measurement of bubble behavior and heat transfer in a fluidized bed …whitty/documents/siddoway...

MEASUREMENT OF BUBBLE BEHAVIOR

AND HEAT TRANSFER IN A FLUIDIZED BED

HAVING HORIZONTAL HEAT EXCHANGE TUBES

by

Michael Siddoway

A thesis submitted to the faculty of the Department of Chemical Engineering

in partial fulfillment of the requirements for the degree of

Bachelor of Science

Institute for Combustion and Energy Studies

The University of Utah

May 2006

ii

Table of Contents

Abstract.............................................................................................................................. iv

1. Introduction................................................................................................................. 1 1.1. Black Liquor Steam Reforming .......................................................................... 1 1.2. Cold Flow Modeling........................................................................................... 1 1.3. Objectives ........................................................................................................... 1

2. Literature Review ....................................................................................................... 3

2.1. Flow in Beds with Horizontal Tube Banks......................................................... 3 2.2. Particle Segregation ............................................................................................ 3 2.3. Heat Transfer in Beds with Heating Tubes......................................................... 4

3. Experimental Methods................................................................................................ 5

3.1. Scaling Parameters.............................................................................................. 5 3.2. Fluidized Bed Description .................................................................................. 6 3.3. Particle Description........................................................................................... 10 3.4. Minimum Fluidization Velocities ..................................................................... 10 3.5. Bubble Voidage and Frequency........................................................................ 11 3.6. Segregation ....................................................................................................... 16 3.7. Heat Transfer from Heaters to Bed................................................................... 18

4. Results and Discussion ............................................................................................. 23

4.1. Minimum Fluidization Velocities ..................................................................... 23 4.2. Bubble Voidage and Bubble Frequency ........................................................... 25 4.3. Segregation ....................................................................................................... 29 4.4. Heat Transfer .................................................................................................... 34

5. Conclusions............................................................................................................... 41

5.1. Bubble Voidage ................................................................................................ 41 5.2. Segregation ....................................................................................................... 41 5.3. Heat Transfer .................................................................................................... 41

6. References................................................................................................................. 43

7. Appendices................................................................................................................ 44

7.1. Voidage Plots .................................................................................................... 44 7.2. Voidage Tables ................................................................................................. 69 7.3. Segregation Data............................................................................................... 94 7.4. Heat Transfer .................................................................................................... 96

iii

List of Figures Figure 3-1 - Rendering and Photo of the Cold Flow Fluidized Bed....................................6 Figure 3-2 - Diagram of Distributor (Dimensions in inches) ..............................................7 Figure 3-3 - Photo of Distributor in Empty Bed ..................................................................8 Figure 3-4 - Diagram of Tube Banks (Dimensions in Inches).............................................9 Figure 3-5 - Photo of Tube Bank Region of the Bed...........................................................9 Figure 3-6 - Diagram of Bubble Detector Probe ...............................................................12 Figure 3-7 - Theory Behind the Design of Bubble Detector .............................................13 Figure 3-8 - Voidage Calibration Curve for 180 to 250 Micron Particles.........................14 Figure 3-9 - Photo of Tube Bank Region with Copper Tubes Installed ............................21 Figure 4-1 - Pressure Drop versus Velocity for 500 to 750 Micron Particles ...................23 Figure 4-2 - Pressure Drop versus Velocity for 180 to 250 Micron Particles ...................24 Figure 4-3 - Minimum Fluidization Velocities versus Particle Diameter..........................25 Figure 4-4 - Three Trials of Weight Percent of Large Particles at Different Heights

of the Bed without Tube Banks Installed......................................................31 Figure 4-5 - Weight Percent of Large Particles at Different Heights in the Center of

the Bed with Tube Banks Installed and Superficial Velocity of 1.07 ft/s.....32 Figure 4-6 - Weight Percent of Large Particles at Different Heights at the Walls of

the Bed with Tube Banks Installed and Superficial Velocity of 1.07 ft/s.....33 Figure 4-7 - Correlation of Heat Transfer Coefficients on Middle Tubes with Height.....36 Figure 4-8 - Average Heat Transfer Coefficients (W/m2·K) at Tubes at velocity of

1.07 ft/s .........................................................................................................38

List of Tables Table 3-1 - Operating Conditions in the Real Gasifier and the Cold Flow Model..............5 Table 3-2 - Thermal Conductivity Values .........................................................................19 Table 4-1 - Data used for Calculating Reproducibility......................................................27 Table 4-2 - Average Heat Transfer Coefficients of Each Tube Bank................................36 Table 4-3 - Heat Transfer Coefficient Correlations with Particle Size..............................37 Table 4-4 - Table of Average Heat Transfer Coefficients at Different Velocities ............39

iv

Abstract

To model the University of Utah black liquor gasifier, a cold flow model was built to

measure several of the properties at a small scale. Several properties were measured such

as minimum fluidization velocity, void fraction in the tube bundle region, segregation and

heat transfer. This was done for three different particle sizes, and three different

superficial velocities. The main conclusions were that most of the voidage was found to

be in the center of the tube bundles at the bottom, but as they reached the top, they were

more distributed. It was also found that the total voidage increased with elevation. It was

found that there was minimal segregation of particle sizes and operating conditions of the

experiments that were performed. It was found from the heat transfer experiments that

the heat transfer in the bed was fairly uniform, with the exception of the second heater

bundle. It was also found that as particles grow, the heat transfer coefficients decrease.

It is recommended that the findings that were found in these studies be analyzed

during the maintenance of both the University of Utah and Georgia-Pacific’s Big Island

Unit. The findings may show that the problems that are being experienced may be

caused by some of the same phenomena that were seen in the cold flow model.

1

1. Introduction

1.1 Black Liquor Steam Reforming

The University of Utah has designed and constructed a black liquor steam reformer as

part of a program sponsored by the United States Department of Energy to provide

technical support for demonstration of the MTCI steam reforming technology at Georgia-

Pacific’s Big Island unit. The University of Utah unit consists of a vertical pressurized

fluidized bed into which black liquor and steam are injected. The fluidized bed has four

horizontal banks of 20 heaters, with each bank oriented perpendicular to each adjacent

bundle. These heat up the bed, which causes the steam to react with the black liquor to

form mainly carbon monoxide gas (CO) and hydrogen gas (H2). This gas is used for

energy production, but the University of Utah gasifier will be used for experimental and

data collecting purposes only.

1.2 Cold Flow Modeling

The cold flow modeling involved scale down of the University of Utah gasifier and was

used to study flow properties of the gas and solids and some heat transfer properties.

Instead of steam, air at room temperature and atmospheric pressure was used as the

fluidizing gas. There was no modeling of gas production or black liquor injection in the

cold flow model.

1.3 Objectives

The main objective to doing these experiments with the cold flow model was to quantify

and visualize some of the flow properties of the bed. Three main aspects were focused

2

on: (1) bubble flow, (2) particle segregation, and (3) heat transfer. There was a method

devised to measure bubble voidage in the tube bundle region. This helps us to visualize

if gases tend to flow upward through the tubes, or around them. There are studies on

segregation of different sized particles. This shows how the bed performs when there are

different sized solids being fluidized. Finally, there have been some studies on heat

transfer. These are especially important, because heaters will transfer heat to the bed,

which will cause the reforming reactions to occur. These tests will bring much benefit to

quantifying the behavior of the bed. These results can help in future maintenance and

analysis of the bed. These results can then be compared with Computational Fluid

Dynamics (CFD) models to see how the bed will perform.

