed to conductive  Figure 3.7: Magnetic Field Strength in Plane of Transmitter from Near Field Equation (3.4).  Chapter 3. Present Configuration  79  particles and a transmitter/receiver configuration, adapted here.  Single coil arrange-  ments are typically part of a circuit, which senses a change of inductance in the coil when the target particles are in close vicinity to the coil. Ferromagnetic target particles cause the coil's inductance to increase, which is manifest by the current in the coil lagging behind the original current when the particles were not present. Single coil configurations can also be used to detect conductive, non-permeable particles. However, at best, such particles can only produce a change in inductance one half that of permeable particles of the same size (Bohn, 1968). This effect can also be seen in Figure 1.5 where, if curves of higher permeabilities were plotted, the real part of the response function would converge to a limit of -2.0, compared to +1.0 for the non-permeable case. By comparison, the maximum imaginary reponse of a highly permeable sphere is 1.75 times that of a nonpermeable sphere. Conductive particles cause a decrease in the coil's inductance, and the resulting coil current leads the original current. There are two disadvantages of the single loop/ferromagnetic technique compared to the present approach. First, in addition to the Lorentz force, due to eddy currents in the particles, there is also a magnetization force which must be considered in the case of ferromagnetic particles.  This force,  (/* - /i ) (if • v ) H 0  is the same force that  accounts for an iron object being drawn towards a magnet, and therefore, it might affect the tracer's trajectory in the non-uniform exciting field. The second disadvantage of the single-loop configuration is its limited potential for increased sensitivity compared to the transmitter/receiver arrangement.  In the latter case, because the two coils are nulled  relative to each other, the current in the transmitter can be increased without effecting the receiver coil (Burke, 1986). As shown in Figure 3.9, below, a tenfold increase in the current of the transmitter coil would significantly reduce the size of tracer which could be sensed. In the case of a single sensing loop, even though an increase in the coil's current  Chapter 3. Present Configuration  80  would cause the field due to a given particle to increase, the effect would be measured relative to the higher current in the coil, and therefore sensitivity would not improve. The riser, in which the experiments were conducted, presents a very difficult environment in which to sense individual tracer particles, using the EMI technique. There are large and random fluctuations in electrostatic charge, sometimes resulting in considerable spark discharges. Furthermore, there are mechanical vibrations, and the sensing region is large relative to the size of any tracer particle. The tracer particles themselves move at high velocity, and can pass the sensor multiple times during one voyage through the riser as they move upward in the core or downwards along the outer wall. In addition, the shape of the tracer, dictated by hydrodynamic considerations, is less than ideal in terms of induction, due to the demagnetization effect, as described in Section 2.2, above. In order to succeed, the final sensor configuration, described in detail in Sections 3.1, and in theory in Section 3.2, had to incorporate maximum sensitivity to the tracer's signal, as well as maximum rejection of all other signals. This design objective was achieved by combining three separate concepts: 1. the diametral form of the sensing coil, 2. multiplication of the sensor's response by a quadrature signal, and 3. shielding of the assembly The singular purpose underlying all three ideas was to minimize noise. In addition, the diametral form also served to enhance the signal from the tracer. For completeness, it should be mentioned that, in addition to the overwhelming noise generated outside the sensing coil, there is inherent noise in the coil itself, as well as in the downstream amplifi.cation process. These are known as thermal noise and internal noise  Chapter 3. Present Configuration  81  respectively, and they set the ultimate minimum detectable field. The challenge here was to reduce, to manageable levels, the much greater external noise, so these other sources were not considered. Okada and Iwai (1988) formulates the equations which express the minimum detectable field for a small loop. The originality of the solution here is that existing ideas have been utilized, sometimes in an unusual way, to overcome the unique difficulties arising from this specific application. For example, in the case of the diametral form, I have made use of certain of its characteristics, which are not typically exploited in other applications. The purpose of this section is to briefly summarize why each of these ideas was crucial to the success of my design.  3.4.1  Successful Decoupling due to D i a m e t r a l Design  For the case of a circumferential transmitter and diametral receiver, the signal induced in one of the semicircles of the receiver can be calculated using Faraday's law, Equation (2.2). The magnetic flux, / B • dS, passing through one lobe of the receiver, based on the nearfield equation (Section 3.3) is: (3.5) where H \WF is evaluated at z" = I, in the plane of the receiver and R.R is the radius of Z  the receiver. The signal induced in the one semicircle of this configuration is then:  (3.6)  The total signal from both semicircles is hopefully close to zero, due to the counter series winding of this coil. This "figure-eight" configuration is widely accepted as a means of  Chapter 3. Present Configuration  82  nulling out a large exciting field in geophysical and security applications. It serves that purpose here also, as well as two others, of equal importance. When a tracer passes through the diametral coil, the induced signal is considerably greater than that generated by a circumferential sensing coil. This occurs because in the region where the exciting field, Ho, is weakest, along the centerhne of the riser, the receiver geometry is such that a large portion of the field lines, emanating from a tracer located there, cuts the receiver coil. Secondly, just as any loop acts as an antenna, collecting electromagnetic radiation from its surrounding environment, so too does the coil here. However, because of its counter-series winding, the coil rejects any such signal common to both lobes of the "figure eight". The presence of the diametral wire bundle in the flow was initially perceived as a disadvantage, because it interferes with the hydrodynamics of the flow, introduces vibrations in the coil, and may obstruct tracer particles, thereby adversely affecting the accuracy of the results. The latter objection is not significant when only passage time between injector and sensor is sought. It does become a serious disadvantage however, when interpreting recirculation patterns based on second and succeeding passages through the sensor. Vibrations in the coil were a serious source of noise until quadrature multiplication was adopted, greatly reducing their effect. The modification of the flow due to this intrusive sensor remains a problem, of somewhat unknown significance.  The greatest disruption  to the flow probably occurs in the wall region, where the solids concentration is highest. However, in this region, the projected area of the tube, protecting the diametral bundle, is less than 1.8% of the annulus area for an annulus thickness of 5mm. No disruption of the flow at the wall was observed. Therefore, it seems reasonable to assume that this  Chapter 3. Present Configuration  83  intrusive sensor had minimal impact on the flow. Pressure profile measurements were not made, but might have further substantiated this assumption.  3.4.2  Phase of Response Considerations  A strategy of multiplying the receiver signal by another signal, 90° out of phase with it, was apphed in order to allow the diametral configuration to be adapted to the vibrationinducing flow inside the riser. This quadrature multiplication complements the diametral configuration because it reduces the noise generated by coil distortion, due to the vibrations. This strategy differs in a subtle, but far-reaching way from that of an earlier circuit (Fitzgerald, 1980). In the latter, the received signal was multiplied by the same signal sent to the transmitter, ci>o, so that the noise, which in that arrangement is 90° out of phase with <f> , was obliterated, after multiplication and then averaging. The strategy 0  pursued here is exactly the opposite to that earlier approach. Purposely the receiver signal was multiplied by another signal, c4 adjusted to approximately 90° out of phase l5  with d> , so that the whole signal is obliterated after averaging. Any physical distortion 0  of the diametral receiver coil, due to vibrations, for example, upsets the null. However, the imbalance signal is 180° out of phase relative to <f>o, and is, therefore, cancelled out in this approach. This effect can be graphically displayed on the oscilloscope by shaking the sensor assembly and adjusting' the phase of c6 until the effects of the vibrations a  disappear from the oscilloscope trace.  This concept was adapted from a geophysical  technique, where sensing for the quadrature response (i.e.  90° out-of-phase with the  exciting field) has certain advantages (Telford et al., 1976). In the strategy adopted here, only a response signal which is 90° out of phase relative to the exciting voltage survives after averaging. Not only is the average of two quadrature  84  Chapter 3. Present Configuration  signals zero, as discussed above, but so too is the average of two signals having different frequencies, helping eliminate noise from other sources, such as that due to the everpresent 60 Hz. Proof of this is given in Appendix D. Since the second integral in Equation (3.1) is multiplied by i, the response due to the in-phase component of the moment, m , is out of phase, while that due to the quadrature z  component, is in-phase with the exciting field. Therefore, because the exciting field is approximately 90° out of phase with the exciting voltage, (see Section 3.1, above), the quadrature response is approximately 90° out of phase with this voltage. At best, the magnitude of the quadrature response of a conductive sphere is only 35% of the in-phase component.  Nevertheless, in light of the resulting reduction in noise, the quadrature  approach was judged far superior in this application. The prototype security system was operated at 6 kHz, its maximum frequency, because, for the size of tracer particle being used, 6.35 mm diameter, the quadrature component of the response, at this frequency, was still to the left of the maxima on the non-permeable curve in Figure 1.5.  A n even higher frequency would be appropriate,  especially for smaller tracer particles. Figure 3.8 shows the ratio of the imaginary component of the dipole moment to the exciting field as a function of sphere radius, at a frequency of 6 kHz. This curve is calculated from Equations (1.2), (1.3), and (2.3), above. It shows the responses of a solid copper sphere, a solid aluminum sphere and copper spherical shells of two thicknesses. A point is also plotted on this graph showing the approximate quadrature response of the 6.35 mm diameter aluminum alloy sphere used in these experiments. For any given radius, there is a maximum response which can be achieved, assuming a material of the appropriate conductivity, and/or wall thickness, for a shell can be found. When the response parameter, ] K a | , equals 11.61 for a solid sphere, the imaginary part 2  2  Figure 3.8: Ratio of Imaginary Response to Exciting Field for a Sphere at 6 kHz.  Chapter 3. Present Configuration  86  of the complex number in Equation (2.3) is equal to its maximum value of 0.355. This maximum response is also plotted in Figure 3.8, and it is the locus of "knees" of all of the different curves representing different conductivities. Similarly, the imaginary part of the shell reponse has a maximum value of 0.50 when the parameter in the parenthesis in (1.3) has a value of 3.0. The curve for this maximum response of a shell has not been plotted, but for each radius, it would be displaced 41% above, and parallel to, the curve of the maximum solid sphere response, on these axes. At this operating frequenc}', 6 kHz, which was the equipment's maximum, a 3.4 mm diameter solid aluminum sphere would have a response an order of magnitude lower than the 6.35 mm aluminum shell. For this smaller solid sphere, the moment can be improved by increasing the frequency, had this capability been available, but only to the maximum solid response curve. Increasing the frequency also effects a proportional increase in the sensor's signal through the coefficient of the second term on the right hand side of Equation (2.4). B y increasing the frequency 3.2 times to 19.3 kHz, the imaginary component of the dipole moment, m, would be a maximum for the 3.4 mm aluminum sphere. This would result in an increase in the sensor's signal to 5.4 times that produced at 6 kHz; this would be a little more than half of the signal from the 6.35 mm shell at 6 kHz. If the frequency was instead increased to 116 kHz, the imaginary part of m would remain unchanged from that at 6 kHz, for the 3.4 mm aluminum sphere, but the sensor's signal would be improved 19.4 times, and this would be nearly twice the signal available from the 6.35 mm shell at 6 kHz.  3.4.3  Effective Shielding F r o m Electric F i e l d Fluctuations  One particularly troublesome form of noise was the occurrence of spikes, which are similar in appearance to the tracer signals, on the oscilloscope screen. Because this form of noise varied from day to day, and often increased in frequency as a run progressed, it was  87  Chapter 3. Present Configuration  assumed to be associated with the build-up and discharge of electrostatic charges within the C F B equipment. A shield (described in Section 3.1) was adopted which had been used earher on small loops intruding into the flow. Although less than perfect, it did help to reduce this type of noise.  There was probably some leakage, and this design  could be improved by possibly encasing the whole sensor assembly, from flange to flange inclusive, with a shield. In addition to direct protection from discharge, the shield also helped reduce noise due to fluctuating electric fields, as streamers of particles, presumably highly charged, passed by one side of the sensor or the other. As explained by King et al. (1945), the signal generated in such a shielded loop depends solely upon the electric field generated at the gap of the shield. In this particular application, a gap exists between the shield surrounding the diametral bundle and the shield surrounding the circumferential part of the coil. As well, the circumferential shield is not continuous and therefore, there are, in effect, three gaps — one between the two circumferential legs, and one each between the diametral shield and each circumferential leg. When a package of highly charged particles passes by the diametral shield and momentarily charges it relative to the circumferential shields, the two latter gaps experience the same electric field, generating the same noise signal in each lobe. Due to the "figure eight" configuration the net response of the receiver coil to such an event is zero.  3.5  3.5.1  Limitations of the E M I Technique  Global vs. Local Indications  As previously mentioned, a sensor was sought to make a global measurement — the time of flight of a tracer particle from one level in the riser to another. The significance of tracer speed, direction, or position, as it passed through the sensor, was not initially appreciated.  