Sep 23, 1983 - September 23, 1983. Typed by Linda S. Crooks for. Frederick A. Kamke. Redacted for Privacy. Redacted for Privacy. Redacted for Privacy ...
AN ABSTRACT OF THE THESIS OF
Doctor of Philosophy
Frederick A. Kamke for the degree of Forest Products
presented on
in
September 23, 1983
.
Title: Engineering Analysis of a Rotary Dryer: Drying of Wood Particles
Redacted for Privacy Abstract approved:
Dr. James B. Wilson
Rotary dryers are the most commonly used wood drying system in the particleboard industry.
These dryers also play an increasingly
important role in drying wood residues for fuel.
Many potential
benefits may be realized through an improved understanding of the rotary drying process.
A rotary dryer simulation model was developed, in the form of a computer program, for the purpose of analyzing the drying behavior of wood particles.
The model is applicable to single pass rotary
drums, with or without a centerf ill flighting section.
Modifica-
tions to the base program could be made to allow for alternative rotary drum designs, such as multiple pass drums. The approach used in the model development analyzed the rotary drying process in a sequential manner.
Beginning with a study of
particle residence time in a rotary drum, the process of heat transfer, and then mass transfer, were incorporated to yield a complete rotary dryer simulation model.
The resultant computer
program does not require empirical constants or equations developed for a particular rotary dryer system.
Experiments on a commercially manufactured rotary dryer were performed to check the performance of the simulation model as a predictor of overall residence time and drying behavior.
The
variables tested were drum rotation rate, gas flow rate, and inlet gas temperature.
Measurements of gas temperature, particle
temperature, and particle moisture content were obtained along the drum length.
Comparison between the predictions and the measured
results were good, indicating a percent root mean square error of 22.2 in the prediction of the outlet particle moisture content.
A series of computer simulation trials were performed to check the affect of inlet particle moisture content, blend-box gas temperature, drum diameter, air leakage, drum length, gas volumetric flow rate, particle size, particle sphericity, drum speed, and angle of repose on dryer behavior.
It was discovered that an optimal gas
flow rate exists at which the greatest extent of drying may be achieved.
In addition, the presence of centerf ill flights enhances
the extent of drying in a rotary dryer.
The rotary dryer simulation model developed in this study should prove useful for optimizing process parameters in the drying of wood particles.
C
Copyright by Frederick A. Kamke September 23, 1983 All Rights Reserved
Engineering Analysis of a Rotary Dryer: Drying of Wood Particles by
Frederick A. Kamke
A THESIS submitted to
Oregon State University
in partial fulfillment of the requirements for the degree of Doctor of Philosophy
Completed September 23, 1983 Commencement June 1984
APPROVED:
Redacted for Privacy Prof d6r of Forest Products in charge of major
Redacted for Privacy Head of Department of Forest Products
Redacted for Privacy Dean of Graduat
chool
Date thesis is presented
Typed by Linda S. Crooks for
September 23, 1983
Frederick A. Kamke
COMMITTEE MEMBERS:
Redacted for Privacy Dr.
ames B. Wilson, Associate Professor, Forest Products
Redacted for Privacy Dr. Charles E. Wicks, Pro essor and Head, Chemical Engineering
Redacted for Privacy Dr. Helmuth Resch, Professor and Head, Forest Products
Redacted for Privacy ,
Dr. Philipl E. Humphsista t Professor, Forest Products
Redacted for Privacy Dr.
oeI Davis, Associate Professor, Mathematics
ACKNOWLEDGEMENTS
This work is dedicated in memory of my father Donald Arthur Kamke, whose understanding and support allowed me to pursue a college education.
I owe devoted gratitude to my wife Carol.
Through her love,
hard work and care we shared all of the frustrations and joys of my graduate career.
A special thanks must go to Jim Wilson. friendship made the task much more bearable.
His guidance and As my advisor, Jim gave
me enough latitude to explore many avenues, but always kept a watchful eye so I would not stray too far.
I'm also indebted to Helmuth Resch for his support, and for allowing me to directly pursue the PhD degree with the Forest Products program at Oregon State University.
"Doc" Wicks was very influential in my graduate studies.
He
always found the time to provide his much needed advice and instruction.
Acknowledgement must be given to the Weyerhaeuser Company for providing the use of their rotary dryer at the Weyerhaeuser Technology Center in Federal Way, Washington.
In particular, Stan Terada's
expertise and great patience were invaluable.
Stan, along with Jay
Miller, contributed many hours of enduring labor, without which this work could not have been completed.
Weyerhaeuser's Grant Karsner,
Frank Beall and Ferhan Kayihan also played notable roles toward the successful completion of this research.
I'm grateful to have been a recipient of the Weyerhaeuser Company Foundation Fellowship and to Jack Winjum of Weyerhaeuser for his sincere interest in the success of the fellowship program. Recognition was also earned by the Radiation Center at Oregon State University for making available an excellent facility.
Of
special note, Casey Bennett and Roman Schmitt provided instruction and a helping-hand when needed most.