3

2. Literature Review

2.1 Flow in Beds with Horizontal Tube Banks

The article by Hull et al. [4] is a comprehensive study of bubble hydrodynamics in a

fluidized bed with horizontal tubes. There was a semi empirical study done on the

correlation of bubble size with height, bubble splitting, bubble velocity, and bubble

fraction. Data was obtained using digital image analysis using a two-dimensional (thin)

fluidized bed, which can be readily extrapolated to three-dimensional beds. The

conclusions with bubble growth and splitting will be the most useful to our experiments.

The studies of bubble behavior within the tube bank region are very useful to our studies.

Several empirical correlations were developed that could be used to determine bubble

size, bubble velocity, and bubble fraction from particle size, and velocities of fluidizing

gases.

2.2 Particle Segregation

The textbook by Kunii and Levenspiel [6] give some calculations for segregation. It was

shown that the experiments that we performed will not segregate very well if at all,

because the particles are the same density. There would be more segregation if the

particles had much different densities, or if the fluidization velocity was in-between the

two particle sizes’ minimum fluidization velocity.

4

2.3 Heat Transfer in Beds with Heating Tubes

The article by Borodulya et al. [1] considers the effects of pressure and temperature on

the heat transfer in a fluidized bed. This article gives expressions that can be used in

calculation heat transfer in a fluidized bed. Although the system used in our experiments

will operate at atmospheric pressure, this will be useful because there will be pressure

drop with the height of the bed. Also the University of Utah unit will have much higher

temperature and pressure than the cold flow model. This gives two main equations that

can be used to find the Nusselt Number for a wide range of temperatures and pressures.

The article by Chandran et al. [2] explains an experimental study to explore the effects of

horizontal tubes in fluidized beds. Studies were performed using one horizontal tube and

a bank of ten horizontal tubes. The study involved varying pressure, particle size, and

flow rates. It was found that heat transfer increased as pressure increased and particle

size decreased. Heat transfer varies significantly with the location of the measurements

in the bed. It was found that the heat transfer coefficient at the bottom of a tube bundle is

significantly lower than an inner-row position. It was also found that the heat transfer

coefficient depends on circumferential position on the tube, particle size, gas flow rate,

and system pressure and that there are no real correlations for them, which is why the

main conclusion from this study shows that some of the existing correlations for heat

transfer from horizontal tubes need to have a mechanistic model to measure the heat

transfer coefficients.

5

3. Experimental Methods

3.1 Scaling Parameters

To make a model of the fluidized bed, it needed to be scaled down from the large scale to

a much smaller size. In scaling, four dimensionless parameters must be kept as similar as

possible between the real unit and the model: Reynolds number, ρudp/μ, Froude number

pgdu / , density ratio, ρsolids/ρfluid, and geometric similarity, L/D, where ρgas is the

density of the gas, ρsolids is the density of the solids, dp is the particle diameter, D is the

column inner diameter, u is the superficial velocity, μ is the gas viscosity, g is the

acceleration of gravity, and L is the length of the column, or height of the bed (Kunii &

Levenspiel). Operating conditions of the two units are shown in Table 3-1. Although

these conditions are not exactly the same, it was assumed that they were similar enough

to do cold flow experiments with no problems.

Table 3-1 - Operating Conditions in the Real Gasifier and the Cold Flow Model

Characteristic Gasifier Model Average pressure in bed 290 kPa 42 psia 103 kPa 15 psia Operating temperature 604 °C 1120 °F 20 °C 68 °F Bed diameter 0.254 m 10.0 in 0.164 m 6.5 in. Expanded bed height 1.27 m 50.0 in 0.864 m 34.0 in. Heating tube diameter 0.0173 m 0.680 in 0.0109 m 0.433 in. Particle diameter 300 µm 0.0118 in 215 µm 0.00787 in Particle density 2,275 kg/m3 142 lb/ft3 2,500 kg/m3 156 lb/ft3 Superficial gas velocity 0.396 m/s 1.30 ft/s 0.326 m/s 1.07 ft/s Gas density 0.633 kg/m3 0.0395 lb/ft3 1.222 kg/m3 0.0761 lb/ft3 Gas viscosity (x 105) 3.08 kg/m-s 2.07 lb/ft-s 1.80 kg/m-s 1.21 lb/ft-s Reynolds number 2.44 4.42 Froude number 7.30 7.36 Density ratio 3,595 2,045 Geometric similarity (bed/particle) 10,160 9,906

6

3.2 Fluidized Bed Description

The model of the fluidized bed is constructed of a vertical acrylic tube, 53” high and 6.5”

inner diameter. There are four horizontal bundles of glass tubes from 14” to 28” from the

bottom of the bed. The tubes have about 7 mm inner diameters, 11 mm outer diameter

and extend all the way through the main vertical tube. Each bundle consists of four

horizontal offset layers of five tubes. The tubes of each bundle are perpendicular to the

tubes of the adjacent bundle. The bed is constructed modularly, so that it can be rotated

and several configurations can be achieved. A rendering and photo of the fluidized bed

are shown in Figure 3-1.

Figure 3-1 - Rendering and Photo of the Cold Flow Fluidized Bed

3.2.1 Distributor

At the bottom of the bed, there is a distributor designed to distribute airflow throughout

the bottom of the bed, rather than just one place. The distributor is constructed of two

7

0.125" thick plates with two layers of high-density fabric sandwiched in between. Each

plate has 42 holes, 0.5625" diameter each, to evenly distribute the gas. The 42 holes are

evenly spaced in three rings, which are concentric with the center of the plate. The first

ring has 8 holes with centers each 1.000" from the center of the plate. The second ring

has 14 holes with centers each 1.875" from the center of the plate. The third and final ring

has 20 holes each 2.750" from the center of the plate. In the center of the plate is a 0.875"

hole connected to a pipe and ball valve for solids removal. This is representative of the

solids removal system in the real system. A diagram with dimensions of the distributor is

shown in Figure 3-2. A photo is shown in Figure 3-3.

Figure 3-2 - Diagram of Distributor (Dimensions in inches)

8

Figure 3-3 - Photo of Distributor in Empty Bed

3.2.2 Lower Bed Section

Between the distributor and the lowest tube bundle, a straight, 16-inch long acrylic tube

was placed. There are no ports or holes, because this is only a cold flow model and

liquor injection is not considered.

3.2.3 Tube Bundles

To represent the heater bundles in the real system, four identical tube bundle sections

were manufactured. Each has 20 horizontal glass tubes (0.43" OD) running across the

whole bed. In heat transfer experiments, some of the glass tubes were replaced with

copper tubes. The four sections (3.75" tall each) are stacked on top of one another, with

each oriented such that the tubes are perpendicular to the sections above/below. A

diagram with the dimensions of the tube bundle sections is presented in Figure 3-4. A

photo of the tube section is shown in Figure 3-5.