Chapter 3. Present Configuration  88  The importance of two of these local variables, speed and direction, became obvious when tracer particles occasionally exited the riser after an unexpected even number of recorded responses (Section 4.2.3). It became apparent that, for any response other than the first, it could not be ascertained whether the tracer was coming from below or above the sensor. Despite my efforts described in Section 4.1 below, I was unable to obtain the requisite information to overcome this ambiguity. Because of this limitation, multiple sensors of this design, widely spaced along the riser, could not be used to determine the residence time in the intervening regions, as the tracer passed up through the riser. For a single sensor of this type, the second and succeeding responses for a tracer cannot be analyzed with any confidence to reveal the structure of any internal recirculation in the riser. However, there is one local indicator that the sensor reveals quite distinctly, and that is the semicircle through which the tracer is passing.  Although these data were  not recorded during the tests, the asymmetrical location of both the solids feed and the riser exit suggests that the solids may be asymmetrically distributed azimuthally in the entrance and exit regions (Rhodes et al., 1989).  Therefore, this capability of  differentiating semicircle position may be utilized to test such a supposition. This same capability also hints at the solution to the problem of distinguishing speed and direction. Such an adaptation is the next evolutionary step in the sensor's development, and it is discussed in Section 3.6, below.  3.5.2  M i n i m u m Tracer Size  The size of tracer particles is of great importance, if the hydrodynamics of the riser are to be fully understood. For example, in a coal combustor, it is not only important to know the R T D of the largest coal particles in the various regions, but also to determine how that R T D changes as the coal particles decrease in size in the process of burning. These  89  Chapter 3. Present Configuration  elementary tests were limited to a single, large size of tracer in a scaled, cold-model of a CFB. The oscillator circuit, in this equipment, was limited by a maximum frequency of 6 kHz, which gives a good signal-to-noise ratio for the tracer particles selected for this work. At this frequency, a smaller tracer, gives a smaller response, which would have been more difficult to differentiate from the noise. The effect of increasing the frequenc}', to compensate for a smaller tracer, can be calculated, and this has been illustrated, by example, at the end of Section 3.4.2, above. In order to still be within the small-loop regime, the total length of wire used to wind either coil should be less than around 0.1A (Section 3.1). Based on the present receiver coil, the maximum frequency would then be 315 kHz; however, at this higher frequency, the coil would probably have to be redesigned (eg. fewer turns) to take account of the resulting increased parasitic capacitance, kt this frequency, the minimum sized solid tracer which will give the same response as the 6.35 mm diameter aluminum shell at 6 kHz has a radius, a i , given by: TO  ^m(X+iY) 6 where: X (X m  0.4  (  2cw  \  n  3 =  ' V6.35 x I O " / 3  -f iY) = the imaginary component of the response function for a solid  sphere of radius dmin-  The 0.4 in the denominator of the second term is the imaginary component of the response of the 6.35 mm diameter aluminum shell at 6 kHz. This equation can be solved as a function of conductivity, using Equation (1.2), and the result is plotted as one of the curves in Figure 3.9. If a response an order of magnitude lower was acceptable, or alternatively, the current in the transmitter was increased by an order of magnitude, then smaller particles could be detected as shown in the figure. Higher frequencies could be  Chapter 3. Present Configuration  90  used (within the quasi-static limitation discussed in Section 1.3.1), if the coil had correspondingly fewer turns. For example, if only 50 turns were used in the coil, a maximum frequency of 630 kHz could be used, and the particle sizes which would give the same response as the aluminum shell at 6 kHz are shown in the figure. Although this latter tack does not offer any improvement in sensing smaller particles, it ma}' shift the minimum point of the curve to the conductivity of a readily available, or more appropriate, material.  More importantly, it results in a coil with fewer turns, which might exhibit  lower noise due to fluctations in inter-turn spacing (Section 1.3.2).  3.5.3  Noise  The drawback of the diametral configuration is the shielded bundle of wires passing through the riser. This arrangement allows physical disturbances to be transformed into electrical noise via two possible routes. First, vibrations cause fluctuations in the spacing between turns, especially at the four pinch point at the ends of the bundle, resulting in variation in the coil's inductance. Second, particles impacting on the shield causes the spacing between the shield and the bundle to vary, resulting in random fluctuations in the coil's parasitic capacitance. Previously, in Section 2.3.1, the circumferential receiver coil was modelled as an open loop. There it was concluded that the mutual inductance, dependent on how the transmitter and receiver coils were oriented relative to each other, solely determined the direct coupling between the two coils. In fact, the diametral coil is not an open loop because the local amplifier, shown in Figure 3.4, contains resistors which allow current to flow in this coil. Furthermore, besides the resistors, the parasitic capacitance, inherent in all coils, also provides a route for current flow. Therefore, the magnetic flux, c6 = J B • ds, through the receiver coil, in the absence of the tracer particle, has contributions from both the exciting field, as well as the induced current,  Figure 3.9: Locus of particle diameters and conductivites giving the same as, or 10% of the response as a 6.35 mm aluminum shell at 6 kHz.  co  92  Chapter 3. Present Configuration  which generates a field proportional to the loop's self inductance, L. Since the mutual inductance, M , is, by definition, the ratio of flux to current, where the flux is due to an external current, the total flux through the receiver coil can be more accurately described by: 4> = MI + Li I where  =  current in the transmitter coil  % — current in the receiver coil  The voltage induced in the receiver coil is then expressed by: ^, , d<t> , dl dM di EMF = -f = M — + I— +L— dt dt dt dt r r  r  T  r  .dL +i— dt  Only the first term in this equation was considered in Section 3.4.1, and as a source of noise it was minimized by decoupling the two coils with the counter-series winding. Similarly, the contribution of the third term to each lobe results in a zero net contribution for the whole coil, assuming each lobe has the same value of L. The second term as a noise source, was resolved by multiplying by the quadrature component.  The last term arises from vibrations as discussed above. These cause not  only the amplitude of the signal to fluctuate, but also its phase, enabling this noise to bypass the multiplication stratagem. Noise due to electrostatic discharges and the passage of packets of charged particles past the sensor in not entirely eliminated by the present shielding arrangement. Although I believe the shield to be effective when such sources of noise interact with the diametral bundle (Section 3.4.3), where one or the other of the circumferential legs of the shield is involved, this shield may be somewhat ineffective. A different coil configuration, such as that described below in Section 3.6, having only a single (albeit, extended) gap would  Chapter 3. Present Configuration  93  not suffer this limitation.  3.6  Recommendations  3.6.1  Resolving Local Indicators  The capability of the diametral configuration to determine the semi-circle through which the particle is passing, can be adapted to another configuration to resolve the local indicators, tracer speed and direction. Instead of having the two lobes of the "figure-eight" in the same plane, as is the case of the diametral coil, the lobes can be concentric, and separated axially. This configuration would consist of two closely-spaced circumferential coils, one above and one below the transmitter coil. The two would be connected in counter-series to attain the requisite null. Final adjustment to null would be made by precisely moving the transmitter coil up or down by means of a set of adjusting screws. Although it has been shown in Sections 2.1 and 3.2 that the response of a diametral coil to a tracer travelling near the axis can be up to sixteen times greater than that of a circumferential coil, the proposed double circumferential coil configuration would significantly reduce noise due to vibrations, as discussed immediately above, possibly even improving the signal-to-noise ratio. Furthermore, the objections of flow disruption and tracer obstruction would be entirely ehminated. This configuration would be capable of resolving speed and direction because the resultant signal can be readily identified as to which of the two coils generated it. A tracer approaching the pair interacts first with the closer coil and then, after a small but finite lag time, interacts with the other. The order of the two observed signals gives the direction of the tracer's travel, and their displacement along the time axis of the  Chapter 3. Present Configuration  94  oscilloscope, indicates its speed. If the tracer approaches close enough to the assembly to interact with both coils, but then fails to pass through, I would expect three signals to be generated by the two coils, rather than two.  3.6.2  Scale-Up  Whether one uses the double circumferential configuration recommended above or the diametral arrangement used in these tests, the question of scale up must be addressed. The model developed in Sections 2.1 and 3.2 above, has been apphed to calculate the response for both the circumferential and diametral configurations, but for a coil diameter twice the size used in this work. The results, plotted in Figure 3.10, for the circumferential case, and Figures 3.11 and 3.12, for the diametral case, are compared to the results of the earlier calculations, Figure 2.1, 3.5 and 3.6, respectively.  Without considering  the effect of the decrease in the exciting field, these plots indicate that the diametral configuration, upon scaling up, suffers little loss in sensitivity for the moment component for tracers moving near the centerhne and a slight decrease for tracers near the wall. The circumferential coil, which had earlier (Section 2.1) been shown to be much less sensitive to centerhne tracers compared to the diametral case, loses 50% of that sensitivity upon scale-up. This configuration suffers an even greater loss in sensitivity (63.5%) for tracers near the wall. Coincidentally, at this larger size, the response of the circumferential coil is nearly independent of the tracer's radial position, compared to the smaller coil. As well, the exciting field is more uniform over a given radial area than for the smaller transmitter coil. For both configurations, there is an additional decrease in response due to the weaker exciting field resulting from scale-up of the transmitter coil. It can be seen from the development in Section 3.3, that increasing the transmitter radius, a, causes a much greater  c/o  <S.o\ <Zsn. ox»i o.o<  OJOS  o os  « . » \ O A ! O^SJ, Q.QA,  AY  Chapter 3. Present Configuration  I m p /4:Tr — 2 2  z  Q  97  nd  integral Equation (3.1)  Chapter 3. Present Configuration  98  decrease in the exciting field for a larger than for a small r. Therefore, in consideration of both effects, the circumferential configuration is an even less favorable candidate in a scaled up version than the diametral coil. However, as just mentioned, without the diametral bundle exposed to vibrations, and the effect of electrostatic fluctuations reduced due to a more effective shield, the circumferential coil may incur less noise, thereby possibly offering an improvement in the signal-to-noise ratio. For the same number of turns as the diametral coil (100 in the prototype), the circumferential configuration would require a greater length of wire, and therefore the maximum frequency at which it could be operated would be less than for the diametral coil (refer to Section 3.5.2).  3.6.3  Local Flow Rate Determination  Rubinovitch and Mann (1983) and Mann and Rubinovitch (1983) developed an expression which relates single particle tracer results to the flow rate through a local region for a continuous flow system at steady state:  ^local =  W  °  E  M  where ^local W  0  E [N]  ^  =  o  w r a  ^ through the local zone e  =  net flow rate through the system  =  mean number of visits to the zone per particle ft: ^ HiLi i  with n - = measured number of visits to the zone by the i t  of tracers used in the test.  n  th  tracer, and m the total number  Chapter 3. Present Configuration  99  If the E M I sensor can be adapted to discriminate speed and direction, as recommended above, then a signal corresponding to a high upward speed can be logically associated with a tracer in the core zone, while a slow downward indicator would be representative of a tracer in the annulus. Since these two zones together represent the total cross-section of the riser, and therefore W  COTC  add up to one. Because  Wi  o c a  i  -f Wannuius = W , the corresponding values of E [N] must 0  can be greater than W , especially where there is internal 0  recirculation within the riser, E [N] is assigned a positive value for the core zone and a negative value for the annulus zone. Although Mann and Rubinovitch(1983) utilized the concept of a tracer particle as representing a fluid element, in the context of the present investigation, the hollow aluminum tracer particles (which are large compared to the sand particles) might be considered to represent coal particles of size much larger than the mean particle size in a C F B C system. The fact that there is an absence of such particles (other than the tracer spheres themselves) in this system does not detract from the results, because in a real system, these particles are present in such low concentration that they have virtually no effect on the system's hydrodynamics, or on each other. The tracer can therefore be assumed to follow the same trajectory through the riser as if there was a significant fraction of such particles. Applying this analysis to data in which particle radial position has been resolved will show to what extent, if any, particles of a given size preferentially occupy one radial region as opposed to another at different axial positions.  Together with gas. composition, gas velocity and temperature data in  these regions, these data will be of assistance in predicting the reaction history of large particles as they pass through the riser.  Chapter 4  Experimental W o r k  The experimental component of this project represents the minor part of the effort. The experimental work can be logically divided into two parts, verification of the E M I technique and actual measurements in the C F B . The first part, covered in the first section of this chapter, had two objectives.  The first was to characterize the shape of  the oscilhscope signal when a tracer passed by the sensor so that true signals could be differentiated from false signals, which are called noise spikes, resulting from electrostatic interference during C F B operation. The second purpose of the verification tests was to identify any additional information which could be discerned from the oscilhscope traces. The second part of this chapter gives the results of actual application of the sensor to measurements in the C F B .  