Finally, appreciation is due Mike Milota for unselfishly giving of his time during the experimental stages of this work.
TABLE OF CONTENTS
Introduction
1
Literature Review Residence Time and Particle-Gas Stream Interactions Residence Time Particle-Gas Stream Interactions
4 4 4 9
Heat Transfer
11
Mass Transfer
15
Wood Drying Models
22
Residence Time Model Development Longitudinal Advance Per Cascade Time Per Cascade Total Residence Time Allowance for Underloaded Flights Equivalent Particle Diameter
29 30 30 31 34 35 36
Solution Procedure
37
Angle of Repose Experimentation and Results
39 40
Residence Time Experiment Equipment and Procedure Results and Discussion
46 46 48
Comparison Between Experimental Results and Predicted Behavior
51
Residence Time Simulation Trials
57
Heat Transfer Model Development Energy Balance Heat Loss Heat Transfer During Particle Fall Soaking Volumetric Heat Transfer Coefficient
61 62 62 62 66 67 70
Solution Procedure
72
Results and Discussion
76
Notation Program and Listing Program (RDS) Simulation Dryer Rotary
155
1.03 K= 6, Through 1 Runs Test for Output Simulation Generated Computer
179
.
.
.
.
H.
G.
Appendix
Appendix
A. Appendix
Wall. Drum the of Resistance Thermal
Appendix
Coefficient Transfer Heat Volumetric the Calculating of Method Indirect
146
C.
Properties Gas of Evaluation
148
D.
Properties Wood of Evaluation
151
E.
Calculation Temperature Wet-bulb
153
F.
Wood in Water of Energy Sorption
154 .
.
.
.
B.
Appendix Appendix Appendix Appendix
Conclusions and Summary
130
Notation of List
133
Bibliography
139
Appendices
145 145
Behavior dicted Pre- and Results Experimental Between Comparison
103
Trials Simulation Dryer Rotary
120
Model the of Applications
125
Procedure Solution
86
Discussion and Results Procedure and Equipment Experiment Dryer Rotary
89 89
98
Drying Balances Energy and Material Development Model Transfer Mass
83 80 80 80
VI.
V.
LIST OF FIGURES
flE!
Figure
Schematic Diagrams of Rotary Drum Cross Sections Showing Typical Particle Lifting Flight Systems.
7
2
Section View of Particles in Flight.
7
3
Measured Drying Rates of Wood Particles In a FlashTube Versus Wood Moisture Content (Malte et al.,
1
1977).
26
Vertical and Longitudinal Motion of Particle During a Cascade With Cocurrent Flow.
33
5
Section View of Rotary Drum Cross Section.
33
6
Experimental Rotary Drum For Measuring The Angle of Repose.
41
Experimentally Measured Angle of Repose For Wood Particles as a Function of Froude Number and Moisture Content.
44
Experimentally Measured Angle of Repose For Wood Particles as a Function of Periphery Flight Angle and Moisture Content.
44
Rotary Drum Experimental Set-up With Irradiated Particle Detection System.
47
Wood Particle Size Distribution Used in Residence Time Experiment.
49
Sample Strip-Chart Recorder Output Showing Detector Response to Tagged Particles.
50
12
Experimentally Measured Residence Time Distributions.
52
13
Predicted Versus Actual Residence Time for Wood Particles in the Experimental Rotary Drum.
55
14
Predicted Effect of Gas Velocity on Residence Time.
58
15
Predicted Effect of Drum Speed on Residence Time.
58
16
Predicted Effect of Drum Diameter on Residence Time.
59
17
Predicted Effect of Particle Size on Residence Time.
59
4
7
8
9
10
11
Longitudinal Cross Section View of Rotary Drum Showing Particle Flow Path With Centerf ill Flights.
63
Schematic Diagram of Wood Particle Bed on Lifting Flight, Assuming a Rectangular Cross Section.
69
Temperature Profile of Wood Particle Bed at End of Time on Flight, Assuming a Rectangular Cross Section.
69
Longitudinal Thermal Profile of Heat Transfer in a Rotary Drum With Cocurrent Flow.
77
Schematic Diagram of Bound and Free Water in the Wood Structure.
90
23
Rotary Dryer Experimental Set-up.
91
24
Rotary Dryer Experiment Particle Size Distribution.
92
25
Inlet and Outlet Particle Temperature Measurement
18
19
20
21
22
26
27
28
29
30
31
32
33
34
35
Set-ups.
95
Sampling Device for Extracting Particle Samples From the Drum Interior.
96
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 1, K = 1.0.
105
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 2, K = 1.0.
106
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 3, K = 1.0.
107
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 4, K = 1.0.
108
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 5, K = 1.0.
109
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 6, K = 1.0.
110
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 1, K = 1.03.
113
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 2, K = 1.03.
114
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 3, K = 1.03.
115
36
37
38
39
40
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 4, K = 1.03.
116
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 5, K = 1.03.
117
Comparison of Rotary Dryer Simulation With Measured Results From Test Run No. 6, K = 1.03.
118
Predicted Versus Actual Outlet Particle Moisture Content For The Rotary Dryer Test Runs, K = 1.0.
