William M. Goldblatt - Open Collections

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 SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF

D O C T O R OF PHILOSOPHY

in T H E FACULTY OF 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 COLUMBIA 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 purposes may be granted by the head of my

department or by his or her representatives. It is understood that copying or

publication of this thesis for financial gain shall not be allowed without my written

permission.

Department

The University of British Columbia Vancouver, Canada

Date 6 /?'6re/Q*-y /?9 I

DE-6 (2/88)

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. The crux of this approach is being able to sense individual tracer particles. 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

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the riser. The information obtainable from such a configuration would greatly enhance understanding of the detailed trajectories within the riser.

in

Table of Contents

A B S T R A C T ii

List of Tables vii

List of Figures "vu

A C K N O W L E D G E M E N T S x

1 Introduction 1

1.1 Circulating Fluidized Beds (CFB) 2 1.2 Residence Time Distribution Techniques in the CFB 6

1.2.1 Previous Measurements 10 1.2.2 Single Particle vs. Pulse Response 12

1.3 Electro-magnetic Induction (EMI) 15 1.3.1 Other Applications and Their Relevance 15 1.3.2 Special Considerations in the CFB 24

2 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

3 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

i v

3.5 Limitations of the EMI Technique 87 3.5.1 Global vs. Local Indications 87 3.5.2 Minimum Tracer Size 88 3.5.3 Noise . . . ; 90

3.6 Recommendations 93 3.6.1 Resolving Local Indicators 93 3.6.2 Scale-Up 94 3.6.3 Local Flow Rate Determination .- 98

4 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 Application of the Technique in the CFB 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

5 Summary 135 5.1 Implications of This Work 135 5.2 Recommendations for Future Work . 137

5.3 Overall Conclusions 140

Bibliography 145

A Dipole Moment of a Non-Permeable Thin Shell Based on Ue 154

B Derivation of Equations Used in Sections 2.1 and 3.2 156

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 (Ug) from Orifice Measurements 160

D Multiplication of Two Sinusoids Followed by Integration . 162

v

E Terminal Velocity Calculation for a Sphere 164

F Data from C F B Tests and Statistical Evaluation of Results 165 F . l Can the Results of Runs #7a and #7b be considered to come from the

same Population? 165 F.2 Which of Runs 1 Through 7a Share the Same Probability Law? 166

vi

L i s t of Tab les

2.1 M for Spheres Compared to £ r e s i d u a l / M o for Materials of Figure 2.2. . 40

4.1 Oscilloscope Signal During Drop Tests I l l 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

vii

L i s t o f F i gu res

1.1 Schematic of a Circulating Fluidized Bed Combustor (Grace, 1990). . . 3 1.2 Regime Map of Solids-Gas Flow (Grace, 1990). 5 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 2 a 2 | and of Relative Permeability / i / / / 0 - (Grant and West, 1965) 19

1.6 Transient Approach — Transmitter and Receiver Alternately on (Grant and West, 1965) 22

2.1 Response of Circumferential Case, R\oop = 0.095m 36 2.2 Typical Demagnetization Curves of Various Permanent Magnet Materials

Stablein (1982) 39 2.3 Satellite Receiving Loop Perpendicular to Plane of, and Tangent to Trans

mitter Coil 45 2.4 Satellite-Sector Receiving Loop ("figure-eight") Parallel to Plane of Cir

cumferential Transmitter Loop 47 2.5 Cross-Section of Centerline Transmitter/External Satellite Loop Receiver

(transmitter is perpendicular to plane of page) 51 2.6 Two External Axial Transmitters with Four Receiver Loops in Nulled Po

sitions (showing resultant exciting field at P) 52 2.7 Waveform of Current with Sinusoidal Applied Voltage to a Non-Linear

Conductor (adapted from Ashworth et al., 1946) 59 2.8 Shearing Correction of a Magnetization Curve (Chikazumi and Charap,

1964) '. 61 2.9 Assumed Magnetization Curves in Dilute Samples of Three Sizes of Fer

romagnetic 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 Fitzger

ald, 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 Equa

tion (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 102

4.2 Velocity of 6.35 mm Diameter Al Shell Calculated on the Basis of Equation (4.1) with V^tij = 0 104

4.3 Sketch of Characteristic Oscilloscope Trace for a Typical Tracer Pass-Through 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

ereton, 1987). 128 4.9 Time-of-Flight Histograms C F B Tests 130

ix

A c k n o w l e d g e m e n t s

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.

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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

I n t r o d u c t i o n

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 asso

ciated 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 mon

itored 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 circulat

ing around a C F B are typically much smaller than these tracer particles. Nevertheless,

the CFB was still chosen because some or all of the fuel fed to CFB combustors, for

example, may be of a comparatively large particle size. In addition, agglomeration can

occur in some CFB 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 circu

lating 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 C i r c u l a t i n g F l u i d i z e d Beds ( C F B )

The CFB 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 CFB compared with lower velocity particulate-gas

contacting schemes are a relatively high throughput of gas without significant bypass

ing, 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 CFB 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 investi

gation 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 con

ventional 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


C o o l i n g wate rwa l l

Cyclone

Sec . a i r

Fue l , Sorbent

Flue gas to Superheater, Ecooomizef, Atrheater, Baghouse

Standpipe

Primary air

Drain

Figure 1.1: Schematic of a Circulating Fluidized Bed Combustor (Grace, 1990).


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 re

searchers (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 disap

pearing 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, Br

ereton, 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 CFB combustors, causes sep

aration 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


Figure 1.2: Regime Map of Solids-Gas Flow (Grace, 1990).


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 Time 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


to

or O f— ZD CO. oc CO Q txi

> o cn <

O u i X

/ A b r u p t e x i t

Legend O A Symbol Ugjm/s] G s (kg/m 2s)

/ / O 7 . 1 A 4 5

7 3

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).


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. Al

ternatively, 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, RTD

measurements can provide clues oil how the solids mix, and the structure of internal

recirculation; such information cannot be derived from local measurements without sig

nificant 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


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


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

the flow of 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,


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 RTD 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 dilute-

suspension, 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


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


(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 stick-

slip 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 CFB 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 CFB is ques

tionable. 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


same order as the inverse of the pulse injection time, 1 sec - 1.

The single particle tracer technique, adapted in this investigation, avoids this quasis-

teady 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 CFB, 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 be

cause it can account for the tracer's whereabouts, by region, during the whole time the


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 pri

mary 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. Electromag

netic 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 CFB 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 CFB.

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 frequencjr usually less than 5 kHz. As in the sensor developed here, this field


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 prop

agation (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 accu

mulation 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 fluctu

ations 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, un

less 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.


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:

E M F R C E M F R T

where:

subscripts R, C, and T represent receiver, conductor and transmitter, respectively.

E M F ^ B = E M F in coil A due to current flow in coil B

k*AB — coefficient of coupling between coils A and B

a = LJLCJRC

UJ = angular frequency • 2TT/

LC = self inductance of the conductor

RC = resistance of the conductor 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

hrchcR cr + ia

1 + a 2 (1.1)

C i i a p t e r 1. Introduction

Transmitter Receiver Transmitter Receiver

Transmitter Receiver Transmitter Receiver

k + k + k -TR TC CR

Transmitter-receiver 1 c o u p ( ; ' * Circuit-receiver coupling Transmitter-circuit J

Figure 1.4: Effect of Coils Relative Positions on Coupling (Grant and West, 1965)

Chapter 1. Introduction 1 9

Figure 1.5: Real and Imaginary Parts of Response Function as a Function of Response Parameter \K2a2\ and of Relative Permeability p/p0. (Grant and West, 1965)


uniform primary field has in-phase and quadrature (i.e. 90° out of phase) components

which are functions of a response parameter, K2a2, and the sphere's permeability, p.