4.1  Validation of the E M I Technique  From its inception, the EMI sensor was developed to make global measurements. Though the oscilloscope signal -indicates the actual passage of the tracer through the sensing region, the underlying purpose was to measure the total passage time spent between the injection point and the sensor. In addition to this objective, we hoped to extract any additional information from the response, shown on the oscilloscope, as the tracer passed through. This local information includes tracer speed and direction of travel, as well as the specific location (i.e. radial and azimuthal coordinates) where the tracer penetrates  100  Chapter 4. Experimental Work  101  the sensing plane. In addition, if second and latter tracer passages are to be interpreted unambiguously, then it is essential to be able to differentiate such anomalies as tracer impacts on the diametral bundle, resulting in bounce-back, as well as the tracer particle approaching the sensing region, then reversing direction, without passing through. In order to determine if such local information could be derived from the displayed signal, a small test program was conducted with the sensor outside the riser. Furthermore, a characteristic form of the oscilhscope trace had to be identified so that false signals would not be misinterpreted when collecting data in the C F B .  4.1.1  Method  Tracer particles were dropped, one at a time, through the sensor, while it was mounted atop a plexiglass pipe.  A special jig was constructed (Figure 4.1) which allowed the  particles to be dropped, in rapid succession, through the sensor at different radial and azimuthal positions. The jig is mounted above the sensor with its indexed hinge directly over the center of the sensor and its body in line with the diametral bundle (except for tests 7 and 10, when the jig was first indexed to the 45° position and then, for test 7 aligned with the diametral bundle, and for test 10 aligned 90° to the diametral bundle). Tracer particles are then placed in the holes of the jig with the retainer positioned underneath them. The jig is then pivoted about its hinge to any one of the six indexed angular positions, and the retainer, is rotated away, allowing one particle at a time to fall through the sensor, each at a different radial position. The jig can then be quickly reloaded, after repositioning the retainer, and accurately indexed to a new angular position. This allowed a whole set of responses, corresponding to the different positions, to be stored in one record length on the storage oscilloscope. The jig could also be adjusted in height above the sensor, allowing the response to be evaluated for different particles  Chapter 4. Experimental Work  102  Retainer  Indexing  nechanisN  Not t o s c a l e Dimensions i n «« Clear a c r y l i c with nylon f i t t i n g s  Figure 4.1: Jig for Releasing Particles from Reproducible Positions in Rapid Succession.  Chapter 4. Experimental Work  103  velocities. In order to attain a desired velocity, as the particle passed through the sensor, the requisite height was calculated from the solution of: /  —dU  = /  w  Jo n-  dz = z  Jo  (4.1) ^  '  where U  =  z  — drop height, with initial particle velocity equal to zero  g  =  acceleration of gravity  m  =  mass of the particle = ^ d^p for a spherical particle  -fdrag  =  drag force  =  velocity of particle  p  for a sphere  -C D with C  = £ (1 4- 0.173*e - ) + 0  D  for Re =  657  l + l M  %$*->.»  < 3.8 x 10 (SeviUe, 1989) 5  at 25 °C and 1 atm: p = density of air = 1.177 kg/m  3  d — diameter of a sphere p  p = viscosity of air = 1.846 x 1 0  -5  kg/ms  Equation (4.1) is based on a force balance on the particle: dU  " i — = -^drag + rng where f  = £ £ = Uf.  The air is assumed to be stagnant, and forces other than gravity and drag (e.g. buoyancy) are ignored. As a result of the numerical integration of Equation (4.1), a plot of U versus position, z, was obtained for the 6.35 mm diameter hollow aluminum sphere, as shown in Figure 4.2. For the large spheres and heights used in this experiment (< 1.5 m), only a small error is introduced by not considering drag, so that calculating velocity based solely on gravitational acceleration is acceptable.  105  Chapter 4. Experimental Work  In order to evaluate the response when a tracer approaches the sensing region, but does not pass through it, particles were dropped through the sensor and then bounced back off a hard surface, approaching the sensor from the underside. By adjusting either the initial drop height or the height of the sensor above the hard surface, the rebounding particle could be made to approach the sensor to various degrees.  4.1.2  Results  Tests were conducted to measure the effects of several local variables on the response, as measured on the oscilloscope. These variables were: 1. the response parameter, o~pwd?/4, characterizing the particle, 2. the position where the particle passes through the sensing plane, and 3. the speed of the particle as it passes through the sensing plane. In addition, observations were made of the axial extent of the sensing region, as well as the effect of the magnetic field on the tracer's trajectory, and the effect of particle collisions with the diametral bundle on the oscilloscope trace. The response parameter was varied by using 6.35 mm diameter aluminum shells and solid copper spheroids of approximately 2.4 mm diameter. The latter were copper shot particles, which showed a considerable variation in both shape, and size; because of this size irregularity, comparisons with, and between tests 2 and 4 are tenuous.  The coppper shot was used because it was readily  available, and its calculated imaginary response at 6 kHz, as can be seen in Figure 3.8, was approximately 0.03 times that of the aluminum shell. When the two different particles were each dropped from the same height, it was assumed that drag was negligible in both cases so that they reached the same velocity as they passed through the sensor plane.  Chapter 4. Experimental Work  106  The effects studied in these tests were:  Tests I and 2  -  various horizontal positions at high velocity for two different tracers  3 and 4  -  various horizontal positions at low velocity for two different tracers  5 and 6  -  impacts on diametral bundle  7  -  passage through one semicircle and the other  8 and 9  -  passage through one side and the other  10  -  passage through one quadrant and the adjacent one  II and 12  -  approach sensing plane  13  -  bounce-back through sensing plane  During these tests, the particles were observed from above as they dropped. At no time, did any noticeable deflection occur, except when bouncing was caused purposely. The signal generated by a tracer passing straight through the sensor has the form given in Figure 4.3. Also shown in this figure, for the purpose of comparison, is the form of noise spikes which would typically occur when the sensor was being used during a run in the CFB. These spikes sometimes made it difficult to differentiate a tracer signal from a false signal. The actual signal traces for these tests, photographed from the oscilloscope screen, are shown in Figure 4.4 and the maximum and minimum voltages of the peaks are given in Table 4.1. Results can be summarized as follows:  Figure 4.3: Sketch of Characteristic Oscilloscope Trace for a Typical Tracer Pass-Through  Chapter 4. Experimental Work  Test t z Cu sphere 4.9«'s  Test f l a l s h e l l 4.9H/S  Test #3 fll s h e l l 3.3n/s  Test f4 Cu sphere 3.3R/S  Length of one voltage/tine unit  Test t s Shell s t r i k e s bounces back  tube,  Figure 4.4: Actual Oscilloscope Traces for Local Response Tests.  Chapter 4.  Experimental Work  Teh  prerorr 5s  T e s t #7  Test #6 S h e l l s t r i k e s tube, pass thru  prerorr g,e  Vi  s  _  .  Semicircle  Tek  TeJ<  su  , .„  K&JSed  dichotomy  f i r s t peak t7)  ft«  Test t9 ft™  proton B.S»  °PP°  Figure 4.4 Actual Osciloscope Traces (Cont.)  s l t e  S  l  d  e  apter 4.  Experimental Work  Test #ie Quadrant s y n n e t r y  su  PcfttpcT  &  Test _ 2 Pass t h r u i b o u n c back and approach i r  Test #11 Pass thru,bounc back and approach  T e l <  Test # 1 3 Pass t h r u , bounce back, pass t h r u  Figure 4.4 Actual Osciloscope Traces (Cont.)  Chapter 4. Experimental Work  111  Table 4.1: Oscilloscope Signal During Drop Tests The azimuthal angle, #, is relative to the diametral tube and the radial position, r, is relative to the axis of the sensor assembly.  Test  o, [°] r, [mm]  Max. amplitude of 1st peak, [v]  Max. amphtude of 2nd peak, [v]  #1  6.35mm <j> A l shell dropped from 1.383m; V \ sensor = 4.9m/s 71.4 15 +10.4 -2.6 45 +7.4 38 - 2.0 90 38 +7.0 -2.0 71.4 90 +9.2 -2.4  #2  2.4mm <f> Cu sphere dropped from 1.383m; 15 50.8 +0.78 45 38 +0.44 90 38 +0.58 90 71.4 +0.54  #3  6.35mm <f> A l shell dropped from 0.567m; 71.4 +14.6 15 45 38 +11.6 90 38 +10.4 71.4 90 +14.6  #4  2.4mm <f> Cu shell dropped from 0.567m; V | sensor 15 71.4 +0.66 45 38 +0.98 90 38 +0.50 71.4 90 +1.04  #5  same as #3, but shell strikes tube at r — 12.7mm and bounces back +10.0 -3.1  p  = 4.9m/s -0.20 -0.14 -0.18 -0.18  V^| nsor se  lp|sensor  p  = 3.3m/s -4.2 -2.8 -2.6 -3.6 = 3.3m/s -0.12 -0.12 -0.16 -0.26  Chapter 4. Experimental Work  112  Table 4.1: Oscilloscope Signal During Drop Tests (Cont.) Test #6  #7  #8 #9 #10  #11  #12  #13  (9, [°] r, [mm]  Max. amplitude of 1st peak, [v]  Max. amplitude of 2nd peak, [v]  same as #5, but shell strikes tube at r =- 71.4mm, glances off and spirals through sensor -14.4 +14.6 same as #3 45 38 +10.0 -2.6 -45 38 -10.2 +3.0 no results same as #3, but sensor turned over 45 38 +11.4 -2.8 same as #3, but 6 measured relative to a radial line perpendicular to the tube bundle -45 38 +10.6 -2.6 -15 25.4 +10.2 -2.6 -3.4 0 71.4 +1.48 + 15 25.4 +10.4 -2.6 +45 38 +11.8 -2.8 same as #3, but particle passes through sensor, bounces back and approaches sensor, but does not pass through -3.8 1st signal 45 38" +10.0 -13.8 2nd signal +14.6 same as #11, but particle just reaches sensing region at z ~ 60mm -2.8 1st signal 45 38" +10.6 +2.4 -1.6 2nd signal same as, #3, but particle bounces through plane, then falls through again 45 38* +10.2 -3.0 1st signal -5.4 2nd signal +14.6 -9.6 3rd signal +10.8  Position for initial pass-through  Chapter 4. Experimental Work  113  1. The larger aluminum shells give a response slightly more than an order of magnitude greater than that of the copper particles, for all positions and both speeds (Tests 1 vs. 2 and 3 vs. 4). 2. For a given velocity, the response varies with the position where the particle passes through the plane. The weakest response is at an angular position of 90° to the tube bundle and a radial position of 38 mm, which is in approximate agreement with the calculated results shown in Figure 3.6, above. (Test 1-4). 3. For a given position, the amplitude of the signal is inversely proportional to particle velocity. (Test 1 vs. 3). 4.  (a) A particle colliding with the tube bundle and bouncing back from whence it came (i.e. not passing through the plane) gives a characteristic oscilloscope signal very similar to that of a particle passing through. (Test 5). (b) A particle glancing the tube bundle and then spiralling around and through the plane gives two symmetrical, inverse peaks which have the same absolute magnitude, unlike the characteristic signal. (Test 6).  5. Passage through one half-circle gives the inverse response of passage through the other half-circle. (Test 7). 6. Passage through a given point in the sensing plane from above or from below is indistinguishable, within positioning accuracy. (Test 8 vs. 9). 7. The responses to passages through two positions, symmetrical with respect to a radius perpendicular to the diametral tube, are the same, within positioning accuracy, for a given velocity. (Test 10).  Chapter 4. Experimental Work  114  8. When a particle approaches the sensing plane and reverses direction, without passing through, a. response similar to that described in 4(b), above, is observed. (Test 11). 9. On the basis of the rebound test, the limit of the sensing region is roughly estimated to be 60 mm from the plane of the sensor for the 6.35 mm diameter aluminum shell. (Test 12). 10. The magnetic field does not interact with the tracer in such a way that it interferes with its trajectory.  4.1.3  Discussion  In summary, with the exception of differentiating which half circle the particle passes through, no local information can be readily extracted from the amplitude of the peaks, reported above, or any other observable characteristic of the oscilloscope signal. This results because the signal, for a particular tracer, is a function of at least two independent variables, the tracer's speed and its horizontal position. Therefore, a specific signal does not uniquely determine either of these two variables. The apparent speed dependence is actually an artifact of the time constant in the integrator, rather than a direct indication of the particle's speed.  The response resulting from a glancing impact, as  well as from the particle approaching, but not passing through the sensor, appears to be distinctly different from the typical response, being symmetrical with respect to the time axis. However, the collision bounce-back response is indistinguishable from the typical response. Therefore, deciphering these anomahes, especially in the presence of noise due to discharges, is difficult, if not impossible. Nevertheless, under all the test conditions, the oscilhscope tracer always displayed  Chapter 4. Experimental Work  115  a positive and negative component relative to the zero line. This characteristic allowed a tracer-induced signal to be readily differentiated from noise spikes which were always manifest as either completely positive or completely negative, as exemplified in Figure 4.3. Because the present configuration is unable to sense whether peaks are due to the spheres approaching from above or below, the direction of the particle's trajectory is unknown. Therefore, with a single sensor, for second and succeeding signals, it is unknown which region, above or below the sensor, the tracer has resided in since the previous signal. 4.2  A p p l i c a t i o n of the Technique i n t h e C F B  This section describes the limited application of the EMI device in a 0.152 m ID riser. The purpose of these measurements is as much to demonstrate the technique, as to further the understanding of how solids move in the CFB. Because the application of the sensor to measurements in the CFB represents a minor portion of this investigation, the thrust of future research should be to use it to gather further data. 4.2.1  Apparatus  Scaled C F B  The unit, in which -measurements were made, as well as all of its supporting infrastructure, has been described, in detail, by Burkell (1986) and Brereton (1987). Shown diagrammatically in Figure 4.5 (Brereton, 1987), the 0.152 m ID x 9.14 m tall clearacrylic riser conducts ambient-temperature, high-velocity air upwards at a superficial velocity of up to 9 m/s, carrying particles with it. The L-valve, at the bottom of the return leg, allows control of the solids flux through the riser. The gas velocity is determined  Chapter 4. Experimental Work  116  Aif  Ptimmf  Out  Y *nd  Secondary Cyclone*  Ground irrg 'spider  Modified Butterfly Valve  Storage Bed  Bubbttng (storage] Bed Aeration  Secondary Air  Tangeotfal Opposed  njecior s c a t 1 e-  Figure 4.5: Scaled Circulating Fluidized Bed (Brereton, 1987)  Chapter 4. Experimental Work  117  from pressure measurements made with a 50.8 mm diameter orifice in the 76.2 mm ID line supplying the air from the blower; the superficial velocity is calculated by iteratively solving a set of equations adapted from Considine (1957), and given in Appendix C. The solids flux is calculated based on the passage time of observable individual sand particles between horizontal lines at 0.1 m intervals, marked on the vertical leg of the L-valve. From measurements of Burkell (1986), the solids flux for the sand is directly related to the passage time and is expressed by: G, =  1.6 x 10  2  , , 4.8 k g / m s 2  t < 33 s  where G,  =  solids (i.e. sand) flux  t  =  time [s] for particles in L-valve to move 0.1 m  The riser is made up of a series of flanged sections, allowing the EMI device to be installed at various levels; however, the data is limited to a single position, 1.63 m below the centerhne of the exit pipe (i.e.  7.64 m above the distributor).  