121
Effect of Variations of Selected Rotary Dryer Parameters, By Plus and Minus 50 Percent, on the Outlet Particle Moisture Content. Base Case is Equivalent to Conditions in Test Run No. 2.
122
41
Comparison of Rotary Dryer Simulation Results for Test 126 Run No. 2 With and Without Centerfill Flights.
42
Schematic Diagram of Triple Pass Rotary Dryer.
128
LIST OF TABLES
Table 1
Page
Experimental Data for the Kinetic Angle of Repose for Wood Particles in a Rotary Drum. Moisture Content = 10% (dry basis).
43
Experimental Data for the Kinetic Angle of Repose for Wood Particles in a Rotary Drum. Moisture Content = 146% (dry basis).
43
3
Rotary Dryer Experimental Design.
90
4
Summary of Rotary Dryer Test Results.
99
5
Summary of Rotary Dryer Parameter Values Used in Figure 40.
124
Coefficients Used in Gas Property Equations.
150
2
6
ENGINEERING ANALYSIS OF A ROTARY DRYER: DRYING OF WOOD PARTICLES
I.
INTRODUCTION
Rotary dryers have been the most commonly used wood drying system in the particleboard industry since their adaptation from the agricultural industry in the 1940's.
In addition to the extensive
use of rotary dryers for drying alfalfa and other agricultural crops, food stuff, and aggregates, these dryers also play an increasingly important role in drying wood residues for fuel (Mohr, 1982; Vala, 1982; Oswald and Junge, 1980; Kirk and Wilson, 1983). Until recently their effectiveness as a wood particle drying system, as well as for other materials, has been judged primarily by convenience rather than performance.
This kind of attitude was
tolerable during the days of cheap energy and inexhaustible "woodwaste" raw material.
However, with today's strive for greater
efficiency in allmodes of production, a closer examination of this drying process is in order.
Many potential benefits may be realized through an improved understanding of the rotary drying process.
One such benefit could
be energy savings, whose magnitude can be determined by estimating the energy cost of drying in the particleboard industry.
For
example, the annual wood consumption for particleboard manufacture in the United States is approximately five billion kilograms on a dry basis.
About 60 percent moisture content (dry basis) must be
removed with a drying process which is about 50 percent efficient. This amounts to an equivalent annual power requirement of over
2
450 million cubic meters of natural gas.
Whereas predrying wood
fuel for the approximately 1,700 industrial boilers fired with wood and bark residues in the United States could yield about a 10 to 15 percent increase in steam production or fuel savings (this assumes only a 10 percent moisture content reduction).
In addition,
potential benefits could be realized in improvements of dryer control strategies and better control of dryer exhaust gas emissions. The rotary drying process can be broken down into three parts: momentum transfer, heat transfer, and mass transfer.
All three of
these transfer processes are interdependent and occur simultaneously. This study examines momentum, heat and mass transfer for the rotary dryer in a sequential fashion.
Beginning with momentum transfer,
in the form of a residence time analysis, a complete rotary dryer simulation model is developed by incorporating heat. and mass transfer into the analysis in a step by step manner.
In this way, a very
thorough understanding of the wood particle rotary drying process is attained.
Rotary dryers used for wood particles are usually direct fired, are not sloped to the horizontal, and operate under cocurrent flow. The wet wood particles are continuously lifted by the rotation of the drum with the aid of particle lifting flights.
The wet material
cascades off the flights and passes through the hot moving gas stream.
Each time a particle cascades, it is moved along the
length of the drum as a result of the gas-particle interaction. Convective heat and mass transfer are the primary modes of drying. The approach used for this analysis, contrary to other studies reported in the literature, does not require empirical constants or
3
equations developed for a particular rotary dryer system.
It
relies entirely on first principles and empirical relationships developed independently from rotary dryers.
This requires the
operation of a rotary dryer be examined in terms of its component parts and processes.
While limited in its accuracy for specific
rotary dryers, this type of an approach provides a great deal of insight toward the affect of design and operating variations on rotary dryer performance.
The primary objective of this study was to develop a rotary dryer simulation model which could predict the drying behavior of wood particles.
Secondly, it was desired to study the rotary dryer
in terms of its component parts to identify the mechanisms involved. Third, the affect of a centerfill flighting section was to be considered in the model.
And finally, experiments were to be
performed on a rotary dryer system to check the simulation results.
The same system was used for all of the rotary dryer experiments.
The drum was 1.2-meters in diameter by 5.5-meters in length.
A centerf ill flighting section was included and the flow was cocurrent.
The rotary drying system was commercially designed and
manufactured, but was instrumented for experimental applications.
Use of the dryer was provided by the Weyerhaeuser Company and access to it was limited.
Therefore, all of the experiments con-
ducted were treated as mill trials.
4
LITERATURE REVIEW
II.
Upon review of the literature pertaining to rotary dryers, one finds three particular topics of study: residence time in rotary
drums, heat transfer in rotary drums, and examination of the complete rotary drying process.
Each of these subjects are treated separately
in the following literature survey.