This complex response is incorporated in the response function for a sphere:

x i Y = M 1 + K2a2) + M s i n h (Ka) - (2/i + p0)Ka cosh(Ka) % \p0(\ + K2a?) - p] sinh(Ka) + (p - po)Ka cosh(Ka) ^ ' '

where p0 = free space permeability = Air X 10 - 7 H/m

Ka = (^^p -)* (1 + *) (K is commonly known as the wave number)

u> = 2 7 r / , [radians/sec]

cr = conductivity of sphere, [mhos/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, |Jf 2 a 2 | . The plot is

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, Ue, derived by Wait (1969). The dipole

moment, m,htu, generated by such a shell in a uniform primary field, Hoetwt, is inferred

from Ue in Appendix A and is shown to be given by:

-mshen = -2irb3H0e^ ( l - — ) (1.3) V 3 -f tctu) J

where

b = radius to outside of shell, [m]

a = a,p0Arb, [s]

Ar = shell thickness [ml « (—*—) 7

a, = conductivity of shell, [mhos/m]


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 tracer-

sensing 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. An

other approach, described by Anderson et al. (1983), depends upon magnetomechanical

coupling in amorphous metal targets. This results in each target having an identifiable


Pr imary f ield 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

i t .

Total field at conductor

D e c a y d u e t o O h « i c l o s s

Total field at receiver

2

emf induced. in receiver < d u e t o

d e c a y i n g f i e l d )

t R e c e i v e r o f f

Figure 1.6: Transient Approach — Transmitter and Receiver Alternately on (Grant and West, 1965)


signature in its response. There are also simpler techniques, which utilize induced mag

netization 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 highljr permeable target, mag

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 con

sidered 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


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 Spec ia l C o n s i d e r a t i o n s 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 hydro

dynamics 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 mag

netic field, B, the force on a charge, Q, travelling at a velocity, v, is the Lorentz force,

expressed by:

FL= 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


an incremental length, S£, of the secondary coil is shown by Matthews (1980) to be I.

S F= I, SI x B

where

Is = current in the secondary coil

B = primary magnetic field

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 is non-zero.

1This 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

I — nq v

where n — number of free charges, q, per unit length.

, which equals:

The Lorentz force on all the charges in length d£ is:

d F= - (ndiq) [v x 5)

d F= I [dl x B


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:

kAB - (kAkB)^

where kA — 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 (dp = 6.35mm) compared to

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" config

uration can also serve to increase the coupling between the tracer and the receiver, kcR-

This 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 con

verted 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


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 indi

cated 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 dis

charging 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 applica

ble. 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


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 addi

tives (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 mea

sures to suppress noise are directed at either accessories to the radio, such as noise lim-

iters 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 se

ries. 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

Our 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

approaching tracer particle, two sensing loops will be examined in detail. The circumfer

ential 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 configu

rations 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

be briefly described in this chapter. In order to illustrate how a loop responds to an

(Grant and West, 1965):

B= 4T IV + -*2)1

(2.1)

31

Chapter 2. Our Early Approaches to EMI Sensing 32

where

p0 — magnetic permeability of free space(practically the same as in the riser)

mz = z-component of the magnetic dipole moment

(i.e. parallel to the axis of the riser)

unit vectors in two orthogonal directions

p2 = x2+y2

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:

EMF = y f B-dS= I ^ d S (2.2) dt ./loop ./loop dt

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:

dBz dBz dmz dBz dz dt dmz dt dz dt

where ^ = VPx = 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):

mz = -27rrJ il • H0 eiu,t (X + iY) (2.3)

where


rp = radius of the tracer particle

H0etui = exciting field at the tracer's location

(A' +iY) = in-phase (X) and quadrature (Y) components of the induced

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:

dmz

—-— = icum, dt

We will discuss mz in more detail in Section 2.2 for permanent magnet tracers and in

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 = Z\

p2 = r2 - [2R (cos 6 cosv + sin 8 sin v)]r + R2

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:

EMFC = VPz I [ ^rdrdv + iu> I [ mz^rdrdv (2.4) Jv Jr OZ Jv Jr Omz


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 Equa

tion (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\QO-p is the radius of the loop.

Due to symmetry considerations:

EMFC = f(R,zi)

1This result follows directly from Maxwell's equation, y- B= 0. Applying the divergence theorem gives:

y-BdV-^B-dS-Q

Therefore: fB-dS-f B -dS+ I B -dS - 0

J t ./interior ./exterior


Figure 2.1 is a plot of the two integrals in Equation (2.4) showing the relative contri

bution of each to EMFC.

2.2 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


Velocity Component IiVpz-nizPo/Air = 1*' integral Equation (2.4).

Moment Component I2umizpo/4ir = 2nd integral Equation (2.4).

Figure 2.1: Response of Circumferential Case, h\ = 0.095m.


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 slow-

moving 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 i d 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 mag

netic field intensity within the tracer, - f f a c t u a i ; the abscissa, was equal to the externally

applied field (in excess of the earth's field), ^ a pp U e d> which is zero in this case. The

moment was then obtained by:

B = Mo (âctual + M ) (2-5)

and by assuming # a cttial = 0;

TO = \irrlM = l O T 3 g res idua l ( f o r a s p h e r e ) 3 3 po

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:

âctual = âpplied " D M ( 2 - ° )

where D = the demagnetization factor = 0.333 for a sphere. Therefore, when ^ a p p U e a

1 =

file:///irrlM


0, Equation (2.5) and (2.6) give:

B = Po (l ~ -p) #actual

= -ôâctual ( f o r a sphere) (2.7)

Equation (2.7) is the operating line for a spherical magnet, and it intersects the

hysteresis curve in the second quadrant at the operating point (Hop, Bop). The actual

moment per unit volume for a spherical magnet is then:

M = ^ - H o p (2.8) 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 aban

doned in favour of the induced-dipole approach, which eventually allowed resolution of

the various obstacles.


Figure 2.2: Typical Demagnetization Curves of Various Permanent Magnet Materials Stablein (1982) (1) hard ferrite; (2)AlNiCo, high BT grade; (3) AINiCo, high He grade; (4) Mn-Al-C alloy: (5) RECo5 alloy; (6) RE{Co, Cu, Fe ) 7 alloy.

Chapter 2. Our Early Approaches io EMI Sensing 40

Table 2.1: M for Spheres Compared to 5 r e s id u a lJpo for Materials of Figure 2.2.

Materials Hop, A / m B0p, W b / m 2 Msphere> A / m ^residual//1"' A / m

1 -1.03 x 105 0.26 3.1 x 105 3.1 x 105

2 -4.91 x 104 0.12 1.5 x 105 9.6 x 105

3 -1.18 x 105 0.29 3.5 x 10s 6.0 x 10s

4 -1.40 x 105 0.35 4.2 x 10s 4.7 x 105

5 -2.42 x 105 0.60 7.2 x 105 7.4 x 105

6 -2.72 x 105 0.67 8.0 x 105 8.2 x 105

I n d u c i n g a n d Sens ing a M a g n e t i c D i p o l e

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


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 config

urations 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 Primary Field

Loop Transmitter/Loop Receiver

The simplest induction configuration consists of a circumferential transmitter and re

ceiver. For this case, Bohn (1968) shows that, based on Neumann's formula, the mutual

inductance between the two coils is expressed by:

MTR

where

= poNTNRy/TTrR (jf ~ K ) F 2E_

Chapter 2. Our Early Approaches to EMI Sensing 4 2

A7 = number of turns in the respective coil

r = radius of the respective coil

Po = AT x 10 - 7 H/m = permeability of free space

I = axial distance between the two coils

F = elliptic integral of the first kind

J° y/l-K*sm2f3

E = 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 K2 < 1, these expansions are:

1 . 3 . 5 . . . ( 2 , - 1 ) , f 2 - 4 - 6 . . . 2 n Jo

E(K,-) = - - - K 2 H S1n28d6-— f2 sin*6d6... V ' 2/ 2 2 Jo 2- 4 Jo

• - l - 3 - 5 - . . ( 2 n - 3 ) ^ f f s i n ^ w _ 2 - 4 - 6 . . . 2 n Jo

The signal at the receiver, assumed to be an open loop, due to direct coupling with the

transmitter is:

EMFRT = -MTR^-ITeiwi = -iwMTRITeiwt

dt


where

ITelwt = time-varying current in the transmitter

Evolving directly from the permanent-magnet approach, however, two-coil configura

tions were initially considered without regard to the direct coupling between the trans

mitter 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 transmit

ter 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:

kTR

where

kAB = (^fcs)^ kA = 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

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


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, al

though 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 com

pared to the field lines generated by the transmitter. It was only when this new perspec

tive 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 over

whelming 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


Figure 2.3: Satellite-Receiving Loop Perpendicular to Plane of, and Tangent to Transmitter Coil (solids and gas flow in the cross-hatched area)


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 ac

curately 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);


(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


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.