Similarly, tracer  particle injection can be made through any of the multitude of pressure taps installed along the length of the riser. Here too, experiments were limited to a single injection point, through a tap directly opposite to, and on the centerhne of, the solids reentry point. This position was assumed to be a closed boundary, although some of the entering sand was observed to fall to-the distributor, 0.16 m below this plane, before being accelerated upwards. The time for this small diversion was assumed to be small compared to the time required to reach the sensor. Tracer Injection and Recovery The tracer injector, shown schematically in Figure 4.6, uses a pulse of compressed air to slam the sleeve forward. This action simultaneously isolates the tracer from the  Chapter 4,  Experimental  Work  cc UJ •ft  l-l-C  I K E 11  o <xc nj l_ e o u> u^.«-i..-t cr in wo TD . w —< OOICIPW »>-•»-.-< l_ C CL  OT3N  O-Oi  o  O—•  •It) O  O  ci  c ~-<  xt «» *» w •oro -a aj  N  cn  o>  a a.  B o CO  H Pi bO  a o/  :> ai a 1  Pt Lf o •oc (U<U IAO  <nw u c_r£ eo  E  Chapter 4. Experimental Work  119  magazine containing the other tracer spheres, and strikes the individual tracer particle, shooting it forward into the riser. The particle is driven into the riser by the impact of the firing pin inside the sleeve. The pulse of compressed air, which has moved the sleeve, does not directly contact the particle, but slowly dissipates into the riser around the outside of the sleeve, long after the particle has been injected. The pulse of compressed air is controlled by a solenoid valve, activated by an electrical switch, which concurrently initiates a trace on the storage oscilloscope. The injector is purged continuously with a small amount of air, to prevent sand from jamming its mechanism. Because only a single sensor is available, it is essential that each tracer particle be captured after leaving the riser. Otherwise, it would recycle through the return leg, making later tracer passage-times ambiguous. The tracer spheres are therefore captured on a screen having openings of 1.7 X 1.7 mm, installed 0.65 m below the return of the primary cyclone, Figure 4.5. The n3don screen, together with its expanded metal support, was cut into an ellipse and mounted in the return leg at a 45° angle (to the horizontal), facilitating recovery of the tracers at the end of each run, through an access port, using a vacuum cleaner. Sometimes, the sand particles, which would normally flow smoothly through this screen, would accumulate, as if the screen was bhnded. This phenomena may arise from interparticle transfer of electrostatic charge, which would adversely affect the bulk-flow properties.  The run could not continue under such conditions since the  accumulated solids would eventually either burst the screen or completely block the primary cyclone return, disabling it. Despite the inaccessibility of the screen, this problem was resolved by introducing a grounded "spider" a few milhmetres above, and parallel to the screen. The "spider" consisted of eight horizontal copper leaves, each approximately 15 mm high x 0.5 mm thick xl50 mm long, evenly spaced around a central support. This assembly was hung from a rod which passed through the primary cyclone and was  Chapter 4. Experimental Work  120  externally grounded. This device appears to work because it provides an effective route through which the distributed charge can readily dissipate to ground, thereby allowing the sohds to flow unhindered through the screen. Such a device might even be used to control the flow of charged particles by regulating the rate at which charge is drawn away from the grounding plane. Researchers at the University of Surrey are investigating this phenomenon (Seville, 1990).  4.2.2  Particulate and Tracer Properties  Particulate Carrier All of the experiments were conducted using grade F75 Ottawa Sand. Its key properties, reproduced in Table 4.2, were measured by Burkell (1986). Particulate samples were withdrawn from the vertical leg of the L-valve, as well as from the riser outlet, during operation, and these were analyzed using sieves. The cumulative particle size distribution for these samples, as well as the manufacturer's specifications for grade F75, are shown in Figure 4.7, with a single smooth curve, fitted by eye, which gives a good fit for all the samples. This implies little or no segregation or changes in particle properties over the time in which these experiments were performed. The Sauter mean particle size, averaged over the four L-valve samples, was 169 pm, 13.5% larger than that reported by Burkell (1986).  This discrepancy can be ascribed to the loss of fines, as well as stabilization  against attrition, over the years. This material exhibits considerable triboelectric charging during high-velocity conveying. This attribute was a major source of noise, not just for the sensor developed, but also for a data logging computer that has been used on the unit by others (Burkell, 1986; Brereton, 1987; Wu, 1989).  121  Chapter 4. Experimental Work  Table 4.2: Properties of F-75 Ottawa Sand (Burkell, 1986)  Ottawa Sand  Property  Mean Particle Diameter, d Particle Density, p  pm  p  p  Bulk Density, pb  148  kg/m  3  2650  kg/m  3  1550 0.42  Loose Packed Voidage, e Particle Terminal Velocity, U , based on air properties at 25°C  0.99  t  m/s  Archimedes Number  290  Uf  Calculated  m/s  0.023  Uf  Experimental  m/s  0.021  m  m  Bulk Density at Minimum Fluidization, p f m  1500 kg/m  3  Bed Voidage at Minimum Fluidization, e f  0.43  Angle of Repose  29°  m  3oJ  i  •  0-1  •  O.T /  '  •  £  5  i  /O  Cumulative A smaller than diameter  • go  •  •  i  i  i  i  i  •  '  1  da 4o So 40 70 so 90 J6J9 _ S p e c s , f o r F?5 'Ottawa O sand A v e r a g<0CL e o f I4n c L. -) v a l v e  Figure 4.7: Cumulative PSD of F-75 Ottawa Sand  A  ^  samples  Q  Samolp  f  r  o  m  r  i  s  e  r  • JW  Chapter 4. Experimental Work  123  Tracer Particles The tracer particles used in these experiments were 6.35 mm OD aluminum spherical shells, having a wall thickness of 500 pm. They are produced by Industrial Tectonics, Inc. of Ann Arbor, Michigan, and were selected on the basis of two criteria, their low effective density, allowing for a reasonable terminal velocity for their size, and their excellent electromagnetic response to an exciting field of 6 kHz. They were also robust enough to survive repeated injections, conveying through the riser and capture in the return loop. The density of these shells, determined from the calculated volume and measured mass, is 754 kg/m . Using the method (Grace, 1986) given in Appendix E , the terminal 3  velocity of these particles was calculated to be 11 m/s.  Ideally, the tracers' density  should have been closer to that of coal, approximately 1400 k g / m , to simulate what 3  might happen to larger particles of fuel in a C F B C system; a coal particle of the same size would have a terminal velocity of nearly 15 m/s. Rather than seek a tracer with a more realistic density, I decided to use the hollow aluminum spheres for the purpose of demonstrating the technique, as well as collecting some data regarding the movement of large, low-density particles in a C F B system. The calculated quadrature response of the aluminum shell tracer is shown in Figure 3.8. This is only an approximation because: 1. The conductivity of the aluminum can only be crudely estimated at 2x 10 mhos/m 7  (Chatterfield, 1989), due to the unknown effects of coldworking on the conductivity, as well as the lack of electrical data for this particular alloy, 3003. The error bar around the aluminum-shell point in Figure 3.8 shows the range of the calculated response, if the conductivity is 25% greater, or less, than the assumed conductivity.  Chapter 4. Experimental Work  124  2. The shell thickness (500 pm) compared to the skin depth (1450 pm at 6 kHz) stretches one of the assumptions used in developing the response function of a shell, as shown in Appendix A. In practice, this tracer gave an excellent signal on the oscilloscope, at times nearly two orders of magnitude above the noise. The typical peak of a tracer's response is 10 V , while the background noise, was generally of the order of 150 mV. However, spikes, of similar magnitude to that produced by the tracer, were occasionally observed. These spikes were attributed to electrostatic discharges in the vicinity of the sensor. However, because the spikes had a shape on the screen distinctively different from that produced by tracer spheres as discussed in Section 4.1.3, I was able to differentiate unambiguously between the desired signal and this noise.  4.2.3  Experimental Procedure  The sensor was placed in the riser so that the diametral tube bundle was perpendicular to the outlet pipe axis. The magazine of the injector was loaded with 100 tracer particles, which I deemed to be a sufficient-sized sample, and a small quantity of purge air was turned on prior to starting the C F B . The air was then turned on in the riser, and adjusted roughly to provide a desired superficial gas velocity.  Solids circulation was  then established by turning on aeration air to the L-valve. The air and solids flow rates were then adjusted alternately, until the desired operating conditions were achieved. Periodically, during a run, these rates were checked. Air to the return leg was adjusted to insure that the solids inventory there was in a bubbling state; only under such a condition, could solids return from the secondary cyclone dipleg. The local amplifier, at the sensor, was attached by shielded cable to the cabinet  Chapter 4. Experimental Work  125  containing the rest of the electronic equipment. The fully processed signal was delivered via. coaxial cable from the cabinet to a Tektronix 2230 storage oscilloscope. The external input of the scope was connected to a switch, which controlled the injector solenoid, so that the trace began the instant of tracer particle injection. The trace recorded the sensor's processed signal for a period of time which, from experience, was adjusted to be longer than the longest time the tracer was expected to be in the riser under the given operating conditions. After each trace was completed, and the tracer sphere had presumably left the riser, the digital capability of the scope was employed to measure the times elapsed between tracer injection and each recorded signal. The signal's time was arbitrarily defined as the zero crossover between the signal's maximum and minimum (see Figure 4.3). Sometimes, the trace would display several signals; the corresponding times were recorded on a data sheet. I had initially considered that the order of the signals, for a given tracer, could be used to infer the tracer's direction at each signal. I reasoned that for the first signal, the tracer would be moving up, while for the second signal, it would be moving down and so on for odd and even signals.  However, I later realized that assigning upward velocity to odd  signals and downward velocity to even ones was not reliable, since there were instances when a tracer exhibited an even total number of signals and, yet, left the riser. Excluding run #7a, of the 62 instances when tracers exhibited multiple signals, 20 exhibited an even total number, and 42 exhibited an odd total number of signals. As the characterization of the coil shows, in Section 4.1, above, tracers hitting the diametral bundle and bouncing back give signals indistinguishable from that of a pass-through tracer. The projected area of the tube, shielding the diametral bundle, represents 3.3% of the cross-sectional area of the riser, so that, on average, for a run, during which 100 tracers pass through the riser, about three of those passages can be expected to involve a collision with the bundle.  126  Chapter 4. Experimental Work  Of those possible collisions, only a small fraction could reasonably be expected to result in the tracer bouncing back to the region from whence it came. However, whether the tracer collides with the bundle or not, the first passage times are an accurate indication of the residence times. Succeeding times, which might be used to quantify recirculation cells, may be corrupted by bouncing and reversing occurrences.  4.2.4  Results  Tests were conducted under seven different operating conditions to measure the times of flight of the 6.35mm diameter hollow spheres between the injection point, opposite the solids reentry point and the sensor, located 7.48m higher up in the riser. In addition to the time of flight, which is defined as the time elapsed between injection and the first signal of the oscilloscope trace, data were also collected on second, and succeeding signal times. These latter data, however, are ambiguous, as explained above, and therefore it is difficult to draw any conclusions based on the second, and subsequent signals. In any case, with the exception of run #7a, no more than about 10% of the observations showed two or more signals. The nominal operating conditions for the tests, all using Ottawa sand, are reported in Table 4.3. These were selected to avoid the choking regime, the conditions for which were previously determined for this material and apparatus by Brereton (1987), and are plotted in Figure 4.8, along with a fitted line.  Operation in the choking regime was  avoided because severe slugging could occur under these conditions, even to the extent of damaging the riser. Furthermore, it was observed that, when the apparatus is operated in this regime, the transition between smooth fluidization and severe slugging may occur after a considerable delay, presumably during which time the solids inventory in the riser has slowly risen to the point of choking. This unsteady-state transition is not only  Chapter 4. Experimental Work  127  Table 4.3: Schedule of Experimental Runs Sensor at 1.63m below outlet pipe centerhne, 7.64m above the distributor of column.  u.  Solids Flux G kg/m s  7 m/s  14.3  #3  #7  35.4  #1  #5  56.6  #2  #4-  2  s  68.9  9 m/s  #6  * Repeated build-up on screen required intermittent halt in solids flow.  unsatisfactory in terms of tracer tests, but is also hazardous; an unsuspecting operator, assuming that steady state has been achieved, may go off to carry out measurements, only to be caught unprepared, when the riser suddenly begins to shake violently, as choking occurs.  Data The peak times, as measured for the seven runs, are reported in Appendix F , together with the corresponding actual operating conditions. Only the first peak times were sorted, in order of increasing times, for each run, and histograms were then constructed. Each of these histograms shows the fraction of the total number of tracers injected for a run (usually 100), whose first peak time falls within each time interval, which was arbitrarily set at 1.0 s. The height of each bar in the histogram is equal to the corresponding fraction divided by the time interval, giving it units of (s ). The histograms, grouped by nominal _1  Chapter 4. Experimental Work  Figure 4.8: Choking Regime for Sand in 0.15m Diameter Riser (data points from Brere ton, 1987).  Chapter 4. Experimental Work  129  superficial gas velocity, are shown in Figures 4.9(a) and (b). Run #7 encompasses two separate runs, 7a and 7b, the latter being a limited repeat run. Run #7a exhibited oscilloscope traces that were very different in nature from those observed during any of the previous runs. First, the noise content was higher, with noise spikes very similar in form to, and thus difficult to distinguish from, the tracers' peaks. Second, there were more frequent instances of multiple peaks for some of the tracers, far more and spread over a greater time span than for the previous tests. The noise may have been due to another experiment, which was conducted nearby during this run; there seemed to be some correlation between the noise observed on the oscilloscope and instances when a solenoid switched in the other experiment. On another day, when the other apparatus was off, run #7b was conducted, using only 31 tracer particles, instead of the typical 100 particles. During this latter run, only one tracer exhibited multiple peaks, compared to run #7a, where 19% of the tracers produced multiple peaks. The results for the first peak times for both runs #7a and #7b are included in Figure 4.9(b).  