In addition, a review of the
pertinent wood drying literature is also included.
Residence Time and Particle-Gas Stream Interactions
Residence Time
Momentum transfer in rotary drums is generally studied in terms of residence time and holdup of solids inside the drum.
These
quantities are related as shown by Equation 1.
t =
where:
(1)
PB
t = residence time, s.
S = solids feed rate, kg/s. H = holdup, m3.
PB = bulk solids density, kg/m3.
Residence time is dependent on the particle flow path, which consists of flow in a particle-gas stream and travel on particle lifting flights.
The arrangement and shape of particle lifting
flights will influence the particle flow path. typical flighting systems for rotary drums.
Figure 1 shows two
The dotted lines
indicate possible paths for a particle cascade.
Each cascade results
in longitudinal motion of a particle along the length of the drum.
5
Other factors that will influence the residence time are number of flights, gas flow rate, particle feed rate, particle characteristics, drum diameter, drum length, drum slope, and rate of drum rotation. Research into residence time in rotary drums has progressed
over the last 40 years from purely empirical functions describing the process to theoretical relationships requiring computer solutions to complex systems of differential equations.
The works presented here
summarize the progress that has been made in this area of study. Friedman and Marshall (1949) summarized the work of Prutton,
Miller and Schuette (1942), and Smith (1942) on residence time and holdup in rotary drums.
From this earlier work the following
empirical equations were derived.
t
=
13.8 L
0
± 118.1
BLG
(tan a)NC"dd
B = 0.005(d )-0.5 where:
a = drum slope, degrees. L = drum length, m.
N = rate of rotation, rev./min. d
= drum diameter, m.
d
= particle diameter, m. G = gas flow rate, kg/s.
In Equation 2 the plus sign refers to countercurrent flow and the minus sign to cocurrent flow. An empirical relationship for residence time in rotary drums was also developed by Saeman and Mitchell (1954).
The method
6
employed resulted in a range of predicted residence times using Equation 4.
60L
-
f(H) ddN(sin a - KvG)
where:
f = average residence time, s. f(H) = function of drum holdup. VG = gas velocity, m/s. K = constant, s/m.
The limiting values for the holdup function
were
Tr
and 2 depending
on the degree of loading.
Miskell and Marshall (1956) studied residence time in a 0.14-meter diameter by 1.0-meter long rotary drum using a radioactive tracer technique.
Results indicated that an optimal holdup
condition existed, at which the deviation from the average residence time was minimized.
A rigorous analysis of flight geometry and drum loading was performed by Kelly and O'Donnell (1968).
For the equal angular
distribution flight shown in Figure 2, the average residence time is calculated by Equation 5.
-
where:
KcL y[sin a ± f(G)]
t,
mo 7- kg
)
Kc = cascade factor = average distance of particle fall, m. f(G) = function of gas-particle interaction mo
= ratio of actual to design flight holdup at 0 = O.
g = acceleration due to gravity, m/s2.
7
Periphery Flights
Figure 1.
Periphery and Centerfill Flights
Schematic Diagrams of Rotary Drum Cross Sections Showing Typical Particle Lifting Flight Systems.
Equal Angular Distribution Flight
Particles
Ns%%%soe Square Flight, 1.
0 = Flight angle to horizontal. (/) = Kinetic angle of repose.
Figure 2.
Section View of Particles in Flight.
Rectangular Cross Section
8
The cascade factor, Kc, defines the effective length of the drum and must be found experimentally.
The gas-particle interaction function
for was approximated using the Schiller and Naumann (1933) relation
drag forces assuming spherical particles.
FD =
where:
Tird
p
(6)
v rp (1 + 0.15 Re0.687)
FD = drag force due to gas-particle interaction, N. = relative particle velocity, m/s.
vr
1.1 =
gas viscosity, Pas.
Re = Reynolds number.
Glikin (1978) used a similar theoretical approach to derive Equation 7. 0.5]
sT5
T
Le
=
Y(sin a ± Jvr2) where:
7
+ (--Z)
(7)
30N
= average flight angle from which a particle cascades, degrees.
J = drag factor. Le = effective drum length, m.
The drag factor, J, was estimated similarly to the gas-particle interaction function, f(G), of Equation 5 using the Schiller and Naumann equation.
The average flight angle from which a particle
cascades, U, is a function of the flight geometry and the kinetic
angle of repose, see Figure 2. Equation 7 is completely general to any flight geometry pro-
vided the relationship between the kinetic angle of repose and the flight angle is known.
9
As a follow-up to their earlier study, Kelly and O'Donnell (1977) modified their residence time model to allow for kiln action and bouncing as possible modes of advance along the length of the drum.
Particle-Gas Stream Interactions
It appears from the work reported thus far, that the particlegas stream interaction is an important and complex component of the residence time analysis.
The complexity is due to the possibility
of irregular particle shapes and particle-particle interactions.
The literature contains a vast collection of works dealing with fixed orientation drag on ideally defined shapes, such as spheres and cubes.
However, the more difficult problem as expressed above, has
not yet been solved.