9

Figure 3-4 - Diagram of Tube Banks (Dimensions in Inches)

Figure 3-5 - Photo of Tube Bank Region of the Bed

10

3.2.4 Upper Bed Section

The upper bed section is very similar to the bottom bed section, except the acrylic tube is

24 inches long. On the top of the top acrylic piece is a ring that seals off the bed and

allows for a filter bag to be placed over the top to keep solids inside the bed.

3.3 Particle Description

Three sizes of particles were obtained to experiment with in the bed. The average size of

the particles in the real system is expected to be about 300 microns. This scales to about

200 microns for the cold flow model. Some particles were obtained in a range of 180 to

250 microns, some in a range of 70 to 110 microns, and some with a range of 500 to 750

microns. Their mean diameters were approximated by averaging the maximum and

minimum particle sizes. This method yielded 215 microns, 90 microns, and 625 microns,

respectively for the three mean particle diameters. These particles were made of soda

lime glass. Their absolute particle density was 2500 kg/m3. These particles were not

completely transparent, but enough to be able to send a light signal through from one of

the tubes to the other in the bed. The particles were spherical and quite uniform in size

and shape.

3.4 Minimum Fluidization Velocities

3.4.1 Theoretical Calculations

The minimum fluidization velocity can be found theoretically using the equation below.

( ) ( )pmf

mfmfgmf

pmf

mfmfmf

dLu

dLu

p 32

23

2 175.11150ε

ρεε

με −+

−=Δ (3.1)

11

In this equation, the minimum fluidization velocity, umf, can be solved by finding the

roots of the equation. The voidage at minimum fluidization, εmf, is estimated to be about

0.4. The bed height at minimum fluidization, Lmf, is estimated to be 0.70 meters. The gas

viscosity, μ, and density, ρ, are determined for ambient air. The pressure drop over the

bed, ΔP, is found using the following equation.

gLP sss ρε )1( −=Δ (3.2)

The slumped bed height, Ls, is estimated to be about .66 meters. The slumped voidage,

εs, is estimated to be about 0.36, the density of the particles, ρs, is 2500 kg/m3.

3.4.2 Experimental Methods

The minimum fluidization velocity can be found theoretically by plotting the pressure

drop of the bed versus the velocity. There is a positive slope until it gets to the minimum

fluidization velocity. As velocity increases after that, the slope is still positive, but much

less than before the minimum fluidization velocity.

3.4.3 Comparison of Calculated and Experimental Values

The actual and calculated minimum fluidization velocities can be compared to each other

to show that the flows are similar and that the particles behave in an expected manner.

3.5 Bubble Voidage and Frequency

3.5.1 Description of Bubble Detector

To measure bubble voidage and to count bubbles, a device was developed using light

transmission to measure instantaneous bubble voidage. The device consists of an

infrared LED that emits infrared radiation at a wavelength of 880 nm, with a sensor of the

12

same wavelength to detect the transmission. The emitter was a Fairchild Semiconductor

QEE123 and the sensor was a Fairchild Semiconductor QSE114. These were chosen,

because they were small enough to fit inside the tubes, but they had to be powerful

enough to transmit their light from one tube through the solids and into the sensor. These

also had to emit and detect at 90˚ angles from the standard LED. These were mounted

sturdily on two flat metal spatulas to assure that they are aimed at each other at all times.

A diagram of the probe is shown in Figure 3-6.

Figure 3-6 - Diagram of Bubble Detector Probe

This was built so it could be placed in two adjacent glass tubes and log data at specific

point. The sensor acts as a variable switch. When more of the specified radiation was

received, more electricity was conducted through the sensor, and when there was none,

the switch was open. This could then be calibrated to relate the signal voltage to a bubble

fraction.

3.5.2 Data Acquisition

To gather data from the sensor, a data acquisition device was needed. The data

acquisition device used for these experiments was a Labjack U12. This device is USB

compatible and capable of logging data with rates up to 1200 Hz. The data that was

IR Emitter

IR Sensor

Metal Spatulas

13

acquired from the Labjack could be exported to a spreadsheet to perform calculations.

Figure 3-7 is a simple diagram to show the theory of the bubble detector.

Figure 3-7 - Theory Behind the Design of Bubble Detector

3.5.3 Calibration

Because the signal from the Labjack was not directly proportional to the bubble voidage,

a calibration curve needed to be set up to translate the signal to the bubble voidage. To

do this, two tubes that were identical to the tubes in the fluidized bed were placed at a

distance of 9.8 mm away from each other. They were laid horizontally in a box. They

were placed so one tube was above the other. Some particles were placed inside the box

and on the tubes so that the level of particles sloped linearly from being completely

covered with particles on one end, to just air on the other end. Because this was linear,

and the distance in the tube was known, the void fraction could then be determined from

the distance in the tube. This was done assuming that a completely packed bed meant

zero bubble voidage and a completely empty bed was full bubble voidage. One particular

challenge was to receive a signal in a completely packed bed, and yet not to exceed the

+1.3 V

GND

+5 V

AI

Particles Interrupt Light

14

maximum signal before it was completely void. This goal was achieved by varying the

power sent to the emitter, by placing resistors in series with the emitter, until above

described goal was achieved. The calibration curve calculated seemed to have two parts.

When there was a lot of signal, voltage received was linear when plotted against void

fraction, but as it got smaller, it suddenly switched to an inverse polynomial curve. When

these two different parts of the curve were separated, a calibration curve could be written

for each. When calculating the void fraction of the data taken in the system, an “if”

statement was written to distinguish which formula to use and then calculate the data. A

sample of one of these calibration curves may be found in Figure 3-8.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 1.00 2.00 3.00 4.00 5.00 6.00

Voltage Signal (V)

Void

spa

ce b

etw

een

tube

s (m

m)

AOEAOSAVESeries4

Figure 3-8 - Voidage Calibration Curve for 180 to 250 Micron Particles

Bubble frequency was also found using this same detector. This was simply done by

counting every time that voltage reached above a certain designated minimum bubble

void fraction. For each different particle size, a new calibration curve was made, because

15

the signal for the voidage was not universal for all of the particle sizes. Each of the

different sizes of glass beads had different transparencies, and they apparently refracted

the light uniquely.

3.5.4 Procedure of Measuring Bubbles

Data was logged at each of the 16 levels in 16 locations at each level, which totals 256

data logs per particle size. Because there are five tubes on each level, there are 4 spaces

between tubes that can be measured. In each of these spaces, data was measured at 4

lengths along the tube: the center, two centimeters, four centimeters and six centimeters

from the center of the tubes and symmetry was assumed for the opposite end of the tubes.