4.2.5  Discussion  The time-of-flight histograms are discrete representations of continuous frequency densities, and, as such are comparable to the commonly cited RTD. A time-of-flight density is identical to the RTD, for the region between the sensor and the closed boundary at the injector, only when there are no subsequent passages through the sensor. If the tracer does return to the region, after exiting through the sensor plane, the additional time that the tracer dwells within the region is included, by definition, in the RTD, differentiating it from the time-of-flight density. The time-of-flight density gives an indication of the region's overa.ll hydrodynamics whereas subsequent passages through the sensor reflect not only the local mixing occurring in the immediate neighborhood of the sensor, but  Chapter 4.  Experimental  130  Work  Z  Run  .18 -  Z  .18  Run I  I an  3S.4  Run  3  14.3  tz  e  Ti«e of f i r s t  z<  ZQ  tc  ze  passaged)  (a) Runs 1-3, V = 7 m/s. g  -  .30  2 kg/« s  Run  6,  Run  4  €8.9  .28 .16  m—,-, S8.e  "h  •  rf  Run 35.  h-rn _  3* u  c o  Z3' tr <u  S 4  Run 14.3  •  t.  7  7R 78  r 4  8  12  Tine of f i r s t  16  20  24  passage(s)  (b) Runs 4-7, V = 9 m/s. g  Figure 4.9: Time-of-Flight Histograms C F B Tests.  Chapter 4. Experimental Work  131  also the flow patterns downstream of (i.e. above) the sensor. For example, if the sensor was placed higher up in the riser, closer to the abrupt exit, where considerable refluxing can be observed, I would expect that the velocity density, calculated from the time-offlight density and the distance between the injector and the sensor, would not change substantially from that obtained at the present sensor position. However, I believe the occurrences of subsequent passages would increase dramatically. I do not have data to substantiate this conjecture, but believe the time-of-flight data obtained here are global in nature, compared to the local nature of subsequent-passage data; in Chapter 5, the potential uses of such local information is addressed. The RTD cited here is not that obtained by measuring the response, at an open boundary to a pulse injection. In such a case, even if the response measurement was limited to tracer material moving upward in the core (as done by Kojima et al., 1989, for example), there is no way to distinguish between time spent within the region and time spent outside it, after which some of the tracer material may return to the region, and be recorded again during a subsequent exit. The resulting response curve would be skewed to much longer times, compared to the RTD, as described above. Recalling that the terminal velocity of these tracer particles is 11 m/s in air, it may seem surprising that these spheres are transported up the riser at all, at these superficial gas velocities. However, experimental evidence from Geldart and Pope (1983), who studied entrainment from Bubblingfluidizedbeds, suggests that large particles are conveyed upward as a result of momentum interchange during collisions with fast-moving fine particles. Results from an earlier paper (Geldart et al., 1979) indicate that the flux of large particles increases with the fines flux. This same effect is apparent in the results shown in Figure 4.9. When the solids flux is increased above 14.3 kg/m s, at both gas velocities, 2  the histograms shift to shorter times, indicating an increase in tracer velocity compared  Chapter 4. Experimental Work  132  to that measured at the 14.3 kg/m s circulation rate. Geldart's work, however, did not 2  anticipate that above some flux of fines, the transport of large particles is unaffected by further increases in solids flux. The statistical evaluation in Appendix F shows that the sample times from runs 1 and 2 are from a common population, as are those from runs 4, 5, and 6. Despite increasing flux, at a given superficial gas velocity, the RTD of the tracer particles does not change significantly beyond fluxes of 14.3 kg/m s. This 2  effect may be due to the limited surface of the tracer available for momentum-transferring collisions. This hypothesis suggests that the RTD of a larger tracer would continue to show an effect of increasing solids fluxes, beyond the 14.3 kg/m s threshold. Geldart et 2  al. (1979) offer evidence to support the inverse of my hypothesis — they observed that smaller, denser target particles, offering a smaller area for collisions, are less affected by fines. The results of Satija and Fan (1985) for a multisohd pneumatic transport bed, show that the effect offinesflux on coarse particles' terminal velocities levels out as the fines flux is increased, supporting the observations made here. Further, the smaller the size of the coarse particles, the sooner this plateau in terminal velocity occurs, giving further support to the hypothesis that surface area of the coarse particles may be the limiting factor in a driving mechanism of momentum-transferring collisions. Even if the frequency of collisions is limited by the available surface of the tracer particles, each collision at a higher superficial gas velocity would transfer more momentum than a collision at a lower gas velocity. In addition, at the higher gas velocity, the sand (i.e.  fines) particles will regain their former velocities faster, after collisions, due to  greater gas drag, more quickly regenerating the source of momentum available for further collisions. The higher energy of collisions at the higher gas velocity is suggested by the shorter times in the higher gas velocity histograms (Figure 4.9(b)), compared to those at the lower gas velocity (Figure 4.9(a)). A model of particle collisions in the core region  Chapter 4. Experimental Work  133  is incorporated in a comprehensive CFB combustor model being developed by Senior (1989). Of course, particle/particle collisions are just one aspect of the hydrodynamics driving the tracer up through the riser. The differences in the histograms at the two gas velocities, described in the previous paragraph, could be equally well explained by the change in flow structure, at the macro level, under the different conditions. These changes in flow structure are manifest, for example, by changes in the pressure profile along the riser (Brereton, 1987), as well as in the manner in which the solids enter the riser from the L-valve (Patience, 1990). At the higher velocity it appears that there is less of a dense region at the base of the riser, and that it is less dense, or that the extent of refluxing at both the wall and in the core are reduced compared to the conditions at the lower velocity. All of these factors might effect the tracer particle's traverse through the riser, and certainly, further data collection, using this sensor, or its successor, would serve to confirm or reject these conjectures. Nevertheless, these conjectures seem somewhat inconsistent with my observations that, changes in solids flux, above the threshold, which are also accompanied by these obvious changes in the macroflowstructure, do not affect changes in the RTD of the tracers, at a given velocity. The data in Figure 4.9(a), at the lower velocity, suggests another characteristic that has also been observed by other investigators. Roberts (1986), Ambler et al. (1990) and Patience (1990) have all reported a himodal form of the RTD of a fast bed, under certain operating conditions. The indication of a second peak in the data presented here is not very pronounced in Figure 4.9(a). However, if runs #1 and #2 are plotted cumulatively on log-probability paper, a straight line fit, indicative of a simple skewed distribution, is not apparent. Therefore, these data may indicate a bimodal response; that it is not very pronounced, may be due to two possible factors:  Chapter 4. Experimental Work  134  (a) Fine particles may behave differently in the riser than large particles, especially in terms of being incorporated into downward-moving clusters and/or refiuxing flow at the wall.  These structures  are often used to explain the bimodal  response. (b) Refiuxing at the abrupt exit of the riser is not part of the region studied here, but was included within the closed boundary of the aforementioned  pulse-  response tests. In these latter tests, the sensor was in the exit channel connecting the top of the riser and the cyclone.  Chapter 5  Summary  5.1  Implications of This Work  The open boundaries within flow vessels limit conventional RTD techniques, such as the pulse-response method, to measure either a lumped RTD at the closed-boundary exit of the vessel, or, if responses are measured within the vessel, a distribution that can only be interpreted on the basis of an assumed model of the flow (e.g. plug flow with axial dispersion). In the former case, any conclusions to be drawn as to the detailed flow structure within the vessel, depend upon a preconceived model of that flow (e.g. core/annulus flow). The single-particle tracer technique, on the other hand, gives unambiguous information at open boundaries, the interpretation of which is model independent. Widespread application of this technique has not occurred because a practical sensor did not exist. However, as a result of this investigation, a prototype sensor has been established, which not only is capable of obtaining limited open-boundary information, but also avoids the hazards, expense and licensing requirements of competing radioactive-tracer methods. This prototype sensor signals the entry of the tracer into its sensing volume, and after the injection of many tracers, one at a time, a frequency density can be constructed from these data. In the context of the riser of the CFB, where the sensor was tested, the frequency density of only the first peak times represents the time of flight between the point of  135  Chapter 5.  Summary  136  tracer injection and the sensor plane. It is directly related to the collection of trajectories the individual tracers follow in their passage through the riser. If there was some change in the time-averaged flow structure of the riser, this frequency density would be expected to change. In this investigation, the flow structure was purposely changed by varying the operating conditions of the riser (i.e. superficial gas velocity and sohds flux) and monitoring the resultant influence on the time-of-flight frequency density. The results suggest some features of the actual mechanism by which the tracers are conveyed through the riser. Additional insight could be gained into this mechanism by using tracers having different properties (e.g. size, density, shape). Using the existing tracers, the relative importance of the various flow regions (e.g. dense regions at the top and bottom, core/annulus in the middle), in determining tracer trajectories, could be evaluated by moving the sensor to different positions along the riser and monitoring the time-of-flight density of each region, in turn.  The prototype sensor, in its present configuration is  limited to monitoring relatively large tracer particles, which nonetheless are significant in terms of C F B applications. However, the underlying principle of the sensor allows for further sensitivity improvements, by using higher frequencies, within limits, as discussed in Section 3.5.2. Although the sensor can presently only sense whether a tracer is in its sensing volume, a modification has been recommended which would allow both the speed and direction of travel to be resolved as the tracer passes the sensor. Determination of these local properties, especially, direction, would permit unambiguous interpretation of second and subsequent peak times. At present, it is unclear what these peak times signify, and therefore these data have not been used.  Chapter 5. Summary  5.2  137  Recommendations for Future W o r k  More data should be gathered using the present sensor. As mentioned briefly above, data could be obtained for different sensor positions along the riser and also for different tracer particles. In addition, data could be collected with the present tracers under a wider range of operating conditions, including a variety of different circulating solids. An additional sensor of the same design as the present one could be placed at the solids-reentry point of the riser, a closed boundary. With such an arrangement, it would no longer be necessary to capture tracer particles after they left the riser, since their reentry with the other solid particles into the riser would also be monitored. In addition, another sensor, placed at the riser outlet, would give a positive indication that a tracer has left the riser, and another tracer could then be introduced without danger of overlap. The capability of the present sensor to differentiate between tracer passage through one semicircle of the sensing plane or the other, should be exploited to determine if there is azimuthal asymmetry in the way the tracers pass through the riser. As an alternative to collecting additional data with the present sensor, the modified sensor, having the additional capabilities described above, could be developed. As described in Section 3.6.1, the modified sensing coil would actually consist of two axialrydisplaced circumferential coils, each of which would generate its own identifiable signal, displaced in time from each other on the oscilloscope trace, as the tracer passed through the pair. The signals from such a configuration could also be interpreted in such a way that false signals due to tracers approaching, but then changing direction and not passing through the sensor's complete sensing volume, would be eliminated. (This would be accomplished by placing the two sensing coils far enough apart so that their individual sensing volumes do not overlap). In hght of these false signals, it was not feasible in the  Chapter 5. Summary  138  work described here to install multiple sensors, of the present design, along the length of the riser in order to obtain R T D data as a function of axial position. False signals would have made the data collected from multiple sensors ambiguous, as discussed in Section 3.5.1 above, for the case of a single sensor of the present design. Elimination of false signals in the modified design would make multiple sensors viable. In order to illustrate the potential advantage of multiple sensors fo the modified design, the nature of the expected data and its interpretation can be projected. Masson et al. (1981) have made a similar evaluation of their data in a bubbling fluidized bed. For each run, consisting of a large number of tracer injections, the raw data (probably electronically logged) would consist of a set of individual records, each of which represents the history of the traverse of just one of the tracer particles through the riser. A record can be regarded as a matrix, each row of which represents a single pair of signals from a sensor, as the tracer passes through it. In the rare case that the tracer reverses direction while in the sensing volume, one or three signals might be generated. If the tracer experienced no backflows of the order of the spacing between sensor assemblies, then the record for that traverse would have exactly the same number of rows as the number of sensors along the riser. However, since there is significant internal recirculation within the riser, more rows would be expected in a record than the number of sensors, since it is likely that tracers will pass through some of the sensors more than once. The information in each row of a record would include the identification of the sensor, the median time of the two signals, and the time delay and order of the two signals. The latter information, together with the known axial displacement of the two coils, give the speed and direction of the tracer particles, as it passes through the sensing volume. For each sensor displaying a sufficient number of repeat passages, two speed-frequency histograms could be constructed from the whole set of records (i.e.  the run), one for  Chapter 5. Summary  139  the upward moving and one for the downward moving tracer particles, at that sensor location. Since each sensor corresponds to the boundary between two (arbitrary) regions, each row of a record containing signal pairs (i.e. tracer has passed through the complete sensing region) represents a transition between one region and the adjacent one.  