A rather extensive literature review on the subject of drag on This review
bodies in a gas stream was presented by Mason (1980).
included considerations of acceleration in a fluid, turbulence, surface roughness, particle shape, and multiparticle systems.
The
author concluded that none of the correlations found in the literature proved to be reliable over an entire range of flow conditions or particle shapes.
Mason's own work on freely-falling wood chips yielded the following empirical relationships for estimating drag coefficients for three different particle shapes: For flat plates in the maximum drag orientation:
CD = 0.60 [0.0176 (21w) + 1.13]; 1 < (2./w)
(I)
and T < (4) + 180-360/nc + w)
1
hc =cbc
+c2 + bc2) tan(360/nc-w)
tan(4) + 180-360/nc + w - T)/
[tan(360/nc-w) + tan(4) + 180-360/nc + w-T)])
For T > (90-180/nc + w) and y > 1
hc =
2c /tan(T -
(I)
and T >
(41)
(4) + 180-360/nc + w)
- 180+360/nc)
(42)
33
Figure 4.
Vertical and Longitudinal Motion of Particle During a Cascade With Cocurrent Flow.
Figure 5.
Section View of Rotary Drum Cross Section.
34
The average angle of entry onto the centerf ill flights, Te, and
the average angle of entry onto the peripheral flights, %, are represented by points B and D respectively in Figure 1.
If a
completely vertical fall is assumed these angles may be determined by plane geometry.
For a more rigorous technique the radial dis-
placement due to the angular momentum transferred from the moving flight to the particle should be taken into account.
In practice,
with rotation rates below ten revolutions per minute and drum diameters of three meters or less, this allowance is negligible. and 711-e are used to calculate the vertical
The angles
distances of fall, y and
yc,
for both stages of the falling period.
The time of fall per cascade, tf, is then given by:
tf = (2gy)
0.5
+ (2gyc)
0.5
(43)
The time of travel on the flights is given by Equation 44.
t = [(360 + 77) -
1%) + a -
e)1/36N
(44)
Total Residence Time
The total residence time is calculated as shown by Equation 45,
where the number of cascades, C, is determined by dividing the length of the drum by the longitudinal advance per cascade, x, from Equation 35.
tT = C(t + tf)
(45)
In practice, rotary drum dryers with centerf ill flights will have short segments ahead and behind the centerf ill section to allow for
35
a smooth particle infeed and outfeed.
These segments are treated in
a similar manner as outlined above but without the centerf ill flights.
The total residence time in the drum must then include
the time spent in these unobstructed segments.
Allowance for Underloaded Flights
Up to this point the analysis has been based on the assumption that the drum is fully loaded.
This means at 0 = 0 the flight has
just become filled to capacity and cascading begins.
This condition
generally would not be achieved in a wood particle drying operation.
Material feed rates are often limited by burner capacity and drying rates.
Overloading is undesirable since this would cause an
accumulation of particles on the bottom of the drum that do not participate in continual cascading.
The result is a decrease in the
gas-particle interaction, requiring additional residence time to achieve the desired degree of drying.
For these reasons rotary drum
dryers used for drying wood particles are operated below the design holdup of the flights.
If the drum holdup is less than the design drum holdup, the cascading is not initiated at 0 = 0, but occurs at some greater peripheral flight angle.
Underloading will therefore result in a
larger value for 0, which is the basis for the residence time calculation.
To account for underloading an iterative procedure is proposed.
First, the residence time and drum holdup are calculated as outlined previously.
The calculated drum holdup, H, is then compared to the
36
design drum holdup, H*, and a fractional drum holdup, m, is determined as follows:
m = H/H*
(46)
If m is less than one an iteration is required.
Assuming m is
linearly related to the peripheral flight holdup, a new value for the flight holdup when cascading begins,
h(0), is calculated as:
h(0) = m h (0)
(47)
This value is then compared to successive values of h (0) as 0 is increased until h(01) just exceeds h (0), at which point the peripheral flight angle when cascading begins will be identified. Equation 38 then becomes:
h(0i)
0 dh
0
The procedure for calculating the total residence time and the drum holdup is then repeated and successive iterations performed until convergence of the total residence time and the fractional drum holdup is achieved.
Equivalent Particle Diameter
When dealing with fluid dynamic properties of irregularly shaped particles it is common practice to approximate them as spheres and calculate an equivalent particle diameter. Levenspiel (1980) is given by: (a + 1) -
2
d
A method proposed by
37
ds = mean aperature size of two screens defining a particle
where:
size.
a = sphericity, the ratio of the surface area of a sphere to the surface area of the particle of an equivalent volume.
Other methods of dealing with irregularly shaped particles are available in the literature (Torobin and Gauvin, 1960; Heywood, 1962; Coulson and Richardson, 1978; Mason, 1980).
The above method
was chosen because of its ease of application in a closed form equation.
Solution Procedure
A computer simulation program called RESTIME has been developed to predict the average residence time in single-pass rotary drums with or without centerfill flights.
The output contains a complete
description of the particle flow path, including: distances of particle fall, time of fall, time of travel on lifting flights,
longitudinal advance per fall, drum holdup, and the average residence time.