At each of these points, data was taken at a rate of 600 Hz for 30 to 40 seconds. Average

void fraction is calculated by first calculating the void fraction at each of the data points

in the log. Then this calculated data was integrated with respect to time using the

trapezoidal rule, and divided by the total time to get the average void fraction. The basic

equation for calculating this is:

∑−

= +

+

−+1

1 1

11 N

i ii

ii

f tttεε

(3.3)

where tf is the total time of the log or the final time, N is the total number of data points,

εi is the void at data point i, and ti is the time at data point, i. This has to be done at each

of the points. A matrix for each level with both average void fraction and average bubble

frequency can be shown using this data. From this data a three dimensional surface can

be plotted at each level to further visualize the data. This procedure was performed with

all three particle sizes, and plots of average bubble void fraction were created for each

size and each level. Tests were not performed with size mixtures, because the different

16

sizes have different transparencies. Because there may be differences in concentrations

of the different particle sizes, there may not be accurate measurements from the bubble

detector.

3.6 Segregation

It was thought that when a mix different particle sizes was run, they might tend to

segregate from each other. A method was devised to test the extent of segregation

throughout the bed.

3.6.1 Description of Particle Mixture

First, glass beads in two different sizes, specifically 500 to 750 and 180 to 250 micron,

were mixed 50/50 by bulk volume. These solids were then poured into the fluidized bed

to a packed height of 26 inches. The fluidized bed was run at a superficial velocity of

1.07 ft/s for approximately 20 minutes to ensure that the particles had fully established

their flow and had been given a chance to segregate before any particle sampling was

attempted.

3.6.2 Description of Equipment Used

The sampling device was designed to remove a small sample of bed particles from any

location in the fluidized bed, except the tube banks, while the bed was running. The

device consisted of a 60-inch long probe with a bend at the end approximately 3 inches

long. This was done so sampling could be done in between and below the tube banks in

the center of the bed without cutting or drilling through the walls. This device could also

remove a sample of particles against the walls in the tube regions. The probe was

connected to a hose with vacuum on the other end. This hose was then attached to a trap

17

that would collect the particles. This also made the particle sample easy to remove and

analyze. A simple ball valve was placed in between the probe and the trap to stop the

flow of particles when inserting the probe and then when removing the sample from the

trap.

3.6.3 Types of Experiments

There were four main types of segregation experiments. Measurements were taken while

the bed had tube bundles installed and without. Then measurements were taken in the

center of the bed and against the wall of the bed at each height.

3.6.4 Procedure of Removing Samples

To remove a sample of particles, first a hole needed to be punched in the top filter

material and the probe inserted through the hole. Then sampling at different locations

could be performed. Sampling is best done by removing particles from top to bottom. A

sample of about 100-400 grams was collected at each height and sieved using a 420-

micron sieve. These separated portions were then weighed and then we could get a ratio

or percentage of each. Samples were collected at 10 heights in the bed, approximately 4

inches away from each other and in between the tube banks. Specifically, measurements

were taken at heights of 40, 36, 32, 28, 24, 20, 16, 12, 8, and 4 inches from the bottom

when there were no tubes and heights of 36, 32, 28, 23, 19, 15, 11, 8, 4, and 1 inch from

the bottom when the tubes were in the bed. Three trials of this were performed at the

center of the bed as well as against the walls of the bed. Each trial was then plotted on a

“percent weight big particles versus height” graph. In between each trial, the particles

18

that were removed from the sampling were remixed so the bed was at 26 inches and the

bed was run for approximately 20 minutes again to assure proper mixing and segregation.

3.7 Heat Transfer from Heaters to Bed

Because the real gasifier supplies heat to the bed via the heater bundles, measurements of

the heat flux with the cold flow model can be very useful. The data from this experiment

could help the real system by showing how much heat from the heaters is transferred to

the bed. This could help to solve problems in the future if there is fouling in the heaters

or if the heaters heat up the bed more or less in certain locations.

3.7.1 Description of Method

Heat flux measurements were taken by placing a small heater with a constant power

output inside one of 16 copper tubes that replaced 16 of the glass tubes in the bed. The

temperature of a thermocouple within the heater was measured and the heat flux could

then be calculated. This was done while the bed was fluidized at a superficial velocity of

1.07 ft/s with the 180 to 250 μm particles. A heat transfer coefficient, h, could be

calculated, assuming there was no axial heat transfer, using the thermal conductivities of

the materials and the temperature gradient. The general heat flux equation for this system

is:

cCuh

hp RRR

TTqfIV

++−

== ∞.

** (3.4)

where V is volts supplied to the heater, I is the amperage to the heater, fp is the power

factor, q is the total energy given to the heater, Th is the temperature measured from the

heater, T∞ is the temperature of the bed, and R is the resistances of h, the heater, Cu, the

19

copper tube, and c, due to heat transfer to the bed. The resistances of the heat transfer,

tube and heater are as follows:

Lrh

Rc ***2*1

2π= (3.5)

Cu

Cu kLrr

R***2

ln1

2

π

⎟⎠

⎞⎜⎝

⎛

= (3.6)

h

h kLR

***41

π= (3.7)

where h is the heat transfer coefficient, r2 is the outer diameter of the copper tube, r1 is

the inner diameter of the tube, which is where the heater contacts the tube, L is the length

of the heater (1 inch), and k is the thermal conductivity, with subscripts, Cu for the

copper tube and h for the heater. This equation could be rearranged to find h:

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−=

∞Cuh

p

h RRfIV

TTLr

h

******2

1

2π

(3.8)

The heater was assumed to have a constant thermal conductivity of 13 W/m2·K. The

heater’s resistance is very small and the temperature drop can be shown to be negligible,

but the heater’s resistance was still used in the calculations. The thermal conductivities

of the materials used in the calculations are shown in Table 3-1.

Table 3-2 - Thermal Conductivity Values

kh, thermal conductivity of heater 13 W/m2·K 7.75 Btu/hr·ft2·R kCu, thermal conductivity of Cu tube 401 W/m2·K 232 Btu/hr·ft2·R

20

The measurement would be made at steady state at several velocities at several locations

in the bed. Symmetry was assumed along the lengths of the tubes, like was done in the

bubble measurements.

3.7.2 Description of Equipment

The heater used was a cylinder shape of 0.25 inch diameter and 1 inch length. The heater

was custom built by Watlow and contained a K-type thermocouple in its center. This was

powered by a Variac, which could be set at a constant voltage, which would supply a

constant power output to the heater. The thermocouple was then connected to a

thermocouple display. The heater was wired such that voltage and amperage could be

monitored using a digital multi-meter. The temperature of the bed would rise slightly as

the bed operated, so a thermocouple was also placed in the bed to monitor its

temperature.

3.7.3 Difficulties and Solutions

When the Variac was set at a constant power output, its actual power output would vary

enough to change the heat transfer coefficient calculation. This problem was solved by

measuring the power at each steady state measurement. Initially, the measurements were

performed with the original glass tubes. It was found that glass tubes provided results

that seemed wrong. All of the measurements were very different from one another and

there were no trends. It was found later that the glass tubes had non-uniform wall

thickness. More importantly, the glass had such a low thermal conductivity and the small

variations in wall thickness could significantly impact the temperature measurements. It

21

was decided to replace four tubes of each tube bank with copper tubes. A photo of the

tube bank region with copper tubes installed is shown in Figure 3-9.