L i n e T r a n s m i t t e r / L o o p Rece i ve r

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

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

and Collin, 1961):

Vol (2.9) 27TT


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 satellite-

sector 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.

' r 2. a Ppi-o,

E»oS,


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).


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 p , in parallel. The parasitic capacitance is included in the.latter.


If the load's resistance, RL, and inductance, L, are known, the values of (7„ and Cp can

be calculated, for a given frequency, by simultaneously solving:

Attempts to obtain matching, at frequencies in the range 50-100 kHz, were unsuc

cessful, due to the sensitivity of the load impedance to slight variations in the two capac-

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

= 50 n

itances. Under some circumstances, a 1% increase in Cp would increase the resistance of


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 reso

nance introduces a reactive component (inductive for higher frequencies, capacitive for

lower frequencies), and the sensitivity of the load to these deviations is directly propor

tional 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


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):

/ < , ° . , (2.10) 7r(a + b) 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.


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 N o n l i n e a r M e t h o d s

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:

Ic = A • EMFST

where:

A and n — characteristics of the non-Ohmic conductor

Ic = eddy current in the conductor

EMFCT = induced E M F in the conductor due to current flow in the transmitter

= -iu)McTheiut

> 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


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 (103-104 volts/m) are not achieved in

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 ma

terials. 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 (-âctual is the field experi

enced within the material, as opposed to the applied, external field, .âpplied)- The second

favourable trait of ferromagnetic candidates is the highly non-linear relationship between

the dipole moment and .âctual- 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 iâctual exceeds Hc). Upon


0 1 2 3 4 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).


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 i ? a c tua i has already

been given in Section 2.2, above. 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 ifapPiied • The response of such a

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.


M

Figure 2.8: Shearing Correction of a Magnetization Curve (Chikazumi and Charap, 1964).


First, I considered a multitude of aligned high aspect-ratio particles, uniformly dis

seminated 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 Denveiope = | for a sphere, the ratio of the dipole

moment per unit volume of the envelope, pM„, to the applied field, i ^ a p P i i e d , is given by:

pM, _ p # a P P ~ + I P + D p a r t ( 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 pMa/Happ, 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:

t Chapter 2. 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 magne

tization 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 magne

tization 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 promis

ing avenues because, like the preceding alternative, it presented practical difficulties in

fabricating such a tracer.


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.

C h a p t e r 3

P resent C o n f i g u r a t i o n

3.1 Sensor and Assoc i a t ed E l ec t ron i cs

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


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>0 and c6j, which

are of equal amplitude and frequency, but out of phase with each'other by an adjustable

amount. Part of the signal, <j)0, is amplified and used to excite the transmitter coil.

The phase of the transmitter current, as well as the resultant exciting magnetic field is

approximately 90° out of phase with c60 (lagging), assuming that the power amplifier has

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 c60- This signal from the receiver coil is multiplied by the other signal, aV

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


T r a n s m i t t e r A m p l i f i e r

«*>PUT —I—MA,

E x c i t i n g and S h i f t e d S i g n a l s G e n e r a t o r

£_VvV ' V j M —

Figure 3.3: Transmitter Circuits for Security Application (taken directly from Fitzgerald, 1979).


Remote flmplif i e r

-to

fieri***

USHTS

o-i^f 34,0V.

M«Jt«pU

M u l t i p l i e r / l n t e g r a t o r

SUA.

-4> 3Wt

5 — \

BiJC ah y W"V\, «u

1—*M UAA/ 1

MfSJCM

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

Figure 3.4: Receiver Circuits for Security Application (taken directly from Fitzgerald, 1979).


3.2 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 EMFC, from Equation (2.4), and a contribution due to the field

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:

EMFD = EMFC + 2 [vpt P P00? ^rdrdv + iu> P / * l o o P mz^rdrdv\ [ Jn JO OZ J-K Jo 0mz J

(3.1)

Due to symmetry considerations:

EMFD=g(R,Zl,6)

Figure 3.5 and 3.6 are plots of the integrals in Equation (3.1) for several values of 8.

Although the values of Ix in these plots are greater than the corresponding values

of I2, in order to obtain the values of the integrals, the former are multiplied by the

velocity of the tracer particle, Vpz, which is of the order of 10 m/s, whereas the latter are

multiplied by the angular frequency, u>, which has a value of 3.76 x 104 s - 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).


G=37r/8 B=n/2

Figure 3.6: Moment Component of Response Diametral Case. Coil Rad. = 0.095m.

I2urmzp0/4TT = 2 n d integral Equation (3.1)


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 configu

rations, 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 diame

tral coil. Although it does not take' account of the downstream signal conditioning, the

model is an essential tool for further development of the technique.


3.3 Exciting Field Due to the Circumferential Transmitter

The induced dipole moment, mz, of the tracer depends, in part, on the exciting field,

Ho elut, at the tracer's location (Equation (2.3)). The exciting field, for both the circum

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 mz 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 trans

mitter coil, is given by:

= — fl - -kP2(x) + —k2PJx) 2a I 2 2 W 8 4 V ;

for r" < Va2 - z"2 (3-2)

and

HZ\NF = L f fc-fP 2 (»)- | fc-!P 4 (x) JLa L I

P 8(x) + . . .

for r" > Va2 - z"2 (3.3)

where


k

x +1

I = instantaneous current in the transmitter coil

a = radius of circumferential transmitter coil

Pn = Legendre polynomial of order 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:

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):

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; Fitzger

ald, 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

z = z -f t

+ for z" = 0 (3.4)

Figure 3.7: Magnetic Field Strength in Plane of Transmitter from Near Field Equation (3.4).


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 be

hind 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 non-

permeable 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, is the same force that (/* - /i0) (if • v ) H

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


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 environ

ment 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


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, some

times 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 Successfu l D e c o u p l i n g due to D i a m e t r a l Des i gn

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 near-

field equation (Section 3.3) is:

where HZ\WF is evaluated at z" = I, in the plane of the receiver and R.R is the radius of

the receiver.

The signal induced in the one semicircle of this configuration is then:

winding of this coil. This "figure-eight" configuration is widely accepted as a means of

(3.5)

(3.6)

The total signal from both semicircles is hopefully close to zero, due to the counter series


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 vi

brations 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 be

tween 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


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 vibration-

inducing flow inside the riser. This quadrature multiplication complements the diametral

configuration because it reduces the noise generated by coil distortion, due to the vibra

tions.

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>0, was obliterated, after multiplication and then averaging. The strategy

pursued here is exactly the opposite to that earlier approach. Purposely the receiver

signal was multiplied by another signal, c4l5 adjusted to approximately 90° out of phase

with d>0, so that the whole signal is obliterated after averaging. Any physical distortion

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 c6a until the effects of the vibrations

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


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 ever-

present 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, mz, is out of phase, while that due to the quadrature

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, be

cause, for the size of tracer particle being used, 6.35 mm diameter, the quadrature com

ponent of the response, at this frequency, was still to the left of the maxima on the

non-permeable curve in Figure 1.5. An 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 2 a 2 | , equals 11.61 for a solid sphere, the imaginary part

Figure 3.8: Ratio of Imaginary Response to Exciting Field for a Sphere at 6 kHz.


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). By 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 From Electric Field 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


assumed to be associated with the build-up and discharge of electrostatic charges within

the CFB 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 de

pends 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 mo

mentarily 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 Limitations of the E M I Technique

3.5.1 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.