The following is a step by step solution procedure used by
the program RESTIME:
Drum dimensions, gas flow rate, particle feed rate, and particle characteristics are input to the program.
Preliminary calculations are performed in order to determine the flighting geometry within the drum. As a first estimate, design drum loading is assumed. An equivalent particle diameter is estimatedwith Equation 49.
38
Equation 38 is used to calculate the peripheral flight angle at which an average particle is released. A check is made to determine if centerf ill flights are present.
If centerfill flights are involved, Equation 39
is solved for the centerf ill flight angle at which an average particle is released.
This calculation is dependent
on the cascading pattern of the peripheral flights as defined by h(0).
Through considerations of the flighting geometry calculated in step 2, the average angles of entry on to the peripheral flights and the centerfill flights are calculated.
These
are points D and B respectfully in Figure 1. The time of particle fall is calculated by Equation 43. If centerfill flights are absent, yc
= 0.
Knowing the distance and time of particle fall, the longiThis
tudinal advance is estimated from Equations 35 and 37.
involves an iterative solution, since the drag coefficient may not be solved for explicitly.
The time of travel on the lifting flights is calculated by Equation 44.
The total time per cascade is then the sum of
the falling time and the time on the lifting flights. The total number of cascades is determined by dividing the drum length by the longitudinal advance per cascade.
If a
centerf ill flight section was involved, the number of
cascades in the drum sections without centerf ill must be evaluated separately.
39
The overall residence time is then the product of the number of cascades in the centerf ill section and the associated
time per cascade, plus the product of the number of cascades
in the unobstructed sections and the associated time per cascade.
The drum holdup is now calculated by Equation 1 and compared to the value estimated in step 3.
If they are in
sufficient agreement (one percent deviation is allowed in the program) the program terminates with an output listing.
If the calculated drum holdup is greater than the
design drum holdup, the program terminates with a warning message that the drum is loaded beyond its capacity.
If
none of these criteria are met, a new estimate of the drum holdup is made using an average value of all the iterations Equation 48 is then used to estimate the
made thus far.
new peripheral flight angle at which an average particle is released.
Steps 6 through 13 are repeated until the
termination criteria is met.
Usually less than five
iterations are required.
Angle of Repose
The angle of repose,
cO,
for particles carried in lifting
flights was illustrated in Figure 2 as simply the angle the particle bed surface makes relative to the horizontal.
When the
particle bed is in motion, this is known as the kinetic angle of repose.
40
A force balance was presented by Schofield and Glikin (1962) which specifies the kinetic angle of repose for free flowing particles based on frictional resistance, gravitational and centripetal forces.
The resultant relationship for
(1)
is shown in
Equation 50.
tan
where:
(I)
=
n - nFr sin 0 + Fr cos 0 1 - nFr cos 0 - Fr sin 8
(50)
Fr = Froude number, rdve2/g. n = friction factor.
V0 = angular velocity, s-1. rd = drum radius, m.
Kelly and O'Donnell (1968) experimentally verified this behavior using pumice particles in a rotary drum with fully enclosed cylinders for flights.
Experimentation and Results
The angle of repose for wood particles was photographically examined using the experimental rotary drum pictured in Figure 6. A total of 713 measurements were taken.
The parameters examined
included: wood particle moisture content, drum speed and drum diameter.
Because the flights were square as shown in Figure 2,
and not fully enclosed cylinders as used by Kelly and O'Donnell,
measurements of
(1)
and 8 were made only in the upper half of the
drum where normal cascading occurs.
Direct measurement of the angle of repose was not possible since the particle bed surface was irregular and seldom contained in a single plane.
It was decided to graphically calculate the flight
Repose. of Angle The Measuring For Drum Rotary Experimental
6.
Figure
-
5,2
41
-
42
holdup from the photographs and then back-calculate an effective angle of repose using the tip of the flight lip as a reference point.
Tables 1 and 2 tabulate the effective angle of repose data
for wood particles with moisture contents of 10 and 146 percent on a dry basis.
Values of
(PI
from Tables 1 and 2 are plotted as a function of
Froude number in Figure 7.
As shown, there is no apparent correla-
tion of ci) with the Froude number in the range studied.
The
variation about the mean was high, with an average standard deviation of approximately 12 degrees.
Figure 7 does show an effect of moisture content on the angle of repose.
The 146 percent moisture content particles exhibited a
mean angle of repose of approximately eight degrees higher than the 10 percent moisture content particles.
This difference was sig-
nificant at a 99 percent confidence level. Figure 8 is a plot of the angle of repose versus the flight angle for a Froude number of 0.019.
There is an apparent relation-
ship, however, the trend does not conform to the curve predicted by Equation 50, which, with a negligible Froude number, would predict a horizontal line.
The above arguments suggest that Equation 50 does not apply to wood particles.
Wood particles cannot be considered a free-flowing
material as assumed for Equation 50.
Observations of wood particles
cascading in a rotary drum revealed that there is not an even flow of material from the lifting flights but rather an intermittent release of particles.