Figure 3-9 - Photo of Tube Bank Region with Copper Tubes Installed

The two middle top and bottom tubes were used to measure differences in heat flux from

the top of the heater bundles to the bottom. On the second row from the top, the middle

and end tubes were used to measure differences in heat flux from the middle to the sides,

and also the middle to the top and bottom. The copper tubes had an inner diameter of

0.250 inches and an outer diameter of 0.375 inches. This outer diameter was slightly

different from the outer diameter of the glass tubes, but it was assumed that the difference

made to the flow of particles and gases would be negligible. After using this method

with the copper tubes, there were much better data and trends could be noticed.

22

3.7.4 Heat Transfer with Different Velocities

Other than 1.07 ft/s, heat flux was measured at two other superficial velocities, 1.57 ft/s

and 0.535 ft/s, which are 1.47 x 1.07 ft/s and 0.50 x 1.07 ft/s, respectively. These were

not as extensive, though. Experiments at these velocities were only performed in the

copper tubes in the third tube bank from the bottom. This way they could be compared to

the same location at different velocities to see if the heat transfer coefficients change and

how.

3.7.5 Heat Transfer with Different Particle Sizes

In addition to the experiments done with 180 to 250 micron particles, the heat transfer

tests were run with 70 to 110 micron particles and 500 to 750 micron particles. Similar to

experiments when varying the velocity, measurements when running different particle

sizes were only done in the copper tubes in the third bank from the bottom of the bed.

23

4. Results and Discussion

4.1 Minimum Fluidization Velocities

4.1.1 500 to 750 Micron Particles

The minimum fluidization velocity calculated using Equation 3.1 is 1.00 ft/s. When

pressure drop was plotted against the velocity the plot in Figure 4-1 was generated.

7

7.5

88.5

9

9.5

1010.5

11

11.5

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Velocity (ft/sec)

Pres

sure

Dro

p (in

of H

2O)

Increasing VDecreasing V

Figure 4-1 - Pressure Drop versus Velocity for 500 to 750 Micron Particles

The experimental data show that the minimum fluidization velocity for the 500 to 750

micron particles is around 0.81 ft/s, which can be shown by the cusp in the graph. This is

slightly less than calculated minimum fluidization velocity of 1.00 ft/s.

24


The calculated minimum fluidization velocity for the 180 to 250 micron particles is 0.135

ft/s. When the pressure drop was plotted against the velocity, the plot in Figure 4-2 was

generated.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.000 0.050 0.100 0.150 0.200 0.250

Velocity (ft/s)

Pres

sure

Dro

p (in

of H

2O)

IncreasingVelocity

DecreasingVelocity

Figure 4-2 - Pressure Drop versus Velocity for 180 to 250 Micron Particles

The experimental minimum fluidization velocity is around 0.13 ft/s. This can be shown

by the cusp on the plot in Figure 4-2. These two values match very well


The calculated minimum fluidization velocity for the 70 to 110 micron particles was

about .0317 ft/s. It was found that the minimum fluidization velocity was too small to

measure. The particles fluidized below the capability of flow measurement devices. A

plot of minimum fluidization velocity versus particle size may be seen in Figure 4-3.

25

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800

Average Particle Diameter (microns)

Min

imum

Flu

idiz

atio

n Ve

loci

ty

(ft/s

) CalculatedExperimental

Figure 4-3 - Minimum Fluidization Velocities versus Particle Diameter

4.2 Bubble Voidage and Bubble Frequency

All of the results from the bubble voidage experiments which include the surface plots of

each row’s voidage distribution and tables of the measured voidage are appended in

Section 7.2. Bubble voidage is defined as the amount of empty space contained within

the bubbles, ignoring inter-particle voidage in the dense phase, while total voidage is

defined as the amount of empty space found in the bubble and within the dense phase of

the particles. The bubble voidage fraction and voidage fraction are defined by:

Lvi

i =ε (4.2)

where εi is the void fraction at increment i, either total voidage or bubble voidage, v is the

voidage distance of i, and L is the distance between the tubes.

26

4.2.1 Reproducibility of Bubble Detector

Before the bubble detector experiments were performed, the sixth and eleventh tube

levels were measured five times, respectively, to make sure that the results were

reproducible. In these, the surface plots all held the same general shape. The relative

standard deviation of all the measurements was on average 10%. This was not perfectly

accurate, but because the shapes of the surface plots were very close to one another, the

results would be accurate enough for the intents of the experiments. The reproducibility

data are found in Table 4-1.

27

Table 4-1 - Data used for Calculating Reproducibility

Location Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Average S.D. R.S.D. 6L-1-0 35.3% 34.1% 30.8% 34.6% 31.2% 33.2% 0.020 0.0616L-1-2 30.9% 34.7% 29.8% 31.9% 34.5% 32.3% 0.022 0.0676L-1-4 21.6% 24.5% 24.9% 23.5% 22.6% 23.4% 0.014 0.0596L-1-6 13.4% 11.7% 12.6% 12.9% 15.1% 13.2% 0.013 0.0986L-2-0 32.7% 29.5% 30.0% 30.3% 34.9% 31.5% 0.023 0.0736L-2-2 30.0% 31.5% 27.0% 27.9% 27.1% 28.7% 0.020 0.0696L-2-4 23.1% 23.0% 25.9% 25.9% 21.8% 23.9% 0.019 0.0796L-2-6 14.1% 9.5% 11.7% 12.9% 15.2% 12.7% 0.022 0.1746L-3-0 32.4% 29.1% 30.6% 29.9% 33.4% 31.1% 0.018 0.0576L-3-2 34.3% 29.2% 26.9% 26.1% 30.6% 29.4% 0.033 0.1116L-3-4 26.0% 20.7% 32.0% 24.4% 25.2% 25.7% 0.041 0.1586L-3-6 16.6% 11.8% 13.9% 14.3% 14.0% 14.1% 0.017 0.1206L-4-0 24.1% 24.5% 24.7% 25.8% 30.1% 25.8% 0.025 0.0956L-4-2 28.5% 29.1% 24.8% 27.0% 30.4% 28.0% 0.022 0.0776L-4-4 23.3% 24.6% 23.9% 21.2% 21.4% 22.9% 0.015 0.0676L-4-6 10.6% 15.5% 12.0% 13.1% 13.4% 12.9% 0.018 0.14211L-1-0 28.8% 31.1% 33.6% 27.2% 30.9% 30.7% 0.026 0.08611L-1-2 32.6% 23.8% 28.7% 25.2% 33.0% 27.7% 0.041 0.14911L-1-4 23.8% 23.8% 27.8% 24.9% 27.7% 26.0% 0.020 0.07811L-1-6 19.0% 17.1% 17.0% 16.0% 18.7% 17.2% 0.011 0.06511L-2-0 30.0% 26.2% 29.0% 26.7% 27.5% 27.3% 0.013 0.04611L-2-2 30.6% 26.5% 26.8% 30.5% 24.5% 27.1% 0.025 0.09311L-2-4 25.1% 24.0% 21.3% 23.7% 24.8% 23.5% 0.015 0.06511L-2-6 17.3% 17.5% 15.2% 16.8% 24.7% 18.6% 0.042 0.22711L-3-0 31.4% 25.8% 28.6% 26.9% 23.3% 26.2% 0.022 0.08611L-3-2 31.7% 29.5% 23.7% 31.2% 33.8% 29.6% 0.043 0.14411L-3-4 24.6% 27.9% 26.0% 18.9% 24.9% 24.4% 0.039 0.15911L-3-6 19.3% 15.8% 18.6% 18.2% 16.3% 17.2% 0.014 0.08011L-4-0 27.4% 25.1% 27.0% 28.3% 25.9% 26.5% 0.014 0.05211L-4-2 23.7% 21.3% 22.8% 20.5% 26.4% 22.7% 0.026 0.11511L-4-4 21.4% 19.4% 21.4% 24.0% 19.6% 21.1% 0.021 0.10011L-4-6 18.9% 16.7% 15.4% 13.8% 11.6% 14.4% 0.022 0.153