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 Min imum 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 RTD of the largest coal particles in the various regions, but also to determine how

that RTD changes as the coal particles decrease in size in the process of burning. These


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 T Oi n, given by:

^m(X+iY) ( 2 c w \ 3

=

6 0.4 ' V6.35 x IO" 3 /

where: Xm(X -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 re

sponse 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


used (within the quasi-static limitation discussed in Section 1.3.1), if the coil had corre

spondingly 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 mini

mum 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 No i s e

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


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 = current in the transmitter coil

where % — current in the receiver coil

The voltage induced in the receiver coil is then expressed by:

^ , r r , d<t> ,rdl TdM rdi .dL EMF = -f = M — + I— +L— +i—

dt dt dt dt 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


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 indi

cators, 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 sig

nificantly 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


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 ex

citing 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 de

velopment 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 AY

« . » \ O A ! O^SJ, Q.QA,


I2mzpQ/4:Tr — 2nd integral Equation (3.1)


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 di

ametral 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 pos

sibly 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 re

quire 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 = ^ o w r a ^ e through the local zone

W0 = net flow rate through the system

E [N] = mean number of visits to the zone per particle ft: ^ HiLi ni

with nt- = measured number of visits to the zone by the ith tracer, and m the total number

of tracers used in the test.


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 WCOTC -f Wannuius = W0, the corresponding values of E [N] must

add up to one. Because W i o c a i can be greater than W0, especially where there is internal

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 Work

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 EMI

technique and actual measurements in the CFB. 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 CFB 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 CFB.

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 CFB.

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 un

derneath 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 posi

tion. 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


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.


velocities. In order to attain a desired velocity, as the particle passed through the sensor,

the requisite height was calculated from the solution of:

/ w—dU = / dz = z (4.1) Jo n- Jo ^ '

where

U = velocity of particle

z — drop height, with initial particle velocity equal to zero

g = acceleration of gravity

m = mass of the particle = ^ d^pp for a spherical particle

-fdrag = drag force

= -C D for a sphere

with CD = £ (1 4- 0.173*e0-657) + l + l M % $ * - > . »

for Re = < 3.8 x 105 (SeviUe, 1989)

at 25 °C and 1 atm:

p = density of air = 1.177 kg/m 3

dp — diameter of a sphere

p = viscosity of air = 1.846 x 10 - 5 kg/ms

Equation (4.1) is based on a force balance on the particle:

dU

" i — = - ^ d r a g + 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.


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 Resu l t s

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.


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 f l a l s h e l l 4.9H/S

Test t z Cu sphere 4.9«'s

Test #3 fll s h e l l 3.3n/s

Test f4 Cu sphere 3.3R/S

Length of one v o l t a g e / t i n e u n i t

Test t s S h e l l s t r i k e s tube, bounces back

Figure 4.4: Actual Oscilloscope Traces for Local Response Tests.


prerorr 5s Teh

Test #6 S h e l l s t r i k e s tube, pass t h r u

Tes t #7 S e m i c i r c l e dichotomy

Vi prerorr g,es . T e J < Tek su proton B.S»

_ , .„ Test t9 K&JSed f i r s t peak t7) ft« ft™ ° P P ° s l t e S l d e

Figure 4.4 Actual Osciloscope Traces (Cont.)

apter 4. Experimental Work

Test #ie Quadrant synnetry

Test #11 Pass thru,bounc back and approach

su PcfttpcT e.ss T e l <

&2 Test i r _ Pass thruibounc back and approach

Test #13 Pass t h r u , bounce back, pass t h r u

Figure 4.4 Actual Osciloscope Traces (Cont.)


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, [°] Max. amplitude

r, [mm] of 1st peak, [v] Max. amphtude of 2nd peak, [v]

#1 6.35mm <j> Al shell dropped from 1.383m; Vp\ sensor = 4.9m/s 15 71.4 +10.4 -2.6 45 38 +7.4 - 2.0 90 38 +7.0 -2.0 90 71.4 +9.2 -2.4

#2 2.4mm <f> Cu sphere dropped from 1.383m; V^| s e nsor = 4.9m/s 15 50.8 +0.78 -0.20 45 38 +0.44 -0.14 90 38 +0.58 -0.18 90 71.4 +0.54 -0.18

#3 6.35mm <f> Al shell dropped from 0.567m; lp|sensor = 3.3m/s 15 71.4 +14.6 -4.2 45 38 +11.6 -2.8 90 38 +10.4 -2.6 90 71.4 +14.6 -3.6

#4 2.4mm <f> Cu shell dropped from 0.567m; V p | sensor = 3.3m/s 15 71.4 +0.66 -0.12 45 38 +0.98 -0.12 90 38 +0.50 -0.16 90 71.4 +1.04 -0.26

#5 same as #3, but shell strikes tube at r — 12.7mm and bounces back +10.0 -3.1


Table 4.1: Oscilloscope Signal During Drop Tests (Cont.)

Test Max. amplitude Max. amplitude

(9, [°] r, [mm] of 1st peak, [v] of 2nd peak, [v]

#6 same as #5, but shell strikes tube at r = - 71.4mm, glances off and spirals through sensor

+14.6 -14.4 #7 same as #3

45 38 +10.0 -2.6 -45 38 -10.2 +3.0

#8 no results #9 same as #3, but sensor turned over

45 38 +11.4 -2.8 #10 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 0 71.4 +1.48 -3.4

+ 15 25.4 +10.4 -2.6 +45 38 +11.8 -2.8

#11 same as #3, but particle passes through sensor, bounces back and approaches sensor, but does not pass through

45 38" +10.0 -3.8 1st signal +14.6 -13.8 2nd signal

#12 same as #11, but particle just reaches sensing region at z ~ 60mm

45 38" +10.6 -2.8 1st signal +2.4 -1.6 2nd signal

#13 same as, #3, but particle bounces through plane, then falls through again

45 38* +10.2 -3.0 1st signal +14.6 -5.4 2nd signal +10.8 -9.6 3rd signal

Position for initial pass-through


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 ra

dius perpendicular to the diametral tube, are the same, within positioning accuracy,

for a given velocity. (Test 10).


8. When a particle approaches the sensing plane and reverses direction, without pass

ing 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 D i s cuss i on

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 indepen

dent 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 depen

dence 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


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 un

known. 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 Techn ique i n the 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 A p p a r a t u s

Sca led C F B

The unit, in which -measurements were made, as well as all of its supporting infras

tructure, 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 clear-

acrylic 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 re

turn leg, allows control of the solids flux through the riser. The gas velocity is determined


Modified Butterfly Valve

Secondary Air

A i f O u t

Ptimmf Y * n d Secondary C y c l o n e *

Ground irrg ' s p i d e r

Storage Bed

Bubbttng (storage] Bed Aeration

Tangeotfal Opposed

n j e c i o r

s c a t 1 e-

Figure 4.5: Scaled Circulating Fluidized Bed (Brereton, 1987)


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:

1.6 x 102 , , 2 G, = 4.8 kg/ms 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

•It)

l-l-C I K E 11 o <xc nj l_ e o u> u^.«-i..-t cr in wo

TD . w—< O O I C I P W »>-•»-.-< l_ C

CL O-Oi

O T 3 N O—•

cn a a.

c ~-< N

o>

a o / 1

xt «» *» w •oro -a aj

Pt o •oc

(U<U IAO <nw u c_r£ e o

Lf :> ai a

o

O

O

ci B o

CO

H Pi bO

E


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


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 proper

ties, 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 con

veying. 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).