This was most apparent at flight angles
43
Table 1.
Experimental Data for the Kinetic Angle of Repose for Wood Particles in a Rotary Drum. Moisture Content = 10 % (Dry Basis).
Drum Diameter
Drum Speed
Froude Number
Mean Angle of Repose
Standard Deviation
(m)
(rpm)
(103)
(degree)
(degree)
0.46
2.7 6.1
14.0 0.61
2.7 6.1
14.0 0.91
2.7 6.1
14.0
Table 2.
1.88 9.58 50.04
77.6 77.9 76.9
10.6 12.0 10.1
2.49 12.70 66.89
75.2 78.1 80.3
18.7 15.2 14.2
3.71 18.95 99.79
84.1 86.8 85.1
10.0 9.3 10.6
Experimental Data for the Kinetic Angle of Repose for Wood Moisture Content = 146 % Particles in a Rotary Drum. (Dry Basis).
Drum Diameter
Drum Speed
Froude Number
Mean Angle of Repose
Standard Deviation
(m)
(rpm)
(103)
(degree)
(degree)
84.9 89.3 85.8
8.9 7.9
14.0
1.88 9.58 50.04
0.61
2.7 6.1 14.0
2.49 12.70 66.89
85.4 87.6 90.9
9.6 12.9 14.2
0.91
2.7 6.1 14.0
3.71 18.95 99.79
89.6 95.9 85.3
11.5 10.6 12.7
0.46
2.7 6.1
9.3
44
0 = 146 % Moisture (Dry Basis) 0= 10 % Moisture (Dry Basis)
0 95
k op
90
0
0
8
85
0 0 t-I AO
0
80 0 0
0 75 0
25
50
75
100
Froude Number (103) Figure 7.
Experimentally Measured Angle of Repose For Wood Particles as a Function of Froude Number and Moisture Content.
140 0= 146 % Moisture (Dry Basis) 0= 10 % Moisture (Dry Basis)
0 0
0 0
0
0 00
60
90
100
0 c8
60
1
30
Flight Angle (degree) Figure 8.
Experimentally Measured Angle of Repose For Wood Particles as a Function of Periphery Flight Angle and Moisture Content.
45
greater than 90 degrees when typically almost the entire flight holdup would fall in one lump.
Particle geometry and moisture content appear to be controlling factors in determining the angle of repose. bridging matrix as they rest on a flight.
Wood particles form a Partial collapse of the
matrix occurs when its weakest component fails, thus initiating a cascade of particles.
The ability of the matrix to stay intact
depends on the particle geometry.
Long and curly particles, such as
planer shavings, tend to interlock and strengthen the matrix, leading to a high angle of repose.
Whereas, granular particles, like saw-
dust, approach a more free flowing state with a lower angle of repose.
Moisture content apparently affects the angle of repose as the result of two factors: the presence of surface moisture and a change in the bulk density.
Conceivably, a cohesive force is developed
between the particles when sufficient surface moisture is present. This is a combined result of hydrogen bonding between the water and the wood and surface tension effects.
An increase in the amount of
surface moisture results in a greater influence of these surface effects.
Higher particle moisture contents also result in higher
bulk densities.
This could cause more intimate contact between the
particles on the flights due to greater compaction, possibly resulting in more interlocking between the particles.
The effect of
moisture content on the angle of repose is shown in Figures 7 and 8.
A statistical analysis indicated the higher moisture content particles had a significantly greater angle of repose.
46
Residence Time Experiment
Equipment and Procedure
Residence time was measured experimentally using a radioactive tracer technique.
The rotary drum used was a commercial model,
1.2-meters in diameter by 5.5-meters in length.
A centerf ill
flighting section was included, and the gas-particle flow was cocurrent.
Drum speed and particle size were the independent
variables examined.
The principle behind the radioactive tracer technique is simply to tag a particle with a radioactive isotope of sufficient energy, such that the tagged particle may be "seen" using detection equipment, which is sensitive to the presence of radioactivity. Two
A diagram of the experimental setup is shown in Figure 9. gamma ray detectors were positioned inside the dropout hopper at the exit end of the drum.
The signal from each detector was
individually processed through a separate preamplifier and amplifier circuit.
The resulting two signals were then joined and routed
through a single rate meter, and the output transmitted to a scaler and a strip-chart recorder.
A remote switch at the particle inlet
controlled the strip-chart recorder and initiated the starting time for each run.
An aqueous NaNO3 solution was exposed to a neutron bombardment in the nuclear reactor on the Oregon State University campus. resultant solution contained Na24.
The
This nuclide was selected
because of its relatively energetic gamma rays at 1.37 and 2.75 MeV
Exhaust gas and fines to cyclones
Particles
Test particles NaI(T1) detector
/ Remote Baffles
7
f
Switch
Drop-out hopper --1 Inlet air
NaI(T1) detector
7 Particles Preamp.
Amp.
--OP
Rate Meter Scaler
Preamp.
Amp.
1 Chart Recorder olStrip-
Figure 9.
Rotary Drum Experimental Set-up With Irradiated Particle Detection System.