The voidage plots for 70 to 110 micron particles are presented in Figures 7-1 to 7-16

from top to bottom. The overall trend of the void fractions of these was increasing with

elevation. Within each tube bundle, however, the highest voidage was on the bottom and

28

that decreased until it got to the top tube of the bundle. When analyzing the profiles of

each level, the top tube bundles’ void fractions seemed uniform across the whole layer.

The middle two tube bundles had void fractions that were fairly symmetrical, but with the

most voidage in the center of each layer. The bottom bundle’s voidage profiles showed

that the location with the most voidage was located in the same direction that the tubes

were biased to, since they were staggered in the vertical direction. The bottom tube

bundle’s bubble frequency decreased from bottom to top, while the rest of the tube

bundles’ bubble frequencies increased from bottom to top.



from top to bottom. Again, the general trend of the void fractions was increasing with

elevation. Within each tube bundle, they showed slightly different patterns. The bottom

bundle’s void fractions were increasing with elevation. The second, third, and fourth

tube bundles were decreasing with elevation. It seem as though there is a transition zone

at the bottom of the bed where the large bubbles coming out of the distributor are broken

up to much smaller bubbles. In each of the layers, generally the locations with the most

voidage were located near the edge that the layer of tubes was biased to. When analyzing

the profiles, when transitioning between bundles, the void fractions from the top layer of

each bundle are almost superimposed upon the voids from the bottom of the next layer

up. There showed to be a general trend of increasing bubble frequency throughout the

bed from top to bottom. In the bottom tube bundle it was increasing with elevation.

Bubble frequency in the second and third tube bundles was decreasing with elevation.

The top bundle also showed that its bubble frequencies were increasing with elevation.

29



from top to bottom. These particles were a lot larger than the other particles used, and

they showed different trends than the other sizes. The general trend of the void fractions

was decreasing with elevation. In the bottom three tube bundles, there were very similar

patterns. The bottom layer showed the greatest void fraction, the second and third layers

were very close to each other, and the top tube was smaller than the rest. The top tube

bundle’s void fractions showed that voidage was decreasing with elevation, but the top

two levels were very similar. There was a general trend of decreasing bubble frequency

with elevation. Also, within the bottom three tube bundles there was also decreasing

bubble frequency with elevation. The top bundle showed that the bottom three layers’

bubble frequencies were very close, but the top layer’s bubble frequencies were much

higher. When these particles were fluidized with the same superficial velocities as the

other sizes, the bed did not expand very much. The top of the fluidized particles was just

over the top of the tube bundles at standard velocity. This is because the fluidization

velocity was only slightly above the minimum fluidization velocity.

4.3 Segregation

In all of the segregation experiments, the particles follow certain patterns, but they stay

essentially well mixed. This agrees with what Kunii and Levenspiel [6] found. They

have found that when mixing particles of similar densities, but with different sizes, the

segregation is minimal. However particles with the same size and different density will

segregate quickly. Particles may also segregate if the velocity is below the minimum

30

fluidization velocity of one fraction of particles. The data used to generate all the plots

are appended in Section 7.3

4.3.1 Reproducibility of Samples

Before samples were taken from the bed, some experiments were determined how

reproducible the data would be from these tests. There were four samples taken from two

places in the bed. At the location in the tube region, the average large particle fraction

was 49.9% with a standard deviation of 0.42%. At the location below the tube region the

average was 49.8% with a standard deviation of 0.98%. These results are reproducible

for the intents of these segregation experiments.

4.3.2 Results without Tubes Installed

When three trials of the above described procedure were performed, the curve in Figure

4-4 was generated. This plots the percent large particles of each sample versus the height

at which it was sampled.

31

46.0%

47.0%

48.0%

49.0%

50.0%

51.0%

52.0%

53.0%

0 4 8 12 16 20 24 28 32 36 40

Inches from bottom

% B

ig P

artic

les

Trial 1Trial 2Trial 3

Figure 4-4 - Three Trials of Weight Percent of Large Particles at Different Heights of the Bed without Tube Banks Installed

4.3.3 Discussion of Results without Tubes Installed

These samples followed a general trend of slightly more large particles at the top of the

bed than at the bottom. Throughout the bed there is approximately a 50/50 weight

mixture of the two particles. It was expected that the smaller particles would segregate to

the top of the bed, but these studies show that is not true. This could be due to the fact

that there is no bubble breakup and that the bubbles are getting larger as they rise to the

top. While running the bed at a superficial velocity of 1.07 ft/s and without tubes, the bed

was slugging. Overall there is a very small deviation from a 50/50 weight mixture.

Because the bed is slugging and there is no bubble breakup, this probably keeps the bed

mixed well, while holding the shown segregation patterns. The bed was also running

over both of the particle’s minimum fluidization velocities. If it were running at a

velocity somewhere between the two minimum fluidization velocities, there may have

been more segregation.

32

4.3.4 Results with Tube Bundles Installed in Bed

In the center of the bed, particle samples were removed and sieved at heights of 36, 32,

28, 23, 19, 15, 11, 8, 4, and 1 inch from the bottom. At the walls, an additional

measurement at 40 inches from the bottom was sampled. When three trials of this type

were done in the center of the bed with a superficial velocity of 1.07 ft/s, the curve in

Figure 4-5 was generated. Three trials of the measurements at the wall generated the

curve in Figure 4-6. The tube region is from 11 inches from the bottom up to 28 inches

from the bottom. Each measurement in between 11 and 28 inches from the bottom of the

bed is between two tube banks.