Table 4.2: Properties of F-75 Ottawa Sand (Burkell, 1986)

Property Ottawa Sand

Mean Particle Diameter, dp pm 148

Particle Density, pp kg/m 3 2650

Bulk Density, pb kg/m 3 1550

Loose Packed Voidage, e 0.42

Particle Terminal Velocity, Ut, based on air properties at 25°C m/s

0.99

Archimedes Number 290

Umf Calculated m/s 0.023

Umf Experimental m/s 0.021

Bulk Density at Minimum Fluidization, pmf kg/m 3

1500

Bed Voidage at Minimum Fluidization, emf

0.43

Angle of Repose 29°

3oJ i • • ' • i • • • i i i i i • 1 ' • 0-1 O.T / £ 5 /O go da 4o So 40 70 so 90 J6J9 JW

_ S p e c s , f o r F?5 'Ottawa C u m u l a t i v e A s m a l l e r O sand <0CL I n c . ) t h a n d i a m e t e r A A v e r a g e o f 4 L - v a l v e ^ samples Q Samolp f r o m r i s e r

Figure 4.7: Cumulative PSD of F-75 Ottawa Sand


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 3 . Using the method (Grace, 1986) given in Appendix E, the terminal

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 kg/m 3 , to simulate what

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 CFB system.

The calculated quadrature response of the aluminum shell tracer is shown in Fig

ure 3.8. This is only an approximation because:

1. The conductivity of the aluminum can only be crudely estimated at 2x 107 mhos/m

(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.


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 CFB. 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


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.


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 Resu l t s

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


Table 4.3: Schedule of Experimental Runs

Sensor at 1.63m below outlet pipe centerhne, 7.64m above the distributor of column.

Solids Flux u. Gs kg/m 2s 7 m/s 9 m/s

14.3 #3 #7

35.4 #1 #5

56.6 #2 #4-

68.9 #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 _ 1). The histograms, grouped by nominal


Figure 4.8: Choking Regime for Sand in 0.15m Diameter Riser (data points from Brere ton, 1987).


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 D i s c u s s i o n

The time-of-flight histograms are discrete representations of continuous frequency densi

ties, 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

http://overa.ll


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r 4 8 1 2 1 6 2 0 2 4

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Figure 4.9: Time-of-Flight Histograms C F B Tests.


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-of-

flight 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 stud

ied entrainment from Bubbling fluidized beds, suggests that large particles are conveyed

upward as a result of momentum interchange during collisions with fast-moving fine par

ticles. 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/m2s, at both gas velocities,

the histograms shift to shorter times, indicating an increase in tracer velocity compared


to that measured at the 14.3 kg/m2s circulation rate. Geldart's work, however, did not

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/m2s. This

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/m2s threshold. Geldart et

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 of fines flux 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


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 macro flow structure, 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:


(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 con

necting 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 de

tailed 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 inde

pendent. 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 infor

mation, 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 trajecto

ries 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 re

sults 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 trac

ers 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 CFB 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.


5.2 Recommendations for Future Work

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 modi

fied 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 axialry-

displaced 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 pass

ing 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


work described here to install multiple sensors, of the present design, along the length

of the riser in order to obtain RTD 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


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 deter

mined. 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 search

ing 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 con

tingency tables, for example, it could be ascertained if certain groups are statistically

independent of neighboring groups. For example, the RTD 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. However, two regions in the dilute section probably

have related distributions. If regions are found to be statistically independent, then


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 O v e r a l l C o n c l u s i o n s

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 RTD 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


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 CFB 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, sug

gests that inter-particle collisions are responsible for the conveyance of these tracer

particles through the riser.

N o m e n c l a t u r e

Symbol Definition Units

A characteristic coefficient of non-Ohmic conductor -a radius m amin radius of smallest spheres giving desired response m

Ar Archimedes number = pg (pg — pg)g dp

3 /u.g

2 -

B, Bz magnetic field/flux density, z-component Wbm - 2

b outside radius of shell m

CD drag coefficient -CP, CB capacitance (paralle, series) F

D demagnetization factor -d" dimensionless diameter (Figure 1.2) -dp diameter of particle . • m

E(N) mean number of visits to zone per particle -EMFc, EMFn electromotive force generated in circumferential, V

diametral coil EMFCT electromotive force in conductor due to current V

in transmitter

F ^ drag force N Fi Lorentz force N / frequency Hz

G3 solids flux kg/m2s g acceleration due to gravity m/s2

H, Hj, magnetic field strength A m - 1

He coercive field strength A m - 1

H, saturation field strength A m - 1

HZ\NF z-component of field calculated using the near A m - 1

field equation

142


current, in secondary coil

\K2a2\ kA

L I

response parameter fraction of total flux generated by A passing another coil

coefficient of coupling between coils A and B

inductance axial distance between coils

H m

M, Ms

M, MAB

m m , " I s h e l l , mz

NA

n n

magnetic dipole moment per unit volume, A m - 1

at saturation mutual inductance, between coils A and B W b A - 1

mass of particle kg dipole moment, of shell, z component Am 2

number of turns in coil A characteristic exponent of non-Ohmic conductor -number of free charges per unit length C m - 1

Q Q

R R, RL -Rioopj RR

Re _ _ »

Ar

quality factor -charge C

radial position of tracer m resistance, of inductor Q radius of loop, of receiver m Reynolds number = pgdpU/fig -radial distance, relative to transmitter coil m radius of coil, of particle m shell thickness m

dS incremental area m

t time

u,ut

u,ug

ue

particle velocity,terminal m/s gas velocity, superficial m/s total magnetic potential A dimensionless velocity (Figure 1.2),terminal

143


Vp, Vpz particle velocity, z-component m/s v velocity vector m/s

W mass flow of gas through orifice kg/s Wiocal mass flow rate of solids through local region kg/s W0 mass flow rate of solids through system kg/s

XL, XC inductive, capacitive reactance Q X - f iY complex response function -

z, zi, z', z" axial or vertical position, relative to loop, relative to receiver, relative to transmitter

m

a UJL/R a a, fi0 Ar b s

8 angle rad

6 angular position of tracer rad v, v" angular position, relative to rad

transmitter coil

A wavelength m

fi, fio permeability of freespace Hm"1

p - y/x2 Ar y2 m p, Pp, pg density, of particle, of gas kg/m3

cr, <Te condcutivity, of the shell mhos m

<f> magnetic flux Wb (j>o, <f>\ phase angles rad

u> angular frequency s _ 1

144

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Appendix A

Dipole Moment of a Non-Permeable Thin Shell Based on Ue

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.

Ar « 8, = (-2— V (A.l) \o-.fiwJ

For the opposite extreme, Ar » 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, Ue, at point (r, 6) in the medium

external to a hollow shell as:

2n + 1 = ANQI f_l ^ n b2n+1

1 ^ l R ,7=i n + 1 £ n + 1 r n + 1 [ In Ar 1 + iaw.

where

A = cross sectional area of thin solenoid

Af0 = 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,(i0Arb (assuming / i s h e U = fi0)

d = shell thickness

P n ( c O S 0 )

154

file:///o-.fiwJ

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, H0> is:

2 r 2 1

3 + iocw.

The corresponding magnetic field components are:

H0 cos 6

Hr =

He

6Ue -b 3 r

dr

rd6

1 -

lb*_ 2 r 3

1 -

3 + iavj.

3

3 + ictw.

Hn cos 6

Ho sin 6

The field around a magnetic dipole given by Plonsey (1961) is:

5=^= m (2 cos 6 ar -f sinfl a e) fio Airr3

By matching components in Equation (A.2) and (A.3), it can be shown that

3

(A.2)

(A.3)

= ^ b

155

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 Circumfer

ential 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}rstem is (it, 6, —z{). 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

1 5 6

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 = vector from the particle's position to (r, v, 0) from the loops centre Then:

p = | p | = J(r cos v — R cos 6)2 + (r sin v — R sin 6y (B.l)

B.2 Integrands and Inner Integrals of Equation 2.4

Based on the assumption in that the exciting field, and therefore mz, are uniform in

space, the z-component of Equation (2.1) is differentiated resulting in:

8BZ pomz

8z 47T

(/) 2 +z 2 )4z-(2z 2 -^)5z

{p2 + z2)i

Simphfying, making the transformation in Equation (B.l), as well as z = zj, the first

integrand in Equation (2.4) becomes:

9z/r 15zjV" dBz Pomz

-T = dz 47T (B.2)

157

where Q = p2 + z2 = r2 - [2#(cos Ocosv + sin (9 sin «)] r 4- (#2 + )

Similarly: dBT 2z2 - p2

dmz AT ^ 2 + 2 2 p

and the second integrand in Equation (2.4) becomes:

dBz mz- r am.

p0mz

AT

3z2r r

0\ The inner integrals of Equations (2.4) and (3.1) are then:

dBz

dz rdr p,omz

AT

15z?

|9zz

-VQ 5aQ3

-VQ 3aQ2

- - / 2a J

ZaJ

dr

2a J Q2VQ dr 1],.