Power Source
48
per disintegration and the fact that the test site location and travel time were in keeping with the 15 hour half-life.
The wood particles used were commercially prepared and exhibited the size distribution shown in Figure 10.
Representative test
particles were selected from three size classes defined by a sieve analysis.
A total dry weight of 1.2 grams per size class was used.
Enough particles for six test runs were prepared, with the number of test particles used per run varying from 46 to about 300 depending on the particle size class.
Test particles were tagged with a predetermined amount of the Na24 solution.
They were then dried to approximate equilibrium with
ambient conditions using a heat lamp and a weight scale.
Approxi-
mately 20 hours elapsed from the time the test particles were tagged and the first experimental run was begun.
At the start of each run, test particles were simultaneously injected through an access port at the particle inlet immediately ahead of the rotating drum. bulk particle feed.
These particles became mixed with the
The temperature of the gas stream approximated
the ambient temperature and all the particles used were previously dried.
Results and Discussion
Individual tagged particles were detected at the drum exit.
A
portion of the readout from the strip-chart recorder is shown in Figure 11.
The peaks shown were interpreted as individual particles
as they passed very near a detector.
0.5
"I.
0.4
Median = 1.63 mm
0 w 0 0-
0.3
Mean = 2.06 mm
-
Relative Frequency = Weight Fraction Incremental Screen Opening
w 44
w
0.2
m w
-
p4
0.1
1
1.0
2.0
3.0
4.0
5.0
6.0
Actual Screen Opening (mm) Figure
10.
Wood Particle Size Distribution Used in Residence Time Experiment.
7.0
8.0
Particles. Tagged to Response Detector Showing Output Recorder Strip-Chart Sample
[III _L,
.
I,
,
2,1or,.,'1,-1,1
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,
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i-
-
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it
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,
,-
ItI
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_1
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tiff
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11
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ikr Iii ni
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-
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11. Figure
mi
iiiii.,
LA ,a.1 ALT ,, ,11,11411
,
Ilaili
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--!--.--r-T11-111-
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50
51
From the strip-chart recorder output, frequency histograms were prepared, see Figure 12.
With the exception of the smallest
particles at a drum speed of 7.2 revolutions per minute, all of the distributions tailed off to the right.
The one exception resulted
because that test run was terminated early due to a clogged outlet screwfeed conveyor.
Comparison Between Experimental Results and Predicted Behavior
Means and standard deviations from Figure 12 are plotted in Figure 13 along with the mean residence time predictions from the computer program RESTIME.
The 45 degree line indicates what would
be an ideal fit between actual and predicted results. The affect of drum speed is readily apparent from Figure 13. Increasing the drum speed decreased the average residence time.
The
change in the residence time was not proportional to the change in the drum speed.
Of particular interest in Figure 13 is the effect of particle size.
RESTIME predicted a much more significant effect of particle
size than was shown by the actual data. particles act independently. not the case.
RESTIME assumes that the
Experimentation showed that this was
The lesser affect of particle size becomes apparent
when one recalls the test procedure.
Test particles of discrete
size were injected into the rotary drum and mixed immediately with the bulk particle flow.
The size distribution of the bulk
particles was shown in Figure 10.
During a cascade the particles
fall in curtains, separated by relatively particle free areas-, as
25
Mean = 8.3 Std = 1.6
20
Mean = 14.4 Std = 3.2
5
0
5
10
15
Residence Time (min)
a. Drum Speed = 7.2 rpm Particle Size = -1.88 +1.53 mm
Figure 12.
0
5
10
15
20
Residence Time (min)
b. Drum Speed = 3.0 rpm Particle Size = -1.88 +1.53 mm
Experimentally Measured Residence Time Distributions. Gas Velocity = 1.58 m/s Feed Rate = 0.334 dry kg/s.
25
30
25
Mean = 7.9 Std = 2.0
20
= 15.3 Std = 3.4
_r-
ri-1
5
10
15
Residence Time (min)
c. Drum Speed = 7.2 rpm Particle Size = -3.35 +1.88 mm
Figure 12.
Continued.
5
10
15
20
Residence Time (min)
d. Drum Speed = 3.0 rpm Particle Size = -3.35 +1.88 mm
25
11
30
25
Mean = 17.2 Std = 3.6
= 8.6 Std = 2.5
20
15
0 cu
IL
1-1
44
10 4-1 4-1
5
0
I
0
5
10
15
Residence Time (min)
e. Drum Speed = 7.2 rpm Particle Size = - 5.14 +3.35 mm
Figure 12.
Continued.
n
I
5
1 171 10
15
20
Residence Time (min)
f. Drum Speed = 3.0 rpm Particle Size = -5.14 +3.35 mm
25
30
55
Drum Speed (rpm)
Particle Size (mm) -1.88 +1.53
3.0 7.2
-3.35 +1.88
3.0 7.2
-5.14 +3.35
3.0 7.2
3.0
mean = 2.06
7.2
I
Symbol
A
0 0
0 0
0
2500
2000
Ideal Fit cu
H 1500 cu