47.0%

48.0%

49.0%

50.0%

51.0%

52.0%

53.0%

0 4 8 12 16 20 24 28 32 36

Inches from Bottom

% L

arge

Par

ticle

s


Figure 4-5 - Weight Percent of Large Particles at Different Heights in the Center of the Bed with Tube Banks Installed and Superficial Velocity of 1.07 ft/s

|--------Tube Region--------|

33

42%43%44%45%46%47%48%49%50%51%52%53%

0 4 8 12 16 20 24 28 32 36 40

Inches from Bottom

% B

ig P

artic

les


Figure 4-6 - Weight Percent of Large Particles at Different Heights at the Walls of the Bed with Tube Banks Installed and Superficial Velocity of 1.07 ft/s

4.3.5 Similarities of Results at Wall and Center with Tubes Installed

In both of these tests, it seems that there are three different forms of behavior. Below the

tube banks, it seems there is a good distribution of both particle sizes. Measurements

from the tube region show that there is almost a linear relationship of particle size to

height. There is a larger amount of large particles at the bottom and then at the top of the

tubes there are a lot less large particles. Above the tube region, there is a sudden large

amount of particles as height increases. At the top of the bed, there is the highest

concentration of large particles. At the walls, there is a slightly lower large particle

concentration than in the center of the bed. The wall and center measurements follow

almost the same pattern for particle size distribution, in the respect that in the tube region

there is a drop of concentration of large particles with height in the tube region, and that

there are three separate circulation zones. While the tubes are in the bed, there is a lot

|--------Tube Region-------|

34

more bubble breakup and there isn’t any slugging. This allows the bed to establish its

flow patterns similar to the real system.

4.3.6 Differences in Results at Wall and Center with Tubes

In the measurements with tubes, there are three distinct circulation zones. The

measurements of segregation do not have the distinct circulation zones as seen in the

measurements with tubes. This must be largely due to the lack of bubble breakup and the

slugging. The measurements without tubes seem to be a little more random than the

measurements with tubes. We can conclude through these studies that the tube bundles

create these circulation zones and they break up the bubbles quite well. We can also

conclude that there is a little segregation of the particles and overall, there is a good

mixing of the particles along the full length of the bed. The most segregation occurs at

the walls while there are tubes in the bed.

4.4 Heat Transfer

The heat transfer results give some conclusions that were expected and some that were

not. Heat transfer is very dependent upon fluidization state, particle size, voidage, and

geometry. Much of the data obtained from these experiments are comparable to similar

experiments performed elsewhere. The expected may not always be the case, because the

fluidized bed may be unique in its flow patterns. All of the data and calculations

gathered from the heat transfer experiments, which include the measurements of steady

state temperature, voltage, amperage, and calculated heat transfer coefficients, are

appended in Section 7.4.

35

4.4.1 Description of Measurements

After the temperature and power were measured, the local heat transfer coefficients could

be calculated. Unlike the voidage measurements, profiles cannot be plotted, because only

four tubes per bank had copper tubes that would allow the heat transfer experiments to be

performed. The tubes were placed in specific locations, so they could be measured

relative to one another to gather information about the whole tube region of the bed.

4.4.2 Reproducibility of Measurements and Calculations

Before any measurements were taken, some data was taken to determine the

reproducibility of the heat transfer measurements. Six trials were performed at two

different locations, one in the middle of one tube in the bottom tube bank and one in the

middle of one tube in the third from bottom bank to determine how well they could be

reproduced. At the bottom the data showed 1.00% relative standard deviation, and the

measurements from the top bundle showed 0.67% relative standard deviation.

4.4.3 Comparison of Heat Transfer between Tube Banks

In each tube bank, the results could be averaged to find an average heat transfer

coefficient for each bank to compare to the others. When this was done, it was found that

there was about the same average heat transfer coefficient for the bottom and two top

tube banks. The second tube bank from the bottom was significantly lower than the rest

of these. The values of the tube bank average heat transfer coefficients are shown in

Table 4-2.

36

Table 4-2 - Average Heat Transfer Coefficients of Each Tube Bank

Tube Bank

(1=bottom, 4=top) Average Heat Transfer Coefficient (W/m2·K)

1 248 2 216 3 245 4 240

4.4.4 Correlation of Heat Transfer Coefficient with Height

To compare heat transfer coefficients with height, the average of the measurements were

compared with their height in the bed. This was similar to the bank averages. A plot of

the average heat transfer coefficients for the center tubes is shown in Figure 4-7.

200 210 220 230 240 250 260 270

35 40 45 50 55 60 65 70 75 Height from bottom of bed (cm)

Hea

t Tra

nsfe

r Coe

ffici

ent

(W/m

2 K)

Figure 4-7 - Correlation of Heat Transfer Coefficients on Middle Tubes with Height

All of the tubes along the centerline have similar heat transfer coefficients, except for

those in the second tube bank, and the lowest tube on the third tube bank. The top tube

had a slightly smaller heat transfer coefficient than the others also. In the bottom tube

37

bank the top and bottom tubes’ heat transfer coefficients were very close. In the second

bank, heat transfer decreased with elevation. The third bank’s heat transfer increased

with elevation. The top bank’s heat transfer coefficients were increasing with elevation,

except for the top tube. This may be, because on the top of a horizontal tube, there is

what is called the “Lee Stack Region.” This is where the particles pile on top of the tube

and do not move. This may occur more on the top tubes where there are no bubbles

moving around on the top and solids falling down on it from the adjacent tubes above it.

A picture showing the heat transfer measurements were taken and their respective

locations may be seen in Figure 4-8.

4.4.5 Particle Size Effects on Heat Transfer

When the temperature measurements were measured using different particles sizes, the

bed behaved as expected according to Kunii and Levenspiel [6]. At the same velocity the

heat transfer coefficients increased as particle size decreased. A plot of average heat

transfer coefficient of the bank versus particle size is shown in Table 4-3. The smallest

particles experience the most heat transfer, because they have a lot more surface area of

the particle in contact with the tube to transfer heat away from the tube.

Particle Size (μm)

Average Heat Transfer Coefficient (W/m2·K)

70 to 110 267.8 180 to 250 245.0 500 to 750 242.4

Table 4-3 - Heat Transfer Coefficient Correlations with Particle Size

38

Bank 4Bank 4

Bank 3Bank 3

Bank 2Bank 2

Bank 1Bank 1

241

258

254

234

252

259

223

251

211

212

229

214

249

242

249

249

Figure 4-8 - Average Heat Transfer Coefficients (W/m2·K) at Tubes at velocity of 1.07 ft/s

39

4.4.6 Velocity Effects on Heat Transfer

When the superficial velocities were changed, the average heat transfer coefficient from

the third bank gave some interesting data. When the bed was running at 1.07 ft/s, the

tubes had, on average, the lowest heat transfer coefficients. When the bed was running at

both 1.57 ft/s and 0.54 ft/s, the average heat transfer coefficients increased. This is

contrary to what was found by Kunii and Levenspiel [6], whose data shows that the heat

transfer coefficients will increase to a limit asymptotically with higher velocity. Table

4-4 shows the average heat transfer coefficient from the third tube bank with their

respective velocities. The reason for the low heat transfer coefficient at 1.07 ft/s is

unclear.

Superficial Velocity (ft/s)

Average Heat Transfer Coefficient (W/m2·K)

0.54 257.5 1.07 245.0 1.57 258.2

Table 4-4 - Table of Average Heat Transfer Coefficients at Different Velocities

4.4.7 Voidage Effects on Heat Transfer

Although a heat transfer profile could not be generated from the few data points that were

measured, the heat transfer coefficients were compared with their respective locations’

void fractions. It wasn’t observed in every location, but mostly, if there was more

voidage, there was usually less of a heat transfer coefficient. As the measurements were

closer to the wall, the correlation between the voidage and the heat transfer coefficient do

not always hold up. Most of the heat transfer is done by the solids, but only if they are

flowing well. This can be seen at the wall, because the solids are flowing slowly, and

there is little voidage in the wall. Two (Banks 2 and 4) of the wall measurements were

40

lower than average and the other two (Banks 1 and 3) were about average with the rest of

the bundle.