Q3VQ\

(B.3)

where a, b, c

J Q2VQ r dr

J Q3y/Q

k

I dBz

mz— rdr dm.

p.0mz

+

AT

2br +4c qVQ .

Zz2

coefficient of quadratic Q

2 ( 2 " - + 6 ) (± , ou\

2 ( 2 a r + f c ) V ^ , 4* r dr

SqQ3 •• S J 0*,J

Aac - b2

Aa

upper hmit of integration

lower hmit of integration

-VQ _b_ j dr 3aQ2 2a J Q2VQ

When q = 0 the inner integrals are:

f Ê±rdr\ - •fJL°rnz

Jr dz Q~° AT

-1 + 3 ( s+ ' ) 8 a ( i + r ) _

158

I5zf 7

a 5 i r ,

dBz mz— rdr umz

g=0 u,0mz J Szf

47T 1 a 2

+

1 3

0 2

-1

3 ( £ + > \ ) 3 8 g (^+^) 4 .

6

B.3 Justification of the form of Equation 3.1

For a tracer approaching one semicircle (0 < 6 < TT) the contribution due to that semi

circle is:

fir roo r2ir foo - INTD drdv + / / INTD dr dv

JO JR, JIT JO loop

The contribution due to the other semicircle is:

(B.4)

P P00? INTD drdv (B.5) Jir 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 contri

bution 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] rlir poo / / l o o p INTD drdv+ / INTD dr dv

Jir Jo Jir JR-I loop

The total contribution is then:

rir foo f Z i r oo flir pR-i EMFD = / / INTD drdv+ / INTD drdv + 2* / l o o p INTD dr dv

Jo JR* JIT JR, JV JO loop loop

Since the first two terms are equal to EMFc, this equation is the same as Equation (3.1).

159

Appendix C

Calculation of Superficial Gas Velocity (Ug) from Orifice Measurements

Considine (1957) gives the equation for the mass flow of gases through an orifice as:

W = CmvKYFad2-Jhî (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 = CsiKYd2 = \f&p~^ (C.2)

The units for the two equations are, respectively:

358.98 H H H i n ' i n ^ o ^ ) '

Multiplying the former equation by:

• ( 1kg lh \ \ 2.21b 3 6 0 0 s /

and then setting it equal to the latter, allows C$i to be calculated. It is equal to

1.1106 kg/s 2m. The values of the other variables in Equation (C.2) are:

160

7 = Pup* m.w. 8314 T

Y = 1- (0.41 +0.35 *£ 4)-=-g * A P v P u p

A" = i\>*(l+6*A)

A = 1000 -(4 * / / ) / ( 7 r * / x * J D p i p e ) i

b = (0.002 + 0.026 *B4)* K<f>

K<t> = 0.6004 + 0.35 + B4

B = d/Dpipe

where

d — orifice diameter

0.5 < B < 0.7

m.w. = molecular weight of gas = 28.9 for air

T = operating temperature (°K)

Pup = pressure upstream of the orifice (Pa)

A P = differential pressure across orifice (Pa)

Cp/Cv — 1.4 for a diatomic gas such as air

For a given set of (P u p , A P ) at given operating conditions, Equation (C.2) can be

solved iteratively for W. The value of Ug in the 152.4 mm ID riser, at a temperature T

(degrees K) at a pressure of 1 atm., is then determined by:

Ug\'T = W*42.483

161

Appendix D

Multiplication of Two Sinusoids Followed by Integration

Let the product of the two signals be represented by:

f(t) = A s in^f ) * B sin(u;2< + B)

where

A,B = amplitudes of the two signals

i v i , u } 2 — frequencies of the two signals

8 = 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;2<) cos B + sin (wit) cos (u>20 sin 6} (D.l)

The product is integrated over time, and, if the two signals have the same frequency,

Wj = UJ2 = u, the integral is:

1 = AB cos 6 f sin 2u}t \ sin 3 /1 cos 2wt \ 1

2 V1 2 J + ~2~ \2 ' 2 J J

If the two signals are in quadrature, 0 — , Equation (D.2) becomes:

(D.2)

I = ABl-{1--2 V2 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 2WT I = AB- (CUT -

2 A 2

162

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 Equa

tion (D.l) is:

r2it

I\ — AB cos/3 / sm(wit) sm(cj2t)dt = 0 (wj ^ u;2) Jo

while the second term is given by:

/ • 2 7 T

I2 = AB sin/3 / sm(u>it) cos(u;2t)dt = 0 Jo

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:

p{pp ~ p)g d" = d

A dimensionless terminal velocity is defined in terms of d", depending upon the flow

regime. In the Stokes' regime, where:

Ret < 0.8, d' < 2.5

the value of J7t" is ^ . In the Newton's law regime, where:

750 < Ret < 3.4 x 105, 60 < d" < 3500

the value of f/t* is 1.73\/d~. The value of the terminal velocity. Ut, is calculated from C/t"

using:

ut = I1{pp-P)9.

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 kg/m 3 for air at S.T.P.

p = viscosity of the gas = 1.846 x 10 - 5 kg/ms for air at S.T.P.

g = gravitational constant = 9.81 m/sec2

d = diameter of the sphere (m)

164

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:

The null hypothesis, H0, that the two samples come from the same population, is tested

by determining, at the 5% significance level, if:

Wn = 5 + 11 + 14 + 18 + 19 . . . + 130 = 2035

^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% signifi

cance 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 Which of Runs 1 Through 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 ANOVA 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, H0, that the

tests under consideration all have the same distribution. The hypothesis is accepted if a

summary statistic, U, equal to:

i J Ea

is less than the value of %2, at some arbitrary significance level (e.g. 0.05) and at (I —

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 %2 test can be safely

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:

EH =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 2s, are from a

different population than the results at the higher fluxes.

167

Table F . l : Number of Observations bj' Time Intervals.

> 3 > 5 > 7 > 9 Run < 3s < 5 < 7 < 9 < 11 > 11 Total

1 8 27 26 13 6 19 99 2 11 25 21 15 8 20 100 3 2 13 11 8 12 53 99 4 58 32 8 1 0 0 99 5 43 39 9 8 1 0 100 6 54 32 9 3 2 0 100 7a 23 40 15 8 3 11 100

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 0.015 0.028 O.C 43

P|4,5,6 0.518 0.344 0.087 0.040 0.010 0 O.C 50

Tests Considered U Degrees of Xo.05,d/ Ha

Freedom (df)

1,2,3 , 46.1 10 18.3 reject 1,2 •1.5 5 11.1 accept 4,5,6,7a 58.7 12 21.0 reject 4,5,6 9.8 6 12.6 accept

168

Table F.2: Measured Peak Times, Run l-7b.