By  comparing consecutive rows, the time the tracer spends in each region could be determined. For each region, these data, over the set of all the records, could be presented as a residence-time density histogram. Recirculation cells within the riser could be identified by searching the set of records for the relative frequency of certain sequences of transitions. For example, the abrupt exit of the riser presumably results in considerable recirculation, due to reflection of solids from the top. Therefore, a much higher frequency of sequential repeat signals would be expected from a sensor just below the exit, compared to the frequency of a sequence of this sensor's signal followed by the exit sensor's signal. The cycle time distribution above or below a given sensor could be obtained by searching each record for repeat (though not necessarily sequential) signals from that sensor. Times between the first and second, and any odd/even order appearances correspond to time spent above, whereas times between the second and third, and any even/odd order appearances correspond to time spent below that sensor. By comparing the RTD of regions, or groups of regions, to other groups, using contingency tables, for example, it could be ascertained if certain groups are statistically independent of neighboring groups. For example, the R T D in the dense section at the bottom of the riser, might reasonably be expected to be nearly independent of that in the more dilute middle section. have related distributions.  However, two regions in the dilute section probably  If regions are found to be statistically independent, then  Chapter 5. Summary  140  Markov chain analysis, a powerful stochastic tool, could be readily apphed (Rubinovitch and  Mann, 1983). Furthermore, if regions, or groups of regions, are to be treated as  subsystems, which are then connected in series and/or parallel to synthesize a complex flow network model, it is required that they be statistically independent (Nauman and Buffham, 1983).  5.3  Overall  Conclusions  1. The single-particle tracer technique represents a straight-forward method of keeping account of the traverse of tracer particles through a flow vessel. Over the passage of many tracers, the accumulated data represents the RTD, within an axial region. This technique enables the collection of meaningful data at open boundaries, a feat beyond conventional R T D methods. 2. In order to implement the single-particle approach, a sensor was developed based on electromagnetic inductance, capable of sensing individual particles. Although the prototype was used to measure relatively large tracers, the underlying principle of the sensor allows for improved sensitivity and smaller tracers. 3. The sensor was tested in the riser of a C F B , where there is considerable background electrical noise due to vibrations and electrostatics.  The noise was subdued by  incorporating three features into the sensor's design: a "figure-eight" receiver coil, shielding and multiplying the resultant signal by a quadrature signal. 4. The prototype only senses when a tracer is in the neighborhood of the sensor. A recommended modification would increase the capability of the sensor to include the detection of speed and direction of travel, as the tracer passes through the  Chapter 5.  Summary  141  sensor. Such information would permit multiple sensors to be installed along the riser providing vastly greater insight into the flow mechanism. 5. The limited data collected from the C F B shows that, at a given superficial gas velocity, above a certain solids flux, the time-of-flight histogram does not change appreciably with increasing solids flux, despite obvious changes in the macro flow structure in the riser. This, together with evidence from previous studies, suggests that inter-particle collisions are responsible for the conveyance of these tracer particles through the riser.  Nomenclature  Symbol  Definition  Units  A a ai  characteristic coefficient of non-Ohmic conductor radius radius of smallest spheres giving desired response  m m  Ar  Archimedes number = p (p — p )g d  m  n  B, B b  g  z  CD C, C P  B  D d" d p  E(N) EMFc,  g  g  3 p  /u.  2 g  -  magnetic field/flux density, z-component outside radius of shell  Wbm m  drag coefficient capacitance (paralle, series)  F  demagnetization factor dimensionless diameter (Figure 1.2) diameter of particle  m  .•  -2  mean number of visits to zone per particle electromotive force generated in circumferential, diametral coil electromotive force in conductor due to current in transmitter  V  F ^ Fi /  drag force Lorentz force frequency  N N Hz  G g  solids flux acceleration due to gravity  kg/m s m/s  magnetic field strength coercive field strength saturation field strength z-component of field calculated using the near field equation  Am Am Am Am  EMFCT  3  H, Hj, He H, H \NF Z  EMFn  142  V  2  2  - 1  - 1  - 1  - 1  Symbol  Definition  Units  current, in secondary coil response parameter fraction of total flux generated by A passing another coil  \K a \ 2  2  k  A  coefficient of coupling between coils A and B L I  M, M  s  M, m  M  ,  "Ishell,  m  N  AB  A  n n  z  m  inductance axial distance between coils magnetic dipole moment per unit volume, at saturation mutual inductance, between coils A and B mass of particle dipole moment, of shell, z component number of turns in coil A characteristic exponent of non-Ohmic conductor number of free charges per unit length  H m Am  WbA kg Am 2  Cm  quality factor charge  C  Ar  radial position of tracer resistance, of inductor radius of loop, of receiver Reynolds number = p dpU/fi radial distance, relative to transmitter coil radius of coil, of particle shell thickness  m Q m m m m  dS  incremental area  m  t  time  Q Q  R  R, RL -Rioopj  Re _  RR  g  _»  u,u u,u u  t g  e  g  particle velocity,terminal gas velocity, superficial total magnetic potential dimensionless velocity (Figure 1.2),terminal  143  - 1  m/s m/s A  - 1  - 1  Symbol  Definition  Units  V, V v  particle velocity, z-component velocity vector  m/s m/s  mass flow of gas through orifice mass flow rate of solids through local region mass flow rate of solids through system  kg/s kg/s kg/s  XL, XC X -f iY  inductive, capacitive reactance complex response function  Q -  z, zi, z', z"  axial or vertical position, relative to loop, relative to receiver, relative to transmitter  m  p  pz  W Wiocal  W  0  a  UJL/R  a  a, fi Ar b  s  8  angle  rad  6 v, v"  angular position of tracer angular position, relative to transmitter coil  rad rad  A  wavelength  m  fi, fio  permeability of freespace  Hm"  Ar y density, of particle, of gas  m kg/m  0  p p, Pp, p cr, <T  g  e  y/x  2  2  condcutivity, of the shell  <f> (j>o, <f>\  magnetic phase angles  u>  angular frequency  3  mhos m flux  144  1  Wb rad s  _1  Bibliography  [1] A A R L Handbook (1987). American Radio Relay League, Newington, C T . [2] A d a m s , C . K . (1988). Gas mixing in fast fluidized beds, in "Circulating Fluidized Bed Technology II", 299-306, P. Basu and J . F . Large, eds., Pergamon, Oxford. [3] A m b l e r , J . P . A . (1988). Residence time distribution of binary solids mixtures in a circulating fluidized bed. M.A.Sc. Thesis, University of Waterloo, Waterloo, ON. [4] A m b l e r , P . A . , M i l n e , B . J . , Berruti, F . , and Scott, D . S . (1990). Residence time distribution of solids in a circulating fluidized bed: experimental and modelling studies. Chemical Engineering Science, 45(8):2179-2186. [5] Anderson, P . M . , Kearney, J . E . and Breets, G . R . (1983). Coded surveillance system having magnetomechanical marker, European patent application #83103464.0, Dec.21. [6] A r i s , R . (1959). Notes on the diffusion-type model for longitudinal mixing in flow, Chem. Eng. Sci., 9:266-267. [7] Ashworth, F . , Needham, W . and Sillars, R . W . (1946). Silicon carbide nonOhmic resistors, J . Instn. Elec. Engrs., 93, pt.I, 385-405. [8] A v i d a n , A . A . (1980). Bed expansion and solid mixing in high velocity fluidized beds, Ph.D. dissertation, City University of New York, New York. [9] Bader, R . , Findlay, J . and K n o w l t o n , T . M . (1988). Gas/solids flow patterns in a 30.5 cm diameter circulating fluidized bed, in "Circulating Fluidized Bed Technology II", 123- -137, P. Basu and J.F. Large eds., Pergamon, Oxford. [10] Baillie, L . A . (1986). Tracer analysis of fluid catalyst flow in refinery catalytic cracking units, Part. Science and Tech., 4:343-352. [11] B a s u , P . and Haider, P . K . (1989). Combustion of single carbon particles in a fast fluidized bed of fine solids, Fuel, 68:1056-1063. [12] Bean, C P . (1955). Hysterisis loops of mixtures of ferromagnetic micropowders, J. Appl. Physics, 26:1381-1383. [13] Beck, M . S . and Wainwright, N . (1969). Current industrial methods of solids flow detection and measurement, Powd. Technol., 2:190-197. 145  Bibliography  146  [14] Bellgardt, D . and Werther, J . (1986). A novel method for the investigation of particle mixing in gas-solid systems, Powder Technology, 48:173-180. [15] Bierl, T . W . , Gajdos, L . J . , Mclver, A . E . and McGovern, J . J . (1980). Studies in support of recirculating bed reactors for the processing of coal, D O E report Ex-C-76-01-2449, July. [16] Bischoff, K . B . and McCracken, E . A . (1966). Tracer tests in flow systems, Ind. Eng. Chem., 58:18-31. [17] Bohn, E . V . (1968). Introduction to electromagnetic fields and waves, AddisonWesley, Reading, Mass., 221-223. [18] Borodulya, V . A . , Epanov, Y . G . , and Teplitskii, Y . S . (1982). Horizontal particle mixing in a free fluidized bed, J . Engng. Phys., 42:528-533, May. [19] Bozorth, R . M . (1951). Ferromagnetism, D. Van Nostrand [20] Brereton, C . M . H . (1987). Fluid mechanics of high velocity fluidized beds, Ph.D. dissertation, University of British Columbia, Vancouver. [21] Brereton, C . M . H . , Grace, J . R . , and Y u , J . (1988). Axial gas mixing in a circulating fluidized bed, in "Circulating Fluidized Bed Technology II", 307-314, P. Basu and J.F. Large,eds., Pergamon, Oxford. [22] Brotz, W . (1956). Untersuchungen iiber transportvorgange in durchstromtem, gekorntem Gut, Chemie- Ing-Techn., 28:165-174. [23] Burke, H . E . (1986). Handbook of magnetic phenomena, Van Nostrand Reinhold Co., New York. [24] Burkell, J . (1986). Solids circulation measurements in circulating fluidized beds, M.A.Sc. thesis, University of British Columbia, Vancouver. [25] Chatterfiled, D . (1989). Alcan Aluminum Co., private communication. [26] Chikazumi, S. and Charap, S.H. (1964). Physics of magnetism, John Wiley & Sons, New York. [27] Chmielewski, A . G . and Selecki, A . (1977). Lateral mixing of solid particles in gas fluidized bed, Inz. Chem., 7:549-560. [28] Chmielewski, A . G . and Selecki, A . (1979). Application of radioactive tracers to some processes on a large scale, Isotopenpraxis, 15:276-281.  Bibliography  147  [29] Considine, D . M . (1957). Process instruments and controls handbook, McGrawHill, New York. [30] Corion Technologies (1989). Electrostatic problems in bulk solids processsing, advertising brochure. [31] C r a n k u r t , N . T . and Yerushalmi, J . (1978). Gas backmixing in high velocity fluidized beds, in "Fluidization" Proc. of the 2nd Engineering Foundation Conf., 387-392, J . F . Davidson and D.L. Keairns eds., Cambridge University Press, Cambridge. [32] C r o w , E . L . , Davis, F . A . , Maxfield, M . W . (1960). Statistics manual, Dover Publications, Inc., New York. [33] D r y , R . J . , Christensen, I . N . , and W h i t e , C . C . (1987). Gas-sohds contact efficiency in a high-velocity fluidised bed, Powder Technology, 52:243-250. [34] Durney, C . H . , Harris, L . D . and Alley, C . L . (1982). Electric circuits: theory and engineering applications, Holt, Rhinehart and Winston, New York. [35] Dwight, H . B . (1922). Skin effect and proximity effect in tubular conductors, Journal AIEE, 203-209, March. [36] Fearson, E . R . (1974). Open-strip ferromagnetic marker and method and system for using same, U.S. patent #3,790,945, Feb.5. [37] Fitzgerald, T . J . (1979). Oregon State security system, instruction manual for equipment on loan from Harrison Cooper Associates, Salt Lake City. [38] Fitzgerald, T . J . (1980). Cold modelling of fluidized combustors, EPRI CS-1476 final report, Palo Alto, C A . [39] Fitzgerald, T . J . (1989). TRW, private communication. [40] Geldart, D . , Cullinan, J . , Georghiades, S., Silvray, D . and Pope, D . J . (1979). The effect of fines "on entrainment from gas fluidised beds, Trans. I. Chem. E . , 57:269-275. [41] Geldart, D . and Pope, D . J . (1983). Interaction of fine and coarse particles in the freeboard of a fluidized bed, Powder Technology, 34:95-97. [42] Grace, J . R . (1986). Contacting modes and behavior classification of gas-solid and other two-phase suspensions, Can. J . Chem. Engng., 64:353-363. [43] Grace, J . R . (1990). High-velocity fluidized bed reactors, Chem. Eng. Science, 45:1953-1966.  Bibliography  148  [44] Grace, J.R. and Baeyen, J . (1986). Instrumentation and experimental techniques, in "Gas-Fluidization Technology", Chap. 13, 415-462, D. Geldart, ed., Wiley-Interscience, New York. [45] Grace, J.R., Zhao, J . , W u , R . L . , Senior, R . C , Legros, R., Brereton, C . M . H . , and Lim, C . J . (1990). Spatial variations inside a pilot scale circulating fiudiized bed combustion unit. Proc. Workshop Materials Issues in Circulating Fluidized Bed Combustors, EPRI, Palo Alto, CA, 10:1-21. [46] Grant, F.S. and West, G . F . (1965). Interpretation theory in apphed geophysics, McGraw Hill, New York. [47] Haider, P . K . and Basu, P. (1989). Mass transfer from a coarse particle to a fast bed of find solids, AIChE Sym. Series, 84:58-67. [48] Hartge, E . - U . , Rensner, D . and Werther, J . (1988). Sohds concentration and velocity patterns in circulating fluidized beds, in "Circulating Fluidized Bed Technology II", 165-180, P. Basu and J.F. Large eds., Pergamon, Oxford. [49] Hayt, W . H . (1974). Engineering electromagnetics, 3rd ed., McGraw Hill, New York. [50] Herb, B., Tuzla, K . and Chen, J . C . (1989). Distribution of sohd concentrations in circulatingfluidizedbed in Proc. Int'l. Conf. Fluid, 6th, 65-72, J.R. Grace, L.W. Shemilt and M.A. Bergougnou eds. Eng. Found., New York. [51] Himmelblau, D . M . , and Bischoff, K . B . (1968). Process analysis and simulation: deterministic systems, John Wiley and Sons, New York. [52] Himmelblau, D . M . (1970). Process analysis by statistical methods, John Wiley & Sons, New York. [53] Irons, G . A . and Chang, J.S. (1982). Particle fraction and velocity measurements in gas-powder streams by capacitance transducers, Int. J. Multiphase Flow, 9:289297. [54] Ishida, M . , Shirai, T . and Nishiwaki, A . (1980). Measurement of the velocity and direction of flow of sohd particles in afluidizedbed, Powder Technol., 27:1-6. [55] Ishida, M . and Hatano, H . (1984). The behavior of gas and sohd particles in a gas-solid fluidized bed detected by optical fiber probes in Proc. Int. Conf. Fluid., 4th, 61-68, D. Kunii and R. Toci eds., Eng. Found., New York. [56] Ishii, H . , Nakajima, T . , and Horio, M . (1989). The clustering annular flow model of circulatingfluidizedbeds., J. Chem. Engng. Japan, 22(5):484-490.  