4.4.8 Overall Heat Transfer Parameters

There are several parameters that influence the amount of heat flux from the tubes to the

bed. The main parameter is how much particles and gas pass by the tube. If the

measurement is near the wall or the center will influence how much the solids can flow

near them. Most of the heat transferred from the tubes to the bed is by solids moving

against the tubes. This is mainly because the solids have higher thermal conductivity and

specific heat that the fluidizing gases. The voidage greatly affects the way the tubes can

transfer heat to the bed. If there is more voidage, there are less solids coming in contact

with the tubes, thus lowering the heat transfer rate.

41

5. Conclusions

5.1 Bubble Voidage

It was found that the general trend of all particle sizes was that the voidage increased with

elevation, except with the larger particles. The experiments with the larger particles (500

to 750 micron) showed a trend that is decreasing with elevation. There was also a trend

that the voidage does not stay completely distributed. Usually there is more voidage in

the middle of the tube banks and sometimes there is more voidage at the edges. This

occurs mainly at the bottom of the bed and as the bubbles rise, the voidage distributes

throughout the bed. When going from one tube bank to the next, the void profiles are

similar, so the void must be in a form of a continuum from the top to the bottom.

5.2 Segregation

Segregation in the bed is very minimal, although very repeatable. This may be due to the

fact that we are above the minimum fluidization velocity for both particle sizes in the

mix. Also, the densities of the two particle sizes are identical, and Kunii and

Levenspiel [6] indicate that under such conditions there will be no segregation. In the

real system there will be very minimal density differences, so there will be minimal

segregation also.

5.3 Heat Transfer

The heat transfer experiments gave some results that were expected and some that were

not. It was shown that heat transfer basically remained constant throughout the bed,

except in the second tube bank. As particle size increased, the heat transfer decreased.

42

The velocity effects were contrary to what was expected. The voidage found in the

previous experiments show that there is an effect of voidage on heat transfer. In places

where there is higher voidage there is less heat transfer, which is what was also expected.

This may have an effect on the real system, because the particles will grow over time as

liquor is injected. This may cause some difficulties of heat transfer to the bed after the

particles have grown to a size that is too large, or cause overheating of the bed heaters.

Because of these, the main mechanism for heat transfer is most likely conduction from

the heater tube to the individual particle. If there are particles flowing by the tube, heat

will be transferred to them easier than it can be transferred to air only.

43

6. References

1. Borodulya, V.A., Teblitsky, Y.S., Sorokin, A.P., Markevich, I.I., Hassan, A.F.,

Yeryomenko, T.P., Heat Transfer between a surface and a fluidized bed:

consideration of pressure and temperature effects. Intermountain Journal of Heat and

Mass Transfer. 34(4). 47-53. (1991).

2. Chandran, R., Chen, J.C., Staub, F.W., Local Heat Transfer Coefficients around

Horizontal Tubes in Fluidized Beds. Journal of Heat Transfer. 102(2), 152-157.

(1980).

3. DeNevers, Noel, Fluid Mechanics for Chemical Engineers. 2nd Ed., McGraw Hill,

San Francisco. (1991).

4. Hull, A.S., Chen, Z., Fritz, J.W., Agarwal P.K., Influence of horizontal tube banks on

the behavior of bubbling fluidized beds 1. Bubble Hydrodynamics. Powder

Technology,. 111(3), 192-199 (2000).

5. Incropera, F.P and Dewitt, D.P., Fundamentals of Heat and Mass Transfer, Fifth Ed.

John Wiley and Sons, New York, p. 480-496, (2002).

6. Kunii, D., Levenspiel, O. Fluidization Engineering. 2nd Ed. Butterworth—

Heinemann. Boston. 1991.

7. Zenz, F.A. Fluidization and Fluid-Particle Systems. Pemm-Corp Publications.

Nelsonville, NY. 1989.

44

7. Appendices

7.1 Voidage Plots

The following voidage profiles are plotted using the data that was gathered. One the left

horizontal axis, the numbers 1-7 show the length along the tubes that the measurement

was taken. The number 1 means the wall closest to the measure and 7 is the mirror image

of 1. The number 4 is the middle of the tube. The right horizontal axis is the space

between the tubes, so 1 would be the far left space and 4 would be the far right space.

The level and particle size used are in the figure description. The scale is the same for all

measurements with the same particle size, so they can be easily compared.

45


1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%

Figure 7-1 - Level 16 Void Fraction Profile using 70 to 110 Micron Particles.

1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%

Figure 7-2 - Level 15 Void Fraction Profile using 70 to 110 Micron Particles.

46

1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%

Figure 7-3 - Level 14 Void Fraction Profile using 70 to 110 Micron particles.

1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


47

1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


48

1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


49

1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%

Figure 7-9 - Level 8Void Fraction Profile using 70 to 110 Micron particles.

1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


50

1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


51

1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


52

1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


1 2 3 4 5 6 7S1

S344.0%46.0%48.0%50.0%52.0%54.0%56.0%58.0%60.0%62.0%64.0%66.0%68.0%70.0%72.0%

70.0%-72.0%

68.0%-70.0%

66.0%-68.0%

64.0%-66.0%

62.0%-64.0%

60.0%-62.0%

58.0%-60.0%

56.0%-58.0%

54.0%-56.0%

52.0%-54.0%

50.0%-52.0%

48.0%-50.0%

46.0%-48.0%

44.0%-46.0%


53

7.1.2 180 to 250 Micron particles

1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%

Figure 7-18 -Level 15 Void Fraction Profile using 180 to 250 Micron particles.

54

1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


55

1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


56

1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


57

1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


58

1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


59

1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


60

1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


1 2 3 4 5 6 7S1

S341.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%53.0%54.0%55.0%56.0%57.0%58.0%59.0%60.0%61.0%62.0%63.0%

62.0%-63.0%61.0%-62.0%60.0%-61.0%59.0%-60.0%58.0%-59.0%57.0%-58.0%56.0%-57.0%55.0%-56.0%54.0%-55.0%53.0%-54.0%52.0%-53.0%51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%


61

7.1.3 500 to 750 Micron particles

1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


62

1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


63

1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


64

1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


65

1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


66

1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


67

1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.0%43.0%44.0%45.0%46.0%47.0%48.0%49.0%50.0%51.0%52.0%

51.0%-52.0%50.0%-51.0%49.0%-50.0%48.0%-49.0%47.0%-48.0%46.0%-47.0%45.0%-46.0%44.0%-45.0%43.0%-44.0%42.0%-43.0%41.0%-42.0%40.0%-41.0%39.0%-40.0%38.0%-39.0%37.0%-38.0%36.0%-37.0%


1 2 3 4 5 6 7S1

S336.0%37.0%38.0%39.0%40.0%41.0%42.

measurement of bubble behavior and heat transfer in a fluidized bed …whitty/documents/siddoway...

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