Run #1 Ug = 7.12 m/s, 35.43 kg/m 2 s

Peak Particle Appearance

No. Times (sec) 1. 4.15 26. 5.33 51. 2.26 76. 3.16 2. 5.14 27. 3.02 52. 6.63 5.16 3. 5.78 28. 6.44 53. 4.32 6.52 4. 6.01 29. 7.55 54. 11.28 77. 5.43

9.26 30. 4.24 55. 11.82 78. 5.75 10.29 6.88 56. 16.94 79. 3.50

5. 6.41 7.98 57. 6.63 80. 2.26 6. 13.86 31. 22.00 58. 5.57 5.08 7. 9.26 32. 2.22 59. 10.61 5.84 8. 8.93 7.61 60. 7.96 81. 7.48 9. 5.95 9.00 61. 3.07 82. 3.81 10. 3.88 33. 7.03 62. 3.72 83. 5.82 11. 3.86 34. 5.56 63. 7.94 84. 12.58 12. 13.11 35. 2.68 64. 9.62 85. 4.35 13. 11.24 36. 12.80 65. 4.01 86. 4.10 14. 11.36 37. 11.58 66. 3.12 87. 4.28 15. 3.68 38. 13.52 67. 7.88 88. 7.22 16. 4.30 39. 19.14 68. 19.91 89. 2.70 17. 3.49 40. 4.55 69. 7.28 90. 6.38 18. 4.38 41. 6.50 70. 6.49 91. 12.10 19. 9.92 42. 5.60 71. 6.63 13.56 20. 12.86 43. 6.88 72. 5.10 13.70 21. 2.96 44. 8.05 73. 6.74 92. 2.78 22. 4.24 45. 6.38 74. * 93. 14.68 23. 7.37* 46. • 5.52 75. 6.86 94. 7.47 24. 18.27 47. 2.09 95. 5.81 25. 11.98 67.02 96. 4.44

48. 10.00 97. 3.66 49. 4.64 98. 3.50 50. .4.58 99. 8.18

100. 10.86 12.42 12.56

* oscilloscope failed to trigger 169

Table F.2 (continued) Run #2 Ug = 6.99 m/s, G, = 56.57 kg/m2s

Particle No.

Peak Appearance Times (sec)

1. 4.61 26. 11.13 51. 8.12 76. 9.04 2. 7.44 27. 4.14, 4.34 52. 8.39 77. 6.38 3. 6.29, 6.43, 28. 5.28, 7.50, 53. 14.30 78. 19.30

6.92 8.87 54. 1.62 79. 8.21 4. 3.28 29. 3.21 55. 5.44 80. 7.01 5. 9.59 30. 17.53, 19.15, 56. 2.67 81. 19.05 6. 4.93 20.64 57. 25.62, 27.08, 82. 11.35 7. 23.57 31. 8.86 31.08, 33.37, 83. 10.75 8. 4.44 32. 4.58, 4.88, 34.22 84. 2.81 9. 3.96 7.81, 8.54 58. 12.76 85. 5.98, 7.96 10. 5.94 33. 6.86 59. 13.90 86. 3.16 11. 11.70 34. 11.06 60. 6.06 87. 11.44 12. 9.30 35. 2.34 61. 6.58 88. 3.97 13. 4.57 36. 10.92 62. 5.24 89. 8.57 14. 9.82, 13.24 37. 6.35 63. 10.96 90. 7.25 15. 5.92 38. 4.61 64. 4.14 91. 4.43 16. 5.48 39. 5.72 65. 7.23 92. 12.32 17. 6.18 40. 3.62 66. 4.98 93. 3.46 18. 1.78 41. 2.34 67. 4.25 94. 16.24 19. 7.02, 8.30 42. 1.68 68. 4.06 95. 8.29, 10,48, 20. 12.92 43. 4.84, 8.94, 69. 16.33 10.86 21. 2.48, 4.44, 10.81, 13.01, 70. 4.10 96. 7.52

4.84, 8.42 15.59 71. 2.51 97. . 6.76 10.01 44. 9.34 72. 8.05 98. 8.81

22. 8.82, 9.20' 45. •2.48 73. 11.50 99. 4.04 23. 3.82 46. 12.68 74. 3.52 100. 12.34 24. 5.06 47. 6.78, 9.20, 75. 5.44 25. 3.83 9.55

48. 2.74 49. 5.48 50. 6.10

170

Table F.2 (continued) Run #3 Ug = 7.09 m/s, Gs = 14.28 kg/m 2s

Particle No.


1. 7.08 26. 6.45 51. 11.50 76. 14.74 2. 51.22 27. 7.54 52. 10.97 77. 13.36 3. 11.45 28. 3.50 53. 18.60 78. 14.52 4. 23.05 29. 8.49, 10.26, 54. 50.92 79. 6.61 5. 20.90 12.17 55. 7.24, 7.86 -80. 39.56 6. 75.70 30. 3.70 56. 33.98 81. 6.42 7. 6.73 31. 19.01, 23.28, 57. 11.40 82. 70.86 8. 4.52 23.57 58. 12.91 83. 21.11 9. 38.08, 38.50, 32. 51.33 59. 4.69 84. 30.44

38.63 33. 18.80 60. 30.49 85. 16.22, 16.69 10. 56.93, 65.34, 34. 22.15 61. 3.48 86. 5.96

65.47 35. 9.23, 9.97, 62. 15.22 87. 13.72 11. 9.36 10.13, 10.32, 63. 9.70, 13.74, 88. 9.62 12. 6.54, 7.83, 10.82 15.93 89. 9.50

7.95, 10.25, 36. 16.12 64. 13.48 90. 10.00, 13.73, 10.72, 11.10, 37. 4.24 65. 26.33 91. 4.62 14.94, 15.23 38. 29.04 66. 3.40 92. 10.32, 11.58,

13. 49.85 39. 26.11 67. 12.70 12.49 14. 9.44 40. * 68. 3.37 93. 25.34 15. 19.13 41. 5.22 69. 7.48 94. 2.56 16. 7.52 42. 5.92 70. 18.67 95. 3.66 17. 10.76 43. 5.34, 5.50, 71. 18.17 96. 58.65 18. 17.08 5.93 72. 11.56 97. 15.82, 16.06 19. 31.14 44. 34.36 73. 8.80 98. 16.52 20. 4.25 , 45. 15.22, 16.78, 74. 14.30 99. 4.36, 5.77, 21. 4.38 " 16.94 75. 25.12 100. 4.23 22. 14.90, 15.10, 46. 18.02

15.39, 17.66, 47. 9.90 18.46 48. 5.31

23. 8.26 49. 9.90 24. 5.88 50. 13.21 25. 12.18

* no show - unexplained

171

Table F.2 (continued) Run #4 Ug = 9.18 m/s, G, = 56.31 kg/m 2s

Particle No.


1. 2.02 26. 2.99, 5.09, 51. 2.21 76. 2.46 2. 2.64 5.35 52. 2.98 77. 2.98, 3.24, 3. 6.07 27. 2.52 53. 3.05 3.58, 5.86 4. 2.41 28. 4.35 54. 3.00, 3.82, 6.81 5. 4.72 29. 1.93 3.98, 4.27 78. 1.64 6. 3.62 39. 2.66 55. 2.52 79. 2.11 7. 2.99 31. * 56. 7.35 80. 1.26 8. 5.31 32. 3.78 57. 1.50 81. 2.59 9. 5.47 33. 2.49 58. 1.40 82. 5.19 10. 2.04 34. 2.15 59. 2.36 83. 2.73 11. 4.26 35. 2.75 60. 4.90 84. 2.56 12. ' 3.08 36. 2.08 61. 3.02 85. 3.64 13. 2.62 37. 3.88 62. 2.48 86. 2.73 14. 1.85 38. 3.52 63. 4.23 87. 3.43 15. 3.90 39. 3.37 64. 4.72 88. 1.71 16. 2.83, 3.17 40. 3.24 65. 4.71 89. 3.01 17. 1.79 41. 2.89 66. 5.14 90. 3.54 18. 4.34 42. 1.77 67. 5.66, 7.30, 91. 3.13 19. 1.93 43. 3.25 8.08 92. 2.82 20. 3.05 44. 1.93 68. 4.28 93. 1.90 21. 1.94 45. 4.00 69. 2.78 94. 1.52 22. 3.94 46. 1.57 70. 1.69, 3.69 95. 1.88 23. 5.67 47. 2.22 71. 2.02 96. 2.54 24. 1.50* 48. • 2.45 72. 1.96 97. 3.43 25. 3.06, 3.52, 49. 1.58 73. 2.39, 7.54 98. 5.31

3.81 50. 1.44 8.23 •99. 1.58 74. 3.30 100. 2.15 75. 3.26

* oscilloscope shut off - due to electrostatic charges?