Bibliography  149  Jagota, A . K . , Rhodes, E . and Scott, D . S . (1973). Measurement of residence times, and film and drop velocities in two-phase annular flow, Can. J . Chem. Engng., 51:393-400. K a n e r , R . B . and M a c D i a r m i d , A . G . (1988). Plastics that conduct electricity, Scientific American, 258:106-111. K a u f m a n , A . A . and Keller, G . V . (1985). Inductive mining prospecting pt. 1 theory, Elsevier, Amsterdam. K i n g , R . W . P . , M i m n o , H . R . and W i n g , A . H . (1945). Transmission hnes, antennas and waveguides, McGraw-Hill, New York. K o j i m a , T . , Ishihara, K . - I . , G u i l i n , Y . , and Furusawa, T . (1989) Measurement of solids behavior in a fast fluidized bed, J . Chem. Engng. Japan, 22(4):341356. K o n d u k o v , N . B . , Kornilaev, A . N . , Skachko, I . M . , Akhromenkov, A . A . and Kruglov, A . S . (1964). An investigation of the parameters of moving particles in a fluidized bed by a radioisotopic method, Int'l. Chem. Eng., 4:43-47. Krambeck, R . J . , K a t z , S. and Shinnar, R . (1969). Interpretation of tracer experiments in systems with fluctuating throughput, I & E C Fundamentals, 8:431441. K u n i t o m o , K . and Hayashi, Y . (1988). Residence time distribution and reduction degree distribution of fine iron ore in circulating fluidized bed, presented at the 2nd SCEJ Symp. on Circulating Fluid beds, 125-132. Langford-Smith, F . (1953). Radiotron designers handbook, 4th ed., Wireless Press, Harrison, N.J., 1325-1326. Larson, H . J . (1982). Introduction to probability theory and statistical inference, 3rd ed., John Wiley and Sons, New York. Levenspiel, O . (1972). Chemical Reaction Engineering, 2nd ed., John Wiley & Sons, New^ York. L i n , J . S . , C h e n , M . M . , and C h a o , B . T . (1985). A novel radioactive particle tracking facility for measurement of solids motion in gas fluidized beds, AIChE J . , 31:465-473, March. Lorrain, P . and Corson, D . R . (1970). Electromagnetic fields and waves, 2nd ed., W.H. Freeman &; Co., San Francisco.  Bibliography  150  Louge, M . (1990). Cornell Univ., private communication. M a n n , U . and Rubinovitch, M . (1983). Measuring local flow rates in process units, Ind. Eng. Chem. Process Des. Dev., 22: 545-547. Marsheck, R . M . and Gomezplata, A . (1965). Particle flow patterns in a fluidized bed., AIChE J . , 11:167-173. Masson, H . , D a n g I r a n , K . , and Rios, G . (1981) Circulation of a large isolated sphere in a gas sohd fluid bed, I. Chem. E . Symp. Series, (65):Sz/K/l-Sz/K/13. Mathews, P . W . (1980). Forces and fields, 2nd ed., Versatile Pubhshing Co., Vancouver. M a t h u r , M . P . and K l i n z i n g , G . E . (1984). Flow measurement in pneumatic transport of pulverized coal, Powd. Technol., 40:309-321. M a y , W . G . (1959). Fluidized bed reactor studies, Chem. Eng. Progr., 55(12):4956. Meunier, M . A . , Chamberland, A . , Bergougnou, M . A . and Briens, C . L . (1989). Sohd circulation ina cold model fluidized bed using heat tracing techniques, paper no. C4a presented at the 39th Can. Chem. Eng. Conf., Hamilton, October. M o r i , Y . and Nakamura, K . (1966). Sohd mixing in a fluidized bed, Kagaku Kogaku, 4:154-157. Moroney, M . J . (1963). Facts from figures, Penguin Books, Baltimore. Naor, P . and Shinnar, R . (1963). Representation and evaluation of residence time distributions, Ind. Eng. Chem. Fund., 2:278-286. N a u m a n , E . G . and Buffham, B . A . (1983). Mixing in continuous flow systems, John Wiley &; Sons, New York. N a u m a n , E . B . ,(1984). New results and old problems in residence time, I. Chem. E . Symp. Series, 87:569-581/ N i e h , S., C h a o , B . T . and Soo, S . L . (1986). An electrostatic induction probe for measuring particle velocity in suspension flow, Part. Sci. and Techn., 4:113-130. Novikoff, E . B . (1978). Method and apparatus for producing uniform electromagnetic fields in an article detection system, U.S. patent # 4,118,693, Oct.3. Okada, T . and Iwai, A . (1988). Natural V L F radio waves, John Wiley & Sons, New York.  Bibliography  151  [86] O k i , K . , Walawender, W . P . and F a n , L . T . (1977). The measurement of local velocity of sohd particles, Powder Technol., 18:171-178. [87] Patience, G . S . (1990). Circulating fluidized beds: hydrodynamics and reactor modelling, Ph.D. dissertation, Ecole Polytechnique, Quebec. [88] P i c a r d , P . A . (1934). Method of identifying objects by modification of a magnetic field, French patent #763 681, Feb.19. [89] Plonsey, R . and Collin, R . E . (1961). Principles and applications, of electromagnetic fields, McGraw Hill, New York. [90] R a m o , S. and W h i n n e r y , J . R . (1953). Fields and waves in modern radio, 2nd ed., J . Wiley & Sons, New York. [91] R e h , L . (1986). The circulating fluidized bed reactor — a key to efficient gas/sohd processing, in "Circulating Fluidized Bed Technology", 105-118, P. Basu ed., Pergamon, Toronto. [92] Rhodes, M . J . , M i n e o , H . and H i r a m a , T . (1990). Particle residence time distribution measurements in the 30.5 mm diameter riser of a cold model circulating fluidised bed, presented at 17th Annual Research Meeting, Swansea, 5 April, Inst. Chem. Engrs. [93] Richardson, R . H . (1981). Method and apparatus for generating alternating magnetic fields to produce harmonic signals from a metallic strip, U.S. patent #4,300,183, Nov.10. [94] Riley, C A . and Louge, M . (1989). Quantitative capacitive measurements of voidage in gas-solid flows, Part. Sci. and Technol., 7:51-59. [95] Roberts, C . (1986). The residence time distribution of solids in a fast-fluidized bed, B.Sc. thesis, University of British Columbia, Vancouver. [96] Rowe, P . N . and Sutherland, K . S . (1964). Solids mixing in gas fluidised beds, pt.II. The behavior of deep beds of dense material, Trans. Inst. Chem. Engrs., 42T55-T63. [97] R u b i n o v i t c h , M . and M a n n , U . (1983). Single particle approach for analyzing flow systems, pt. 1: Visits to flow regions, AIChE J . , 29: 658-662. [98] Santos, V . A . , and Dantas, C . C . (1983). Measurements of catalyst residence time in fluidized bed reactor using intrinsic tracer, Chemiker-Zeitung, 107:239241.  Bibliography  152  [99] Satija, S and F a n , L . S . (1985). Terminal velocity of dense particles in the multisolid pneumatic transport bed, Chem. Eng. Sci., 40:259-267. [100] Schmalfeld, V . J . (1976). Feststoff - bewegung in einem gas-feststoff-flie/3bett, VDI-Z, 188(2):65-72, January. [101] Seinfeld, J . H . and Lapidus, L . (1974). Mathematical methods in chemical engineering v.3: process modelling, estimation and identification, Prentice Hall Inc., Englewood Cliffs, New Jersey. [102] Senior, R . , (1989). Modelling of circulating fluidised bed combustion, research proposal, Dept. of Chem. Engng., University of British Columbia, Vancouver. [103] Seville, J . (1989). C H M L 561 - Particulate and Multiphase Systems, Graduate course notes, University of British Columbia, Sept.-Dec. [104] Seville, J . (1990). University of Surrey, Guildford, personal communication. [105] Sokolnikoff, I.S. and Redheffer, R . M . (1958). Mathematics of physics and modern engineering, McGraw-Hill, New York. [106] Stablein, H . (1982). Hard ferrites and plasto ferrites in ferromagnetic materials, in "Ferromagnetic materials", v.3, E.P. Wohlfarth ed., North-Holland Publishing Co., New York. [107] Stansel, F . R . (1951). The characteristics and some applications of varistors, Proc. IRE, 39:347-358. [108] Tardos, G . and Pfeffer, R . (1980). A method to measure electrostatic charge on a granule in a fluidized bed, Chem. Eng. Comm., 4:665-671. [109] Telford, W . M . , Geldart, L . P . , Sheriff, R . E . and K e y s , D . A . (1976). Apphed geophysics, Cambridge University Press, Cambridge. [110] T e r m a n , F . E . (1955). Electronic and radio engineering, McGraw-Hill, New York, p.121. [Ill] Tesche, F . R . (1951). Instrumentation of electromagnetic modelling and application to electromagnetic prospecting, PhD dissertation, Physics, U C L A , Los Angeles. [112] T u r t o n , R . and Levenspiel, O . (1989). An experimental investigation of gasparticle heat transfer coefficients in fluidized beds of fine solids, in "Fluidization VI", 669-675, J.R. Grace, L . W . Shemilt and M.A. Bergougnou eds., Engineering Foundation, New York.  Bibliography  153  [113] Valenzuela, J . A . and Glicksman, L . R . (1984). An experimental study of solids mixing in a freely bubbling two-dimensional fluidized bed, Powder Technol., 38:6372. [114] Wait, J . R . (1953). A conducting permeable sphere in the presence of a coil carrying an oscillating current, Can. J . Physics, 31:670-678. [115] Wait, J . R . (1969). Electromagnetic induction in a sohd conducting sphere enclosed by a thin conducting spherical shell, Geophysics, 34:753-759, October. [116] W a i t , J . R . (1982). Geo-electromagnetism, Academic Press, New York. [117] Waldie, B . and Wilkinson, D . (1986). Measurement of particle movement in a spouted bed using a new microprocessor based technique, Can. J . Chem. Eng., 64:944-949. [118] Weinstein, H . , Shao, M . and Wasserzug, L . (1984). Radial sohd density variation in a fast fluidized bed, AIChE Symp. Serv., 80(341):117-121. [119] W e n , C . Y . and F a n , L . T . (1975). Models for flow systems and chemical reactors, Marcel Dekker, New York. [120] W u , R . L . , L i m , C . J . , Grace, J . R . and Brereton, C . M . H . (1990). Instantaneous local heat transfer and hydrodynamics in a circulating fluidized bed, Inter. J. Heat Mass Transfer, in press. [121] Yerushalmi, J . (1982). Applications of fluidized beds, in "Handbook of Multiphase Systems", sec. 8.5, G. Hetsroni, ed., Hemisphere, Washington. [122] Yerushalmi, J . and A v i d a n , A . (1985). High velocity fluidization, in "Fluidization", 226-291, 2nd ed., J . F . Davidson, R. Clift and D. Harrison eds., Academic, London.  Appendix A  Dipole M o m e n t of a Non-Permeable T h i n Shell Based on U  e  Wait's (1969) shell model is based on the assumption that the shell's thickness, A r , is small compared with the skin depth of the conductive material of the shell, i.e.  V  Ar « For the opposite extreme, A r »  (A.l)  8, = (-2— \o-.fiwJ  8„, the shell responds exactly the same as a sohd  sphere having the same diameter as the outer diameter of the shell. For the thick-shell case, the primarj' field will barely penetrate the outer surface of the shell before it is damped out by an induced current, countering it.  Whatever is in the interior of the  sphere is of no consequence since the primary field does not interact with it. Wait (1969) gives the total magnetic potential, U , at point (r, 6) in the medium e  external to a hollow shell as: ANQI f_l  =  ^  l  R  n  ^  ,7=i  +  n  b 1  £  n + 1  2n+1  r  n + 1  [  1  2n + 1 In Ar 1 + iaw.  where A  =  cross sectional area of thin solenoid  Af  =  turns per unit length of solenoid  I  =  current through solenoid  b  =  outside radius of shell  £  =  distance between a thin solenoid and centre of shell  a  =  a,(i Arb (assuming  d  =  shell thickness  0  0  /i  s  h  e  U  =  fi ) 0  154  Pn(cOS0)  For ^j)  1)  o l u  J' ^  n e n r s  ^ term of the summation need be retained. The first term  on the right hand side, ^ j = f , is the potential due to the primary field. The field strength of the source at the center of the shell is: #0 = - ^ ^  (Wait, 1953)  Therefore, the potential due solely to the induced dipole in a uniform field, H  2r  1  2  3 + iocw.  0>  is:  H cos 6 0  The corresponding magnetic field components are: 6U  r  =  r  -b3  e  H  dr  1 -  3 + iavj.  Hn cos 6 (A.2)  He  lb*_  rd6  2r  3  1 -  3  3 + ictw.  Ho sin 6  The field around a magnetic dipole given by Plonsey (1961) is:  5=^= fio  (2 cos 6 a -f sinfl a )  m  Airr  r  e  3  By matching components in Equation (A.2) and (A.3), it can be shown that 3  =^ b 155  (A.3)  Appendix B  Derivation of Equations Used in Sections 2.1 and 3.2  B.l  Translating the Origin from the Dipole to the Centre of the Circumferential Loop  The variables of the new coordinate system based on the origin '0' are r , v, and z'. The dipole!s position, shown above, relative to this s} stem is (it, 6, —z{). r  Since the  dipole's field is symmetric, the field is independent of the angle (relative to the origin at the dipole) and is determined solely by the old-coordinate-system variables p and z.  To find the value of the field at any point in the loops plane, (r, v, 0), given the  particles position, (R, 6, —z/), the corresponding values of p and z must be found. The  156  transformation between z and z' is given by: z = z -t Zl  so that when z' = 0 (i.e. the plane of the loop), z = z/. In order to find p, we project the particle onto the plane of the loop and use vector addition to obtain:  It is obvious that P — r — R, where: R  =  vector to the particle's projection from the loops centre  r  =  vector to the position (r, v, 0) from the loops centre  P = Then:  vector from the particle's position to (r, v, 0) from the loops centre p = | p | = J(r cos v — R cos 6) + (r sin v — R sin 6y  (B.l)  2  B.2  Integrands and Inner Integrals of Equation 2.4  Based on the assumption in that the exciting field, and therefore m , are uniform in z  space, the z-component of Equation (2.1) is differentiated resulting in: 8B  Z  pom  (/) +z )4z-(2z -^)5z  47T  {p + z )i  z  8z  2  2  2  2  2  Simphfying, making the transformation in Equation (B.l), as well as z = zj, the first integrand in Equation (2.4) becomes: dB  z  dz -T =  Pom  z  9z/r  47T  157  15zjV"  (B.2)  where Q = p + z = r - [2#(cos Ocosv + sin (9 sin «)] r 4- (# + 2  2  2  )  2  Similarly: dB  2z  2  T  dm  AT ^ 2  z  +  -p 2  2  2p  and the second integrand in Equation (2.4) becomes: mz  dB  z  am.  pm  r  0  3z r 2  z  r  (B.3)  0\  AT  The inner integrals of Equations (2.4) and (3.1) are then: dB  z  p,om  rdr  dz  3aQ  z  AT  -VQ  15z?  5aQ  dr  -VQ  |9z  z  2  2  --/  3  2a J  I  dB  p. m  z  0  m— rdr dm.  Zz  2  z  AT  z  ZaJJ Q VQ 2a dr 1],.  -VQ  Q VQ\ 3  _b_  3aQ  2  j  dr  2a J Q VQ 2  2br +4c  +  qVQ .  where a, b, c  coefficient of quadratic Q 2 ( 2 " - + 6 ) (±  Q VQ  J  2  r  2(2ar+fc)V^  dr  J Q y/Q 3  SqQ  ,  Aac - b  dr  , 4* r  ••  3  ou\  S J  0*,J  2  Aa  k  upper hmit of integration lower hmit of integration When q = 0 the inner integrals are: f ^E± d \ Jr  dz  r  r  ~°  Q  -  -1  • ° fJL  rnz  3(s+')  AT  158  +  8 a ( i + r ) _  I5zf ir,  7  a5  dB m — rdr um z  z  z  u, m J Szf 0  g=0  z  47T  1  1  a  2  3(£+>\)  + 3  8 g  (^+^) . 4  6  -1  3  02  B.3  Justification of the form of Equation 3.1  For a tracer approaching one semicircle (0 < 6 < TT) the contribution due to that semicircle is:  roo  fir  r2ir foo  -  INTD drdv + / JO  JR,  /  (B.4)  INTD dr dv  JO  JIT  loop The contribution due to the other semicircle is:  PP ? 00  Jir  INTD drdv  (B.5)  Jo  where INTD = the integrands of Equation (2.4). Equation (B.4) is multiplied by —1 and added to (B.5) to calculate the total contribution because the two semicircles are wound in counterseries so that opposite induced voltages are additive. The second term of (B.4) can be broken up to give: [2ir pR]  /  /  Jir  Jo  l  o  rlir poo o  p  INTD drdv+  /  INTD dr dv  Jir JR-I  loop The total contribution is then: rir  EMF  D  = /  Jo  foo /  JR*  loop  fZir  INTD drdv+  JIT  ^oo  flir pR-i  /  INTD drdv + 2*  JR,  loop  Since the first two terms are equal to EMFc,  JV  /  JO  l  o  o  p  INTD dr dv  this equation is the same as Equation (3.1).  159  Appendix C  Calculation of Superficial Gas Velocity (U ) from Orifice Measurements g  Considine (1957) gives the equation for the mass flow of gases through an orifice as:  W = C KYF d -Jh^i 2  mv  a  (C.l)  where C W P = 358.98 when all quantities are in Imperial units. In order to convert the equation into SI units, the value of C$i must be determined in: W = CsiKYd  = \f&p~^  2  (C.2)  The units for the two equations are, respectively: 358.98  HHHin'in^o^)'  Multiplying the former equation by: • ( 1kg \ 2.21b  lh 3  6  0  0  \ s  /  and then setting it equal to the latter, allows C$i to be calculated. 1.1106 kg/s m. The values of the other variables in Equation (C.2) are: 2  160  It is equal to  7  =  P * m.w.  Y  =  1 - (0.41 +0.35 *£ )-=-g * A P v P  A"  =  i\>*(l+6*A)  A  =  1000 - ( 4  b  =  (0.002 + 0.026 *B )* K<f>  K<t> B  4  *//)/(7r* x* D /  J  p i p e  )  u p  i  4  = =  8314 T  up  0.6004 + 0.35 + B  4  d/D  pipe  where — orifice diameter  d 0.5 < B < 0.7 m.w.  =  molecular weight of gas = 28.9 for air  T  =  operating temperature (°K)  P  =  pressure upstream of the orifice (Pa)  AP  =  differential pressure across orifice (Pa)  up  C /C p  v  — 1.4 for a diatomic gas such as air  For a given set of ( P , A P ) at given operating conditions, Equation (C.2) can be up  solved iteratively for W. The value of U in the 152.4 mm ID riser, at a temperature T g  (degrees K) at a pressure of 1 atm., is then determined by: U \' = W*42.483 g  T  161  Appendix D  Multiplication of Two Sinusoids Followed by Integration  Let the product of the two signals be represented by: f(t)  = A s i n ^ f ) * B sin(u;2< + B)  where A,B ivi,u}  8  2  =  amplitudes of the two signals  —  frequencies of the two signals  =  phase shift between the two signals  Applying a trigonometry identity to the second term, the product can be expanded to:  f(t) = AB [sin (wit) sin (u; <) cos B + sin (wit) cos 2  (u>0 sin 6} 2  (D.l)  The product is integrated over time, and, if the two signals have the same frequency, Wj = UJ = u, the integral is: 2  1 = AB  cos 6 f 2  sin 2u}t \  V  1  J  2  +  cos 2wt \ 1  sin 3 /1 ~2~  \2  '  2  JJ  If the two signals are in quadrature, 0 — ^, Equation (D.2) becomes: I =  AB -{ -2 V2 l  1  2  J  which is zero for r = 2ir, ATT, 6ir ... If the two signals are in phase, 6 = 0, Equation (D.2) becomes: ,„1/ sin 2 W T I = AB- (CUT 2A 2 162  (D.2)  which is not periodic and increases monotonically. If the two signals have different frequencies, then by using Euler's formula, it can be shown (Sokolnikoff and Redheffer, 1958) that the integral of the first term of Equation (D.l) is: r2it  I\ — AB cos/3 / Jo  sm(wit) sm(cj t)dt = 0 2  (wj ^ u; ) 2  while the second term is given by: /•27T  I2 = AB sin/3 / Jo  sm(u>it) cos(u;2t)dt = 0  Therefore, regardless of the phase relationship, the time-averaged product of two signals of different frequencies is zero. When the signals have the same frequency, the time-averaged product is zero when they are in quadrature and non-zero when they are in-phase.  163  Appendix E  Terminal Velocity Calculation for a Sphere  A dimensionless diameter, d", is expressed by:  d" = d  p{pp ~  p)g  A dimensionless terminal velocity is defined in terms of d", depending upon the flow regime. In the Stokes' regime, where:  Re < 0.8, d' < 2.5 t  the value of J7" is ^ . In the Newton's law regime, where: t  750 < Re < 3.4 x 10 , 60 < d" < 3500 5  t  the value of f/* is 1.73\/d~. The value of the terminal velocity. U , is calculated from C/" t  t  using:  u = t  I {pp-P)9. 1  Between these two regimes, and somewhat overlapping, U{ is given by a set of equations given by Grace (1986). p  =  density of the gas = 1.177 k g / m for air at S.T.P.  p  =  viscosity of the gas = 1.846 x 1 0  g  =  gravitational constant = 9.81 m/sec  d  =  diameter of the sphere (m)  3  -5  164  kg/ms for air at S.T.P. 2  t  Appendix F Data from CFB Tests and Statistical Evaluation of Results  F.l  Can the Results of Runs #7a and #7b be considered to come from the same Population?  Since we do not want to assume a normal distribution, the Wilcoxon-Mann-Whitney test is employed. It is the most powerful alternate to the t-test among the non-parametric tests (Himmelblau, 1970). The procedure for this test is given by Larson (1982) and involves combining the two samples, sorting the resulting hst in order of increasing times, and then identifying the positions (i.e. ranks) of the times originating from one of the samples. The sum of the ranks for run #7b is: W  n  = 5 + 11 + 14 + 18 + 19 . . . + 130 = 2035  The null hypothesis, H , that the two samples come from the same population, is tested 0  by determining, at the 5% significance level, if: ^0.025 <  <  VQ.025  where  m  =  number of sample times in run #7b  n  =  number of sample times in run #7a  These statistics are calculated to be: 165  io.025  =  1683.6  Vo.025  =  2408.4  Since Wn lies between these limits, the null hypothesis is accepted, at the 5% significance level and the results from runs #7a and #7b are likely from the same population. The significance level in this test, as well as for the next test, is equal to the probability that the hypothesis is true, even if the test indicates it should be rejected (i.e. Type I error). The probability that the hypothesis is, in fact false, even though the test indicates it should be accepted (as we have just done for the case above) cannot easily be defined for these types of tests (i.e. non-parametric tests) (Bendat, 1966). If a model, such as the normal distribution, for example, had been fit to the data, not only could this so-called Type II error be evaluated, but also the minimum sample size could have been readily determined for a desired significance level. Fitting a model to the data would allow the sample to be summarized by two (for the normal distribution) or three statistics (or, parameters) and the goodness of fit of the model could have been evaluated using the %  2  test, for example.  F.2  W h i c h of Runs 1 T h r o u g h 7a Share the Same Probability Law?  The results plotted in Figures 4.9(a) and 4.9(b) are grouped by superficial gas velocity because, except for the lowest solids flux, the results at each gas velocity appear to be unaffected by the solids flux.  In order to determine whether the samples at a given  velocity do, in fact, statistically represent populations having the same distribution, contingency tables are used, in what is called a test of homogeneity for the populations (Larson, 1982); alternatively, the Kruskal-Wallis A N O V A could be used, which is also a non-parametric test. For each element of the contingency table, there is an observed 166  value, 0{j, of the number of observations during run i, which fall into time interval j, and a corresponding expected value, Eij, derived from the null hypothesis, H , that the 0  tests under consideration all have the same distribution. The hypothesis is accepted if a summary statistic, U, equal to:  i  J  E  a  is less than the value of % , at some arbitrary significance level (e.g. 0.05) and at (I — 2  1) x (J — 1) degrees of freedom, where / is the number of runs being considered and J is the number of intervals. Table F . l gives the observed values in 2 second intervals from < 3s to < lis. When necessary, in order to maintain all expected values > 5, so that the % test can be safely 2  apphed (Crow et al., 1960; Moroney, 1963), intervals are combined, for some groups of runs. The expected values are not shown in the table, but are calculated by:  H  E  =Pj*J2 ° i i j  where  j  =  interval index  i  =  run index  The results of this analysis, as given in the table, confirm the earlier supposition that, at each velocity, the results obtained at the lowest solids flux, 14.3 kg/m s, are from a 2  different population than the results at the higher fluxes.  167  Table F . l : Number of Observations bj' Time Intervals.  Run  < 3s  > 3 < 5  > 5 < 7  > 7 < 9  < 11  > 11  Total  1 2 3 4 5 6 7a  8 11 2 58 43 54 23  27 25 13 32 39 32 40  26 21 11 8 9 9 15  13 15 8 1 8 3 8  6 8 12 0 1 2 3  19 20 53 0 0 0 11  99 100 99 99 100 100 100  P|l,2,3  0.070  0.218  0.195  0.121  0.087  0.309  P|l,2  0.095  0.261  0.236  0.141  0.070  0.196  PU,5,6,7a  0.446  0.358  0.108  0.050  P|4,5,6  0.518  0.344  0.087  Tests Considered  1,2,3  ,  1,2 4,5,6,7a 4,5,6  > 9  0.015 0.028 O.C43 0.040 0.010 0 O.C50  U  Degrees of Freedom (df)  Xo.05,d/  H  46.1 •1.5 58.7 9.8  10 5 12  18.3 11.1 21.0 12.6  reject accept reject accept  6  168  a  Table F.2: Measured Peak Times, Run l-7b. Run #1 U = 7.12 m/s,  35.43 kg/m s 2  g  Particle No. 1. 2. 3. 4.  5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.  Peak Appearance Times (sec) 4.15 5.14 5.78 6.01 9.26 10.29 6.41 13.86 9.26 8.93 5.95 3.88 3.86 13.11 11.24 11.36 3.68 4.30 3.49 4.38 9.92 12.86 2.96 4.24 7.37* 18.27 11.98  26. 27. 28. 29. 30.  31. 32.  33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.  5.33 3.02 6.44 7.55 4.24 6.88 7.98 22.00 2.22 7.61 9.00 7.03 5.56 2.68 12.80 11.58 13.52 19.14 4.55 6.50 5.60 6.88 8.05 6.38 • 5.52 2.09 67.02 10.00 4.64 .4.58  51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75.  2.26 6.63 4.32 11.28 11.82 16.94 6.63 5.57 10.61 7.96 3.07 3.72 7.94 9.62 4.01 3.12 7.88 19.91 7.28 6.49 6.63 5.10 6.74  * 6.86  * oscilloscope failed to trigger 169  76.  77. 78. 79. 80.  81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91.  92. 93. 94. 95. 96. 97. 98. 99. 100.  3.16 5.16 6.52 5.43 5.75 3.50 2.26 5.08 5.84 7.48 3.81 5.82 12.58 4.35 4.10 4.28 7.22 2.70 6.38 12.10 13.56 13.70 2.78 14.68 7.47 5.81 4.44 3.66 3.50 8.18 10.86 12.42 12.56  Table F.2 (continued) Run #2 U = 6.99 m/s, G, = 56.57 kg/m s 2  g  Particle No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.  22. 23. 24. 25.  Peak Appearance Times (sec) 4.61 7.44 6.29, 6.43, 6.92 3.28 9.59 4.93 23.57 4.44 3.96 5.94 11.70 9.30 4.57 9.82, 13.24 5.92 5.48 6.18 1.78 7.02, 8.30 12.92 2.48, 4.44, 4.84, 8.42 10.01 8.82, 9.20' 3.82 5.06 3.83  26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43.  44. 45. 46. 47. 48. 49. 50.  11.13 4.14, 4.34 5.28, 7.50, 8.87 3.21 17.53, 19.15, 20.64 8.86 4.58, 4.88, 7.81, 8.54 6.86 11.06 2.34 10.92 6.35 4.61 5.72 3.62 2.34 1.68 4.84, 8.94, 10.81, 13.01, 15.59 9.34 •2.48 12.68 6.78, 9.20, 9.55 2.74 5.48 6.10  170  51. 52. 53. 54. 55. 56. 57.  58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75.  8.12 8.39 14.30 1.62 5.44 2.67 25.62, 27.08, 31.08, 33.37, 34.22 12.76 13.90 6.06 6.58 5.24 10.96 4.14 7.23 4.98 4.25 4.06 16.33 4.10 2.51 8.05 11.50 3.52 5.44  9.04 6.38 19.30 8.21 7.01 19.05 11.35 10.75 2.81 5.98, 7.96 3.16 11.44 3.97 8.57 7.25 4.43 12.32 3.46 16.24 8.29, 10,48, 10.86 96. 7.52 97. . 6.76 98. 8.81 99. 4.04 100. 12.34 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95.  Table F.2 (continued) Run #3 U = 7.09 m/s, G = 14.28 kg/m s 2  g  Particle No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.  13. 14. 15. 16. 17. 18. 19. 20. 21. 22.  23. 24. 25.  s  Peak Appearance Times (sec) 7.08 51.22 11.45 23.05 20.90 75.70 6.73 4.52 38.08, 38.50, 38.63 56.93, 65.34, 65.47 9.36 6.54, 7.83, 7.95, 10.25, 10.72, 11.10, 14.94, 15.23 49.85 9.44 19.13 7.52 10.76 17.08 31.14 4.25 , 4.38 14.90, 15.10, 15.39, 17.66, 18.46 8.26 5.88 12.18  26. 27. 28. 29. 30. 31. 32. 33. 34. 35.  36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.  6.45 7.54 3.50 8.49, 10.26, 12.17 3.70 19.01, 23.28, 23.57 51.33 18.80 22.15 9.23, 9.97, 10.13, 10.32, 10.82 16.12 4.24 29.04 26.11 * 5.22 5.92 5.34, 5.50, 5.93 34.36 15.22, 16.78, " 16.94 18.02 9.90 5.31 9.90 13.21  51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75.  11.50 10.97 18.60 50.92 7.24, 7.86 33.98 11.40 12.91 4.69 30.49 3.48 15.22 9.70, 13.74, 15.93 13.48 26.33 3.40 12.70 3.37 7.48 18.67 18.17 11.56 8.80 14.30 25.12  * no show - unexplained 171  76. 77. 78. 79. -80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100.  14.74 13.36 14.52 6.61 39.56 6.42 70.86 21.11 30.44 16.22, 16.69 5.96 13.72 9.62 9.50 10.00, 13.73, 4.62 10.32, 11.58, 12.49 25.34 2.56 3.66 58.65 15.82, 16.06 16.52 4.36, 5.77, 4.23  Table F.2 (continued) Run #4 U = 9.18 m/s, G, = 56.31 kg/m s 2  g  Particle No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.  Peak Appearance Times (sec) 2.02 2.64 6.07 2.41 4.72 3.62 2.99 5.31 5.47 2.04 4.26 ' 3.08 2.62 1.85 3.90 2.83, 3.17 1.79 4.34 1.93 3.05 1.94 3.94 5.67 1.50* 3.06, 3.52, 3.81  26. 27. 28. 29. 39. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.  2.99, 5.09, 5.35 2.52 4.35 1.93 2.66  * 3.78 2.49 2.15 2.75 2.08 3.88 3.52 3.37 3.24 2.89 1.77 3.25 1.93 4.00 1.57 2.22 • 2.45 1.58 1.44  51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75.  2.21 2.98 3.05 3.00, 3.82, 3.98, 4.27 2.52 7.35 1.50 1.40 2.36 4.90 3.02 2.48 4.23 4.72 4.71 5.14 5.66, 7.30, 8.08 4.28 2.78 1.69, 3.69 2.02 1.96 2.39, 7.54 8.23 3.30 3.26  76. 77.  78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. •99. 100.  * oscilloscope shut off - due to electrostatic charges?  172  2.46 2.98, 3.24, 3.58, 5.86 6.81 1.64 2.11 1.26 2.59 5.19 2.73 2.56 3.64 2.73 3.43 1.71 3.01 3.54 3.13 2.82 1.90 1.52 1.88 2.54 3.43 5.31 1.58 2.15  Table F.2 (continued) Run #5 U = 9.15 m/s, G, = 37.4 kg/m s 2  B  Particle No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.  20. 21. 22. 23. 24. 25.  Peak Appearance Times (sec) 8.37 2.96 3.66 7.28 2.65 3.80 5.88 3.22 4.56 8.10 1.67 3.26 4.16 4.06 2.24 5.02 10.08 4.01 5.59 2.52 2.82 3.36 3.60 1.54 1.88, 3.14 5.58 7.52  26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.  4.86 1.97 5.22 3.66 2.39 3.82 4.48 3.14 2.00 4.72 2.54 3.58 1.78 2.89 1.54 4.34 2.44 3.16 2.00 3.45 2.43 8.07 3.20 3.57 7.94  51. 52. 53. 54.  55. 56. 57. 58. 59. 60. 61.'  62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75.  1.66 4.37 4.71 4.71 4.89 5.23 5.60 2.86 1.53 3.06 2.12 5.63 3.73 1.26 3.29 4.08 6.31 6.44 2.47  * 3.22 6.06 2.30 2.05 1.43 1.84 3.08 8.09 6.45 2.52 3.50 3.29 5.60  * no show - injection malfunction 173  76. 77. 78. 79. 80.  81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100.  101.  4.68 3.68 2.34 1.79 2.36 4.02 2.35 1.66 2.05 4.02 1.89 3.10 3.63 7.10 6.05 2.66 1.72 2.10 3.99 2.84 1.74 1.70 3.05 1.94 1.99 2.84 4.94  Table F.2 (continued) Run #6 U = 9.04 m/s, G, = 68.9 kg/m s 2  g  Particle No. 1. 2. 3. 4.  5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.  20. 21. 22. 23. 24. 25.  Peak Appearance Times (sec) 3.635 2.440 1.845 2.670 4.775 6.150 2.20 3.250 2.885 2.375 4.37 3.07 2.43 2.89 3.52 4.03 3.00 4.87 1.70 1.86 6.45 5.74 6.44 7.31 3.774.57 1.97 1.73 2.00 8.33  26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.  50.  2.37 4.76 1.96 2.00 1.76 3.26 1.30 5.13 2.43 2.66 5.24 9.92 3.26 3.05 2.27 1.97 2.08 1.69 2.44 1.74 4.38 4.74 2.22 6.55 9.06 10.03 3.94 4.37  51. 52. 53.  54. 55. 56. 57. 58. 59. 60. 61.  62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75.  2.53 2.79 9.27 14.21 15.30 2.92 5.93 2.24 3.98 4.54 2.48 2.73 2.22 4.79 6.03 2.07 2.02 2.60 3.16 3.41 5.50 2.94 2.36  * * 2.43 4.20 2.97 4.96  76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91.  92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102.  * particle didn't appear - injector malfunction  174  2.13 3.49 3.14 3.59 2.73 3.02 3.87 2.99 2.45 6.15 2.82 8.22 7.35 2.67 1.75 3.04 4.90 5.34 2.64 4.90 2.69 3.23 1.55 1.93 3.21 4.07 4.59 1.63 6.45 10.84 11.49  Table F.2 (continued) Run #7a U = 8.9 m/s, G . = 14.3 kg/m s 2  g  Particle No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. ' 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.  100.  Peak Appearance Times (sec) 4.11, 4.70 3.05, 5.54 5.70 5.66 16.63 5.58 12.40 4.74, 6.22 6.34 3.32, 11.80 21.39 4.40 1.78 1.68 3.72, 10.36, 14.91 4.97 3.82 2.55 2.85 3.68 4.90 5.00 2.94 12.37 2.66, 4.30, 4.50 2.47 * 8.06 26.51  3.50 11.33 39.64  26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44.  45. 46. 47. 48. 49. 50.  3.82 9.48 2.62 3.68 6.55 2.76 6.70, 8.32 5.56 2.88, 27.16 43.58 7.40, 28.47 53.16 2.89 8.97 4.21 5.72 1.88 2.44 3.05 3.05 2.62, 3.97, 4.78, 5.96, 6.50 2.43 3.24 3.00 4.20 .7.64 4.32  51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75.  5.06 32.06 47.38  3.38 5.31 15.04 4.98 17.42 8.87 4.70 3.78 4.68 8.90 14.26 6.10 5.64  76.  77. 78. 79.  80. 81. 82. 83.  * 2.82 5.95 3.96 4.69 8.40 9.46 6.55 5.32 3.26 1.68 17.98, 37.36, 40.50, 45.74  5.66 35.54 54.18  84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 101.  * particle didn't appear - injector malfunction 175  2.57, 5.02 5.32, 16.14 18.02, 23.26 28.18 5.76, 21.72 2.93, 21.72 2.75, 4.40 5.18, 8.18 8.61 3.54 3.28 10.23 3.15, 4.82, . 6.27, 7.64, 8.08 14.02 3.18 4.28 2.48 3.96 4.39, 8.76, 9.03 7.30 11.12, 15.12, 15.53, 15.97 4.10 3.28 5.18 4.52 4.94 4.92 12.74 2.33 6.59  Table F.2 (continued) Run #7b U = 8.9 m/s, G, = 14.1 kg/m s 2  g  Particle No. 1. 2. 0 o.  4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.  Peak Appearance Times (sec) 2.26  * * * * t 9.12 3.10 10.53 3.20 3.28 2.74 3.45 3.93 12.96 3.14 9.50 2.53 2.88 4.991, 6.65, 7.49 3.63 3.23. 10.74 3.75 3.84  26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.  3.42 3.11 3.80 4.92 6.88 5.73 18.22 9.94 2.60 12.19 2.74  51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75.  76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100.  * particle didn't appear - injector malfunction f injector jammed - clean & restart  176  


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