172

Table F.2 (continued) Run #5 UB = 9.15 m/s, G, = 37.4 kg/m2s

Particle No.


1. 8.37 26. 4.86 51. 1.66 76. 4.68 2. 2.96 27. 1.97 52. 4.37 77. 3.68 3. 3.66 28. 5.22 53. 4.71 78. 2.34 4. 7.28 29. 3.66 54. 4.71 79. 1.79 5. 2.65 30. 2.39 4.89 2.36 6. 3.80 31. 3.82 5.23 80. 4.02 7. 5.88 32. 4.48 5.60 81. 2.35 8. 3.22 33. 3.14 55. 2.86 82. 1.66 9. 4.56 34. 2.00 56. 1.53 83. 2.05 10. 8.10 35. 4.72 57. 3.06 84. 4.02 11. 1.67 36. 2.54 58. 2.12 85. 1.89

3.26 37. 3.58 59. 5.63 86. 3.10 12. 4.16 38. 1.78 60. 3.73 87. 3.63 13. 4.06 39. 2.89 61.' 1.26 88. 7.10 14. 2.24 40. 1.54 3.29 89. 6.05 15. 5.02 41. 4.34 4.08 90. 2.66 16. 10.08 42. 2.44 6.31 91. 1.72 17. 4.01 43. 3.16 6.44 92. 2.10 18. 5.59 44. 2.00 62. 2.47 93. 3.99 19. 2.52 45. 3.45 63. * 94. 2.84

2.82 46. 2.43 64. 3.22 95. 1.74 3.36 47. 8.07 65. 6.06 96. 1.70

20. 3.60 48. 3.20 66. 2.30 97. 3.05 21. 1.54 49. 3.57 67. 2.05 98. 1.94 22. 1.88, 50. 7.94 68. 1.43 99. 1.99 23. 3.14 69. 1.84 100. 2.84 24. 5.58 70. 3.08 101. 4.94 25. 7.52 71. 8.09

72. 6.45 73. 2.52 74. 3.50 75. 3.29

5.60

* no show - injection malfunction

173

Table F.2 (continued) Run #6 Ug = 9.04 m/s, G, = 68.9 kg/m2s

Peak Particle Appearance

No. Times (sec) 1. 3.635 26. 2.37 51. 2.53 76. 2.13 2. 2.440 27. 4.76 52. 2.79 77. 3.49 3. 1.845 28. 1.96 53. 9.27 78. 3.14 4. 2.670 29. 2.00 14.21 79. 3.59

4.775 30. 1.76 15.30 80. 2.73 6.150 31. 3.26 54. 2.92 81. 3.02

5. 2.20 32. 1.30 55. 5.93 82. 3.87 6. 3.250 33. 5.13 56. 2.24 83. 2.99 7. 2.885 34. 2.43 57. 3.98 84. 2.45 8. 2.375 35. 2.66 58. 4.54 85. 6.15

4.37 36. 5.24 59. 2.48 86. 2.82 9. 3.07 37. 9.92 60. 2.73 87. 8.22 10. 2.43 38. 3.26 61. 2.22 88. 7.35 11. 2.89 39. 3.05 4.79 89. 2.67 12. 3.52 40. 2.27 6.03 90. 1.75 13. 4.03 41. 1.97 62. 2.07 91. 3.04 14. 3.00 42. 2.08 63. 2.02 4.90 15. 4.87 43. 1.69 64. 2.60 5.34 16. 1.70 44. 2.44 65. 3.16 92. 2.64 17. 1.86 45. 1.74 66. 3.41 93. 4.90 18. 6.45 46. 4.38 67. 5.50 94. 2.69 19. 5.74 47. 4.74 68. 2.94 95. 3.23

6.44 48. 2.22 69. 2.36 96. 1.55 7.31 49. 6.55 70. * 97. 1.93

20. 3.77- 9.06 71. * 98. 3.21 21. 4.57 10.03 72. 2.43 99. 4.07 22. 1.97 50. 3.94 73. 4.20 100. 4.59 23. 1.73 4.37 74. 2.97 101. 1.63 24. 2.00 75. 4.96 102. 6.45 25. 8.33 10.84

11.49

* particle didn't appear - injector malfunction

174

Table F.2 (continued) Run #7a Ug = 8.9 m/s, G . = 14.3 kg/m2s

Particle No.


1. 4.11, 4.70 26. 3.82 51. 3.38 76. 2.57, 5.02 2. 3.05, 5.54 27. 9.48 52. 5.31 5.32, 16.14

5.70 28. 2.62 53. 15.04 18.02, 23.26 3. 5.66 29. 3.68 54. 4.98 28.18 4. 16.63 30. 6.55 55. 17.42 77. 5.76, 21.72 5. 5.58 31. 2.76 56. 8.87 78. 2.93, 21.72 6. 12.40 32. 6.70, 8.32 57. 4.70 79. 2.75, 4.40 7. 4.74, 6.22 33. 5.56 58. 3.78 5.18, 8.18

6.34 34. 2.88, 27.16 59. 4.68 8.61 8. 3.32, 11.80 43.58 60. 8.90 80. 3.54

21.39 35. 7.40, 28.47 61. 14.26 81. 3.28 9. 4.40 53.16 62. 6.10 82. 10.23 10. 1.78 36. 2.89 63. 5.64 83. 3.15, 4.82, . 11. 1.68 37. 8.97 64. * 6.27, 7.64, 12. 3.72, 10.36, 38. 4.21 65. 2.82 8.08

14.91 39. 5.72 66. 5.95 84. 14.02 13. 4.97 40. 1.88 67. 3.96 85. 3.18 14. 3.82 41. 2.44 68. 4.69 86. 4.28

' 15. 2.55 42. 3.05 69. 8.40 87. 2.48 16. 2.85 43. 3.05 70. 9.46 88. 3.96 17. 3.68 44. 2.62, 3.97, 71. 6.55 89. 4.39, 8.76, 18. 4.90 4.78, 5.96, 72. 5.32 9.03 19. 5.00 6.50 73. 3.26 90. 7.30 20. 2.94 45. 2.43 74. 1.68 91. 11.12, 15.12, 21. 12.37 46. 3.24 75. 17.98, 37.36, 15.53, 15.97 22. 2.66, 4.30, 47. 3.00 40.50, 45.74 92. 4.10

4.50 48. 4.20 93. 3.28 23. 2.47 * 49. .7.64 94. 5.18 24. 8.06 50. 4.32 95. 4.52 25. 26.51 96. 4.94

97. 4.92 98. 12.74 99. 2.33

100. 3.50 5.06 5.66 101. 6.59 11.33 32.06 35.54 39.64 47.38 54.18

* particle didn't appear - injector malfunction

175

Table F.2 (continued) Run #7b Ug = 8.9 m/s, G, = 14.1 kg/m2s

Particle No.


1. 2.26 26. 3.42 51. 76. 2. * 27. 3.11 52. 77. 0 o. * 28. 3.80 53. 78. 4. * 29. 4.92 54. 79. 5. * 30. 6.88 55. 80. 6. t 31. 5.73 56. 81. 7. 9.12 32. 18.22 57. 82. 8. 3.10 33. 9.94 58. 83. 9. 10.53 34. 2.60 59. 84. 10. 3.20 35. 12.19 60. 85. 11. 3.28 36. 2.74 61. 86. 12. 2.74 37. 62. 87. 13. 3.45 38. 63. 88. 14. 3.93 39. 64. 89. 15. 12.96 40. 65. 90. 16. 3.14 41. 66. 91. 17. 9.50 42. 67. 92. 18. 2.53 43. 68. 93. 19. 2.88 44. 69. 94. 20. 4.991, 6.65, 45. 70. 95.

7.49 46. 71. 96. 21. 3.63 47. 72. 97. 22. 3.23. 48. 73. 98. 23. 10.74 49. 74. 99. 24. 3.75 50. 75. 100. 25. 3.84

* particle didn't appear - injector malfunction f injector jammed - clean & restart

176

William M. Goldblatt - Open Collections

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